Journal of Mechanical Engineering 2014 9 by Darko Svetak

http://www.sv-jme.eu

60 (2014) 9

Strojniški vestnik Journal of Mechanical Engineering

Since 1955

Papers

539

Gašper Šušteršič, Ivan Prebil, Miha Ambrož: The Snaking Stability of Passenger Cars with Light Cargo Trailers

549

Łukasz Pejkowski, Dariusz Skibicki, Janusz Sempruch: High-Cycle Fatigue Behavior of Austenitic Steel and Pure Copper under Uniaxial, Proportional and Non-Proportional Loading

561

Jiang Ding, Yangzhi Chen, Yueling Lv, Changhui Song: Position-Parameter Selection Criterion for a Helix-Curve Meshing-Wheel Mechanism Based on Sliding Rates

571

Rok Kopun, Leopold Škerget, Matjaž Hriberšek, Dongsheng Zhang, Wilfried Edelbauer: Numerical Investigations of Quenching Cooling Processes for Different Cast Aluminum Parts

581

Ming Xu, Jing Ni, Guojin Chen: Dynamic Simulation of Variable-Speed Valve-Controlled-Motor Drive System with a Power-Assisted Device

592

Caglar Conker, Ali Kilic, Selcuk Mistikoglu, Sadettin Kapucu, Hakan Yavuz: An Enhanced Control Technique for the Elimination of Residual Vibrations in Flexible-Joint Manipulators

600 Yibo Sun, Xinhua Yang: Study on the Correction of S-N Distribution in the Welding Fatigue Analysis Method Based on the Battelle Equivalent Structural Stress by Rough Set Theory

Journal of Mechanical Engineering - Strojniški vestnik

Contents

9 year 2014 volume 60 no.

Strojniški vestnik – Journal of Mechanical Engineering (SV-JME) Aim and Scope The international journal publishes original and (mini)review articles covering the concepts of materials science, mechanics, kinematics, thermodynamics, energy and environment, mechatronics and robotics, fluid mechanics, tribology, cybernetics, industrial engineering and structural analysis. The journal follows new trends and progress proven practice in the mechanical engineering and also in the closely related sciences as are electrical, civil and process engineering, medicine, microbiology, ecology, agriculture, transport systems, aviation, and others, thus creating a unique forum for interdisciplinary or multidisciplinary dialogue. The international conferences selected papers are welcome for publishing as a special issue of SV-JME with invited co-editor(s). Editor in Chief Vincenc Butala University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Technical Editor Pika Škraba University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Founding Editor Bojan Kraut University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Editorial Office University of Ljubljana, Faculty of Mechanical Engineering SV-JME, Aškerčeva 6, SI-1000 Ljubljana, Slovenia Phone: 386 (0)1 4771 137 Fax: 386 (0)1 2518 567 info@sv-jme.eu, http://www.sv-jme.eu Print: Littera Picta, printed in 400 copies Founders and Publishers University of Ljubljana, Faculty of Mechanical Engineering, Slovenia University of Maribor, Faculty of Mechanical Engineering, Slovenia Association of Mechanical Engineers of Slovenia Chamber of Commerce and Industry of Slovenia, Metal Processing Industry Association President of Publishing Council Branko Širok

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Vice-President of Publishing Council Jože Balič University of Maribor, Faculty of Mechanical Engineering, Slovenia

Cover: The top photo shows the test vehicle towing an instrumented light cargo trailer during a hard obstacle avoidance manoeuvre performed for acquisition of the required measurement system parameters. The rendered images below show the detailed mechanical model of the vehicle-trailer combination as developed and used in the research of the snaking stability of passenger cars with light cargo trailers.

Courtesy: University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Institutional prices include print & online access: institutional subscription price and foreign subscription €100,00 (the price of a single issue is €10,00); general public subscription and student subscription €50,00 (the price of a single issue is €5,00). Prices are exclusive of tax. Delivery is included in the price. The recipient is responsible for paying any import duties or taxes. Legal title passes to the customer on dispatch by our distributor. Single issues from current and recent volumes are available at the current single-issue price. To order the journal, please complete the form on our website. For submissions, subscriptions and all other information please visit: http://en.sv-jme.eu/. You can advertise on the inner and outer side of the back cover of the magazine. The authors of the published papers are invited to send photos or pictures with short explanation for cover content. We would like to thank the reviewers who have taken part in the peerreview process.

ISSN 0039-2480 © 2014 Strojniški vestnik - Journal of Mechanical Engineering. All rights reserved. SV-JME is indexed / abstracted in: SCI-Expanded, Compendex, Inspec, ProQuest-CSA, SCOPUS, TEMA. The list of the remaining bases, in which SV-JME is indexed, is available on the website.

The journal is subsidized by Slovenian Research Agency. Strojniški vestnik - Journal of Mechanical Engineering is also available on http://www.sv-jme.eu, where you access also to papers’ supplements, such as simulations, etc.

Instructions for Authors All manuscripts must be in English. Pages should be numbered sequentially. The maximum length of contributions is 10 pages. Longer contributions will only be accepted if authors provide justification in a cover letter. Short manuscripts should be less than 4 pages. For full instructions see the Authors Guideline section on the journal’s website: http://en.sv-jme.eu/. Please note that file size limit at the journal’s website is 8Mb. Announcement: The authors are kindly invited to submitt the paper through our web site: http://ojs.sv-jme.eu. Please note that file size limit at the journal’s website is 8Mb. The Author is also able to accompany the paper with Supplementary Files in the form of Cover Letter, data sets, research instruments, source texts, etc. The Author is able to track the submission through the editorial process - as well as participate in the copyediting and proofreading of submissions accepted for publication - by logging in, and using the username and password provided. Please provide a cover letter stating the following information about the submitted paper: 1. Paper title, list of authors and affiliations. 2. The type of your paper: original scientific paper (1.01), review scientific paper (1.02) or short scientific paper (1.03). 3. A declaration that your paper is unpublished work, not considered elsewhere for publication. 4. State the value of the paper or its practical, theoretical and scientific implications. What is new in the paper with respect to the state-of-the-art in the published papers? 5. We kindly ask you to suggest at least two reviewers for your paper and give us their names and contact information (email). Every manuscript submitted to the SV-JME undergoes the course of the peer-review process. THE FORMAT OF THE MANUSCRIPT The manuscript should be written in the following format: - A Title, which adequately describes the content of the manuscript. - An Abstract should not exceed 250 words. The Abstract should state the principal objectives and the scope of the investigation, as well as the methodology employed. It should summarize the results and state the principal conclusions. - 6 significant key words should follow the abstract to aid indexing. - An Introduction, which should provide a review of recent literature and sufficient background information to allow the results of the article to be understood and evaluated. - A Theory or experimental methods used. - An Experimental section, which should provide details of the experimental set-up and the methods used for obtaining the results. - A Results section, which should clearly and concisely present the data using figures and tables where appropriate. - A Discussion section, which should describe the relationships and generalizations shown by the results and discuss the significance of the results making comparisons with previously published work. (It may be appropriate to combine the Results and Discussion sections into a single section to improve the clarity). - Conclusions, which should present one or more conclusions that have been drawn from the results and subsequent discussion and do not duplicate the Abstract. - References, which must be cited consecutively in the text using square brackets [1] and collected together in a reference list at the end of the manuscript. Units - standard SI symbols and abbreviations should be used. Symbols for physical quantities in the text should be written in italics (e.g. v, T, n, etc.). Symbols for units that consist of letters should be in plain text (e.g. ms-1, K, min, mm, etc.) Abbreviations should be spelt out in full on first appearance, e.g., variable time geometry (VTG). Meaning of symbols and units belonging to symbols should be explained in each case or quoted in a special table at the end of the manuscript before References. Figures must be cited in a consecutive numerical order in the text and referred to in both the text and the caption as Fig. 1, Fig. 2, etc. Figures should be prepared without borders and on white grounding and should be sent separately in their original formats. Pictures may be saved in resolution good enough for printing in any common format, e.g. BMP, GIF or JPG. However, graphs and line drawings should be prepared as vector images, e.g. CDR, AI. When labeling axes, physical quantities, e.g. t, v, m, etc. should be used whenever possible to minimize the need to label the axes in two languages. Multi-curve graphs should have individual curves marked with a symbol. The meaning of the symbol should be explained in the figure caption. Tables should carry separate titles and must be numbered in consecutive numerical order in the text and referred to in both the text and the caption as

Table 1, Table 2, etc. In addition to the physical quantity, e.g. t (in italics), units (normal text), should be added in square brackets. The tables should each have a heading. Tables should not duplicate data found elsewhere in the manuscript. Acknowledgement of collaboration or preparation assistance may be included before References. Please note the source of funding for the research. REFERENCES A reference list must be included using the following information as a guide. Only cited text references are included. Each reference is referred to in the text by a number enclosed in a square bracket (i.e., [3] or [2] to [6] for more references). No reference to the author is necessary. References must be numbered and ordered according to where they are first mentioned in the paper, not alphabetically. All references must be complete and accurate. All non-English or. non-German titles must be translated into English with the added note (in language) at the end of reference. Examples follow. Journal Papers: Surname 1, Initials, Surname 2, Initials (year). Title. Journal, volume, number, pages, DOI code. [1] Hackenschmidt, R., Alber-Laukant, B., Rieg, F. (2010). Simulating nonlinear materials under centrifugal forces by using intelligent crosslinked simulations. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 7-8, p. 531-538, DOI:10.5545/sv-jme.2011.013. Journal titles should not be abbreviated. Note that journal title is set in italics. Please add DOI code when available and link it to the web site. Books: Surname 1, Initials, Surname 2, Initials (year). Title. Publisher, place of publication. [2] Groover, M.P. (2007). Fundamentals of Modern Manufacturing. John Wiley & Sons, Hoboken. Note that the title of the book is italicized. Chapters in Books: Surname 1, Initials, Surname 2, Initials (year). Chapter title. Editor(s) of book, book title. Publisher, place of publication, pages. [3] Carbone, G., Ceccarelli, M. (2005). Legged robotic systems. Kordić, V., Lazinica, A., Merdan, M. (Eds.), Cutting Edge Robotics. Pro literatur Verlag, Mammendorf, p. 553-576. Proceedings Papers: Surname 1, Initials, Surname 2, Initials (year). Paper title. Proceedings title, pages. [4] Štefanić, N., Martinčević-Mikić, S., Tošanović, N. (2009). Applied Lean System in Process Industry. MOTSP 2009 Conference Proceedings, p. 422-427. Standards: Standard-Code (year). Title. Organisation. Place. [5] ISO/DIS 16000-6.2:2002. Indoor Air – Part 6: Determination of Volatile Organic Compounds in Indoor and Chamber Air by Active Sampling on TENAX TA Sorbent, Thermal Desorption and Gas Chromatography using MSD/FID. International Organization for Standardization. Geneva. www pages: Surname, Initials or Company name. Title, from http://address, date of access. [6] Rockwell Automation. Arena, from http://www.arenasimulation.com, accessed on 2009-09-07. EXTENDED ABSTRACT By the time the paper is accepted for publishing, the authors are requested to send the extended abstract (approx. one A4 page or 3.500 to 4.000 characters). The instructions for writing the extended abstract are published on the web page http://www.sv-jme.eu/ information-for-authors/. COPYRIGHT Authors submitting a manuscript do so on the understanding that the work has not been published before, is not being considered for publication elsewhere and has been read and approved by all authors. The submission of the manuscript by the authors means that the authors automatically agree to transfer copyright to SV-JME and when the manuscript is accepted for publication. All accepted manuscripts must be accompanied by a Copyright Transfer Agreement, which should be sent to the editor. The work should be original by the authors and not be published elsewhere in any language without the written consent of the publisher. The proof will be sent to the author showing the final layout of the article. Proof correction must be minimal and fast. Thus it is essential that manuscripts are accurate when submitted. Authors can track the status of their accepted articles on http://en.svjme.eu/. PUBLICATION FEE For all articles authors will be asked to pay a publication fee prior to the article appearing in the journal. However, this fee only needs to be paid after the article has been accepted for publishing. The fee is 300.00 EUR (for articles with maximum of 10 pages), 20.00 EUR for each addition page. Additional costs for a color page is 90.00 EUR.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9 Contents

Contents Strojniški vestnik - Journal of Mechanical Engineering volume 60, (2014), number 9 Ljubljana, September 2014 ISSN 0039-2480 Published monthly

Papers Gašper Šušteršič, Ivan Prebil, Miha Ambrož: The Snaking Stability of Passenger Cars with Light Cargo Trailers Łukasz Pejkowski, Dariusz Skibicki, Janusz Sempruch: High-Cycle Fatigue Behavior of Austenitic Steel and Pure Copper under Uniaxial, Proportional and Non-Proportional Loading Jiang Ding, Yangzhi Chen, Yueling Lv, Changhui Song: Position-Parameter Selection Criterion for a Helix-Curve Meshing-Wheel Mechanism Based on Sliding Rates Rok Kopun, Leopold Škerget, Matjaž Hriberšek, Dongsheng Zhang, Wilfried Edelbauer: Numerical Investigations of Quenching Cooling Processes for Different Cast Aluminum Parts Ming Xu, Jing Ni, Guojin Chen: Dynamic Simulation of Variable-Speed Valve-Controlled-Motor Drive System with a Power-Assisted Device Caglar Conker, Ali Kilic, Selcuk Mistikoglu, Sadettin Kapucu, Hakan Yavuz: An Enhanced Control Technique for the Elimination of Residual Vibrations in Flexible-Joint Manipulators Yibo Sun, Xinhua Yang: Study on the Correction of S-N Distribution in the Welding Fatigue Analysis Method Based on the Battelle Equivalent Structural Stress by Rough Set Theory Klemen Rupnik, Jože Kutin, Ivan Bajsić: A Method for Gas Identification in Thermal Dispersion Mass Flow Meters

539 549 561 571 581 592 600 607

Received for review: 2014-01-21 Received revised form: 2014-03-25 Accepted for publication: 2014-04-04

Original Scientific Paper

The Snaking Stability of Passenger Cars with Light Cargo Trailers Šušteršič, G. – Prebil, I. – Ambrož, M. Gašper Šušteršič – Ivan Prebil – Miha Ambrož*

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia This paper presents research conducted to determine whether the detailed multibody system (MBS) model presented in the paper is applicable to modelling the snaking phenomenon and to validate the model, including the parameter values, so that it can be used in further research of vehicle safety systems. Experiments and simulations both show – and with good agreement – that the system of a passenger car and a cargo trailer can become unstable at motorway velocities if the trailer is loaded inappropriately. Based on an analysis of the measured data, the impact-damping phenomenon and its influence on snaking damping have been identified. An MBS analysis of the computationalfluid-dynamics-determined aerodynamic influences on the system’s response to an impulse disturbance has shown these influences to be negligible. We have devised the principles and apparatus for measuring the steering-wheel angle, the articulation angle and the lateral force of the trailer’s tow bar. Measuring the last of these makes possible an on-the-fly determination of the trailer’s yaw inertia, one of the most influential parameters with respect to the snaking phenomenon. Keywords: vehicle-trailer system, trailer, snaking, stability, dynamics, MBS

0 INTRODUCTION There are many phrases that other authors have used to describe the “snaking” phenomenon. Some examples are: “vehicle-trailer system high speed instability” and “divergent oscillation that is often associated with high speed and initial impulse” [1] or: “vehicle-trailer instability that is dynamic in nature and may lead to oscillatory response with increasing amplitude” [2], where it is also termed “sway”; or “motion that involves the oscillation in yaw of a towed vehicle at high speed which can lead to loss of control of the coupled combination” [3]; and finally “characteristic oscillatory yawing and rolling motions of car–trailer combinations at moderate to high road speeds” [4] and [5]. This phenomenon, which we shall call snaking, demonstrates the dynamic instability [6] of a vehicletrailer system. It is of interest to the community of researchers and practitioners, including vehicle manufacturers, trailer manufacturers, accident researchers and reconstructionists, road designers and builders, policy makers and, last but not least, the drivers of trailer-towing passenger cars, primarily caravan and boat owners and, as demonstrated in this article, the towers of cargo trailers . Several approaches to the modelling and evaluation of snaking have been identified [8]. Analytical approaches [2] and [6] to [8] utilise yaw plane models of the vehicle-trailer system and implement the state space and Routh criteria. Numerical approaches [2], [4], [5], [7] and [8] either use the yaw plane models and numerical integration of their governing equations or the multi-body

dynamics modelling approach. Research has also been conducted into snaking based exclusively on experimental investigations [1], [3] and [9]. It has been demonstrated that the snaking phenomenon would set in at lower velocities in some systems than in others, with all of the above approaches. In order to provide the full control of the model, required to use it for the particular problem and further research, a new model had to be developed. The specific goal of this study was to determine whether a detailed MBS (multibody system) simulation model could be suitable for modelling the snaking phenomenon. The model of a system comprising a passenger vehicle and a light cargo trailer was prepared by building a detailed geometrical model and a detailed mechanical model, including the aerodynamic forces. The model’s parameter values were obtained from measurements on a real car-trailer system. The aerodynamic forces were obtained from a computational fluid dynamics (CFD) simulation. A set of full-scale experimental runs was devised and performed. The detailed MBS model was validated by a comparison of the measured data and the simulation results. 1 MATERIALS AND METHODS 1.1 The System of a Passenger Car and a Light Cargo Trailer The towing vehicle in the system comprising a passenger car and a light cargo trailer is a compact, multi-purpose, Opel Zafira, while the trailer is a “uni TRACK 700” from Agromex. The towing vehicle was

*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, SI-1000 Ljubljana, Slovenia, miha.ambroz@fs.uni-lj.si

539

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 539-548

not equipped with directional stability systems such as ESP. The basic properties of the car and the trailer are given in Table 1 below. Table 1. Vehicle system properties as used in experiments and simulation Curb Yaw inertia Wheelbase Towbar Front/rear [mm] length [mm] track [mm] weight [kg] [kgm2] Towing vehicle Trailer

1530

2577

2694

1487/1470

130

248

1750

1300

The towing passenger car carries a crew of two – the driver and the operator of the measurement system. The trailer was loaded with cargo arranged around a wooden frame placed in the middle of the trailer’s cargo area as described in section 1.3. This ensured that the cargo was immobilised and that there was an increase in the trailer’s yaw inertia. 1.2 Mechanical Model The mechanical model of the car-trailer system is based on the detailed MBS mechanical model presented in [8]. The geometrical model is shown in Fig. 1 for the light cargo trailer and in Fig. 2 for the passenger car. The MacPherson front suspensions on the car are modelled with the lower control arm (LCA) connected to the vehicle body through two control-arm bushings. The MacPherson strut is connected to the control arm by a kinematic spherical joint at the bottom and to the vehicle body at the top by a kinematic universal joint. Bump stops and suspension-travel limiters are also included in the model and generate forces according to the splines obtained from measurements.

Fig. 1. Geometrical model of the trailer

The anti-roll bar is modelled with two rigid bodies, connected to each other by a revolute joint and a torsion spring element acting between them. The rack-and-pinion-type steering system is modelled with the steering wheel attached to the vehicle body by a revolute joint. The translational motion of the steering rack is driven by the rotation of the pinion gear. The vehicle’s steering actions are performed by applying the steering wheel rotation. The twist-beam-type rear suspension is modelled with each of the trailing-arm bodies connected to the car body with a revolute joint and a torsion spring element acting between both trailing-arm bodies. These are connected to the vehicle body by a damper and a spring on each side. The bump stops and the suspension-travel limiters are also implemented in the model. The trailer’s suspension, attached to the trailer body, is modelled with each of the trailing arms connected to the trailer body through a revolute joint and a linear torsion spring and damper element.

Fig. 2. Geometrical model of the passenger car (left – rear suspension, right – front suspension)

540

Šušteršič, G. – Prebil, I. – Ambrož, M.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 539-548

The application of external forces and moments is facilitated so that aerodynamic forces can be applied to the system at the vehicle as well as at the trailer body. The tyre forces are modelled by implementing the Magic Formula model [9]. A set of mathematical equations is generated and solved automatically by the MBS modelling environment MSC.ADAMS [10].

Fig. 3 shows the measured characteristics for some force-generating suspension elements.

1.3 Acquisition of the Parameter Values Geometrical models of the car’s suspension parts were prepared for a previous investigation [8], for the test vehicle as well as for the test trailer. These provide the geometrical parameters as well as the mass and inertia properties of the individual vehicle components included in the mechanical model. The mass of the vehicle and the location of the centre of mass are determined experimentally in a way, similar to that presented in [11]. The inertial properties of the vehicle were provided to us by the manufacturer (2011 e-mail from Adam Opel AG; unreferenced). The mass and inertial properties of the driver and the operator were estimated by using human-like geometrical forms, to which densities were assigned that resulted in appropriate masses for the driver and the operator. All the vehicle force-generating elements were removed from the vehicle for characterisation in order to obtain their net forces, similar as in the procedure, described in [12]. The vehicle springs, the bump stops, the suspension-travel limiters and the bushings were all characterised on a laboratory universal testing machine. While the vehicle springs exhibited highly linear behaviour, the other elements behaved in a nonlinear manner, necessitating the implementation of spline curves for a faithful representation of their properties. The bushings mounted on the vehicle were axially symmetric, but the axial stiffness was different when loaded from front to rear than when loaded from rear to front. A custom mounting device made possible a characterisation on the universal testing machine. The bushings were modelled in a preloaded state, resembling that on the real vehicle. Vehicle dampers were characterised on a testing machine that was capable of higher-speed operation. The measurements were carried out at 50 mm of travel and maximum velocities of 52, 104, 157, 209 and 262 mm/s. Based on the damper measurements, two nonlinear damping force vs. damper rod velocity splines were generated for the characteristics of the front and rear dampers.

Fig. 3. Data from a few force-generating element characterization experiments

The front anti-roll bar and the stabilising influence of the twist axle were characterised by securing the attachment points and observing the relative rotation of the two suspension arms for various values of the applied torsion moment. The trailer’s suspension spring and damping characteristics were characterised as shown in [8] by applying known torsional moments and by determining the free oscillation decay. The range of suspension velocities occurring during the free oscillation, from which the rate of decay was determined (around 1.75 Hz), also encompasses the range of suspension velocities at the snaking frequency present in our model’s response (around 1 Hz), as both motions had similar amplitudes. The steering ratio was determined by simultaneously measuring the steering wheel’s angle of rotation and the rack’s translation. The wheel alignment of the model was set up according to the vehicle-service manual [13]. The tyre model’s parameter-set values were acquired for the specific make, model, size, speed rating and load rating [14]. The modelling and the model verification tests were conducted on a system with a 750-kg cargo trailer

The Snaking Stability of Passenger Cars with Light Cargo Trailers

541

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 539-548

rather than a caravan, which tempted us to consider the aerodynamic forces as being negligible. However, the report of Darling and Standen [9] prompted us to consider the influences of the aerodynamic forces as well. We utilised a 3D CFD software application XFlow. Detailed geometrical models of the towing vehicle and the trailer were included in the simulation. A single-phase external flow model was used. The Large Eddy Simulation (LES) approach for turbulence was employed with the Wall-Adapting Local Eddy (WALE) scheme. Zero roughness on the surface was assumed and the pressure gradient was not taken into account. The geometrical model of the vehicle body [8] was obtained by photogrammetric modelling and consists of 3898 polygons. The trailer’s geometrical model was the same as used in the MBS simulations. First, a simulation of the MBS vehicle-trailer system was carried out to obtain the motion of the system without any aerodynamic influences. Next, the maximum amplitude and the frequency of trailer’s yaw motions from this simulation were used as inputs for the CFD analysis to obtain the aerodynamic forces and the moments on the trailer. The aerodynamic forces relate directly to the vehicle’s velocity and the trailer’s yaw angle. The simulation results

give a distinct curve of larger amplitude with the superimposed influences of smaller amplitudes and higher frequencies. A 3-Hz low-pass filter revealed the sine-like form of the signal, as shown in Fig. 4. All of the aerodynamic forces and moments were applied at a point on the trailer model according to the CFD analysis results. This greatly simplified the inclusion of the aerodynamic influences in the model. The simulations were then carried out, including the forces determined in the previous steps.

Fig. 4. Resulting lateral force from the CFD analyses, low-pass filtered at 3 Hz

Fig. 5. Measurement system schematic

Fig. 6. Tow bar equipped with strain gauges

542

Šušteršič, G. – Prebil, I. – Ambrož, M.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 539-548

1.4 Test Equipment and Procedure 1.4.1 Equipment The measurements were carried out with a measurement system based on a NI PXI platform consisting of a chassis, a controller module and multiple DAQ modules. The complete measurement system is schematically presented in Fig. 5. A non-contact optical sensor was used to measure the vehicle’s longitudinal and lateral velocities, triaxial accelerometer modules were used for the acceleration measurements, and an incremental rotary encoder (Fig. 6) was used to measure the articulation angle. A magnetic linear encoder, modified and fitted to the steering shaft (Fig. 7), was used to measure the angle of the steering wheel. Strain gauges arranged in a full-bridge circuit, which provided temperature compensation and isolation from any axial forces (Fig. 8), were used to measure the lateral force on the tow ball. The application that facilitated the acquisition, storage and reviewing of the acquired test-run data was developed in the LabVIEW environment.

symmetrically, front to rear as well as left to right, except for one row sacks. This row was placed as far as possible to the front in the first test case (TC1) and as far as possible to the rear in the second test case (TC2), providing the difference in the weight distribution. A total of 76 experimental runs were conducted in the TC1 and TC2 configurations, all on an airport runway. The test procedure for a single experimental run began by accelerating the vehicle to the desired velocity and engaging the car’s cruise control. The operator started data acquisition and the driver then initiated the disturbance manoeuvre according to [15]. The initial impulse displacement of the steering wheel was completed by a subsequent steering correction in the opposite direction (see Fig. 9) in order for the car to regain its initial path. The steering wheel was then held fixed in the straight-ahead position. Once the system oscillation had settled down, the next disturbance was applied to the steering wheel. 2 ANALYSIS OF THE MEASUREMENTS AND THE SIMULATION RESULTS 2.1 General

Fig. 7. Linear magnetic encoder fitted to the steering shaft

Fig. 8. Implementation of a rotary encoder for the measurement of the articulation angle

1.4.2 Procedure The validation experiments were conducted with two trailer-load distributions. Both contained the same amount of cargo material and were loaded

An example of the measured data for one individual disturbance and the system’s response, complete with simulation results for comparison, is shown in Fig. 9. All the test-run data were processed offline in the manner outlined in ISO 9815 [15] in order to determine the value of the most frequently used parameter that is indicative of the level of system stability, i.e., “the damping D”. The system is stable (the amplitude of sways subsides over time) as long as the D value is positive. The speed at which the system D value becomes negative is called the zero damping speed. The D values of the individual test runs plotted with respect to the vehicle’s velocity are presented in Fig. 10. Although it is common practice to plot a root-mean-square linear interpolation through all the data points on graphs such as these, we shall, for now, restrain ourselves from this practice. Although care was taken to immobilise the cargo carried by the trailer, movement of the cargo was nevertheless detected while reviewing the video footage of the cargo. In order to provide for an appropriate number of system sways needed to determine the damping parameter D, the disturbance at lower velocities, especially with the more stable TC1 configuration, had to be quite harsh. In some cases the individual cargo sacks became dislodged

The Snaking Stability of Passenger Cars with Light Cargo Trailers

543

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 539-548

Fig. 9. Disturbance and response of the system as measured and simulated for a single test run

b) Fig. 10. Damping ratios for both sets of test runs for a) TC1 test case and b) TC2 test case

from their initial positions and came into impact-like contact with each other and with the side walls of the trailer’s cargo compartment. The movement of the cargo and the interaction between the cargo and the trailer can account for significant additional damping in the system. This socalled “impact damping” or “particle impact damping” is a consequence of particle-to-wall and particle-toparticle collisions in which kinetic energy is dissipated due to frictional and inelastic losses. Although many papers were published on this topic [16] to [21], the data and the theory therein do not allow us to make any sensible evaluation of the influence of impact damping in our experimental studies. However, the damping ratios from the measurement runs are consistently higher than those from the simulated runs, as seen in Fig. 11. This does not contradict the found presence of impact damping in the system. 544

It is clear that it would not be appropriate to regress to linearity through all the measured data points in Fig. 10, thus only the “no-cargo-movement” (8 tests for TC1 and 21 for TC2) data was used for the validation of the model and parameter values. 2.2 Validation of the Model and Parameter Values We validated the model, including the parameter values described previously, by comparing the measured data with the simulation results. The simulations were carried out in such a way that made the simulated test runs comparable to the experimental test runs. The disturbance was introduced to the model of the vehicle-trailer system in the simulated test runs through a prescription of the time series of the steering-wheel angle data measured on the vehicle during the actual experimental test runs. The initial velocity of the vehicle model was prescribed to be the

Šušteršič, G. – Prebil, I. – Ambrož, M.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 539-548

Fig. 11. Comparison of measured and simulated damping ratios

Fig. 12. A model of the trailer with the tow bar considered as an overhanging elastic beam

value measured during the actual experimental test run and this velocity was kept constant by the actions of the driver model. Both the measured and the simulated steering-wheel angle and vehicle velocities are shown for comparison in Fig. 9. While the simulation results and the measurements in TC2 (the less-stable configuration) show good agreement, it is necessary to comment on the TC1 configuration results. It should be noted that only the test runs with no or only a small amount of cargo movement should be taken into consideration when plotting the linear regression. Consequently we find that the data for the measurement data points at the highest system velocities (shown as larger squares in Fig. 11) is too scarce to be of real value. Fig. 11 shows that the measured and simulated damping became increasingly similar as the system velocity increased. This is due to the drop of the initial impulse and the consequent decrease in the cargo movement. The test runs where the cargo movement with the cargo-area wall impact occurred demonstrate a large increase in damping.

2.3 Implications of the Trailer Tow Bar’s Lateral Force Measurement The comparison of the simulated and measured values of the lateral trailer hitch force reveals that although the basic forms of both curves and the amplitude values match closely, an oscillation with a frequency higher than that of the snaking can be clearly identified, superimposed on the measured force curve (Fig. 9). The superimposed force is a consequence of the fact that the trailer’s tow bar is not rigid in the actual system, but rather acts as an elastically deformable beam element connecting the trailer to the vehicle. The trailer wheels rotate freely. The mode of the trailer motion that sets on when moving the hitch point of the trailer tow bar left to right can be described as rotation of the trailer about the centre of rotation (CoR) as shown in Fig. 13. As such, the frequency of this superimposed force component could give us some insight into the actual trailer yaw inertia as long as we

The Snaking Stability of Passenger Cars with Light Cargo Trailers

545

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 539-548

have some basic geometrical data for the trailer and the trailer’s tow bar. To check the validity of the above proposition, we utilised the theory of beam deflection [22]. We modelled the trailer’s tow bar as an overhanging beam, as shown in Fig. 12.

Fig. 13. Interpretation of the trailer with a deformable trailer tow bar as a yaw pendulum

To write the equation for the beam deflection, we first express the beam’s bending moment M according to Fig. 12:

M ( x ) = FA ⋅ x + FB ⋅ ( x − a ) .

Next, we double integrate the beam-deflection equation:

d2 y = M ( x), dx 2

and consider the boundary conditions in order to obtain the deflection equation: x  1  x 3  x  x  x 3 ax 2  xa 2  y ( x) = F 1− +  − 1 − 3   . (1)  − EI  6  a  a  6 2  6  a  

Eq. (1) can be used to determine the ratio of F/y(l), which represents the spring stiffness k of the spring in the model shown in Fig. 13. Since the trailer is basically carrying out a yawing motion around its centre of rotation, we substitute the translational spring of stiffness k with a rotational spring of stiffness krot, placed at the centre of rotation. Having small f, equating the forces produced with each spring leads us to: 546

krot ⋅ φ = k ⋅ ∆y = k ⋅ d ⋅ φ

and krot = k ⋅ d .

From the equation of oscillation of a simple 1D torsional pendulum, the trailer’s yaw inertia can be expressed as:

J T = krot ω 2 , (2)

where ω = 2πν, ν being the frequency of oscillation. The spectra of trailer hitch forces for all the TC2 measurements are shown in Fig. 14 and the frequency of the superimposed force component is clearly identifiable on every test run with a value close to 5 Hz. The value of the trailer’s inertia that is determined from Eq. (2) based on this frequency, turns out not to be the best estimator for the actual yaw inertia of the trailer (141 kgm2, determined from the spectral analysis vs. 248 kgm2, estimated from the geometrical modelling). It is nevertheless reasonable to consider that the frequency response of a trailer with a nongranular immobilised cargo would demonstrate a characteristic that estimates the trailer’s yaw inertia with greater accuracy. The trailer’s inertia measured with a relatively high-frequency oscillation might not have included all of the loose cargo. In other words, some of the cargo could have been excluded from the oscillating system due to the transfer of an individual cargo particle motion. An “on the fly” evaluation of the trailer’s yaw inertia by analysing the lateral forces of the trailer’s tow bar is perfectly technically feasible. Since the trailer’s yaw inertia is one of the most influential parameters for the snaking phenomenon, a materialisation of this idea could deliver a warning safety system similar to a low-tyre-pressure detection system. 2.4 Influence of Aerodynamic Forces All the simulations in this study were made with the aerodynamic influences (longitudinal and lateral forces, yaw moment) included. In the previous sections a description of how they were estimated in terms of their shape and size is provided. Here we give a comparison of the simulation results for the system model incorporating the aerodynamic influences and without them. Fig. 14 shows the articulation angle during the system’s response to a disturbance impulse. Clearly, the influence of the aerodynamic forces can be described as marginal throughout the entire speed range in this specific case. A slight influence of the aerodynamic forces only begins to show at the highest velocities. This is a consequence of the aerodynamic forces increasing with the system velocity and the

Šušteršič, G. – Prebil, I. – Ambrož, M.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 539-548

Fig. 14. Comparison of systems with and without aerodynamic influences; a) articulation angle amplitude decay, b) damping D over a range of velocities

Fig. 15. Spectral analysis of the lateral forces on the trailer tow bar

increasing yaw amplitude of the trailer. The latter is a consequence of a decrease in the system’s stability with the increased longitudinal velocity. The stability of the system with aerodynamic influences is only marginally higher than in the system without them. The results presented in Fig. 15 indicate that the aerodynamic influences can safely be removed from consideration when simulating the snaking phenomenon with a system based on a passenger car and a light cargo trailer for trailers that have geometries and sizes similar to that used in this study (see Fig. 2). 3 CONCLUSIONS The results of the experimental investigation show that a system composed of a passenger car and a cargo trailer can easily become unstable at legal motorway speeds (80 to 100 km/h in Slovenia and most of Europe) if the trailer is not correctly loaded. The

simulation results follow the experimental findings closely, thus proving the multi-body system (MBS) approach to the modelling of the snaking phenomenon is appropriate. The coupled MBS-CFD modelbased research of the aerodynamic influences on the system’s response showed that those influences do not need to be considered when dealing with trailers that have geometries and sizes similar to the one used in this study. We have determined that the impact damping, occurring due to the energy dissipation of the impact-like interaction of the unsecured cargo and the trailer, can greatly improve the stability of the system. The approaches to measuring the articulation angle and the steering-wheel angle that we have proposed and the devices we have implemented performed flawlessly and show great potential for further use. This is also true for the implementation of a lateral tow-bar force measurement, which has proven itself to be of great value. Its fidelity

The Snaking Stability of Passenger Cars with Light Cargo Trailers

547

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 539-548

promises to enable on-the-fly determination of some of those trailer parameters that influence the snaking phenomenon the most and are left to the (often uninitiated) user’s discretion. Following the verification of our model with a slightly improved experimental set-up, investigations into the influence of the amplitude of the disturbance impulse on the system’s stability could be carried out. The validated detailed model as presented in the paper is needed for an in-depth investigation of the snaking phenomenon. Some preliminary tests have shown that the influence of the impulse amplitude on system’s stability might not be negligible. The influences of the system’s roll properties could also be evaluated through the MBS. Finally, a design of experiment (DOE) approach could also be used to test for the interaction or synergetic (in a positive or negative sense of the word) influence of multiple system parameters. 4 REFERENCES [1] Darling, J., Tilley, D., Gao, B. (2009). An experimental investigation of car–trailer high-speed stability. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, vol. 223, no. 4, p. 471-484, DOI:10.1243/09544070JAUTO981. [2] Hac, A., Fulk, D., Chen, H. (2008). Stability and control considerations of vehicle-trailer combination. SAE Technical Paper Ser., no. 2008-01-1228, p. 1-15. [3] Killer, C.J. (2003). The Dynamics of Towed Vehicles [Final year project], University of Bath, Bath. [4] Sharp, R.S., Alonso Fernandez, M.A. (2002). Car– caravan snaking Part 1: the influence of pintle pin friction. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 216, no. 7, p. 707-722, DOI:10.1243/09544060260128760. [5] Sharp, R.S., Alonso Fernandez, M.A. (2002). Car– caravan snaking Part 2: active caravan braking. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 216, no. 7, p. 723-736, DOI:10.1243/09544060260128779. [6] Karnopp, D. (2004). Vehicle Stability. Marcel Dekker, New York, DOI:10.1201/9780203913567. [7] Bundorf, T.R. (1967). Directional control dynamics of automobile- travel trailer combinations. SAE Technical Paper 670099, p. 667-680, DOI:10.4271/670099. [8] Šušteršič, G., Ambrož, M., Prebil, I. (2011). Application of rigid multi-body system modelling to determination of passenger-car and trailer combination lateral stability. Trans & MOTAUTO, p. 26-29.

548

[9] Darling, J., Standen, P.M. (2003). A study of caravan unsteady aerodynamics. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, vol. 217, no. 7, p. 551-560, DOI:10.1243/095440703322114933. [10] MSC.ADAMS. (2007). MSC.Software Corporation, Santa Ana. [11] UNECE Regulation no. 66 (2006). Uniform technical prescriptions concerning the approval of large passenger vehicles with regard to the strength of their superstructure. United Nations Economic Commission for Europe. Geneva. [12] Krishnasamy, P., Jayaraj, J., John, D. (2013). Experimental investigation on road vehicle active suspension. Strojniški vestnik - Journal of Mechanical Engineering, vol. 59, no.10, p. 620-625, DOI:10.5545/ sv-jme.2012.925. [13] Legg, A.K., Mimi, L., Martyn, R. (2003). Vauxhall Astra and Zafira service and Repair Manual. Haynes Publishing, Sparkford. [14] Michelin, Michelin Engineering & Services Automotive, from http://www.michelin-engineeringand-services.com/, accessed on 2013-10-04. [15] ISO 9815:2010(E). Road vehicles - Passenger-car and trailer combinations - Lateral stability test. International Organization for Standardization, Geneva. [16] Friend, R.D., Kinra, V.K. (2000). Particle impact damping. Journal of Sound and Vibration, vol. 233, no. 1, p. 93-118, DOI:10.1006/jsvi.1999.2795 [17] Saeki, M. (2002). Impact damping with granular materials in a horizontally vibrating system. Journal of Sound and Vibration, vol. 251, no. 1, p. 153-161, DOI:10.1006/jsvi.2001.3985. [18] Mao, K., Wang, M.Y., Xu, Z., Chen, T. (2004). DEM simulation of particle damping. Powder Technology, vol. 142, no. 2-3, p. 154-165, DOI:10.1016/j. powtec.2004.04.031. [19] Marhadi, K.S., Kinra, V.K. (2005). Particle impact damping: effect of mass ratio, material, and shape. Journal of Sound and Vibration, vol. 283, no. 1-2, p. 433-448, DOI:10.1016/j.jsv.2004.04.013. [20] Afsharfard, A., Farshidianfar, A. (2012). Design of nonlinear impact dampers based on acoustic and damping behavior. International Journal of Mechanical Sciences, vol. 65, no. 1, p. 125-133, DOI:10.1016/j. ijmecsci.2012.09.010. [21] Fleissner, F., Gaugele, T., Eberhard, P. (2007). Applications of the discrete element method in mechanical engineering. Multibody System Dynamics, vol. 18, no. 1, p. 81-94, DOI:10.1007/s11044-0079066-2. [22] Nash, W.A. (1998). Schaum’s Outline of Theory and Problems of Strength of Materials, McGraw-Hill, New York.

