Journal of Mechanical Engineering 2014 1 by Darko Svetak

http://www.sv-jme.eu

60 (2014) 1

Strojniški vestnik Journal of Mechanical Engineering

Since 1955

Contents

Papers

Darja Steiner Petrovič, Roman Šturm: Fine-structured Morphology of a Silicon Steel Sheet after Laser Surface Alloying of Sb Powder

Pavel Žerovnik, Dušan Fefer, Janez Grum: Surface Integrity Characterization Based on Time-Delay of the Magnetic Barkhausen Noise Voltage Signal

Govindaraj Elatharasan, Velukkudi Santhanam Senthil Kumar: Corrosion Analysis of Friction Stirwelded AA 7075 Aluminium Alloy

Tomaž Berlec, Janez Kušar, Janez Žerovnik, Marko Starbek: Optimization of a Product Batch Quantity

43 Jijun Yi, Tao Zeng, Jianhua Rong: Topology Optimization for Continua Considering Global Displacement Constraint 51

Tomasz Trzepieciński, Hirpa G. Lemu: Frictional Conditions of AA5251 Aluminium Alloy Sheets Using Drawbead Simulator Tests and Numerical Methods

Tamás Mankovits, Tamás Szabó, Imre Kocsis, István Páczelt: Optimization of the Shape of Axi-Symmetric Rubber Bumpers

Journal of Mechanical Engineering - Strojniški vestnik

12 Wei Teng, Feng Wang, Kaili Zhang, Yibing Liu, Xian Ding: Pitting Fault Detection of a Wind Turbine Gearbox Using Empirical Mode Decomposition

1 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 420 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 surface modifying a nonoriented, electrical steel with Sb using laser surface alloying was examined. Sb is a surface active element with Pauling electronegativity greater than 2.0 (upper figure). The study represents a novel approach to the tailoring of the commodity. The specifics of the selected surface modification that ensure a fine-structured morphology may consequently have a beneficial effect on the further development of new soft magnetic materials. Image Courtesy: University of Ljubljana, Faculty of Mechanical Engineering, Slovenia & Institute of Metals and Technology, 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.

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Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1 Contents

Contents Strojniški vestnik - Journal of Mechanical Engineering volume 60, (2014), number 1 Ljubljana, January 2014 ISSN 0039-2480 Published monthly

Editorial

Papers Darja Steiner Petrovič, Roman Šturm: Fine-structured Morphology of a Silicon Steel Sheet after Laser Surface Alloying of Sb Powder Wei Teng, Feng Wang, Kaili Zhang, Yibing Liu, Xian Ding: Pitting Fault Detection of a Wind Turbine Gearbox Using Empirical Mode Decomposition Pavel Žerovnik, Dušan Fefer, Janez Grum: Surface Integrity Characterization Based on Time-Delay of the Magnetic Barkhausen Noise Voltage Signal Govindaraj Elatharasan, Velukkudi Santhanam Senthil Kumar: Corrosion Analysis of Friction Stirwelded AA 7075 Aluminium Alloy Tomaž Berlec, Janez Kušar, Janez Žerovnik, Marko Starbek: Optimization of a Product Batch Quantity Jijun Yi, Tao Zeng, Jianhua Rong: Topology Optimization for Continua Considering Global Displacement Constraint Tomasz Trzepieciński, Hirpa G. Lemu: Frictional Conditions of AA5251 Aluminium Alloy Sheets Using Drawbead Simulator Tests and Numerical Methods Tamás Mankovits, Tamás Szabó, Imre Kocsis, István Páczelt: Optimization of the Shape of AxiSymmetric Rubber Bumpers

List of Reviewers in 2013

5 12 21 29 35 43 51

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1 Editorial

Editorial

60 years

Since 1955: of Strojniški vestnik – Journal of Mechanical Engineering international members of the editorial board appeared for the first time in journal’s colophon in 1997, from 1998 SV-JME has been listed in the Science Citation Index (SCI), and from 2010 the articles are published only in English language with a one-page abstract in Slovenian.

I am writing this jubilee editorial on the New Year’s Eve, a time we express to each other the best wishes for the coming year, and also look in the past and think about the outcomes and efficiency of our actions and creation. The journal’s editorial team is once again departing from a very successful and also strenuous year. The journal was born in 1955 and is now entering its 60th year. Even though the teenage days are long gone, they are still present in our hearts and work activities. Every year, the journal is becoming more mature. This virtual youth fills us with new hope and goals, providing the necessary energy and enthusiasm. Strojniški vestnik – Journal of Mechanical Engineering (SV-JME) has been an influential and high-quality journal from the very beginning in 1955, when an idea to publish printed technical word was born in order to bundle more and more diverse research activities in mechanical engineering. Initially focused on the homeland, and gradually developed to address the international audiences, SV-JME has always operated in the scope of modest possibilities of a small nation. But even in smallness it is possible to reach significant international publicity. Allow me to mention a man of historic importance, the father of our journal, the founding and long-time editor distinguished prof. dr. h.c. Bojan Kraut.

The journal’s international reputation is increasing every year, and in 2012 it passed into the second quality quartile (Q2). In addition to the authors and editorial board, the credits for this success also go to our reviewers (the list of reviewers in 2013 is published on pages 72 to 74).

In 60 years, the journal changed in terms of design, content and language. In volume 38, the articles were published for the first time both in Slovenian and English language, the names of

We would like to take this opportunity and thank all reviewers for their appreciated time and their selfless loyalty to the journal, which makes it possible to review the articles in time and with high quality. 3

The inflow of articles is greater every year, and in 2013 the editorial board has received more than 450 of them, publishing about a fifth. SV-JME’s impact factor is now 0.883 (2012), closely related to citations of our articles. The journal in electronic form is available free of charge at the journal’s website, and so are a leaflet with the list of all articles published in the last two years and all volumes from 2005, while the printed journal is payable.

and dedication in an ever increasing volume of editorial work, as well as the website editor Mr. Darko Švetak for his quality web administration. A special acknowledgement goes to the Slovenian Research Agency (ARRS) for co-funding the journal and thereby enabling sustainable improvements. We can ascertain the journal would not be able to survive without the financial support of ARRS. I thank everyone who participated in any way in raising the journal’s reputation and its recognisability worldwide during the 60 years it has been published. Let us wish our journal bon voyage in 2014, and let us never forget: only by common endeavours can the small become big. In the name of our editorial board, I wish you a successful and scientifically creative 2014, an interesting and diverse read in monthly numbers of our journal, many success in basic research, attentiongrabbing development of advanced technologies and interdisciplinary discoveries, as well as new scientific findings to be published in our journal. Trust us, we trust you!

Vincenc Butala Editor-in-chief

REFERENCES At this distinguished jubilee, I would like to thank the members of SV-JME’s International Editorial Board and the members of the Publishing Council for their contribution and steadfastness in realising the strategic goals of our journal. Prof. dr. Branko Širok vas elected the president of the Publishing Council in September 2013, and also undergoing changes is the International Editorial Board. Special attention and acknowledgement goes to the former president of the Publishing Council prof. dr. Jožef Duhovnik, our excellent and creative cooperation was very fruitful. I thank the journal’s technical editor Ms. Pika Škraba for her tirelessness

[1] Butala, V. (2010). Strojniški vestnik – Journal of Mechanical Engineering: 55 years. Kalin M., (ed.). Zgodovina strojništva in tehniške kulture na Slovenskem (The history of Mechanical Engineering and Technical Culture in Slovenia). University of Ljubljana, Faculty of Mechanical Engineering, Ljubljana, p. 95-105. [2] Butala, V. (2011). Editorial, Let’s observe Our achivements and harness the power of our diversity. Strojniški vestnik – Journal of Mechanical Engineering, vol. 57, no. 12, p. 867-868. [3] ISI Web of Knowledge, Thomson Reuters, available at: http://apps.webofknowledge.com/CitationReport. do?product=WOS&search_mode=CitationRepor t&SID=S2XZVoOpVxW19Y8YuBL&page=1&cr_ pqid=1&viewType=summary accessed 2014-01-02.

Original Scientific Paper

Received for review: 2013-07-26 Received revised form: 2013-09-30 Accepted for publication: 2013-10-30

Fine-structured Morphology of a Silicon Steel Sheet after Laser Surface Alloying of Sb Powder Steiner Petrovič, D. – Šturm, R. Darja Steiner Petrovič1,* – Roman Šturm2 1 Institute 2 University

of Metals and Technology, Ljubljana, Slovenia of Ljubljana, Faculty of Mechanical Engineering, Slovenia

An experiment was designed to investigate the feasibility of surface modifying a fully processed, non-oriented, electrical steel sheet with antimony (Sb) using laser surface alloying (LSA). The post-exposure microstructural characterization of the modified steel sheet was performed using light microscopy (LM) and field-emission scanning electron microscopy (FE-SEM/EDS). Microhardness measurements confirmed the differences in the microhardness profile along the depth direction as a result of the applied laser-alloying treatment. The additive nature of the laser treatment and the specific cooling conditions create unique solidification conditions that ensure not only a high microhardness of approximately 400 HV0.1 of the modified layer, but also its fine-structured morphology. Keywords: antimony, laser surface alloying, non-oriented electrical steel

0 INTRODUCTION Non-oriented electrical steel sheets are soft magnetic materials produced from silicon steels. The Worldsteel Committee on Economic Studies, Brussels reports that the world-wide production of electrical sheet and strip in 2011 was 11.25 million tons [1]. Silicon steels are fundamental to the economy of electrical appliances, and offer the best combination for transmitting and distributing electrical energy. The properties required of these steels are high permeability and induction, low magnetic losses, and low magnetostriction [2]. International and national standards (e.g., EN 10106:2009) [3] only specify the maximum loss, and often also the minimization of polarization/permeability. Steels with a high content of silicon as the main alloying element are brittle and exhibit poor workability. Therefore, researchers are replacing the practice of adding silicon with alternatives – one of them being the addition of antimony (Sb) [4] to [7]. The positive effect of an Sb addition to silicon steels is reflected in a greater remanent induction and a lower coercive force, which should lead to a smaller area for the demagnetization loop and so to smaller inductive energy losses for nonoriented electrical steel sheet [6] and [7]. At present only high-permeability grades with excellent magnetic properties can provide a higher added value for electrical steels. The magnetic behaviour of electrical steels depends critically on the microstructure and the texture. Accordingly, a special design of silicon steel, by adding surfaceactive elements (i.e., Sb) is expected to give improved magnetization properties for these soft magnetic materials [4], [5] and [7].

According to Takashima et al. [8], an Sb addition to 1.85% Si non-oriented electrical steels, with 0.25% Mn and 0.3% Al, improved the magnetic properties due to an increase of the (100) and (110) texture components and a decrease of the (111) texture component. The initial annealing treatment promotes an increase in the grain size and, additionally, Sb segregation at the grain boundaries. After cold rolling, during final annealing, the Sb prevents the nucleation of recrystallization near the original grain boundaries and decreases the formation of (111) grains [6] and [7]. In order to improve the crystallographic texture of non-oriented electrical steels, the amount of Sb should be between 0.015% and 0.15%. The effect of Sb on the crystallographic texture depends on the hot-band annealing temperature, and its effectiveness is reduced when hot-band annealing is not performed [4] and [9]. On the other hand, various laser melting procedures can be effectively used during the creation of functional parts [10] to [13]. In recent years a laser beam has been used for a wide range of applications in order to modify the microstructure and the properties of the steel. The role of laser technology intensively increased in surface engineering. The most important processes are as follows: laser heat treatment, laser remelting, laser cladding and laser alloying [14]. Laser surface alloying (LSA) has attracted considerable attention in recent years as an efficient method to improve the chemical and mechanical surface properties of engineering components. The improvement in these properties by the LSA technique is achieved by introducing alloying materials into the laser-melted component surface, typically in the form of powder. For laser surface alloying, adding pre-paste metal powder on the substrate surface is a

*Corr. Author’s Address: Institute of Metals and Technology, Lepi pot 11, 1000 Ljubljana, Slovenia, darja.steiner@imt.si

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 5-11

common practice. Because of the desire to mix the coating powder with the substrate, a thin layer of prepaste coating of the order of 0.1 mm to less than 1 mm of powder on the substrate is normally applied. The particles introduced in the interaction zone tend to completely dissolve in the liquid phase, thereby modifying the chemical composition of the surface layer. After the laser melting of both the coating powder and the substrate, an alloyed layer with a thickness normally less than 1 mm is obtained. The unique advantages of the LSA technique for surface modification are now well recognised and include the possibility of localised treatment, refinement of the grain size because of rapid quench rates and the generation of metastable structures with novel properties that are not achievable with competing methods [15] to [17]. The objective of the present study is to combine these two possible approaches, i.e., laser alloying of a surface-active element. The feasibility of the modification of a fully processed silicon steel sheet by the laser surface alloying of Sb powder will be investigated and discussed.

Mode structure multimode – top hat Energy input Ei = 10.7 J/mm2 Pulse duration tb = 8 ms Pulse frequency ν = 7 Hz Laser beam Travel speed vb = 150 mm/min Beam diameter on The specimen surface Db = 1.4 mm Beam overlapping 40% of Db

Fig. 1. Size distribution of Sb powder particles

1 EXPERIMENTAL PROCEDURE 1.1 Selection of Electrical Steel and Alloying Powder The chemical composition of the non-oriented electrical steel (NOES) under investigation is given in Table 1. The alloying material was antimony (Sb) powder containing 0.012 wt.% C and 0.019 wt.% S. The dimensions of the non-oriented electrical steel specimens were 70×20×0.5 mm. Table 1. Chemical composition of non-oriented electrical steel (wt.%) C 0.004

Si 2.1

Al 0.9

Mn 0.2

N 0.004

P 0.01

Fe Balance

In Fig. 1 the size distribution of the Sb powder particles is presented. 1.2 Selection of the Laser Remelting Conditions Laser alloying of the thin surface layer was performed with a Nd:YAG laser system OR-LASER with a laser source maximum power P = 80 W. The following laser parameters were selected: Laser source power P = 40 W Max. pulse energy E = 60 J 6

A thin layer of pre-paste Sb coating (with an approximate thickness of 0.15 mm) was applied to the substrate surface. For better adhesion of the Sb to the substrate surface, the Sb powder was mixed with alcohol to form a sort of wet paste. To avoid blowing away the Sb powder during the protective Ar gas flow, the experiment was performed in a regular air atmosphere. For this reason and the fact that the surface of fully processed electrical steel sheets is oxidized, a stationary air atmosphere seems to be more relevant for achieving the primary aim of the study. The particles introduced in the interaction zone were expected to completely dissolve in the liquid phase, thereby modifying the chemical composition of the surface and subsurface layer. However, the physical properties of the main elements of the electrical steel, i.e., Fe, Si, and Al, and that of the Sb powder shown in Table 2 are very different. In particular, the Sb element volatilizes dramatically when melted due to its low melting point. Therefore, it is difficult to prepare Sb-type thermoelectric materials with a stoichiometric ratio. For the extensive application of Sb-type thermoelectric materials, it is necessary to develop optimal laser alloying parameters.

Steiner Petrovič, D. – Šturm, R.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 5-11

Table 2. The physical properties of the main chemical elements involved in the laser alloying process Melting point [°C] Boiling point [°C] Lattice type

Sb 630.6 1587 Simple trigonal

Fe 1535 2750 b.c.c.

Si 1410 2355 Diamond cubic

Al 660.3 2467 b.c.c.

1.3 Metallographic Analysis For the metallographic analyses the sample was ground and polished according to standard metallographic techniques. The metallographic analyses were performed using a Microphot FXANikon light microscope and a JEOL JSM 6500-F field-emission scanning electron microscope with an associated energy-dispersive spectrometer (EDS). In this study, the FE-SEM/EDS analyses were performed at a 15-kV accelerating voltage. In FESEM/EDS analyses the teardrop-shaped interaction volume extends from less than 100 nm to around 5 µm into the surface, depending on the element and the accelerating voltage. The factors that determine the detection limits of the EDS are the counting time, the accelerating voltage, the beam current, the line used to measure the element and the compositions of both the sample and the standards. The Vickers microhardness HV0.1 was measured using an Instron, Wilson-Wolpert Tukon 2100B hardness tester. The thermodynamic calculations were performed using ThermoCalcTCFE5. Additionally, a computer simulation of the solidification of the selected multi-component alloy was performed with the Scheil-Gulliver model. However, in the Scheil-Gulliver model no kinetic description of the solidification is given [18]. 2 RESULTS AND DISCUSSION 2.1 Dimensions of the Surface-Alloyed Layer When applying laser surface alloying it is important to ensure sufficient energy input so that melting of the thin surface layer is guaranteed. The size of the alloyed layer was defined in the cross-section of the specimen. For metallographic analysis, the specimen was cut in the transverse direction, ground, polished and etched for observation with a light microscope. The depth of the alloyed trace was then measured. The depth of the surface-alloyed layer was approximately 0.1 mm.

2.2 Microstructure Analysis of the Surface-Alloyed Layer In this study a commercial, fully processed specimen of non-oriented, electrical steel sheet of thickness 0.5 mm was used. Its oxide scale and the microstructure are represented in Figs. 2a and b, respectively. For the purposes of a standard metallographic investigation three lamellae were embedded (Fig. 2b).

Fig. 2. Oxide scale, and the microstructure of the fully processed, non-oriented electrical steel sheet: a) non-etched, LM, 500× and b) etched by Nital, LM, 50×

The oxidized surface of non-oriented electrical steels is a consequence of the fabrication route, which includes final annealings for decarburization and recrystallization (Figs. 2a and b). The oxide scale of non-oriented electrical steel sheet formed in an industrial process is composed of iron oxide(s), silica, alumina and other complex oxides. The scale is normally several micrometres thick, with up to a micrometre of surface corrugation (Fig. 2a). Since the surface of fully processed, non-oriented electrical steel sheets is already oxidized, this may be an additional source of possible oxidation during the laser surface alloying [19]. Due to the high silicon content, the microstructure of the selected alloy consists of α-ferrite, i.e., the b.c.c. phase (Fig. 2b). For the prediction of the solidification process of the Fe-Si-Al alloy a modified Scheil-Gulliver solidification model can be used. This model assumes that the diffusion coefficients in the liquid phase are equal to infinity, whereas in the solid phases they are equal to zero, and that the local equilibrium is always held at the interphase between the liquid and solid phases. The modified Scheil-Gulliver model also allows equilibrium back diffusion of interstitial elements in solid phases [18]. The plotted diagram in Fig. 3.a shows how the mole fraction of the individual solid phases varies

Fine-structured Morphology of a Silicon Steel Sheet after Laser Surface Alloying of Sb Powder

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with temperature. Assuming the full-equilibrium calculation model, the calculated liquidus and solidus temperatures are 1512 and 1489 °C, respectively (black dashed curve). In the simulation using the modified Scheil-Gulliver model the back-diffusion of fast-diffusing components (i.e., carbon) and a possible α→γ transformation are taken into account. Here, the calculated liquidus temperature is 1371 °C. Compared to full-equilibrium conditions, the solidification sequence in this case proceeds with the precipitation of α-ferrite over a much broader temperature interval.

The calculated values from Fig. 3a can be valuable for the prediction of the liquidus temperature. In the process of laser surface remelting, full-equilibrium conditions of the solidification cannot be achieved. Instead, due to the significantly higher solidification rates present the formation of hardening structures occurs. In Fig. 3b the calculated phase equilibria (mass fraction of stable phases) in the temperature range 400 to 1600 °C are shown. Because of the limited solubility of Sb in α-ferrite at room temperature, Sbrich precipitates (rhombohedral phase) are formed, whereas approximately 0.03 wt.% Sb is dissolved in the ferrite. The post-exposure metallographic analysis revealed the modified subsurface region in the ferritic steel sheet (Fig. 4). There is also evidence for a high cracking susceptibility of the alloyed layer.

Fig. 4. SE image of the cross-section of the Sb-modified nonoriented electrical steel sheet using laser alloying

Fig. 3. a) Mole fractions of individual solid phases as a function of temperature (black curve for modified Scheil-Gulliver calculation and black dashed curve for full-equilibrium calculation); b) mass fraction of equilibrium phases as a function of temperature for the selected Fe-Si-Al alloy with Sb addition

The distribution of Sb along the penetration depth direction of the laser-treated silicon steel can be seen from the corresponding EDS analyses (Fig. 5, Table 3). The Sb enrichments were measured in spectra 1 and 2. The approximate penetration depth of the Sb was 0.1 mm, which corresponds to the dimensions of the remelted layer. Across the melt pool the as-solidified microstructure is present (Fig. 6a). The reaction front of the solidification can be seen at an approximate depth of 0.1 mm. Moreover, the solidification conditions cause a very fine-structured morphological texture in the melt pool (Figs. 6a and b). From a comparison of Figs. 2b and 6a and b, these differences in the size and morphology of the bulk and surfacetreated material can be clearly seen.

Steiner Petrovič, D. – Šturm, R.

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shows the microhardness values through the alloyed layer. From the results shown in Fig. 7 it can be concluded that: • After laser alloying of the Sb powder to the surface layer of non-oriented electrical steel an average microhardness level of around 410 to 420 HV0.1 was obtained.

Fig. 5. Distribution of the elements Sb, Fe, Si, and C along the penetration depth direction of the laser-treated silicon steel (X-ray linescan) Table 3. EDS analysis from Fig. 4 (results are given in wt.%) C* Al Si Fe Spectrum 1 5.84 / 0.94 66.85 Spectrum 2 4.90 / 1.15 65.92 Spectrum 3 3.99 / 2.16 93.85 Spectrum 4 2.44 0.76 2.16 94.64 Spectrum 5 5.24 0.82 2.18 91.76 Spectrum 6 7.56 0.91 1.87 89.66 Spectrum 7 9.15 0.83 2.05 87.98 *Cummulative value of adsorbed and bulk carbon content.

Sb 26.36 28.02 / / / / /

The high cooling rates of the homogeneous melt give us the important effect of the formation of a fine dendrite microstructure. Thus, the formation of a very fine and homogeneous microstructure of the solution crystals of iron-silicon-antimony alloy system can be explained by the thermo-kinetic processes caused by the rapid cooling rates (Fig. 4). In the investigated microstructure, some solidification cracks and pores are also visible (Fig. 6b). The cracks occur most probably due to the synergistic effects of high contents of Si and Sb in the remelted layer. In the literature, crack- and pore-free coatings on low silicon steel (1 wt.% Si) based on Fe3Si have already been reported [20]. 2.3 Microhardness in the Remelted Layer The microhardness was measured in accordance with the Vickers method, i.e., a diamond pyramid hardness measurement, through the depth of the alloyed layer. The hardness was measured at a load of 100 N. Fig. 7

b Fig. 6. a) As-solidified microstructure across the melt pool; b) finestructured morphology in the sub-surface region of the modified layer; cracks and pores are also visible

• There is a significant decrease in the microhardness in the transition zone from the alloyed layer to the base metal. • The microhardness of the silicon steel substrate is 200±5 HV0.1. The comparison of the results of the metallographic analyses and the microhardness measurements shows a very good agreement. The results of the microhardness measurements correspond to the morphological changes in the surface alloyed layer (Figs. 4 and 7).

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can be minimized by the optimization of the applied process parameters. Nevertheless, the specifics of the selected surface modification that ensure a finestructured morphology may consequently have a beneficial effect on the further development of new soft magnetic materials produced from silicon steels. 4 ACKNOWLEDGEMENTS The authors would like to acknowledge the Slovenian Research Agency for its financial support (Programmes P2-0050 and P2-0270). 5 REFERENCES Fig. 7. Microhardness profile along the penetration depth direction of the laser-treated silicon steel sheet

In the process of laser surface remelting, the full-equilibrium conditions of the solidification cannot be achieved. Instead, due to the very high cooling rates a fine-structured dendrite morphology with an increased microhardness evolved. Using laser treatment the alloying with Sb is limited only to the region of the melt pool. As evident from Fig. 5, no further diffusion of Sb into the steel matrix occurs. 3 CONCLUSIONS An experiment was designed to investigate the modification of a fully processed, non-oriented electrical steel sheet with antimony using laser surface alloying. The applied laser treatment is appropriate for the modification of silicon steel sheet with Sb. The following findings confirm the feasibility of the laser surface alloying of Sb powder in non-oriented electrical steel: • With the applied parameters the approximate penetration depth of Sb by laser alloying was 0.1 mm. • The additive nature of the process and the specific cooling conditions create unique solidification conditions that ensure a fine-structured morphology. • Process of laser surface alloying caused an increase in the hardness in the alloyed surface layer. This preliminary study represents a novel approach to the tailoring of the commodity (i.e., electrical steel). A limitation here is the very high cracking susceptibility of the alloyed layer which 10

[1] Steel Statistical Yearbook (2012). Worldsteel Committee on Economic Studies, Brussels. [2] Cullity, B.D., Graham, C.D. (2009). Introduction to Magnetic Materials. John Wiley & Sons, Hoboken. [3] SIST EN 10106:2007. Cold rolled non-oriented electrical steel sheet and strip delivered in the fully processed state, Slovenian Institute for Standardization, Ljubljana. [4] Rodrigues, M.F., Da Cunha, M.A., Paolinelli, S.D.C., Cota, A.B. (2013). Texture and magnetic properties improvement of a 3% Si non-oriented electrical steel by Sb addition. Journal of Magnetism and Magnetic Materials, vol. 331, p. 24-27, DOI:10.1016/j. jmmm.2012.11.009. [5] Huang, W.Y., Chang, S.K., Zhou, S.C. (2006). The effect of alloys on the magnetic properties of high grade non-oriented electrical steels. Proceedings of the 9th International Steel Rolling Conference and 4th European Conference. Paris. [6] Jenko, M., Vodopivec, F., Praček, B. (1992). AES studies of antimony segregation on the surface of a Fe-Si-C alloy. Vacuum, vol. 43, no. 5-7, p. 449-451, DOI:10.1016/0042-207X(92)90054-Z. [7] Jenko, M., Vodopivec, F., Praček, B., Godec, M., Steiner, D. (1994). AES studies of antimony surface segregation in nonoriented silicon steel. Journal of Magnetism and Magnetic Materials, vol. 133, no. 1-3, p. 229-232. DOI:10.1016/0304-8853(94)90533-9. [8] Takashima, M., Obara, T., Kan,T. (1993). Texture improvement in high-permeability non-oriented electrical steel by antimony addition. Journal of Materials Engineering and Performance, vol. 2, no. 2, p. 249-254, DOI:10.1007/BF02660293. [9] Irie, T.C., Matsumura, K.I., Nakamura, H.C., Shimanaka, H.F., Suzuki, T.C. (1980). Method of Producing Non-Oriented Silicon Steel Sheets Having an Excellent Electro-magnetic Property. United States Patent, Alexandria. [10] Šturm, R., Grum, J. (2011). The influence of retained austenite on residual stresses in laser remelted cast iron. Journal of Materials Engineering and Performance,

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vol. 20, no. 9, p. 1671-1677, DOI:10.1007/s11665-0119833-3. [11] Thijs, L., Kempen, K., Kruth, J.P., Van Humbeeck, J. (2013). Fine-structured aluminium products with controllable texture by selective laser melting of prealloyed AlSi10Mg powder. Acta Materialia, vol. 61, no. 5, p. 1809-1819, DOI:10.1016/j.actamat.2012.11.052. [12] Ravnikar, D., Mrvar, P., Medved, J., Grum, J. (2013). Microstructural analysis of laser coated ceramic components TiB2 and TiC on aluminium alloy EN AW6082-T651. Strojniški vestnik - Journal of mechanical Engineering, vol. 59, no. 5, p. 281-290, DOI:10.5545/ sv-jme.2012.904. [13] Sušnik, J., Šturm, R., Grum, J. (2012). Influence of laser surface remelting on Al-Si alloy properties. Strojniški vestnik - Journal of Mechanical Engineering, vol. 58, no. 10, p. 614-620, DOI:10.5545/sv-jme.2012.696. [14] Major, B. (2006). Laser processing for surface modification by remelting and alloying of metallic systems. Pauleau, Y., (ed.). Materials Surface Processing by Directed Energy Techniques. Elsevier, Amsterdam, p. 241-274. [15] Dobrzanski, L.A., Bonek, M., Hajduczek, E., Klimpel, A. (2005). Alloying the X40CrMoV5-1 steel surface layer with tungsten carbide by the use of a high power diode laser. Applied Surface Science, vol. 247, no 1-4, p. 328-332, DOI:10.1016/j.apsusc.2005.01.126.

[16] Nath, S., Pityana, S., Majumdar, J.D. (2012). Laser surface alloying of aluminium with WC+Co+NiCr for improved wear resistance. Surface & Coatings Technology, vol. 206, no. 15, p. 3333-3341, DOI:10.1016/j.surfcoat.2012.01.038. [17] Sun, G., Zhang, Y., Liu, C., Luo, K., Tao, X., Li, P. (2010). Microstructure and wear resistance enhancement of cast steel rolls by laser surface alloying NiCr–Cr3C2. Materials and Design, vol. 31, no. 6, p. 2737-2744, DOI:10.1016/j.matdes.2010.01.021. [18] Andersson, J.O., Helander, T., Höglund, L., Shi, P., Sundman, B. (2002). Thermo-Calc & DICTRA, computational tools for materials science. Calphad, vol. 26, no. 2, p. 273-312, DOI:10.1016/S03645916(02)00037-8. [19] Steiner Petrovič, D., Mandrino, Dj. (2011). XPS Characterization of the oxide scale on fully processed non-oriented electrical steel sheet. Materials Characterization, vol. 62, no 3, p. 503-508, DOI:10.1016/j.matchar.2011.03.011. [20] Dong, D., Liu, C., Chen, S., Zhang, B. (2009). Characterization of Fe3Si-based coatings on low silicon steel by pulsed Nd:YAG laser cladding. International Journal of Minerals, Metallurgy and Materials, vol. 16, no. 2, p. 208-214, DOI:10.1016/S1674-4799(09)600352.

Fine-structured Morphology of a Silicon Steel Sheet after Laser Surface Alloying of Sb Powder

nija

Original Scientific Paper

Received for review: 2013-07-04 Received revised form: 2013-08-31 Accepted for publication: 2013-09-27

Pitting Fault Detection of a Wind Turbine Gearbox Using Empirical Mode Decomposition Teng, W. – Wang, F. – Zhang, K.L. – Liu, Y.B. – Ding, X. Wei Teng1,2,* – Feng Wang1 – Kaili Zhang1 – Yibing Liu1 – Xian Ding1

1 North

2 Taiyuan

China Electric Power University, School of Energy Power and Mechanical Engineering, China University of Technology, Key Laboratory of Advanced Transducers and Intelligent Control Systems, Ministry of Education, China

The conventional method of detecting a gear fault is to demodulate the vibration signal collected from the gearbox based on the Hilbert transform; however, this requires human intervention and lacks sophistication. Empirical mode decomposition (EMD) is a significant timefrequency tool for adaptively decomposing vibration signals into a collection of intrinsic mode functions (IMFs); a fault feature can be extracted from one of IMFs to reveal the fault location and fault level of a gear or bearing in the mechanical drive system. In this paper, a multi-harmonic vibration model of a gearbox with fault modulation is presented, a conventional demodulation analysis using Hilbert transform is introduced, and the principle of EMD is illustrated. The Hilbert demodulation analysis and EMD are applied to processing field vibration signals collected from a wind turbine gearbox to detect a gear-pitting fault. The results show that EMD can extract the fault modulation information more adaptively and intelligently than Hilbert demodulation analysis can. Keywords: empirical mode decomposition, adaptively, fault detection, wind turbine, gearbox

0 INTRODUCTION In recent years, wind energy has had great development due to the ongoing need for renewable energy. At the same time, the failure rate of key components in wind turbines has greatly increased because of severe operational environments. The wind turbine gearbox is one of the most fragile components in the turbine because of extreme differences in temperature and complicated alternating loads from wind turbulence. In many wind farms throughout the world, gearboxes fail only several thousand hours after wind turbine is put into operation, and its service life is much less than designed. For example, between 2000 and 2004 in Sweden the downtime resulting from gearbox failure was longer than that from other components [1]. In China, the bearings and gears in wind turbines can easily be destroyed because the wind load is unbalanced and irregular with regard to time [2]. Wind turbines will shut down if gearboxes fail, with consequential inevitable economic losses. Therefore, finding a fault feature-extracting method of wind turbine gearbox under a complicated operating environment remains an urgent task, as does building a maintenance mechanism with high efficiency that can guarantee wind turbine and power grid safety. Many new techniques for fault feature extraction have emerged for rotating machine health diagnosis. For example, Wang et al. combined a complex wavelet transform-based envelope extraction of speed-varying vibration signals with computed order tracking to eliminate speed dependence in the sampled data [3], which showed the effectiveness in identifying 12

bearing structural defects under varying operating conditions. Li et al. adopted an adaptive stochastic resonance to extract the fault feature of machine accuracy decay in boring and milling machines [4]. Significant motor features, such as bearing failure, broken rotor bar, phase unbalance etc. from vibration signals are extracted through the scale-invariant feature transform algorithm to generate the faulty symptoms [5]. Generally, the structure of a wind turbine gearbox is complex and diverse, consisting of multistage planetary gears and ordinary gears. Therefore, many signal-processing methods were applied to different types of gearboxes in order to find existing or potential faults. Barszcz and Randall [6] detected a tooth crack in the planetary gear of a wind turbine using spectral kurtosis. Yang et al. [7] used continuous wavelet transform to diagnose gearboxes in wind turbine test rig. Tang et al. [8] studied Morlet wavelet transformation and Wigner-Ville distribution, and detected a simulant groove on a wind turbine gearbox test-bed. A discrete wavelet transform is applied to the demodulated current signal of an induction motor to detect a multistage gearbox fault by removing the intervening neighbouring features [9] and [10]. The previous studies accumulated rich experience in fault diagnosis of wind turbines. However, affected by random excitation of variable rotational speed and alternating load, vibration signals from wind turbine gearbox are non-stationary or nonlinear, so conventional signal processing methods, such as Fourier transform and wavelet analysis et al., lack processing ability for these types of signals. Empirical mode decomposition (EMD) was presented

*Corr. Author’s Address: North China Electric Power University, School of Energy Power and Mechanical Engineering, Beijing, 102206, China, tengw@ncepu.edu.cn

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by Huang et al. [11] to adaptively decompose a nonstationary signal into a collection of intrinsic mode functions (IMFs); EMD has been widely applied to measurement analysis and fault diagnosis in mechanical transmission. For example, Loutridis [12] constructed a variable stiffness dynamic model of a single-stage gear transmission, and employed the energy of the second IMF from EMD as the fault feature to denote the gear crack depth. Liu et al. [13] developed a B-spline EMD as a filter bank to analyse the vibration signals from automobile gearbox, which showed that the Hilbert spectrum was more effective than continuous wavelet transform in the detection of the vibration signatures. Fast Fourier transform of IMF from EMD was utilized to detect bearing faults [14]. Yu et al. [15] and Cheng et al. [16] used time-frequency entropy from Hilbert-Huang to accurately identify gear status with or without fault; they proposed a local Hilbert energy spectrum to provide energy distribution based on EMD to extract the characteristic information of a gear fault. A merit index was introduced by Ricci and Pennacchi [17] to select IMF automatically, and the defective gearbox was always identified univocally by using the merit index. Planetary gearbox faults can be found by matching the dominant peaks in the envelope spectrum and the spectrum of instantaneous frequency with the theoretical characteristic frequencies of faulty gears through the joint application of the amplitude and frequency demodulation methods [18]. Zhang and Zhou [19] used ensemble empirical mode decomposition and an optimized support vector machine to realize multi-fault diagnosis in rolling element bearings. The abovementioned research shows that EMD can adequately process non-stationary vibration signals. However, these successful cases are mostly based on simulation signals or test rigs, which are significantly different from actual situations. There are few applications on field vibration signals, and the effectiveness of EMD for field data cannot be validated, especially for wind turbine gearboxes under variable rotational speed and alternating load. This paper is organized as follows: a vibration model of a gearbox with fault modulation and a conventional demodulation analysis using the Hilbert transform are discussed in Section 1. In Section 2, the principle of EMD is presented. In Section 3, the structure and parameters of an actual wind turbine gearbox are introduced, the feature frequencies of the gearbox are calculated, and the field vibration signals are analysed to detect a gear pitting fault based on EMD and Hilbert demodulation, respectively.

In addition, the fault cause of wind turbine gearbox is also discussed in this section. The conclusions are given in Section 4. 1 VIBRATION SIGNAL OF GEARBOX AND DEMODULATION ANALYSIS 1.1 Vibration Signal of Gearbox During gear mesh in the gearbox, the excitation due to variable stiffness generates vibration signal consisting of typical multi-harmonic components. The signal above mentioned can be described as [20]:

x(t ) = ∑ xm cos( 2π f z mt + ϕ m ), (1) m =1

where x(t) denotes the vibration time signal of gearbox, xm denotes the amplitude of the m order harmonic, φm denotes the phase of the m order harmonic, and fz denotes the gear mesh frequency, which is also a carrier frequency. When a defect happens in a gear system, there will be a multi-component amplitude modulation phenomenon in the gearbox vibration signal. The modulation function can be shown as:

am (t ) = ∑ Am ,n cos( 2π f n nt + α m ,n ), (2) n =1

where am(t) denotes a amplitude modulation function, Am,n denotes the amplitude of the n order harmonic of the modulation function, αm,n denotes the phase of the n order harmonic of the modulation function, and fn denotes the rotational frequency of the shaft fixed with defective gear, which is also a modulation frequency. From Eqs. (1) and (2), the model of gearbox vibration signal with fault modulation can be shown as:

x(t ) = ∑ xm [1 + am (t ) ] cos ( 2π f z mt + ϕ m ). (3) m =1

1.2 Hilbert Demodulation Analysis The Hilbert transform is an attractive method for demodulation of a vibration signal with fault modulation. For a gearbox vibration signal consisting of multiple harmonics and noise, the key step of demodulation analysis using the Hilbert transform is to separate it using a band-pass filter. Neglecting the phase information, the vibration signal in Eq. (3) after band-pass filtering can be processed as:

xm (t ) = xm 1 + Am , x cos( 2π f x t )  cos ( 2π f z mt ) , (4)

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where Am,x denotes the amplitude of a certain order harmonic of the modulation function, and fx denotes a certain modulation frequency. Applying the Hilbert transform [21] and [22] to Eq. (4), the following is obtained: 1 1 ∞ x (τ ) x m (t ) = xm (t ) * = ∫ m dτ = π t π −∞ t − τ = xm 1 + Am , x cos(2π f x t )  sin ( 2π f z mt ) . (5) An analytic expression is given as:

zm (t ) = xm (t ) + j x m (t ). (6) Then the envelope of xm(t) is shown as: 2 | zm (t ) |= xm2 (t ) + x m (t ) =

= xm | 1 + Am , x cos(2π f xt ) | . (7)

The envelope in Eq. (7) is the amplitude of modulation signal in some frequency band and the corresponding phase is described as: x m (t ) θ (t ) = arctan = 2π f z mt. (8) xm (t )

x(t) and steps 1) and 2) will be repeated until h1(t) becomes one IMF, which can be described as:

3) Subtracting the first IMF c1(t) from x(t), the remaining signal r1(t) can be shown as:

h1 (t ) = x(t ) − m(t ). (9)

If h1(t) cannot satisfy the two conditions of IMF above, it will be treated as a raw signal similar to 14

r1 (t ) = x(t ) − c1 (t ). (11)

4) Then, treating r1(t) as a raw signal similar to x(t), and the second, the third until the n order IMF can be calculated by repeating the above steps, which can be noted as c2(t), c3(t), …, cn(t). The iterative process will not end until it satisfies some criterion, and the last residual signal is rn(t). Thus, the primary raw signal x(t) can be decomposed into a collection of IMFs and a residual signal, which is shown as: n

x(t ) = ∑ ci (t ) + rn (t ). (12)

i =1

Then, after applying the Hilbert transform to each IMF, the result is 1 ∞ c (τ ) c i (t ) = ∫ i dτ . (13) π −∞ t − τ

The analytical function zi(t) is calculated as:

2 EMPIRICAL MODE DECOMPOSITION Empirical mode decomposition is an effective timefrequency tool for processing non-stationary or nonlinear vibration signals, which can decompose a signal into a collection of intrinsic mode functions (IMFs), each of which can be linear or nonlinear. There are two conditions that each IMF must satisfy [11]: a) the number of extrema (maxima and minima) must be equal to the number of zero crossing points or differ at most by one; b) at any point, the mean value of the envelope defined by the local maxima and the one defined by the local minima is zero. The procedure of EMD can be described as: 1) All the local extrema in the raw signal x(t) are sought out and the maxima should be connected using a cubic spline line, and the same with the local minima. Then, the upper and lower envelopes arise, as well as the mean value m(t) of the above envelopes. 2) Subtracting the mean envelope m(t) from x(t), h1(t) can be shown as:

c1 (t ) = h1 (t ). (10)

zi (t ) = ci (t ) + j ⋅ c i (t ) = ai (t ) ⋅ e jφi (t ) . (14)

where the amplitude function, i.e. the envelope of ci(t), is ai (t ) = ci (t ) 2 + c i (t ) 2 . (15)

The phase function can be described as: c i (t ) φi (t ) = arctan . (16) ci (t )

Then the instantaneous frequency of each IMF is shown as: dφ (t ) ωi (t ) = i . (17) dt 3 TESTING AND ANALYSIS OF WIND TURBINE GEARBOX In a wind farm in Inner Mongolia, China, maintenance technicians observed intense noise in a wind turbine gearbox when making a routine inspection. Therefore, vibration testing was carried out on this fixed-pitch and fixed-speed wind turbine, whose nominal output power was 600 kW.

Teng, W. – Wang, F. – Zhang, K.L. – Liu, Y.B. – Ding, X.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 12-20

Although force measurement with simple signal processing showed the effectiveness in identifying the fault rating and fault type of bearing [23], it cannot be applied to the sealed wind turbine gearbox, because there are no spaces provided to install force transducers. In this case, acceleration measurement was adopted; this is commonly used to monitor and diagnose gear faults. The acceleration transducer is based on piezoelectric effect, with a dynamic response range from 0.1 to 10000 Hz, a resonance frequency about 30000 Hz, and a sensitivity of 500 mV/g. Theoretically, the acceleration transducers should be installed on the location with maximum casing deformation to obtain excellent testing performance, however, modal analysis for casing is necessary; this will enhance computational complexity. Therefore, setting aside the question of the best transducer location, we glued four acceleration transducers on the casing of the gearbox from low- to high-speed stages, which are shown as Figs. 1a and b. The vibration signals from acceleration transducers are transferred to data acquisition system and then to a host computer through Ethernet. The data acquisition system is shown in Figs. 1c and d; it has a 14-bit analogue-todigital converter. In order to obtain a wide frequency band, the sample frequency is 16384 Hz, and the cutoff frequency of the anti-aliasing filter is 7000 Hz.

Fig. 1. Test system on field wind turbine gearbox; a) two transducers in the front of the gearbox, b) two transducers in the rear of the gearbox, c) data acquisition system, d) data analysis and processing

3.1 Structure of Wind Turbine Gearbox A wind turbine gearbox is a device that converts the low rotational speed of turbine’s rotor into the high speed of generator. The structure of the tested wind

turbine gearbox is shown in Fig. 2; it consists of a onestage planetary gear and two-stage ordinary gears.

Fig. 2. Structure of wind turbine gearbox 1-casing, 2-sun gear, 3-turbine’s rotor, 4-planetary arm, 5-ring gear, 6-planetry gear; there are a total of three planets in all, 7-sun shaft, 8-wheel, 9-middle shaft, and 10-high-speed shaft

The multistage transmissions in a wind turbine gearbox can be divided into three parts, which can be seen as the planetary stage, middle stage and highspeed stage in Fig. 3. Among which, Zs denotes the number of sun gear teeth, Zp denotes the number of planet teeth, Zc denotes the number of ring gear teeth, Zmi denotes the number of drive gear teeth in the middle stage, Zmo denotes the number of non-drive gear teeth in the middle stage, Zhi denotes the number of drive gear teeth in the high-speed stage and Zho denotes the number of non-drive gear teeth in the highspeed stage. From Fig. 3, it can be determined that the rotational speed of the planetary arm in the gearbox is equal to that of the turbine’s rotor, that the planetary gear is driven by the arm and meshed with the sun gear and the ring gear, and the sun gear and wheel (8) in Fig. 2 are concentric. The mechanical power generated from turbine rotation is first transferred to the sun shaft through the planetary stage, then to the middle shaft through the middle stage, and finally to the high-speed shaft through the gear mesh of the high-speed stage, which is connected with the shaft of generator. The numbers of teeth in wind turbine gearbox are listed in Table 1. Table 1. The numbers of teeth of multiple gears in wind turbine gearbox Zp 43

Zs 21

Zc 117

Pitting Fault Detection of a Wind Turbine Gearbox Using Empirical Mode Decomposition

Zmi 68

Zmo 20

Zhi 54

Zho 21

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3.2 Hilbert Demodulation Analysis

Fig. 3. Definition of multistage transmissions in wind turbine gearbox

The rotational speed of turbine’s rotor is 26.8 rpm, and the total transmission ratio of the gearbox is 56.56. The relative feature frequencies of vibration signal from the gearbox are calculated as follows: the shaft rotational frequency is: f n = n / 60. (18)

The mesh frequency of ordinary gear is: f z = nZ / 60, (19)

and the mesh frequency of planetary gear is:

f z = na Z c / 60, (20)

where n denotes a certain shaft’s rotational speed whose unit is rpm, Z denotes the number of the ordinary gear teeth, na denotes the rotational speed of the planetary arm, and Zc denotes the number of the ring gear teeth. From Eqs. (18) to (20), it is possible to calculate multistage shaft rotational frequencies and gear mesh frequencies in the wind turbine gearbox, shown in Table 2.

Gear crack or pitting in a gearbox leads to a modulation phenomenon, which takes the gear mesh frequency, gear natural frequency, or casing natural frequency as a carrier frequency, and takes the rotational frequency of the shaft fixed with defective gear as the modulation frequency. In order to identify the defective gear, Hilbert demodulation analysis is adopted. At first, a modulation signal is separated from the raw signal through a band-pass filter; next, the modulation signal is processed using the Hilbert transform to obtain the modulation frequencies that are characteristic of the fault. The time vibration signals of four acceleration transducers are shown in Fig. 4. The vibration amplitude of first transducer fixed on the planetary stage of the gearbox is shown in Fig. 4a, which is obviously smaller than other transducers due to the low rotational speed of the turbine’s rotor. From the time signals in Fig. 4, little fault information about the gearbox can be determined. Consequently, the time signals in the frequency domain are converted using the Fourier transform, and the results of the second transducer are shown in Fig. 5. The linear power spectrum density (PSD) in Fig. 5b and the logarithmic power spectrum density in Fig. 5c both represent the mesh frequency (195 Hz) of the middle stage and its harmonics, which show greater vibration energy in the middle stage than others. For the obvious modulation phenomenon in Fig. 5c (shown as enclosed in ellipse),

Table 2. Shaft rotational frequencies, gear mesh frequencies Rotational frequency Rotor Sun shaft Middle shaft High-speed shaft Mesh frequency Planetary stage Middle stage High-speed stage

Frequency [Hz] 0.447 2.9 9.8 25.3 Frequency [Hz] 52.32 196.39 530.25

Fig. 4. Time vibration signals from the four acceleration transducers; a) the first, b) the second, c) the third and d) the fourth

Teng, W. – Wang, F. – Zhang, K.L. – Liu, Y.B. – Ding, X.

StrojniĹĄki vestnik - Journal of Mechanical Engineering 60(2014)1, 12-20

two 6-order Butterworth band-pass filters are used to process the time signals, and the cut-off frequencies are 820, 972, 1500 and 1800 Hz, respectively. Next, the Hilbert transform is used to analyse the filtered time signals, and the envelopes with corresponding PSD are shown in Figs. 6 and 7, respectively. Fig. 6b distinctly shows the rotational frequency of the high-speed shaft and its harmonics. The analogous result arises in Fig.7b, in which the humps represent the rotational frequency of the middle shaft and its harmonics. The demodulated frequencies (rotational frequency of the high speed and middle shaft) and harmonics in Figs. 6 and 7 show that the gears in the high-speed stage can be faulty or even fail. Fig. 5. Time signal from the second transducer and its PSD; a) time signal, b) linear power spectrum density and c) logarithmic power spectrum density

Fig. 6. The results after band-pass filtering with cut-off frequency 1500 and 1800 Hz; a) envelope of filtered time signal, and b) envelope spectrum

Fig. 7. The results after band-pass filtering with cut-off frequency 820 and 972 Hz; a) envelope of filtered time signal, and b) envelope spectrum

3.3 Vibration Analysis Based on EMD Next, the vibration signal is decomposed from the second transducer using EMD without the modulation frequency band (enclosed in ellipse) considered in Fig. 5c. The decomposition process is carried out according to Eqs. (9) through (17). The first four IMFs are listed in Fig. 8, and the corresponding envelope spectra of the IMFs are shown in Fig. 9. The rotational frequency of the high-speed shaft and its harmonics are visible in IMF1, as is the rotational frequency of the middle shaft in IMF2, which shows that EMD can extract the modulation frequency automatically without pre-processing as with Hilbert demodulation analysis. Considering occasionality in the above single group of vibration signal, 57 groups are gathered each minute over the course of about one hour and processed based on EMD. The span of each group signal is one second. The waterfall map of the first IMFâ&#x20AC;&#x2122;s envelope spectrum is shown in Fig. 10. The rotational frequency of the high-speed shaft and its harmonics are clearly visible throughout, which confirms that the defective gear exists in the highspeed stage. In Fig. 10, the amplitudes of the feature frequencies fluctuate distinctly along groups axis due to the varying speed and load of stochastic wind in one hour, while the feature frequencies almost remain unchanged along the frequency axis because of the characteristics of fixed pitch and fixed speed of the wind turbine. For future study, a quantitative index denoting the fault level of the defective gear for wind turbine gearbox under varying speed and alternating load will be a significant issue. Fifty-seven groups of vibration signal are analysed using the Hilbert demodulation; the results are shown as in Fig. 11. In the first 15 minutes, the wind speed

Pitting Fault Detection of a Wind Turbine Gearbox Using Empirical Mode Decomposition

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 12-20

Fig. 10. Waterfall map of the first IMFs after EMD from 57 groups of vibration signal

Fig. 8. The first four IMFs of vibration signal from the second transducer

Fig. 11. Waterfall map of the 57 groups of vibration signal using Hilbert demodulation with the cut-off frequency 1500 and 1800 Hz of band-pass filter

Fig. 9. The envelope spectra of the first four IMFs of vibration signal from the second transducer

is 8.5 to 10.7 m/s, which generates lager excitation energy than speeds of 5.5 to 6.3 m/s in the following 42 minutes. Although the wind speed is varied, the rotational speed of wind turbine remains steady at about 26.8 r/min due to the stalling characteristics of fixed pitch blades. The lager excitation energy in the first 15 minutes caused the resonance range (modulation frequency band) of the gearbox to deviate from 1500 to 1800 Hz. Therefore, for the first 15 groups, the multi-harmonic components of high 18

speed shaft cannot be demodulated effectively using the band-pass filter with cut-off frequencies 1500 and 1800 Hz. In contrast, due to the resonance range between 1500 and 1800 Hz in the later 42 minutes, the Hilbert demodulation can still obtain multi-harmonic components of the high-speed shaft. Compared with the Hilbert demodulation analysis as shown in Fig.11, EMD is more adaptive to obtain better demodulation effect in Fig. 10, especially for the first 15 groups. To be precise, the cut-off frequency of the band-pass filter in the Hilbert demodulation requires human selection and it is difficult to obtain the optimal value. EMD can extract the fault feature frequency more adaptively, and be independent of the selection of the modulation frequency band. Only the vibration signal of the second transducer is studied above; the other three ones should be discussed. Next, the vibration signals from all the four acceleration transducers are analysed using EMD.