Šušteršič, G. – Prebil, I. – Ambrož, M.

Received for review: 2013-12-10 Received revised form: 2014-03-28 Accepted for publication: 2014-05-13

Original Scientific Paper

High-Cycle Fatigue Behavior of Austenitic Steel and Pure Copper under Uniaxial, Proportional and Non-Proportional Loading Pejkowski, Ł. – Skibicki, D. – Sempruch, J. Łukasz Pejkowski* – Dariusz Skibicki – Janusz Sempruch

University of Technology and Life Sciences in Bydgoszcz, Poland Austenitic steel EN: X2CrNiMo17-12-2 (ASTM: 316L) and copper Cu-ETP (DIN: E-Cu58, EN: CW004A, ASTM: C11000) were subjected to tension-compression, torsion and complex loads, including non-proportional loads. The non-proportionality of the state of stress resulted from a phase shift of the value δ = 90° of load components with sine signals and variable ratio of shear to normal stress λ. On the basis of the results, Wöhler’s curves were prepared, presenting the dependency of fatigue life to equivalent stress levels. Their analysis shows that fatigue life is strictly connected with the value of coefficient λ. The existence of its critical value can also be observed, which results in the highest fatigue life reduction. The value is different for each material. Furthermore, fractographic tests were conducted showing the influence of the level and type of load on the fracture face. Keywords: multi-axial fatigue, high cycle fatigue, non-proportional load, fractography, out-of-phase

0 INTRODUCTION The negative impact of the non-proportionality of stress components on fatigue strength and fatigue life [1] and [2] was observed in relation to a significant number of materials. Its direct effect is the phenomenon of additional hardening [3] to [5]. Nonproportionality can result from periodic load signals with phase shift (Fig. 1a) [6] to [8], asynchronous periodic signals (Fig. 1b) and random signals (Fig. 1c) [9] to [11] among other factors In cases of periodic out-of-phase signals of components of stress, the most damaging to the material, regardless of its type, is phase shift, expressed by the value of angle δ = 90°. The degree of non-proportionality of stress condition also depends on the ratio of amplitudes of shear to normal stress λ = τa / σa, which is usually omitted in works that analyse non-proportional loads. The objective of the this study is to analyse the influence of the λ ratio on fatigue life and the fatigue fracture surface morphology and crack plane

orientation (which often are the subject of interest [9], [12] and [13]) for copper Cu-ETP and austenitic steel X2CrNiMo17-12-2. The materials were selected for tests due to their potentially high sensitivity to nonproportionality of load [14]. 1 TESTS CONDITIONS All fatigue tests were conducted with application of a fully reversed sine signal (R = –1) of constant amplitude, with stress control, using an Instron 8874 biaxial testing system with a load range of ±25 kN for tension-compression and ±100 Nm for torsion (Fig. 2). Specimens were made by the machining of material as delivered. Specimen dimensions are presented on Fig. 3. Chemical composition of the tested steel and copper type are presented in Tables 1 and 2. The specimens were subject to tensioncompression, torsion, proportional load (λ = 0.5) and non-proportional loads (0.3 < λ < 0.8, δ = 90°).

Fig. 1. Examples of loads signals causing non-proportional condition of stress; a) out-of-phase load signals b) asynchronous load signals, and c) random load signals Table 1. Chemical composition of X2CrNiMo17-12-2 steel (% weight) C <0.03

Si <1

Mn <2

Ni 10 to 13

P <0.045

S <0.015

Cr 16.5 to 18.5

*Corr. Author’s Address: University of Technology and Life Sciences, Kordeckiego 20, Bydgoszcz, Poland, lukasz.pejkowski@utp.edu.pl

Mo 2 to 2.5

N <0.11

549

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 549-560

Table 2. Chemical composition of Cu-ETP copper (% weight) Cu >99.9

Bi <0.0005

O <0.04

Pb <0.005

Fig. 3. Geometry of tested specimens

Fig. 4 shows state of stress on the surface of the specimen and distribution of normal stress σα, shear stress τα and von Mises equivalent stress σMα acting on specimen surface, depending on the direction expressed by α angle. 2 TEST RESULTS 2.1 Fatigue Life Fig. 2. Instron 8874 biaxial testing system

Values of amplitudes were selected in order to obtain the exact value of amplitude (denoted as in subscript) of root mean square of the second invariant of stress deviator, J 2,a [15], multiplied by fatigue limits ratio for a given load level. The value can be written as follows:

τ σ eq = −1 J 2,a = const. (1) σ −1

The above value is the equivalent stress according to von Mises criterion:

σ eq = 3 J 2,a , (2)

with consideration of fatigue limits ratio for torsion and tension-compression τ-1/σ-1, in place of the constant value 3 . The von Mises criterion does not take into account the non-proportionality of load. The choice of such a criterion has been made deliberately, in order to show how the variable degree of nonproportionality, depending on the value of λ ratio, affects the fatigue life. TC indicates the results for tension-compression, T is torsion, P5 proportional load of coefficient λ = 0.5 and non-proportional loads, expressed as NP, of values of coefficient λ = 0.3, 0.4, 0.5, 0.53, 0.6, 0.7, 0.8, respectively. 550

A summary of the test results is presented in Tables 3 and 4. Fig. 5 presents Wöhler’s curves obtained for copper Cu-ETP. On the ordinate axis, the values of equivalent stress σeq (according to von Mises criterion) and on abscissa axis lives expressed with number of cycles N were identified. The curves were described with the Basquin equation:

σeq = ANB, (3)

coefficient A and exponent B of which were obtained via least square linear regression. The procedure of generating a line of best fit is well known in fatigue literature and its description can be found in [16] as well as in other sources. The resulting coefficients of determination R2 are denoted in Figs. 5 and 8. After transformation of the Basquin equation: 1

 σ B N =  eq  , (4)  A 

it is possible to calculate the fatigue life as the material is supposed to reach for the specific value of equivalent stress. The values of equivalent stresses calculated for various loads were placed into a transformed Basquin’s equation coefficients, which were determined for tension-compression; in this way the calculated fatigue lives Ncal were specified. Then they were compared with experimental fatigue lives

Pejkowski, Ł. – Skibicki, D. – Sempruch, J.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 549-560

Fig. 4. a) Out-of-phase tension-compression and torsion – state of stress illustrated b) distribution of Von Mises equivalent stress σMα, normal stress σα and shear stress τα on a plane tangent to specimen surface in case of tension-compression, c) torsion, d) proportional tensioncompression with torsion λ = 0.5, e) proportional tension-compression with torsion λ = 0.8, f) non-proportional tension-compression with torsion λ = 0.3, g) non-proportional tension-compression with torsion λ = 0.5, and h) non-proportional tension-compression with torsion λ = 0

Fig. 5. Wöhler’s curves obtained for Cu-ETP copper for various load types

Nexp achieved for tension-compression. Comparative results are presented in Fig. 6. Solid and dotted lines on the figure symbolize scatter bands, which indicate lives that are two and three times longer or shorter than experimental ones.

Fig. 7 presents a graph of dependency of fatigue life on λ at the level of equivalent stresses σeq = 160 MPa. Analogously, the following were prepared: Wöhler’s curves (Fig. 8), a fatigue life comparison

High-Cycle Fatigue Behavior of Austenitic Steel and Pure Copper under Uniaxial, Proportional and Non-Proportional Loading

551

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 549-560

Table 3. Test history for all fatigue specimens for Cu-ETP copper

Table 4. Test history for all fatigue spec. for X2CrNiMo17-12-2 steel

Specimen no.

Load type

σa [MPa]

τa [MPa]

δ [°]

N [no. of cycles]

Specimen no.

Load type

σa [MPa]

τa [MPa]

δ [°]

N [no. of cycles]

2 3 4 5 73 8 9 10 11 74 12 13 14 15 30 22 29 55 69 46 47 48 56 70 16 17 18 19 50 51 68 52 53 54 58 67 37 35 45 49 57 71 23 31 43 59 65 72 28 20 27 60 66

TC TC TC TC TC T T T T T P5 P5 P5 P5 N3 N3 N3 N3 N3 N4 N4 N4 N4 N4 N5 N5 N5 N5 N5 N5 N5 N53 N53 N53 N53 N53 N6 N6 N6 N6 N6 N6 N7 N7 N7 N7 N7 N7 N8 N8 N8 N8 N8

220 200 180 150 160 0 0 0 0 0 130 150 135 145 170 180 190 160 150 170 180 190 160 150 145 160 180 200 170 190 150 180 170 190 160 150 151.1 160 169 169 142.2 133.4 137.1 144.8 129.6 121.9 121.9 114.3 113.4 120 126.7 106.7 100

0 0 0 0 0 90 110 100 120 85.4 65 75 67 72 51 54 57 48 45 68 72 76 64 60 72 80 90 100 85 95 75 96 90.7 101.3 85.3 80 90.7 96 101.4 101.4 85.3 80 96.0 101.4 90.7 85.3 85.3 80 90.7 96.0 101.4 85.4 80

0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90

11,247 37,432 128,933 816,270 601,749 432,462 17,893 78,004 10,269 607,029 184,190 34,694 142,212 55,991 125,877 74,163 35,145 235,151 272,506 64,318 40,812 23,197 130,741 164,044 189,644 76,203 37,971 12,829 34,726 15,371 159,779 32,710 44,034 13,770 73,917 125,195 74,900 51,551 22,322 21,833 101,644 130,712 74,395 48,146 110,808 115,927 137,314 215,815 117,308 80,724 45,681 249,457 326,218

1 2 3 4 5 6 7 11 8 10 9 15 16 21 22 23 24 72 33 34 35 36 37 38 39 73 40 41 46 71 47 48 49 42 45 54 53 61 62 63 64 70 108 112 13 114 43 44 50 51 55 56 57 58 59 60 96 105 106 107 115 116 117 118

TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC T T T T T T T T P5 P5 P5 P5 P8 P8 P8 N5 N5 N5 N5 N5 N5 N5 N5 N5 N6 N6 N6 N6 N8 N8 N8 N8 N8 N8 N8 N8 N8 N8 N10 N10 N10 N10 N12 N12 N12 N12

350 350 350 330 330 330 342 325 325 311 303 325 311 325 325 303 311 333.3 0 0 0 0 0 0 0 0 270 285 299 285 247 233 219 333 320 310 300 333 320 310 300 333 310 333 320 300 333 320 310 300 333 320 310 300 320 300 260 244 251,8 270,5 203,1 209,9 216,6 225,5

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 310 300 290 260 250 270 280 276 135 142.5 149.8 142.5 204.6 193.1 181.4 166.5 160 155 150 166.5 160 155 150 166.5 186 199,8 192 180 275.1 264.3 256.1 247.8 275.1 264.3 256.1 247.8 264.3 247.8 260.0 240 251,8 270,5 243,7 251,9 259,9 270,6

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90

23,420 14,937 18,048 75,013 49,513 68,038 25,225 139,108 89,469 199,142 632510 146,934 147,769 190,912 112,227 235,423 174,567 39,467 9,108 10,197 11,202 135,216 599,432 106,582 58,678 30,801 167,175 81,692 14,444 98,892 35,318 61,307 215,220 24,697 45,993 106,276 127,454 23,027 62,307 158,758 368,041 26,124 35,742 20,109 27,697 86,619 12,810 28,491 28,341 34,506 10,264 10,856 29,734 11,663 23,124 40,540 30,219 120,406 46,128 14,952 67,318 63,312 40,951 14,395

graph (Fig. 9), and a graph of fatigue life dependency on λ (Fig. 10), for X2CrNiMo17-12-2 steel for tension-compression (TC), torsion (T), proportional load (P) of λ value 0.5 and 0.8 and non-proportional (NP) with λ = 0.5, 0.8 and 1.0. In case of both tested materials, the fatigue lives of specimens subject to uniaxial load and proportional 552

Pejkowski, Ł. – Skibicki, D. – Sempruch, J.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 549-560

Fig. 7. Dependency of fatigue life on λ for Cu- ETP, at the level of σeq = 160 MPa

Fig. 6. Comparison of experimental fatigue lives for tensioncompression with calculated fatigue lives for Cu-ETP copper

load, yielding the same value of equivalent stress σeq, are very close. At the same time, the fatigue life of specimens subject to non-proportional loads is lower. Fatigue life reduction significantly depends on λ. Its highest reduction in the case of copper can be observed for λ = 0.53 ≈ τ-1/σ-1, and for steel for λ = 0.8 ≈ τ-1/σ-1. 2.2 Macrofractography Fig. 11 presents, on the background of Wöhler’s curves, the images of fracture surfaces morphology and cracks of Cu-ETP specimens subject to tensioncompression (TC). In all fracture surfaces, the tensilemechanism, indicating mode and fracture load can

be observed. Fracture is perpendicular to the load direction. There was Case A and B crack growth (Case A grew along the surface of a material; Case B grew into the depth of a material [3]). At higher load levels, there are ratchet marks visible, indicating the initiation of cracking with multiple origins and a relatively big fast fracture zone. In Fig. 12, images of surface fracture morphology and Cu-ETP cracks from specimens being subjected to torsion are shown. Cracks were loaded in mode II, meaning that the shear mechanism operated. In all specimens, the direction of macro-crack is compliant with the direction of maximum shear stress. Fig. 13 shows images of surface fracture morphology and Cu-ETP cracks from specimens being subjected to a proportional load of coefficient λ = 0.5. The fracture face of the most loaded specimen resembles the fracture face of a specimen subject to tension-compression of low stress value. There are no ratchet marks and many origins, and the fracture

Fig. 8. Wöhler’s curves obtained for X2CrNiMo17-12-2 steel for various load types High-Cycle Fatigue Behavior of Austenitic Steel and Pure Copper under Uniaxial, Proportional and Non-Proportional Loading

553

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 549-560

zone is relatively small. One can observe more crack growth in Case A than in a case of pure shear. The higher the load level, the greater the number of origins and ratchet marks, being inclined and tapered, indicating the participation of torsion.

plane is perpendicular to the specimen axis. On the fracture surface of specimens subject to lower loads, there are many river marks visible. Their endings indicate the fracture propagated in many directions. The macro-crack plane is located at an angle of 45° in relation to the specimen axis. For λ = 0.5, the fracture surface of the specimen subject to the highest loads is characterised by and extremely large fracture zone meaning that the material was under significant stress. The surface of the fatigue zone is irregular and the crack propagated from many origins and on various planes. In the case of a specimen subject to load of the lowest value, the fracture zone is smaller and fatigue zone as well as the macro-crack also indicate that the crack propagated on many planes.

Fig. 9. Comparison of experimental fatigue lives for tensioncompression with calculated fatigue lives for X2CrNiMo17-12-2 steel

Images of surface fracture morphology and cracks in Cu-ETP specimens for non-proportional loads of three various values of coefficient λ are presented in Fig. 14. In the case of λ = 0.3, surface fractures of the most highly loaded specimen, is as for the specimen subject to tension-compression. There are no ratchet marks, and in the vicinity of the fracture zone there are several progression marks visible. The macro-crack

Fig. 10. Dependency of fatigue life on λ for X2CrNiMo17-12-2 steel, at the level of σeq = 310 MPa

The predominance of Case A crack growth is visible. The macro-crack of the specimen subject to a non-proportional load of coefficient λ = 0.7, of the highest value is perpendicular to the specimen axis.

Fig. 11. Fractography of Cu-ETP for tension-compression

554

Pejkowski, Ł. – Skibicki, D. – Sempruch, J.

Strojni拧ki vestnik - Journal of Mechanical Engineering 60(2014)9, 549-560

Fig. 12. Fractography of Cu-ETP for torsion

Fig. 13. Fractography of Cu-ETP for proportional load ( 位 = 0.5)

The predominance of Case A crack growth is even higher and the fracture surface bears friction marks. The macro-crack and fracture surface of the specimen subject to loads of lower value indicate cracks in many

origins and crack development on a greater number of planes. To summarize, the characteristic feature of fracture surfaces of copper specimens subject to nonproportional load is the crack growth on many planes.

High-Cycle Fatigue Behavior of Austenitic Steel and Pure Copper under Uniaxial, Proportional and Non-Proportional Loading

555

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 549-560

Fig. 14. Fractography of Cu-ETP for non-proportional loads (λ = 0.3, 0.5 and 0.7)

Fig. 15. Fractography of X2CrNiMo17-12-2 for tension-compression

Fig. 15 presents fracture surfaces morphology and cracks of specimens made of steel X2CrNiMo17-12-2, subject to tension-compression. The tensile mechanism causing the Case A and B crack growth can be observed. The fracture is perpendicular to the load direction. In the fatigue zone, there are no progression marks or ratchet marks. The crack initiation was of a single origin. The fracture zone decreases along with the load reduction. Fig. 16 shows fracture surfaces morphology and specimen cracking of X2CrNiMo17-12-2, which were subject to fully reversed torsion. In cases with a high 556

load level, the crack direction is compliant with the direction of maximum shear stress. There is a Case A crack growth. The fracture surface is featureless due to friction. The reduction of load level caused the change of macro-crack direction by 45°. For medium load levels, one can observe that the crack propagated on two planes, whilst for the lower load level only on a single plane. Fracture surfaces and cracks of X2CrNiMo17-12-2 specimens subject to proportional loads of coefficient values λ = 0.5 and 0.8 are presented in Fig. 17. In the case of λ = 0.5, cracks propagated at

Pejkowski, Ł. – Skibicki, D. – Sempruch, J.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 549-560

Fig. 16. Fractography of X2CrNiMo17-12-2 for torsion

Fig. 17. Fractography of X2CrNiMo17-12-2 for proportional load (λ = 0.5, 0.8)

the angle of 7°, and for λ = 0.8 at the angle of 15°. The difference is 8°, and it is identical with the value of change of angle of principal axes between these load cases. Fracture surfaces are similar to fracture surface for tension-compression with the difference that the crack propagated more inward with regards to the material (Case B), rather than along the crack length. Fig. 18 shows fracture faces morphology and cracks of X2CrNiMo17-12-2 steel specimens subject to non-proportional loads of coefficient values λ = 0.5 and 0.8. In cases of λ = 0.5, the crack propagated along perpendicular direction to the specimen axis and

more inwards with regard to the material (Case B) than for λ = 0.5 (more torsion), where it propagated more along the direction of the crack length (Case A) and at an angle of 30°. Load non-proportionality resulted in the crack surface and its edge being highly irregular, indicating that the crack propagated on various planes. Similar to the case of Cu-ETP, the characteristic feature of fracture surfaces of specimens subject to nonproportional load is the crack propagation on many planes.

High-Cycle Fatigue Behavior of Austenitic Steel and Pure Copper under Uniaxial, Proportional and Non-Proportional Loading

557

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 549-560

Table 5. Summary of fracture features for Cu-ETP copper

High stresses

Macro fracture plane direction Crack growth case Number of origins Ratchets marks presence Progression marks / river marks presence

Low stresses

Macro fracture plane direction Crack growth case Number of origins Ratchets marks presence Progression marks / river marks presence

Tension

Torsion

Proportional

λ=0 ┴ σ1max

λ=∞ ||τα max

λ = 0.5 ┴ σ1max

λ = 0.3 ┴ σ1max

λ = 0.5 ┴ σ1max

λ = 0.7 ┴ σ1max

┴ σ1max

||τα max

┴ σ1max

||τα max

┴ σ1max

A≈B multiple yes yes / no A≈B single no yes / no

A multiple no no / no

A≈B multiple tapered no / no

Non-proportional

A≈B single no yes / no

difficult to identify multiple tapered no / no

A≈B single tapered no / yes

A≈B single no no / no A>B single no no / no

A >> B single yes no / no

A >> B single no no / no

Table 6. Summary of fracture features for X2CrNiMo17-12-2 steel

High stresses

Macro-fracture plane direction Crack growth case Number of origins Ratchets marks presence Progression marks / river marks presence

Low stresses

Macro-fracture plane direction Crack growth case Number of origins Ratchets marks presence Progression marks / river marks presence

Tension

Torsion

λ=0 ┴ σ1max

λ=∞ ||τα max

λ = 0.5

λ = 0.8

difficult to identify

A multiple no no / no

B≈A single no no / no

A≈B multiple no no / no

┴ σ1max

┴ σ1/2max

difficult to identify

B≈A single no no / no

A≈B single no no / no

A≈B single no no / no A≈B single no no / no

A multiple no no / no

Proportional

Non-proportional

Fig. 18. Fractography of X2CrNiMo17-12-2 for non-proportional loads (λ = 0.5, 0.8)

558

Pejkowski, Ł. – Skibicki, D. – Sempruch, J.

λ = 0.5 ┴ σMmax

λ = 0.8 ┴ σMmax

┴ σMmax

A≈B single no no / no A≈B single no no / no

A >> B single no no / no A >> B single no no / no

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 549-560

The summaries of fracture features are presented in Tables 5 and 6. Fracture surfaces of specimens subjected to nonproportional loads are different than for specimens subjected to proportional loads. Generally, in cases of non-proportional loads, cracks grow on many planes, thus the fracture surfaces are irregular. Similarly to fatigue lives, the features of fracture surfaces strongly depend on the λ ratio. For high values of λ, more Case A than B crack growth mode can be observed, while in the case of proportional loads there was a similar amount of Case A and B crack growth mode. The influence of the most damaging value of λ ratio is also visible. Fracture surfaces are most irregular for the most non-proportional load, and cracks nucleated from many origins and propagated on many planes. The fracture zones are large, which indicates a high stress level. 3 SUMMARY AND CONCLUSIONS A detailed study of the impact of shear to normal stress amplitudes, λ = τa / σa, on the fatigue life and fracture surface morphology of materials sensitive to non-proportional loadings has been conducted. Both tested materials showed high sensitivity to non-proportionality of load. In the case of Cu-ETP copper application of fatigue criterion in a manner stressing the impact of non-proportional loads, it resulted in over-estimation of fatigue strength by about 22% and fatigue life by about 450% in extreme cases. ForX2CrNiMo17-12-2 steel, it was ca. 10% and ca. 650%, respectively. For both materials the value of shear to normal stress ratio λ had significant impact on fatigue life. Values of coefficient λ close to relation τ-1 / σ-1 turned out to be the most damaging both for copper and for austenitic steel. A similar dependence on the value of the λ ratio was observed in case of fracture surfaces. It had an impact on their morphology and the orientation of the macro-fracture plane. It is worth emphasizing that for both materials the critical value of λ was different. This allows for the creation of the hypothesis that for materials subject to out-of-phase loads the most damaging are loads with components shifted in phase by 90° and of shear-tonormal stress ratio equal to τ-1 / σ-1. Therefore, it seems that for estimation of fatigue strength and fatigue life in the conditions of nonproportional loads, the relation of fatigue limits τ-1 / σ-1 is of very high importance.

The microscopic models of non-proportional fatigue failure mechanisms are highly general, regardless of the material (steel [17], aluminium alloy [18], non-ferrous metals, [19] to [21], general (hypothetic) [22]). At this stage of research, it is difficult to directly show their relationship with macroscopic phenomena presented in the article. 4 ACKNOWLEDGEMENT The project has been financed by the Polish National Science Centre. Project number: N N501 120940. 5 REFERENCES [1] McDiarmid, D.L. (1986). Fatigue under out-ofphase bending and torsion. Fatigue & Fracture of Engineering Materials & Structures, vol. 9, no. 6, p. 457-475, DOI:10.1111/j.1460-2695.1987.tb00471.x. [2] Ellyin, F., Golos, K., Xia, Z. (1991). In-phase and outof-phase multiaxial fatigue. Journal of Engineering Materials and Technology-Transactions of the ASME, vol. 113, no. 1, p. 112-118, DOI:10.1115/1.2903365. [3] Socie, D.F., Marquis, G.B. (1999). Multiaxial Fatigue. SAE International, Washington D.C. [4] Fatemi, A., Shamsaei, N. (2011). Multiaxial fatigue: An overview and some approximation models for life estimation. International Journal of Fatigue, vol. 33, no. 8, p. 948-958, DOI:10.1016/j.ijfatigue.2011.01.003. [5] Noban, M., Jahed, H., Ibrahim, E., Ince, A. (2012). Load path sensitivity and fatigue life estimation of 30CrNiMo8HH. International Journal of Fatigue, vol. 37, no. p. 123-133, DOI:10.1016/j. ijfatigue.2011.10.009. [6] Zenner, H., Simburger, A., Liu, J. (2000). On the fatigue limit of ductile metals under complex multiaxial loading. International Journal of Fatigue, vol. 22, no. 2, p. 137-145, DOI:10.1016/S0142-1123(99)00107-3. [7] Verreman, Y., Guo, H. (2007). High-cycle fatigue mechanisms in 1045 steel under non-proportional axialtorsional loading. Fracture of Engineering Materials & Structures, vol. 30, no. 10, p. 932-946, DOI:10.1111/ j.1460-2695.2007.01164.x. [8] Papadopoulos, I.V. (2001). Long life fatigue under multiaxial loading. International Journal of Fatigue, vol. 23, no. 10, p. 839-849, DOI:10.1016/S01421123(01)00059-7. [9] Karolczuk, A. (2006). Plastic strains and the macroscopic critical plane orientations under combined bending and torsion with constant and variable amplitudes. Engineering Fracture Mechanics, vol. 73, no. 12, p. 1629-1652, DOI:10.1016/j. engfracmech.2006.02.005. [10] Marciniak, Z., Rozumek, D., Macha, E. (2008). Fatigue lives of 18G2A and 10HNAP steels under variable amplitude and random non-proportional bending with torsion loading. International Journal

High-Cycle Fatigue Behavior of Austenitic Steel and Pure Copper under Uniaxial, Proportional and Non-Proportional Loading

559

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 549-560

of Fatigue, vol. 30, no. 5, p. 800-813, DOI:10.1016/j. ijfatigue.2007.07.001. [11] Banvillet, A., Łagoda, T., Macha, E., Niesłony, A, Palin-Luc, T., Vittori, J.-F. (2004). Fatigue life under non-gaussian random loading from various models. International Journal of Fatigue, vol. 26, no. 4, p. 349363, DOI:10.1016/j.ijfatigue.2003.08.017. [12] Roy, M., Nadot, Y., Maijer, D.M., Benoit, G. (2012). Multiaxial fatigue behaviour of A356-T6. Fatigue & Fracture of Engineering Materials & Structures, vol. 35, no. 12, p. 1148-1159, DOI:10.1111/j.14602695.2012.01702.x. [13] Zhang, J., Shi, X., Bao, R., Fei, B. (2011). Tension– torsion high-cycle fatigue failure analysis of 2A12-T4 aluminum alloy with different stress ratios. International Journal of Fatigue, vol. 33, no. 8, p. 1066-1074, DOI:10.1016/j.ijfatigue.2010.12.007. [14] Borodii, M.V., Shukaev, S.M. (2007). Additional cyclic strain hardening and its relation to material structure, mechanical characteristics, and lifetime. International Journal of Fatigue, vol. 29, no. 6, p. 1184-1191, DOI:10.1016/j.ijfatigue.2006.06.014. [15] Papadopoulos, I.V., Davoli, P., Gorla, C., Filippini, M., Bernasconi, A. (1997). A comparative study of multiaxial high-cycle fatigue criteria for metals. International Journal of Fatigue, vol. 19, no. 3, p. 219235, DOI:10.1016/S0142-1123(96)00064-3. [16] Lee, Y.L., Pan, J., Hathaway, R., Barkey, M. (2004). Fatigue Testing and Analysis. Butterworth-Heinemann, Oxford.

560

[17] Kida, S., Itoh, T., Sakane, M., Ohnami, M., Socie, D. F. (1997). Dislocation Structure and Non-Proportional Hardening of Type 304 Stainless Steel. Fatigue & Fracture of Engineering Materials & Structures, vol. 20, no. 10, p. 1375-1386, DOI:10.1111/j.1460-2695.1997. tb01496.x. [18] Zhang, J., Shi, X., Fei, B. (2012). High cycle fatigue and fracture mode analysis of 2A12–T4 aluminum alloy under out-of-phase axial–torsion constant amplitude loading. International Journal of Fatigue, vol. 38, p. 144-154, DOI:10.1016/j.ijfatigue.2011.12.017. [19] Bentachfine, S., Pluvinage, G. (1996). Biaxial low cycle fatigue under non-proportional loading of a magnesiumlithium alloy. Engineering Fracture Mechanics, vol. 54, no. 4, p. 513-522, DOI:10.1016/0013-7944(95)002235. [20] Zhang, J., Jiang, Y. (2005). An experimental investigation on cyclic plastic deformation and substructures of polycrystalline copper. International Journal of Plasticity, vol. 21, no. 11, p. 2191-2211, DOI:10.1016/j.ijplas.2005.02.004. [21] Ding, X., He, G., Chen, C. (2010). Study on the dislocation sub-structures of Al–Mg–Si alloys fatigued under non-proportional loadings. Journal of Materials Science, vol. 45, no. 15, p. 4046-4053, DOI:10.1007/ s10853-010-4487-3. [22] Colak, U.O. (2004). A viscoplasticity theory applied to proportional and non-proportional cyclic loading at small strains. International Journal of Plasticity, vol. 20, no. 8-9, p. 1387-1401, DOI:10.1016/j. ijplas.2003.07.002.

Pejkowski, Ł. – Skibicki, D. – Sempruch, J.

Original Scientific Paper

Received for review: 2013-11-27 Received revised form: 2014-02-19 Accepted for publication: 2014-03-31

Position-Parameter Selection Criterion for a Helix-Curve Meshing-Wheel Mechanism Based on Sliding Rates Ding, J. – Chen, Y.Z. – Lv, Y.L. – Song, C.H. Jiang Ding – Yangzhi Chen* – Yueling Lv – Changhui Song South China University of Technology, China The space curve meshing wheel (SCMW) is an innovative gear mechanism mediating transmission between space curves instead of classic space surfaces; the most common type of SCMW is the helix curve meshing wheel (HCMW). In this study, we propose a position-parameter selection criterion of the HCMW based on its slide rates. The sliding rates of the contact curves at the meshing point are defined and calculated; the optimal meshing condition of the HCMW is attained by analyzing the features of the slide rates; the position-parameter selection criterion is subsequently attained as well as corresponding contact curve equations. Both simulation and practical examples using different positionparameters are provided to verify the transmission continuity, and their slide rates are calculated. The calculating result shows that the HCMW coincident with the position-parameter selection criterion has better slide rates and, therefore, can have better tribological performance. The design method proposed in this paper aims to change the current situation so that the position-parameters of the HCMW are determined according to designers’ experience, and theoretically provides a foundation for its standardized production in industry. Keywords: gear, space curve meshing wheel, helix curve meshing wheel, position-parameter, parameter selection, sliding rate

0 INTRODUCTION Closely related to the friction and wear performances of meshing gear teeth, the slide rate is an important index for estimating the transmission quality of a gear pair [1]. To reduce wear and to prevent the scuffing of the gears, the slide rates of the two surfaces should be close and minimized in many situations. For example, in precision instruments, cycloid gears with the same slide rates at every meshing point are more commonly used than involute gears, which have different slide rates at different meshing points. As the traditional gear pairs mediate transmission between two conjugate surfaces [2] to [4], the current research is mainly about the slide rates between two surfaces [5] and [6]. Recently, the Space Curve Meshing Wheel (SCMW) was proposed, based on the space curve meshing theory [7] to [10], instead of the classic space surface meshing theory [2]. Mediating transmission between the contact curves on the surfaces of the driving and driven tines, the SCMW possessed the advantages of small size, a large transmission ratio, and high design flexibility. Since its invention, progress has been attained in many aspects, including meshing equations [7] to [11], design criteria [12], contact ratio [13], bending stress [14], manufacturing technology [15] and [16], and practical application [17] to [21]. At present, the most common SCMW is the Helix Curve Meshing Wheel (HCMW), as shown in Fig. 1. The modification coefficients of the transitional gears are important factors affecting the slide rates of the conjugate surfaces; similarly, the position-

parameters (a and b in Fig. 1, further details in section 1.2) of the HCMW influence the meshing radii and, subsequently, the slide rates of the contact curves. However, the position-parameters are currently selected according to designers’ experience. If they are not selected properly, the slide rates may be so large that the tines will wear out quickly.

Fig. 1. Helix Curve Meshing Wheel; a) non-vertical case and b) vertical case

In this paper, a position-parameter selection criterion for the HCMW based on its slide rates

*Corr. Author’s Address: South China University of Technology, School of Mechanical and Automotive Engineering, Guangzhou, China, meyzchen@scut.edu.cn

561

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 561-570

is proposed. It should be noted that the positionparameters also affect other parameters, such as the maximum radius or the height of the HCMW pair, but their effects on the meshing radii and the subsequent slide rates are direct and primary. Additionally, the space curve meshing skew gear mechanism (SCMSGM) in [11] is the latest SCMW. However, its geometric conditions remain under research, and its slide rates will be studied afterward. According to its current application [17] to [21], this study mainly focuses on the HCMW under operation conditions of self-lubrication and dry friction. In addition, the relative slide speed between the driving and driven tines should be preserved to form a hydrodynamic film with lubricant to reduce the wear under operation conditions. The definitions of the slide rates are still available in that occasion, while the position-parameter selection criterion is slightly different. 1 SLIDE RATES 1.1 Slide Rates between Two Conjugate Space Curves The working part of the SCMW is a pair of conjugate space curves named “contact curves”. As shown in Fig. 2, suppose that the contact curves, which are 2 1 denoted as Γ1 : r1 = r1( ) ( t ) and Γ 2 : r2 = r2( ) ( t ) , mesh at point M at the given start moment. After a period of Δt, point M1 on the curve Γ1 meshes with point M2 on the curve Γ2. The corresponding arc lengths  = s , while the  = s and MM are denoted as MM 1 1 2 2 corresponding chord lengths are | MM 1 | = |Δr1| and | MM 2 | = |Δr2|. Therefore, lim s1 = lim ∆r1 and ∆t →0 ∆t →0 lim s2 = lim ∆r2 . ∆t →0

∆t →0

The slide directions of Γ1 and Γ2 can be attained from either Eqs. (1) or (2). Take Eq. (1) for example: when σ1 > 0, i.e. s1 > s2, the relative slide direction of Γ2 comparing with Γ1 is from M to M2 and consistent with the moving direction of the meshing point; when σ1 < 0, i.e., s1 < s2, the relative slide direction of Γ2 comparing with Γ1 is from M2 to M and reverse with the moving direction of the meshing point. 1.2 Slide Rates of the SCMW Contact Curves As the SCMW is mainly designed to operate in conditions with low loads, the elastic deformation [12] has insignificant impact on the slide rates, and the contact curve equations of the SCMW are used for analysis. The contact curve equations are attained in the space curve meshing coordinates, as shown in Fig. 1. The coordinate o1 – x1y1z1 is stationary with respect to the driving wheel, and the coordinate o2 – x2 y2z2 to the driven wheel. In a non-vertical case, the distance from o2 to x1 is denoted as a; in a vertical case, the distance from o2 to z1 as b. As shown in Fig. 2, the driving and driven contact curves of the SCMW are denoted as T

1 1 in o1 – x1y1z1 and r1( ) =  xM( ) yM(1) zM(1)  T 2 2 r2( ) =  xM( ) yM( 2) zM( 2)  in o2 – x2 y2z2. Their differential equations are as in Eqs. (3) and (4):

d1r1( )  (1) =  x 'M dt

y '(M)

1 z '(M)  , (3)

d 2 r2( )  ( 2) =  x 'M dt

y '(M )

z '(M )  , (4)

Fig. 2. Slide rates of conjugate space curves

The slide rates of space curves are defined as the limit value of the ratio of the lengths difference between two relative arcs divided by the length of the given arc: 562

σ 1 = lim

s1 →0

∆r − ∆r2 s1 − s2 = lim 1 , (1) 0 ∆ t → s1 ∆r1

∆r ( 2) − ∆r (1) s2 − s1 σ 2 = lim = lim . (2) s2 →0 ∆t →0 s2 ∆r ( 2)

1 ∆r d r( ) lim 1 = 1 1 t →0 ∆r dt 2

d 2 r2( dt

d1r1( ) 1

d 2 r2(

. (5)

From Eqs. (1) and (3) to (5), the slide rate of the driving contact curve is as in Eq. (6):

σ1 = 1 −

( x '( ) ) + ( y '( ) ) + ( z '( ) ) ( x '( ) ) + ( y '( ) ) + ( z '( ) ) 2 M

1 M

2 M

1 M

2 M

1 M

. (6)

From Eqs. (2) to (5), the slide rate of the driven contact curve is as in Eq. (7):

Ding, J. – Chen, Y.Z. – Lv, Y.L. – Song, C.H.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 561-570

σ 2 = 1−

( ) ( ) ( ) ( x '( ) ) + ( y '( ) ) + ( z '( ) ) x '(M1) 2 M

+ y '(M1) 2 M

+ z '(M1) 2 M

. (7)

1.3 Slide Rates of the HCMW Contact Curves The driving contact curve of the HCMW in o1 – x1y1z1 is circular helix curve, and its equation is as below [9]:

 xM(1) = m1 cos t  (1)  yM = m1 sin t ( tS ≤ t ≤ t E ) , (8)  (1)  zM = nπ + nt

where m1 is the helix radius, m1 > 0; n is the pitch coefficient, equaling the ratio of the pitch and 2π [9], and usually n > 0 as the driving cylindrical helix is a right-hand screw; t is an independent parameter indicating the length of the contact curve; ts and tE are the starting and ending values for the meshing point, respectively. In this paper, ts = –π, so the initial value of the 1 driving contact curve height is zM( ) = 0 , which means that the driving curve begins from the plane x1o1y1; tE = –π/2, i.e., tE – ts = π/2, so a quarter of a circle is used. The transmission ratio of the HCMW pair is denoted as i12, and the angle between the angular velocity of the driving and driven wheels is denoted as θ, 0 ≤ θ ≤ π. The driven contact curves for non-vertical and vertical cases are reflected in Eqs. (9) and (10), respectively [9]:

 ( 2)  m1 − a t +π   xM =  cos θ − n ( t + π ) sin θ  cos i   12   ( 2)  m1 − a  t +π , (9) − n ( t + π ) sin θ  sin  yM = −  i12  cos θ    z ( 2) = −n t + π cosθ ( )  M  t +π  ( 2)  xM = − ( nt + nπ − b ) cos i 12   ( 2) t +π . (10)  yM = ( nt + nπ − b ) sin i12   z ( 2) = 0  M 

Eqs. (9) and (10) are a common conical helical curve and a planar Archimedean helical curve,

respectively. It can be proved from both Eqs. (9) and (10) that the initial value of the driven contact curve 2 height is zM( ) = 0 , and the driven curve begins from the plane x2o2 y2. Differential equations of Eqs. (8) to (10) are as in Eqs. (11) to (13):  x '(M1) = −m1 sin t  (1)  y 'M = m1 cos t , (11)  (1)  z 'M = n

 ( 2)  x 'M       ( 2)  y 'M      ( 2)  z 'M  

=−

t +π t +π  ( 2) nt + nπ − b sin − n cos  x 'M = i12 i12 i12   ( 2) nt + nπ − b t +π t +π cos + n sin . (13)  y 'M = i12 i12 i12   z '( 2) = 0  M 

=−

1  m1 − a   t +π − n ( t + π ) sin θ  sin   i12  cos θ   i12

 + 

 t +π  + n sin θ cos    i12   t +π 1  m1 − a  − n ( t + π ) sin θ  cos   i12  cos θ   i12

  − , (12) 

 t +π  −n sin θ sin    i12  = − n cosθ

From Eqs. (6), (11) and (12), the slide rates of the HCMW contact curve for non-vertical case are as in Eqs. (14) and (15): 2

σ 1 =1 −

σ 2 = 1−

 1  m1 − a  − n ( t + π ) sin θ   + n 2     i12  cos θ m12 + n 2 m12 + n 2 2

 1  m1 − a  − n ( t + π ) sin θ   + n 2     i12  cos θ

, (14)

. (15)

From Eqs. (7), (11) and (13), the slide rates of the HCMW contact curve for vertical case are as in Eqs. (16) and (17):

Position-Parameter Selection Criterion for a Helix-Curve Meshing-Wheel Mechanism Based on Sliding Rates

563

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 561-570

σ1 = 1 −

 nt + nπ − b  2   +n i12   m12 + n 2

, (16)

The same monotonicity can be attained in the vertical HCMWs. The only difference is that the meshing radius of the driven contact curves (see Eq. 30 in section 2.2) is required as: – (nt + nπ – b) > 0.