Teng, W. – Wang, F. – Zhang, K.L. – Liu, Y.B. – Ding, X.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 12-20

The first IMFs and corresponding envelope spectra are shown in Fig. 12. Due to the larger distance from the first transducer location to the high-speed stage gear pair, the envelope spectrum in Fig. 12a has no fault features about 25.3 Hz and its harmonics. In Figs. 12b and d, there are components of 25.3 Hz and its harmonics distinctly in the second transducer and the forth transducer. As for the third transducer in Fig. 12c, the envelope spectrum of the first IMF represents fewer fault features than Figs. 12b and d. The reason may be that the third transducer is installed on the ribbed slab of the casing where it is not overly sensitive to the excitation of the high-speed stage.

Fig. 13. Pitting in high-speed stage of wind turbine gearbox

4 CONCLUSION The Hilbert demodulation analysis is an effective tool for detecting faults in a wind turbine gearbox; however, this method relies on human intervention to select the modulation frequency band of the bandpass filter. An empirical mode decomposition can decompose the vibration signal of field gearbox and extract the fault feature frequency from an intrinsic mode function adaptively. In this paper, EMD is successfully applied to detect gear pitting faults in a wind turbine gearbox. Due to its better adaptability, EMD can be intelligently used as a powerful tool of fault diagnosis in the wind turbine gearbox. 5 ACKNOWLEDGEMENTS Fig. 12. The first IMFs and their envelope spectra from the four transducers; a) the first, b) the second, c) the third, and d) the forth

3.4 Discussion about Fault Cause Observing the inner condition from the peephole of the wind turbine gearbox, we determined that the two gears of the high-speed stage were seriously affected by pitting, shown as in Fig. 13. After consultation with field technicians, a reason was determined. Because the effect of thermal expansion was not considered when assembling the high-speed shaft of the gearbox with the shaft of generator, an inherent error arose due to the high temperature and high speed during the actual operation of gearbox. Therefore, the high-speed shaft of gearbox was off-centre or bent, which can cause pitting and wear in the gears at the high-speed stage.

The research presented in this paper was supported by National Natural Science Foundation of China (No. 51305135), the Fundamental Research Funds for the Central Universities of China (No. 12MS06) and the Key Lab of Advanced Transducers and Intelligent Control System (Taiyuan University of Technology), Ministry of Education, Taiyuan, China (No. 201305). 6 REFERENCES [1] Ribrant, J., Bertling, L.M. (2007). Survey of failures in wind power systems with focus on Swedish wind power plants during 1997-2005. IEEE Transactions on Energy Conversion, vol. 22, no. 1, p. 167-173, DOI:10.1109/ TEC.2006.889614. [2] Liu, W.Y., Tang, B.P., Jiang, Y.H. (2010). Status and problems of wind turbine structural health monitoring techniques in China. Renewable Energy, vol. 35, no. 7, p. 1414-1418, DOI:10.1016/j.renene.2010.01.006. [3] Wang, J.J., Gao, R.X., Yan, R.Q. (2013). Multiscale enveloping order spectrogram for rotating machine health diagnosis. Mechanical Systems

Pitting Fault Detection of a Wind Turbine Gearbox Using Empirical Mode Decomposition

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and Signal Processing, in Press, DOI:10.1016/j. ymssp.2013.06.001. [4] Li, B., Li, J.M., Tan, J.Y. (2012). AdSR based fault diagnosis for three-axis boring and milling machine. Strojniski vestnik - Journal of Mechanical Engineering. vol. 58, no. 9, p. 527-533, DOI:10.5545/ sv-jme.2011.272. [5] Do, V.T., Chong, U.P. (2011). Signal model-based fault detection and diagnosis for induction motors using features of vibration signal in two-dimension domain. Strojniski vestnik - Journal of Mechanical Engineering. vol. 57, no. 9, p. 655-666, DOI:10.5545/ sv-jme.2010.162. [6] Barszcz, T., Randall, R.B. (2009). Application of spectral kurtosis for detection of a tooth crack in the planetary gear of a wind turbine. Mechanical Systems and Signal Processing, vol. 23, no. 4, p. 1352-1365, DOI:10.1016/j.ymssp.2008.07.019. [7] Yang, W., Tavner, P.J., Wilkinson, M.R. (2009). Condition monitoring and fault diagnosis of a wind turbine synchoronous generator drive train. IET Renewable Power Generation, vol. 3, no. 1, p. 1-11, DOI:10.1049/iet-rpg:20080006. [8] Tang, B.P., Liu, W.Y., Song, T. (2010). Wind turbine fault diagnosis based on Morlet wavelet transformation and Wigner-Ville distribution. Renewable Energy, vol. 35, no. 12, p. 2862-2866, DOI:10.1016/j. renene.2010.05.012. [9] Mohanty, A.R., Kar, C. (2006). Fault detection in a multistage gearbox by demodulation of motor current waveform. IEEE transactions on Industrial Electronics, vol. 53, no. 4, p. 1285-1297, DOI:10.1109/ TIE.2006.878303. [10] Amirat, Y., Benbouzid, M.E.H., Al-Ahmar, E., Bensaker B., Turri S. (2009). A brief status on condition monitoring and fault diagnosis in wind energy conversion systems. Renewable and Sustainable Energy Reviews, vol. 13, no. 9, p. 2629-2636, DOI:10.1016/j. rser.2009.06.031. [11] Huang, N.E., Shen, Z., Long, S.R. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London Series, vol. 454, p. 903-995, DOI:10.1098/rspa.1998.0193. [12] Loutridis, S.J. (2004). Damage detection in gear systems using empirical mode decomposition. Engineering Structures, vol. 26, no. 12, p. 1833-1841, DOI:10.1016/j.engstruct.2004.07.007. [13] Liu, B., Riemenschneider, S., Xu, Y. (2006). Gearbox fault diagnosis using empirical mode decomposition and Hilbert spectrum. Mechanical Systems and Signal

Processing, vol. 20, no. 3, p. 718-734, DOI:10.1016/j. ymssp.2005.02.003. [14] Rai, V.K., Mohanty, A.R. (2007). Bearing fault diagnosis using FFT of intrinsic mode functions in Hilbert-Huang transform. Mechanical Systems and Signal Processing, vol. 21, no. 6, p. 2607-2615, DOI:10.1016/j.ymssp.2006.12.004. [15] Yu, D.J., Yang, Y., Cheng, J.S. (2007). Application of time-frequency entropy method based on HilbertHuang transform to gear fault diagnosis. Measurement, vol. 40, no. 9-10, p. 823-830, DOI:10.1016/j. measurement.2007.03.004. [16] Cheng, J.S., Yu, D.J., Tang, J.S. (2008). Application of frequency family separation method based upon EMD and local Hilbert energy spectrum method to gear fault diagnosis. Mechanism and Machine Theory, vol. 43, no. 6, p. 712-723, DOI:10.1016/j. mechmachtheory.2007.05.007. [17] Ricci, R., Pennacchi, P. (2011). Diagnostics of gear faults based on EMD and automatic selection of intrinsic mode functions. Mechanical Systems and Signal Processing, vol. 25, no. 3, p. 821-838, DOI:10.1016/j.ymssp.2010.10.002. [18] Feng, Z.P., Zuo, M.J., Qu, J.(2013). Joint amplitude and frequency demodulation analysis based on local mean decomposition for fault diagnosis of planetary gearboxes. Mechanical Systems and Signal Processing, vol. 40, no. 1, p. 56-75, DOI:10.1016/j. ymssp.2013.05.016. [19] Zhang, X.Y., Zhou, J.Z. (2013). Multi-fault diagnosis for rolling element bearings based on ensemble empirical mode decomposition and optimized support vector machines. Mechanical Systems and Signal Processing, vol. 41, no. 1-2, p. 127-140, DOI:10.1016/j. ymssp.2013.07.006. [20] McFadden, P.D. (1986). Detection fatigue cracks in gears by amplitude and phase demodulation of meshing vibration. Journal of Vibration and Acoustics, vol. 108, no. 4, p. 165-170, DOI:10.1115/1.3269317. [21] Fan, X.F., Zuo, M.J. (2006). Gearbox fault detection using Hilbert and wavelet packet transform. Mechanical Systems and Signal Processing, vol. 20, no. 4, p. 966982, DOI:10.1016/j.ymssp.2005.08.032. [22] Feldman, M. (2011). Hilbert transform in vibration analysis. Mechanical Systems and Signal Processing, vol. 25, no. 3, p. 735-802, DOI:10.1016/j. ymssp.2010.07.018. [23] Slavic, J., Brkovic, A., Boltezar, M. (2011). Typical bearing-fault rating using force measurementsapplication to real data. Journal of Vibration and Control, vol. 17, no. 14, p. 2164-2174, DOI:10.1177/1077546311399949.

Teng, W. – Wang, F. – Zhang, K.L. – Liu, Y.B. – Ding, X.

Original Scientific Paper

Received for review: 2012-12-11 Received revised form: 2013-03-11 Accepted for publication: 2013-07-05

Surface Integrity Characterization Based on Time-Delay of the Magnetic Barkhausen Noise Voltage Signal Žerovnik, P. – Fefer, D. – Grum, J. Pavel Žerovnik1 – Dušan Fefer2 – Janez Grum1,*

1 University

of Ljubljana, Faculty of Mechanical Engineering, Slovenia of Ljubljana, Faculty of Electrical Engineering, Slovenia

2 University

The captured magnetic Barkhausen noise (BN) signal is composed of a series of voltage impulses changes produced by movements of the magnetic domains. In most cases the captured voltage signals cannot be directly related to individual parameters to assess the material state, i.e. the properties, of the surface layer. For further efficient analysis of the voltage signals, an appropriate method for signal processing should be chosen in order to use the characteristic value of the voltage signal. Our method of processing represents the time delay of a BN voltage signal, i.e. the maximum voltage value of the signal, with reference to the sine wave of the magnetizing current. Measurement of the time delays of the voltage signals was carried out under optimum magnetizing conditions, which gave us the greatest number of voltage impulses in the signal. These are influenced by the turns and orientation of the magnetic domains. The aim of this research was to compare the voltage-signal time delay obtained with quenched and tempered specimens at two neighbouring temperatures. The temperature differences ranged from ∆T1 = 10 °C, up to ∆T2 = 25 °C. These small temperature differences in the tempering-temperature produced small differences in the micro hardness of the individual specimens and found out whether there were significant differences between micro hardnesses. The assessment of the reliability of the prediction of micro hardness was carried out using the Student’s t-test. Keywords: micro-magnetic method, Barkhausen noise, time delay of the voltage signal, micro hardness, Student‘s t-test, reliability

0 INTRODUCTION Many authors have reported different methods of measuring and processing the captured Barkhausen noise (BN) voltage signals in their research. Jiles and Suominen [1] found that micro-hardness and residual stresses were determined from the captured voltage signal of Barkhausen noise according to the measured depth. They found that at the same analyzing frequency and given specific electric conductivity and relative permeability of the material, a smaller depth of the micro magnetic change was obtained and vice versa. Wojtas and Suominen [2] and [3] stated that the X-ray measurement method is a reliable method for residual stress characterization, but it is slow and appropriate only for laboratory conditions. On the other hand, the magnetic Barkhausen noise (MBN) technique is fast and based on calibration curves for the determination of residual stresses. Savaş and Gür [4] studied non-destructive evaluation of surface residual stresses in shot peened steel components using the magnetic Barkhausen noise method. For this purpose, various sets of steel specimens were prepared by a controlled shot peening process with different intensities, impact angles and coverage values. The measurements showed that a clear relationship exists between surface residual stresses and the Barkhausen noise signals. Grum and Žerovnik [5] also assessed the residual stresses in

steel 1C40 that had been hardened and tempered. The assessment of the efficiency of the determination of residual stresses by the micro-magnetic method based on the BN was carried out by means of measurement of residual stresses using the relaxation method. Comparative through-thickness measurements showed that the micro-magnetic method was suitable for the determination of residual stresses since it gives a real-time variation of residual stresses in a thin surface layer of the material concerned in a very short time. Žerovnik et al. [6] assessed the microstructure, hardness, and residual stresses on induction surfacehardened specimens. The most commonly chosen feature of the BN is the square mean value of the voltage signal V2RMS. Desvaux et al. [7] studied ultrasonic shot peening, which allows for control of the introduction of residual stresses on the raceways and increases the fatigue resistance of the bearings. The level of residual stresses that are introduced can be verified by BN at any point on the bearing raceway surface and subsurface and guaranteed to 100% on a complete manufacturing lot. Kikuchi et al. [8] determined the magnetic BN energy and the peak in the V2RMS voltage signal reflects the number of pinning sites for domain wall motion. These therefore rise sharply in an initial stage of cold rolling and almost saturate at a higher reduction ratio. On the contrary, the coercive force and the magnetizing current at the peak in the V2RMS

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

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voltage increase monotonically due to the increase in dislocation density below 10% and the formation of the cell structure. Žerovnik and Grum [9] discovered that the microstructure and micro hardness have a significant effect on the relative permeability µr and measurement depth z. The results showed that the damping of the micro magnetic parameter with depth reaches its maximum in the soft specimen, and vice versa. Lo et al. [10] studied the effects of microstructural variations with depth on the Barkhausen effect (BE) signals in surface-modified ferrous materials through measurements and simulations based on a hysteretic-stochastic model. Theoretical analysis showed that the model parameters, which describe the domain-wall pinning strength and the range of interaction of a domain wall with pinning sites, are related to each other. Pepelnjak and Barišič [11] have measured the strains occurring during sheet material plastic deformation using an optical measurement system. The strains were measured up to the tearing limit in order to determine the forming limit diagram using the Marciniak testing method. Due to the plane strain problem and fixing the focus distance between the observed sheet metal surface and the lens, only one charge-coupled device (CCD) camera was used. Sablik et al. [12] presented one model of the effect of plastic deformation on magnetoacoustic emission (MAE), where one must first treat the non-180deg domain wall motion. In this paper, they take the Alessandro-Beatrice-BertottiMontorsi (ABBM) model and modify it to treat non180deg wall motion. They then insert a modified stress-dependent Jiles-Atherton model, which treats plastic deformation, into the modified ABBM model to treat MAE and MBN. An experimental study by Vashista and Paul [13] was undertaken to investigate the role of process parameters on the grindability of medium carbon steel in a high-speed grinding domain with particular emphasis on surface integrity. Surface residual stress on the ground specimens has been assessed using X-ray diffraction techniques and BN analysis. High-speed grinding with cubic boron nitride (CBN) wheels, unlike conventional grinding, provided compressive residual stress throughout the experimental domain. This can be attributed to the desirable temperature control since the single layer CBN wheel had higher thermal conductivity than conventional wheels and grinding fluid took away a substantial part of the grinding heat flux. Micromagnetic or BN parameters correlated linearly with the residual stress, indicating its applicability in assessing the surface integrity of high-speed ground steel. Koomatsubara et al. [14] captured the BN of soft 22

ferrites and silicon steels. The experimental data are discussed in terms of the relevant quantities: saturation flux density (Bs), conductivity sigma, cross-sectional area of samples (SO) and grain diameter (d). At low field velocities mod (H), magnetization processes are dominated by independent displacements of 180 degrees walls. The peak noise power (Pm) in the vicinity of the coercive field is proportional to the field velocity mod (H) mod. These two simple results reflect nonoverlapping Barkhausen pulses. Krause et al. [15] compares the anisotropy of surface MBN and the pulse height distributions between two samples of oriented 3% Si-Fe steel laminate at equivalent flux densities. Differences between the two samples were observed in the anisotropic behavior of the MBN-Energy and pulse height distributions for flux density amplitudes between 1.3 and 1.6 T, the typical operating range of transformer laminates. These were attributed to differences in the number and structure of the 180° domain walls. Schneider et al. [16] studied the surface acoustic waves as a means of evaluating surface-hardened steels. A generalized dispersion curve was calculated using the theory of the surface acoustic wave to deduce the hardening depth from the velocity. Using this methodology, it was found that the hardening depth could be determined with an error not higher than 15%. 1 EXPERIMENTAL SET-UP For these investigations an experimental setup was arranged to capture voltage signals of the MBN. It consisted of a magnetisation unit, a sensor for capturing voltage signals, a signal amplifier with a relevant band-pass filter, and a computer-aided unit for determination of the microstructure or micro hardness and residual stresses. Fig. 1 shows a block scheme of the experimental setup for micromagnetic testing based on the BN.

Fig. 1. Experimental setup for capturing the voltage signal of the magnetic Barkhausen noise

Žerovnik, P. – Fefer, D. – Grum, J.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 21-28

In the analysis of the BN at the chosen depth, it was important to filter the BN voltage signals. A frequency filter provided a signal of the voltage induced in the measuring coil sensing the changes during the process of specimen magnetization. Thus a Butterworth filter of the fourth order was applied in a series connection with a low-pass and high-pass filter of the second order. Thus, in the experimental setup, four different band-pass Butterworth filters of the fourth order pass signals in different frequency ranges.

very fine feathers of cementite in the ferritic matrix (Fig. 2c).

2 THE ANALYZED MATERIAL AND SELECTION OF OPTIMAL MAGNETIZING PARAMETERS In our research, we used 1C55 heat-treated carbon steel with a 0.58% carbon content, which is used in the production of various machine parts exposed to heavy loading. Table 1. Chemical composition of steel 1C55 [wt.%] C Si Mn Cr Ni Cu Al Sn Mo V Ti 0.58 0.26 0.63 0.10 0.15 0.28 0.02 0.013 0.03 0.01 0.002

For this purpose, ferromagnetic steel bands of 150×30×5 mm were subjected to three types of heat treatment: • Soft-annealed specimens, annealed at a temperature of TSA = 690 °C, with an average microhardness of 224 HV0.2. • Specimens quenched in oil at a temperature of TH = 850 °C, with an average micro hardness of 803 HV0.2. • Specimens quenched in oil at a temperature of TH = 850 °C, tempered to a temperature of TT = 300 °C, with an average micro hardness of 511 HV0.2. After different heat treatments of steel 1C55 we obtained different structural changes and different profiles of micro hardness. At the soft annealed temperatures TSA = 690 °C, a fine pearlite-ferrite microstructure forms. The size and density of the coagulated cementite in the pearlite grains determine steel hardness after heat treatment (Fig. 2a). The specimens quenched in oil at a temperature of TH = 850 °C show a microstructure of fine tetragonal martensite (Fig. 2b). With the specimens quenched in oil at a temperature of TH = 850 °C and tempered to a temperature of TT = 300 °C, martensite will disintegrate into a bainite microstructure. Thus, the bainite microstructure shows

Fig. 2. The microstructure and micro hardness of individual heat-treated 1C55 steel specimens; a) soft annealed, b) quenched in oil, c) quenched and tempered

Before initiating these experiments, it was necessary to select the optimum magnetization parameters. Various magnetization parameters affect the shape of the signals captured and the number of voltage impulses in the signal. In the first phase, the number of voltage impulses in the voltage signal was determined as a function of the magnetizing frequency (fe), and the magnetizing current (I). The experimental work accomplished hitherto indicates that voltage signals having a higher density of voltage impulses provide more useful data on the material.

Fig. 3. Density of voltage impulses in the signal as a function of the magnetizing frequency and constant magnetizing current

The Barkhausen voltage signals were captured from soft annealed 1C55 carbon steel at a temperature

Surface Integrity Characterization Based on Time-Delay of the Magnetic Barkhausen Noise Voltage Signal

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 21-28

TSA of 690 °C. Fig. 3 shows the number of voltage impulses in the signal as a function of the magnetizing frequency and a constant magnetizing current. Fig. 4 shows the number of voltage impulses in the signal as a function of the magnetizing current and a constant magnetizing frequency. The diagrams in Figs. 3 and 4 indicate that the density of impulses in the voltage signal is reduced if the magnetizing frequency and the magnetizing current increase and vice versa.

the sinusoidal of the magnetizing current. In the first phase, we sketched out an envelope of the captured voltage signal of BN. The time delay was measured from the highest point of the envelope (which also represents the area with the highest voltage impulses) to the sinusoidal of magnetizing current, as shown in Fig. 5.

Fig. 5. Definition of the time delay of the BN voltage signal with reference to the sinusoidal of the magnetizing current

Fig. 4. Density of voltage impulses in the signal as a function of the magnetizing current and constant magnetizing frequency

3 PROCESSING THE BN VOLTAGE SIGNAL ON THE BASIS OF TIME DELAYS The captured BN voltage signal is composed of a series of voltage impulses. In the first phase the voltage impulses rise as they near the centre of the voltage signal and then decrease in the same manner toward zero. Changes in voltage impulses are caused by the movements of magnetic domains. The whole captured voltage signal of an MBN is unstationary. In limited parts of the voltage signal the stationary can be defined as stationary in the narrow or the wide part of the signal. In the central part of the captured voltage signal we can assume the stationary in wide range. This means that when evaluating the voltage signal it is sufficient that the first two central moments (arithmetic mean of the signal mx2 and signal variance σ2) are time independent. In most cases the captured voltage signals cannot be directly related to individual parameters to assess the state, i.e. properties, of the surface layer. For further efficient analysis of the voltage signals, an appropriate method for signal processing should be chosen in order to use the characteristic value of the voltage signal. In the analysis of the captured voltage BN signals we noticed various time delays according to 24

We found that different magnetizing parameters, as the current of the material, affected the size of the time delays. In the analysis of the magnetizing parameters we focused on the two most important ones, which were the magnetizing current I and the magnetizing frequency fe. The current of the material is affected by heat treatment with consequent changes in microstructure and hardness, in the mechanical treatment with cutting, on the level of plastic deformation and so on. The plot of the envelope of the voltage signal and the measurement of time delays from the sinusoidal of the magnetizing current were carried out with computer aid. 3.1 The Influence of Various Magnetizing Parameters on the Time Delays of BN Signals Figs. 6 and 7 show the time delays of the voltage signals with different magnetization parameters. We need to change both the magnetizing current and the magnetizing frequency fe. Fig. 6 shows the time delay of the signals captured with different magnetizing current intensities and a constant magnetizing frequency fe of 2.5 Hz. The longest time delays are obtained with the lowest magnetizing current intensities so that with a current intensity I of 0.25 A, the time delay t equals 4.70 ms. The shortest time delay t, i.e. 0.80 ms, is obtained with a magnetizing current I of 3 A. Fig. 7 shows the time delays of the signals as a function of different magnetizing frequencies and a constant magnetizing current. Higher magnetizing

Žerovnik, P. – Fefer, D. – Grum, J.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 21-28

frequencies produce shorter time delays so that with a frequency fe of 10 Hz a time delay t of 1.40 ms is obtained whereas with a lower frequency fe, i.e. 2.5 Hz, the time delay t of the signal is considerably longer, i.e. 4.70 ms.

Fig. 6. Variation in the time delays of the maximum voltage values of BN signals as a function of different magnetizing current intensities and constant magnetizing frequency

•

the highest density of voltage impulses is obtained with a magnetizing frequency f of 2.5 Hz and a magnetizing current I of 0.25 A and • the longest time delays t, i.e. 4.70 ms, are obtained with a magnetizing frequency f of 2.5 Hz and a magnetizing current I of 0.25 A (to a specimen in the soft annealed state). Data on time delays of the voltage signals, including the calculated mean values and data on microhardness are given in Table 2. The data indicate that there are differences in the time delays of the individual specimens in different states. For the specimens with higher hardness, a longer time delay is obtained and vice versa.