σ 2 = 1−

2 1

m +n

2 2

 nt + nπ − b  2   +n i   12

. (17)

From Eqs. (20) and (25), the maximum limit of t is denoted as tmax uniformly:

tmax

2 POSITION-PARAMETER SELECTION CRITERION BASED ON SLIDE RATE 2.1 Monotonicity and Feasible Region of Sliding Rates The non-vertical HCMW is illustrated as an example. Differentials of Eqs. (14) and (15) are as in Eqs. (18) and (19), respectively: m −a  n sin θ  1 − n ( t + π ) sin θ   cosθ 

σ 1'=

2 12

2 1

m +n

 1  m1 − a  − n ( t + π ) sin θ   + n 2   θ i cos    12

, (18)

(25)

 m1 − a  n cos θ sin θ − π = b −π  n

(θ ≠ π 2 ) (θ = π 2 )

. (26)

As shown in Fig. 3, σ1ʹ → 0 and σ2ʹ → 0 if t → tmax. Therefore, from Eqs. (14) to (17) and (26), the maximum σ1 and the minimum σ2 are as in Eqs. (27) and (28) for both non-vertical and vertical cases:

σ 1 → σ 1max =1 −

σ 2 → σ 2 min = 1 −

n 2 1

m + n2

, (27)

m12 + n 2 . (28) n

m − a  n sin θ m12 + n 2  1 − n ( t + π ) sin θ   .  cosθ σ2 ' = − 3/ 2 (19) 2   1  m − a    i122    1 − n ( t + π ) sin θ   + n 2     i12  cos θ 

n > 0 is supposed in section 1.3. The meshing radius of the driven contact curves should be above zero (see Eq. 30 in Section 2.2), so: m1 − a − n ( t + π ) sin θ > 0. (20) cos θ

If θ ≠ 0 and θ ≠ π are supposed, then: sin θ > 0,

(21) 3/ 2

2   1  m − a   1 − n ( t + π ) sin θ   + n 2    i cos θ    12  

> 0, (22)

i122 > 0 , (23)

m12 + n 2 > 0 . (24)

From Eqs. (20) to (24), it can be concluded that σ1ʹ > 0 and σ2ʹ < 0. Therefore, in the non-vertical HCMWs, σ1 is monotonically increasing while σ2 is monotonically decreasing. 564

Fig. 3. Monotonicity and feasible region of sliding rate equations

It should be noted that θ ≠ 0 and θ ≠ π are supposed in Eqs. (21) and (22). The non-vertical HCMWs when θ = 0 or θ = π are also called parallel-axis HCMWs. Their driving and driven contact curves are circular helix curves, and their slide rates equations are constant functions. However, the maximum values of σ1 and σ2 are the same as Eqs. (27) and (28). The allowable slide rate is denoted as [σ], [σ] > 0. According the monotonicity of σ1 and σ2, their feasible regions are shown in Fig. 3 and Table 1. In Fig. 3, the intersection of the two curves is defined as a pitch

Ding, J. – Chen, Y.Z. – Lv, Y.L. – Song, C.H.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 561-570

position, i.e. t = tp . It can be concluded that if and only if t = tp, σ1 = σ2 = 0

(29)

In the following section, Eq. (29) will be used to obtain the optimal meshing condition of the HCMW. Table 1. Feasible region of sliding Rates

σ1 σ2

t < tp 0 < |σ1| < [σ] 0 < σ2 < 1

t = tp 0

tp < t < tmax 0 < σ1 < 1 0 < |σ2| < [σ]

Substituting Eq. (33) into Eq. (9), or substituting Eq. (34) into Eq. (10), the same equations of the driven contact curve can be attained: t +π  ( 2)  xM = i12 m1 + n sin θ ( ( tS + t E ) 2 − t ) cos i 12   ( 2) t +π  yM = − i12 m1 + n sin θ ( ( tS + t E ) 2 − t ) sin i12   z ( 2) = −n t + π cosθ ( )  M  (35) ( 0 ≤ θ ≤ π ).

(

)

(

)

2.2 Optimal Meshing Condition of the HCMW and PositionParameter Selection Criterion

3 DESIGN EXAMPLE

The driven contact curve is either a common conical helical curve in a non-vertical case or a planar Archimedean helix in a vertical case. Therefore, from Eqs. (9) and (10), the helical radius of the driven contact curve is defined as Eq. (30):

In this section, the HCMW with different positionparameters are designed as examples both in simulation and a practical experiment to verify their transmission continuity; their slide rates will also be calculated for comparison.

 m1 − a − n ( t + π ) sin θ  m2 =  cos θ − ( nt + nπ − b ) 

(θ ≠ π 2 ) (θ = π 2 )

3.1 Contact Curve Equations . (30)

When t = tp, m2 = m2p is defined as pitch radius of the driven contact curve. From Eqs. (29) and (30), it can be derived that when t = tp,

m2 p = i12 m1. (31)

Eq. (31) is defined as the optimal meshing condition of the HCMW. From Eq. (30), the range of m2 depends on the value range of t and thus the range of m2 may not cover mP2. To guarantee that the entire meshing process has appropriate average slide rates, it is recommended that:

Table 2. Parameters chosen

t p = ( tS + t E ) 2. (32)

From Eqs. (30) to (32), the position-parameter for the non-vertical HCMW case is: a = (1 − i12 cos θ ) m1 − n sin θ cosθ ( ( tS + t E ) 2 + π ) , (33)

and for the vertical HCMW is:

For the design of the HCMW, θ is determined according to the directions of the input and out shafts; i12 according to the transmission demand; m1, n and the driving and driven tine radii, which are denoted as r1 and r2, according to the bear capable demand [14]; ts and tE, i.e. the range of t, according to the contact curve lengths desired. With the parameters given above, the driving and driven contact curves can be derived from Eqs. (8) and (35). The corresponding position-parameter for installation, either a or b, can be derived with Eq. (33) or Eq. (34).

b = i12 m1 + n ( ( tS + t E ) 2 + π ) . (34)

Eqs. (33) and (34) can serve as the selection criterion of the position-parameters for the HCWM.

i12

2π/3

6 mm 6 mm –π –π/2

12 0.6 mm 0.5 mm

To be more specific, numerical examples of nonvertical HCMWs are provided, and the parameters are chosen as in Table 2. From Table 2, the contact ratio ξ = Z1 (tE – ts) / 2π =1.25 [13]. From Table 2 and Eqs. (8) and (35), the driving and driven contact curves are as below:

 xM(1) = 6 cos t  (1)  yM = 6 sin t , (36)  (1)  zM = 6 (π + t )

Position-Parameter Selection Criterion for a Helix-Curve Meshing-Wheel Mechanism Based on Sliding Rates

565

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 561-570

t +π  ( 2)  xM = 12 − 3 3 ( t + 3π 4 ) cos 2  t +π  ( 2) . (37)  yM = − 12 − 3 3 ( t + 3π 4 ) sin 2   zM( 2) = 3 ( t + π )  

(

)

(

)

As shown in Fig. 5, these driven wheels can mesh with the same driving wheel. It can be concluded that the value of a influences the intersection point of the center lines of driving and driven wheels. The values of a mainly change the meshing radii of the driven wheels and subsequently the slide rates of the HCMW pairs.

From Eq. (31), m2p = 12 mm and from Eq. (33), ap = 14.041 mm. As a comparison, with the same driving contact curve, the previous driven contact curve [9] is derived from Eq. (9) as below: t +π  ( 2)  xM = 2a − 12 − 3 3 ( t + π ) cos 2  t +π  ( 2) . (38)  yM = − 2a − 12 − 3 3 ( t + π ) sin 2   zM( 2) = 3 ( t + π )  

(

)

(

)

From Eq. (20), a > 10.081 mm is required. Different values of a are selected as Table 3. An equation of the driven contact curve can be derived by submitting each value of a into Eq. (38). It is worth noticing that Eq. (37) is equal to Eq. (38) when a3 = 14.041 mm. Table 3. Values of a [mm]

12.041

13.041

a3 (ap) 14.041

15.041

16.041

3.2 Simulation As shown in Fig. 4, according to the parameters in Table 2 and the different a values in Table 3, a driving wheel and driven wheels of different sizes can be attained in Pro/Engineering.

Fig. 4. Simulation of driving and driven wheels

566

Fig. 5. Different driven wheels meshing with the same driving wheels

3.3 Transmission Continuity Test As shown in Fig. 6, the driving wheel and the driven wheels were manufactured through selective laser melting (SLM) technology [16] and post-processed with electrochemical brushing process [15]. Within the processing capacity of the SLM, the manufacturing cost decreases as the weight of the HCMW decreases. Mainly operating in conditions with low loads, the HCMW is usually small and light. Therefore, the SLM technology was chosen in this paper and will be recommended for large-scale industry. To verify their transmission continuity, the rotation speeds of the wheels were measured with a test rig developed by our research team [9], which is shown in Fig. 7. The test procedure is shown in Fig. 8, and the test condition in Table 4.

Fig. 6. Manufactured driving wheel and driven wheels

Ding, J. – Chen, Y.Z. – Lv, Y.L. – Song, C.H.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 561-570

Fig. 8. Test procedure Fig. 7. Test rig: 1) DC power, 2) 4-DOF moveable platform, 3) fixed bracket, 4) driven wheel, 5) driving wheel, 6) DC motor, and 7) cable connected to acquisition card and computer Table 4. Test condition Voltage on motor Currency on motor Angular velocity of motor shaft Torque transmitted Encoder Data-acquisition frequency

1.1 V 0.1 A 36° / s 0.18 Nm 1 Hz

Table 5. Transmission ratio

a Practical value Theoretical value Relative error [%]

1.99

2.00

0.5

2.00 2 0

2.01

2.00

0.5

Continuous records of the test are shown in Fig. 9. As shown in Table 5, all the driven wheels can continuously commit the transmission within the allowable error range [9].

Fig. 9. Continuous records of the test Position-Parameter Selection Criterion for a Helix-Curve Meshing-Wheel Mechanism Based on Sliding Rates

567

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 561-570

Table 6. Maximum absolute values of σ1 and σ2 corresponding to different a

a [mm]

12.041

13.041

14.041

15.041

16.041

Range of σ1

–0.003 to 0.249

–0.090 to 0.202

–0.182 to 0.141

–0.279 to 0.069

–0.379 to –0.012

0.249

0.202

0.182

0.279

0.379

Range of σ2

0.012 to 0.275

–0.074 to 0.218

–0.164 to 0.154

–0.253 to 0.083

–0.332 to 0.003

0.275

0.218

0.164

0.253

0.332

|σ1|max |σ2|max

b) Fig. 10. Slide rates of the driving and driven contact curves; a) σ1 vs. t and b) σ2 vs. t

It should be noted that the accuracy of setting the parameter a in the test rig is 0.1 mm, which is much lower the accuracy of the simulation in the previous section and the theoretical calculation in the next section. Furthermore, only the transmission continuity of the HCMWs is verified in the experiment.

As shown in Fig. 10, the slide rates of Eq. (38) with different position-parameters are calculated from Eqs. (14) and (15) and drawn with MATLAB. As shown in Table 6, the ranges of σ1 and σ2 are measured from Fig. 9. Since the signs of σ1 and σ2 indicate the relative slide direction, only the maximums of their absolute values are compared. The result shows that when a = ap = 14.041 mm, both |σ1|max and |σ2|max achieve their minimums simultaneously. Although all five pairs of the HCMW can mediate the transmission, the one coincident with the position-parameter selection criterion has the best slide rates.

1. The optimal meshing condition is attained from the analysis of the slide rate, and it shows that the slide rates of the HCMW are zero if and only if the meshing radius of the driven contact curve equals the product of the transmission ratio and the meshing radius of the driving contact curve; 2. The mesh at the midpoint of the contact curves should be coincident with optimal meshing condition, which is defined as the positionparameter selection criterion; 3. Numerical examples show that the HCMWs coincident with the position-parameter selection criterion that possesses the best slide rates. However, some issues remain to be improved: an experimental measure method of the HCMW slide rates has yet to be proposed; the slide rates’ effects on the friction and wear of the HCMW remain to be explored; the forming conditions of the hydrodynamic film should be studied to determine whether the HCMW will work with lubricant in the future; furthermore, the allowable slide rates under lubricant condition need to be determined for standardization production.

4 CONCLUSIONS AND PROSPECTS

5 ACKNOWLEDGMENT

This paper presents the position-parameter selection criterion of the HCMW based on its slide rates. Specifically, the results can be concluded as below:

Funding supports from the National Natural Science Foundation of China (No. 51175180) are gratefully acknowledged.

3.4 Slide Rate Discussion

568

Ding, J. – Chen, Y.Z. – Lv, Y.L. – Song, C.H.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 561-570

6 NOMENCLATURE a

Position-parameter, distance from point op to axis z b Position-parameter, distance from point op to axis x i12 Transmission ratio M Meshing point  Arc length between M and M1 MM 1

 Arc length between M and M2 MM 2 MM 1 Contact vector from M and M1 MM 2 Contact vector from M and M2 n Pitch parameter of driving curve r1 Driving curve equation in vector form r1 Driving tine radius r2 Driven curve equation in vector form r2 Driven tine radius s1 Arc length on driving curve s2 Arc length on driven curve t Scope parameter of helix curve ts Starting value of t tE Ending value of t tp t when HCMW in pitch position tmax Maximum available value of t Z1 Number of driving tines Z2 Number of driven tines Γ1 Driving curve Γ2 Driven curve θ Included angle between angular velocity vectors σ1 Slide rate of driving curves σ2 Slide rate of driven curves [σ] Available slide rate (superscript) Corresponding coordinate 7 REFERENCES

[1] Wu, X.T. (2009). Principle of Gearing. Xi’an Jiaotong University Press, Xi’an. (in Chinese) [2] Litvin, F.L. (2008). Gear Geometry and Applied Theory. Shanghai Science and Technology Publishers, Shanghai. (in Chinese) [3] Bergseth, E. Björklund, S. (2010). Logarithmical crowning for spur gears. Strojniški vestnik - Journal of Mechanical Engineering, vol. 56, no. 4, p. 239-244. [4] Staniek, R. (2011). Shaping of face toothing in flat spiroid gears. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 1, p. 47-54, DOI:10.5545/svjme.2010.093. [5] Puccio, F.D., Gabiccini, M., Guiggiani, M. (2006). Generation and curvature analysis of conjugate surfaces via a new approach. Mechanism and Machine

Theory, vol. 41, no. 4, p. 382-404, DOI:10.1016/j. mechmachtheory.2005.07.008. [6] Ciulli, E., Bartilotta, I., Polacco, A., Manconi, S., Vela, D. (2010). A model for scuffing prediction. Strojniški vestnik - Journal of Mechanical Engineering, vol. 54, no. 4, p. 267-274. [7] Chen, Y.Z., Xing, G.Q., Peng, X.F. (2007). The space curve mesh equation and its kinematics experiment. 12th IFToMM World Congress, Besançon. [8] Chen, Y.Z., Xiang X.Y., Luo, L. (2009). A corrected equation of space curve meshing. Mechanism and Machine Theory, vol. 44, no. 7, p. 1348-1359, DOI:10.1016/j.mechmachtheory.2008.11.001. [9] Ding, J., Chen, Y.Z., Lv, Y.L. (2012). Design of Space-Curve Meshing-Wheels with Unequal Tine Radii. Strojniški vestnik - Journal of Mechanical Engineering, vol. 58, no. 11, p. 633-641, DOI:10.5545/ sv-jme.2012.493. [10] Chen, Z., Chen, Y.Z., Ding, J. (2013). A generalized space curve meshing equation for arbitrary intersecting gear. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 227, no. 7, p. 1599-1607, DOI:10.1177/0954406212463310. [11] Chen, Y.Z., Lv, Y.L., Ding, J, Chen, Z. (2013). Fundamental design equations for space curve meshing skew gear mechanism. Mechanism and Machine Theory, vol. 70, p. 175-188, DOI:10.1016/j. mechmachtheory.2013.07.004. [12] Chen, Y.Z., Hu, Q., Su, L. (2010). Design criterion for the space-curve meshing-wheel transmission mechanism based on the deformation of tines. Journal of Mechanical Design, vol. 132, no. 5, p. 054502, DOI:10.1115/1.4001535. [13] Chen, Y.Z., Luo, L., Hu, Q. (2009). The contact ratio of a space-curve meshing-wheel. Journal of Mechanical Design, vol. 131, no.7, p. 074501, DOI:10.1115/1.3116343. [14] Liang, S.K., Chen, Y.Z. (2012). Research on the maximum bending stress on driving tine of SCMW. Applied Mechanics and Materials, vol. 184-185, p. 445-449, DOI:10.4028/www.scientific.net/AMM.184185.445. [15] Chen, Y.Z., He, E.Y., Chen, Z. (2012). Investigations on precision finishing of space curve meshing wheel by electrochemical brushing process. The International Journal of Advanced Manufacturing Technology, vol. 67, no. 9-12, p. 2387-2394, DOI:10.1007/s00170-0124659-1. [16] Chen, Y.Z., Sun, L.H, Wang, D., Yang, Y.Q., Ding, J. (2010). Investigation into the process of selective laser melting rapid prototyping manufacturing for spacecurve-meshing-wheel. Advanced Material Research, vol. 135, p. 122-127, DOI:10.4028/www.scientific.net/ AMR.135.122. [17] Chen, Y.Z., Chen, Z., Ding, J. (2011). Space Curve Mesh Driving Pair and Polyhedral Space Curve Mesh Transmission, US Patent, Aplication no. PCT/

Position-Parameter Selection Criterion for a Helix-Curve Meshing-Wheel Mechanism Based on Sliding Rates

569

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 561-570

CN2010/078294, US Patent and trademark office, Washington D.C. [18] Chen, Y.Z., Fu, X.Y., Ding, J., Liang, S.K. (2013). Geometric Design of Micro-Reducer With MultiOutput Shafts Distributed in Regular Polygon Form. Journal of Mechanical Design, vol. 135, no. 5, p. 051104, DOI:10.1115/1.4024084. [19] Chen, Y.Z., Ding, J., Yao, C.H., Lv, Y.L. (2012). Polyhedral space curve meshing reducer with multiple output shafts. ASME 2012 International Mechanical

570

Engineering Congress & Exposition, Houston, vol. 3, p. 1505-1511, DOI:10.1115/IMECE2012-86087. [20] Chen, Y.Z., Chen, Z, Ding, J. (2013). Space Curve Mesh Driving Pair and Polyhedral Space Curve Mesh Transmission, U.S. Patent, Appliacion No. 20130145876, US Patent and trademark office, Washington D.C. [21] Chen, Y.Z., Ding, J., Lv, Y. (2013) Design of polyhedral helix curve meshing reducer. Journal of Mechanical Design, vol. 136, no. 4, paper no. 044503, DOI:10.1115/1.4026571.

Ding, J. – Chen, Y.Z. – Lv, Y.L. – Song, C.H.

Original Scientific Paper

Received for review: 2014-01-29 Received revised form: 2014-05-09 Accepted for publication: 2014-05-21

Numerical Investigations of Quenching Cooling Processes for Different Cast Aluminum Parts

Kopun, R. – Škerget, L. – Hriberšek, M. – Zhang, D. – Edelbauer, W. Rok Kopun1,* – Leopold Škerget2 – Matjaž Hriberšek2 – Dongsheng Zhang3 – Wilfried Edelbauer3 2 University

1 AVL - AST d.o.o., Slovenia of Maribor, Faculty of Mechanical Engineering, Slovenia 3 AVL List GmBH, Austria

This paper discusses a recently improved computational fluid dynamics (CFD) methodology for virtual experimental investigation of the heat treatment for cast aluminium parts. The immersion quenching process of the heated work piece in a sub-cooled liquid pool is handled by employing the Eulerian multi-fluid modeling approach, which is implemented within the commercial CFD code AVL FIRE®. The applied heat and mass transfer rate is modeled based on a different boiling regime, which is controlled by the Leidenfrost temperature. The objective of the presented research is to present an updated quenching model by applying variable Leidenfrost temperatures . Furthermore, simulation results are compared with available measurements for a wide variety of quenching scenarios involving immersion cooling of the step plate and real cylinder head with different solid parts’ orientations. The temperature histories predicted by the presented model fit very well with the available experimental data at different monitoring locations. Keywords: multiphase flow, immersion quenching, cast aluminium parts, computational fluid dynamics

0 INTRODUCTION Modern powertrain development of the internal combustion engine (ICE) is driven in the direction of reducing the weight ratio by replacing heavier metals with light low-cost alloys. An accurate prediction and optimization of the heat transfer characteristics within automotive, aerospace and processing industries is one of the more important influential factors for reducing fuel consumption and emission values [1]. For work pieces of complex geometrical nature, like the internal combustion engine’s cylinder head and the deformation associated with thermal stress are a challenge to structural design optimization, where the difficulty arises from the ability to predict and analyze quench cooling heat transfer [2]. The immersion quenching cooling process from among all other heat treatment techniques has been long identified as one of the more important ways of achieving the desirable microstructure and mechanical properties of the metal piece [3]. This process provides even temperature distribution during the cooling process, leads to reduction of the residual stress levels, and consequently prevents distortion and cracking of the cast parts. During the immersion quenching process, a metal piece is heated up to a microstructure-dependent temperature, stays there for a while, and is then immediately submerged into a sub-cooled liquid like water, oil or polymers. Therefore, all three boiling regimes appear during the immersion quenching cooling process [4]. The film boiling regime occurs immediately after the heated piece is dipped into

the sub-cooled liquid domain. The heat transfer of the cooling rate in this regime is relatively small, since the film is stable and the vapor blanket acts like an insulator. As soon as the surface temperature of the heated piece drops below the minimum film collapse temperature, also known as the Leidenfrost temperature, transitiive boiling starts, and the hot surface is partly wetted due to the collapse of the vapor film [5]. As the time proceeds, the hot surface temperature drops and the heat flux increases. When the wall heat flux reaches the maximum heat flux or the so-called critical heat flux, the nucleate boiling regime is entered. There the vapour film becomes unstable and starts to disappear. This results in a higher heat transfer rate between the metal and the fluid, and leads to faster cooling. As soon as the surface temperature of the heated part drops below the boiling temperature of the fluid, the convective heat transfer without phase change occurs, and the cooling flow rate becomes stable and low. Over recent years many analytical approaches for immersion quenching have been investigated and phenomena like vapor pocket generation, stagnation region, flow dynamics etc. have been successfully resolved by several researchers [2] to [5]. Based on the complexities and phenomena of multi-phase flows during immersion quenching applications, heat and mass transfer empirical models were proposed and developed. One of them is the model for mass transfer prediction, as proposed by Wang et al. [6], who assumed that the mass transfer rate due to boiling was proportional to the heat transfer rate in the fluid system. This model was later improved by Srinivasan

*Corr. Author’s Address: AVL-AST d.o.o., Ul. kneza Koclja 22, 2000 Maribor, Slovenia, rok.kopun@gmail.com

571

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 571-580

et al. [7], and it has already been implemented within the commercial computational fluid dynamics (CFD) code AVL FIRE® where it is applied for the numerical simulations of quenching processes [8]. Published works like Wang et al[6], Srinivasan et al [7] and Greif et al [8], consider two separate domains, water and solid, which require separate simulations for each of them. The two simulations can be numerically coupled at the contact interface and communicate via the so-called ACCI (AVL code coupling interface) method after each time-step. The present paper describes a newly-developed quenching application method, where water and solid domains are treated as one. The methodology is known as the multi-material (MMAT) approach, where the surface temperature and local heat transfer coefficients are exchanged after each iteration and no longer after each time- step, as in the previously applied ACCI coupling method. The boiling phase change process between the heated part and the sub-cooled liquid side is handled by utilizing the Eulerian multi-fluid modelling approach. While for the fluid domain, general equations are solved within the framework of the multi-fluid modeling approach, only the energy equation is solved in order to predict the thermal field within the solid region. Additional to the MMAT approach, a new approach for modeling the variable Leidenfrost temperature threshold is also presented during this work. As long as the surface temperature is above the Leidenfrost threshold, film boiling appears, while transition boiling occurs when the surface temperature drops below the Leidenfrost temperature. Thus, the Leidenfrost threshold is a very important parameter for the numerical simulation of the quenching process, since it determines which regime is responsible for the calculation of the heat transfer coefficient. In previously published works [6] to [8] a constant Leidenfrost temperature threshold is assumed over the entire domain. This assumption has only limited validity, as discussed in the experimental work of Lübben et al. [9]. According to Lübben et al [9], it could be summarized that the Leidenfrost temperature for the quenching process depends on several factors, like the pool temperature (sub-cooling effect) [10], dipping and wetting velocity of the heated work piece [11], geometry and shape of the work piece, system pressure [12], surface roughness [5], etc. From previous work [13] it can be observed that, due to vapor bubbles rising from the bottom to the top of the quenched work piece, there is a higher vapor

572

concentration at the top. This leads to the fact that transition boiling occurs at a lower temperature level in the upper part of the work piece, and consequently the Leidenfrost temperature is lower at the upper part of the quenched surface. Therefore, a model capable of resolving the spatially changing Leidenfrost temperature is of essential importance for achieving better agreement between the predicted results and the available measurement data. The temperature distribution within the solid part, obtained from the CFD simulation, can serve as a realistic input for subsequent finite element analysis (FEA) of thermal stresses within the quenched solid part [14]. This paper is organized as follows. In section 1 the mathematical model is described based on the previous work of Srinivasan et al. [7]. Brief introductions of the simulation set-up and experimental description are given in sections 2 and 3. Two different quenching orientations with various solid parts have been conducted, where the comparisons of the simulated results of a real-time quenching process with the available measurement data are presented and discussed in section 5. Conclusions and remarks are made in section 6. 1 MATHEMATICAL MODEL The Eulerian multi-fluid model considers each phase as interpenetrating continua coexisting within the flow domain, with inter-phase transfer terms accounting for phase interactions where conservation laws apply [15]. From the theoretical work of Drew and Passman [16] the ensemble averaged continuity and momentum equations are presented as: 1.1 Continuity Equation

N ∂α k ρ k + ∇ ⋅ (α k ρ k v k ) = ∑ Γ kl , (1) ∂t l =1,l ≠ k

subject to the compatibility condition:

∑α k =1

= 1, k = 1,..., N , (2)

where α, ρ and stand for volume fraction, density and velocity vectors. The phase change rate (in this particular case, boiling) is Γk and the subscript k is the phase indicator (k = l or k = v). Subscripts v and l denote the vapor and liquid phases in the current work.

Kopun, R. – Škerget, L. – Hriberšek, M. – Zhang, D. – Edelbauer, W.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 571-580

1.2 Momentum Equation

∂α k ρ k v k + ∇ ⋅ (α k ρ k v k v k ) = −α k ∇p + ∂t

+∇ ⋅ α kτ k + α k ρ k g +

∑

l =1,l ≠ k

M kl + vinnt

∑

l =1,l ≠ k

Γ kl , (3)

with p, g, τ and vint are respectively the pressure, gravity vector, stress tensor and interfacial velocity. The interfacial momentum term is given by: M kl = FD + FWL + FL , (4)

where FD indicates the drag force, FWL the wall lubrication force and FL the lift force. Detailed information concerning modeling the interfacial forces is described in the work of Kopun et al. [13]

∂ρ m h + ∇ ⋅ ( ρ m ⋅ v ⋅ h ) = ∇ ⋅ q +ρ m ⋅ θ + ∂t ∂p + ρ m ⋅ g ⋅ v + ∇ ⋅τ ⋅ v + α m + ∂t N

∑

l =1,l ≠ k

H vl + hint

∑

l =1,l ≠ k

Γ kl ,

(5)

k =1

µ m = ∑ α k µ k , ρ m = ∑ α k ρ k , κ m = ∑ α kκ k , (6)

where q is the heat flux, θ is the specific enthalpy source, and the interfacial energy exchange between phases v and l is denoted as Hvl. Dynamic viscosity and thermal conductivity are presented as μ and κ, respectively. The heat flux q is given by:

1.4.1 Film Boiling Model The Bromely’s model [17], originally applied for a horizontal tube, is employed to predict the film boiling heat transfer coefficient h͂ FB is described by:

 κ v3 ρv ∆ρ g ( H fg + C1∆T' )   h FB = 0.62  db µv ∆T'  

, (9)

where db is the length scale (vapor bubble diameter), is the vapor thermal conductivity, Δρ = ρl – ρv is the density and C1 = 0.4·Cpv stands for the specific heat of the vapor. 1.4.2 Transition Boiling Model

with the mixture properties defined as:

where Cm, Cb, h͂ b, Aint, ΔT′ and Hfg are the closure coefficient, the boiling correction coefficient, the boiling heat transfer coefficient, interfacial area density, wall superheated temperature, and the latent heat of vaporization, respectively. The following subsections describe the applied models for heat transfer coefficient hFB of the different boiling regimes

With the assumption that the heat transfer rate between the vapor and liquid phases is rapid, then they are in thermal equilibrium [6] and [7]. In this case, the mixture enthalpy equation is solved, as described by:

Cm ⋅ Cb ⋅ hb ⋅ Aint ⋅ ∆T' , (8) H fg

1/ 4

1.3 Energy Equation

Γc =

κm ∇h. (7)  C p ,m

The heat transfer coefficient, for the transition boiling regime is given by:

hTB =

QCHF ⋅ φ + QMHF ⋅ (1.0 − φ ) , (10) T'w − T'sat

where the corresponding heat flux is computed as QCHF, which denotes the Critical Heat Flux, and QMHF which stands for the Minimum Heat Flux. Detailed information about the applied quenching model in more detail can be obtained from AVL FIRE® Multifluid model solver theory guide [15] and the references [6] to [8], [13],[18] and [19]. 1.5 Variable Leidenfrost Temperature Model

1.4 Boiling Model Based on the assumption that the boiling heat transfer rate is proportional to the phase change rate, the mass transfer predominantly controls the heat transfer. Thus, the phase change rate due to boiling can be written as:

The Leidenfrost temperature is used to distinguish between film boiling and transition boiling regimes. As described above, it can be observed that the Leidenfrost temperature varies along the gravitational direction. Due to the higher vapor concentration at the top of the quenched work piece, transition boiling occurs there at a lower temperature level, and

Numerical Investigations of Quenching Cooling Processes for Different Cast Aluminum Parts

573

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 571-580

consequently, the Leidenfrost temperature is lower within the upper region and higher in the lower region. Based on extended measurements, a physically meaningful variable Leidenfrost temperature model has been developed. The proposed Leidenfrost temperature as a function of the vertical position depends on the vapor distribution is written as:

TLeid ( z ) = TLeid ,ref −

∆TLeid ,range zmax − zmin

and communicate via the so-called ACCI interface, Fig. 1a, whereas in the MMAT approach only one simulation with conformed computational mesh is applied describing water and solid domains Fig. 1b.

( z − zmean ), (11)

where ΔTLeid,range is the range of the Leidenfrost temperature, TLeid,ref , is the mean Leidenfrost temperature, z is the coordinate in the gravitational direction, and zmean the position where TLeid,ref is valid. Thus, the term zmax – zmin describes the maximum extension of the quenched work piece in the gravitational direction. The model implies that the Leidenfrost temperature decreases linearly from TLeid,max, at the bottom, to TLeid,min, at the top. Detailed information concerning the variable Leidenfrost temperature treatment can be obtained from the references [18]. 2 SIMULATIONS SET UP

Fig. 2. Computational domain set up with boundary conditions; a) step plate and b) cylinder head

The presented MMAT approach triggers data exchange between the solid and liquid domains over the interface region, which is similar to the ACCI approach. The applied MMAT method is however different as the surface temperature and local heat transfer coefficients are exchanged after each iteration and no longer after each time-step, see Fig. 1. In the case of the ACCI methodology two separate simulations are numerically coupled at the interface

Fig. 2 displays the physical domains and the boundary conditions applied in the CFD simulations. In the current study, two different cases involving immersion quenching of the step-plate and real cylinder head configurations were investigated. The total number of cells for the step-plate test piece (Fig. 2a) was about 800,000 whereas the solid domain consisted of approximately 70,000 cells. The simulation set-up for the real cylinder head consisted

574

b) Fig. 1. Data exchange between liquid and solid domains; a) ACCI interface and b) MMAT interface Kopun, R. – Škerget, L. – Hriberšek, M. – Zhang, D. – Edelbauer, W.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 571-580

a) b) Fig. 3. Detailed positions of the monitoring points are presented for; a) step plate and b) cylinder head

of approximately 2,400,000 cells for the liquid domain and about 2,100,000 cells within the solid domain Fig. 2b. With reference to the liquid domain, the prescribed atmospheric pressure is exerted at the outlet boundary on the top (green surface), and the inlet section is the given velocity boundary condition at the bottom (black surface). The dipping velocity is used to define the inlet velocity rising up from the initial water level (yellow part at the side) toward the outlet region. In current simulations, a constant velocity of 0.14 m/s is used until the final submerging depth has been reached. The domain walls at the sides are treated as adiabatic. Boundary conditions, dipping velocity, meshes and model parameters between the quenching scenarios (different orientations) during the entire simulation stayed the same Temperature measurements along the presented pieces were performed at different positions, and they are referred to as T1, T2, T3, T4, T5, T6, T7, T8 and T9, as shown in Fig. 3a for step plate and Fig. 3b for cylinder head. The numerical simulations were performed with commercial CFD code in which the Finite Volume approach with discretization of the governing equation and a SIMPLE algorithm for multiphase flows were used. The normalized residual limit for mass, momentum, and volume fraction were set at, the energy equation convergence limit was lowered to the value of. Only the energy equation was solved within the solid domain, whereas in the liquid part additional mass and momentum equations were solved. 3 EXPERIMENTAL WORK For the presented study, experimental investigations of the immersion quenching process were performed

by the Nemak Company. Aluminium alloys made of AlSi7MgCu0 with material properties for thermal conductivity 183 [W/mK], specific heat 1166 [J/kg K] and density 2591 [kg/m3] were used for quenching simulation as displayed on Fig. 4. Inside the work piece three thermocouples for step plate and nine thermocouples for the cylinder head, of type “K” (NiCrNi) connected to the multi-meter (DEWE-TRON 2000) were used to record the temperature profiles. Fig. 3 shows the dimensions of the sample and the positions of the thermocouples, illustrated by dots, and referred to as T1, T2, T3, T4, T5, T6, T7, T8 and T9. The total height of the rectangular step plate solid was 201 mm, the width 149 mm and the variable thickness along the length, where the cylinder head shared the dimensions of 412×167×137 mm (length, width and height).

a) b) Fig. 4. Aluminium alloy; a) step plate, and b) cylinder head

An air-forced oven was used to heat up the work piece to a uniform temperature of 780 K. Then the sample was carried from the oven to the pool filled with pre-heated water and submerged using the crane at a constant dipping velocity of 0.14 m/s. The environmental temperature was 294 K. The temperature profiles during quenching were

Numerical Investigations of Quenching Cooling Processes for Different Cast Aluminum Parts

575

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 571-580

recorded and several experiments were performed. Measurements at the test station were performed using different operating loads (different orientations and different aluminium alloys), with the cooling time set at 100 s. Detailed information concerning the measurement can be found in Kopun et al. [18]. 4 SIMULATION RESULTS AND DISCUSSION The comparison was performed next of the measured temperatures and numerically predicted results. This focused on the temperature distribution and on the phase distribution within the water domain represented by volume fraction. The presented study utilises four different orientations to cover the wide variety of quenching scenarios, as depicted in Fig. 5. The first orientation, shown in Fig. 5a stands for the step plate with the thick part up position, whereas by changing the solid orientation by 180°, the second orientation with thin part up appears; see Fig. 5b. The third orientation, shown in Fig. 5c features a so-called horizontal orientation which is similar to submerging a cup in an upside-down fashion. The fourth orientation, as demonstrated in Fig. 5d, features the submerging of a sideways cup, is so-called vertical orientation. Immersion quenching has been performed inside preheated water of 353 K.

a) b) c) d) Fig. 5. Aluminium orientation of the quenched pieces; a) step plate thick part up, b) step plate thin part up, c) cylinder head horizontal orientation, and d) cylinder head vertical orientation

4.1 Case A: Step-Plate with Different Orientations The first case presented in this article demonstrates the numerical simulation of a so-called step plate immersed in a pool with a water temperature of 353 K. In Figs. 6 and 7 the measured and numerically predicted temperatures were compared at different monitoring points, T1, T2 and T3, along the height of the aluminium test piece.

576

Fig. 6. Comparison between numerically predicted and measured solid part temperatures for step plate thick part up orientation

Fig. 7. Comparison between numerically predicted and measured solid part temperatures for step plate thin part up orientation

It can be seen from Fig. 6 that, for the thick part up case, the film boiling regime lasted up to 19s for areas around the monitoring point T1, where a fast transition regime was present later on The Leidenfrost temperature predictions varied between 660 K for point T3 to 550 K for the monitoring location T1, where excellent agreement between the numerical and measured data with the aforementioned new Leidenfrost temperature assumption were presented.