Table 2. Mean values of the time delays of the voltage signals with data on microhardness for the individual heat treated specimens Micro hardness HV0.2

Time delays (mean values) t [ms]

Quenched, TH = 850 ºC

803

13.1

Quenched and tempering TH = 850 ºC, TT = 300 ºC

511

9.3

Soft annealed, TSA = 690 ºC

224

4.7

Heat treatments

Fig. 8 shows microhardness HV0.2 of the specimens in three different states as a function of time delays of the voltage signals.

Fig. 7. Variation of time delays of the maximum amplitude values of BN signals as a function of different magnetizing frequencies and constant magnetizing current

3.2 The Influence of Heat Treatment on the Time Delay of Voltage Signals We continued our research with the measurement of time delays of voltage signals. The measurements were performed on specimens that were heat treated with consequent change in microstructure and micro hardness (Fig. 2). Measurement of the time delays of the voltage signals was carried out under optimum magnetization conditions. The optimum magnetization conditions are the ones giving the highest number of voltage impulses in the signal. They are influenced by the turns and orientation of the magnetic domains. Based on the given criteria related to the density of impulses in the BN voltage signal and the length of time delays of the signal, it can be stated that:

Fig. 8. Microhardness as a function of time delays from specimens of steel 1C55 in three different states

Results of the statistical analysis between the time delays of the voltage signals and the corresponding hardness are very favourable since the calculated correlation coefficient rt/HV is equal to 0.989. 4 DETERMINATION OF THE MICRO HARDNESS AND RELIABILITY ASSESSMENT Determination of the micro hardness is based on a calibration curve. The calibration of the experimental system and elaboration of the calibration curves were

Surface Integrity Characterization Based on Time-Delay of the Magnetic Barkhausen Noise Voltage Signal

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followed by measurements, and later a classification of the specimens with an unknown state. The calibration procedure and determination of micro hardness by means of the calibration curve is shown in Fig. 9. The left part of Fig. 9 shows the procedure for elaborating the calibration curves using etalons with a known micro hardness, whereas the right part shows the procedure for testing an unknown specimen, i.e. determination of the characteristics of the surfacehardened layers. The time delay was measured from the highest point of the envelope (which also represents the area with the highest voltage impulses) to the sinusoidal of the magnetizing current. The plot of the envelope of voltage signal and the measurement of time delays from sinusoidal of magnetizing current were carried out with computer aid. The data indicate that there are differences in the time delays of the individual specimens in different states. For the specimens with higher hardness, a longer time delay is obtained and vice versa. The following findings can be stated: • When measuring specimens with an unknown micro hardness or unknown specimens, a suitable calibration curve determined on the basis of a preliminary measured micro hardness after heat treatment should be selected; • A suitable calibration curve having been selected, measurement is carried out on the specimens with an unknown micro hardness. The time delays are then measured. By means of the calibration curve, the corresponding micro hardness value is determined. The analysis of the results obtained made it possible to determine the reliability of the assessment of micro hardness of a given specimen based on the time delay of the voltage signal captured. The assessment of the reliability of predicting micro hardness was carried out using the Student’s t-test. Micro hardness measurement reliability analysis was conducted on the hardened and tempered specimens. For each high-tempering temperature three specimens were available. Three measurements were taken for each specimen, which means that nine measurements at the same tempering temperature were performed. The aim of the research was to compare the voltage-signal time delay obtained with the quenched and tempered specimens at two neighbouring temperatures. The temperature differences ranged from ∆T1 = 10 °C, up to ∆T2 = 25 °C. The second aim of the research was to distinguish small differences in the micro hardness of the two neighbouring specimens 26

and to find out whether there were significant differences.

Fig. 9. Determination of micro hardness by means of calibration curves

In the study the quenched and tempered specimens tempered from TT1 = 300 °C to TT5 = 400 °C were used. Four different tempering temperatures rising gradually by 25 °C were chosen. Fig. 10 shows envelopes of the voltage signals captured from the samples in different states. The first envelope with a time delay t = 4.85 ms belongs to the quenched specimen in oil from TH = 850 °C and with the tempering temperature TT = 400 °C. The last envelope with a time delay t = 9.30 ms belongs to the quenched specimen in oil from TH = 850 °C and with the tempering temperature TT = 300 °C. The harder specimens show a lower and flatter envelope with a longer time delay with regard to the sinusoidal of the magnetizing current and vice versa.

Fig. 10. Voltage signal envelopes for quenched and tempered specimens at different temperature

In Table 3 the comparative results of the micro hardness significance of the neighbouring temperatures are given for four different neighbouring tempering-temperature pairs only. A confidence limit was determined and hypotheses were chosen on the basis of the calculation of significance for the

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Table 3. Test of micro hardness significance for different neighbouring tempering-temperature pairs (∆T2 = 25 °C) Neighbouring tempering temperature (TT1 = 300 °C to TT2 = 325 °C) (TT2 = 325 °C to TT3 = 350 °C) (TT3 = 350 °C to TT4 = 375 °C) (TT4 = 375 °C to TT5 = 400 °C)

Micro hardness from calibration curves (time delay) (H1 = 511 / H2 = 482) (H2=482 / H3 = 464) (H3 = 464 / H4 = 439) (H4 = 439 / H5 = 415)

Significance a = 2P 0.000924 0.000382 0.000049 0.000013

Limit of confidence P

Results

0.05 0.05 0.05 0.05

(H1 ≠ H2) (H2 ≠ H3) (H3 ≠ H4) (H4 ≠ H5)

Table 4. Comparative results of micro hardness significance for neighbouring tempering-temperature pairs (∆T1 = 10 °C) Neighbouring tempering temperature H (TT1 = 300 °C – TT2 = 310 °C) H (TT2 = 310 °C – TT3 = 320 °C) H (TT3 = 320 °C - TT4 = 330 °C) H (TT4 = 330 °C - TT5 = 340 °C) H (TT5 = 340 °C – TT6 = 350 °C) H (TT6 = 350 °C – TT7 = 360 °C) H (TT7 = 360 °C - TT8 = 370 °C) H (TT8 = 370 °C - TT9 = 380 °C) H (TT9 = 380 °C - TT10 = 390 °C) H (TT10 = 390 °C - TT11 = 400 °C)

Micro hardness from calibration curves (time delay) (H1=511 / H2=486) (H2=486 / H3=478) (H3=478 / H4=480) (H4=480 / H5=462) (H5=462 / H6=458) (H6=458 / H7=451) (H7=451 / H8=443) (H8=443 / H9=434) (H9=434 / H10=421) (H10=421 / H11=415)

individual tempering temperatures. All of the first four results of significance were lower than the chosen limit of confidence (0.00092; 0.00038; 0.00004; 0.00001 < 0.05), which indicates that a hypothesis on the equality of the micro hardness among the tempering temperatures chosen was rejected and there were significant differences between the micro hardness chosen. In Table 4 comparative results of micro hardness significance are given for neighbouring temperingtemperature pairs. Tempering temperatures rose gradually by 10 °C between two neighbouring specimens. Most of the results of significance in Table 4 were higher than the chosen limit of confidence, which means that the differences in the micro hardness between the two neighbouring specimens were insignificant. 5 CONCLUSION The time delays are defined between the sinusoidal of the magnetizing current and the maximum amplitudes of the BN voltage signals. Statistical analysis was applied to the assessment of the reliability of micro hardness prediction, based on the time delays of the voltage signals. The aim of the research was to produce small differences in micro hardness of the individual specimens and to find out whether there were significant differences. In addition to the assessment of reliability the power of the statistical

Significance a = 2P 0.04876 0.23940 0.46178 0.04124 0.74187 0.25892 0.52365 0.41278 0.32785 0.95387

Limit of confidence P 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05

Results (H1 ≠ H2) (H2 = H3) (H3 = H4) (H4 ≠ H5) (H5 = H6) (H6 = H7) (H7 = H8) (H8 = H9) (H9 = H10) (H10 = H11)

relationship between the time delays and micro hardness in the entire tempering-temperature range was assessed. The statistical analysis provided the following findings: • The time delays of the captured BN voltage signal is a good estimator of the micro hardness of the 1C55 heat-treated carbon steel, which is indicated by the high values of the calculated correlation coefficients (rt˝/HV0.2 = 0.989). • The temperature differences ranging by ∆T2 = 25 °C give us significant differences in micro hardnesses, determined from the time delays, between neighbouring tempering-temperature pairs. • The temperature differences ranging by ∆T1 = 10 °C show mostly insignificant differences in micro hardnesses, determined from time delays, between neighbouring tempering-temperature pairs. • The results of the micro hardness assessed from the time delay of the BN differ from the average by 16 HV from the measured Vickers hardness. We estimated that this new micro magnetic method of signal processing is fast, reliable, repeatable and represents a successful estimator for determining the micro hardness of the steel 1C55 in different states.

Surface Integrity Characterization Based on Time-Delay of the Magnetic Barkhausen Noise Voltage Signal

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 21-28

6 REFERENCES [1] Jiles, D.C., Suominen, S. (1994). Effects of surface stress on barkhausen emissions, model predictions and comparison with X–ray diffraction studies. IEEE Transactions on Magnetics, vol. 30, no. 6, p. 49244926, DOI:10.1109/20.334267. [2] Wojtas, A. (2004). Surface and subsurface residualstresses after shot peening-their qualitative and quantitative analysis by X-Ray diffraction and Barkhausen noise analysis. Metal Finishing News, Wetzikon. [3] Suominen, L., Tiitto, K. (1994). Use of X-ray diffraction and Barkhausen noise for the evaluation of stresses in shot peening. Proceedings of 4th International Conference on Residual Stresses, Baltimore, p. 443448. [4] Savaş, S., Gür, H. (2010). Monitoring variation of surface residual-stresses in shot peened steel components by the magnetic Barkhausen noise method. Insight, vol. 52, no. 12, p. 672-677. [5] Grum, J., Žerovnik, P. (2000). Use of the Barkhausen Effect in the Measurement of Residual Stresses in Steel. Insight, vol. 42, no. 12, p. 796-800. [6] Žerovnik, P., Grum, J., Žerovnik, G. (2010). Determination of hardness and residual-stress variations in hardened surface layers with magnetic barkhausen noise. IEEE Transactions on Magnetics, vol. 46, no. 3, p. 3221-3224, DOI:10.1109/TMAG.2009.2032417. [7] Desvaux, S., Gualandri, J., Carrerot, H. Lamare, A. (2003). Industrial application process of impruvement of the high precision bearings service life – prestress, Barkhausen noise. International Conference on Barkhausen Noise and Micromagnetic Testing ICBM, p. 49-62. [8] Kikuchi, H., Ara, K., Kamada, Y., Kobayashi, S. (2009). Effect of microstructure changes on Barkhausen noise properties and hysteresis loop in cold rolled low carbon steel. IEEE Transactions on Magnetics, vol. 45, no. 6, p. 2744-2747, DOI:10.1109/TMAG.2009.2020545.

[9] Žerovnik, P., Grum, J. (2009). Determination of residual stresses from the Barkhausen noise voltage signal, 10th International Conference of the Slovenian Society for Non-Destructive Testing, Ljubljana, p. 437-445. [10] Lo, C.C.H., Kinser, E. R., Jiles, D.C. (2006). Analysis of barkhausen effect signals in surface - modified magnetic materials using a hysteretic-stochastic model. Journal of Applied Physics, art. no. 08B705, DOI:10.1063/1.2163272. [11] Pepelnjak, T., Barisic, B. (2009). Computer-assisted engineering determination of the formability limit for thin sheet metals by a modified Marciniak method. Journal of Strain Analysis, vol. 44, no. 6, p. 459-472, DOI:10.1243/03093247JSA503. [12] Sablik, M.J., Augustyniak, B., de Campos, M.F., Landgraf, F. (2008). Modeling of effect of plastic deformation on Barkhausen noise and magnetoacoustic emission in iron with 2% silicon. IEEE Transactions on Magnetics,vol. 44, no. 1, p. 3221-3224, DOI:10.1109/ TMAG.2008.2002803. [13] Vashista, M., Paul, S. (2008). Study of the effect of process parameters in high-speed grinding on surface integrity by Barkhausen noise analysis. Journal of Engineering Manufacture, vol. 222, no. 12, p. 16251637, DOI:10.1243/09544054JEM1214. [14] Koomatsubara, M., Porteseil, J.L., Nakamura, H. (1988). Comparison of Barkhausen noise power between soft ferrites and silicon steels. IEEE Transactions on Magnetics, vol. 24, no. 2, p. 17041706, DOI:10.1109/20.11576. [15] Krause, T.W., Szpunar, J.A., Atherton, D.L. (2003). Anisotropic flux density dependence of magnetic Barkhausen noise in oriented 3% Si-Fe steel laminates. IEEE Transactions on Magnetics, vol. 44, no. 1, p. 562566, DOI:10.1109/TMAG.2002.806352. [16] Schneider, D., Hofmann, R., Schwarz, T., Grosser, T., Hensel, E. (2012). Evaluating surface hardened steels by laser-acoustics. Surface & Coatings Technology, vol. 206, p. 2079-2088, DOI:10.1016/j. surfcoat.2011.09.017.

Žerovnik, P. – Fefer, D. – Grum, J.

Original Scientific Paper

Received for review: 2012-07-24 Received revised form: 2013-04-22 Accepted for publication: 2013-05-13

Corrosion Analysis of Friction Stir-welded AA 7075 Aluminium Alloy Elatharasan, G. – Senthil Kumar, V.S. Govindaraj Elatharasan – Velukkudi Santhanam Senthil Kumar* Anna University, College of Engineering, Guindy, India Friction stir-welding of AA7075 has become widely practiced in the fabrication of light-weight structures requiring high strength-to-weight ratios and superior corrosion resistance. The friction stir-welding (FSW) process and tool parameters play a key role in determining the joint’s characteristics. In this paper, the corrosion resistance of a friction stir-welded alloy was studied via polarization and electrochemical impedance spectroscopy in 3.5% NaCl. The microstructure of different positions along the thickness of the aluminium alloy plate has been investigated with regard to varying parameters, including rotary speed and transverse speed. The heat-affected zones of the weld exhibited the highest susceptibility to inter-granular corrosion. The results also show that sound joints in AA7075 can be achieved using friction stirwelding. Corrosion resistance decreases with the increase of traverse speed from 0.37 to 0.76 mm/s at a rotary speed of 800 rpm. Corrosion resistance at a rotary speed of 1000 rpm is lower than that at 1200 rpm; an increase in the corrosion resistance may also be reached via the breaking down and dissolution of the inter-metallic particles. Keywords: friction stir-welding, aluminium alloy, AA7075, corrosion

0 INTRODUCTION Friction stir-welding (FSW), a new solid-state joining technique, was invented by The Welding Institute (TWI) [1]. This technique avoids the formation of solidification cracking and porosity. Moreover, it significantly improves the weld properties and has been extensively applied in joining light metals [2], especially aluminium and its alloys. FSW is ideal for joining aluminium alloys; especially the AA2000 and AA7000 series [3]. High-strength aluminium alloys, such as 7XXX, are commonly used in aerospace applications due to their light weight and high strength. These alloys are difficult to weld using conventional fusion welding and are typically joined though FSW [4]. Friction stir-welding has been successfully used in joining primary structures in the Eclipse 500™ jet [5]. The corrosion properties of FSW in 2XXX, 5XXX and 7XXX series aluminium alloys have been studied by a number of authors [6,7]. For highstrength alloys, such as 7075, the heat-affected zones of the weld exhibit the highest susceptibility to intergranular corrosion, which correlates with copper depletion along the grain boundaries [8]. An analysis was conducted on the welded surfaces instead of the section [9], taking into account that the surface is the part more exposed to the environment. Corrosion being a surface phenomenon, an approach of reducing or removing these second phase particles from the surface can be adopted. In such a situation, the corrosion resistance of the alloy is expected to be improved. The composition of the micro-constituents (i.e. their size, quantity, location, continuity and

corrosion potential relative to that of the adjacent α-Al matrix) is the decisive aspect of microstructure that affects the corrosion behaviour of the alloy [10]. Recent work on AA2024 T351 [11] showed the correlation between welding parameters (rotation speed and travel speed) on the corrosion behaviour and the precipitation of the age-S phase, while for the 7XXX alloys, changes in electrochemical behaviour have been attributed to the precipitation of the η phase. The corrosion behaviour of FSW aluminium alloys has been studied in recent years [12]. Generally, it has been found that the weld zones are more susceptible to corrosion than the parent metal. Buchheit [13] and Paglia [14] evaluated stress corrosion cracking susceptibility of friction stirwelded 7050-T7451 and 7075-T651, using the SSRT method in a NaCl solution. Peening techniques, such as shot and laser peening, can be helpful in mitigating the surface residual stresses, and therefore enhance the fatigue properties and SCC. Trdan et al. [15] confirmed that the specimens of AlMgSiPb alloy after corrosion testing were shown to be a more corrosion resistant material with a smaller number of pits than AlSi1MgMn aluminium alloy. Oosterkamp et al. [16] identified that the role of the tool pin in friction stir-welding is to shear the material to its back side during the translation of the tool, and the inserted rotating pin brings the material at both sides of the joint line to the plastic state, aided by the frictional heat input of the shoulder. Elangovan et al. [17] identified that the triangular pin profiled tool showed almost matching tensile properties to that of square pin followed by threaded, taper and straight cylindrical pins, respectively.

*Corr. Author’s Address: Dprt. of Mechanical Engineering, College of Engineering Guindy, Anna University, Chennai 600025, Tamilnadu, India, vsskumar@annauniv.edu

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 29-34

In this study, the corrosion properties of the friction stir-welded 7075-T6 aluminium alloy plates have been investigated by polarization and electrochemical impedance spectroscopy in 3.5% NaCl. The root side of the weld exhibited the highest susceptibility to inter-granular corrosion. 1 EXPERIMENTAL PROCEDURE

uses a non-consumable threaded tool made of heattreated high carbon steel with a shoulder diameter of 18mm by 6mm pin diameter and length 5.7mm. The hardness value was 60 HRC, and the tool nomenclature is shown in Fig. 2. Rotational speeds and traverse speeds are varied in this study. Three rotational speeds (800, 1000 and 1200 rpm) and two traverse feeds (0.37 and 0.76 mm/s) were used.

Aluminium alloy AA7075-T6 (Al–Zn–Mg–Cu), for which T6 heat treatment consists of being solution heat treated and artificially aged at 190°C for 12 h, and H321 denotes a strain hardened and stabilized condition, with the alloy approximating the quarterhard state after the thermal stabilization treatment. AA7075-T6 is one of the strongest aluminium alloys currently in industrial use. Table 1. Chemical composition [wt. %] of base metal AA7075

Mg 2.1

Mn 0.12

Zn 5.1

Fe 0.35

Cu 1.2

Si 0.5

Cu 1.2

Al bal

Table 2. The mechanical properties of base metal

AA7075

Young modulus [GPa] 71

Yield strength [MPa] 469

Tensile strength [MPa] 578

Elongation [%] 11

Fig. 2. Friction stir-welding tool nomenclature

The alloy derives its strength from precipitation of Mg2Zn and Al2CuMg phases. The chemical composition of the AA7075- T6 alloy [16] (by weight percentage) given in Table 1. The yield and tensile strengths are given in Table 2.

Fig. 3. Microstructure of the parent metal

Fig.1. Friction stir-welding operation

Plates having the dimensions of 50×100×6 mm (width×length×thickness) were friction stir-welded. The samples were friction stirred with an indigenously developed machine. The process is shown in Fig.1; it 30

Fig. 3 shows the microstructure of the AA7075-T6 alloy, revealing the presence of an insoluble (Fe, Mn)Al6 alloy formed along the direction of rolling. Among the elongated grains of aluminium solid solution, some fine precipitates of Mg2Si were also seen. Fig. 4 shows a photo-micrograph of the interface junction of the AA7075-T6 alloy on one side and the weld FSW zone. On the other side, the direction of the

Elatharasan, G. – Senthil Kumar, V.S.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 29-34

grain changed due to the spinning action of the tool in AA7075-T6 alloy. The left side shows the weld metal that has fragmented particles of Mg2Si. FSW samples of 1×1 cm were cut from the plate after making slices 1 cm thick. A 3.5% sodium chloride solution was used in this study. Electrochemical measurements were made using the Solartron electrochemical system (Model 1280 B).

The aluminium alloy was mechanically polished with 1/0, 2/0, 3/0 emery papers and then dipped in a 5% NaOH solution for 2 minutes to activate the surface. After this stage, the samples were cleaned with cleaning powder to remove the black smudge formed over the surface, washed thoroughly with running water and then dipped in a concentrated HNO3 solution for 30 seconds. 2 CHARACTERIZATION STUDIES AND RESULTS 2.1 Tafel Polarization

Fig. 4. Microstructure of the stir zone

The 1280B electrochemical workstation provides the combined facilities of an electrochemical interface (ECI) and a frequency response analyser (FRA). The ECI can be used either as a potentiostat or galvanostat with selectable control loop bandwidth to ensure stable operation for various types of cells. The FRA provides a precision signal generator and an analyser for measuring cell impedance data. When used with Z Plot for Windows, it offers a complete range of EIS (Electrochemical Impedance Spectroscopy) techniques, including AC impedance and harmonic analysis. The use of CorrWare with the 1280B allows all standard DC electro analytical analysis techniques to be programmed, including electrochemical noise. A7075 alloy was used as the working electrode in the conventional three-electrode assembly with platinum foil as counter electrode and saturated calomel electrode (SCE) as reference electrode. For the electrochemical impedance tests, the samples were immersed in the electrolyte for 30 minutes before the test. The samples were exposed in such a way that only the nugget was subjected to the corrosion tests and the rest of the areas were masked. EIS measurements were carried out in the frequency range of 10 kHz to 0.01 Hz.

Fig. 5 shows the typical polarization curves of the samples to find the pitting corrosion resistance. Anodic polarization curves were obtained by exposing the nugget area alone to 3.5% NaCl solution at different welding parameters. The material of the stir zone shows a classic passive region with current density, which is practically independent of applied potential up to pitting potential Epit forming the passive film, which protected the Al alloy from corrosion. AA 7075 surface studies were carried out by passing a fixed current for a fixed duration of time. In this regard, current densities of 15 and 20 mA/cm² were applied, and the corresponding potential transients were recorded for a period of 1 hour. 2.2 Electrochemical Impedance Measurements Electrochemical Impedance Spectroscopy (EIS) a.c. signals of 20 mV amplitude and various frequencies varying from 10 kHz to 0.01Hz at open circuit potentials were imposed on the aluminium alloy; the nugget was exposed to a 3.5% NaCl solution, and the results were plotted in Fig. 5. From the impedance plots, the charge transfer resistance (Rct) and the double layer capacitance (Cdl) values were calculated using ZsimpWin 3.21 software with an equivalent circuit, where Rs is the solution resistance. In most cases, k is found to be in an order of 0.012 to 0.03V. The charge transfer resistance Rct is a measure of the corrosion rate and is calculated as [18]: icor = (ba * bc) / [2.3 (ba + bc) Rct ] = k/ Rct , where icor is a corrosion current, ba an anodic Tafel slope, and bc a cathodic Tafel slope. Using the above relationships, the corrosion reactions are determined via Tafel polarisation methods.

Corrosion Analysis of Friction Stir-welded AA 7075 Aluminium Alloy

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 29-34

Table 3. Corrosion values on AA 7075 alloy

BM RSFSW CSFSW

Impedance method Charge transfer Double layer resistance capacitance Rct [Ωcm2] Cdl [µF/cm2] 2915 21 7426 25 4444 14

Anodic Tafel slope ba [mV] 10.241 10.040 19.250

Polarization method Cathodic Tafel Corrosion slope current bc [mV] icor [µA/cm2] -523.10 32 -823.91 42 -883.78 12

Corrosion potential Ecor [V] –0.80786 –0.87038 –0.84334

BM = Base Metal, RSFSW= Root side FSW

3 DISCUSSION 3.1

Corrosion Behaviour

3.1.1

Tafel Polarization Test

Tafel polarization tests were carried out to determine the pitting corrosion resistance. Anodic polarization curves were obtained by exposing only the nugget area to a 3.5% NaCl solution. icor is the corrosion current density derived by extrapolating the anodic and cathodic Tafel lines at Ecor in the absence of inhibitor. It is found that the corrosion potential Ecor and icor values (as shown in Table 3 on the different welding position) were shifted to a more anodic direction from the bottom (Ecor = 0.84334 V, icor = 12 µA/cm²) to the top (Ecor = 0.87038 V, icor = 42 µA/cm²) of WNZ (Weld Nugget Zone), and t along the thickness of WNZ in a 3.5 wt.% NaCl solution at different welding parameters. The polarization resistance decreases from the top to the bottom.

3, which clearly shows a slight improvement in the corrosion resistance. The low frequency impedance indicates the corrosion resistance of the surface. In Fig. 7, it is observed that the top has higher impedance than that of the bottom, because the semicircle radius of Nyquist plot is as follows: Top > Middle > Bottom. As expected, the lower traverse speed samples present higher impedance than that exhibited by the higher traverse speed in the same solution. Fig. 6 shows polarization resistance and a corrosion current density curve for different positions of pitting resistance has improved in all parameters compared to the base material (Ecor = 0.80786 V and icor = 32 µA/cm2).