Kopun, R. – Škerget, L. – Hriberšek, M. – Zhang, D. – Edelbauer, W.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 571-580

Fig. 8. Liquid volume fraction and the surface temperature distribution at different time steps; a) 1 s, b) 5 s, c) 20 s for thick part up orientation and d) 1 s, e) 5 s, f) 20 s for thin part up orientation are presented

Similarly to the thick part up orientation, the results in the thin part up case were also well predicted and showed an excellent agreement between the numerical and available measured data, as seen in Fig. 7. Approximately 5 s shorter cooling time was achieved with the second orientation, where the Leidenfrost temperature prediction stayed the same as in the aforementioned case (550 K for monitoring point T3 and 660 K for the monitoring point T1). The maximum deviation between the numerical and measured data was less than 2 s for all monitoring points in both orientations. The liquid volume fraction and temperature distribution within the structure at different time instants are displayed in Fig. 8a) for the thick part up case and Fig. 8b) for the thin part up case. It can be seen that the vapour film around the entire solid piece was present after 5 s, where a different trend in the temperature distribution was quite evident. The step plate in the thick part up case was still incompletely cooled down after 20 s (see Fig. 8f), where the uniform temperature had already been establish for the thin part up position. Detailed comparison between different pool temperatures can be obtained from Kopun et al. [18]. 4.2 Case B: Cylinder Head with Different Orientations The model’s capability of predicting quench rates was tested on the simplified cylinder head, where the comparison between the measured and numerically predicted temperature history at nine different monitoring locations along the solid piece are presented, see Figs 9 and 10. A wide range of cooling regions were measured and carried out within the

aluminium solid region, where different submerging orientations had been observed. Fig. 9 shows the numerically predicted results compared with the average value of the corresponding measured cooling curves of monitoring points T1 to T9 for horizontal orientation. In regard to all monitoring points it can be seen that the simulated film and transition boiling regime were in very good agreement with the available measured data. This implied that the proposed variable Leidenfrost temperature model could reasonably re-produce the cooling history. The predicted Leidenfrost temperatures varied from 563 K at point T3 to 713 K at monitoring point T5. The maximum deviation between the simulation and experiment was less than 4 s at all monitoring points. It was further observed that the entire aluminium cylinder head cooled down to the pool temperature after approximately 40 s. By changing the cylinder head position to vertical orientation, it was discovered in Fig. 10 that the predicted boiling regimes, film and nucleate were well described, and again they agreed well with the measurement values. All the model’s parameters were exactly the same as in previous case for the horizontal orientation. Due to the larger vertical extension, only the Leidenfrost temperature range had increased. ΔTrange in Eq. (11) was set to 200 K for the vertical orientation instead of 150 K for the horizontal. The predicted Leidenfrost temperature in the vertical case varied from 543 K at monitoring point T5 to 743 K at monitoring point T9. The maximum deviation between the measured data and the numerical results for all monitoring points was less than 4 s. The liquid volume fraction and the surface temperature distribution at different time instants during the entire quenching cooling process for

Numerical Investigations of Quenching Cooling Processes for Different Cast Aluminum Parts

577

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 571-580

Fig. 9. Comparison between numerically predicted and measured solid part temperatures for horizontal quenching orientation with water temperatures of 353 K at monitoring points T1 to T9

Fig. 10. Comparison between numerically predicted and measured solid part temperatures for vertical quenching orientation with water temperatures of 353 K at monitoring points T1 to T9

horizontal orientation are presented in Fig. 11. It was found in Fig. 11a that rapid boiling occurred at a time of close to 5 s, where transition boiling was

the dominant regime and the surface temperature was somewhere around 753 K. As soon as the surface temperature dropped below the Leidenfrost

578

Kopun, R. – Škerget, L. – Hriberšek, M. – Zhang, D. – Edelbauer, W.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 571-580

Fig. 11. Liquid volume fraction and the surface temperature distribution at different time steps: a) 5 s, b) 15 s, c) 25 s and d) 50 s for horizontal and vertical orientations

temperature, transition boiling and later nucleate boiling took place. At a time of 25 s, it was observed in Fig. 11c, that boiling occurred only at the upper parts of the cylinder head, where there were still some hot temperature areas, especially in those regions of higher material thickness. The temperature of the bottom region was already too low for phase change. Due to the special geometrical configuration it can be seen in Fig. 11d that the gas phase was trapped in the middle part of the cylinder head, and couldn’t escape. This was caused by the low positions of the inlet/ outlet channels. Thus, quenching of this cylinder head in the horizontal position should not be recommended. By comparing the vertical orientation with the horizontal case, it can be seen that the surface temperature distribution was significantly different between the two cases. After 5 s, the bottom area reached a temperature of about 570 K, (see Fig. 11e), whereas for the horizontal orientation case, the surface temperature of the same region was close to 750 K. It can be seen in Fig. 11g that almost half of the workpiece had cooled down to the liquid pool temperature after a time of 25 s, whereas the phase change distribution was present only at the upper parts of the cylinder head. As demonstrated in Fig.

11h, similar to the case with horizontal orientation, a homogeneous temperature field was established after 50 s and no more vapour was produced. 5 CONCLUSIONS The applied CFD code AVL FIRE® is capable of predicting real time quenching effects for simple step plate and cylinder head applications with different solid parts’ orientations. It can be seen that the implemented model’s extensions for variable Leidenfrost temperature approximation in combination with the Multi-Material model showed good agreement between numerical results and measurements. The film and transition boiling regimes were well described and numerically predicted. The variable Leidenfrost temperature had a significant effect on the simulation. It has been demonstrated that by changing the quenched pieces’ orientation, the solid parts cool with different trends. It was found that, based on geometrical configuration, the gas phase was trapped inside the structure regarding the horizontal case. By changing the orientation to vertical, this trapping phenomenon did not occur anymore. The cooling curves were well predicted,

Numerical Investigations of Quenching Cooling Processes for Different Cast Aluminum Parts

579

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 571-580

and there was a very good agreement between the numerical and measured data. It can be concluded that the introduction of a Multi-Material model, which would enable exchange of simulation data during the iterative solution process would lead to further improvements in computational results after each iteration. This, together with the improved CFD model provides a solid basis for future research within the field of real-time immersion quenching applications. 6 FUNDING This research work was partly funded by the European Union, European Social Fund and SPIRIT Slovenia, Slovenian Public Agency for Entrepreneurship, Innovation, Development, Investment and Tourism. Parts of the results presented in this paper were obtained within the FFG funded project QUENCH-IT, project number 828697. 7 REFERENCES [1] Abdulhay, B., Bourouga, B., Dessain, C. (2011). Experimental and theoretical study of thermal aspects of the hot stamping process. Applied Thermal Engineering, vol. 31, no. 5, p. 674-685, DOI:10.1016/j. applthermaleng.2010.11.010. [2] Srinivasan, V., Greif, D., Basara, B. (2012). On the heat and mass transfer modeling to simulate quenching heat treatment process. 6th International Quenching and Control of Distortion Conference, Chicago, [3] Moravčik, R., Stefanikova M., Čička R., Čaplovič L., Kocurova, K., Šturm, R. (2012). Phase transformation in high alloy cold work tool steel. Strojniški vestnik Journal of Mechanical Engineering, vol. 58, no. 12, p. 709-715, DOI:10.5545/sv-jme.2012.531. [4] Babu, K., Prasanna Kumar, T.S. (2009). Mathematical modelling of surface heat flux during quenching. The Minerals, Metals & Material Society and ASM International, vol. 41B, p. 214-224, DOI:10.1007/ s11663-009-9319-y. [5] Meduri, P.K., Gopinath W.R., Vijay D.K. (2009). Wall heat flux partitioning during subcooled forced flow film boiling of water on a vertical surface. International Journal of Heat and Mass Transfer, vol. 52, no. 15-16, p. 3534-3546, DOI:10.1016/j. ijheatmasstransfer.2009.02.040. [6] Wang, D.M, Alajbegovič, A., Su, X.M., Jan, J. (2003). Numerical simulation of water quenching process of an engine cylinder head. Proceedings of ASME FEDSM, 4th ASME JSME Joint Fluids Engineering Conference, Hawaii, DOI:10.1115/FEDSM2003-45538.

580

[7] Srinivasan, V., Moon, K., Greif, D., Wang, D.M, Kim, M. (2010). Numerical simulation of immersion quench cooling process using an Eulerian multi-fluid approach. Applied Thermal Engineering, vol. 30, no. 5, p. 499509, DOI:10.1016/j.applthermaleng.2009.10.012. [8] Greif, D., Kovacic, Z., Srinivasan, V., Wang, D.M., Suffa, M. (2009). Coupled numerical analysis of quenching process of internal combustion engine cylinder head. BHM Journal, vol. 154, no. 11, p. 509517, DOI:10.1007/s00501-009-0514-6. [9] Lübben, T., Frerichs, F., Zoch, H.-W. (2011). Rewetting behaviour during immersion quenching. Strojarstvo, vol. 53, no. 1, p. 45-52. [10] Dhir, V.K., Purohit, G.P. (1978): Subcooled film boiling heat transfer from spheres. Nuclear Engineering and Design, vol. 47, no. 1, p. 49-66, DOI:10.1016/00295493(78)90004-3. [11] Drucker, M., Dhir, V.K. (1981). Effects of high temperature and flow blockage on the reflood behavior of a 4-rod bundle. EPRI Report INIS, OSTI ID: 5714419. [12] Cheng, S.C., Lau, P.W.K., Poon, K.T. (1985). Measurements of true quench temperature of subcooled water under forced convective conditions. International Journal of Heat and Mass Transfer, vol. 28, no. 1, p. 235-243, DOI:10.1016/0017-9310(85)90025-0. [13] Kopun, R., Greif, D., Edelbauer, W., Zhang, D., Tatschl, R., Stauder, B. (2013). Advances in numerical investigation of immersion quenching at different pool temperatures. 22nd International Conference SAE, Sao Paulo, p. 369, DOI:10.4271/2013-36-0369. [14] Trzepiecinski, T., Lemu, H.G. (2014), Frictional conditions of AA5251Aluminium alloy sheets using drawbead simulator tests and numerical methods. Journal of Mechanical Engineering, vol. 60, no. 1, p. 51-60, DOI:10.5545/sv-jme.2013.1310. [15] AVL LIST GmbH (2013). FIRE CFD solver, Eulerian multi-fluid model. Solver Theory Guide, Graz. [16] Drew, D.A., Passman, S.L. (1999). Theory of Multicomponent Fluids. Springer, New York, DOI:10.1007/b97678. [17] Bromely, L.A. (1950). Heat transfer in stable film boiling. Chemical Engineering Progress, vol. 58, p. 6772. [18] Kopun, R., Škerget, L., Hriberšek, M., Zhang, D., Stauder, B., Greif, D. (2014). Numerical simulation of immersion quenching process for cast aluminium part at different pool temperatures. Applied Thermal Engineering, vol. 65, no 1-2, p. 74-84, DOI:10.1016/j. applthermaleng.2013.12.058. [19] Kopun, R., Greif, D., Zhang, D., Stauder, B., Škerget, L., Hriberšek, M. (2013). Numerical investigation for immersion quenching of single and clustered test piece configuration. JSAE Annual Congress, Nagoya.

Kopun, R. – Škerget, L. – Hriberšek, M. – Zhang, D. – Edelbauer, W.

Original Scientific Paper

Received for review: 2013-11-05 Received revised form: 2014-04-05 Accepted for publication: 2014-05-26

Dynamic Simulation of Variable-Speed Valve-Controlled-Motor Drive System with a Power-Assisted Device Xu, M. – Ni, J. – Chen, G. Ming Xu*– Jing Ni – Guojin Chen

Hangzhou Dianzi University, School of Mechanical Engineering, China The variable-speed electrohydraulic drive has been applied in hydraulic machines having power matching means. However, further development has been restricted by its slow response and poor low-speed behavior. Owing to these disadvantages, a novel drive principle comprising a variable-speed valve-controlled-motor drive with an accumulator-based power assisted unit (PAU) is proposed. The PAU is an energy assisting and recycling device, which can release or absorb hydraulic energy according to the system's requirements. With the aid of PAU, the proposed drive is expected to improve response and control precision compared with the variable-speed drive. The proposed drive principle system is a multi-input-multi-output (MIMO) complicated nonlinear system with time-varying, which increases the control difficulty. A mathematical model of the proposed drive was first derived then a hybrid control strategy was presented. The dynamic simulations of three traditional drives and the novel one were performed using AMESim-Simulink co-simulation models. The four drives have been tested using three common variable-load disturbances. Comparisons of simulation results show that the proposed drive principle system demonstrates a good dynamic performance, which can not only achieve the expected energy saving target, but also significantly improve the response and control precision over the existing variable-speed drive system. Keywords: variable-speed, energy saving, variable-load, response, hydraulic motor

0 INTRODUCTION The variable-speed electrohydraulic drive uses a variable-speed electric-motor to drive a hydraulic fixed displacement pump, by adjusting the electricmotor speed to regulate the hydraulic pump output flow rate so as to meet the load-demand. It is a typical power matching hydraulic system. Compared with the conventional pump-controlled-motor drive principle which uses a constant-speed electric-motor to drive a hydraulic variable displacement pump, the variablespeed drive can achieve a large adjustable speed-ratio. In addition, the hydraulic fixed displacement pump has a simpler structure, a longer service life and lower noise than variable displacement pump. The frequency converter was first used to adjust the electric-motor speed. In recent years, the servo-motor was chosen gradually to drive the hydraulic fixed displacement pump. However, the variable-frequency is still the primary technique for its low price and minimal modification to the original hydraulic system. In the past twenty years, the variable-speed drive has been widely studied to be applied in hydraulic machines, such as injection molding machine, hydraulic elevator, wind turbine, shield machine [1] to [3]. Helduser studied the energy saving performance of variablespeed drive used in injection molding machine [4]. Xu discussed the variable-speed hydraulic elevator [5]. Lovrec explored the application possibilities of variable-speed drive in molding machine [6]. Chiang studied a 2MW wind turbine based on high-power variable-speed drive technology [7].

However, the variable-speed drive has two critical disadvantages, slow response and poor control precision, which resulting from the large inertia of the electric-motor [8] and hydraulic pump. In order to overcome these problems, a compound drive principle (or called variable-speed valve-controlled-actuator drive) was built, where a proportional directional valve (or a servo directional valve) was added into the variable-speed (variable-frequency) drive system. In the compound drive system, the frequency converter adjusts the electric-motor speed to satisfy the actuator flow-demand and the proportional directional valve controls the actuator position or speed. The compound drive can improve the control precision and lowspeed performance compared to the variable-speed drive system [9]. It can also improve the actuator deceleration process for the short response time of the proportional directional valve. But it is unable to improve the response when accelerating [10]. Therefore, it is mainly applied in hydraulic elevators etc., which do not require a fast response [11] to [12]. The variable-speed electrohydraulic drive with a power assisted unit (PAU) has been proposed in order to improve responsiveness, especially when accelerating. This drive is distinguished from the compound drive by the inclusion of a PAU. The electric motor-pump cannot always speed up as needed when accelerating, so the PAU releases energy to improve the acceleration response. When the actuator is decelerating but the electric motor-pump cannot slow down as needed, the PAU absorbs energy

*Corr. Author’s Address: Hangzhou Dianzi University, School of Mechanical Engineering, Hangzhou, China, xumzju@163.com

581

StrojniĹĄki vestnik - Journal of Mechanical Engineering 60(2014)9, 581-591

for use in the next working cycle. In other cases, the PAU is turned off. The hydraulic motor is an important actuator in a hydraulic system. It was used mostly in the pumpcontrolled-motor drive system, which normally responds badly and has poor control precision. This paper focus on the modeling and dynamic performance of a variable-speed valve-controlled-motor drive system with a PAU. Three typical variable-load disturbances were implemented to test the dynamic performances of the four drive principles, which are the valve-controlled-motor drive, the variable-speed pump-controlled-motor drive, the variable-speed valve-controlled-motor drive, and the variablespeed valve-controlled-motor drive with a PAU. The purpose is to demonstrate the dynamic performance of the proposed drive principle system compared to the others. 1 PRINCIPLE OF PROPOSED DRIVE Fig. 1 shows the proposed drive principle system, where pe, ps indicate the oil pressure of the PAU and of the hydraulic pump outlet respectively. Ve, Vg, V1, V2 indicate the oil-chamber volume of the PAU, the hydraulic pump outlet, the high-pressure and the low-pressure chamber of actuator respectively. A nm indicates the rotary speed of actuator, fin is the input frequency of frequency converter, ud is the control voltage of proportional directional valve, ut is the control voltage of proportional flow valve, and TL is the load-torque. There are two power sources, the main power source (the electric motor-pump) and the PAU. The main power source is composed of a hydraulic fixed displacement pump, a frequency converter and an electric-motor, where the hydraulic pump is driven by a three-phase asynchronous electric-motor via a frequency converter. Since the main power source often cannot meet the flow-demand of hydraulic motor acceleration, the PAU was added into the variablespeed valve-controlled-motor drive system. The PAU is virtually a valve-controlled-accumulator unit. A bladder accumulator was chosen as the energy storage element for its fast response, simple structure and low price. The proportional flow valve controls the flow rate assisted or recycled. It can also be a servo valve or a high-speed on/off valve. The relief valve is used as a safety valve. The PAU is a semi-active device, whose discharging & absorbing function depends on the pressure difference between the PAU and hydraulic pump outlet, so the pressures pe and ps should be measured. A hydraulic motor, whose type model is 582

the same as the actuator, is used for a loading pump. Different loads can easily be simulated and produced by setting the cracking pressure of the loading valve (the proportional relief valve in the loading system). As shown in Fig. 1, the main purpose of the proportional directional valve is to accelerate the response when decelerating. The spool-opening of the proportional directional valve can be decreased rapidly, thus speeding up the hydraulic motor response when decelerating. In general cases, the proportional directional valve maintains its maximum spool-opening. In addition, the rotational direction of hydraulic motor can be conveniently switched by using the proportional directional valve. Therefore, the hydraulic pump is only needed to rotate toward one direction so as to reduce the impact caused by switching directions. The four compared drive principle are explained as follows. 1. Valve-controlled-motor drive. The PAU is closed (the flow valve in the PAU is closed). The electric-motor speed maintains 1500 r/min continuosly. The proportional directional valve controls the flow rate inpouring into the hydraulic motor chamber therefore it can control the speed of the hydraulic motor. The relief valve works continuosly. 2. Variable-speed pump-controlled-motor drive. The PAU is closed. The speed of hydraulic fixed displacement pump can be adjusted via the frequency converter. The proportional directional valve only controls the rotational direction of hydraulic motor with maximum spool-opening. 3. Variable-speed valve-controlled-motor drive. The PAU is closed. The proportional directional valve and the speed-controlled hydraulic pump control the hydraulic motor together. 4. Variable-speed valve-controlled-motor drive with a PAU. On the basis of variable-speed valvecontrolled-motor drive, the PAU provides for a better acceleration response. When the actuator is accelerating but the electric motor-pump cannot always speed up as needed, the PAU releases energy to improve the acceleration response. When the actuator is decelerating but the electric motor-pump cannot always slow down as needed, the PAU absorbs energy. In other cases, the PAU is turned off. The parameters of PAU (i.e. accumulator volume, accumulator precharge pressure, etc.) are very important to the proposed drive system [10]. This paper aims to demonstrate the dynamic performance

Xu, M. â&#x20AC;&#x201C; Ni, J. â&#x20AC;&#x201C; Chen, G.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 581-591

Fig. 1. Principle of variable-speed valve-controlled-motor drive system with a PAU

of the proposed drive system without a general discussion of PAU. 2 MATHEMATICAL MODEL In this section, the mathematical model of proposed drive system is derived. 2.1 Frequency Converter - Electric Motor The frequency converter-electric motor can be represented by Eq. (1).

np =

Kf fin , (1) TIM s +1

where np is the rotational speed of hydraulic pump, Kf is the gain coefficient, TIM is the time coefficient, which increases accompanied by the increment of the electric motor-pump rotational inertia.

2.2 Hydraulic Fixed Displacement Pump The flow rate discharged by hydraulic fixed displacement pump can be represented by the Eq. (2). Qp = Dp np − k tc ps , (2)

where Dp is the displacement of hydraulic fixed displacement pump, ktc is the leakage coefficient. 2.3 Relief Valve The proposed drive system is a power matching hydraulic system, where the relief valve is used as a safety valve. So the mathematical model can be represented by the Eq. (3).

 K ( p − pcr ) ps ps ≥ pcr Qcr =  r s , (3) ps < pcr 0 

where Kr is the gain coefficient of relief valve, pcr is the preset cracking pressure of relief valve.

Dynamic Simulation of Variable-Speed Valve-Controlled-Motor Drive System with a Power-Assisted Device

583

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 581-591

2.4 PAU

Qa = −

The principle of PAU is shown in Fig. 2.

dpa dt . (8) 12

pa07 ⋅ Va0 ⋅

1.4 pa 7

Since the parameter pa cannot be detected in a physical system, we suppose that pe is equal to pa in the discharging or absorbing process of accumulator. Then Eq. (8) can be represented as: 5

Qa = −

by: Fig. 2. Principle of accumulator-based PAU

pa ⋅ Va1.4 = const. (4)

The derivation of Eq. (4) is:

1.4 pa ⋅ Va0.4

dVa dp + Va1.4 ⋅ a = 0. (5) dt dt

Then the oil flow rate discharged by accumulator can be derived such that:

dp Va ⋅ a dVa dt , (6) =− Qa = 1.4 pa dt

and also

pa ⋅ Va1.4 = const. = pa0 ⋅ Va01.4 , (7)

where pa0 is the initial pressure of nitrogen gas in the accumulator, Va0 is the initial volume of nitrogen gas in the accumulator; both are known. Using Eq. (6) and (7), Eq. (8) can be deduced. 584

1.4 pe 7

The proportional flow valve can be represented

Qe = Cd ⋅ Wt ⋅ X vt

In Fig. 2, pa is the pressure of nitrogen gas in the accumulator, Va is the volume of nitrogen gas, Qa is the oil flow rate discharged or absorbed by the accumulator, Qe is the oil flow rate discharged or absorbed by the PAU, and Qer is the overflowing flow rate by the relief valve in PAU. The modeling of proposed PAU is deduced as follows. In the proposed drive system, the time required for oil to be discharged or absorbed by PAU is very short, so the nitrogen gas in the accumulator can be supposed to work in an adiabatic process. Eq. (4) can be established by Boyle's law.

dpe dt . (9) 12

pa07 ⋅ Va0 ⋅

2 pe − ps sgn( pe − ps ), (10) ρ

where Cd is the discharge coefficient of flow valve, Wt is the spool area gradient of flow valve, Xvt is the spool displacement of flow valve, ρ is the oil density,  1 pe > ps  sgn( pe − ps ) =  0 pe = ps . −1 p < p e s 

For the flow valve, the relationship between the spool displacement and control voltage can be simplified as: X vt K tv = , (11) 1 ut s +1 ωt where Ktv is the gain coefficient of flow valve and ωt is the natural frequency of flow valve. Putting Eq. (11) into Eq. (10), and defining K t = K tv ⋅ Cd ⋅ Wt ⋅ 2 / ρ , Eq. (12) can be deduced: Qe =

Kt ⋅ ut 1 s +1 ωt

pe − ps sgn( pe − ps ). (12)

The relief valve in PAU can be represented by:

 K ( p − pec ) pe Qer =  er e  0

pe ≥ pec , (13) pe < pec

where Ker is the gain coefficient of relief valve, pec is the cracking pressure of relief valve. Ignoring the leakage, the flow in the PAU pipeline is represented by Eq. (14):

Xu, M. – Ni, J. – Chen, G.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 581-591

Qa − (Qe + Qer ) =

Ve dpe ⋅ , (14) Eh dt

where Ve is the oil-tank volume of PAU (sum of the accumulator oil-tank volume and the PAU pipeline volume), and Eh is the bulk modulus of hydraulic oil. The relief valve was used as a safety valve in the PAU, which is closed during normal operation, so Qer can be supposed to zero. The Eq. (14) can be simplified as:

Qa − Qe =

Ve dpe ⋅ . (15) Eh dt

The mathematical model of the proposed PAU can be described by the Eqs. (9), (12) and (15). 3.5 Proportional Directional Valve The directional valve can be represented as the following linearized equation:

QL = K qd X vd − K cd pL , (16)

where QL represents the loading flow rate, pL represents the loading pressure, Xvd represents the spool displacement of proportional directional valve, the flow gain coefficient is K qd = ∂QL ∂X vd , and the flow-pressure gain coefficient is K cd = ∂QL ∂pL . The relationship between the spool displacement and control voltage can be simplified as:

where Kdv is the gain coefficient and ωd is the natural frequency of proportional directional valve. 2.6 Actuator and Loading System The actuator and loading system can be represented by the mass conservation equation and Newton's second law.

Ts  Tf =  Tc sgn(nm )

nm = 0 , (21) nm ≠ 0

where Ts is the static friction torque and Tc is the Coulomb friction torque. Tj is the torque produced by hydraulic loading pump: Tj = Dpj ( p j1 − p j2 ), (22) where Dpj is the displacement of the hydraulic loading pump and pj1, pj2 represents the pressure of highpressure chamber and low-pressure chamber in the hydraulic loading pump, respectively. 3 SPEED CONTROL STRATEGY Fig. 3 shows the speed-control principle of proposed drive system. There are four inputs (nin, nm, ps, pe) and three outputs (fin, ud, ut).

X vd K dv = , (17) 1 ud s +1 ωd

where Dm is the displacement of hydraulic motor, θm is the rotary angle of hydraulic motor, Ctm is the leakage coefficient, Vt is the total volume of hydraulic motor, Jt is the total inertia conversed to the hydraulic motor shaft, Bm is the viscous damping coefficient of hydraulic motor, TL is the total loading torque, Tf is the friction torque, and Tj is the torque produced by the hydraulic loading pump. The friction torque Tf can be represented by:

QL = Dm

V dpL dθ m + Ctm pL + t , (18) dt 4 Eh dt

Dm pL = J t

d 2θ m dθ + Bm m + TL , (19) 2 dt dt

TL = Tf + Tj , (20)

Fig. 3. Speed-control schematic diagram

The speed-control strategy can be explained as follows. 1˝. If nin > nm, the hydraulic motor needs to accelerate. fin and ud should be enlarged. If pe > ps, the PAU will be open to release energy. If pe < ps, the PAU is closed. 2. If nin < nm, the hydraulic motor needs to decelerate. fin and ud should be reduced. If pe > ps, the PAU is closed. If pe < ps, the PAU recovers energy. 3. If nin = nm, the electric-motor maintains its current speed, the proportional directional valve is used for speed-control. If pe > ps, the PAU is close. If pe < ps, it recovers energy.

Dynamic Simulation of Variable-Speed Valve-Controlled-Motor Drive System with a Power-Assisted Device

585

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 581-591

4. If nin is very small, the electric-motor maintains the allowable minimum speed. The proportional directional valve is used for speed-control. If pe > ps, the PAU is closed. If pe < ps, it recovers energy. The proposed drive system is a complicated MIMO system coupled with strong nonlinear and time-varying parameters. The hybrid control strategy based on Proportion-Integration-Differentiation (PID), which only focuses on system input and output, was chosen to realize the control strategy. The detailed strategies of the three controlled-objects are discussed as below [9] and [13].

3. PAU The control expression is shown as Eq. (25). nm0 is the allowable smallest speed of hydraulic motor, which is determined by the allowable minimum-speed of electric-motor.

1. Frequency converter The control expression is shown as Eq. (23), where the input-feedforward plays a major role in reference tracking, and the PID corrects the error caused by load disturbance. The input range of frequency converter is from 0 to 50 Hz.

1 e(k ) ≤ ee , , ktp, kti, ktd represent the where λe =  0 e(k ) > ee PID control parameters of PAU respectively, ee is the integral separation threshold of PAU. The proposed drive system will increase the control complexity. A lot of control parameters (shown in Eqs. (23) to (25)) should be determined before simulation. The tuning methods are discussed in [9].

fin = min[max( K in ⋅ nin + u (k ) , 0), 50], (23)

where u (k ) = kfp e(k ) + λf kfi ∑ e(i ) + kfd [e(k ) − e(k − 1)], 1 e(k ) ≤ ef , kfp, kfi, kfd e(k ) = nin (k ) − nm (k ), λf =  0 e(k ) > ef represent the PID control parameters of frequency converter respectively, ef is the integral separation threshold of frequency converter. The parameter Kin equals to the reciprocal of actuator speed-gain. In variable-speed drive, the frequency converter controls the speed of hydraulic motor along. If the frequency converter has an input frequency fin , the hydraulic motor steady-state speed is ns accordingly. The hydraulic motor speed-gain is defined as ns / fin. And Kin is defined as fin / ns. 2. Proportional directional valve The control expression is shown as Eq. (24), where the control voltage range is from –10 to 10 V. k

ud = min(max((kdp ⋅ e(k ) + λd kdi ⋅ ∑ e(i) + i =0

+ kdd ⋅ [e(k ) − e(k − 1)]), −10),10),

(24)

1 e(k ) ≤ ed , kdp, kdi, kdd represent the where λd =  0 e(k ) > ed PID control parameters of proportional directional valve respectively and ed is the integral separation threshold of directional valve. 586

k   k tp ⋅ e(k ) + λe k ti ⋅ ∑ e(i ) +k td ⋅ [e(k ) − e(k − 1)] i = 0  k   k tp ⋅ e(k ) + λe k ti ⋅ ∑ e(i ) +k td ⋅ [e(k ) − e(k − 1)] i =0  k ut =   k tp ⋅ e(k ) + λe k ti ⋅ ∑ e(i ) +k td ⋅ [e(k ) − e(k − 1)] i =0  k  ( ) k ⋅ e k + λ k ⋅ e ti ∑ e(i ) +k td ⋅ [e( k ) − e( k − 1)]  tp i =0   0

nin > nm , pe > ps nin < nm , pe < ps nin = nm , pe < ps

, (25)

nin < nm0 , pe < ps others

4 DYNAMIC SIMULATION Fig. 4 shows the AMESim-Simulink co-simulation model of proposed drive system. In AMESim, a large set of validated libraries of pre-defined components representing the hydraulic, electric or mechanical behaviour of the system can employed in creating the system simulation model [9] and [14]. In the co-simulation, the hydraulic model is established in AMESim while the control model is established in Simulink. The co-simulation combines the advantages of the two softwares. As shown in Fig. 4, the simulation model of loading system is simplified. Because the proportional directional valve can switch the rotational direction of hydraulic motor easily, the loading system is not necessary to switch the load-torque direction. So the simplification of loading system does not influence the simulation results. The principal parameters in the simulation model are shown in Table 1. To comprehensively study the dynamic performance of proposed drive principle system, three typical variable-load disturbances are implemented: square-wave variable load; fast time-varying & small disturbance variable load; slow time-varying & large disturbance variable load. For comparisons, the simulations of the other three drive principle systems are also studied.

Xu, M. – Ni, J. – Chen, G.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 581-591

spool-opening without actuator speed regulation, the overshoot of curve 2 is the largest. Curve 3 has smaller overshoot and little adjusting time than Curve 2. Curve 4 has the smallest error in the four drive principle systems (detailed comparisons are shown in Table 2).

Fig. 4. AMESim-Simulink co-simulation model Table 1. Principal parameters in simulation model Parameter

Dp Dpj Kf Jt pa0 pcr Eh ωd

Value 20 mL/r 30 mL/r 30 r/(min·Hz) 0.1 kgm2 2 MPa 10 MPa 700 MPa 20 Hz

Parameter

Dm TIM Bm Va0 Ts Tf ρ ωt

Fig. 5. Comparisons of hydraulic motor speed in square-wave variable-load simulations

Value 30 mL/r 3 0.0166 Nm/(r/min) 6.3 L 4.47 Nm 13.3 Nm 850 kg/m3 20 Hz

The expression of each controlled-object in the above three drive principle systems is the same as in the proposed drive principle system. Correspondingly, the conditions of simulations are the same, as well as the control parameters. The reference speed of the hydraulic motor is 600 r/min in all simulations. In the following texts and figures the numbers 1 to 4 represent the valve-controlled-motor drive, the variable-speed pump-controlled-motor drive, the variable-speed valve-controlled-motor drive and the proposed drive respectively. 4.1 Square-Wave Variable-Load Fig. 5 shows the comparisons of hydraulic speed in the square-wave variable-load simulations, where the square-wave cycle lasts 10 s. pload is the cracking pressure of loading valve (the proportional relief valve in the loading system). Since the proportional directional valve in the variable-speed drive system keeps its maximum

Fig. 6. Comparisons of electric-motor speed in square-wave variable-load simulations

Fig. 6 shows the comparisons of electric-motor speed in the square-wave variable-load simulations. The electric-motor speed is always 1500 r/min in the valve-controlled drive system. Curve 4 has the smallest change in the other three drive systems. Fig. 7 shows the control voltage comparisons of the proportional directional valve in the square-wave variable-load simulations. The hydraulic power consumptions of systems using four different drive principles are shown in Fig. 8. They are calculated by the Eq. (26):

P = ps ⋅ Qs . (26)

Dynamic Simulation of Variable-Speed Valve-Controlled-Motor Drive System with a Power-Assisted Device

587

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 581-591

The hydraulic power required by a valvecontrolled-motor drive system is always the largest. The hydraulic power of the proposed drive system is basically the same as in the other two drive systems.

1 n ∑ (nin (i) − nm (i))2 , n i =0 numerical value of sampling times. Where MSE =

n is the

4.2 Fast Time-Varying & Small-Disturbance Variable-Load The loading pressure of fast time-varying & smalldisturbance variable-load is represented by: pload = 4 + 0.5 ⋅ sin(2π ⋅1) MPa. (27) Fig. 9 shows the comparisons of hydraulic motor speed in the fast time-varying & small disturbance variable-load simulations. The error in the system 2 is the largest, which even reaches to ±40 r/min. The error is about ±25 r/min in the Curve 1. Curve 4 has the smallest speed tracking error in the four drive systems.

Fig. 7. Comparisons of directional valve control voltage in squarewave variable-load simulations

Fig. 9. Comparisons of hydraulic motor speed in fast time-varying & small-disturbance variable-load simulations

Fig. 8. Comparisons of hydraulic power consumptions in squarewave variable-load simulations

Table 2 shows the mean square errors (MSE) of hydraulic motor speed tracking and average hydraulic power consumptions in the square-wave variable-load simulations. It can be seen that the proposed drive system obtains the best reference-tracking precision on the basis of energy savings. Table 2. MSEs and average hydraulic power consumption in square-wave variable-load simulations System MSE [r2/min2] Average hydraulic power [kW]

588

1 2 3 4 1223.34 653.01 448.75 301.76 5.00 2.38 2.40 2.39

Fig. 10. Comparisons of electric-motor speed in fast time-varying & small-disturbance variable-load simulations

Fig. 10 shows the electric-motor speed comparisons in the fast time-varying & smalldisturbance variable-load simulations. Fig. 11 shows

Xu, M. – Ni, J. – Chen, G.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 581-591

the comparisons of hydraulic pump outlet pressure. In Curve 4, there are some big pressure overshoots resulting from the release of oil by PAU.

Fig. 13. Comparisons of hydraulic power consumption in fast timevarying & small-disturbance variable-load simulations

Fig. 11. Comparisons of hydraulic pump outlet pressure in fast time-varying & small-disturbance variable-load simulations

Table 3. MSEs and average hydraulic power consumption in fast time-varying & small-disturbance variable-load simulations System MSE [r2/min2] Average hydraulic power [kW]

1 282.97 5.00

2 3 4 892.08 286.12 109.29 2.44 2.54 2.54

4.3 Slow Time-Varying & Large-Disturbance Variable-Load Simulation The slow time-varying & large-disturbance variableload is represented by:

Fig. 12. Comparisons of proportional directional valve control voltage in fast time-varying & small-disturbance variable-load simulations

Fig. 12 shows the comparisons of proportional directional valve control voltage. The control voltage in Curves 3 and 4 decreases rapidly so as to overcome the speed overshoot caused by disturbances. Fig. 13 shows the comparisons of hydraulic power consumption. Table 3 shows the MSEs of hydraulic motor speed tracking and average hydraulic power consumption. The MSE of the proposed drive system is the smallest in the four drive systems while the hydraulic power consumption is only half of the valve-controlledmotor drive system.

pload = 4 + 2 ⋅ sin(2π ⋅ 0.1) MPa. (28)

Fig. 14 shows the comparisons of hydraulic motor speed. The speed tracking error in Curve 1 is the biggest, because the spool-opening of the directional valve changes dramatically so as to suppress the disturbance.

Fig. 14. Comparisons of hydraulic motor speed in slow timevarying & large-disturbance variable-load simulations

Dynamic Simulation of Variable-Speed Valve-Controlled-Motor Drive System with a Power-Assisted Device

589

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 581-591

Fig. 15 shows the comparisons of directional valve control voltage. And Fig. 16 shows the comparisons of hydraulic pump outlet pressure.

Fig. 17. Comparisons of hydraulic power consumption in slow time-varying & large-disturbance variable-load simulations

Fig. 15. Comparisons of directional valve control voltage in slow time-varying & large-disturbance variable-load simulations

Table 4. MSEs and average hydraulic power consumption in slow time-varying & large-disturbance variable-load simulations System MSE [r2/min2] Average hydraulic power [kW]

1 2204.49 5.00

2 89.63 2.45

3 89.62 2.45

4 20.99 2.42

5 CONCLUSIONS

Fig. 16. Comparisons of hydraulic pump outlet pressure in slow time-varying & large-disturbance variable-load simulations

Fig. 17 shows the hydraulic power consumptions in the four drive systems. It can be seen that the valve controlled drive system has the highest power consumption. The hydraulic power consumptions in the other three drive systems are almost the same. Table 4 shows the MSEs of hydraulic motor speed tracking and average hydraulic power consumption. The MSE in proposed drive system is the smallest in the four drive systems while the hydraulic power consumption is basically the same as that seen in the variable-speed drive system and in the variable-speed valve-controlled-motor drive system.

590

A variable-speed valve-controlled-motor drive system with an accumulator-based power-assisted unit is a good solution for improving the response and control precision of hydraulic motor drives. However, it is a complicated non-linear MIMO control system coupled with time-varying that worsens dynamic performance. Therefore, a PID based hybrid control strategy is presented. The novel drive principle will increase the cost of the drive system and control complexity, but the cosimulation results show that it not only achieves the expected energy savings target, but also demonstrates a good anti-interference performance. 6 ACKNOWLEDGEMENT This research was supported by the National Natural Science Foundation of China (Grant No. 51205099), Zhejiang province key science and technology innovation team (Grant No. 2010R50003-3). 7 REFERENCE [1] Ristic, M. (2008). Conversant technology – New key aspects: Development of variable speed drives. Proceedings of International Fluid Power Conference, Dresden, p. 93-108.

Xu, M. – Ni, J. – Chen, G.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 581-591

[2] Manasek, R. (2000). Simulation of an electro-hydraulic load-sensing system with AC motor and frequency changer. Proceeding of the 1st FPNI-PhD Symposium, Hamburg , p. 311-324. [3] Peng, T.H., Xu, B., Yang, H.Y. (2004). Development and research overview on variable frequency hydraulic technology. Journal of Zhejiang University (Engineering Science), vol. 38, no. 2, p. 215-221, DOI: 10.3785/j.issn.1008-973X.2004.02.019. (In Chinese) [4] Helduser, S. (2003). Improved energy efficiency in plastic injection molding machines. The 8th Scandinavian International Conference on Fluid Power, Tampere, p. 1219-1229. [5] Xu, B., Yang, J., Yang, H.Y. (2005). Comparison of energy saving on the speed control of the VVVF hydraulic elevator with and without the pressure accumulator. Mechatronics, vol. 15, no. 10, p. 11591174, DOI:10.1016/j.mechatronics. 2005.06.009. [6] Lovrec, D., Kastrevc, M., Ulaga, S. (2009). Electrohydraulic load sensing with a speed-controlled hydraulic supply system on forming-machines. International Journal of Advanced Manufacture Technology, vol. 41, no. 11, p. 1066-1075, DOI:10.1007/s00170-0081553-y. [7] Chiang, M.-H. (2011). A novel pitch control system for a wind turbine driven by a variable-speed pumpcontrolled hydraulic servo system. Mechatronics, vol. 21, no. 4, p. 753-761, DOI:10.1016/j. mechatronics.2011.01.003. [8] Marinković, Z., Marinković, D., Petrović, G., Milić, P. (2012). Modelling and simulation of dynamic

behaviour of electric motor driven mechanisms. Technical Gazette, vol. 19, no. 4, p. 717-725. [9] Xu, M., Jin, B., Chen, G.J., Ni, J. (2013). Speedcontrol of energy regulation based variable-speed electrohydraulic drive. Strojniški vestnik - Journal of Mechanical Engineering, vol. 59, no. 7-8, p. 433-442, DOI:10.5545/sv-jme.2012.911. [10] Shen, H.K., Jin, B., Chen, Y. (2006). Research on variable-speed electrohydraulic control system based on energy regulating strategy. ASME International Mechanical Engineering Congress and Exposition, Chicago. [11] Xu, M., Jin, B., Shen, H.K., Li, W. (2010). Analysis and design of energy regulation device in energy regulation based variable speed electro-hydraulic control system. Chinese Journal of Mechanical Engineering, vol. 46, no. 4, p. 136-142, DOI:10.3901/JME.2010.04.136. (in Chinese) [12] Xu, M., Jin, B., Yu, Y.X., Shen, H.K., Li, W. (2010). Using artificial neural networks for energy regulation based variable-speed electrohydraulic drive. Chinese Journal of Mechanical Engineering, vol. 23, no. 3, p. 327-335, DOI:10.3901/CJME.2010.03.327. [13] Liu, G.P., Daley, S. (2000). Optimal-tuning nonlinear PID control of hydraulic systems. Control Engineering Practice, vol. 8, no. 9, p. 1045-1053, DOI:10.1016/ S0967-0661(00)00042-3. [14] Tič, V., Lovrec, D. (2012). Design of modern hydraulic tank using fluid flow simulation. International Journal of Simulation Modelling, vol. 11, no. 2, p. 77-88, DOI:10.2507/IJSIMM11(2)2.202.

Dynamic Simulation of Variable-Speed Valve-Controlled-Motor Drive System with a Power-Assisted Device

591

Original Scientific Paper

Received for review: 2014-01-23 Received revised form: 2014-05-01 Accepted for publication: 2014-05-23

An Enhanced Control Technique for the Elimination of Residual Vibrations in Flexible-Joint Manipulators Conker, C. – Kilic, A. – Mistikoglu, S. – Kapucu, S. – Yavuz, H. Caglar Conker1,* – Ali Kilic2 – Selcuk Mistikoglu1 – Sadettin Kapucu2 – Hakan Yavuz3 1 Mustafa

Kemal University, Faculty of Engineering, Turkey University, Faculty of Engineering, Turkey 3 Cukurova University, Faculty of Engineering, Turkey

2 Gaziantep

One method used to reduce or eliminate residual vibrations is to modify the input signal by using previously determined system parameters. In order to eliminate the residual vibration completely, these system parameters must be very accurately determined. In real systems, achieving such accuracy may not always be possible. To address this problem and to provide a solution, a new residual vibration elimination method is introduced in this study, which has proven to be useful especially in cases of uncertain parameters of estimated or predicted systems. It is shown that the technique is capable of handling high levels of uncertainty and is able to successfully eliminate or reduce residual vibrations in flexible systems. In this approach, the desired position of the system is primarily divided into two equal parts, and the generated input signal is used to eliminate vibration. This study presents theoretical and experimental results of the techniques applied to a flexible mechanical system; a comparative study of robustness performance is also provided. Simulation and experimental results show that the oscillations are considerably decreased with a high degree of robustness in the presence of uncertainty regarding system parameters. Keywords: residual vibration, input shaping, flexible-joint manipulator, command shaping

0 INTRODUCTION Motion control studies have become a key subject of robotics and other automation-related research areas. In the manufacturing industry, high-speed and sensitive motion control are necessary for highspeed and high quality production [1]. However, the requirement for high speed makes sensitive motion control difficult to accomplish due to residual vibrations. Therefore, finding a balance between the speed of motion and the elimination, or at least the reduction of, residual vibration has become an important part of the study of motion control and related practical applications [2] to [4]. When a force applied to a flexible mechanical system causes motion, it results in vibrations. Controlling the behaviour of such mechanical systems is generally difficult. In particular, the situation worsens if light and flexible components are used for a fast response. There are some studies relating to the control of the vibration of mechanical systems with flexible elements [5] to [7]. Command pre-shaping or input-shaping based methods have attracted the attention of some researchers [8] to [10]. A feedforward control is suggested as another input-shaping method, in which the shape of the command signal is altered to reduce system oscillations [11]. The initial works were conducted by Smith [12], whose technique is based on dividing a step input into two smaller steps, one of which is delayed in time. Next, the super-positioning of the step responses results in the cancellation of vibration on the system and provides a reduction in the settling time. However, 592

there are some problems related to the robustness of the method due to uncertainties in the natural frequency and damping ratio. Aspinwall [13] also suggested a different command-shaping approach. This method is based on shaping a rectangular or a ‘bang-bang’ forcing function. Another suggestion came from Meckl and Seering [14], who advised the construction of the input signal from either ramped sinusoids or versine functions. Due to the advantage of the rectangular function used in this method, the motion of the system is completed in a shortened period owing to the shape of the signal. Piazzi and Visioli [15] recently suggested a new technique based on shaping the input signal via inverse dynamic analysis. They proposed a polynomial function as a desired output to produce the input signal. Sahinkaya [16] and [17] suggested using a third order exponential function for the output motion to shape input signals using inverse dynamics. Another approach to the problem is the use of an input-shaping technique that is based on convolving the reference command with a sequence of impulses [18] and [19]. This approach is reported in [20] to [22]. The increasing number of impulses used in the shaped signal leads to improvements in robustness to uncertainty in the system parameters. However, it also causes longer delays in system responses [23] and [24]. Magee and Book [25] suggested using an adaptive approach to implement a two-mode shaper. In this study, a new residual vibration elimination method is presented. The benefit of the new technique is that it has a wider frequency range for which the results are insensitive to estimation errors of natural

*Corr. Author’s Address: Mustafa Kemal University, Dept. of Mechanical Engineering, Hatay, Turkey, cconker@mku.edu.tr

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 592-599

frequency. The input-shaping technique proposed in this study neither limits nor increases/decreases travelling time, i.e. without time limitation or time penalty. Due to their definition, most input-shaping methods, however, increase the travelling time by at least a half damped period or more [24], [26] and [27]. Further details on the comparison of methods of residual vibration elimination, such as zero vibration, zero vibration derivative, zero vibration double derivative and extra insensitive are provided by Singhose [7], Singhose et al. [27] and Vaughan et al. [28]. In the proposed approach, the distance to be travelled by the system is primarily divided into two equal parts. In the generation of each of the input signals, cycloid-plus-ramped and versine-plus-ramp functions are used [29]; then these two signals are joined to form the input signal applied to the system used in the elimination of residual vibration. Hence, a more robust method is obtained in reducing the residual vibrations. The proposed method has been applied in a flexible mechanical system. In the further sections of the presented work, the simulation and the experimental results of the new methods have been presented. In order to demonstrate the effectiveness of the proposed technique, the simulation and experimental results are compared with the results reported by Kapucu et al. [29]. The simulation and the experimental results show that the residual vibrations are considerably decreased with a high degree of robustness in the presence of uncertainty regarding the system parameters. The outline of the paper is as follows: the first section presents the details of the experimental setup, which is followed by a section in which detail of the model of the system is provided. In the third section, the input-shaping methods are presented. In fourth section, the results related to computer simulation and experiments are presented. In the last section, concluding comments are made.

1 EXPERIMENTAL SETUP The experimental setup used for performance analysis of the techniques is shown in Fig. 1. The experimental setup consists of a compound pendulum bonded to the sliding member (cart) fixed on the horizontal position of the hydraulically driven Stanford type manipulator, details of which are presented by Kapucu [29]. 2 MODELLING OF THE SYSTEM The mathematical model of the test setup is developed by using the Lagrange method. The model neglects the Coulomb friction of the joint and assumes that the manipulator is working in the horizontal plane and the pendulum in a vertical plane. Then, the equations of motion of the flexible system are [29]:

+ m p )  x + m p lθcosθ + cc x − m p lθ 2 sin θ = = P1 A1 − P2 A2 ,

(1)

m p l cosθ  x + m p lθ + c pθ + m p lg sin θ = 0, (2)

where; mp is the mass of the pendulum (including the equivalent mass of the slender aluminium bar), Mc the mass of sliding member (cart and translating link), cc the damping coefficient of the hydraulic cylinder, cp the damping coefficient of the pendulum, A1 the piston area, A2 the area of piston rod side, P1 the pressure having impact on piston area, P2 the pressure having impact on the area of the piston rod side. The control system of the hydraulic cylinder and the servo valve is shown in Fig. 1. The generated force on the hydraulic piston is controlled by an electrohydraulic servo-valve. The control variable is the position of the spool of the servo valve that is defined by equations that are provided by Baysec and Jones [30].

b) Fig. 1. a) The hydraulically activated cart and pendulum system; and b) its schematic illustration An Enhanced Control Technique for the Elimination of Residual Vibrations in Flexible-Joint Manipulators

593

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 592-599

3 INPUT-SHAPING METHODS The presented study deals with two different approaches used in the elimination of residual vibration. The first method (Method A) is proposed by Kapucu et al. [29], details of which are presented in Section 3.1. The second method (Method B) is the proposed new method, details of which are presented in Section 3.2.

The solution of the equation of motion, Eq. (3), under the effect of the positional input Eq. (5) and the corresponding velocity Eq. (6) yields the following excursion distance values (L1, L2 and L3) for zero residual vibration with zero initial conditions: L1 =

3.1 Method A: A Ramp-Plus-Ramped Cycloid-Plus-Ramped Versine-Based Reference Input Pre-Shaping Technique In this approach, the reference input is composed of three functions. The total distance to be covered within a specified time is divided into three parts. Each part is travelled by each of the three functions within the same travel time. Provided that the specified move time and the total distance are unchanged, vibration can be eliminated by adjusting the excursion distance of each function. Each component of the input creates such oscillations that they cancel each other out. This results in a reduction of residual vibration. Most elastic mechanical systems can be modelled with a second order differential equation. The motion equation of such a system with damping ratio ζ and natural frequency ωn can be defined as:  x(t ) + 2ζωn x (t ) + ωn 2 x(t ) = 2ζωn y (t ) + ωn 2 y (t ), (3) where ωn = k m . A motion profile of a cycloid-plus-ramped versine-plus-ramp function is expressed as: L Rt L Rt L Y = 1 + 2 [ Rt − sin( Rt ) ] + 3 + 2π 2π 2π L3 + [1 − cos( Rt ) ] , (4) 2π where L1 is the maximum excursion distance to be travelled by ramp motion profile, L2 the maximum excursion distance to be travelled by cycloid motion profile, L3 the maximum excursion distance to be travelled by ramped versine motion profile, t time into motion, τ the travelling time, and R = 2π / τ. Furthermore, the total distance can be written as L = L1 + L2 + L3, then arranging the equation above becomes:

L LRt L2 Y (t ) = − sin( Rt ) + 3 (1 − cos( Rt ) ) . (5) 2π 2π 2π The corresponding velocity profile is:

594

LR LR L2 R − cos( Rt ) − 3 sin( Rt ). (6) Y ( t ) = 2π 2π 2π

LR ( R − 2ζωn ) LTn (Tn − 2ζτ ) = , ωn 2 τ2

  T2 R2  L2 = L 1 − 2  = L 1 − n2  ,  τ   ωn  2 Lζ R 2 Lζ Tn L3 = , L = L1 + L2 + L3 . (7) = ωn τ

where ωn is the natural frequency, and Tn the natural frequency period. Variations of L1, L2 and L3 are possible with traveling time τ to result in an oscillationfree displacement of the system. Theoretically, there is no traveling time restriction on the system, and this is the main advantage of this reference input-shaping technique [29]. 3.2 Method B: Proposed Input-Shaping Technique The proposed input-shaping method (Method B) utilises the first technique (Method A) presented in Section 3.1. With Method A, the Eqs. (4) to (7) are used to generate the command input required for the system. The proposed method, in contrast, divides the travelling time into two sections and calculates the command input as two separate inputs and then joins them to form the new input. The calculations for the new method are as follows, where the input is divided into two sections, and each one is calculated independently to form the first and the second parts of the input signal.

L = La + Lb , La = Lb = L 2 , (8)

τ = τ a + τ b , τ a = τ b = τ 2 , (9) Ra ,b = 2π

L1( a ,b ) =

L2( a ,b ) =

LRa ,b ( Ra ,b − 2ζωn )

L (1 − Ra ,b )

Conker, C. – Kilic, A. – Mistikoglu, S. – Kapucu, S. – Yavuz, H.

, τ a ,b (10)

ωn

ωn 2 , L3( a ,b ) =

2 Lζ Ra ,b

ωn

. (11)

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 592-599

τ  0 ≤ t ≤ 2 → Y    Y = τ ≤ t ≤ τ → Y 2   

L1a Rat L2 a + ( Rat − sin( Rat ) ) +  2π 2π  L Rt L + 3a a + 3a (1 − coos( Rat ) )   2π 2π  . (12) L Rt L = 1b b + 2b ( Rbt − sin( Rbt ) ) +   2π 2π  L Rt L  + 3b b + 3b (1 − cos( Rbt ) )  2π 2π

As defined in Eqs. (8) to (12), the new method allows a virtual division of the motion of the system into two steps. Because the first step is completed with almost steady motion and with relatively reduced vibration levels, the second part of the motions starts with the advantage of very little or almost no residual vibrations. Consequently, the result of the second part of the motion yields better performance relative to the previously mentioned method. The details provided in Fig. 2 illustrate the command inputs generated using two different methods considered for analysis. The details on the generation of input-shaping functions for Methods A and B can be found in Sections 3.1 and 3.2, respectively. As illustrated in Fig. 2, Method A consists of two components with which the resulting residual vibration cancels out due to reverse act. However, Method B consists of four parts resulting in eliminated residual vibration at half way to the destination position. These features of the input signals can be seen clearly in Fig. 2.

Fig. 2. The input-shaping methods and generated input commands for total travelling distance of L = 0.09 m and travelling time τ = 0.9703 s (Ra,b = 12.8503, L1a,b = 2.7508, L2a,b = -2.2680, L3a,b = 0.0172)

4 SIMULATION AND EXPERIMENTS In order to perform a comparison amongst the inputshaping methods and the experimental results of the

techniques, the previously described experimental setup and the mathematical model of the system is used. The experimental setup is driven using each input and the resulting residual vibrations as well as the cart position are measured. The Matlab model of the system is also provided with the same input commands to demonstrate the correlation between the theoretical and experimental results obtained. For the randomly selected motion time τ = 0.9703 s and the travel distance of the hydraulic cylinder L = 0.09 m, the generated input commands are applied to the Matlab model of the system and the experimental setup. The results of the study are presented in Figs. 3 to 5 for Methods A, B. In Figs. 3 to 5, ωn* represents the estimated values the natural frequencies of the system. In Figs. 3 to 5, the reference input and displacement of the hydraulic cylinder are given in meters. In contrast, the pendulum oscillation is given in the unit of radians. It can be seen that the simulation and test results match up very closely. This simply indicates that the behaviour of the developed Matlab model and the experimental setup are very much the same. This is mainly due to the accurate mathematical model of the mechanical [29] and the hydraulic systems [30]. In Figs. 3 to 5, simulation and experimental results of Methods A and B are illustrated. In these figures, an estimation error of ±25% is introduced to the natural frequency of the system used in the calculation of the input signals. Figs. 3 to 5 are plotted with estimation errors of –25, 0, +25%, respectively. In Figs. 3 to 5, it can be seen that Method A, the estimation error causes increasing residual vibrations of the pendulum ranging from 4.68×10-4 to 1.92×10-2 rad. It can be seen that increase error in estimation of the natural frequency of the system causes increasing residual vibrations. These results are also validated in Fig. 6 (Method A) and Fig. 7 (Method A) where different predicted natural frequencies and sensitivity curves are presented, respectively. In Figs. 3 to 5, however, the results differ, ranging from 3.195×10-3 to 1.23×10-2 rad. As can be seen from Figs. 3 to 5, the increase in estimation of the natural frequency of the system causes much less increase in residual vibrations. Therefore, it can be concluded that the proposed new method is better in comparison to the old method. This conclusion is much clearer from the Fig. 7 (Method B) where the sensitivity curve for the new method is provided. The proposed new method has a wider insensitivity to variation of natural frequency resulting in a wider spectra compared to the old method.

An Enhanced Control Technique for the Elimination of Residual Vibrations in Flexible-Joint Manipulators

595

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 592-599

Fig. 3. Method A and Method B with a) experimental and b) simulation results for total travelling distance of L = 0.09 m and travelling time τ = 1.293 s for -25% estimation error of natural frequency

Fig. 4. Method A and Method B with a) experimental and b) simulation results for total travelling distance of L = 0.09 m and travelling time τ = 0.9703 s for accurate estimation of natural frequency

Fig. 5. Method A and Method B with a) experimental and b) simulation results for total travelling distance of L = 0.09 m and travelling time τ = 0.776 s for +25% estimation error of natural frequency

596

Conker, C. – Kilic, A. – Mistikoglu, S. – Kapucu, S. – Yavuz, H.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 592-599

Fig. 6. Pendulum positions of different predicted natural frequencies for input-shaping Methods A and B-related experimental results for total travelling distance of L = 0.09 m, travelling time τ = 0.9703 s

Fig. 7. Robustness of the system to uncertainties in the mode frequencies and damping ratios for the studied; a) Method A and b) Method B

In order to estimate the robustness of the proposed methods against estimation error of the natural frequency of the model parameters, an error function has been defined as:

ε ( ωn ) =

ωn − 1, (13) ωn*

where, ωn , ωn* shows actual and predicted values the natural frequencies of system, respectively. Due to the very low level of the damping ratio of the system (ζ = 0.08), its variation due to estimation error does not seem to affect the results as shown in Fig. 7. Therefore, the robustness analysis is performed only for the natural frequency estimation error-related variations.

In Fig. 7, the variation of the residual vibration is presented against estimation error in the natural frequency and damping ratio. It can clearly be seen that the variation of error or uncertainty of damping ratio has a relatively reduced effect on the residual vibration of the system. Therefore, the uncertainties of the damping ratio do not play an important role in affecting the behaviour of the system due to its very low value, ζ = 0.08. In contrast, the estimation error in the natural frequency appears to affect the motion of the system and the resulting residual vibration levels. The figure also shows that the proposed method provides a more robust response relative to Method A. It is noteworthy that the lowest level of residual vibration is achieved using the proposed new technique.

An Enhanced Control Technique for the Elimination of Residual Vibrations in Flexible-Joint Manipulators

597

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 592-599

5 CONCLUSION In this study, a new residual vibration elimination method is introduced, and a comparative study of two input-shaping techniques is performed. Both the theoretical and practical results have shown that the new technique seems to perform better relative to the other method mentioned. • From the simulation and experimental results, it is possible to conclude the following: • It is shown that the proposed method (Method B) is far more robust than the old method (Method A). In other words, the proposed new method has a relatively wider insensitive natural frequency spectra in comparison to the old one. • The advantage of the proposed technique is that it neither limits nor increases the move time, i.e. no time limitation or time penalty. Most conventional input-shaping methods, however, tend to increase the travelling time by at least a half damped period or more. It is shown that proposed new technique is simple and easy to implement, and can be considered to be a versatile and effective way to determine a trajectory resulting in reduced or eliminated residual vibrations of flexible systems with high robustness. Therefore, it can be concluded that the proposed new method (Method B) is better relative to the old one (Method A) and to other conventional methods. 6 REFERENCES [1] Radoičić, G., Jovanović, M. (2013). Experimental identification of overall structural damping of system. Strojniški vestnik – Journal of Mechanical Engineering, vol. 58, no. 4, p. 260-268, DOI:10.5545/ sv-jme.2012.569. [2] Changa, P.H., Park, H.S. (2005). Time-varying input shaping technique applied to vibration reduction of an industrial robot. Control Engineering Practice, vol. 13, no. 1 p. 121-130, DOI:10.1016/j. conengprac.2004.02.009. [3] Jokić, M., Stegić, M., Kranjčević, N. (2012). Structural stiffness optimization with respect to vibration response. Transactions of FAMENA, vol. 36, no. 2, p. 1-8. [4] Golubović, Z., Lekić, Z., Jović, S. (2012). Influence of bucket wheel vertical vibration on bucket wheel excavator (BWE) digging force. Tehnički vjesnik – Technical Gazette, vol. 19, no. 4, p. 807-812. [5] Singhose, W., Pao, L. (1997). A comparison of input shaping and time-optimal flexible-body control. Control Engineering Practice, vol. 5, no. 4, p. 459-467, DOI:10.1016/S0967-0661(97)00025-7.

598

[6] Shan, J., Liu, H., Sun, D. (2005). Modified input shaping for a rotating single-link flexible manipulator. Journal of Sound and Vibration, vol. 285, p. 187-207, DOI:10.1016/j.jsv.2004.08.035. [7] Singhose, W. (2009). Command shaping for flexible systems: A review of the first 50 years. International Journal of Precision Engineering and Manufacturing, vol. 10, no. 4, p. 153-168, DOI:10.1007/s12541-0090084-2. [8] Raubar, E., Vrančić, D. (2012). Anti-sway system for ship-to-shore cranes. Strojniški vestnik – Journal of Mechanical Engineering, vol. 58, no. 5, p. 338-344, DOI:10.5545/sv-jme.2010.127. [9] Singhose, W., Porter, L., Kenison, M., Kriikku, E. (2000). Effects of hoisting on the input shaping control of gantry cranes. Control Engineering Practice, vol. 8, no. 10, p. 1159-1165, DOI:10.1016/S09670661(00)00054-X. [10] Changa, P.H., Park, J. (2001). A concurrent design of input shaping technique and a robust control for highspeed/high-precision control of a chip mounter. Control Engineering Practice, vol. 9, no. 12, p. 1279-1285, DOI:10.1016/S0967-0661(01)00092-2. [11] Kim, D., Singhose, W. (2010). Performance studies of human operators driving double-pendulum bridge cranes. Control Engineering Practice, vol. 18, no. 6, p. 567-576, DOI:10.1016/j.conengprac.2010.01.011. [12] Smith, O.J.M. (1958). Feedback Control Systems, McGraw-Hill, New York. [13] Aspinwall, D.M. (1980). Acceleration profiles for minimizing residual response. ASME Journal of Dynamic Systems, Measurement and Control, vol. 102, no. 1, p. 3-6, DOI:10.1115/1.3140620. [14] Meckl, P.H., Seering, W. (1990). Experimental evaluation of shaped inputs to reduce vibration for a Cartesian robot. ASME Journal of Dynamic Systems, Measurement and Control, vol. 112, no. 2, p. 159-165, DOI:10.1115/1.2896122. [15] Piazzi, A., Visioli, A. (2000). Minimum-time systeminversion- based motion planning for residual vibration reduction. IEEE/ASME Transactions on Mechatronics, vol. 5, no. 1, p. 12-22, DOI:10.1109/3516.828585. [16] Sahinkaya, M.N. (2001). Input shaping for vibrationfree positioning of flexible systems. Proceedings of the Institution of Mechanical Engineers, Part I, p. 467-481. [17] Sahinkaya, M.N. (2004). Exponential input shaping for vibration free positioning of lightly damped multimode systems. 7th International Conference on Motion and Vibration Control, p. 8-11. [18] Mimmi, G., Pennacchi, P. (2001). Pre-shaping motion input for a rotating flexible link. International Journal of Solids and Structures, vol. 38, no. 10-13, p. 20092023, DOI:10.1016/S0020-7683(00)00149-9. [19] Cutforth, C.F., Pao, L.Y. (2004). Adaptive input shaping for maneuvering flexible structures. Automatica, vol. 40, no. 4, p. 685-693, DOI:10.1016/j. automatica.2003.11.013.

Conker, C. – Kilic, A. – Mistikoglu, S. – Kapucu, S. – Yavuz, H.

StrojniĹĄki vestnik - Journal of Mechanical Engineering 60(2014)9, 592-599

[20] Park, J.Y., Chang, P.H. (2004). Vibration control of a telescopic handler using time delay control and commandless input shaping technique. Control Engineering Practice, vol. 12, no. 6, p. 769-780, DOI:10.1016/j.conengprac.2003.09.005. [21] Gurleyuk, S.S., Cinal, S. (2007). Robust threeimpulse sequence input shaper design. Journal of Vibration and Control, vol. 13, no. 12, p. 1807-1818, DOI:10.1177/1077546307080012. [22] Gurleyuk, S.S., Hacioglu, R., Cinal, S. (2007). Threestep input shaper for damping tubular step motor vibrations. Journal of Mechanical Engineering Science, vol. 221, no. 1, p. 1-9, DOI:10.1243/0954406JMES381. [23] Singer, N.C. (1989). Residual Vibration Reduction in Computer Controlled Machines. PhD thesis, MIT Artificial Intelligence Laboratory, Massachusetts. [24] Singer, N.C., Seering, W.P. (1990). Preshaping command inputs to reduce system vibration. ASME Journal of Dynamic Systems, Measurement and Control, vol. 112, p. 76-82, DOI:10.1115/1.2894142. [25] Magee, D.P., Book W.J. (1993). Implementing modified command filtering to eliminate multiple modes of

vibration. Proceedings of the American Control Conference, p. 2700-2704. [26] Singhose, W., Seering, W., Singer, N. (1994). Residual vibration reduction using vector diagrams to generate shaped inputs. Journal of Mechanical Design, vol. 116, no. 2, p. 654-659, DOI:10.1115/1.2919428. [27] Singhose, W., Porter, L., Singer, N. (1995). Vibration reduction using multi-hump extra-insensitive input shapers. American Control Conference, p. 3830-3834. [28] Vaughan, J., Yano, A., Singhose, W. (2008). Comparison of robust input shapers. Journal of Sound and Vibration, vol. 315, no. 4-5, p. 797-815, DOI:10.1016/j.jsv.2008.02.032. [29] Kapucu, S., Yildirim, N., Yavuz, H., Baysec, S. (2008). Suppression of residual vibration of a translatingâ&#x20AC;&#x201C; swinging load by a flexible manipulator. Mechatronics, vol. 18, no. 3, p. 121-128, DOI:10.1016/j. mechatronics.2007.10.007. [30] Baysec, S., Jones, J.R. (1987). An improved model of an electro hydraulic servo valve. Proceedings of 7th IFToMM Congress, p. 1489-1494.

An Enhanced Control Technique for the Elimination of Residual Vibrations in Flexible-Joint Manipulators

599

Original Scientific Paper

Received for review: 2013-11-28 Received revised form: 2014-03-18 Accepted for publication: 2014-05-23

Study on the Correction of S-N Distribution in the Welding Fatigue Analysis Method Based on the Battelle Equivalent Structural Stress by Rough Set Theory Sun, Y. – Yang, X. Yibo Sun1,2 – Xinhua Yang1,*

1 Dalian

2 Dalian

Jiaotong University, School of Material Science and Engineering, China Jiaotong University, School of EMU Application and Maintenance Engineering, China

In welding techniques, failure is a key problem that is related to the stability and safety of the welded structure. In the commonly used welding fatigue analysis methods, the Master S-N curve method based on Battelle structural stress solves the problem of inconsistencies in stress calculation and S-N curve selection better than the nominal stress method and hot spot stress method. In this paper, rough set theory was employed to study the S-N distribution based on the Battelle equivalent structural stress. Firstly, rough set analyses of the S-N distribution based on the nominal stress, structure stress and Battelle equivalent structure stress were carried out. Then the S-N distributions based on the three stresses were studied. The results indicated that structural stress rearranges the S-N point making it much more concentrated in the region near the mean S-N curve and that equivalent structural stress places the S-N point more uniformly on both sides of the curve. Subsequently, the corrections from the plate thickness and stress ratio in the Master S-N curve method were studied. It was concluded that with two steps of corrections the decision-making degrees of welding factors are weakened and harmonized in the Battelle equivalent structural stress. This made the S-N distribution much more concentrated and uniform, which allows more accurate welding fatigue prediction by the Master S-N curve. Keywords: welding fatigue, Battelle equivalent structural stress, Master S-N curve method, rough set theory

0 INTRODUCTION As a traditional processing technique welding has been widely used in many fields, such as mechanical manufacturing, aerospace, transportation, etc. During the welding process, metal in the welding zone fuses at high temperature with its property and geometry changed and thus fatigue damage often occurs in the weld seam, which always determines the life of the welded structure. Therefore the fatigue analysis and life prediction of a welding joint are directly related to the stability and safety of the whole structure. Currently, the commonly used welding fatigue analysis and prediction methods mainly include the nominal stress method, hot spot stress method and the Master S-N curve method based on the Battelle equivalent structure stress. The nominal stress method was first proposed for the fatigue analysis of welded structures [1]. Several standard specifications have been established based on this method using a large amount of experimental data [2] and [3]. While it is widely used in engineering applications, some limitations have gradually come to light, such as that the nominal stress of a complex structure is difficult to determine and that inconsistent stress calculation caused by a singularity in the weld toe also makes the stress value less accurate. In addition, it provides S-N curves in accordance with the classification of the welding joints, which do not always clearly correspond to one type, which limits its universality 600

in engineering applications. The hot spot stress method that obtains the stress in the welding toe by extrapolation based on nominal stress was first proposed by Niemi [4]. It characterizes the stress level in the weld toe by hot spot stress, which makes it available for complex welded structures. In theory it provides a general S-N curve based on the hot spot stress to characterize the fatigue strength of various joints [5]. Although it solves some of the problems of the nominal stress method, but it is difficult to establish a uniform hot type and extrapolation formula for various welding types, which limits the application in engineering. In 2001, Dong proposed the Master S-N curve method based on the mesh insensitive structural stress (Battelle equivalent structural stress) [7]. In this method, the Battelle equivalent structural stress, which is not sensitive to the mesh size of finite element analysis, is defined, which makes the stress calculation uniform for various mesh sizes. The stress intensity factor correction, taking into account the influences of joint thickness and load model, etc., is then established based on fracture mechanics and the parameters in the formula are ascertained based on a large number of welding fatigue data. Thus a Master S-N curve is obtained to characterize the fatigue life including various welding joint types [8]. The Master S-N curve method is widely applied in many fields and was adopted by ASME as a standard for welding fatigue analysis [9] and [10].

*Corr. Author’s Address: Dalian Jiaotong University, School of Material Science and Engineering, Dalian, China, yangxhdl@gmail.com

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 600-606

In this paper rough set theory was employed to study the S-N data distribution of welding data based on the Battelle equivalent structural stress. S-N curves are established for Titanium alloy welding joints based on nominal stress, structural stress and Battelle equivalent structure stress in the Master S-N curve method. The S-N distributions based on the three stresses were studied. Corresponding to the computational formulas of the Battelle equivalent structural stress, the corrections of S-N data distribution from joint thickness and load ratio in the Battelle equivalent structural stress are also explored.

to estimate the fatigue life of welding joints. The stress intensity factor in crack propagation theory can be calculated as [11]:

where a is the crack depth, t* is interpreted as a ratio of actual thickness t to a unit thickness, rendering the term dimensionless. fm(a/t) and fb(a/t) are membrane stress and bending stress as a function of crack growth degree, respectively. Using the Paris crack growth law, the prediction of the lifecycle from an infinitesimally small crack to final failure can be expressed as:

1 BASIC PRINCIPLE OF BATTELLE EQUIVALENT STRUCTURAL STRESS In the finite element stress calculation the results are affected by mesh size, which causes inconsistency in calculations for different structures. In order to address this problem, structural stress based on the line force is first defined using the Master S-N curve method. The normal structural stress at each node from elementary structural mechanics theory is given by:

σ s = σ m + σ b , (1)

σm =

σb =

Fy A

Mx W

Fy , (2) l ⋅t Mx

1 ⋅l ⋅t2 6

, (3)

where Fy is the vertical force in the weld toe, Mx is the moment around the weld toe. The line force fy and moment mx are defined as fy = Fy / l, mx = Mx / l as shown in Fig 1.Structural stress can then be expressed as follows [7]:

σs = σm +σb =

fy t

6 mx . (4) t2

Fig. 1. Definition of line force

While structural stress characterizes the stress state in the weld seam, fracture mechanics is employed

∆K = t * [∆σ m f m (a / t ) + ∆σb f b (a / t )], (5)

a / t =1

1 *(1− m2 ) t *d (a / t ) (∆σ s ) − m I (r ), (6) = t n m ∫ ( ) ( ∆ ) C M K C kn a / t =0

where Mkn is the notch stress magnification expressed as Mkn = K / Kn in which K represents the total K due to both the far-field stress and the local notch stress effects and Kn represents only the far-stress contribution to the stress intensity factor. I(r) is a dimensionless function of r and m is the crack growth exponent, which is set to be 3.6 in ASME [9]. A Master S-N curve can be established according to Eq. 6 based on a set of welding fatigue data. Related to Eq. 6 the Battelle equivalent structural stress can be expressed as:

∆σε = t *

(1−

m ) 2

(∆σ s ) − m I (r ), (7)

where t* is dimensionless the equivalent Δσε retains a stress unit. 2 ESTABLISHMENT OF ROUGH SETS ANALYSIS MODEL Rough set theory is a mathematical approach that can be employed to handle imprecision, incompletion, vagueness and uncertainty [12]. In this paper the relationship between welding factors and S-N distribution based on nominal stress (NS), structure stress (SS) and Battelle equivalent structure stress (ES) are analyzed using rough set analysis. Firstly, rough set models were established based on well-documented fatigue data. Titanium alloy low cycle fatigue data for TIG [13], Manual TIG[14], laser welding [15], and various fillet welded joints [16]with different bending versus tension [17] in the as-welded conditions without stress-relief were cited. 106 sets of welding fatigue data were arranged by welding factors including joint type (J), plate thickness (t), load ratio (R), stress ratio (r), welding process (W) and material

Study on the Correction of S-N Distribution in the Welding Fatigue Analysis Method Based on the Battelle Equivalent Structural Stress by Rough Set Theory

601

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 600-606

type (M) and entered into the rough set database as condition attributes. The joint types marked with two capital letters were cited from reference [16]. The first letters refer to the directions along (L) and transverse (C) to the plate rolling. The second letters refer to the butt-welded joints (B), transverse fillet welded joints (T) and longitudinal fillet (L) welded joints. Among the parameters R and r were expressed as:

r = σ b / (σ m + σ b ) , (8)

R = σ min / σ max . (9)

The deviation degrees of every S-N data point to the S-N curves based on NS, SS and ES respectively were discretized as decision attributes. The operation is as as shown in Figs. 2 to 4.