3.1.2 Electrochemical Impedance Spectroscopy Electrochemical Impedance Spectroscopy (EIS) results of the FSW on AA 7075-T6 with 1200 rpm with 3.7 mm/s alloy in 3.5% NaCl. In the case of Tafel polarization, the scanning of potential was done from −0.2V vs. OCP to +0.2V vs. OCP at a scan rate of 1mV/s. From this anodic and cathodic polarization curves, the Tafel regions were identified and extrapolated to Ecor to obtain the corrosion potential icor, using the Corr View software. In the case of electrochemical impedance spectroscopy, a.c. signals of 20 mV amplitude and various frequencies from 10 kHz to 0.01 Hz at open circuit potentials were impressed to the aluminium alloys. The impedance plots are shown in Fig. 5. It shows the effect of air ageing in the Nyquist representation of complex impedance. The charge transfer resistance (Rct) and double layer capacitance (Cdl) obtained from these curves is CSFSW = Crown side FSW. given in Table 32

Fig. 5. Impedance behaviour of friction stir-welded AA 7075 alloy at 20 mA for 1 h in 3.5% NaCl

It can also be easily seen that the susceptibility of material corrosion resistance decreases with an increase of traverse speed from 0.37 to 0.76 mm/s at rotary speed of 800 rpm. Corrosion resistance at rotary speed 1000 rpm is lower than that at 1200 rpm. However, the corrosion resistance decreases with increasing rotary speed due to bigger second-phase particles of Al–Cu–Fe–Zn in the weld.

Elatharasan, G. – Senthil Kumar, V.S.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 29-34

Fig. 6. Effect of the polarization curves for AA 7075 at 20 mA for 1 h in 3.5% NaCl

Fig. 7. EIS curves of friction stir-welded AA 7075 alloy for 1 h in 3.5% NaCl

3.2 Microstructural Studies The micro-structural analysis of the friction stirwelded samples after corrosion was carried out with a scanning electron microscope (SEM) as shown in Fig. 8.

Fig. 8. Scanning Electron Micrograph of FSW AA7075 after Corrosion

The samples were etched using Keller’s reagent to reveal the grain boundaries. FSW AA7075-T6 samples were air-dried and observed within a few minutes after being removed from the test solution.

Observation of welded areas of FSW AA 7075-T6 samples showed an initial stage of inter-granular corrosion on a heat-affected zone with the attack of the precipitate-free zones. Note that the presence of small white grain boundary precipitates and the attack of the precipitates-free zone (black). Pitting corrosion usually occurs in the Al matrix near Cu or Fe inter metallic particle. This acts in a cathodic manner to the AA7075 alloy matrix or at Al-Mg-Zn particles, which acts anodic in 3.5% NaCl solution. 4 CONCLUSION This investigation shows improvement in the corrosion resistance of FSW in AA7075-T6 exposed to a 3.5% NaCl solution at room temperature. The findings of this study can be summarized as follows: 1. FSW AA 7075-T6 alloy surface morphological evaluation in the 3.5% NaCl by electrochemical impedance spectroscopy and potentiodynamic polarization exhibited exceptionally high corrosion protection performance. 2. The microstructure presents dynamically recrystallized and fine-equiaxed grain structure. The sizes of second-phase particles Al–Cu–Fe– Zn increase from the top to the bottom. The Al– Cu–Fe–Zn size increases with the increase in the traverse speed. 3. The localized pitting attack is generally associated with second phase particles. Pits may either initiate near an Al–Cu–Fe–Zn particles, which act catholically to the 7075 alloy matrix, or at Al–Mg–Zn particles, which act anodically to the matrix, thereby preferentially corroding in the 3.5% NaCl solution. The fatigue resistance of the corroded specimens drastically decreased in comparison with the parent metal due to material pitting corrosion. 4. The electrochemical test results indicate that the top of weld has the highest icor and Ecor, which are helpful in inhibiting corrosion attack, but the base material has smallest icor and Ecor in all specimens. The maximum polarization resistance and minimum corrosion current density were on top of the weld. According to the EIS measurements and the simulated results by the equivalent circuits, the impedance values are in a sequence of: Top > Middle > Bottom. The improvement in corrosion resistance correlates well with the increase in grain-boundary precipitate size.

Corrosion Analysis of Friction Stir-welded AA 7075 Aluminium Alloy

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 29-34

5 REFERENCES [1] Thomas, W.M., Nicholas, E.D. (1997). Friction stir welding for the transportation industries. Materials and Design, vol. 18, no. 4-6, p. 269-273, DOI:10.1016/ S0261-3069(97)00062-9. [2] Matrukanitz, R.P. (1990). Selection and weldability of heat-treatable aluminium alloys. ASM HandbookWelding, Brazing and Soldering, vol. 6, p. 528-536. [3] Balasubramanian,V.,Lakshminarayanan, A.K. (2008). The mechanical properties of the GMAW, GTAW and FSW joints of the RDE-40 aluminium alloy. International Journal of Microstructure and Materials Properties, vol. 3, no. 6, p. 837-853, DOI:10.1504/ IJMMP.2008.022618. [4] Thomas, W.M., Nicholas, D., Needham, J.C., Murch, M.G., Templesmith, P., Dawes, C.J. (1991). Friction-stir butt welding, GB Patent No. 9125978.8, International patent application, South Wales. [5] Eclipse Aviation, section on Innovation in Eclipse500 aircraft from http://www.eclipseaviation.com/about/ innovations, accessed at: 2012-03-12. [6] Paglia, C.S., Buchheit, R.G. (2008). A look in the corrosion of aluminium alloy friction stir welds. Scripta Materialia, vol. 58, no. 5, p. 383-387, DOI:10.1016/j. scriptamat.2007.10.043. [7] Hannour, F., Davenport, A., Strangwood, M. (2000). Corrosion of friction stir welds in high strength aluminium alloys. 2nd International Symposium on Friction Stir Welding, Gothenburg. [8] Lumsden, J.B, Mahoney, M.W, Pollock, G., Rhodes, C.G. (1999). Intergranular corrosion following friction stir welding of aluminum alloy 7075-T651. Corrosion Science, vol. 55, no. 12, p. 1127-1135, DOI:10.5006/1.3283950. [9] Zucchi, F., Trabanelli, G., Grassi, V. (2001). Pitting and stress corrosion cracking resistance of friction stir welded AA5083. Materials and Corrosion, vol 52, p. 853-859, DOI:10.1002/1521-4176(200111)52:11<853::AIDMACO853>3.0.CO;2-1. [10] Dix, E.H.Jr. (1946). Corrosion of light metals (aluminum and magnesium). Corrosion of Metals. American Society for Metals. Cleveland.

[11] Jariyaboon, M., Davenport, A.J., Ambat, R., Connolly, B.J., Williams, S.W., Price, D.A. (2007). The Effect of Welding Parameters on the Corrosion Behaviour of Friction Stir Welded AA2024-T351. CorrosionScience, vol. 49, no. 2, p. 877-909 DOI:10.1016/j. corsci.2006.05.038. [12] Wadeson, D.A., Zhou, X., Thompson, G.E., Skeldon, P., Djapic Oosterkamp, L., Scamans, G. (2006). Corrosion behaviour of friction stir welded AA7108 T79 aluminium alloy. Corrosion Science, vol. 48, no. 4, p. 887–897, DOI:10.1016/j.corsci.2005.02.020. [13] Buchheit, R.G., Paglia, C.S. (2004). Localized corrosion and stress corrosion cracking of friction stir welded 7075 and 7050. Corrosion and Protection of Light Metal Alloys. The Electrochemical Society, New Jersey. [14] Paglia, C.S., Buchheit, R.G., (2008). A look in the corrosion of aluminium alloy friction stir welds. Scripta Materialia, vol. 58, no. 5, p. 383-387, DOI:10.1016/j. scriptamat.2007.10.043. [15] Trdan, U., Grum, J. (2012). Evaluation of corrosion resistance of AA6082-T651 aluminium alloy after laser shock peening by means of cyclic polarisation and els methods. Corrosion Science, vol. 59, p. 324-333, DOI:10.1016/j.corsci.2012.03.019. [16] Oosterkamp, A., Djapic Oosterkamp, L., Nordeide, A. (2004). Kissing bond phenomena in solid state welds of aluminum alloys. Supplement to the Welding, vol. 83, no. 8, p. 225S-231S. [17] Elangovan, K., Balasubramanian, V. (2007). Influences of pin profile and rotational speed of the tool on the formation of friction stir processing zone in AA2219 aluminium alloy. Materials Science and Engineering: A, vol. 459, no. 1-2, p. 7-18, DOI:10.1016/j. msea.2006.12.124. [18] Baldwin, K.R., Robinson, M.J., Smith, C.J.E. (1994). The Corrosion Behaviour of Electrodeposited Zinc– Nickel Alloy Coatings on Exposure to the Marine Atmosphere, vol. 3, p. 165–175, The Chameleon Press, London.

Elatharasan, G. – Senthil Kumar, V.S.

Received for review: 2013-01-28 Received revised form: 2013-06-27 Accepted for publication: 2013-08-23

Original Scientific Paper

Optimization of a Product Batch Quantity Berlec, T. – Kušar, J. – Žerovnik, J. – Starbek, M. Tomaž Berlec* – Janez Kušar – Janez Žerovnik – Marko Starbek University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Companies encounter various challenges when entering the global market, one of the most significant being the calculation of the optimal batch quantity of a product. This paper explains how to calculate the optimal batch quantity using first the basic model, and then the extended model that takes into account the tied-up capital in a production, in addition to the costs of changing the batch and storage costs. There is a case study of calculating the optimal batch quantity using the basic and extended models, together with conclusions regarding when either of the two models should be used. For optimal batch quantities we also calculated lead times, corresponding costs of tied-up capital per piece, and the difference between costs per piece when using the basic and extended models. Keywords: optimal batch, tied-up capital, storage costs, time per unit, setup time, lead time, turnaround time, interoperation time

0 INTRODUCTION The goal of calculating the optimal batch quantity of a product is that the product is produced in the required quantity and required quality at the lowest cost [1] to [3]. There are basically two options of planning the batch quantity [4]: • planning a large batch of a product in long intervals, • planning a small batch of a product in short intervals. The advantages of planning a large batch of product are: • price advantage of ordering a large batch (low cost, protection against raising prices, volume rebate), • lower administrative costs, • lower costs of tests and shipping, • low risk of interruption of production because of the large stock. The disadvantages of planning a large batch are: • high tied-up capital, • high storage costs of product inventory. The advantages of planning a small batch of product are: • low tied-up capital, • low storage costs of product inventory, • high flexibility if quantities change at suppliers and buyers. The disadvantages of planning a small batch are: • the costs of frequent ordering, • high risk of interruption of production because of a small product inventory. Somewhere between the large and small batch quantity is the optimal batch quantity, i.e. the quantity in which the cost per product unit is the lowest.

Aggterleky [4] describes the optimal planning planes and the meaning of under- and over planning, and the influence of the reduction of total cost. Wiendahl [5] uses Harris and Andler’s equation for the determination of the optimal quantity. Härdler [6] takes into account the costs of storage and delivery in determining the optimal batch quantity. Muller [7] and Piasecki [8] assert that inventory management is explained only with the basics of an optimal quantity calculation. So, in comparison to the aforementioned papers, where only the determination of the optimum quantity is given, our model is expanded to include the impact of the flow time on the batch quantity or stock. 1 ECONOMIC ORDER QUANTITY – BASIC MODEL Changing the product batch (hereinafter referred to as ‘order’) causes two types of costs [9]: • order change costs, • storage costs. Order change costs include costs for preparing documentation, costs of control and input of goods, costs of workers’ wages, costs of setting up the machines, and costs of producing samples. The order, therefore, causes annual costs, known as order change costs SMen. The higher the ordered quantity is, the lower the influence of the order change costs is (Fig. 1a). The order also causes storage costs, which include the costs of interest on the bound capital and warehouse costs. The order therefore also causes annual storage costs SSkl, which increase proportionally as the ordered quantity increases (Fig. 1b). The sum of the annual order change costs and storage costs has the minimum value of the total costs SVso,min at the optimal batch quantity xOpt (basic model) (Fig. 1c).

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

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 35-42

Fig. 1. a) order change costs, b) Storage costs of order, c) Optimal batch quantity xOpt in the basic model

The optimal batch quantity in the basic model [6] and [7] can be calculated by using the following sequence of steps:

Step 1: Calculation of annual order change costs: L S Men = ⋅ sMen , (1) x

where SMen are annual order change costs [€/a], L annual needs [piece/a], x batch quantity [piece], and sMen order change costs [€]. Step 2: Calculation of annual storage costs: Pulse inflow and steady outflow of goods is assumed (Fig. 2). The annual storage costs depend on the warehouse inventory: x S Skl = ⋅ sObd ⋅ p, (2) 2 where SSkl are storage costs [€/a], x batch quantity [piece], sObd processing costs per piece [€/piece], and p interest rate of tied-up capital [1/a]. Step 3: Calculation of total annual order costs: xOpt:

SVso = S Men + S Skl =

L x ⋅ sMen + ⋅ sObd ⋅ p. (3) 2 x

Step 4: Calculation of economic order quantity

The economic order quantity (i.e. the minimum value of this function) can be found by differentiation. 36

Fig. 2. Storage inventory of goods

Differentiating SVso with respect to x and then equating to zero, we get:

d SVso s ⋅p L = − 2 ⋅ sMen + Obd = 0. dx x 2 The optimal batch quantity xOpt:

xOpt =

2 ⋅ L ⋅ sMen sObd ⋅ p

, (4)

where xOpt are optimal batch quantity [piece], L annual needs [piece/a], sMen order change costs [€], sObd

Berlec, T. – Kušar, J. – Žerovnik, J. – Starbek, M.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 35-42

processing costs per piece [€/piece], and p interest rate of tied-up capital [1/a]. The interest rate of tied-up capital p is calculated on the basis of the bank interest rate for a long-term loan with additional interest using the VDI 3330 guidelines (Table 1).

the cost of order change SMen and storage costs SSkl, it would also be necessary to take into account the costs of execution of operations of an order in the production SIzv and costs of disposal (transition) SPre.

Table 1. Interest rate of tied-up capital, in [%] A. Bank interest rate for a long-term capital loan Additional interests: limitation losses caused by break or rupture transport storage and write-off warehouse management control insurance B. SUM OF ADDITIONAL INTERESTS INTEREST RATE OF TIED-UP CAPITAL p = A + B

7.15 3 to 5 2 to 4 2 to 4 1.5 to 2 1 to 2 1 to 2 0.5 to 1 11 to 20 18.15 to 27.15

2 ECONOMIC ORDER QUANTITY – EXTENDED MODEL In our basic model for the calculation of optimal batch quantity only the order change costs SMen and storage costs SSkl were taken into account. Analysis of the diagram of the flow of orders through work systems [10] revealed that during the processing of the observed order in a given workplace, other orders have to wait for the release of capacities, which in turn causes additional costs related to the tied-up capital in production (Fig. 3).

Fig. 4. Tying-up the capital in the material flow from supplier to customer

The optimal batch quantity in the extended model * xOpt will be the one in which the sum of annual order change costs, the storage costs, the costs of execution of operations of an order, and the transition costs will have the minimum value (Fig. 5).

* Fig. 5. Optimal batch quantity xOpt in the extended model

Fig. 3. Flow diagram showing inventory of orders

Tying-up the capital in the material flow from a supplier through production to the customer [11] is shown in Fig. 4. After having carried out an analysis of the flow diagram showing the status of orders, and a diagram of tying-up the capital on the path from supplier to customer, Nyhuis and Fronla [12] concluded that when calculating the economic order quantity, in addition to

* The optimal batch quantity xOpt in the extended model is calculated in the following sequence:

Step 1: Calculation of annual order change costs: L * S Men = * ⋅ sMen , x

* where S Men are annual order change costs [€/a], L annual needs [piece/a], x* batch quantity [piece], sMen order change costs [€].

Optimization of a Product Batch Quantity

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 35-42

Step 2: Calculation of annual storage costs: Pulse inflow and steady outflow of goods is assumed (Fig. 3). The annual storage costs are: * S Skl =

L x* ⋅ s + ⋅ sObd ⋅ p + Men x* 2 (s + s ) ⋅ L ⋅ p ⋅ ∑ TIzv + + Mat Obd 2 ⋅ RC (s + s ) ⋅ L ⋅ p + Mat Obd ⋅ ∑ TPr e , 2 ⋅ RC

* SVso =

x* ⋅ sObd ⋅ p , 2

where S Skl are annual storage costs [€/a], x* batch quantity [piece], sObd processing costs per piece [€/ piece], p interest rate of tied-up capital [1/a]. Step 3: Calculation of annual costs of orderprocessing times: The one-dimensional lead time of an order operation, consisting of the turnaround time of the operation TIzv and the interoperation time TPre is shown in Fig. 6 [10].

L x* (8) ⋅ s + ⋅ sObd ⋅ p + Men x* 2 (s + s ) ⋅ L ⋅ p ⋅  T + T . + Mat Obd  ∑ Izv ∑ Pr e  2 ⋅ RC

* SVso =

The material flow rate ST is defined by the Eq (9): ST =

∑T

Izv

+ ∑ TPr e

TIzv

. (9)

Therefore, Eq. (9) can be transformed to:

∑T

Izv

+ ∑ TPr e = ST ⋅ ∑ TIzv . (10)

The total time of the operation-execution of an order is defined as:

∑T

Fig. 6. Lead time of operation; Tp setup time [min], tObd manufacturing time [min], TIzv turnaround time [day], TPre interoperation time [day], TO lead time of operation [day]

Known order-processing times allow for a calculation of annual costs due to operation-execution times S *Izv : S *Izv =

(sMat + sObd ) ⋅ L ⋅ p ⋅ ∑ TIzv , (5) 2 ⋅ RC

Step 4: Calculation of annual costs due to interoperation time: (sMat + sObd ) ⋅ L ⋅ p * S Pr ⋅ ∑ TPr e , (6) e = 2 ⋅ RC * where S Pr e are annual costs due to interoperation time [€/a], and ΣTPre sum of interoperation times [Wd]. * Vso

Step 5: Calculation of total annual costs S 38

=∑

Tp + x* ⋅ te1 60 ⋅ KAP

, (11)

where ΣTIzv is total time of operation execution of an order [day], Tp setup time [min], te1 time per unit [min/ piece], KAP daily capacities [h/day], x* batch quantity [piece]. If Eqs. (10) and (11) are inserted in Eq. (8), the function for calculating the total order-dependent costs is transformed to:

* Izv

where S are annual costs arising from the operationexecution of an order [€/a], sObd processing costs per piece [€/piece], sMat material costs per piece [€/piece], L annual needs [piece/a], p interest rate of tied-up capital [1/a], RC available time [day/a], ΣTIzv total operation-execution time [day].

Izv

x* L ⋅ s + ⋅ sObd ⋅ p + Men x* 2

* SVso =

T + x* ⋅ te1 (sMat + sObd ) ⋅ L ⋅ p , ⋅ ST ⋅ ∑ p 2 ⋅ RC 60 ⋅ KAP

Step 6: Calculation of the economic order * : quantity xOpt * can be The minimum value of the function SVso * with found by differentiation. Differentiating SVso respect to x* and then equating to zero, we get:

* dSVso s ⋅p L ⋅ sMen + Obd + =2 * 2 dx* x

( )

te1 (sMat + sObd ) ⋅ L ⋅ p = 0, ⋅ ST ⋅ ∑ 2 ⋅ RC 60 ⋅ KAP

* * * * SVso = S Men + S Skl + S *Izv + S Pr e , (7)

Berlec, T. – Kušar, J. – Žerovnik, J. – Starbek, M.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 35-42

2⋅ L

(x ) *

⋅ sMen = sObd ⋅ p +

(sMat + sObd ) ⋅ L ⋅ p t ⋅ ST ⋅ ∑ e1 . 60 ⋅ RC KAP

The economic order quantity (i.e. optimal batch quantity) is therefore:

* Opt

2 ⋅ L ⋅ sMen . (12) )⋅L⋅ p te1 sObd ⋅ p + (sMat +60sObd ⋅ ST ⋅ ∑ KAP ⋅RC

* where xOpt is optimal batch quantity [piece], L annual needs [piece/a], sMen order change costs [€], sObd processing costs per piece [€/piece], p interest rate of tied-up capital [1/a], sMat material costs per piece [€/ piece], RC available time [day/a], ST material flow rate, te1 time per unit [min/piece], KAP daily capacities [h/day]. These models are applicable when there is no fluctuation on the relation market-producer. There are neither distributions of production and demand processes considered nor the stochastic character of the mentioned processes.

3 CASE STUDY OF CALCULATING THE OPTIMAL BATCH QUANTITY OF A PRODUCT Company X, which is a supplier to a car components manufacturer, found it increasingly difficult to be competitive on the global market due to excessively long manufacturing lead times and too high product prices. The company’s management organised a creativity workshop [13] to [15] in order to identify urgent measures, whose implementation would improve their market competitiveness. The results of the creativity workshop showed that it would be necessary to do the following in the company: • significantly reduce the inventory in entry and exit warehouses, and on disposal locations within the production, • significantly reduce the lead times of orders. After the presentation of the results of the creativity workshop, management decided that they would first solve the problem of large stocks (i.e. tied-up capital), which significantly raise the price of products (i.e. non-competitiveness) [16] to [18]. A project team was established in the company, in order to analyse the causes of large stocks and to propose possible solutions. Team members analysed inventories in all warehouses. Together with the heads of warehouses

and the planners of production, they concluded that the batch quantities are defined on the basis of the experience of planners (i.e. estimates), which lead either to excessive stocks or a shortage of goods. Product 1: Shield Time per unit: Operations: te1 [min/piece] 10-CNC milling 1.40 20-washing 2.22 30-examination 2.05 40-assembly of the tube 0.30 TOTAL 5.97 Picture of the product

Setup time: Tp [min] 120 15 25 10 170

Picture of the machine

Product 2: Left suspension support Time per unit: Setup time: Operations: te1 [min/piece] Tp [min] 10-CNC milling I 27.50 210 20-CNC milling II 6.50 30 30-examination-measurements 0.50 10 40-assembly of bearings 1.05 15 TOTAL 35.55 265 Picture of the product

Picture of the machine

Fig. 7. te1 and Tp times for shield and suspension support

The project team contacted the experts for help in solving the problem of over- and understocking of goods. Experts suggested that project team could use Eqs. (4) and (12) in order to calculate the optimal batch quantities of products. It was agreed that the project team would calculate the optimal batch quantities by using both equations and find differences between the results of Eq. (4) and Eq. (12), and finally calculate additional annual costs to thus determine the advantages of using the Eq. (4) or Eq. (12).

Optimization of a Product Batch Quantity

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 35-42

The project team decided that the first experimental calculation of the optimal batch quantity would be carried out for two products: • Product 1: Shield; • Product 2: Left suspension support. The project team obtained the following data from the technology routings for both products: • Data on times per unit te1 and setup times Tp (Fig. 7). • Other data, required for calculation of optimal product batch (Table 2), were obtained from various departments in the company.

• basic model:

Product 1 Product 2 226 196 3.65 45.5 1.52

sTo =

1500 250 20 16 3

In order to assess the usability of the basic and extended model for the calculation of optimal batch quantity for both products, the project team decided that it would carry out the following: • Calculation of optimal batch quantity for Products 1 and 2 using the basic and extended model: • basic model: xOpt =

2 ⋅ L ⋅ sMen , sObd ⋅ p

• extended model: •

x*Opt =

2 ⋅ L ⋅ sMen . )⋅L⋅ p te1 sObd ⋅ p + (sMat +60sObd ⋅ ST ⋅ ∑ KAP ⋅RC

Calculation of batch lead times for Products 1 and 2 using the basic and extended model: • basic model: ∑ Tp + te1 ⋅ xOpt , TO = ST ∙ TIzv , TIzv = 60 ⋅ KAP

(

• extended model: * TO* = ST ∙ TIzv* , TIzv =

• 40

)

∑ (T

* + te1 ⋅ xOpt

60 ⋅ KAP

Calculation of costs per product unit using the basic and extended model:

( sMat + sObd ) ⋅ p ⋅ TO

, sPr e =

sObd ⋅ p ⋅ xOpt 2⋅ L

• extended model: * * * sKos = sObd + sTo + sPr* e +

15000 250 20 16 3

sMen , xOpt

where sKos are costs per product unit [€/piece], sTo costs of tied-up capital per product unit during the lead time [€/piece], and sPre costs of tied-up capital per product unit during interoperation time [€/piece],

Table 2. Data from company departments PRODUCT Sum of order changes SsMen [€] Costs of execution per piece SsIzv [€/piece] Costs of material per piece [€/piece] (incorporated in the costs of execution) Annual needs L [piece/a] Available time RC [day/a] Interest rate of tied-up capital p [1/a] Daily capacities KAP [h/day] Material flow rate ST [-]

sKos = sObd + sTo + sPr e +

•

* sTo =

sMen , * xOpt

sObd ⋅ p ⋅ x*Opt (sMat + sObd ) ⋅ p TO* . ⋅ , s*Pr e = 2⋅ L 2 RC

Calculation of difference of costs per product unit:

∆sKos = sKos − s*Kos .

The calculations were made with MS Excel software. The results are shown in Table 3. The project team charted the influence of the batch quantity on the product costs (Fig. 8). The results listed in Table 3 and Fig. 8 led the project team to the following conclusions: • The calculated optimal batch quantities of both products are significantly different from the current estimated batch quantities. Due to this fact, the storage costs are high. • Batch lead times are too long. • The technology routing of Product 1 defines the short times per unit te1; diagrams on Fig. 8 show that at the transition from the basic to the extended model for calculation of the optimal batch quantity, the batch quantity is only slightly reduced and the total costs of tied-up capital are only slightly higher (if the total time te1 is small, the basic model can be used for calculation of optimal batch quantity). • The technology routing of Product 2 defines the long times per unit te1; diagrams on Fig. 8 show that at the transition from the basic to extended model of calculation, the batch quantity is considerably reduced and the total costs of tiedup capital are much higher (if the total time te1

Berlec, T. – Kušar, J. – Žerovnik, J. – Starbek, M.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 35-42

•

is large, extended model must be used for the calculation of optimal batch quantity). The basic model for calculation of optimal batch quantity does not take into account the tying-up of capital in production, and thus the optimal batch quantities are bigger than in the extended model.

Table 3. Results of calculations of optimal batch quantities for both products

Model Basic Extended

Product 2: SUSPENSION SUPPORT Model Basic Extended

Optimal batch quantity x [piece]

3048

1896

255

163

Batch lead time TO [day]

57.40

35.90

38.88

25.25

3.92

3.89

48.20

47.95

CALCULATION

Costs per product unit sKos [€/piece] Difference of costs per product unit SsKos [€/piece]

Product 1: SHIELD

0.03

0.25

At the presentation of results, the company management agreed that the project team would continue its work in order to reduce lead times of orders. 4 CONCLUSION This paper explains how to calculate the optimal batch quantity of a product (production is within the company) using the known basic and developed extended models; the latter, in addition to the costs of changing the batch (i.e. order) and storage costs, also takes into account the costs of interoperation time and the costs of execution of operations. The project team in the company, which is a supplier of car components manufacturer, carried out some experiments, whose results have shown when to use the basic model and when to use the expanded model for the calculation of the optimal batch quantity. Further experiments in electro-mechanical industry will be needed for reliable decision making regarding the selection of the basic or extended model.

Fig. 8. Dependency diagrams costs vs. batch quantity for Products 1 and 2 Optimization of a Product Batch Quantity

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 35-42

The model also needs to be further developed requiring a connection between the optimal quantities procuring materials in warehouses. The company management decided for the project team to carry out also an AS-IS analysis of value flow for existing batch quantities. After a transition to optimal batches, the project team will repeat the value flow analysis for the same two products and find leadtime savings. 5 REFERENCES [1] Heizer, J., Render, B. (2001). Principles of Operations Management, 6th ed., Prentice Hall, Upper Saddle River. [2] Fogarty, W.D., Blackstone, H.J., Hoffman, R.T. (1991). Production and Inventory Management (2nd ed.). Cengale Learning, Stamford. [3] Slack, N., Chambers, S., Harland, C., Harrison, A., Johnson, R. (1995). Operations Management. Pitman Publishing, London. [4] Aggteleky, B. (1990). Fabrikplanung, Band 3, Carl Hanser Verlag, München, Wien. [5] Wiendahl, H.P. (2008). Betriebsorganistion für Ingenieure. Carl Hanser Verlag, München, Wien. [6] Härdler, J. (2012). Betriebswirtschaftslehre für Ingenieure. Carl Hanser Verlag, München, Wien. [7] Muller, M. (2011). Essentials of Inventory Management, 2nd edition, Amacom, New York. [8] Piasecki, D.J. (2009). Inventory Management Explained: A Focus on Forecasting, Lot Sizing, Safety Stock, and Ordering Systems. Ops Publishing, Kenosha. [9] Vollman, E.T., Berry, L.W., Whybark, D.C., Jacobs, F.R. (2005). Manufacturing Planning and Control Systems. McGrow-Hill, New York.

[10] Wiendahl, H.P. (1994). Load-Oriented Manufacturing Control. Springer-Verlag, London. [11] Arnold, D., Furmans, K. (2009). Materialfluss in Logistiksystemen. Springer Verlag, Heidelberg, DOI:10.1007/978-3-642-01405-5. [12] Nyhuis, P., Fronla, P. (2012). Durchlauforientierte Lösgrössenbestimmung, from http://www. enzyklopaedie-der-wirtschaftsinformatik.de/, accessed at 2012-01-19. [13] Rihar, L., Kušar, J., Duhovnik, J., Starbek, M. (2010). Teamwork as a Precondition for Simultaneous Product Realization. Concurrent Engineering: Research and Applications, vol. 18, no. 4, p. 261-273, DOI:10.5545/ sv-jme.2012.420. [14] Kušar, J., Berlec, T., Žefran, F., Starbek, M. (2010). Reduction of Machine Setup Time. Strojniški vestnik – Journal of Mechanical Egineering, vol. 56, no. 12, p. 833-845. [15] Rihar, L., Kušar, J., Gorenc, S., Starbek, M. (2012). Teamwork in the Simultaneous Product Realisation. Strojniški vestnik – Journal of Mechanical Egineering, vol. 58, no. 9, p. 534-544. [16] Buchmeister, B., Pavlinjek, J., Palčič, I., Polajnar, A. (2008). Bullwhip Effect Problem in Supply Chains. Advances in production engineering & management, vol. 3, no. 1, p. 45-55. [17] Palčič, I., Buchmeister, B., Polajnar, A. (2010). Analysis of Innovation Concepts in Slovenian Manufacturing Companies. Strojniški vestnik – Journal of Mechanical Egineering, vol. 56, no. 12, p. 803-810. [18] Božičković, R., Radošević, M., Ćosić, I., Soković, M., Rikalović. A. (2012). Integration of Simulation and Lean Tools in Effective Production Systems – Case Study, Strojniški vestnik – Journal of Mechanical Egineering, vol. 58, no. 11, p. 642-652, DOI:10.5545/ sv-jme.2012.387.

Berlec, T. – Kušar, J. – Žerovnik, J. – Starbek, M.

Received for review: 2013-01-02 Received revised form: 2013-05-23 Accepted for publication: 2013-11-12

Original Scientific Paper

Topology Optimization for Continua Considering Global Displacement Constraint Yi, J.J. – Zeng, T. – Rong, J.H. Jijun Yi1,2,* – Tao Zeng1 – Jianhua Rong2

1 Changsha

1 Central South University, School of Mechanical and Electrical Engineering, China University of Science & Technology, Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle, China

This paper presents a topology optimization method for continua that minimizes the volume subject to global displacement constraint. The method uses the p-norm displacement to represent the equivalent maximum displacement so as to avoid non-differentiability of the maximum function. Using nodal densities as design variables, a new topology optimization technique for controlling the global maximum displacement precisely is developed. Several examples are presented to demonstrate the effectiveness of the proposed method for achieving convergent optimal solutions of structures with global displacement constraint. Keywords: topology optimization, global displacement constraint, nodal density variable, p-norm displacement

0 INTRODUCTION Finding the best distribution of available material in the predetermined design domain satisfying various conditions is the target of topology optimization for continuum structures. In most topology optimization methods, the optimized goal is to find the structures with maximum stiffness. Stiffness is often closely related to the global displacement and, especially, to the maximum displacement of the structure. So a new topology method for minimizing the volume of the structure subject to global displacement is developed and a new approach to controlling the maximum displacement of the structure is proposed. The topology optimization method based on elements is treated by dividing the design domain into finite elements and each element is taken as a design variable. The solid isotropic material and penalization (SIMP) method [1] and [2] transfers design variables from the discrete variables to contiguous ones with penalization. The evolutionary structural optimization (ESO) method [3] and [4], and its later version, the bi-directional ESO (BESO) method [5], remove inefficient material from the structure based on certain predefined criteria. The level set method represents the structure using a level set model which is embedded in a scalar function. Rong and Liang [6] and Wang et al. [7] investigated the level set method for topology optimization. However, the element-wise topology optimizations exhibit various numerical problems, such as grey-scale, checkerboard pattern and mesh dependency. Therefore, topology optimization methods based on nodal design variables were developed to avoid these problems. Matsui and Terada [8] proposed the concept of continuous distribution. A

Q4/Q4 continuum structural topology optimization is investigated by Rahmatalla and Swan [9]. A 3-D structural topology optimization and novel surface-smoothing scheme based on SIMP and subelement bilinear interpolation was developed using node densities by Song and Kim [10]. An adaptive density point refinement approach for continuum topology optimization on the basis of an analysismesh separated material density field description based on nodal design variables was presented by Wang et al. [11]. Wang et al. [12] proposed topological optimization of structures using a multilevel nodal density-based approximant. The nodal density field using the non-local Shepard function method is transformed to a practical elemental density field via a local interpolation with the elemental shape function. The presented topology optimization method is based on nodal densities and utilizes the rational approximation for material properties (RAMP) interpolation scheme proposed by Stolpe and Svanberg [13]. The discrete nodal topological variables ρi that only take value 0 or 1 are replaced by continuous topological variables between 0 and 1. Consequently, the difficulty of the discrete optimization is avoided by penalization. It is assumed:

f (ρ x ) =

ρx , (1) 1 + v (1 − ρ x )

where ρx is the density of point x, i.e. ρ(x), v is the penalization factor (v is a parameter which in some sense corresponds to p in the SIMP approach), which makes the intermediate densities approach either 0 (void) or 1 (solid). Here, v = 5 is set. The relation

*Corr. Author’s Address: School of Automobile and Mechanical Engineering, Changsha University of Science and Technology, Changsha, China, jijunyi@gmail.com

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 43-50

between the Young’s modulus and the material density at point x is expressed by:

E ( x ) = f ( ρ x ) E 0 , (2)

where E0 is Young’s modulus of the full solid material. The function f(ρx) has the following properties: f (ρ x ) = 0

d f (ρ x ) / d ρ x =

as ρ x → 0+ 1 ≠ 0 as ρ x → 0+ . 1+ v

The volume of an element is given by:

Vi = ∫ 0 ρ dV , (3) Vi

where Vi is the volume of the ith element, Vi 0 is the original volume of the ith element. In this study, minimum volume with a reference domain Ω in R3 is considered while satisfying the global displacement constraint for the structure.  Find: ρ ∈ R Nn   Minimize: V , (4)  f f ( j = 1, 2,..., N dof ; f = 1, 2,, ..., L) Subject to: u j ≤ U  ρi ≤ ρi ≤ 1 (i = 1, 2,..., N n ) 

where V is the structural volume being optimized, u jf is the displacement of the jth degree of freedom of the structure under the fth load case, Ndof is the total degrees of freedom of the structure, U f is its constraint limit, L is the number of the load cases acting on the structure, and ρi is the density of the ith node, ρi is its lower limit, Nn is the total number of nodes. Here, the small positive lower bound ρi = 0.0001 is set so that the structure optimized is always kept non-singular in the optimization process. 1 EQUIVALENT MAXIMUM DISPLACEMENT When the maximum displacement of the structure does not exceed a specified value, the global displacement constraint is satisfied. So, the maximum displacement is naturally the ideal design criterion of optimization models. However, the location of the maximum displacement usually varies following the change of material distribution in the optimization process, so the maximum function is not differentiable. To solve this problem,the maximum displacement needs to be smoothed, and the p-norm or the Kreisselmeier– Steinhauser (KS) function could be used. Similar to 44

the p-norm, geometric average displacement (GAD) is introduced by Kreisselmeier [14] and Qiao and Liu [15], which is expressed as: 1/ p

 1 Ne  U a =  ∑ ∫ δ p d Ωe  . (5) Ω  Ω e=1 e 

Here, Ne is the total number of elements, Ω denotes the volume of the design region, p is the norm parameter and Ωe is the element e solid volume and the displacement of any point inside the element e is δ. On one extreme, as the displacement norm parameter p approaches infinity, the Ua approaches the maximum displacement, and there is no added smoothness. On the other extreme, when p approaches 1, there is excessive smoothness but Ua approaches the average displacement. A good choice for p should, therefore, provides adequate smoothness so that the optimization algorithm performs well and an adequate approximation of the maximum displacement value so that the optimized design satisfies the imposed displacement constrains. Only when p approaches infinity, can the Ua arrive at the constraint of the maximum displacement. To remedy this deficiency, a normalized global displacement measure is proposed to better approximate the maximum displacement. The normalized p-norm displacement uses information from the previous optimization iteration to scale, and the p-norm displacement as α|Ua|, so that it better approximates the maximum displacement. The maximum displacement max(|u|k–1) and the p-norm displacement values from the previous optimization iteration k – 1 are used to define our evolving normalized p-norm displacement constraint at each iteration k as:

max( u ) ≤ U ⇒ α U a ≤ U , (6)

where α is calculated at each optimization iteration k ≥ 1 as follows:

α=

max( u Ua

k −1

)

. (7)

As the design converges, |Ua|k – 1 ≈ |Ua|k , max(|u|k–1) ≈ max(|u|k), so that αk – 1 ≈ αk and hence the desired effect is achieved, i.e. α|Ua| ≈ U .f Note that the constraint α|Ua| ≤ U f is nondifferentiable because the value of α is changing in a discontinuous manner and results in a slightly different optimization problem at every iteration. However, as the optimization converges the changes between successive design iterations diminish and hence α

Yi, J.J. – Zeng, T. – Rong, J.H.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 43-50

converges, thereby reducing the effects of the nondifferentiability and inconsistency. 2 NODAL DESIGN VARIABLES AND THE INTERPOLATION SCHEME Element-independent nodal densities are the design variables in this method. Thus, the relative density at any point is interpolated with an interpolation scheme, which determines the topology, stiffness and volume of material. 2.1 Identifying the Nodes As proposed by Guest et al. [16] and Kang and Wang [17], the scale parameter rmin is set to identify the nodes that influence the density of point x. Nodes are included in the influence domain if they are located within a distance rmin of the point x. This can be visualized by drawing a sphere of radius rmin centered at the point x, thus generating the spherical subdomain Ωx. Nodes located inside Ωx contribute to the computation of density ρ(x) of point x. As the mesh is refined, rmin and consequently Ωx do not change. The only difference between the two meshes is the number of nodes located inside Ωx, and included in the interpolation function. This is essential to generate mesh-independent solutions. 2.2 Shepard Interpolation Scheme Interpolation provides a continuum of density field and mesh-independence, which might alleviate numerical instability and checkerboard effects [18]. In implementing continuum structural topology optimization formulations, many functions are available to interpolate nodal density onto the points inside the element space; –for example, the standard C0 shape functions used in the finite element method. However, each node’s shape function influences only the elements connected to that node. Mesh independency cannot be obtained when interpolation functions are influenced by mesh size. They should be based on a physical length scale that does not change following mesh refinement. Shepard interpolation is proposed by Shepard [19], and used by Kang and Wang [17] to achieve mesh independency. Let ρi (i = 1, 2, ..., n) denote a set of density of nodes inside Ωx at the associated point x = (X, Y, Z), where (X, Y, Z) define the point x location in the Cartesian coordinate system. Thus, the relative density at point x is interpolated by the nodal densities

inside the influence domain Ωx with Shepard’s interpolation method.

  ∑ NDi ( x) ρi ρ = i∈S x ρ  i x

( x ≠ xi ) ( x = xi )

, (8)

where Sx is the sub-domain of design variable located within the influence domain Ωx of point x, and ρi is the density value of the ith node. xi is the position of the point associated with the ith node. The corresponding interpolation function NDi(x) is defined as:

NDi ( x) =

Ri ( x)

∑ R ( x) i =1

(i = 1, 2,..., n). (9)

where Ri(x) = 1 / [ri(x)] and ri(x) = |x – xi|2 being the Euclidean distance from the points x to xi. n is the number of nodes inside the influence domain Ωx. In the method of element independent nodal variable density, the density in the element space is not constant, and the global density field of the structure has C0 continuity. It is easy simple to know from the bounded property of the Shepard interpolation that 0 ≤ ρx ≤ 1 holds if 0 ≤ ρi ≤ 1 (i ∈ Sx). Moreover, the property NDi(x) ≥ 0 also guarantees that the derivative of the density with respect to the design variable will be always non-negative. This property is essential to guaranteeing a correct searching direction in seeking the optimal material distribution by a gradient-based algorithm. 3 SENSITIVITY ANALYSIS The solution of the gradient-based optimization problem requires the computation of sensitivities of the objective function and the constraints. In a finite element analysis, the static behavior of a structure for any load case can be expressed by the following equilibrium equation:

K U = F , (10)

where K is the global stiffness matrix of a structure being optimized and, U and F are the global nodal displacement and nodal load vector, respectively. In the finite element method, the displacement of any point δ can be expressed by:

Topology Optimization for Continua Considering Global Displacement Constraint

δ = N u (11)

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 43-50

Here, N, u denote the general shape function matrix and displacement vector of the ith element, respectively. The adjoint method can be used to determine the sensitivity of displacement by introducing a vector of Lagrange multiplier λ. The modified p-norm displacement can be expressed as: 1/ p

 1 Ne  p U a =  ∑ ∫ ( Nu ) d Ωe  Ω  Ω e=1 e 

Ne ∂U a 1 ∂u ∂U 1− p 1 p −1 = (U a ) p ( Nu ) Ν d Ωe + ∑ ∂U ∂ρ Ω e=1 ∫Ωe ∂ρ p

 ∂K ∂U  U+K +λ T  . ∂ρ   ∂ρ

(13)

The Eq. (13) can be rewritten as: ∂U a = ∂ρ Ne 1  ∂U ∂u 1− p 1 p −1 + =  (U a ) p ( Nu ) N d Ωe + λ T K  ∑ ∫ Ωe ∂ U p Ω e =1   ∂ρ ∂K (14) U. +λ T ∂ρ

To eliminate the unknown ∂U / ∂ρ from the sensitivity expression, let: 1− p

1 Ne ∂u p −1 ∑ ( Nu ) N ∂U d Ωe + λ T K = 0, (15) Ω e=1 ∫Ωe

Pλ = − (U a )

1− p

1 Ne   ∂u  ∑  Ω e=1   ∂U 

∫ ( Nu )

p −1

Ωe

 NT d Ωe . (16)  

So the adjoint vector is defined as:

Kλ = Pλ . (17)

Here, Pλ denotes the adjoint load of adjoint Eq. for yielding the adjoint vector λ. Thus, the sensitivity of the p-norm displacement function is: Nc ∂U a ∂U a ∂ρ ∂K e = = − ρ 2 ∑ λ Te u e , (18) ∂ρ ∂ (1 ρ ) ∂ρ ∂ (1 ρ )

where Nc is the number of element influenced by ρi. K e0 is the element stiffness matrix of the eth element of the solid material. 46

∂K e ∂f ( ρ x ) T B D0 Bd Ωe , (19) =∫ Ωe ∂ρi ∂ρi

+ λ T ( KU − F ) , (12)

where the term λT (KU – F) is equal to zero and, therefore, the modified displacement is identical to the original one. Taking derivatives of Eg. (12) with respect to the design variable ρ gives:

(U a )

The sensitivity of the p-norm displacement requires the computation of the sensitivity of the stiffness matrix with respect to the design variable. The derivative of the elemental stiffness matrix with respect to the design variable is expressed by:

∂f ( ρ x ) ∂f ( ρ x ) ∂ρ x (1 + v) = = NDi , (20) ∂ρi ∂ρ x ∂ρi ((1 − ρ x )v + 1) 2 where B is the usual displacement-strain matrix and D0 corresponds to the constitutive matrix of the solid material. For example, the formulation of the constitutive matrix for 3D isotropic solid structures is: D( x) =  1      ×        

E ( x)(1 − µ ) × (1 + µ )(1 − 2 µ )

µ 1− µ 1

µ 1− µ µ 1− µ 1

1 − 2µ 2(1 − µ )

    0   0   . (21) 0    0    1 − 2µ  2(1 − µ )  0

1 − 2µ 2(1 − µ )

simmetry

Since the stiffness matrix integrand is evaluated at the Gauss points, the densities at these Gauss points are directly computed from the design variables using the interpolation function. Numerical quadrature, such as Gaussian quadrature, is commonly reduced to the evaluation and summation of the stiffness integrand at specific Gauss points. The sensitivity analysis of the objective function in Eq. (4) is calculated similar to that of Eq. (19). The derivative of the total material volume with respect to the design variables can be computed by the Gaussian quadrature method over the influence-domain. Ve = ∫ ρ x d Ωe = ∫

Ωe

∑ ND ( x) ρ d Ω . (22) i

i∈S x

So the total volume is:

Yi, J.J. – Zeng, T. – Rong, J.H.

N el

e =1

V = ∑Ve = ∑ ∫

Ωe

∑ ND ( x) ρ d Ω . (23)

i∈S x

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 43-50

The derivative of V with respect to the design variable: ∂V ∂V ∂ρi = = − ( ρi ∂ (1 ρi ) ∂ρi ∂ (1 ρi )

) ∑ (∫ 2

Ωe

e∈S x

)

NDi d Ωe . (24)

Ne  V min = ∑  ∫Ωe ρ d Ωe e =1   f f  s.t. αU a ≤ U l ( f = 1, 2,, L; l = 1, 2,) , (25)  (i = 1, 2,, N n ) ρi ≤ ρi ≤ 1  

where U l f is expressed as:

)

 U af + min β U af ,(U f − U af )  Ul =  f f f f  U a − min β U a , U − U a , 

(

)

U af ≤ U f U

f a

= f 1,= 2,..., L; l 1, 2,... (26)

U a = U a k − ∑ (U a )′t k tik + ∑ (U a )′t k ti , (27) i =1

i =1

( i = 1,, N n ) ,

and

then Eq.

(25) can be transferred into Eq. (28): Ne  min : V = ∑ ∫Ωe 1 t d Ωe e =1  Nn Nn  f k fk fk f s . t . C t ≤ U − U sign ( ) + U Ai f . (28) ∑ ∑ l a a i i  i =1 i =1   ( f = 1, 2, L; l = 1, 2,)  1 ≤ ti ≤ ti ( i = 1, 2,, N n ) 

If the constant items in the objective function are omitted, solving Eq. (28) can be transferred to solving Eq. (29):    min : ∑ ( bi (ti ) 2 + ai ti )  i =1  , (29) Nn Nn f f fk fk f  s.t. Ci ti ≤ U l − U a sign(U a ) + ∑ Ai ∑  i =1 i =1  1 ≤ ti ≤ ti  t ∈ R Nn

Find

where

In the above, β is a displacement limit changing factor. Typical values of β between 0.01 and 0.20 have been used for displacement constraints in the example problems in this paper. U af k is the p-norm displacement of the structure under the f th load case. U l f ( j = 1, 2,..., J ) are varied by Eq. (26) at every iteration. Assuming that only ti = 1/ρi is changed and is treated as a variable, the first-order series expansion for the p-norm displacement Ua at ti (i = 1, 2, ..., Nnod) can be expressed as:

i =1

( i = 1,, N n )

Ai f = ∑ (U a )′t k tik sign (U af k )

In order to make the approximation functions of the displacement constraint in Eq. (4) hold true at each iteration, an equivalent optimization model (Eq. (25)) with varying displacement constraint limits is built. At each iteration, a quadratic approximation model of the true objective function that satisfies the Taylor expansion is built around the current point. The model is assumed to be a good representative of the objective function in a so-called trust region [20]. Trust regions are used to ensure the robustness of the iteration and make progress toward feasibility and optimality [21].

(

Let Ci f = ∑U a 't k sign (U af k ) i =1

4 TOPOLOGICAL OPTIMIZATION WITH VARYING DISPLACEMENT LIMITS

Thus, the p-norm displacement in the next iteration, U af k +1 , can be estimated by the current iteration k.

where Nn is the number of the nodes in the design domain.

ai =

−3

( ti )

∑(∫ Ne

e =1

Ωe

)

NDi d Ωe , bi =

( ti )

∑(∫ Ne

e =1

Ωe

)

NDi d Ωe .

The programming solving the problem of Eq. (29) can be transferred into solving dual programming problem by using the dual theory [22] and [23]. 5 NUMERICAL EXAMPLES This section illustrates the proposed approach with 3D applications. For simplicity, all the quantities are dimensionless. In addition, Young’s modulus is chosen as 2.1×1011 and Poisson’s ratio as 0.3 for all examples. Let d denote the length of cuboid element diagonal. In the following examples, rmin is set to 1.5d while keeping the same displacement mesh size. As the computing platform, we have used a personal computer with the commercial software package ABAQUS has been used for FEA in this study. Fig. 1a shows a 3D cantilever beam with length of 8, height of 5, and width of 2. The beam is fixed at

Topology Optimization for Continua Considering Global Displacement Constraint

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 43-50

the left end. A concentrated load P = 4800 is applied downward at the center of the right end. The initial displacement at the constraint point, the center of the right end, is 2.851×10–6. A displacement constraint is taken as 7.0×10–6. The cantilever domain is discretized into a mesh of 40×25×10 B8 elements which results in a total of 10,000 elements. There are 41×26×11 design variable points distributed within the initial design domain. The optimized topology is shown in Fig. 1b.

Fig. 3. The maximum displacement-varying history

a) b) Fig. 1. The 3D cantilever beam; a) design domain and boundary conditions; b) topology optimization result obtained from the proposed method

Then, the same problems are solved using the proposed method with varying p parameter in which p is set to even numbers (4, 10, 20, 40) as shown in Fig. 2. With the increase of p parameter, the displacement constraint converges to the same condition (Fig. 3), the material distribution (Fig. 2) and the volume (Fig. 4) move close to the convergence.