According to the nominal stress and the joint geometry in the references, structural stress and Battelle equivalent structural stress were calculated for every set of fatigue data by finite element analysis. With these data the mean S-N curves based on NS, SS and ES were fitted using the least square method and the standard deviations (STDEV) were also calculated. The mean S-N curve and deviation curves with –3 to +3 magnifications were then drawn in each coordinate as shown in Figs. 2 to 4. Seven characteristic curves constituted six regions considered as decision domains which were marked as D(1) to D(6) from left to right. The decision attributes of every set of welding fatigue data were determined by the regions in which the S-N point was found. Figs. 2 to 4 show the S-N curves and data distribution. From the figures it can be seen that fatigue life increases

Fig. 2. Decision division of S-N distribution based on NS

Fig. 3. Decision division of S-N distribution based on SS

602

Sun, Y. – Yang, X.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 600-606

Fig. 4. Decision division of S-N distribution based on ES Table 1. Parts of the attributes in S-N rough set model based on NS J LT CT LL CB CT BUTT BUTT Cruciform

t 2 2 2 10 10 1.6 2.5 5

R 0 0 0 0 0 0.1 0.1 0.1

Condition attributes r 0.29 0.29 0.34 0 0.27 0 0 0.27

W Manual TIG Manual TIG Manual TIG Manual TIG Manual TIG TIG EBW Manual TIG

M JIS H4600 TP340C/H JIS H4600 TP340C/H JIS H4600 TP340C/H JIS H4600 TP340C/H JIS H4600 TP340C/H Ti-6-2 TC4 Ti80

Decision attributes D 3 3 5 4 3 6 5 3

Table 2. Reduction rules of S-N distribution based on NS No. 1 2 3 4

Rules J(LT) and R(0) and r(0.29) and W(M Tig) and M(JIS H4600) J(LL) and R(0) and r(0.34) and W(M Tig) and M(JIS H4600) J(LT) and R(0) and t(2) and W(M Tig) and M(JIS H4600) J(LL) and R(0) and t(2) and W(M Tig) and M(JIS H4600)

→ D(4) or D(5) → D(3) or D(2) → D(4) or D(5) → D(3) or D(2)

Supports 0.83, 0.17 0.86, 0.14 0.83, 0.17 0.86, 0.14

→ D(4) or D(5) → D(4) or D(3) → D(3) or D(4) → D(4) or D(5) → D(4) or D(3) → D(3) or D(4)

Supports 0.83, 0.17 0.86, 0.14 0.83, 0.17 0.83, 0.17 0.86, 0.14 0.83, 0.17

→ D(3) or D(4) or D(5) → D(4) or D(3) → D(3) or D(4) → D(3) or D(4) or D(5) → D(4) or D(3) → D(3) or D(4)

Supports 0.54, 0.31,0.15 0.43, 0.57 0.5, 0.5 0.33, 0.5, 0.17 0.43, 0.57 0.5, 0.5

Table 3. Reduction rules of S-N distribution based on SS No. 1 2 3 4 5 6

Rules J(LT) and R(0) and r(0.29) and W(M Tig) and M(JIS H4600) J(LL) and R(0) and r(0.34) and W(M Tig) and M(JIS H4600) J(LT) and R(0) and r(0.27) and W(M Tig) and M(JIS H4600) J(LT) and R(0) and t(2) and W(M Tig) and M(JIS H4600) J(LL) and R(0) and t(2) and W(Ml Tig) and M(JIS H4600) J(LT) and R(0) and t(10) and W(M Tig) and M(JIS H4600)

Table 4. Reduction rules of S-N distribution based on NS No. 1 2 3 4 5 6

Rules R(0) and r(0.29) and W(M Tig) and M(JIS H4600) R(0) and r(0.34) and W(M Tig) and M(JIS H4600) R(0) and r(0.27) and W(M Tig) and M(JIS H4600) J(LT) and R(0) and t(2) and W(M Tig) and M(JIS H4600) J(LL) and R(0) and t(2) and W(Ml Tig) and M(JIS H4600) J(LL) and R(0) and t(10) and W(M Tig) and M(JIS H4600)

Study on the Correction of S-N Distribution in the Welding Fatigue Analysis Method Based on the Battelle Equivalent Structural Stress by Rough Set Theory

603

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 600-606

from D(1) to D(6). There are also large deviations in the S-N data of D(1) and D(6) and small ones in D(3) and D(4). Parts of the S-N data attributes’ values in the rough set model based on NS are shown as an example in Table 1. 3 RESULTS AND DISCUSSIONS With three welding S-N data distribution rough set models based on NS, SS and ES established in the above procedure, reductions in the genetic algorithm were carried out for the S-N data distribution models including all the factors. To obtain universal laws the reduction results were filtered with the support range removed from 0 to 0.75 and coverage from 0 to 0.05. Two reduction results from the rough set model based on NS and SS were obtained as {J, R, r, W, M}, {J, R, t, W, M} including 36 rules. After filtering 4 rules based on NS and 6 based on SS remained as indicated in Tables 2 and 3. Comparing the two tables, rule 1 and 3 in Table 1 are the same as rule 1 and 4 in Table 2. The decision attributes in rules 2 and 4 are changed from D(3) or D(2) to D(3) or D(4). As indicated in Fig. 2 the decision domains 3 and 4 are next to the mean S-N curve. In addition, two new rules exist in Table 3 whose decision attributes are both D(3) or D(4). So, this shows that the S-N distribution based on SS is more concentrated near the mean S-N curve. Two reduction results from ES as {R, r, W, M}, {J, R, t, W, M} including 34 rules were also investigated. But no rules remained after filtering within the same parameters. To analyze the correction of the S-N distribution from ES, similar rules to the ones in Table 3 were extracted as shown in Table 4. Comparing the rules from ES and SS it was found that the condition attribute of J is eliminated in rules 1 to 3. This means that the decision-making degree of factor J is weakened to some extent. Besides decision attributes D(3) with supports of 0.51 and 0.33 are added in rules 1 and 4. The supports also change from 0.86, 0.14 to 0.43, 0.57 in rules 2 and 5, from 0.83, 0.17 to 0.5, 0.5 in rules 3 and 6. Thus the supports of D(3) and D(4) become closer to each other, which implies that the S-N data in decision domains 3 and 4 distribute more uniformly on both sides of the mean S-N curve based on ES. So this makes the STDEV of the S-N distribution smaller for ES than for NS and SS. As discussed above, the structural stress rearranges the S-N point so that it is much more concentrated in the region near the mean S-N curve and the equivalent structural stress places it more uniformly on both sides of the curve. According to 604

the stress calculation in the Master S-N curve method in Section 1, correction by t and the welded structure in the structural stress calculation in Eq. 4 is first carried out. Then the structural stress correction using both t and r in the equivalent structural stress in Eq. 7 is carried out. With the two steps of correction the concentration and uniformity degrees of S-N distribution are enhanced, which creates a Master S-N curve with a smaller deviation. From the results it was also found that the decision-making degrees of welding factors were weakened in the Master S-N curve method. To study this effect welding factors t and r were chosen to be analyzed because the stress was corrected mainly by the two parameters in the Master S-N curve method. Therefore, the fatigue data based on NS, SS and ES in single series fatigue data with same t and r were analyzed. First, the STDEV of single series in t and r were calculated as shown in Tables 5 and 6. From Table 5 it can be seen that the STDEV decreases when the stress type changed from NS to SS in every t and that this happens again from SS to ES. According to Eq. 4 in the transformation process of NS to SS for a 3D welded structure, the stress is corrected by t and the welded structure. Comparing the STDEV in stress type of NS and SS with the same t it was concluded that the influence of the welded structure could also be corrected in the SS transformation. From Table 6 it can be seen that the STDEV clearly decreases from NS to SS in every r but that no significant change appears from SS to ES. Table 5. STDEV of fatigue data in t series Stress Type NS SS ES Points

t = 1.6 0.93 0.85 0.73 19

t=2 0.41 0.29 0.19 20

t = 2.5 0.41 0.40 0.40 35

t=5 0.59 0.51 0.43 12

t = 10 0.53 0.44 0.34 20

Table 6. STDEV of fatigue data in r series Stress Type NS SS ES Points

r=0 0.74 0.67 0.66 52

r = 0.27 r = 0.29 r = 0.32 r = 0.34 0.21 0.22 0.74 0.19 0.20 0.20 0.66 0.18 0.20 0.20 0.64 0.18 16 13 18 7

To study the correction mechanism in more detail, two rough set models were rebuilt with only one condition attribute of t or r being kept and others being removed. Reductions were carried out within all the rules without filtering. The maximum values of supports that characterized the decision-making

Sun, Y. – Yang, X.

StrojniĹĄki vestnik - Journal of Mechanical Engineering 60(2014)9, 600-606

degrees were recorded at each condition attribute value of t and r. Figs. 5 and 6 indicate the maximum supports for t and r based on NS, SS and ES. From the results the decision-making degrees of t and r are somewhat larger based on NS than the other ones.

0.34. The two histograms show that the differences between the maximum supports for all cases are narrowed. Combined with Table 6, this proves that the decision-making degrees of welding factors are weakened and harmonized in the Battelle equivalent structural stress. The deviations of S-N data from the mean S-N curve are compensated for by the two steps of correction using structural stress and equivalent structural stress, which makes the S-N distribution much more concentrated and uniform. This allows for a more accurate welding fatigue prediction using just one S-N curve to represent the complete S-N data set. 4 CONCLUSIONS

Fig. 5. Maximum support of condition attribute of t based on NS, SS and ES

Fig. 6. Maximum support of condition attribute of r based on NS, SS and ES

This demonstrates that the S-N distribution based on nominal stress is easily affected by welding factors. From Fig. 5 where t equals 1.4, 2, 5 and 10, the maximum supports based on SS were greatly reduced compared to NS. However, Fig 6 shows that the maximum supports based on SS are a little higher than the one based on NS. According to Eq. 4 and Table 5, the stress is corrected mainly by t without r in structural stress. This is the reason that the supports based on SS weaken greatly for t but are enhanced for r. The results from ES in Fig. 5 showed that, compared to SS, the maximum support of t increases to a certain degree, but is still less than the that for NS. Fig. 6 shows that the obvious reduction in the maximum supports of r based on ES can be observed compared to the other two especially in the case of r equal to

Rough set theory was employed to study the S-N distribution based on the Battelle equivalent structural stress in the Master S-N curve method. Rough set models of Titanium alloy welding jointsâ&#x20AC;&#x2122; S-N distribution were established based on nominal stress, the structural stress and Battelle equivalent structural stress. Rough set analyses based on the three kinds of stresses were then carried out using the welding S-N distributions studied. The results indicated that the STDEV decreased gradually in the transformation of stress type from NS to ES. The structural stress rearranges the S-N point so that it is much more concentrated in the region near the mean S-N curve and the equivalent structural stress places it more uniformly on both sides of the curve. Subsequently the correction of the t and r factors in the Master S-N curve method were studied. From the results it was concluded that with these two steps of correction, the decision-making degrees of welding factors are weakened and harmonized in the Battelle equivalent structural stress. This makes the S-N distribution much more concentrated and uniform, which allows for a more accurate welding fatigue prediction by the Master S-N curve. 5 ACKNOWLEDGEMENT The work reported on in this paper was supported by the National Natural Science Foundation of China (Grant No. 51175054) and the Science and Technology Plan project of Liaoning (Grant No. 2011220039). 6 REFERENCES [1] Fricke, W. (2003). Fatigue analysis of welded joints state of development. Marine Structures, vol. 16, no. 3, p. 185-200, DOI:10.1016/S0951-8339(02)00075-8.

Study on the Correction of S-N Distribution in the Welding Fatigue Analysis Method Based on the Battelle Equivalent Structural Stress by Rough Set Theory

605

StrojniĹĄki vestnik - Journal of Mechanical Engineering 60(2014)9, 600-606

[2] BS7608-1993. (1999). Fatigue Design and Assessment of Steel Structures. The British Standards Institution, London. [3] IIS/IIW-1221-93 (1995). Stress Determination for Fatigue Analysis Welded Components. The International Institute of Welding, Abington Publication, Cambridge. [4] Niemi, E. (1994). On the Determination of Hot Spot Stresses in the Vicinity of Edge Gussets. IIW Document XIII-1555-94. Lappeenranta University of Technology, Department of Mechanical Engineering. Lappeenranta, p. 18. [5] Niemi, E., Tanskanen, P. (2000). Hot spot stress determination for welded edge gussets. Welding in the World, vol. 44, no. 5, p. 31-37. [6] Lotsberg, I., Sigurdsson, G. (2006). Hot spot stress S-N curve for fatigue analysis of plated structures. Journal of Offshore Mechanics and Arctic Engineering, vol. 128, no. 4, p. 330-336, DOI:10.1115/1.2355512. [7] Dong, P. (2001). A structural stress definition and numerical implementation for fatigue analysis of welded joints. International Journal of Fatigue, vol. 23, no. 10, p. 865-876, DOI:10.1016/S01421123(01)00055-X. [8] Dong, P., Hong, J.K. (2004). The Master S-N curve approach to fatigue of piping and vessel welds. Welding in the World, vol. 48,no. 1-2, p. 28-36, DOI:10.1007/ BF03266411. [9] ASME (2007). 2007 ASME Boiler and Pressure Vessel Code Section VIII Division 2 Part 5: Design by Analysis Requirement. The American Society of Mechanical Engineers, New York.

606

[10] API (2007). API 579-1/ASME FFS-1 2007 Fitnessfor-Service. The American Petroleum Institute, Washington. [11] Paris, P.C. (1998). Fracture mechanics and fatigue: a history perspective. Fatigue & Fracture of Engineering Materials & Structures, vol. 21, no. 5, p. 535-540, DOI:10.1046/j.1460-2695.1998.00054.x. [12] Pawlak, Z. (1982). Rough set. International Journal of Computer and Information Science, vol. 11, p. 341356, DOI:10.1007/BF01001956. [13] Qi, Y., Deng, J., Hong, Q., Zeng, L. (2000). Electron beam welding, laser beam welding and gas tungsten arc welding of titanium sheet. Material Science and Engineering A, vol. 280, no. 1, p. 171-181. [14] Oh, J., Kim, N., Lee, S., et al. (2003). Correlation of fatigue properties and microstructure in investment cast Ti-6Al-4V welds. Material Science and Engineering, A, vol. 340, no. 1-2, p. 232-242, DOI:10.1016/S09215093(02)00176-4. [15] Casavola, C., Pappalettere, C., Tattoli, F. (2009). Experimental and numerical study of static and fatigue properties of titanium alloy welded joints. Mechanics of Materials, vol. 41, no. 3, p. 231-243, DOI:10.1016/j. mechmat.2008.10.015. [16] Iwata, T., Matsuoka, K. (2004). Fatigue strength of CP Grade 2 Titanium fillet welded joint for ship structure. Welding in the World, vol. 48, no. 7-8, p. 40-47, DOI:10.1007/BF03266442. [17] Mohr, W., Lawmon, J. (2006). Fatigue testing of structural welds for Titanium alloy structures. Proceedings of the 16th International Offshore and Polar Engineering Conference, San Francisco, p. 137144.

Sun, Y. â&#x20AC;&#x201C; Yang, X.

Original Scientific Paper

Received for review: 2014-04-15 Received revised form: 2014-05-26 Accepted for publication: 2014-05-26

A Method for Gas Identification in Thermal Dispersion Mass Flow Meters Rupnik, K. – Kutin, J. – Bajsić, I. Klemen Rupnik* – Jože Kutin – Ivan Bajsić

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia A novel measurement method for identifying the type of gas in a thermal dispersion mass flow meter is presented. The physical background of the gas-identification method is discussed by employing a simple, one-dimensional, mathematical model of a thermal flow sensor. For a practical realization of the gas-identification method, the thermal dispersion mass flow meter has to contain two thermal flow sensors with different constructional or operational parameters. A thermal dispersion mass flow meter containing two thermal flow sensors with circular and square cross-sections was developed and calibrated for five different gases in order to experimentally validate the gas-identification method. If the measurement characteristics for the improper gas are employed, the mass flow readings of the thermal flow sensors will generally differ. The absolute value of the relative difference in the mass flow readings can be used as an objective function for identifying the type of gas from a defined set of gases with known compositions. In addition, the normalized error is proposed as an objective function to consider the dispersion that could be reasonably attributed to the difference in the mass flow readings. Keywords: gas-identification method, thermal dispersion mass flow meter, thermal flow sensors, different constructional parameters, measurement characteristics, experimental validation

0 INTRODUCTION The measuring principle of a thermal mass flow meter is based on the influence of fluid flow (in most cases, a gas flow) on the heat transfer from a heated element [1] and [2]. The thermal mass flow meters are of two basic types: capillary thermal mass flow meters and thermal dispersion mass flow meters. In capillary thermal mass flow meters, the mass flow induces an asymmetry of the temperature profile along the heated capillary tube. In thermal dispersion mass flow meters (both the insertion and the in-line types), the gas is flowing around a thermal flow sensor. The thermal flow sensor typically contains a resistance temperature sensing element that is heated by the supplied electrical power, which results in the increased temperature of the sensing element. A constant temperature difference between the thermal flow sensor and the gas is usually maintained, and the required electrical heating power changes with the mass flow rate. Another possibility is that the thermal dispersion mass flow meter operates with a constant electrical heating power and the established temperature difference changes with the mass flow rate. The operating principles, construction and applications of industrial-grade thermal dispersion mass flow meters were presented by Olin [3] and [4]. The performance of thermal dispersion mass flow meters is affected by the internal structure of the thermal flow sensor, the installation conditions and the process conditions. Badarlis et al. [5] performed the optimization of the heater position within a thermal flow sensor and proposed a new

heater design. Baker and Gimson [6] investigated the influence of the eccentricity of the sensor’s internal structure, and the effects of the insertion length of the sensor and the construction details at the location where the sensor is inserted into the flow pipe. The effect of misaligned flow pipes and the influence of a single bend upstream of the thermal flow sensor were analysed by Gibson [7]. Pape et al. [8] developed a method for correcting the effect of the coatings that are deposited on the thermal flow sensor, which can be carried out simultaneously with a measurement of the mass flow rate. Pape and Hencken [9] investigated a coating diagnostics method that is realized with the help of an additional temperature sensing element within the thermal flow sensor. Besides the mass flow rate (or the local mass velocity) of a gas, the intensity of the convective heat transfer from the thermal flow sensor to the gas is also affected by the thermodynamic and transport properties of the gas, such as the thermal conductivity, the specific heat at constant pressure and the dynamic viscosity. Therefore, the measurement characteristic of a thermal dispersion mass flow meter depends on both the composition and the type of the gas. If a thermal dispersion mass flow meter is employed to measure the mass flow rate of a gas that is different to the gas used for the calibration, an appropriate correction needs to be applied. Such corrections were investigated by, e.g., Lötters [10], Hardy et al. [11] and Popp [12]. It is also possible to perform the calibration for a variety of gases and then the proper measurement characteristic should be selected when the thermal dispersion mass flow meter is being used.

*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, 1000 Ljubljana, Slovenia, klemen.rupnik@fs.uni-lj.si

607

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9 607-616

In both solutions, the gas that is actually flowing through the thermal mass flow meter has to be known. In contrast, the method presented in this paper is capable of an in-situ identification of the type of gas from a defined set of gases with known compositions. The gas-identification method is realized by means of a thermal dispersion mass flow meter containing two different thermal flow sensors. The thermal dispersion mass flow meter with the capability to perform the gas-identification method and the gas-identification method itself are patent pending [13]. This paper is structured as follows. The physical background of the gas-identification method is given in Section 1. In Section 2 the experimental validation of the gas-identification method is presented. Section 3 comprises conclusions based on the findings, and open questions for further research work.

proper measurement characteristics (in this case for gas A) are employed, the mass flow readings of both thermal flow sensors will be equal, m 1( A) = m 2( A) . In contrast, if the improper measurement characteristics (in this case for gas B) are employed, the mass flow readings will differ, m 1( B ) ≠ m 2( B ) . A simple, one-dimensional, mathematical model will be employed to study the basic parameters that influence the results of the gas-identification method. The thermal flow sensor typically comprises a (heated) sensing element on a support structure, a filler material and a sheath, which is schematically presented in Fig. 2.

1 PHYSICAL BACKGROUND A thermal dispersion mass flow meter containing two different thermal flow sensors (1 and 2) is considered. The output signals of the thermal flow sensors can be written as ( P ∆T )i1 and ( P ∆T )i2, where P is the supplied electrical heating power and ∆T is the maintained temperature difference between the thermal flow sensor and the gas. The measurement characteristics of the thermal flow sensors relate the corresponding output signals and the measured mass flow rate m .

Fig. 2. Scheme of the cross-sectional view of a thermal flow sensor

The thermal flow sensor is assumed to be inserted into a pipe with a uniform gas flow with the temperature Tg and the mass flow rate m = ρVAp , where ρ is the density of the gas, V is the average velocity and Ap is the pipe cross-sectional area. The intensity of the convective heat transfer from the surface of the thermal flow sensor to the gas flow is characterized by the convective heat transfer coefficient h. The temperature of the sensing element (represented as the layer jSE in Fig. 2) is T = Tg + ΔT. A constant temperature difference ∆T is maintained by supplying electrical heating power P = RI 2 to the sensing element, where R is the electrical resistance of the sensing element and I is the electrical current passing through it. Assuming a one-dimensional heat transfer only in the radial direction, the output signal of the thermal flow sensor can be written as [14]:

Fig. 1. Measurement characteristics of two different thermal flow sensors (1 and 2) for two different gases (A and B) and the basic principle of the gas-identification method

Fig. 1 shows the basic principle of the gasidentification method. The curves represent the measurement characteristics of two different thermal flow sensors (1 and 2) for two different gases (A and B). Gas A is considered to be the actual gas flowing through the thermal dispersion mass flow meter. If the 608

P = ∆T

∑

N j = jSE +1

1 ln ( rj rj −1 ) 2πLλ j

1 + 2πrN Lh

, (1)

where rj and λj are the outer radius and the thermal conductivity of the jth layer in the thermal flow sensor, respectively, N is the number of all the layers and L is the length of the sensing element. The presented mathematical model neglects the conductive heat transfer in the axial direction and the radiation heat transfer, and assumes a concentric internal structure

Rupnik, K. – Kutin, J. – Bajsić, I.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 607-616

of the thermal flow sensor and the constant thermal conductivities of the layers [15]. The convective heat transfer for a cylinder in a cross-flow is often characterized by a power model [14]:

Nu = a Pr m Re n , (2)

which relates the Nusselt number Nu = hD/λ, the Prandtl number Pr = cp η / λ and the Reynolds number Re = ρVD η , where D is the external characteristic length of the thermal flow sensor, and a, m and n are the parameters of the power model, which are generally dependent on the sensor geometry and the Reynolds number. The thermal conductivity λ, the specific heat at constant pressure cp and the dynamic viscosity η of the gas are evaluated at the film temperature:

T f = (Ts + Tg ) 2, (3)

where Ts is the temperature of the sensor surface. Considering V = m ρ Ap , the convective heat transfer coefficient can be written as:

hi( ) = hi( ) . (5) A

Considering Eqs. (4) and (5), the ratio between the mass flow readings of the ith thermal flow sensor is: mi

( A) B m i( )  c p ,i  ni =   B A m i( )  c (p ,i) 

1 mi − ni

 λi( A)  ni  ( B )   λi 

−1

 ηi( A)  ni  ( B )  . (6)  ηi 

A A m 1( ) = m 2( ) . (7)

In contrast, if the actual gas is gas A and the measurement characteristics for gas B are employed, the mass flow readings of the thermal flow sensors are not equal. The relative difference in the mass flow readings, defined as:

ε=

m 2( B ) − 1, (8) m 1( B )

can be derived from Eqs. (6) and (7): m2

h = a D n−1 Ap − n c p m λ 1−mη m−n m n . (4)

It is evident that the properties of the gas and the mass flow rate affect the output signal of the thermal flow sensor through the convective heat transfer coefficient. If the dimensions and the thermal properties of the sensor are considered to be constant, the output signal can generally be presented as P ∆T = P ∆T ( h ) for a particular thermal flow sensor (valid for a circular shape, as in Eq. (1), or other shape of the cross-section). Let us consider that the output signal of the ith thermal flow sensor is ( P ∆T )i . As evident from Fig. 1, there is a difference between the mass flow A readings m i( ) and m i( B ) , which are calculated from the measurement characteristics for the gases A and B, respectively. This difference between the mass flow readings can be evaluated from the equality A B ( P ∆T )(i ) = ( P ∆T )(i ) , which is fulfilled by the equal heat transfer coefficients:

To perform the gas-identification method, the mass flow readings of both thermal flow sensors should be obtained. If the actual gas is gas A and the measurement characteristics for gas A are employed, the mass flow readings of both thermal flow sensors are (theoretically) equal:

−

−1

 c (pA,2)  n2  λ ( A)  n2 n2  η ( A)  n2  ( B )   2( B )   2( B )  c  λ p ,2   2   η2  ε= − 1. (9) m1 m1 1 m1 − −1 A ) n1 ( A A ( ) ( ) n n n  c p ,1   λ  1 1  η  1  ( B )   1( B )   1( B )  c  λ  η1   p ,1   1 

If the surface temperatures for both thermal flow sensors are equal, Ts,1 = Ts,2 , the corresponding gas properties are also equal, cp,1 = cp,2, λ1 = λ2 and η1 = η2. Because m is typically a constant value of about 1/3 and is independent of the sensor geometry and the Reynolds number [3] and [14], m1 = m2 is also taken into account, and Eq. (9) simplifies to: 1

 c ( A)  m  ( A) 1−m  ( A)  m  n2 λ η  ε =  (pB )   ( B )   ( B )    c p   λ   η     

−

1 n1

− 1, (10)

or written in the form with the Prandtl number: 1

 λ ( A)  Pr ( A)  m  n2 ε =  ( B )  ( B )    λ  Pr    

−

1 n1

− 1. (11)

Fig. 3 presents the relative differences in the mass flow readings for different gases as a function of the parameter n2, where the parameter n1 is set to a constant value of 0.5 and air is considered to be the actual gas (gas A). The thermodynamic and transport properties of the gases were determined using the NIST REFPROP database [16] for a film temperature of 25 °C and a pressure of 100 kPa. If the proper

A Method for Gas Identification in Thermal Dispersion Mass Flow Meters

609

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9 607-616

measurement characteristics are employed (in this case for air), then ε = 0. In contrast, if the measurement characteristics for oxygen, nitrous oxide, carbon dioxide or argon are employed, |ε| > 0 and |ε| increases with the difference between n2 and n1.

A different influence of the gas properties can therefore be achieved by different operational parameters of the thermal flow sensors, e.g., by maintaining different temperatures of the sensing elements.

Fig. 4. Values of the parameter n for sensors with different shapes of cross-sections or orientations with respect to the flow direction, for Reynolds numbers of the order of 10,000 [14] Fig. 3. Relative differences in the mass flow readings for different gases as a function of the parameter n2, for n1 = 0.5 and air as the actual gas

For a practical realization of the gas-identification method (as presented in Section 2), the relative difference in the mass flow readings should be as large as possible, if the improper measurement characteristics are employed. It is evident from Eqs. (9) to (11) and Fig. 3 that the relative difference in the mass flow readings can be influenced by the following parameters: • The value of the parameter n generally depends on the Reynolds number and the sensor geometry [14] and [17]. Different values of the parameters n1 and n2 can therefore be achieved by different constructional parameters of the thermal flow sensors, e.g., by different shapes, orientations with respect to the flow direction or characteristic lengths (which results in different Reynolds numbers at a given mass flow rate). Some examples of the parameter n for different sensor geometries, for Reynolds numbers of the order of 10,000 [14], are presented in Fig. 4. At a given mass flow rate, similar Reynolds numbers are conditional on similar characteristic lengths of the sensors. The relative difference in the mass flow readings ε depends on the difference between n2 and n1 (as shown in Fig. 3) and therefore an appropriate combination of the sensors should be selected to obtain a sufficiently large value of ε. • The thermodynamic and transport properties of the gas are referred to the film temperature (see Eq. (3)) and so they are influenced by the maintained temperature of the sensing element. 610

2 EXPERIMENTAL VALIDATION A thermal dispersion mass flow meter containing two thermal flow sensors with different constructional parameters was developed. It was calibrated for five different gases and used for the experimental validation of the gas-identification method. 2.1 Measurement System The measurement system, employed for both the calibration of the developed thermal dispersion mass flow meter and the experimental validation of the gas-identification method, is schematically presented in Fig. 5. Besides the thermal dispersion mass flow meter, it comprises a gas source (GS), heat exchangers (HE1 to HE3), pressure regulators (PR1 and PR2) and a reference mass flow measurement system (REF). The role of the heat exchangers is to provide a stable gas temperature for the reference mass flow measurement system and for the thermal dispersion mass flow meter. The pressure regulators are used to set a stable inlet pressure for the reference mass flow measurement system with critical flow Venturi nozzles (TetraTec Instruments) [18], where the reference mass flow rate is generated and measured. The expanded measurement uncertainty of the reference mass flow rate does not exceed 0.3%. The expanded measurement uncertainty characterizes the dispersion of the values that could reasonably be attributed to the measurand within an interval having a level of confidence of approximately 95% (coverage factor k = 2) [19]. The developed thermal dispersion mass flow meter contains two heated Pt100 resistance

Rupnik, K. – Kutin, J. – Bajsić, I.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 607-616

Fig. 5. Scheme of the measurement system

temperature sensors (TetraTec Instruments) that operate in the functions of the thermal flow sensors and a Pt100 resistance temperature sensor (TetraTec Instruments) that measures the temperature of the gas. The sensors are installed in the insulated plexiglass pipe with a nominal internal diameter of 24 mm. The thermal flow sensors are positioned in the same cross-sectional plane of the pipe and connected to the measurement circuit. One of the thermal flow sensors has a circular cross-section with a diameter of 2.0 mm and the other thermal flow sensor has a square crosssection with a side length of 2.6 mm. The thermal flow sensor with the circular crosssection was selected because this shape is the most common in commercially available thermal dispersion mass flow meters, and the thermal flow sensor with the square cross-section was selected because, in combination with the sensor with the circular crosssection, a relatively large difference in the mass flow readings could be expected if the improper measurement characteristics are employed (see Section 1). Keep in mind that the characteristic length of the sensor with the square-cross section is 30% larger than the characteristic length of the sensor with the circular cross-section, which results in different Reynolds numbers at a given mass flow rate and may also affect the relative difference in the mass flow readings. Besides the examples presented in Fig. 4, the sensors with other geometries may possibly, if appropriately combined, cause even larger relative differences in the mass flow readings. Therefore, in order to optimize the sensors’ geometries, further experimental or numerical investigations could be performed.

The gas-temperature sensor is positioned upstream of the thermal flow sensors and connected to a measurement transmitter (PICO Technologies, PT-104). The control of the developed thermal dispersion mass flow meter and the processing of the measurement signals are realized with a LabVIEWbased program (National Instruments, Ver. 12.0.1). The measurement circuit for one of the thermal flow sensors is schematically presented in Fig. 6. The thermal flow sensor is connected to a Wheatstone bridge. A programmable DC power supply (National Instruments, PXI-4110) is used to generate the bridge’s supply voltage Ui. A DAQ board (National Instruments, USB-6341) is used to measure both the bridge’s output voltage Uo and the voltage drop U R 1 over the resistor R1. The electrical resistance of the sensing element within the thermal flow sensor is calculated as: 1 + 2U o U i , (12) R=R 1 − 2U o U i where R = ( R1 + R2 + R3 ) 3 is the average electrical resistance of three thermally stable resistors in a Wheatstone bridge. The temperature of the sensing element is determined from the standard relationship between the electrical resistance and the temperature [20]: R = R0 (1 + AT + BT 2 ) , (13) where A = 3.9083×10–3 °C–1 and B = –5.775×10–7 °C–2 are constant values and R0 = 100 Ω is the nominal electrical resistance at 0 °C for Pt100 temperature sensors. The electrical heating power is P = RI2, where the electrical current passing through the sensing element is calculated as I = U R1 R1 . The

A Method for Gas Identification in Thermal Dispersion Mass Flow Meters

611

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9 607-616

measurement circuit for the other thermal flow sensor is the same as the one presented in Fig. 6, where both Wheatstone bridges are connected to the same DC power supply and DAQ board.

Fig. 6. Scheme of the measurement circuit for the thermal flow sensor

Both thermal flow sensors were calibrated (in non-heated mode; I = 1 mA) in the temperature range from 15 to 45 °C, with the reference temperature having an expanded measurement uncertainty of 0.02 °C. The electrical resistances of the thermally stable resistors in both Wheatstone bridges were measured with the expanded measurement uncertainty of a reference value of 0.5 mΩ. The results presented in the following sections were obtained under steady flow conditions. When all the resistance temperature sensors in the developed thermal dispersion mass flow meter were used to measure the temperature of the gas, the temperature differences between them were less than 0.025 °C. 2.2 Calibration of the Thermal Dispersion Mass Flow Meter The thermal dispersion mass flow meter was calibrated for the following gases: air, oxygen, nitrous oxide, carbon dioxide and argon. The reference mass flow rates in the range from 100 to 350 g/min were set and measured by the reference mass flow measurement system with critical flow Venturi nozzles. The temperature difference between each of the thermal flow sensors and the gas was maintained average value at 10 K. The output signal ( P ∆T )(an i over a time period of 30 s) was measured and recorded five times for each mass flow rate. The measurement characteristics of the thermal flow sensors are presented in Figs. 7 and 8. The results were fitted with the Levenberg-Marquardt method using the following form of the measurement model: 612

P = ∆T c + 1

1 c2 + c3 m c4

. (14)

Fig. 7. Measurement characteristics of the thermal flow sensor with the circular cross-section

Fig. 8. Measurement characteristics of the thermal flow sensor with the square cross-section Table 1. Calibration constants and the standard errors of estimates for the measurement model (14) with P/∆T [mW/K] and m [g/min] Thermal flow sensor with the circular cross-section c1 × 103

c3 × 103

SEE × 103

Air

46.80

6.153

162.2

0.838

3.91

Oxygen

44.30

5.417

225.3

0.763

5.49

Nitrous oxide

20.67

1.664

773.7

0.461

3.33

Carbon dioxide

19.62

1.730

726.7

0.462

2.08

Argon

27.55

2.385

42.31

0.530

1.55

Thermal flow sensor with the square cross-section c1 × 103

c3 × 103

SEE × 103

Air

29.49

8.945

108.6

0.952

4.74

Oxygen

30.59

9.051

99.50

0.961

7.28

Nitrous oxide

23.58

4.832

272.6

0.735

12.3

Carbon dioxide

24.24

5.335

200.4

0.779

6.05

Argon

36.38

7.053

52.18

0.998

4.00

Rupnik, K. – Kutin, J. – Bajsić, I.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 607-616

The values of the calibration constants c1, c2, c3 and c4 and the standard errors of estimates SEE are presented in Table 1. The thermal flow sensor with the square cross-section has steeper characteristics than the thermal flow sensor with the circular crosssection. This is probably associated with the value of the parameter c4, which can be related to the parameter n in the power model for convective heat transfer (Eq. (2)); it is generally expected to be greater for the sensor with the square cross-section [14] and [17]. The sensor with the square cross-section also produces larger values of the output signal, which is a consequence of a more intensive heat transfer.

mass flow rate of about 225 g/min of air. The results of the validation experiment, presented in Fig. 9 (with symbols) and in Table 2, show that | ε | > 13% for nitrous oxide, carbon dioxide and argon, while | ε | for oxygen and air is 0.94 and 0.06%, respectively. The absolute value of the relative difference in the mass flow readings | ε | can be defined as the objective function that has to be minimized in order to identify the type of gas. In the given case, air would be properly identified as the actual gas.

2.3 Validation of the Gas-Identification Method On the basis of the obtained measurement characteristics, the relative differences in the mass flow readings, ε = ( m 2 m 1 ) − 1 , can be evaluated. These relative differences are presented in Fig. 9 (with lines) for the defined set of gases, where the actual gas is air. If the measurement characteristics are selected properly (in this case for air), then ε = 0, but otherwise | ε | > 0. If these experimental results are compared to the results of the theoretical model (see Fig. 3), it is evident that ε > 0 for oxygen and ε < 0 for nitrous oxide, carbon dioxide and argon in both cases. The experimental results show that | ε | is greater for nitrous oxide than argon, which contradicts the results of the simple theoretical model. A possible reason for this contradiction could be the limited capability of the one-dimensional mathematical model to describe the actual effects of the gas flow around the thermal flow sensors that are inserted only to certain depths into the flow pipe. These flow conditions also differ, to some extent, from the conditions in which common models for convective heat transfer in the cross-flow were obtained (an example is presented in [21]). In addition to the convective heat transfer that is taken into account in the mathematical model, the radiation heat transfer and the conductive heat transfer in the axial direction [3] affect the performance of the thermal flow sensor as well. Besides, the combined effect of the uncertainties of the gases’ thermodynamic and transport properties on the expanded uncertainty of the theoretically determined ε is up to 4.5% for nitrous oxide and up to 1.4% for argon, for the values presented in Fig. 3 (the uncertainties of the gases’ properties are given in the NIST REFPROP database [16], and the uncertainty of ε is calculated in accordance with [19]). The experimental validation of the gasidentification method was performed at a reference

Fig. 9. Relative differences in the mass flow readings for different gases; the actual gas is air; the results of the validation experiment are presented with symbols Table 2. Results of the validation experiment for the gasidentification method at a reference mass flow rate of 225.10 g/min of air

Air Oxygen Nitrous oxide Carbon dioxide Argon

[%]

224.36 243.28

0.06 0.94

0.04 0.60

Identified as the improper gas due to |En| > 1 o o

384.67

323.16

–16.0

–11.1

413.01

342.36

–17.1

–12.0

610.27

528.02

–13.5

–9.27

m 1

m 2

[g/min]

224.22 241.01

However, the question is, whether the proper gas is identified with a sufficient degree of confidence. For this purpose it is reasonable to define a criterion that accounts for the dispersion that could be reasonably attributed to the difference in the mass flow readings, e.g., the normalized error [22]:

En =

m 2 − m 1

( m 2 ) + U 2 ( m 1 )

, (15)

where U ( m 1 ) and U ( m 2 ) are the expanded measurement uncertainties of the mass flow readings.

A Method for Gas Identification in Thermal Dispersion Mass Flow Meters

613

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9 607-616

If | En | ≤ 1, the difference in the mass flow readings is statistically insignificant, and if | En | > 1, the difference in the mass flow readings is statistically significant. If the difference in the mass flow readings is statistically significant for a particular gas, this gas can be identified as improper. The difference in the mass flow readings must be statistically significant for all but one gas from the defined set of gases in order to identify the proper gas with a sufficient degree of confidence. For the evaluation of the measurement uncertainties in Eq. (15), the sources affecting the dispersion of the estimated difference in the mass flow readings should be taken into account. The combined expanded measurement uncertainty of each mass flow reading is estimated not to exceed 1.1%. This estimation takes into account the following contributions: the measurement uncertainty of the reference temperature in the temperature calibration of the thermal flow sensors, the stability of both the electrical heating power and the maintained temperature difference for each of the thermal flow sensors, and the standard errors of estimates of the fitted measurement characteristics. The measurement uncertainty of the reference mass flow rate is not taken into account, because it does not affect the difference between simultaneous measurements by both thermal flow sensors. The calculated normalized errors for the given validation experiment are presented in Table 2. Nitrous oxide, carbon dioxide and argon can be identified as the improper gases since | En | > 1 (marked with “ü”). The difference in the mass flow readings is statistically insignificant (marked with “o”) for air, which means that air is correctly identified as the proper gas. However, | En | ≤ 1 holds also for oxygen, but it is not the actual gas in the given validation experiment. In order to achieve a statistical significance for all but one gas from the defined set of gases, the developed thermal dispersion mass flow meter could be improved in terms of decreased measurement uncertainties of the mass flow readings or an increased difference in the mass flow readings. The latter can be achieved, for example, by modifying the constructional parameters of the thermal flow sensors in such a way that the difference between the values of the parameters n1 and n2 is increased. 3 CONCLUSIONS The presented measurement method allows us to identify the type of gas flowing through a thermal dispersion mass flow meter. The gas-identification 614

method can be performed simultaneously with the measurement of the mass flow rate. It represents a novel advancement in the field of thermal mass flow meters. In the first part of the paper the basic principle and physical background of the gas-identification method are discussed. In the second part of the paper the experimental validation of the gas-identification method is presented. Here, we summarize the main findings of the performed research work: • If a thermal dispersion mass flow meter contains two different thermal flow sensors and the measurement characteristics for the improper gas are employed, the mass flow readings will generally differ. The difference in the mass flow readings was studied by employing a simple, one-dimensional, mathematical model of a thermal flow sensor. The difference depends on the exponents n1 and n2 in the power model for convective heat transfer, which can be affected by the constructional parameters of the thermal flow sensors, and on the thermodynamic and transport properties of the gas, which can be affected by the operational parameters of the thermal flow sensors. • For a practical realization of the gas-identification method, two thermal flow sensors with different constructional or operational parameters are required. The mass flow readings of the thermal flow sensors are determined for each gas from a defined set of gases. The identified gas is the one that minimizes the defined objective function, e.g., the absolute value of the relative difference in the mass flow readings. The difference in the mass flow readings should be statistically significant for all but one gas from the defined set of gases in order to identify the proper gas with a sufficient degree of confidence. • A thermal dispersion mass flow meter containing two thermal flow sensors with circular and square cross-sections was developed and calibrated for the following gases: air, oxygen, nitrous oxide, carbon dioxide and argon. After this, the validation experiment for the gas-identification method was performed for the same set of gases. The minimum absolute value of the relative difference in the mass flow readings was obtained for air, which was the actual gas flowing through the developed thermal dispersion mass flow meter in this case. Air was also correctly identified by employing the normalized error as the objective function. However, the difference in the mass flow readings was found to be statistically insignificant also for oxygen.