Fig. 4. The volume-varying history

Fig. 5. The design domain and boundary conditions of the 3D, simply supported beam

b) a) Fig. 6. Topology optimization results: a) optimal topology obtained from EIND; b) optimal topology obtained from the element-wise method

d) Fig. 2. Topology optimization results with: a) p = 4; b) p = 10; c) p = 20; d) p = 40

Fig. 5 shows a 3D, simply supported beam with a length of 4, height of 1, and width of 0.4. An external force P = 4000 is applied to the center of top area. The initial displacement at the constraint point, the center of the top area, is 1.1×10–7. A displacement constraint is taken as 2.0×10–7. The design domain is discretized into mesh size of 80×20×8 B8 elements. p is set to 20. 48

b) Fig. 7. Topology optimization results with the coarser mesh: a) optimal topology obtained from EIND; b) optimal topology obtained from the element-wise method

Yi, J.J. – Zeng, T. – Rong, J.H.

StrojniĹĄki vestnik - Journal of Mechanical Engineering 60(2014)1, 43-50

When the nodal density values are used to determine a smooth iso-line that describes the boundary of the optimization layout, as a result, a smooth optimal topology can be obtained in Fig. 6a. Its final volume is 0.947. The results obtained from the element-based approach is shown in Fig. 6b. Its final volume is 1.062. When the mesh is coarser, and the mesh size of 50Ă&#x2014;12Ă&#x2014;5 is used, the results obtained from the element-based approach and the proposed approach based on element independent nodal density are shown in Figs. 7a and 3b, respectively. Their final volumes are 1.071 and 1.155. These figures show that, for the different displacement mesh size, the topology obtained from element independent nodal density has a much better resolution and is smoother than that of the elementbased approach. The solution attained by the proposed method exhibits no checkerboard patterns or mesh dependency. When the same mesh is used, the computational cost for the topology optimization based on element independent nodal density is higher than the elementbased approach. This is mainly attributable to the large number of density nodes in the influence domain. However, the topology resolution resulting from the proposed approach based on the proposed method is higher than that of the element-based approach. To improve the efficiency of the proposed approach, especially for a 3D large-scale optimization problem, the parallel programming technique could be used to carry out the finite element analysis and the optimization procedure. The total CPU time and the CPU time spent on the sensitivity analysis in every optimization iteration are 144 and 123 seconds, respectively. When the codes are reprogrammed with the OpenMP and four threads are used, the total CPU time and the CPU time spent on the sensitivity analysis decrease to 50 and 42 seconds, respectively. By taking this approach, it is possible to obtain benefits from parallelization without the need for extensive modification to the code structure. 6 CONCLUSIONS This paper has developed a topology optimization method for minimizing the volume of a structure subject to the global displacement constraint. In contrast to the element-based procedure, here we take the nodal density as the design variable, which is interpolated into any point by Shepard functions. This technique avoids checkerboard patterns and meshdependency for low order finite elements. With the

help of the global displacement constraint, an optimal structure with appointed deformation can be obtained, and it is unnecessary to know where the maximum displacement is. The proposed method is highly useful with regard to practical engineering applications. The numerical examples demonstrate the effectiveness of the proposed method with respect to the optimal solution and convergence. 7 ACKNOWLEDGEMENTS This work has been supported by National Natural Science Foundation of China (11372055, 11302033), Hunan Provincial Natural Science Foundation of China (12JJ3044), the Key Laboratory of Lightweight and Reliability Technology for Engineering Vehicle, Education Department of Hunan Province (Changsha University of Science & Technology) (2012KFJJ0 2), the Huxiang Scholar Fund (Changsha University of Science & Technology), the Open Fund of State Key Laboratory of Automotive Simulation and Control (20121105). 8 REFERENCES [1] Bendsoe, M.P. (1989). Optimal shape design as a material distribution problem. Structural and Multidisciplinary Optimization, vol. 1, no. 4, p. 193202, DOI:10.1007/BF01650949. [2] Rozvany, G., Zhou, M., Birker, T. (1992). Generalized shape optimization without homogenization. Structural and Multidisciplinary Optimization, vol. 4, no. 3, p. 250-252, DOI:10.1007/BF01742754. [3] Xie, Y.M., Steven, G.P. (1993). A simple evolutionary procedure for structural optimization. Computers & Structures, vol. 49, no. 5, p. 885-896, DOI:10.1016/0045-7949(93)90035-C. [4] Xie, Y.M., Steven, G.P.(1997). Evolutionary Structural Optimization. Springer, Berlin, DOI:10.1007/978-14471-0985-3. [5] Huang, X., Xie, Y.M. (2010). Evolutionary Topology Optimization of Continuum Structures: Methods and Applications. John Wiley & Sons, Chichester, DOI:10.1002/9780470689486. [6] Rong, J.H., Liang, Q.Q. (2008). A level set method for topology optimization of continuum structures with bounded design domains. Computer Methods in Applied Mechanics and Engineering, vol. 197, no. 1718, p. 1447-1465, DOI:10.1016/j.cma.2007.11.026. [7] Wang, M.Y., Wang, X., Guo, D. (2003). A level set method for structural topology optimization. Computer Methods in Applied Mechanics and Engineering, vol. 192, no. 1, p. 227-246, DOI:10.1016/S00457825(02)00559-5. [8] Matsui, K., Terada, K. (2004). Continuous approximation of material distribution for topology

Topology Optimization for Continua Considering Global Displacement Constraint

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optimization. International Journal for Numerical Methods in Engineering, vol. 59, no. 14, p. 1925-1944, DOI:10.1002/nme.945. [9] Rahmatalla, S.F., Swan, C.C. (2004). A Q4/ Q4 continuum structural topology optimization implementation. Structural and Multidisciplinary Optimization, vol. 27, no. 1, p. 130-135, DOI:10.1007/ s00158-003-0365-9. [10] Song, J.-H., Kim, C. (2012). 3-D topology optimization based on nodal density of divided sub-elements for enhanced surface representation. International Journal of Precision Engineering and Manufacturing, vol. 13, no. 4, p. 557-563, DOI:10.1007/s12541-012-0071-x. [11] Wang, Y., Kang, Z., He, Q. (2013). An adaptive refinement approach for topology optimization based on separated density field description. Computers & Structures, vol. 117, p. 10-22, DOI:10.1016/j. compstruc.2012.11.004. [12] Wang, Y., Luo, Z., Zhang, N. (2012). Topological optimization of structures using a multilevel nodal density-based approximant. Computer Modeling in Engineering and Sciences, vol. 84, no. 3, p. 229, DOI:10.3970/cmes.2012.084.229. [13] Stolpe, M., Svanberg, K. (2001). An alternative interpolation scheme for minimum compliance topology optimization. Structural and Multidisciplinary Optimization, vol. 22, no. 2, p. 116-124, DOI:10.1007/ s001580100129. [14] Kreisselmeier, G. (1979). Systematic control design by optimizing a vector performance index. International Federation of Active Control Symposium on ComputerAided Design of Control Systems, p. 113-117. [15] Qiao, H., Liu, S. (2013). Topology optimization by minimizing the geometric average displacement. Engineering Optimization, vol. 45, no. 1, p. 1-18, DOI: 10.1080/0305215X.2012.654789.

[16] Guest, J.K., Prevost, J.H., Belytschko, T. (2004). Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International Journal for Numerical Methods in Engineering, vol. 61, no. 2, p. 238-254, DOI:10.1002/nme.1064. [17] Kang, Z., Wang, Y.Q. (2011). Structural topology optimization based on non-local Shepard interpolation of density field. Computer Methods in Applied Mechanics and Engineering, vol. 200, no. 49, p. 35153525, DOI:10.1016/j.cma.2011.09.001. [18] Diaz, A., Sigmund, O.(1995). Checkerboard patterns in layout optimization. Structural and Multidisciplinary Optimization, vol. 10, no. 1, p. 40-45, DOI:10.1007/ BF01743693. [19] Shepard, D. (1968). A two-dimensional interpolation function for irregularly-spaced data. Proceedings of the 1968 23rd ACM national conference, p. 517-524, DOI:10.1145/800186.810616. [20] Conn, A.R., Gould, N.I., Toint, P.L. (1987). Trust Region Methods. Vol. 1. Society for Industrial and Applied Mathematics, Philadelphia. [21] Byrd, R.H., Gilbert, J.C., Nocedal, J. (2000). A trust region method based on interior point techniques for nonlinear programming. Mathematical Programming, vol. 89, no. 1, p. 149-185, DOI:10.1007/PL00011391. [22] Beckers, M. (1999). Topology optimization using a dual method with discrete variables. Structural and Multidisciplinary Optimization, vol. 17, no. 1, p. 14-24, DOI:10.1007/BF01197709. [23] Rong, J.H., Li, W.X., Feng, B. (2010). A structural topological optimization method based on varying displacement limits and design space adjustments. Advanced Materials Research, vol. 97-101, p. 36093616, DOI:10.4028/www.scientific.net/AMR.97101.3609.

Yi, J.J. – Zeng, T. – Rong, J.H.

Received for review: 2013-07-12 Received revised form: 2013-09-30 Accepted for publication: 2013-10-22

Original Scientific Paper

Frictional Conditions of AA5251 Aluminium Alloy Sheets Using Drawbead Simulator Tests and Numerical Methods Trzepieciński, T. – Lemu, H.G. Tomasz Trzepieciński1 – Hirpa G. Lemu2,*

1 Rzeszow

2 University

University of Technology, Department of Materials Forming and Processing, Poland of Stavanger, Department of Mechanical and Structural Engineering and Materials Science, Norway

This article presents research results on the effect of sheet metal surface roughness, lubricant conditions and sample orientation on the value of friction coefficient in the drawbead region of sheet metal-forming processes. Aluminium alloys with different temper conditions were used as test materials. The experimental results have ascertained several relationships showing the effect of surface profile and lubrication on the value of the friction coefficient. Based on experimental measurements, it may be concluded that the sample orientation and the lubrication conditions are crucial variables influencing the value of the coefficient of friction. Furthermore, a numerical model of the drawbead has been created in Msc.MARC Mentat software, and several simulations have been performed to study the stress/strain state in stretched sample during drawbead simulator tests. Both isotropic and anisotropic material models were used in the simulations taking into account the sample orientation with respect to the rolling direction of the sheet. Keywords: coefficient of friction, drawbead, FEM simulation, friction, sheet metal forming

0 INTRODUCTION Deep drawing is a key manufacturing process for sheet metal products. The quality of the products and the efficiency of the drawing process depend on several parameters. Friction regimes encountered during deep drawing in particular are known to be extremely complex [1] and [2]. This is as a result of the inherent factors, such as the contact pressure, sliding velocity, surface roughness at sheet metal and tool interface, material properties of the tool and the blank, and the properties of the lubrication. Moreover, resistance to friction depends on texture anisotropy [3] and physicochemical factors acting on the contact surface and the dynamics of loads [4]. Previous studies show that friction at the microscopic level is due to adhesion between contacting asperities, the ploughing effect between asperities [5] and the appearance of hydrodynamic friction stresses [6] and [7]. Few regions of the draw piece with different stress and strain states, local sliding velocity, contact pressure and friction conditions exist. General application of numerical simulations of sheet metal forming for proper functioning requires knowledge of suitable mathematical descriptions of friction behaviour. The finite element method (FEM) as a numerical analysis approach is currently widely used in sheet metal modelling and analysis. A description of the drawbead cannot generally be taken into account in the finite element simulation of sheet metal forming processes [8] and [9]. The small radii of the bead and the sharp corners of the die shoulders impose a certain meshing of the sheet passing the drawbead. At the same time, the role of

the experimental approach remains essential [10] for developing numerical methods for the calculation of the friction coefficient and validating the results. Performance of the forming process is secured by controlling the blank holder force, a straining force created by friction between the blank and the tools, which partially controls the material flow. This force cannot fully control the material flow, because it does not make a full contact with the entire blank. Fig. 1 illustrates the drawbead form in deep drawing and how it generates a stable tensile force opposite to the sheet drawing direction by introducing a series of local bending, straightening and reverse bending deformations on the sheet.

Fig. 1. Deformation of the sheet in drawbead region

This article presents the results of studies done on the two main problems: experimental research on frictional conditions of AA5251 aluminium alloys using a drawbead simulator friction test in accordance with the drawbead simulator (DBS) approach proposed by Nine [11], and numerical simulations based on the results of the friction test.

*Corr. Author’s Address: University of Stavanger, N-4036 Stavanger, Norway, Hirpa.g.lemu@uis.no

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1 MATERIALS AND METHODS 1.1 Materials The first task conducted in this research was an experimental work in which four kinds of aluminium alloy sheets with different temper conditions were used. The sheets with temper H14 have a thickness of 0.8 mm while sheets with temper O, H16 and H22 have a thickness of 1 mm. The average sheet thickness varied between ±0.01 mm as a result of the tolerance of the sheet metal fabrication process. A tensile test in the universal testing machine was carried out to determine the mechanical properties of the sheets. The mechanical properties determined in this test (as given in Table 1) are yield stress Rp0.2, ultimate strength Rm, elongation A50, anisotropy coefficient r, strain-hardening coefficient C and strain-hardening exponent n. The samples for the tensile tests were cut in two directions: along the rolling direction (0°)

and transverse to the rolling direction (90°). The mechanical properties of the sheets clearly show that the used aluminium alloy sheets have a wide range of Rp0.2 values based on temper conditions. 1.2 Surface Characterization The measurement of surface roughness parameters was carried out using the Alicona InfiniteFocus instrument. The main standard 3D parameters determined by this measurement (given in Table 2) are: the roughness average Sa, the root mean square roughness parameter Sq, the highest peak of the surface Sp, the maximum pit depth Sv, the surface skewness Ssk, the surface kurtosis Sku, the 10-point peak-valley surface roughness Sz, the density of summits Sds, the texture aspect ratio of the surface Str, the surface bearing index Sbi, the core fluid retention index Sci and the valley fluid retention index Svi. The surface topography of tested materials is also

Table 1. The mechanical properties of the tested sheets Material AA5251 O AA5251 H14 AA5251 H16 AA5251 H22

Orientation [°] 0 90 0 45 90 0 90 0 90

Rp0.2 [MPa] 68 72 212 216 210 184 189 111 122

Rm [MPa] 203 205 234 240 241 232 236 201 207

Mechanical properties A50 C [MPa] 0.18 252 0.25 245 0.04 254 0.04 271 0.04 327 0.05 253 0.06 242 0.19 370 0.21 370

n 0.279 0.270 0.058 0.070 0.078 0.163 0.154 0.239 0.227

R 0.607 0.870 0.478 0.693 0.786 0.528 0.751 0.535 0.793

Table 2. The surface roughness parameters of the tested sheets Material AA5251 O AA5251H14 AA5251H16 AA5251H22

Sa [µm] Sq [µm] Sp [µm] Sv [µm] 0.302 0.376 2.37 1.39 0.340 0.423 2.48 1.62 0.362 0.41 2.98 2.08 0.325 0.401 2.04 1.53

Surface roughness parameters Ssk Sku Sz [µm] Sds* 0.267 3.48 3.26 749 0.298 3.34 3.3 697 0.338 3.67 3.51 685 0.321 3.58 3.43 716

Str 0.029 0.036 0.041 0.031

Sbi 0.241 0.243 0.255 0.263

Sci 1.64 1.67 1.58 1.72

* In [Peaks/mm²] or alternatively the unit [vertexes/mm²] can also be used.

Fig. 2. Surface topography of tested materials; a) AA5251 O, b) AA5251 H14, c) AA5251 H16, d) AA5251 H22

Trzepieciński, T. – Lemu, H.G.

Svi 0.110 0.094 0.112 0.104

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shown in Fig. 2, where each tested surface has an area of 1.4301×1.0849 mm.

Fig. 3. Measurement system used for friction testing; 1 – frame; 2 – front roll; 3 - middle roll; 4 - back roll; 5 – specimen; 6 – supporting roll; 7 and 8 – tension members; 9 and 10 – extensometers; 11 – fixing pin

1.3 Drawbead Test

The pulling and clamping forces were controlled using load cells. To determine the coefficient of friction, carrying out two tests with two samples was found to be necessary. One specimen was pulled between cylindrical rolls supported by bearings, and then the measured pulling force (denoted as Droll) and the clamping force (Croll) gave the bending and unbending resistance of the sheet under “frictionless” conditions, respectively. The sheet is displaced between the rotating rolls so that the friction between the sheet and rolls is minimized while the second specimen is pulled between the fixed rolls. Friction opposes the sliding of the sheet over the fixed rolls. The combined loads required to slide and to bend/unbend the sheet with the fixed rolls are then given by the measured pulling force (Dfix) and the clamping force (Cfix). When the wrap angle of middle rolls is 180°, the coefficient of friction is calculated according to the following expression [11]:

In the drawbead simulator test, the sheet metal was pulled to flow between three cylindrical rolls, each with a radius of 20 mm (Fig. 3). The rolls have been quenched and tempered according to a minimum of 57 HRC. The quenching temperature was 990 °C, and the temper temperature was approximately 500 °C. The test material was cut along the rolling direction into 200 mm long and 20 mm wide strips. To realize various lubricated conditions, both rolls and sheet specimens were degreased by using acetone for dry friction conditions, and machine oil L-AN 46 of 44 mm²s-1 viscosity at 40 °C was used for lubricated conditions. The lubricant was applied in excess to the test strips so that the film thickness could be determined by the process. The sliding speed was set to 1 mm/s and various tribological conditions were obtained by using rolls with different surface roughness values (Ra = 0.32, 0.64 and 1.25 μm) measured along the generating line of the rolls. The rolls were made of cold-worked tool steel X165CrV12. The clearance between working rolls was adjusted and maintained at 1.5t (where t is the sheet thickness). The main purpose of this clearance is to prevent locking of the sheet between the rolls, especially for fixed rolls. The clearance value was estimated based on a trial-and-error method and experience. Taking the clearance into account, the total wrap angle around all rolls is about 310.48°, where the highest wrap angle is on the middle roll.

µ=

D fix − Droll

π ⋅ C fix

, (1)

where Dfix is the pulling force obtained with the fixed rolls, Droll is the pulling force obtained with the freely rotating rolls, and Cfix is the normal force or clamping force obtained with the fixed beads. It has been argued in a previous study [12] that the wrap angle corresponding to the actual engagement of the strip with the roller or bead was not taken into account in the derivation done by Nine [11]. Further, Green [13] states that the tangent-to-tangent bead wrap assumption becomes approximately valid only at extremely deep penetrations. This supports the argument that the validity of the equation derived by Nine [11] is limited to deep penetrations. When the wrap angle is not equal to 180° the friction coefficient is calculated from [14]:

µ=

D fix − Droll sin θ , (2) ⋅ 2θ C fix

where θ is the quarter contact angle of actual engagement of the strip over the bead, and a value of θ = π/2 confirms a full penetration. 2 NUMERICAL MODELLING The simulation of the drawbead simulator test was conducted using MSC.Marc + MENTAT 2010

Frictional Conditions of AA5251 Aluminium Alloy Sheets Using Drawbead Simulator Tests and Numerical Methods

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 51-60

software. Both dry friction and oil-lubricated contacts were considered. The rolls were defined as rigid surfaces. While conducting the modelling, the aluminium sheet metal (AA5251 H14) was initially placed in a horizontal position and held by a frictionless device (Fig. 4a). At the initial stage, the middle roll was moved down to bend the sheet metal while the leading end of the sheet metal was fixed. The middle roll was allowed to travel through the distance at which the centres of curvature for both front and back rolls and the middle roll were at the same height (Fig. 4b). A displacement of 40 mm was then applied to one end of the sample when the required wrap angle was obtained. The numerical analyses were performed for the AA 5251 H14 sheet tested in the following conditions: sample orientation 90°, Ra of rolls 0.63 μm, lubrication conditions. The finite element model of the blank consists of 3600 quad4 shell elements with five integration points through the shell thickness, which are necessary for an acceptable solution [10]. The assumed strain formulation was applied to improve the bending characteristics of the elements. This can substantially improve the accuracy of the solution in terms of the computational costs of assembling the stiffness matrix. An elasto-plastic material model approach was implemented, and three material models have been simulated. In the first material model, the plastic behaviour of the metal was described by the von Mises yield criterion [15]. In the second model, the anisotropy of the material was established using the Hill yield criterion [16]. The Hill formulation is the most frequently used yield function in many research papers on steel sheet metal forming and can be regarded as an extension of the isotropic von Mises function. As reported by Cazacu and Barlat [17], the Hill formulation can also be applied for the material description of aluminium alloys.

The material behaviour for this second formulation is specified using the following properties: Young’s modulus: E = 70000 MPa, Poisson’s ratio ν = 0.33 and mass density r = 2690 kg·m-3. The isotropic hardening behaviour uses the Hollomon power-type law by which the parameters C and n (given in Table 1) are fitted on a stress-strain curve of the tensile test. In the third model, the Barlat yield function has been applied [18]. In the case of anisotropy material models, both 0° and 90° sample orientations have been examined. The balanced biaxial yield stress σb necessary to define Barlat material model was measured in a bulge test and a value of 278 MPa was obtained. Simulations of friction tests were performed for rolls with surface roughness values of Ra = 1.25 µm in dry friction conditions. To describe contact conditions, the Coulomb friction law was applied (as described in an earlier publication by the same authors [19]). 3 DISCUSSION OF EXPERIMENTAL RESULTS 3.1 Friction Coefficient Value In the friction tests, two sets of values for clamping and pulling forces determined for fixed and freely rotating rolls under dry friction and lubricated conditions were received. The average value of friction coefficient was determined from Eq. (1) after rejecting initial transient scope of load forces (Fig. 5).

Fig. 5. Load characteristics of friction tests for AA5251 H14 under following conditions: Ra of rolls 1.25 mm, dry friction, sample orientation at 0°

Fig. 4. Geometry and boundary conditions of FEM model of drawbead simulator test; a) initial configuration and b) start of drawing stage

The average values of the coefficient of friction determined in dry friction μdry and in lubricated conditions μoil are given in Table 3. Upon analysis of the friction test results, the expected relationships are observed. That means values of the friction coefficient in dry friction conditions are higher than those in lubrication conditions. The application of machine oil reduces the value of friction coefficient, but its

Trzepieciński, T. – Lemu, H.G.

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intensity depends on the surface roughness of the rolls. This impact is not strongly evident and will be discussed in detail later in the article. Table 3. Friction coefficient values of tested sheets Material

Ra (rolls) Sample [µm] orientation [°] 0.32

AA5251 O

0.63 1.25 0.32

AA5251 H14

0.63 1.25 0.32

AA5251 H16

0.63 1.25 0.32

AA5251 H22

0.63 1.25

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

Coefficient of friction µdry µoil 0.259 0.205 0.262 0.219 0.245 0.194 0.251 0.201 0.219 0.161 0.238 0.181 0.245 0.190 0.257 0.221 0.222 0.173 0.243 0.196 0.193 0.140 0.205 0.159 0.242 0.183 0.252 0.212 0.215 0.166 0.225 0.169 0.188 0.135 0.19 0.144 0.238 0.175 0.253 0.202 0.197 0.149 0.207 0.157 0.185 0.134 0.188 0.142

orientations and for all tested materials. For all considered friction conditions, the friction coefficient values for samples cut across the rolling direction of the sheet are higher than for samples cut parallel to the rolling direction. The tested sheets exhibit directional surface topography caused by the manufacturing process of the sheets (rolling). The values of the 2D amplitude roughness parameters measured parallel to the rolling direction are lower than those measured in the transverse direction to the rolling direction. Furthermore, rolling causes directional orientation of the material grains parallel to the rolling direction, which is the source of anisotropy. In that case, the evolution of the surface topography during the sheet passing the draw bead is different for both sample orientations. 3.2 Sheet Roughness The plot of the friction coefficient versus Sa parameter for the sheet AA5251 H22 is given in Fig. 7. It is observed in this plot that a local minimum of friction coefficient value at Sa = 0.322 μm exists.

Fig. 7. The friction coefficient value vs. the roughness average Sa of the sheet for orientation at 0°

Fig. 6. Friction coefficient value vs. surface roughness [Ra] of rolls for a) AA5251 O, b) AA5251 H24

As the value of the Ra parameter of the rolls increases, the friction coefficient decreases for both dry friction and lubricated conditions (Fig. 6). The above-mentioned relations are valid for both sample

The above-mentioned relation is observed for all applied friction conditions, sample orientations and surface roughness of rolls, supports the conclusion that favourable conditions of friction reduction exist for this sheet. Shih et al. [20] reported that roughening of asperities observed during stretching of the deformed material tends to decrease the real area of contact, resulting in a lower coefficient of friction. The continued increment of the value of friction coefficient for the sheet in this study (AA5251 H14) at Sa = 0.34 μm may be explained by the fact that (in spite of increasing surface roughness) the lubrication is unable to overcome the dominated metallic contact between the roughness asperities of contact bodies as the larger space contains the lubricant.