Rupnik, K. – Kutin, J. – Bajsić, I.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, 607-616

The presented thermal dispersion mass flow meter has to be calibrated for the gases that are expected to flow through the meter in order to perform the gasidentification method. Considering this requirement, it can be employed in such practical applications where defined gases with known compositions are expected, for example, flow systems with different technical, pure or medical gases. Some possible specific applications are medical gas supply systems in hospitals, laser systems for materials processing, calibration of gas chromatography systems, etc. The presented thermal dispersion mass flow meter could be used to correctly measure the mass flow rate of different gases (within the declared measurement uncertainty) and also employed for safety reasons, e.g., for the detection of the improper gas in a particular distribution pipe in a medical gas supply system. The meter with the integrated gas-identification method has to be capable of identifying the proper gas from the defined set of gases with a sufficient degree of confidence. The presented experimental examples show that nitrous oxide, carbon dioxide and argon were distinguished from air with statistical significance, but it was not possible to distinguish between air and oxygen. Nevertheless, these results can be improved on by decreasing the measurement uncertainties of the mass flow readings. For the developed thermal mass flow meter, the expanded measurement uncertainties of the mass flow readings were estimated to be up to 1.1%. The measurement uncertainty can be reduced by a further optimization of the thermal mass flow meter in the sense of decreasing or correcting the influence of the parameters that affect the mass flow reading, e.g., the heat losses along the stem of the thermal flow sensor. If lower expanded measurement uncertainty, e.g., 0.6% of the reading, was obtained for the presented thermal mass flow meter, even air and oxygen would be distinguished. In addition to decreasing the measurement uncertainty, another possibility for improving the gas-identification capability of the thermal mass flow meter is to optimize its constructional parameters. If two gases have a similar combination of thermodynamic and transport properties, the constructional parameters of the thermal flow sensors have to be sufficiently different in order to achieve a significant difference in the mass flow readings. In this investigation, the developed thermal dispersion mass flow meter was used under steady flow conditions. The influences of the varying mass flow rates and temperatures of the measured flow on the results of the gas-identification method should be

investigated. The presented realization of the thermal dispersion mass flow meter contains two thermal flow sensors and a separate gas-temperature sensor. Another option for a practical implementation would be a configuration where one or more of the thermal flow sensors operates alternately in the function of a thermal flow sensor and in the function of a gastemperature sensor. 4 ACKNOWLEDGEMENT This work was supported in part by the Slovenian Research Agency (ARRS). 5 NOMENCLATURE A constant [°C–1] cross-sectional area of the flow pipe [m2] Ap a, m, n parameters of the convective heat transfer model B constant [°C–2] c1, c2, c3, c4 calibration constants specific heat of the gas [J/kgK] cp D external characteristic length, e.g., diameter, of the thermal flow sensor [m] normalized error En h heat transfer coefficient [W/m2K] I eletrical current passing through the sensing element [A] k coverage factor L length of the sensing element [m] m mass flow rate [kg/s] N number of all layers in the thermal flow sensor Nu Nusselt number P electrical heating power [W] ( P ∆T )i output signal of the thermal flow sensor [W/K] Pr Prandtl number R electrical resistance of the sensing element [Ω] R average electrical resistance of resistors in the Wheatstone bridge [Ω] nominal electrical resistance at 0 °C [Ω] R0 R1, R2, R3 electrical resistances of resistors in the Wheatstone bridge [Ω] Re Reynolds number rj outer radius of the jth layer in the thermal flow sensor [m] SEE standard error of estimate [W/K] T temperature of the sensing element within the thermal flow sensor [°C] temperature of the gas [°C] Tg

A Method for Gas Identification in Thermal Dispersion Mass Flow Meters

615

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9 607-616

Ts ΔT U Ui Uo U R 1 V ε ρ λ λj η

surface temperature of the thermal flow sensor [°C] temperature difference between the sensing element within the thermal flow sensor and the gas [K] expanded measurement uncertainty supply voltage [V] output voltage [V] voltage drop over the resistor R1 [V] average velocity of the gas [m/s] relative difference in the mass flow readings density of the gas [kg/m3] thermal conductivity of the gas [W/mK] thermal conductivity of the jth layer in the thermal flow sensor [W/mK] dynamic viscosity of the gas [Pa s]

Subscripts thermal flow sensor 1 1 2 thermal flow sensor 2 Superscripts (A) gas A (B) gas B 6 REFERENCES [1] Baker, R.C. (2000). Flow Measurement Handbook: Industrial Designs, Operating Principles, Performance, and Applications. Cambridge University Press, New York, DOI:10.1017/CBO9780511471100. [2] ISO 14511:2001. Measurement of Fluid Flow in Closed Conduits – Thermal Mass Flowmeters. International Standardization Organization. Geneva. [3] Olin, J.G. (1999). Industrial thermal mass flowmeters, Part 1: Principles of operation. Measurements and Control, vol. 193. [4] Olin, J.G. (1999). Industrial thermal mass flowmeters, Part 2: Applications. Measurements and Control, vol. 194. [5] Badarlis, A., Kumar, V., Pfau, A., Kalfas, A. (2011). Novel sensor geometry for liquids serving in dispersion thermal flow meters. SENSOR+TEST Conferences 2011 – SENSOR Proceedings, p. 78-83. [6] Baker, R.C., Gimson, C. (2001). The effects of manufacturing methods on the precision of insertion and in-line thermal mass flowmeters. Flow Measurement and Instrumentation, vol. 12, no. 2, p. 113-121, DOI:10.1016/S0955-5986(01)00005-X. [7] Gibson, J. (2003). The Effect of Gas Properties and Installation Effects on Thermal Mass Flowmeters, Report no. 2002/53, TÜV NEL, East Kilbride. [8] Pape, D., Hencken, K., Schrag, D., Ott, S., Bärlocher, A., Kramer, A. (2010). Coating Diagnostics for Thermal Mass Flowmeters. IEEE SENSORS

616

Conference Proceedings, p. 2512-2517, DOI:10.1109/ ICSENS.2010.5690438. [9] Pape, D., Hencken, K. (2012). Dual Sensor Setup for Thermal Mass Flow Sensor Diagnostics. Proceedings of 16. GMA/ITG-Fachtagung Sensoren und Messsysteme, p. 282-290, DOI:10.5162/ sensoren2012/3.1.2. [10] Lötters, J. (1999). Economical Thermal Mass Flow Sensor Based on Constant Temperature Anemometry. Sensor Proceedings. [11] Hardy, J.E., Hylton, J.O., McKnight, T.E. (1999). Empirical correlations for thermal flowmeters covering a wide range of thermal-physical properties. Proceedings of the NCSL Workshop and Symposium, p. 735-750. [12] Popp, O. (2007). Model based calibration and measurement of thermal dispersion gas mass flow meters. SENSOR+TEST Conferences – SENSOR Proceedings, vol. I, p. 205-210. [13] Rupnik, K., Kutin, J., Bajsić, I. (2013). Thermal mass flow meter and the gas-identification method. SI patent application, no. P–201300425, Slovenian Intellectual Property Office, Ljubljana. [14] Cengel, Y.A. (2002). Heat Transfer: A Practical Approach, 2nd ed. McGraw-Hill, New York. [15] Minkina, W. (1999). Theoretical and experimental identification of the temperature sensor unit step response non-linearity during air temperature measurement. Sensors and Actuators A: Physical, vol. 78, no. 2-3, p. 81-87, DOI:10.1016/S09244247(99)00206-X. [16] Lemmon, E.W., Huber, M.L., McLinden, M.O. (2010). REFPROP: Reference Fluid Thermodynamic and Transport Properties, NIST Standard Reference Database 23, Version 9.0. National Institute of Standards and Technology, Gaithersburg. [17] Sparrow, E.M., Abraham, J.P., Tong, J.C.K. (2004). Archival correlations for average heat transfer coefficients for non-circular and circular cylinders and for spheres in cross-flow. International Journal of Heat and Mass Transfer, vol. 47, no. 24, p. 5285-5296, DOI:10.1016/j.ijheatmasstransfer.2004.06.024. [18] ISO 9300:2005. Measurement of Gas Flow by Means of Critical Flow Venturi Nozzles. International Standardization Organization. Geneva. [19] JCGM 100:2008. Evaluation of Measurement Data – Guide to the Expression of Uncertainty in Measurement. Bureau International des Poids et Mesures. Sevres. [20] IEC 60751:2008. Industrial Platinum Resistance Thermometers and Platinum Temperature Sensors. International Electrotechnical Commission. Geneva. [21] Sanitjai, S., Goldstein, R.J. (2004). Forced convection heat transfer from a circular cylinder in crossflow to air and liquids. International Journal of Heat and Mass Transfer, vol. 47, p. 4795-4805, DOI:10.1016/j. ijheatmasstransfer.2004.05.012. [22] ISO 13528:2005. Statistical Methods for Use in Proficiency Testing by Interlaboratory Comparisons. International Standardization Organization, Geneva.

Rupnik, K. – Kutin, J. – Bajsić, I.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9 Vsebina

Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 60, (2014), številka 9 Ljubljana, september 2014 ISSN 0039-2480 Izhaja mesečno

Razširjeni povzetki Gašper Šušteršič, Ivan Prebil, Miha Ambrož: Stabilnost vijuganja osebnih vozil z lahkimi tovornimi priklopniki Łukasz Pejkowski, Dariusz Skibicki, Janusz Sempruch: Visokociklične utrujenostne lastnosti avstenitnega jekla in čistega bakra pri enoosnih, proporcionalnih in neproporcionalnih obremenitvah Jiang Ding, Yangzhi Chen, Yueling Lv, Changhui Song: Kriterij izbire položajnega parametra zobniškega mehanizma z ubirnico v obliki vijačnice na osnovi stopnje drsenja Rok Kopun, Leopold Škerget, Matjaž Hriberšek, Dongsheng Zhang, Wilfried Edelbauer: Numerična analiza procesa gašenja za aluminijaste odlitke poljubnih oblik Ming Xu, Jing Ni, Guojin Chen: Dinamična simulacija motornega pogonskega sistema z variabilno hitrostjo, krmilnimi ventili in servonapravo Caglar Conker, Ali Kilic, Selcuk Mistikoglu, Sadettin Kapucu, Hakan Yavuz: Napredna tehnika krmiljenja za odpravo preostalih vibracij pri manipulatorju s fleksibilnim zgibom Yibo Sun, Xinhua Yang: Raziskava korekcij porazdelitve podatkov S-N pri analizi utrujanja zvarov na osnovi enakovredne napetosti v konstrukciji po metodi Battelle s teorijo grobih množic Klemen Rupnik, Jože Kutin, Ivan Bajsić: Merilna metoda za identifikacijo vrste plina v potopnih termičnih merilnikih masnega toka

Osebne vesti Doktorske disertacije, specialistična dela, diplomske naloge

SI 101 SI 102 SI 103 SI 104 SI 105 SI 106 SI 107 SI 108

SI 109

Prejeto v recenzijo: 2014-01-21 Prejeto popravljeno: 2014-03-25 Odobreno za objavo: 2014-04-04

Stabilnost vijuganja osebnih vozil z lahkimi tovornimi priklopniki Šušteršič, G. – Prebil, I. – Ambrož, M. Gašper Šušteršič – Ivan Prebil – Miha Ambrož*

Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija

V strokovnih krogih je bil identificiran problem ‘vijuganja’ (ang. ‘snaking’) lahkih tovornih priklopnikov, ki jih vlečejo osebni avtomobili. Gre za pojav, ko pri določenih pogojih sistem osebnega vozila s priklopnikom postane nestabilen. Vlečno vozilo in priklopnik začneta v ravnini vozišča nihati okoli navpične osi z naraščajočo amplitudo. Če voznik skupine vozil takšnega gibanja ne zazna pravočasno, praviloma to vodi v izgubo nadzora nad skupino vozil in ima za posledico prometno nezgodo. Drugi avtorji so pojav večinoma obravnavali na skupinah osebnih vozil in stanovanjskih priklopnikov. Cilj predstavljenega dela je bil ugotoviti, ali je podroben model na osnovi sistema togih teles (MBS) mogoče uporabiti za modeliranje pojava vijuganja. Na podlagi rezultatov simulacij ter meritev smo želeli ugotoviti, ali so pojavu vijuganja podvrženi tudi lahki tovorni priklopniki in kako na njihovo gibanje vplivajo posamezni parametri skupine vozil. Za potrebe raziskave je bil razvit podroben MBS model vlečnega vozila in priklopnika. Kot osnova so bili uporabljeni podrobni geometrijski modeli sprednjega in zadnjega obešenja koles vlečnega vozila ter obešenja koles priklopnika. Masne in vztrajnostne karakteristike teles v sistemu so bile deloma pridobljene z geometrijskim modeliranjem in deloma z meritvami. Vzmetne in dušilne karakteristike elementov, ki generirajo sile, so bile izmerjene neposredno na komponentah preizkusnih vozil. Zasnovan in izdelan je bil merilni sistem za merjenje količin na vozilih med vožnjo (zasuk volana, zasuk priklopnika na spenjalni napravi, pospeški, hitrost), ki je skrbel tudi za zajemanje in shranjevanje podatkov ter za zajem slike. S preizkusno skupino vozil, opremljeno z razvitim merilnim sistemom je bilo izvedenih več preizkusnih voženj, pri katerih je bil sistem vozil vzbujan z motnjo v obliki impulznega zasuka volana vlečnega vozila. Za vsako preizkusno vožnjo je bil izmerjen in shranjen časovni potek opazovanih količin na vlečnem vozilu ter na priklopniku. Poleg preizkusnih voženj so bile pod enakimi pogoji (hitrosti) izvedene simulacije z uporabo razvitega MBS modela. Pri tem so bili kot vzbujanje uporabljeni izmerjeni impulzi zasuka na volanu. Za preveritev aerodinamičnih vplivov na gibanje skupine vozil so bile s podrobnim geometrijskim modelom skupine vozil ter pri pogojih, ki so ustrezali eksperimentom, izvedene računalniške simulacije dinamike tekočin (CFD), s katerimi so bili simulirani sile in moment, ki jih na skupini vozil povzroča tok okoliškega zraka. Primerjava rezultatov simulacij z eksperimentalno pridobljenimi podatki kaže, da je pristop z modeliranjem na osnovi sistema teles za zadano nalogo primeren. Rezultati kažejo, da lahko sistem osebnega vozila z lahkim tovornim priklopnikom postane nestabilen že pri s predpisi dovoljenih hitrostih, če je le-ta nepravilno naložen. Simulacija zračnega toka okoli skupine vozil je pokazala, da aerodinamične sile in momenti na lahkem tovornem priklopniku, oblike kakršne je bil uporabljeni, nimajo pomembnega vpliva na njegovo stabilnost. Eksperimentalni rezultati so pokazali, da ima pomemben vpliv na stabilnost priklopnika poleg njegove vztrajnosti in navpične sile na spenjalni napravi tudi delež tovora, ki se lahko omejeno prosto giblje glede na priklopnik. Ta del tovora je lahko podvržen pojavu trčnega dušenja (‘impact damping’), ki je bil ugotovljen pri analizi eksperimentalnih rezultatov in utegne biti predmet nadaljnjih raziskav. Potencial za nadaljnje raziskave in razvoj je sistem, ki bi ga bilo mogoče vgraditi v priklopnik in bi na podlagi podatkov iz zaznaval določil vztrajnost priklopnika ter opozoril voznika na nepravilno naložen tovor. Ključne besede: lahki tovorni priklopnik, skupina vozil, vijuganje, simulacija, dinamika vozil, sistem togih teles, računalniška simulacija dinamike tekočin, trčno dušenje

*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, miha.ambroz@fs.uni-lj.si

SI 101

Prejeto v recenzijo: 2013-12-10 Prejeto popravljeno:2014-03-28 Odobreno za objavo: 2014-05-13

Visokociklične utrujenostne lastnosti avstenitnega jekla in čistega bakra pri enoosnih, proporcionalnih in neproporcionalnih obremenitvah Pejkowski, Ł. – Skibicki, D. – Sempruch, J. Łukasz Pejkowski* – Dariusz Skibicki – Janusz Sempruch

Naravoslovnotehniška univerza v Bidgošču, Fakulteta za strojništvo, Poljska

Članek analizira vpliv razmerja med strižnimi in normalnimi napetostmi λ v pogojih večosnih utrujenostnih obremenitev na utrujenostno trajnostno dobo, morfologijo površine utrujenostnega loma in orientacijo ravnine razpoke. Cilji so bili doseženi z dvoosnimi utrujenostnimi preskusi z bakrom Cu-ETP in avstenitnim jeklom X2CrNiMo17-12-2. Preskušanci so bili obremenjeni z aksialno silo in momentom na standardnem dvoosnem sistemu za preskušanje Instron, pri čemer so bile nadzorovane napetosti. Materiala sta bila izbrana zaradi razmeroma velike občutljivosti na neproporcionalne obremenitve, ki izhaja iz njune majhne vrednosti energije napake zloga. Preskušanci so bili izpostavljeni enoosnim natezno-tlačnim, vzvojnim, dvoosnim proporcionalnim in neproporcionalnim obremenitvam. Neproporcionalnost obremenitev je bila dosežena s faznim zamikom med komponentami obremenitve. Amplitude so bile izbrane tako, da je bila dosežena natančna amplituda kvadratične srednje vrednosti druge invariante deviatorja napetosti, pomnožena z mejnim razmerjem enoosnega utrujanja pri dani stopnji napetosti. Takšen pristop je bil izbran zaradi ponazoritve vpliva različnih stopenj neproporcionalnosti v odvisnosti od razmerja λ na utrujenostno trajnostno dobo in videz loma. Analiza utrujenostne trajnostne dobe je bila opravljena na podlagi krivulj S-N ter grafikonov primerjave izračunane in eksperimentalno določene trajnostne dobe. Analiza površinske morfologije in orientacije razpok je bila opravljena na podlagi slik preskušancev, narejenih po utrujenostni odpovedi. Slike so naložene na krivulje S-N za prikaz vpliva vrste obremenitve in stopnje napetosti na lomne površine in videz razpok. Pripravljene so bile za vse vrste obremenitev in za oba izbrana materiala. Oba preskušena materiala sta zelo občutljiva na neproporcionalne obremenitve. Razmerje med strižnimi in normalnimi napetostmi λ pri obeh materialih značilno vpliva na utrujenostno trajnostno dobo. Tako za baker kot za avstenitno jeklo so najbolj škodljive vrednosti količnika λ blizu mejne vrednosti za enoosno utrujanje. Podobna odvisnost od vrednosti razmerja λ je bila ugotovljena tudi pri lomnih površinah. Razmerje vpliva na morfologijo in na usmeritev makro lomne ravnine. Omeniti je treba, da je kritična vrednost razmerja λ za oba materiala različna. Mogoče je postaviti hipotezo, da so za material najbolj škodljive zunajfazne obremenitve s faznim zamikom komponent 90° ter z razmerjem med strižnimi in normalnimi napetostmi, ki je enako mejnemu razmerju za enoosno utrujanje. Sledi, da je mejno razmerje enoosnih utrujenostnih obremenitev zelo pomembno za ocenjevanje trajne dinamične trdnosti in utrujenostne trajnostne dobe v pogojih neproporcionalnih obremenitev. Glavna novost predstavljene raziskave je podrobna študija vpliva razmerja amplitud strižnih in normalnih napetosti na utrujenostno trajnostno dobo in morfologijo lomne površine materialov, občutljivih na neproporcionalne obremenitve. Ključne besede: večosno utrujanje, visokociklično utrujanje, neproporcionalna obremenitev, fraktografija, zunaj faze

SI 102

*Naslov avtorja za dopisovanje: Naravoslovnotehniška univerza v Bidgošču, Fakulteta za strojništvo, Kordeckiego 20, Bydgoszcz, Poljska, lukasz.pejkowski@utp.edu.pl

Prejeto v recenzijo: 2013-11-27 Prejeto popravljeno: 2014-02-19 Odobreno za objavo:2014-03-31

Kriterij izbire položajnega parametra zobniškega mehanizma z ubirnico v obliki vijačnice na osnovi stopnje drsenja Ding, J. – Chen, Y.Z. – Lv, Y.L. – Song, C.H. Jiang Ding – Yangzhi Chen* – Yueling Lv – Changhui Song Tehniška univerza Južne Kitajske, Kitajska

Inovativni zobniški prenosni mehanizem s prostorsko ubirnico (SCMW) uporablja namesto klasičnih prostorskih krivulj konjugirane prostorske krivulje. Prostorske krivulje opisujejo površino vitkih delovnih elementov oz. zob. SCMW ima prednost majhnih dimenzij, velikega prenosnega razmerja in fleksibilnosti pri snovanju. Mehanizem SCMQ je najpogosteje izveden kot kolo z ubirnico v obliki vijačnice (HCMW), ki je bilo razvito ob upoštevanju enačb ubiranja, konstrukcijskih meril, stopnje prekritja, upogibnih napetosti, proizvodne tehnologije in praktičnih vidikov. Položajni parametri HCMW pa se trenutno izbirajo predvsem na podlagi izkušenj konstruktorja. Če parametri niso izbrani pravilno, se lahko zobje zaradi čezmernega drsenja hitro obrabijo. V članku podajamo predlog kriterija za izbiro položajnih parametrov pri HCMW na osnovi stopnje drsenja. Najprej je opredeljena drsna stopnja dveh konjugiranih prostorskih krivulj v točki ubiranja. Drsna stopnja je pomembna za ocenjevanje kakovosti prenosa zobniške dvojice. Dosedanje raziskave pa so bile usmerjene predvsem v dve konjugirani površini. Drsna stopnja dveh konjugiranih prostorskih krivulj je opredeljena kot mejna vrednost razmerja dolžinske razlike dveh relativnih lokov in dolžine izbranega loka. Iz drsne stopnje je možno ugotoviti relativno smer drsenja pogonske in gnane kontaktne krivulje. V nadaljevanju je izpeljana drsna stopnja pogonske in gnane kontaktne krivulje za SCMW in HCMW. Iz analize drsne stopnje kontaktnih krivulj so pridobljeni optimalni pogoji ubiranja za HCMW. Drsna stopnja je enaka nič samo pod pogojem, da je polmer ubiranja pogonske kontaktne krivulje enak zmnožku prenosnega razmerja in polmera ubiranja pogonske kontaktne krivulje. Sledi določitev kriterija za izbiro položajnega parametra: ubiranje na sredini kontaktnih krivulj mora ustrezati pogoju optimalnega ubiranja. Izpeljane so tudi ustrezne enačbe kontaktnih krivulj, ki izpolnjujejo ta kriterij. Na koncu so predstavljeni še rezultati simulacij in praktični primeri z različnimi položajnimi parametri za preverjanje zveznosti prenosa, izračunana pa je tudi njihova stopnja drsenja. Rezultati izračunov kažejo, da imajo HCMW, zasnovani po kriteriju izbire položajnega parametra, boljšo drsno stopnjo in s tem tudi boljše tribološke lastnosti. Preostaja več raziskovalnih tem: predlog metode eksperimentalne določitve stopnje drsenja HCMW, določitev vpliva stopnje drsenja na trenje in obrabo HCMW, preučitev oblikovanja hidrodinamičnega filma, če bodo HCMW v prihodnje mazani, in določitev dovoljene stopnje drsenja v pogojih mazanja za standardizacijo proizvodnje. Pri tej raziskavi je bila predstavljena metodologija, ki nadomešča izkustveno določanje položajnih parametrov HCMW, podana pa je tudi teoretična osnova za standardizacijo v industriji. Ključne besede: zobnik, kolo z ubirnico v obliki vijačnice, parameter položaja, izbira parametrov, drsna stopnja, kolo z ubirnico v obliki prostorske krivulje

*Naslov avtorja za dopisovanje: Tehniška univerza Južne Kitajske, Guangzhou, Kitajska, meyzchen@scut.edu.cn

SI 103

Prejeto v recenzijo: 2014-01-29 Prejeto popravljeno: 2014-05-09 Odobreno za objavo: 2014-05-21

Numerična analiza procesa gašenja za aluminijaste odlitke poljubnih oblik

Kopun, R. – Škerget, L. – Hriberšek, M. – Zhang, D. – Edelbauer, W. Rok Kopun1,* – Leopold Škerget2 – Matjaž Hriberšek2 – Dongsheng Zhang3 – Wilfried Edelbauer3 2 Univerze

1 AVL - AST d.o.o., Slovenija v Mariboru, Fakulteta za strojništvo Slovenija 3 AVL List GmBH, Austrija

Optimizacija prenosa toplote v avtomobilistični industriji je eden izmed ključnih dejavnikov, ki pripomore k zmanjšanju porabe goriva in znižanju emisij izpustnih sistemov. Učinkovite metode toplotne obdelave, kot je proces gašenja, se uporabljajo pri nadomestitvi delov iz težjih kovin z lažjimi zlitinami (npr. aluminijastimi), kar pripomore k zmanjšanju teže vozila in posledično vpliva na znižanje porabe goriva in emisijskih vrednosti. Proces gašenja s potapljanjem v tekoči fazi je tako eden izmed najpomembnejših industrijskih procesov v avtomobilistični industriji, saj igra prenos toplote ključno vlogo pri določitvi strukturne in mehanske lastnosti materiala (npr. glave motorja). Za dosego želene lastnosti materiala, surovec najprej segrejemo na zelo visoko temperaturo, nato pa ga naglo ohladimo. Natančna napoved hlajenja strukture po celotnem volumnu med procesom gašenja je tako ključnega pomena za določitev materialnih lastnosti in nadaljnji izračun zaostalih napetosti, saj lahko le-te vodijo do nastanka razpok in posledično privedejo do okvare motorja. Prispevek obravnava razvoj in validacijo nedavno izboljšanega numeričnega modela prenosa toplote uporabnega pri procesu gašenja s potapljanjem v kapljeviti fazi implementiranega v komercialni program računalniške dinamike tekočin (CFD) AVL FIRE®. Prenos toplote pri procesu gašenja med surovcem in pregreto tekočo fazo se obravnava s pomočjo Eulerjevega večfaznega pristopa, kjer obravnavamo vsako fazo kot samostojno in neodvisno. Masna, gibalna in energijska enačba se rešujejo neodvisno le za tekočo (vodno) domeno, medtem ko se za trdnino rešuje le energijska enačba. V prispevku je predstavljen nov postopek reševanja Leidenfrost temperature, kjer s konstantne predpostavke čez celoten volumen prehajamo na spreminjajočo se predpostavko Leidenfrost temperature. Rezultati so predstavljeni skupaj z upoštevanjem dodatnih medfaznih sil v kombinaciji z novim več-materialnim pristopom (MMAT) reševanja Eulerjevih enačb. Kapljevita faza in trdna sta obravnavni skupaj v eni domeni, pri čemer se površinska temperatura trdnine in lokalni koeficienti prenosa toplote med trdnino in kapljevito fazo, izmenjujejo iterativno po vsaki iteraciji. Z modifikacijo dodatnih medfaznih sil in spreminjajočo se Leidenfrost temperaturo v kombinaciji z MMAT metodo uporabljeno v komercialnem CFD programskem paketu AVL FIRE® lahko natančneje opišemo in napovemo proces hlajenja strukture po celotnem volumnu med procesom gašenja. Vpliv filmskega in prehodnega režima vrenja je zelo dobro opisan, pri čemer ima nadgrajena spreminjajoča Leidenfrost temperaturna spremenljivka močan vpliv. Primerjavo smo izvedli na testnem aluminijastem preizkušancu z različnimi odebelitvami vzdolž dolžine in poenostavljeni aluminijasti glavi motorja. Preizkušanca sta bila potopljena v kapljevito fazo s temperaturo vode 353 K in različnimi orientacijami potopitve, pri čemer se numerična temperaturna napoved hlajenja strukture po celotnem volumnu med procesom gašenja zelo dobro ujema z eksperimentalno dobljenimi vrednostmi. Ugotovljeno je bilo, da se s spremembo orientacije preizkušanca ohlajata z drugačnim trendom. Maksimalno odstopanje numeričnih rezultatov od izmerjenih vrednosti za obe orientaciji in za vse točke je v vseh primerih manjše od 4 sekund. Na podlagi predstavljenega lahko zaključimo, da je izboljšan CFD model primeren za uporabo hlajenja med gašenjem in da dobljeni rezultati predstavljajo natančne vstopne vrednosti za poznejši izračun zaostalih napetosti in deformacij. Ključne besede: večfazni tok, gašenje aluminijastih litih delov, CFD, Leidenfrost temperatura

SI 104

*Naslov avtorja za dopisovanje: AVL-AST d.o.o., Ul. kneza Koclja 22, 2000 Maribor, Slovenija, rok.kopun@gmail.com

Prejeto v recenzijo: 2013-11-05 Prejeto popravljeno: 2014-04-05 Odobreno za objavo: 2014-05-26

Dinamična simulacija motornega pogonskega sistema z variabilno hitrostjo, krmilnimi ventili in servonapravo Xu, M. – Ni, J. – Chen, G. Ming Xu*– Jing Ni – Guojin Chen

Univerza Hangzhou Dianzi, Šola za strojništvo, Kitajska

Elektrohidravlični pogoni z variabilno hitrostjo (elektromotor s krmiljenjem hitrosti v kombinaciji s konstantno hidravlično črpalko) so obetavni, saj razen večje energijske učinkovitosti kot pogoni z elektromotorjem konstantne hitrosti v kombinaciji s hidravlično črpalko spremenljive delovne prostornine zagotavljajo tudi večjo zanesljivost sistema in širši razpon hitrosti. Pogoni z variabilno hitrostjo so s svojo močjo našli mesto v različnih hidravličnih strojih, njihov nadaljnji razvoj pa bi se lahko ustavil zaradi slabše odzivnosti in pomanjkljivih nizkohitrostnih lastnosti, ki so posledica vztrajnosti elektromotorja in hidravlične črpalke. Cilj raziskave je razvoj nove rešitve krmiljenja hitrosti elektrohidravličnega pogona, ki odpravlja pomanjkljivosti pogonov z variabilno hitrostjo in je primerna za praktično rabo. Predlagan je nov pristop v obliki motornega pogona s krmilnimi ventili in variabilno hitrostjo, ki je opremljen z dodatno servonapravo (PAU) s tlačnim akumulatorjem. PAU je servonaprava s ponovno uporabo energije, ki lahko shranjuje in oddaja hidravlično energijo glede na potrebe sistema. Pri predlaganem pogonu z napravo PAU je mogoče pričakovati izboljšanje odzivnosti in natančnosti krmiljenja v primerjavi s pogonskim sistemom variabilne hitrosti. Predlagani pogonski sistem ima dva vira moči: glavni pogonski vir (električni motor s črpalko) in PAU. Glavni vir moči je sestavljen iz hidravlične črpalke s konstantno delovno prostornino, ki jo prek frekvenčnega pretvornika poganja trifazni asinhronski elektromotor. Ker glavni vir moči pogosto ne more zagotoviti dovolj pretoka za pospeševanje hidromotorja, je bila pogonskemu sistemu s krmilnimi ventili in variabilno hitrostjo dodana še naprava PAU, ki je v osnovi hidravlični akumulator, krmiljen z ventili. Hiter odziv, enostavna zgradba in nizka cena so zagotovljeni s shranjevanjem energije v mehovnem akumulatorju, pretok pri oddajanju in shranjevanju energije pa nadzoruje proporcionalni pretočni ventil. Nov princip pogona sicer prinaša tudi večje stroške pogonskega sistema. Od pogonskega sistema s krmilnimi ventili in variabilno hitrostjo se razlikuje po vključitvi enote PAU. Če sestav elektromotorja in črpalke sam ne more pospešiti dovolj hitro, se vključi enota PAU in oddaja shranjeno energijo za hitrejše pospeševanje. Ko izvršni sestav zavira, vendar se elektromotor in črpalka sama ustavljata prepočasi, PAU shranjuje energijo za naslednji delovni cikel. Naprava PAU se v vseh ostalih situacijah ne vključuje. Nov princip pogona je povezan tudi z zahtevnejšim krmiljenjem. Predlagani pogonski sistem je zahteven sistem vrste MIMO, povezan z močno nelinearnimi in časovno odvisnimi parametri. Izpeljan je bil matematični model sistema in nato je bila izbrana hibridna strategija krmiljenja PID (s proporcionalnim, integralnim in diferencialnim členom), ki upošteva samo vhode in izhode sistema. Dinamične simulacije treh tradicionalnih pogonov in novega pogona so bile opravljene s kosimulacijskimi modeli v paketu AMESim-Simulink. V primerjave so bili vključeni motorni pogon s krmilnimi ventili, motorni pogon variabilne hitrosti s krmilno črpalko in motorni pogon variabilne hitrosti s krmilnimi ventili. Štirje pogoni so bili preizkušeni s tremi običajnimi motnjami variabilne obremenitve, z variabilno obremenitvijo v obliki kvadratnega vala, s hitro časovno spremenljivo variabilno obremenitvijo z majhno motnjo, ter s počasno časovno spremenljivo variabilno obremenitvijo z veliko motnjo. Primerjava rezultatov simulacije je pokazala, da ima predlagani pogonski sistem dobre dinamične lastnosti, ki ne zagotavljajo le pričakovanega prihranka energije, temveč tudi pomembno izboljšujejo odzivnost in natančnost krmiljenja v primerjavi z obstoječim pogonskim sistemom z variabilno hitrostjo. Ključne besede: variabilna hitrost, prihranek energije, variabilna obremenitev, odziv, hidromotor, dinamika

*Naslov

avtorja za dopisovanje: Univerza Hangzhou Dianzi, Šola za strojništvo, Hangzhou, Kitajska, xumzju@163.com

SI 105

Prejeto v recenzijo: 2014-01-23 Prejeto popravljeno: 2014-05-01 Odobreno za objavo: 2014-05-23

Napredna tehnika krmiljenja za odpravo preostalih vibracij pri manipulatorju s fleksibilnim zgibom Conker, C. – Kilic, A. – Mistikoglu, S. – Kapucu, S. – Yavuz, H. Caglar Conker1,* – Ali Kilic2 – Selcuk Mistikoglu1 – Sadettin Kapucu2 – Hakan Yavuz3 1 Univerza

Mustafe Kemala, Tehniška fakulteta, Turčija v Gaziantepu, Tehniška fakulteta, Turčija 3 Univerza Cukurova, Tehniška fakulteta, Turčija

2 Univerza

Krmiljenje gibanj je ena glavnih raziskovalnih tem na področju robotike in avtomatizacije. Visoka hitrost in natančno krmiljenje gibanj sta nujna za visokoproduktivno in visokokakovostno proizvodnjo. Zaradi visokih hitrosti in z njimi povezanih preostalih vibracij pa je obenem tudi težko zagotoviti natančno krmiljenje gibanj. Iskanje ravnotežja med hitrostjo gibanj ter odpravljanjem ali vsaj zmanjšanjem preostalih vibracij je zato pomemben del raziskav krmiljenja gibanj in s tem povezanih praktičnih aplikacij. Ena od metod za zmanjšanje ali odpravo preostalih vibracij je tudi spreminjanje vhodnega signala z uporabo vnaprej znanih sistemskih parametrov. Za popolno odpravo preostalih vibracij je potrebno zelo natančno poznavanje teh parametrov sistema in v realnih sistemih takšne natančnosti ni mogoče vedno doseči. Predstavljena študija podaja obravnavo in rešitev tega problema z novo metodo za odpravljanje preostalih vibracij. Nova metoda je še posebej uporabna pri negotovih parametrih, ki izhajajo iz ocenjevanja ali napovedovanja vedenja sistemov. Pokazano je, da je nova tehnika kos tudi visoki stopnji negotovosti in lahko uspešno odpravlja ali zmanjša preostale vibracije v fleksibilnih sistemih. Prednost predlagane tehnike je v tem, da niti ne omejuje niti ne podaljšuje trajanja premikov, t. j. ne vključuje časovnih omejitev ali časovnih penalov. Večina konvencionalnih metod oblikovanja vhodov pa po drugi strani podaljša čas premika vsaj za pol dušene periode ali več. Nova predlagana metoda za oblikovanje ukazov razdeli čas premika na dva dela, izračuna ukazni vhod kot dva ločena vhoda in ju nato združi v nov vhod. Pri ustvarjanju vsakega vhodnega signala se uporabita funkciji cikloide z rampo ter kosinus versusa z rampo. Referenčni vhod je sestavljen iz treh funkcij. Celotna razdalja, ki jo mora element opraviti v določenem času, se razdeli na tri dele. Vsak del pokriva ena od treh funkcij z enakim časom premika. Če se določeni čas premika in skupna razdalja ne spremenita, je vibracije možno odpraviti s prilagajanjem razdalje premika za vsako funkcijo. Vsaka komponenta vhoda ustvari oscilacije, ki se medsebojno izničijo. Nova metoda omogoča delitev gibanja sistema na dva dela. Ker je prvi korak opravljen z zelo mirnim gibanjem in z zmanjšano stopnjo vibracij, se drugi del gibanja začne z zelo malo ali skoraj brez preostalih vibracij. Drugi del gibanja je zato učinkovitejši pri zmanjševanju preostalih vibracij. Študija predstavlja teoretične in eksperimentalne rezultate tehnik, uporabljenih pri fleksibilnem mehanskem sistemu, podana pa je tudi primerjalna analiza robustnosti. Rezultati simulacij in eksperimentov kažejo, da se oscilacije zmanjšajo v veliki meri, robustnost pa je velika kljub negotovosti sistemskih parametrov. Ključne besede: preostale vibracije, oblikovanje vhoda, manipulator s fleksibilnim zgibom, oblikovanje ukazov

SI 106

*Naslov avtorja za dopisovanje: Univerza Mustafe Kemala, Tehniška fakulteta, Hatay, Turčija, cconker@mku.edu.tr

Prejeto v recenzijo: 2013-11-28 Prejeto popravljeno: 2014-03-18 Odobreno za objavo: 2014-05-23

Raziskava korekcij porazdelitve podatkov S-N pri analizi utrujanja zvarov na osnovi enakovredne napetosti v konstrukciji po metodi Battelle s teorijo grobih množic Sun, Y. – Yang, X. Yibo Sun1,2 – Xinhua Yang1,*

1 Univerza

2 Univerza

Dalian Jiaotong, Fakulteta za materiale in strojništvo, Kitajska Dalian Jiaotong, Fakulteta za železniško tehniko in vzdrževanje, Kitajska

Odpoved zvarov je ključni problem na področju stabilnosti in varnosti varjenih konstrukcij. Trenutno se pri analizi in napovedovanju utrujanja zvarov najpogosteje uporabljajo metoda imenskih napetosti, metoda vročih točk in metoda glavne krivulje S-N na osnovi enakovredne napetosti v konstrukciji po organizaciji Battelle. Metoda enakovredne napetosti v konstrukciji po Battelle v primerjavi s preostalima dvema metodama odpravlja težave z nedoslednostjo pri izračunavanju napetosti in izbiri krivulje S-N. Članek obravnava korekcijo porazdelitve podatkov S-N za zvare z enakovrednimi napetostmi v konstrukciji po Battelle. Najprej so predstavljene formule za izračun enakovrednih napetosti v konstrukciji po Battelle. Nato so opredeljene grobe množice podatkov za porazdelitev S-N pri zvarih delov iz titanove zlitine v odvisnosti od imenskih napetosti, napetosti v konstrukciji in enakovredne napetosti v konstrukciji po Battelle. Podatki o utrujanju zvarov pri delih iz titanove zlitine so bili razporejeni po varilskih dejavnikih; vrsta zvara, debelina plošč, razmerje obremenitve, razmerje napetosti, varilski proces in vrsta materiala pa so bili zapisani v podatkovne baze grobe množice kot atributi pogojev. Stopnje odstopanja vsake podatkovne točke S-N od krivulj S-N na osnovi imenske napetosti, napetosti v konstrukciji in enakovredne napetosti v konstrukciji po Battelle so bile diskretizirane kot atributi odločitev. Glede na imensko napetost in referenčne geometrije spojev sta bili po metodi končnih elementov za vsako skupino podatkov o utrujanju izračunani napetost v konstrukciji ter enakovredna napetost v konstrukciji po Battelle. Iz podatkov o treh vrstah napetosti so bile po metodi najmanjših kvadratov izračunane srednje krivulje S-N, izračunani pa so bili tudi standardni odkloni. Nato so bile izrisane srednja krivulja S-N in krivulje odstopanj s povečavo od –3 do +3. Sedem karakterističnih krivulj tvori šest območij, ki veljajo za domene odločanja in so označena z D(1) do D(6) od kratke do dolge dobe. Atributi odločanja vseh skupin podatkov o utrujanju zvarov so bili opredeljeni z območji, kjer se nahaja točka S-N. Nato je bila opravljena redukcija grobe množice z genetskim algoritmom na podlagi treh napetosti. Rezultati kažejo, da so točke S-N pri napetosti v konstrukciji bolj zgoščene v bližini srednje krivulje S-N, pri enakovredni napetosti v konstrukciji pa so enakomerneje porazdeljene na eni in drugi strani krivulje. Enakovredna napetost v konstrukciji po Battelle zato zmanjšuje standardni odklon porazdelitve S-N. Nato so bile preučene korekcije z ozirom na debelino plošč in razmerje napetosti v metodi glavne krivulje S-N. Opravljena je bila tudi primerjava standardnega odklona podatkov o utrujanju za vrsto debelin plošč oz. razmerij napetosti. Postavljena sta bila modela grobe množice z enim samim atributom pogoja, t. j. debelino plošče oz. razmerjem napetosti. Rezultati kažejo, da sta stopnji odločanja pri debelini plošč in razmerju napetosti na podlagi imenske napetosti razmeroma večji kot pri ostalih dejavnikih, iz tega pa sledi, da dejavniki varjenja enostavno vplivajo na porazdelitev S-N na podlagi imenske napetosti. Izkazalo se je tudi, da je stopnja odločanja dejavnikov varjenja pri enakovredni napetosti v konstrukciji po Battelle oslabljena in harmonizirana. Odstopanja podatkov S-N od srednje krivulje S-N so kompenzirana v dveh korekcijskih stopnjah za napetost v konstrukciji in enakovredno napetost v konstrukciji, zato je porazdelitev S-N bistveno bolj zgoščena in enakomerna. Utrujanje zvara je tako z veliko gotovostjo mogoče napovedati samo z eno krivuljo S-N, ki predstavlja vse podatke S-N. V članku je podrobno analiziran mehanizem za korekcijo napetosti na glavni krivulji S-N s teorijo grobih množic. Razkrito je, zakaj so podatkovne točke S-N pri enakovredni napetosti v konstrukciji po Battelle bistveno bolj zgoščene in enakomernejše. Z dvema korakoma korekture se oslabijo in harmonizirajo stopnje odločanja dejavnikov varjenja. Analiza po metodi grobih množic v tej raziskavi je bila opravljena na podlagi dobro dokumentiranih podatkov o utrujanju titanovih zlitin, količina podatkov o utrujanju zvarov iz ene same vrste poskusov pa za te namene ni dovolj. Zato je težko analizirati nekatere druge posamezne dejavnike, kot so vrsta materiala, postopek varjenja itd. V prihodnjih raziskavah bodo potrebni dodatni podatki, za izboljšanje modela grobe množice pa bodo izvedeni tudi dodatni eksperimenti. Preučena bo tudi izboljšana metoda za diskretizacijo nekaterih atributov pogojev. Ključne besede: utrujanje zvarov, enakovredna napetost v konstrukciji po Battelle, metoda glavne krivulje S-N, teorija grobih množic, korekcija, porazdelitev podatkov *Naslov avtorja za dopisovanje: Univerza Dalian Jiaotong, Fakulteta za železniško tehniko in vzdrževanje, Dalian, Kitajska, yangxhdl@gmail.com

SI 107

Prejeto v recenzijo: 2014-04-15 Prejeto popravljeno: 2014-05-26 Odobreno za objavo: 2014-05-26

Merilna metoda za identifikacijo vrste plina v potopnih termičnih merilnikih masnega toka Rupnik, K. – Kutin, J. – Bajsić, I. Klemen Rupnik* – Jože Kutin – Ivan Bajsić

Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija

V raziskavi je obravnavan razvoj merilne metode za identifikacijo vrste plina v potopnih termičnih merilnikih masnega toka. Merilno načelo termičnih merilnikov temelji na vplivu toka tekočine (v večini primerov toka plina) na prenos toplote z gretega elementa, npr. s termičnega zaznavala pretoka v primeru potopne izvedbe merilnika. Poleg masnega toka (oziroma lokalne masne hitrosti) na intenzivnost konvektivnega prenosa toplote s termičnega zaznavala vplivajo tudi termodinamične in transportne lastnosti merjenega plina, kot so toplotna prevodnost, specifična toplota pri konstantnem tlaku in dinamična viskoznost. Posledično je merilna značilnica termičnega merilnika odvisna od sestave in vrste plina. Če je potopni termični merilnik uporabljen za merjenje masnega toka plina, ki se razlikuje od plina pri umerjanju, je potrebno upoštevati ustrezno korekcijo. Cilj raziskave je bil razviti merilno metodo, temelječo na osnovnem merilnem načelu potopnih termičnih merilnikov, ki bo omogočala identifikacijo vrste plina iz definiranega nabora možnih plinov z znanimi elementnimi sestavami in posledično korekcijo merilne značilnice. Fizikalne osnove identifikacijske merilne metode so podane s pomočjo enostavnega enorazsežnega matematičnega modela termičnega zaznavala. Za praktično izvedbo identifikacijske merilne metode mora imeti potopni termični merilnik dve termični zaznavali, ki se razlikujeta po konstrukcijskih parametrih ali parametrih delovanja. Če sta uporabljeni merilni značilnici za neustrezen plin, tj. plin, ki ni enak dejanskemu merjenemu plinu, se bosta v splošnem izmerjena masna tokova razlikovala. Z namenom eksperimentalne utemeljitve veljavnosti predlagane merilne metode smo razvili in izdelali potopni termični merilnik masnega toka, ki vsebuje termični zaznavali z okroglim in kvadratnim prečnim prerezom. Razviti merilnik smo umerili za pet različnih plinov – zrak, kisik, didušikov oksid, ogljikov dioksid in argon. Pri izvedbi identifikacijske merilne metode smo uporabili dve kriterijski funkciji, in sicer absolutno vrednost relativne razlike izmerjenih masnih tokov in normirani pogrešek. Z obema kriterijskima funkcijama smo zrak pravilno identificirali kot ustrezni plin. S primerno statistično značilnostjo smo didušikov oksid, ogljikov dioksid in argon pravilno identificirali kot neustrezne pline, za kisik pa je bila razlika izmerjenih masnih tokov statistično neznačilna. Nadaljnje izboljšanje rezultatov identifikacijske merilne metode bi lahko dosegli z zmanjšanjem merilne negotovosti razlike izmerjenih masnih tokov ali z optimizacijo konstrukcijskih parametrov termičnega merilnika. Potopni termični merilnik masnega toka z vgrajeno merilno metodo za identifikacijo vrste plina predstavlja inovativno rešitev na področju termičnih merilnikov masnega toka. Identifikacijska merilna metoda se lahko izvede sočasno z merjenjem masnega toka plina, tj. primarno merjene veličine. Za izvedbo identifikacijske merilne metode v merjenem procesu je potrebno termični merilnik umeriti za vse pričakovane pline z definiranimi elementnimi sestavami. Glede na to zahtevo lahko razviti termični merilnik uporabljamo npr. v pretočnih procesnih sistemih z različnimi tehničnimi, čistimi ali medicinskimi plini. Ključne besede: merilna metoda za identifikacijo vrste plina, potopni termični merilnik masnega toka, termični zaznavali pretoka, različni konstrukcijski parametri, merilne značilnice, eksperimentalna utemeljitev veljavnosti

SI 108

*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, klemen.rupnik@fs.uni-lj.si

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, SI 109-114 Osebne objave

Doktorske disertacije, specialistična dela, diplomske naloge

DOKTORSKE DISERTACIJE Na Fakulteti za strojništvo Univerze v Ljubljani so obranili svojo doktorsko disertacijo: ● dne 10. julija 2014 Anže SITAR z naslovom: »Izboljšan prenos toplote pri vrenju v mikrokanalih« (mentor: prof.dr. Iztok Golobič); Že z dosedanjim razvojem mikro obdelovalnih tehnologij je preboj mikro sistemov na področje široke industrijske uporabe le še vprašanje časa. Kljub temu nekateri ključni pojavi in mehanizmi še niso bili podrobno analizirani, kar še posebej velja za vrenje v mikrokanalih. Bistvenega pomena za kakovostne eksperimentalne rezultate na mikro ravni je ustrezna merilna oprema, zato smo izdelali miniaturna uporovna temperaturna zaznavala in umestili miniaturna tlačna zaznavala na mikrokanalno testno sekcijo ter dogajanje spremljali s hitrotekočo kamero, s čimer smo dobili vpogled v stacionarne in dinamične pojave med vrenjem različnih delovnih kapljevin. Večino neželenih pojavov med vrenjem v mikrokanalih smo izločili ali omejili z vpeljavo konstrukcijskih izboljšav, med katere sodijo: (i) tokovni razdelilniki, ki služijo enakomerni porazdelitvi toka delovne tekočine; (ii) tokovni omejevalniki in fluidne diode, ki dušijo parne protitokove, ki se neobhodno pojavijo med vrenjem; (iii) potencialna nukleacijska mesta na dnu in v stenah mikrokanalov, s katerimi znižamo temperaturo pregretja, potrebnega za nastop nukleacijskega vrenja; (iv) zračne reže ob aktivnem nizu mikrokanalov, ki znižujejo toplotne izgube in homogenizirajo temperaturno polje; (v) medsebojna povezanost mikrokanalov, s katero razširimo območje vrenja in s tem izboljšamo prenos toplote. Z analizo vizualizacije vrenja v mikrokanalih smo določili vpliv gostote toplotnega toka na lastno frekvenco in amplitudo nihanja meniskusa, s čimer lahko napovedujemo površino mikrokanalov, na kateri je toplotna prestopnost med vrenjem visoka. Iz eksperimentalnega dela z različnimi delovnimi tekočinami lahko sklepamo, da je za učinkovit prenos toplote med vrenjem ključnega pomena omočljivost kapljevine. S primerjalno analizo prenosa toplote smo ugotovili, da so toplotne prestopnosti pri vrenju samoomočljive vodne raztopine butanola znatno višje v primerjavi s čisto vodo; ● dne 15. julija 2014 Lidija RIHAR z naslovom: »Generalizirani model sočasnega osvajanja izdelka« (mentor: prof. dr. Marko Starbek); Podjetja nastopajo na globalnem trgu in se srečujejo z vprašanjem konkurenčnosti, ki se nanaša

na izpolnjevanje osnovnih zahtev trga: izdelek dati na trg v pravem času, na pravem mestu, v pravi količini, v pravi kakovosti in po pravi ceni. Za zagotovitev konkurenčnosti na trgu bodo morala podjetja preiti iz sekvenčnega na sočasno osvajanje izdelka. V nalogi je predstavljen generaliziran model sočasnega osvajanja izdelka, ki vključuje tako izdelavo ponudbe kot izvedbeni projekt. Pri oblikovanju poteka so upoštevane strategije sočasnega osvajanja izdelka: paralelnost, standardizacija in integracija. Predstavljen je postopek oblikovanja zank in timov sočasnega osvajanja, ki temeljijo na matriki odgovornosti in stopnji sodelovanja med udeleženci projekta. V zaključku je prikazan primer sočasnega osvajanja pedalnega sklopa; ● dne 16. julija 2014 Samo VENKO z naslovom: »Izboljšanje prenosa toplote na toplotno aktiviranih gradbenih konstrukcijah« (mentor: prof. dr. Sašo Medved); Doktorska disertacija predstavlja raziskavo izboljšanja učinkovitosti sistemov za aktivno naravno ogrevanje in hlajenje, ki izhaja iz združevanja toplotno vzbujenih gradbenih konstrukcij in mehanskega prezračevanja. Vtočni zrak, ki se vpihuje ob toplotno vzbujeni gradbeni konstrukciji oziroma navpičnem končnem ploskovnem prenosniku toplote, povzroči preoblikovanje naravne konvekcije v mešano, zaradi česar se poveča izkoristljivost naravnih virov hladu in toplote za hlajenje oziroma ogrevanje stavb. Ugotovili smo, da tak proces še ni bil raziskan in parametrično ovrednoten. Raziskave smo opravili v termostatirani zaprti celici v velikosti realnega prostora s toplotno vzbujenim končnim ploskovnim prenosnikom toplote in sistemom prisilnega prezračevanja. V prvem sklopu raziskav smo analizirali vpliv geometrije prostora in geometrijskih ovir na fenomen naravne in mešane konvekcije. Temu so sledile raziskave konvektivnega prenosa toplote na ogrevanem in hlajenem navpičnem končnem ploskovnem prenosniku toplote pri robnih pogojih, potrebnih za vzpostavitev naravne in mešane konvekcije. Na osnovi meritev lokalnih gostot konvektivnega toplotnega toka smo izdelali večparametrične modele za izračun vrednosti povprečnih in lokalnih toplotnih prestopnosti in Nusseltovih števil. Razvite modele smo uporabili v numerični analizi toplotnega odziva tipičnega pisarniškega prostora. Dokazali smo, da združevanje toplotno vzbujenih gradbenih konstrukcij s sistemom mehanskega prezračevanja na predlagani način, bistveno izboljša prenos toplote na končnem ploskovnem prenosniku toplote, zmanjša SI 109

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, SI 109-114

rabo energije v stavbah za hlajenje ter zaradi manjše velikosti toplotno vzbujenih končnih ploskovnih prenosnikov toplote izboljša ekonomičnost nizkoeksergistkih tehnologij za ogrevanje in hlajenje stavb. Dokazali smo, da lahko zaradi iterakcije med tokom vpihovanega zraka in toplotno vzbujenim ploskovnim prenosnikom toplote zagotovimo visoko kakovost bivalnega ugodja. ● dne 29. avgusta 2014 Boštjan NOVAK z naslovom: »Lasersko podprto tridimenzionalno merjenje oblike stopal v gibanju« (mentor: prof. dr. Janez Možina, somentor: doc.dr. Matija Jezeršek); Delo obravnava razvoj merilnega sistema za merjenje spreminjajoče se oblike stopala med hojo na osnovi laserske triangulacije z večlinijskim osvetljevanjem. Merilni sistem je sestavljen iz pohodnega odra in štirih merilnih modulov, ki po načelu barvne modulacije sočasno zajamejo celotno obliko stopala. Programska oprema omogoča analizo širine, višine, obsega in orientacije stopala na različnih prerezih. V eksperimentalnem delu smo najprej preverili ponovljivost meritev na eni osebi. Ponovljivost je ±0,5% za boso stopalo in ±1% za obuto stopalo, kotne dimenzije pa imajo natančnost ±3°. Meritve spreminjanja dimenzij kažejo, da so v primeru obutega stopala dimenzijske spremembe prerezov do 50% manjše v primerjavi z bosim. Prav tako je razvidno, da se relativne spremembe bosega stopala med različnimi osebami razlikujejo tudi za več kot 50%. Na osnovi teh rezultatov smo razvili algoritem za izračun oblikovnega ujemanja stopala in čevlja. V njem se primerja največje izmerjene dimenzije stopala tekom celotne faze opore s soležnimi prerezi kopita. V primerjavi z obstoječimi rešitvami tako ni potrebno uporabiti parametrov, ki predpisujejo funkcionalno zahtevane zračnosti. S tem je v izračunu upoštevan individualni način hoje posameznika, kar je pomembno pri razvoju obutve po meri. * Na Fakulteti za strojništvo Univerze v Mariboru so obranili svojo doktorsko disertacijo: ● dne 11. julija 2014 Gregor SAGADIN z naslovom: »Večfazni numerični model razpršilnega sušenja suspenzije zeolit - voda« (mentor: prof. dr. Matjaž Hriberšek); V nalogi je obravnavan proces sušenja poroznega delca, sestavljenega iz omočenih kristalov zeolita 4A v razmerah, ki prevladujejo v razpršilnem sušilniku. Obstoječi numerični modeli v inženirskih programskih paketih obravnavajo vso vlago v delcu kot površinsko sušenje pa kot enostopenjsko, kar lahko vodi do netočnih in nepopolnih rezultatov. V SI 110

želji po nadgradnji obstoječih numeričnih modelov je bil razvit model za večstopenjsko sušenje poroznega delca. Le-ta upošteva tudi kristalno vezano vlago, ki v procesu sušenja mokrega jedra prehaja skozi osušeno skorjo. Za opis prehoda vlage skozi osušeno skorjo v drugi stopnji sušenja je bil uporabljen model enostranske Stefanove difuzije, med tem ko je bila tretja stopnja sušenja razvita na osnovi karakteristik materiala, določenih s termo gravimetrično analizo. S pridobljenimi rezultati iz numeričnih simulacij je bila pripravljena primerjava z eksperimentalno pridobljenimi rezultati, ki je pokazala uporabnost ter fizikalno pravilnost uporabljenega numeričnega modela večstopenjskega sušenja; ● dne 11. julija 2014 Rok KOPUN z naslovom: »Numerično modeliranje procesa gašenja z uporabo Eulerjevega večfaznega pristopa« (mentor: prof. dr. Leopold Škerget); Optimizacija prenosa toplote v avtomobilistični industriji je eden izmed ključnih dejavnikov, ki pripomore k zmanjšanju porabe goriva in znižanju emisij izpustnih sistemov. Učinkovite metode toplotne obdelave, kot je proces gašenja, se uporabljajo pri nadomestitvi delov iz težjih kovin z lažjimi zlitinami (npr. aluminijastimi), kar pripomore k zmanjšanju mase vozila in posledično vpliva na znižanje porabe goriva in emisijskih vrednosti. Proces gašenja s potapljanjem v tekoči fazi je tako eden izmed najpomembnejših industrijskih procesov v avtomobilistični industriji, saj igra prenos toplote ključno vlogo pri določitvi strukturne in mehanske lastnosti materiala (npr. glave motorja). Doktorska disertacija obravnava razvoj in validacijo izboljšanega numeričnega modela prenosa toplote pri procesu gašenja s potapljanjem v kapljevini implementiranega v komercialni program računalniške dinamike tekočin (CFD) AVL FIRE®. Prenos toplote pri procesu gašenja med surovcem in pregreto kapljevito fazo se obravnava s pomočjo Eulerjevega večfaznega pristopa, kjer obravnavamo vsako fazo kot samostojno in neodvisno. Masna, gibalna in energijska enačba se rešujejo neodvisno le za tekočo domeno, medtem ko se za trdnino rešuje le energijska enačba. Primerjava rezultatov eksperimentalnih meritev in pripadajočih numeričnih simulacij z uporabo spreminjajoče se Leidenfrost temperaturne predpostavke skupaj z upoštevanjem dodatnih medfaznih sil je pokazala zelo dobro ujemanje. Primerjavo smo izvedli na testnem aluminijastem preizkušancu z različnimi odebelitvami vzdolž dolžine in poenostavljeni aluminijasti glavi motorja. Preizkušanca sta bila potopljena v tekočo fazo s različnimi temperaturami in različnimi orientacijami potopitve, pri čemer se numerična temperaturna

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, SI 109-114

napoved hlajenja strukture po celotnem volumnu med procesom gašenja zelo dobro ujema z eksperimentalno dobljenimi vrednostmi; ● dne 14. julija 2014 Uroš ARTIČEK z naslovom: »Razvoj mikrostrukture pri izdelavi gradientnega materiala H13-Cu s tehnologijo LENS« (mentor: prof. dr. Ivan Anžel); Tehnologija LENS predstavlja sodobno dodajalno tehnologijo nanašanja kovinskih materialov. Prikazana je idejna zasnova uporabe visokotehnoloških materialov v orodjih za brizganje umetnih mas ter orodjih za tlačno litje lahkih kovin in njihovih zlitin, izdelanih z omenjeno tehnologijo. V praksi se pogosto zgodi, da pride med strjevanjem do odstopanj dimenzijskih in oblikovnih toleranc izdelka zaradi neenakomerne porazdelitve temperature v orodju ter posledično v izdelku med ohlajanjem. Hkrati pa toplotna prevodnost orodnih jekel omejuje čas ohlajanja ter posledično produktivnost orodij. Obravnavana problematika sinteze zlitine orodnega jekla H13 in bakra v funkcionalno gradientnih materialih s specifično mikrostrukturo in kombinacijo lastnosti predstavlja nove možnosti optimizacije na tem področju. V disertaciji je predstavljen vpliv plastne gradnje in termičnih pogojev tehnologije LENS na razvoj mikrostrukture in posledično na mehanske lastnosti. Za boljše razumevanje zlitinskega sistema smo okarakterizirali referenčne vzorce, izdelane s tehnologijo litja, kjer smo se približali ravnotežnemu strjevanju. Z uporabo različnih analiznih metod smo določili fazne sestave ter vpliv tehnologije na tvorbo razpok in razvoj mikrostrukture v odvisnosti od kemijske sestave in razmer pri strjevanju. Na področju kemijskih sestav, ki so dovzetne za nastanek razpok, smo odkrili mehanizem zalitja razpok, ki je posledica popolnega močenja bakra in temperaturnih razmer pri nanosu novih plasti. Za razumevanje vpliva faznih sestav na mehanske lastnosti zlitin so bili izvedeni natezni preizkusi ter meritve mikrotrdot. Rezultati kažejo možnost uspešne izdelave vzorcev funkcionalno gradientnih materialov H13-Cu s tehnologijo LENS. Pojasnjen je vpliv pogojev strjevanja na razvoj mikrostrukture ter postavljen model razvoja in stabilnosti mikrostrukture v trdnem; ● dne 21. julija 2014 Matej DROBNE z naslovom: »Analiza utrujanja delovnih valjev pri vročem valjanju pločevine« (mentor: prof. dr. Srečko Glodež); V doktorski disertaciji je obravnavana analiza utrujanja delovnih valjev pri vročem valjanju pločevine. Delovni valji so med obratovanjem mehansko in termično obremenjeni. Pri mehanski obremenitvi lahko ločimo dva območja, in sicer: (i) območje med delovnim valjem in valjancem; (ii) območje med delovnim in podpornim valjem. Pri

termičnih obremenitvah pa lahko opazimo le eno območje, in sicer na mestu, kjer prehaja toplota iz valjanca na delovni valj. Določevanje kontaktnih obremenitev delovnega valja je bilo najprej izračunano analitično, potem pa še numerično. Rezultat numerične analize je služil kot osnova za izračun življenjske dobe. Na osnovi eksperimentalno določenih materialnih podatkov pri sobni in povišani temperaturi ter rezultatov numerične analize smo z uporabo Basquinove enačbe izračunali življenjsko dobo delovnih valjev na dva načina: (i) z uporabo podatkov pri obremenitvenem razmerju R = -1 in upoštevanjem srednje napetosti po Goodmanu; (ii) direktno s podatki pri R = -∞. Poleg določevanja koeficientov za določevanje življenjske dobe delovnih valjev po metodi visokocikličnega utrujanja je bilo v sklopu doktorske disertacije narejeno še veliko eksperimentalnega dela. Prikazana je kemijska analiza preučevanega materiala ter mikrostruktura pred in po termični obdelavi. Prikazan je potek trdote v odvisnosti od globine delovne plast. Določitev nateznih in tlačnih trdnosti je potekalo pri različnih temperaturah glede na pogoje med valjanjem, ko sta v kontaktu delovni valj in valjanec. Prikazani so tudi rezultati upogibnih trdnosti in udarne žilavosti. Eksperimentalno so bili določeni parametri mehanike loma, kjer se je spremljala rast utrujenostne razpoke v preizkušancu. Izvedena je bila podrobna metalografska analiza preizkušancev za določevanje življenjske dobe valjev z uporabo elektronskega mikroskopa. Na koncu se je izvedla tudi analiza obrabne odpornosti na lastno izdelani preizkuševalni napravi SPECIALISTIČNO DELO Na Fakulteti za strojništvo Univerze v Mariboru je z uspehom zagovarjal svoje specialistično delo: dne 14. julija 2014: Peter MLAKAR z naslovom: »Rekristalizacija zlitine Al 7075« (mentor: prof. dr. Ivan Anžel). DIPLOMSKE NALOGE Na Fakulteti za strojništvo Univerze v Mariboru je pridobila naziv univerzitetni diplomirani inženir strojništva: dne 28. avgusta 2014: Sabina TIMPRAN z naslovom: »Vloga vizualizacije v procesu nenehnih izboljšav« (mentor: doc. dr. Nataša Vujica Herzog, somentor: mag. Marko Šverko); SI 111

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, SI 109-114

* Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv magister inženir strojništva: dne 27. avgusta 2014: Bor MOJŠKERC z naslovom: »Ultrazvočne preiskave lepljenih spojev« (mentor: prof. dr. Janez Grum, somentor: doc. dr. Tomaž Kek); Gašper POTOKAR z naslovom: »Namenska prikolica za izvoz lesa« (mentor: prof. dr. Jožef Duhovnik); Luka ROBLEK z naslovom: »Stabilnost geometrijske oblike zobnikov iz polimernih materialov« (mentor: izr. prof. dr. Jože Tavčar, somentor: prof. dr. Jožef Duhovnik); Jure SALOBIR z naslovom: »Uporaba načrtovanja eksperimentov pri brizganju polimernih izdelkov« (mentor: izr. prof. dr. Jože Tavčar, somentor: prof. dr. Jožef Duhovnik); dne 29. avgusta 2014: Peter ARKO z naslovom: »Laserski triangulacijski sistem za adaptivno vodenje varilnega robota« (mentor: doc. dr. Matija Jezeršek); Armin DROZG z naslovom: »Eksperimentalna karakterizacija strukturnega hrupa električnega aktuatorja« (mentor: prof. dr. Miha Boltežar); Tom KUNAVER z naslovom: »Analiza dinamskega odziva strukture pri interakciji s stacionarnim fluidom« (mentor: prof. dr. Miha Boltežar, somentor: dr. Gregor Čepon); Jure PLEŠKO z naslovom: »Razvojno vrednotenje žage za razrez kamene volne« (mentor: prof. dr. Marko Nagode); Jaka JAVH z naslovom: »Na digitalnih slikah temelječa eksperimentalna modalna analiza polnega polja« (mentor: prof. dr. Miha Boltežar, somentor: izr. prof. dr. Janko Slavič); Janez LUZNAR z naslovom: »Dinamično masno uravnoteženje togih rotorjev« (mentor: prof. dr. Miha Boltežar, somentor: izr. prof. dr. Janko Slavič); Matic RESNIK z naslovom: »Rezanje cevi toplotnih izmenjevalcev v jedrskih elektrarnah z elektrotermičnim postopkom« (mentor: doc. dr. Joško Valentinčič, somentor: prof. dr. Mihael Junkar); Aljaž ŽIGON z naslovom: »Kavitacija in kavitacijska erozija v postaji z radialnim tokom« (mentor: izr. prof. dr. Matevž Dular, somentor: izr. prof. dr. Roman Šturm). * Na Fakulteti za strojništvo Univerze v Mariboru je pridobil naziv univerzitetni diplomirani gospodarski inženir: SI 112

dne 28. avgusta 2014: David KOPRIVC z naslovom: »Uporaba orodja 3DVIA Composer pri vzdrževanju v podjetju TAJFUN Planina d.o.o.« (mentor: prof. dr. Borut Buchmeister, prof. dr. Duško Uršič). * Na Fakulteti za strojništvo Univerze v Mariboru je pridobil naziv magister inženir strojništva: dne 28. avgusta 2014: Jernej KUHARIČ z naslovom: »Uporaba merilnih sistemov pri razvoju izdelkov v orodjarni podjetja Carrera Optyl« (mentor: prof. dr. Bojan Ačko). * Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva (UN): 18. junija 2014: Matjaž KERN; 19. junija 2014: Anže KOVAČIČ; 20. junija 2014: Andraž BOLA; 23. junija 2014: Jure PAPEŽ; 24. junija 2014: Primož FLIS in Matic FRAJNKOVIČ; 26. junija 2014: Tadej NOVAKOVIĆ in Matej ZWITTER; 27. junija 2014: Martin PALDAUF; 7. julija 2014: Klemen BIZJAK in Pavel MIHAILOVSKI; 11. julija 2014: Gal GORJUP; 17. julija 2014: Rok PEROŠA; 25. julija 2014: Miha TRUNKELJ; 11. avgusta 2014: Andraž KRŠLIN, David ŠTREMFELJ, Aljaž ULAGA in Jasmina VIDEC; 25. avgusta 2014: Tim BLAŽEK, Dominik BOGDAN, Rok GREGORČIČ, Milan HAFNER, Aljaž JELEN, Rok KOŠNIK,Gaia KRAVANJA, Andrej MRAK, Nada PETELIN, Miha PRIJATELJ, Urban PRIMOŽIČ, Primož ROJKO, David ROPOTAR, Luka SPRINČNIK, Jan ŠVAJGER, Maja TURK, Blaž ZAVRL, Vid ZDOVC in Maja ZUPANČIČ; 26. avgusta 2014: Jan DIMOVSKI, Matic PEČAR, Blaž SLAK in Neža ZEVNIK; 27. avgusta 2014: Luka BERTONCELJ, Jaka BOSTNER, Samo JAMNIK, Marko JAMŠEK, Jernej MUNIH, Tomaž POŽAR in Luka VOUK; 29. avgusta 2014: Žiga DEBEVEC, Matija GABERŠČEK in Ana JENKO.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, SI 109-114

* Na Fakulteti za strojništvo Univerze v Mariboru je pridobil naziv diplomirani inženir strojništva (UN): dne 28. avgusta 2014: Jure ALEKSEJEV z naslovom »Pilotna naprava za pirolizo polietena« (mentor: prof. dr. Aleš Hribernik). * Na Fakulteti za strojništvo Univerze v Mariboru je pridobil naziv diplomirani inženir tehniškega varstva okolja (UN): dne 29. julija 2014: Rok KOROŠEC z naslovom »Sedanja problematika in okoljsko - ekonomska vizija sistema ravnanja z ločeno odpadno embalažo v Sloveniji« (mentorja: prof. dr. Niko Samec, somentor: dr. Filip Kokalj). * Na Fakulteti za strojništvo Univerze v Ljubljani je pridobil naziv diplomirani inženir strojništva: dne 28. avgusta 2014: Mario KORPAR z naslovom: »Določanje efektivnega premera visokohitrostnega vodnega curka« (mentor: doc. dr. Andrej Lebar). * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva: dne 28. avgusta 2014: Dejan MLINARIČ z naslovom: »Tehnološka zasnova orodja za tlačno litje aluminijevih zlitin« (mentor: izr. prof. dr. Ivan Pahole); Boštjan NABERNIK z naslovom: »Posodobitev oblike in izdelave odtočnega dela žleba za stavbno kleparstvo« (mentor: izr. prof. dr. Ivan Pahole, somentor: dr. Tomaž Brajlih); Nejc ŠTUMBERGER z naslovom: »Snovanje, izdelava in testiranje male kurilne naprave na lesne pelete« (mentor: dr. Filip Kokalj, somentor: prof. dr. Niko Samec). * Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva (VS):

dne 27. avgusta 2014: Matjaž CELAR z naslovom: »Termične interakcije med aktivnimi nukleacijskimi mesti pri mehurčkastem vrenju vode« (mentor: prof. dr. Iztok Golobič); Žiga JERAJ z naslovom: »Primerjava kavitacijske erozije na različnih materialih« (mentor: izr. prof. dr. Matevž Dular, somentor: izr. prof. dr. Roman Šturm); Rok KLOBČAR z naslovom: »Proizvodnja električne energije iz nizkotemperaturne toplote s parnim krožnim procesom z organsko delovno snovjo« (mentor: izr. prof. dr. Mihael Sekavčnik); Jure LEBAN z naslovom: »Analiza toka vrednosti« (mentor: izr. prof. dr. Janez Kušar, somentor: prof. dr. Marko Starbek); dne 28. avgusta 2014: Jernej LENKIČ z naslovom: »Zasnova montažnega mesta za vstavljanje grafitnih ščetk in vzmeti na jarem sesalne enote« (mentor: izr. prof. dr. Niko Herakovič); Bor SAVNIK z naslovom: »Napoved porabe končne energije v prometu v Republiki Sloveniji za obdobje 2012-2050« (mentor: izr. prof. dr. Tomaž Katrašnik); dne 29. avgusta 2014: Jure DEŽMAN z naslovom: »Vpliv velikosti delcev na zvočno izolativnost granuliranih materialov« (mentor: prof. dr. Igor Emri); Simon JAKLIČ z naslovom: »Konstrukcija naprave za avtomatsko montažo spiralnih vzmeti na prenapetostno zaščito« (mentor: izr. prof. dr. Jože Tavčar, somentor: prof. dr. Jožef Duhovnik); Vid KODRIČ z naslovom: »Načrtovanje novega noža za uporabo v univerzalnem kuhinjskem aparatu« (mentor: izr. prof. dr. Marko Hočevar, somentor: prof. dr. Branko Širok); Anej PERHAVEC z naslovom: »Konstrukcija rotorja laboratorijske centrifuge iz kompozitnih materialov« (mentor: izr. prof. dr. Jože Tavčar, somentor: prof. dr. Jožef Duhovnik); Marjan SMOLE z naslovom: »Računalniško podprto konfiguriranje talne letališke opreme« (mentor: izr. prof. dr. Jože Tavčar, somentor: prof. dr. Jožef Duhovnik); Miha ANŽIČ z naslovom: »Postavitev tehnologije izdelave ter analiza strošov in geometrijske točnosti valjev za mletje žita« (mentor: doc. dr. Franci Pušavec, somentor: prof. dr. Janez Kopač); Aleksander ČEH z naslovom: »Primerjava MQL obdelave inconela 718 z uporabo dveh različnih hladilnih olj« (mentor: doc. dr. Franci Pušavec, somentor: prof. dr. Janez Kopač); Žiga PRISTOV z naslovom: »Zasnova in razvoj merilnega sistema za kontrolo položaja ležajev v SI 113

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)9, SI 109-114

rotorju bobnastega elektromotorja« (mentor: doc. dr. Primož Podržaj); Aljaž ŽELINŠČEK z naslovom: »Primerjava različnih strategij izdelave pri postopku selektivnega laserskega sintranja« (mentor: prof. dr. Janez Kopač).

Matej DEBELAK z naslovom: »Zasnova in konstruiranje izkoščičevalnika češenj« (mentor: prof. dr. Glodež Srečko).

Na Fakulteti za strojništvo Univerze v Mariboru je pridobil naziv diplomirani inženir mehatronike (VS): dne 28. avgusta 2014: Jaka MOČIVNIK z naslovom: »Robotska proizvodna celica za označevanje izdelkov s signiranjem« (mentorja: izr. prof. dr. Karl Gotlih, doc. dr. Andreja Rojko).

Na Fakulteti za strojništvo Univerze v Mariboru je pridobil naziv diplomirani inženir strojništva (VS): dne 28. avgusta 2014:

SI 114

Technical Editor Pika Škraba University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Founding Editor Bojan Kraut

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Vice-President of Publishing Council Jože Balič

University of Maribor, Faculty of Mechanical Engineering, Slovenia Cover: The top photo shows the test vehicle towing an instrumented light cargo trailer during a hard obstacle avoidance manoeuvre performed for acquisition of the required measurement system parameters. The rendered images below show the detailed mechanical model of the vehicle-trailer combination as developed and used in the research of the snaking stability of passenger cars with light cargo trailers. Courtesy: University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

International Editorial Board Koshi Adachi, Graduate School of Engineering,Tohoku University, Japan Bikramjit Basu, Indian Institute of Technology, Kanpur, India Anton Bergant, Litostroj Power, Slovenia Franci Čuš, UM, Faculty of Mechanical Engineering, Slovenia Narendra B. Dahotre, University of Tennessee, Knoxville, USA Matija Fajdiga, UL, Faculty of Mechanical Engineering, Slovenia Imre Felde, Obuda University, Faculty of Informatics, Hungary Jože Flašker, UM, Faculty of Mechanical Engineering, Slovenia Bernard Franković, Faculty of Engineering Rijeka, Croatia Janez Grum, UL, Faculty of Mechanical Engineering, Slovenia Imre Horvath, Delft University of Technology, Netherlands Julius Kaplunov, Brunel University, West London, UK Milan Kljajin, J.J. Strossmayer University of Osijek, Croatia Janez Kopač, UL, Faculty of Mechanical Engineering, Slovenia Franc Kosel, UL, Faculty of Mechanical Engineering, Slovenia Thomas Lübben, University of Bremen, Germany Janez Možina, UL, Faculty of Mechanical Engineering, Slovenia Miroslav Plančak, University of Novi Sad, Serbia Brian Prasad, California Institute of Technology, Pasadena, USA Bernd Sauer, University of Kaiserlautern, Germany Brane Širok, UL, Faculty of Mechanical Engineering, Slovenia Leopold Škerget, UM, Faculty of Mechanical Engineering, Slovenia George E. Totten, Portland State University, USA Nikos C. Tsourveloudis, Technical University of Crete, Greece Toma Udiljak, University of Zagreb, Croatia Arkady Voloshin, Lehigh University, Bethlehem, USA General information Strojniški vestnik – Journal of Mechanical Engineering is published in 11 issues per year (July and August is a double issue). Institutional prices include print & online access: institutional subscription price and foreign subscription €100,00 (the price of a single issue is €10,00); general public subscription and student subscription €50,00 (the price of a single issue is €5,00). Prices are exclusive of tax. Delivery is included in the price. The recipient is responsible for paying any import duties or taxes. Legal title passes to the customer on dispatch by our distributor. Single issues from current and recent volumes are available at the current single-issue price. To order the journal, please complete the form on our website. For submissions, subscriptions and all other information please visit: http://en.sv-jme.eu/. You can advertise on the inner and outer side of the back cover of the magazine. The authors of the published papers are invited to send photos or pictures with short explanation for cover content. We would like to thank the reviewers who have taken part in the peerreview process.

http://www.sv-jme.eu

60 (2014) 9

Strojniški vestnik Journal of Mechanical Engineering

Since 1955

Papers

539

Gašper Šušteršič, Ivan Prebil, Miha Ambrož: The Snaking Stability of Passenger Cars with Light Cargo Trailers

549

Łukasz Pejkowski, Dariusz Skibicki, Janusz Sempruch: High-Cycle Fatigue Behavior of Austenitic Steel and Pure Copper under Uniaxial, Proportional and Non-Proportional Loading

561

Jiang Ding, Yangzhi Chen, Yueling Lv, Changhui Song: Position-Parameter Selection Criterion for a Helix-Curve Meshing-Wheel Mechanism Based on Sliding Rates

571

Rok Kopun, Leopold Škerget, Matjaž Hriberšek, Dongsheng Zhang, Wilfried Edelbauer: Numerical Investigations of Quenching Cooling Processes for Different Cast Aluminum Parts

581

Ming Xu, Jing Ni, Guojin Chen: Dynamic Simulation of Variable-Speed Valve-Controlled-Motor Drive System with a Power-Assisted Device

592

Caglar Conker, Ali Kilic, Selcuk Mistikoglu, Sadettin Kapucu, Hakan Yavuz: An Enhanced Control Technique for the Elimination of Residual Vibrations in Flexible-Joint Manipulators

600 Yibo Sun, Xinhua Yang: Study on the Correction of S-N Distribution in the Welding Fatigue Analysis Method Based on the Battelle Equivalent Structural Stress by Rough Set Theory

Journal of Mechanical Engineering - Strojniški vestnik

Contents

9 year 2014 volume 60 no.