Frictional Conditions of AA5251 Aluminium Alloy Sheets Using Drawbead Simulator Tests and Numerical Methods

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 51-60

Studies show that surface textures act either as micro-traps for capturing wear debris or as microreservoirs that enhance lubrication [21]. In the case of steel sheets [10] and [22], it is observed that higher Ra parameter value tends to produce lower friction, or this tendency is observed up to a certain Ra value and the value of friction coefficient increases. The roughness acts to separate the surfaces, isolating the areas of direct metallic contact. The larger the amplitude of the roughness, the less the area of contact grows for a given amount of sliding deformation. By limiting the area of direct contact during sliding, the adhesion and deformation components of friction are reduced and the valleys act to trap wear debris, reducing the amount of body wearing [22]. However, Al and Al alloys are relatively soft, and a mechanically mixed layer of ultrafine particles is formed due to deformation [23]. Thus, high Ra values can hardly produce wear debris that act as abrasive particles. For all rollers used in the test, the relation between the Sa parameter and the friction coefficient value is similar. The friction coefficient value has the tendency to decrease with increases of the value of Sa parameters that represent different materials. Taking all of the obtained results into account, the relation between the value of Sa parameter and friction coefficient (Fig. 7) is found to be opposite to that reported in previous researches [10].

Fig. 8. Dependence of parameters Sa, Ssk and Sku of tested sheets

3.3 Effect of Lubrication In order to reduce friction and minimize sheet failure, lubricants are typically applied to portions of the workpiece that undergo severe contact with dies. When lubricant is applied, the frictional resistance of the sheet material decreases and its strain uniformity increases. This means that the application of any lubricant should result in a reduction of the value of the friction coefficient. Comparison of the values of the friction coefficient determined in dry friction and lubricated conditions demonstrate nearly linear relations (Fig. 9). This is particularly evident in the case of the sample orientation at 0° (Fig. 9a). The inclination angle of the trend line for sample orientation 0° and 90° are 42.32° and 45.99° respectively. When the sample has a 0° orientation, a higher value of the friction coefficient in dry conditions is obtained, implying the higher effectiveness of lubrication. The relation for the sample orientation at 90° (Fig. 9b) is the reverse.

Fig. 9. Relation between the friction coefficients determined in dry friction conditions mdry and in lubrication conditions moil for orientation at (a) 0° and (b) 90°

3.4 Lubricant Effectiveness It is evident that rough surfaces enable lubricant adhesion to the sheet material. This effect appears to be due to the manner in which the lubricant is captured by rough areas on the surface of the sheet. To examine the effectiveness of the sheet lubrication, the L-index was introduced, defined as follows:

Trzepieciński, T. – Lemu, H.G.

µdry − µoil . (3) µdry

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As shown in Fig. 10, the L-index value has a nonlinear relation with the value of roughness parameter Ra of rolls. In the case of a sample orientation at 0°, the value of the L-index initially decreases and then shows an increasing tendency. For sample orientation at 90°, however, a continuous increasing trend of the L-index value is observed. The range of L-index value for the samples oriented at 0° is higher (0.19 to 0.275) than for the samples oriented at 90° (0.132 to 0.245); therefore, in the case of the samples cut parallel to the rolling direction, lubricant highly reduced the friction coefficient value. There is no evident relation between the temper conditions of the sheet and L-index value, but for both orientations the sheet H22 exhibits the highest friction reduction. In all cases, the value of L-index is the highest for Ra = 1.25 μm. As stated previously, in the case of higher surface roughness of contact bodies, a high volume of lubricant may be trapped in surface pits and, consequently, the effectiveness of lubrication is higher.

rolling direction by about 0.002. A similar relationship exists for Barlat’s material model. Furthermore, the points of occurrence of maximal effective strains depend on the considered material model. The distributions of normal stress and shear stress in the transverse section after drawing a distance of 20 mm are shown in Fig. 12. The results in these plots show that the maximal values of the normal stress and shear stress for all material yield functions are at the edge of the sample. The values of Barlat’s material model regarding both orientations are the closest to the isotropic model. The local minimum at the middle, i.e. section 0-A’, is related with deformation of the sheets during bending over the rounded bead. It causes local contact of the sheet with the roll surface and thus the values of friction forces along the sample width are not constant. In the case of the Hill yield model at 0° and 90° orientation (Hill 0° and Hill 90°, respectively), the distribution of normal stress on the width of the sample is more uniform. The distribution of stresses for both analysed orientations is similar, but the sample orientation influences the value of stresses. The values of shear stress for Hill’s yield functions are considerably lower than other models and are more uniform, especially in the middle part of the analysed width of the sample. The dominant factors in determining both restraint force and blank thinning of dual-phase steel are bead penetration, flow stress and strain hardening [24]. In contrast, the effects of anisotropy and strip drawing direction with respect to the rolling direction are found to be relatively less influential.

Fig. 10. Effectiveness of lubrication (L-index) as a function of Ra of rolls oriented at (a) 0o and (b) 90°

4 DISCUSSION OF NUMERICAL RESULTS The numerical simulations include Hill’s and Barlat’s materials, and they were performed for both 0° (designated as Hill 0°, Barlat 0°) and 90° (designated as Hill 90°, Barlat 90°) sample orientations with respect to the rolling direction. The results show that the distributions of effective strain for different yield criteria during full penetration have been varying considerably (Fig. 11). Maximal values of effective strains for Hill 0° are higher than the values for sample cut transverse to the

Fig. 11. The distribution of effective strain for different material models and sample orientations 0° and 90°

The distributions of normal stress in longitudinal section after drawing a distance of 20 mm are shown in Fig. 13. The sequence of bending, unbending and reverse bending of the sheet material is clearly

Frictional Conditions of AA5251 Aluminium Alloy Sheets Using Drawbead Simulator Tests and Numerical Methods

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manifested by the cyclic normal stress observed on the longitudinal section of the drawbead region.

Table 4. Comparative experimental and numerical average values of friction test forces at the second stage of the friction simulator test Source Experiment Isotropic model Barlat’s model Hill’s model

Fig 12. Stress distribution along 0-A’ section; a) normal stress and b) shear stress

The highest values of normal stress exist in the region of the middle roll - sheet contact (C–D) located on the side in accordance with the direction of sample pulling. The second peak of stress exists in the region of back roll, between C’–B’ points. The change of stress value from positive to negative is related with bending and unbending of the sheet. On the sample length within the drawbead, places exist where the normal stress equals zero.

Dfix 1803 1712 1817 1697

Force [N] Droll 801 775 822 758

Cfix 1624 1582 1642 1574

Friction coeff.

Error [%]

0.196 0.188 0.192 0.189

–4.08 –2.04 –3.57

The results of the variation of numerically determined test force Dfix both at first and second stages (Fig. 14) show that all the numerical models over-predicted the value of the friction coefficient. The prediction errors of the friction coefficient for numerical models based on isotropic, Barlat’s and Hill’s material models are calculated to be 4.08, 2.04 and 3.57%, respectively. Furthermore, the value of average forces for the numerical model for Barlat’s material model is the closest to the experimental one. For the rest of the FEM models (i.e., isotropic and Hill’s material models), the average values of all test forces are proportionally smaller. As a result of this proportional decreasing tendency of the values of Dfix, Droll and Cfix, the value of friction coefficient does not diverge considerably from the experimental value (Fig. 15).

Fig. 14. The variation of numerical and experimental test force Dfix

Fig. 13. Normal stress distribution along B-B’ section

In addition to the comparative average values of friction test forces, the average value of the friction coefficient at the same stage and the error of numerically determined friction coefficient in relation to the experimental values are tabulated in Table 4. 58

Fig. 15. The variation of friction coefficient value during frictional testing of the sample cut according to the rolling direction

Trzepieciński, T. – Lemu, H.G.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 51-60

5 CONCLUSIONS The material presented in this article is based on studies conducted using two main research approaches: experimental testing and numerical simulation. Numerical simulations are based on the aforementioned friction test using material model that is described by isotropic and anisotropic yield criteria. The main results of the research can be summarized as follows: 1. Application of machine oil reduces the value of friction coefficient, but its intensity depends on the surface roughness of rolls. 2. For all applied friction conditions, the values of the friction coefficient for samples cut across the rolling direction of the sheet were higher than for samples cut in the rolling direction. 3. It has been found that the proposed L-index value has a non-linear relation with the value of the roughness parameter. For the sample orientation at 0°, the L-index value initially decreases and then continues to increase, while a continuous increase of the value is observed for the sample orientation at 90°. 4. The value of friction coefficient for both dry friction and lubrication conditions decreases as the surface roughness (Ra parameter) of the rolls increases. 5. Sample orientation has a clear effect on the values of the friction coefficient and effectiveness of lubrication. When the sample is oriented at 0°, higher value of friction coefficient is obtained in dry conditions implying that the effectiveness of lubrication is higher. For a sample orientation at 90°, the relation is the reverse. 6. The yield criterion has a strong influence on the distribution of normal and shear stresses, but the results for the sample orientation at both 0° and 90° are quite similar. 7. The value of the normal stress on the width of the sheet varies. This requires sensitivity analysis of the effect of sample width on the sheet deformation in drawbead simulator friction test. In order to obtain representative results of numerical simulations of the Nine friction test, conducting a simulation of a 3D model of the drawbead is necessary. 8. In general, the results demonstrate that there is an agreeable harmony between the experimental and numerical models (FEM). The study on the friction coefficient shows prediction errors of less than 5%, and among the selected yield criteria,

Barlat’s material model has the best prediction with an error of about 2%. 6 ACKNOWLEDGEMENT This research was realized with financial support provided by Iceland, Liechtenstein and Norway and was co-financed by European Economic Area and Norwegian Financial Mechanism under the Scholarship and Training Fund. The authors would like to appreciate this financial support. 7 REFERENCES [1] Yang, T.S. (2010). Investigation of the strain distribution with lubrication during the deep drawing process. Tribology International, vol. 43, no. 5, p. 1104-1112, DOI:10.1016/j.triboint.2009.12.050. [2] Yang, T.S. (2007). A refined friction modeling for lubricated metal forming process. Tribology Letters, vol. 27, no. 3, p. 289-300, DOI:10.1007/s11249-0079233-x. [3] Trzepieciński, T., Gelgele, H.L. (2011). Investigation of anisotropy problems in sheet metal forming using finite element method. International Journal of Material Forming, vol. 4, p. 357-359, DOI:10.1007/s12289-0100994-7. [4] Liewald, M., Wagner, S., Becker, D. (2010). Influence of surface topography on the tribological behaviour of aluminium alloy 5182 with EDT surface. Tribology Letters, vol. 39, no. 2, p. 135-142. DOI:10.1007/ s11249-010-9625-1. [5] Wilson, W.R.D. (1991). Friction models for metal forming in the boundary lubrication regime. Journal of Engineering Materials and Technology, vol. 113, no. 1, p. 60-68, DOI:10.1115/1.2903383. [6] Lo, S., Yang, T. (2003). A new mechanism of asperity flattening in sliding contact – the role of tool elastic micro wedge. Journal of Tribology, vol. 125, no. 4, p. 713-719, DOI:10.1115/1.1574518. [7] Yang, T.-S., Lo, S.W. (2006). Contact simulation for predicting surface topography in metal forming. Tribology Letters, vol. 23, no. 2, p. 121-129, DOI:10.1007/s11249-006-9112-x. [8] Firat, M., Livatyali, H., Cicek, O., Fatih, O.M. (2009). Improving the accuracy of contact-type drawbead elements in panel stamping analysis. Materials and Design, vol. 30, no. 10, p. 4003-4011, DOI:10.1016/j. matdes.2009.05.022. [9] Courvoisier, L., Martiny, M., Ferron, G. (2003). Analytical modelling of the drawbeads in the sheet metal forming. International Journal of Machine Tools & Manufacture, vol. 133, no. 3, p. 359-370, DOI:10.1016/S0924-0136(02)01124-X. [10] Trzepieciński, T. (2010). 3D elasto-plastic FEM analysis of the sheet drawing of anisotropic steel sheet metals. Archives of Civil and Mechanical Engineering.

Frictional Conditions of AA5251 Aluminium Alloy Sheets Using Drawbead Simulator Tests and Numerical Methods

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vol. 10, no. 4, p. 95-106, DOI:10.1016/s16449665(12)60035-1. [11] Nine, H.D. (1978). Draw bead forces in sheet metal forming. Proceedings of Symposium on Mechanics of Sheet Metal Forming: Behavior and Deformation Analysis, Plenum Press, Warren, p. 179-211. [12] Manjula, N.K.B., Nanayakkara, P., Hodgson, P.D. (2006). Determination of drawbead contacts with variable bead penetration. Computer Methods in Materials Science, vol. 6, no. 3, p. 188-194, DOI:10536/ DRO/DU:30004084. [13] Green, D.E. (2001). An experimental technique to determine the behaviour of sheet metal in a drawbead. SAE Technical Paper Series, 2001-01-1136. DOI:10.4271/2001-01-1136. [14] Nanayakkara, N.K.B.M.P., Kelly, G.L., Hodgson, P.D. (2004). Determination of the coefficient of friction in partially penetrated draw beads. Steel Grips, vol. 2, no. Supplement, p. 677-680, DOI:10536/DRO/ DU:30002855. [15] von Mises, R. (1913). Mechanik der festen Körper im Plastisch deformablen Zustand, Nachrichten von der Köngl. Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, Göttingen, p. 582592. [16] Hill, R. (1948). A theory of the yielding and plastic flow of anisotropic metals. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 193, no. 1033, p. 281-297, DOI:10.1098/ rspa.1948.0045. [17] Cazacu, O., Barlat, F. (2003). Application of the theory of representation to describe yielding of anisotropic aluminium alloys. International Journal of Engineering

Science, vol. 41, no. 12, p. 1367-1385, DOI:10.1016/ S0020-7225(03)00037-5. [18] Barlat, F., Lege, D.J., Brem, J.C. (1991). A sixcomponent yield function for anisotropic metals. International Journal of Plasticity, vol. 7, no. 7, p. 693712, DOI:10.1016/0749-6419(91)90052-Z. [19] Lemu, H.G., Trzepieciński, T. (2013). Numerical and experimental study of friction behaviour in bending under tension test. Strojniski vestnik – Journal of Mechanical Engineering, vol. 59, no. 1, p. 41-49. DOI:10.5545/sv-jme.2012.383. [20] Shih, H., Wilson, W., Saha, P. (1996). Modelling the influence of plastic strain on boundary friction in sheet metal forming. Proceedings of the NAMRC XXIV, p. 173-178. [21] Sedlaček, M., Vilhena, L.M.S., Podgornik, B., Vižintin, J. (2011). Surface topography modelling for reduced friction. Strojniski vestnik – Journal of Mechanical Engineering, vol. 57, no. 9, p. 674-680, DOI:10.5545/ sv-jme.2010.140. [22] Skarpelos, P., Morris, J.W. (1997). The effect of surface morphology on friction during forming of electrogalvanized sheet steel. Wear, vol. 212, no. 2, p. 165-172, DOI:10.1016/s0043-1648(97)00174-9. [23] Li, X.Y., Tandon K.N. (2000). Microstructural characterization of mechanically mixed layer and wear debris in sliding wear of an Al alloy and an Al based composite. Wear, vol. 245, no. 1-2, p. 148-161. DOI:10.1016/S0043-1648(00)00475-0. [24] Livatyali, H., Firat, M., Gurler, B., Ozsoy, M. (2010). An experimental analysis of drawing characteristics of a dual-phase steel through a round drawbead. Materials and Design, vol. 31, no. 3, p. 1639-1643. DOI:10.1016/j.matdes.2009.08.030.

Trzepieciński, T. – Lemu, H.G.

Received for review: 2013-07-15 Received revised form: 2013-09-11 Accepted for publication: 2013-09-25

Original Scientific Paper

Optimization of the Shape of Axi-Symmetric Rubber Bumpers Mankovits, T. – Szabó, T. – Kocsis, I. – Páczelt, I. Tamás Mankovits1,* – Tamás Szabó2 – Imre Kocsis1 – István Páczelt2 1 University

2 University

of Debrecen, Faculty of Engineering, Hungary of Miskolc, Faculty of Mechanical Engineering, Hungary

The rubber bumpers built into the air-spring structures of buses perform a number of critical tasks. Consequently, designing their shape requires considerable effort. This paper presents a novel solution for determining the required characteristics of axi-symmetric rubber parts, which can efficiently be used in practice. The procedure is based on the finite element method (FEM) and the support vector regression (SVR) model. A finite element code developed by the authors and based on a three-field functional is used for the rapid and appropriately accurate calculation of the characteristics of rubber bumpers. A rubber shape is evaluated via the work difference and the area between the desired and the actual load-displacement curves. The objective of shape optimization is to find the geometry where the work difference is under a specified limit. The tool of optimization is the SVR method, which provides the regression function for the work difference. The minimization process of the work-difference function leads to the optimum design parameters. The efficiency of the method is verified by numerical examples. Keywords: shape optimization, rubber bumper, support vector regression, finite element method

0 INTRODUCTION Designing the suspension systems of vehicles is a demanding engineering task. Currently, driving stability is ensured by electronically controlled active suspension systems. The objectives set in the course of designing include improving travel comfort, decreasing the dynamic loading of the wheels and decreasing the suspension workspace [1]. Similar possibilities are offered by the use of air springs. The rubber bumpers (Fig. 1) built into the air springs of buses perform several crucial functions, such as working together with the air spring as a secondary spring, thus modifying the original characteristics of the air spring when pressed together (characteristics of the dotted and dashed lines in Fig. 2). When the bus is in a stationary position and settles to the ground, the static weight of the chassis and the body rests on the bumper; in this case, the solid line characteristic is active. If the fibre-reinforced bellows of the air spring wears through while the bus is running, the vehicle can safely reach the nearest garage at a limited speed while bouncing on the bumper; no additional damage will occur. It prevents metal-on-metal collision at large dynamic impulses and absorbs the impulse. These rubber bumpers are subject to compressive stress, for which the characteristics show a progressive feature. It is a fundamental requirement that they should have a specified load-displacement curve under load; setting this objective results in a shape optimization task. The aim of the optimization is to achieve a specified characteristic by means of the geometric design of the rubber bumper while the material characteristics remain the same.

Fig. 1. The air spring

The literature does not devote much room to the examination of the rubber bumpers of air springs. Another area for which rubber mounts are used is the flexible support of engines, on which several works have been published. Estimation of the fatigue life of rubber springs, rubber mounts and air springs is carried out in [2] to [5], respectively. In [6], extensive studies on the rubber mounts of engines are performed using the finite element method. Several authors have formulated shape optimization for the specified stiffness of rubber mounts, in which the analysis was done using commercial finite element software or a finite element code of their own development. The stiffness of rubber mounts in three directions on the basis of parameter examinations is optimized in [7]. Optimization based on sensitivity analysis using a

*Corr. Author’s Address: University of Debrecen, Faculty of Engineering, 2-4 Ótemető, 4028 Debrecen, Hungary, tamas.mankovits@eng.unideb.hu

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 61-71

special purpose finite element code is performed in [8] for material properties and shape, where stiffness was also taken into consideration. Determining the shape was done with the aim of minimizing the volume of the rubber part. Rubber mounts undergoing shear are modelled with the finite element method in [9], and the effects of the geometric design and the load on the stiffness of the part are also investigated. For the purpose of minimizing the cross-sectional area and the maximum stress of the rubber mount and for that of maximizing the life cycle, shape optimization using an Ogden-type material model and commercial finite element software is applied in [10]. Several objective functions in a system where the optimization had several stages are handled. A back-propagation neural network (BPN) is used to find the connection between the input and output data and then a micro-genetic algorithm (MGA) is used for global optimization. A large number of finite element running results are used as learning points. The experience gained from the above works also easily lends itself to examining the rubber bumper of air springs. Our research intends to determine the behaviour of rubber bumpers in the complete range of operation, and thus the aim of the shape optimization is to achieve the specified spring characteristics. Since there is no active control in the rubber bumpers, shape optimization may provide the required loaddisplacement curve. In connection with the objective set, achieving the aim of the optimization will require an efficient load-displacement calculation, which is performed using the finite element method. This is the purpose served by the finite element program prepared for the examination of axi-symmetric rubber parts, which can be conveniently fit to the shape optimization procedure.

machines (SVM) for regression problems, e.g. in optimization models. A great number of applications can be found in the fields of materials science, chemistry, economics and data procession, where connections are sought between a number of input data (e.g. some mechanical or chemical property). Although there are results in the field of engineering problems based on SVR models [12], this method is not yet particularly widespread for engineering optimization. The application of SVR in non-linear models has the advantage that the transformation function between input space and the so-called feature space (where a linear regression problem is to be solved) can be hidden [13], and machine learning procedures can be applied to find an appropriate regression function. The novel procedure based on the FEM and SVR is suitable for the shape optimization of rubber bumpers with the specified characteristics. The efficiency of the method is verified by examples. 1 THE OPTIMIZATION METHOD 1.1 The Objective Function of the Shape Optimization In the optimization process, we start from the load-displacement curve of an existing and known construction (Fig. 3). The shape optimization can be formulated as a minimization problem on a given domain by the following. The objective function ΔW : Ω → R gives the area between the desired loaddisplacement curve and the curve obtained by finite element computation for a specific rubber bumper shape (represented by the parameter vector d):

∆W (d) = ∫ Fdes ( s ) − FFEM,d ( s ) ds, (1) 0

Fig. 2. The lift diagram

The support vector regression (SVR) proposed by [11] is a widely used application of support vector 62

(the grey-filled area in Fig. 4). Function ΔW is considered on Ω ⊂ R n , the set of possible design parameter vectors d, s0 is the limit of the operation range, Fdes and FFEM,d denote the spring force of the desired characteristics and the spring force calculated by finite element method for a specific geometry (determined by d), respectively. The optimization range Ω is given by inequality conditions coming from technology limitations, n is the number of the design parameters. Therefore, many design parameters are chosen, so many variables will be in the optimization. Function ΔW has to be minimized by determining the optimum design parameter vector dopt, that is:

Mankovits, T. – Szabó, T. – Kocsis, I. – Páczelt, I.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 61-71

∆W (d opt ) = min ∆W (d). (2) d∈Ω

Since numerical methods are used, the process results in an approximate value of the optimum.

(di , ∆W (di )) ∈ R n+1 , i = 1,..., N play the role of the given data points in the (non-linear) regression procedure. In the SVR model, the so-called kernel functions play a central role. Let t : Ω → Ω′ ⊂ R m be a transformation function mapping the learning points from the input space into what is called the feature space that transforms our non-linear problem into a linear one. It is widely used since the regression function can be expressed as a linear combination of kernel functions ki (d) = t (d)T ⋅ t (di ), (3)

Fig. 3. The optimization task

The first step of the method is to solve a non-linear regression problem for function ΔW. The regression procedure is based on the points (learning points), (di , ∆W (di )) ∈ R n+1 , i = 1,..., N where ΔW(di) are given (measured or calculated with FEM). The SVR model is used to find the regression function; the calculations are carried out with the SVR package of “R” software [14]. Since the values of the regression function provided by the software are available for arbitrary design parameter vectors in Ω, the place of the minimum of ΔW, i.e. the value of the optimum design parameter vector, can be determined numerically.

where ( )T denotes the transpose (see in [11]). The regression function f is looked for in the form:

f (t (d)) = w T ⋅ t (d) + b, (4)

in the feature space, where b ∈ R and w ∈ R m . In the classic models, the optimization is based on the difference between the values of the regression function and the given values at the learning points L(di ) = f (t (di )) − ∆W (di ) , which does not provide a satisfactory solution in many cases. In some cases, it appears to be better to use the ε-insensitive (Vapnik’s) error function Lε to solve the regression problem [11] defined by:  0, if f (t (di )) − ∆W (d i ) ≤ ε  Lε (di ) =  , (5) i i  f (t (d )) − ∆W (d ) − ε , otherwise where ε is a fixed non-negative parameter. According to Eq. (5), the error is zero if the value of a learning point is in the ε-insensitive tube around the regression function (Fig. 5). ε may be regarded as the parameter controlling the smoothness of the solution.

Fig. 4. Derivation of the objective function

1.2 Application of the SVR Model The support vector regression model related to the theory of learning machines and kernel methods and widely used in statistics and lately in engineering calculations also plays a central role in our investigations. In this part, the theoretical background of the method is summarized briefly. Using the finite element method, the values of ΔW are determined for the design parameters and the learning points d1 ,..., d N ∈ Ω ,

Fig. 5. ε-insensitive tube in 1D case

Using the ε-insensitive error function, the optimization problem leads to a constraint quadratic optimization problem, minimize:

Optimization of the Shape of Axi-Symmetric Rubber Bumpers

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 61-71

1 T w ⋅ w, (6) 2

where αi, αi', λi, λi' ≥ 0. The dual optimization problem is the following, maximize:

subject to:

(

−

)

∆W (di ) − w T ⋅ t (di ) + b ≤ ε , i = 1,..., N . (7)

When using regression models, we have to take into consideration that certain learning points will disturb the run of the regression function; therefore, it is expedient to moderate the effect of such high values by means of the slack variables ξi and ξi': the difference of the ith learning point from the function should not be more than ε + ξi and ε + ξi', respectively. The higher the value of the slack variables, the larger the scope for searching for the function. Introducing the slack variables, the following modified constraint quadratic optimization problem is to be solved (see, e.g. [11]), minimize: N 1 T w ⋅ w + C ∑ (ξi + ξi' ), (8) 2 i =1

subject to:

(

)

∆W (di ) − w T ⋅ t (di ) + b ≤ ε + ξi , (9)

)

⋅ t (di ) + b − ∆W (di ) ≤ ε + ξi ' (10)

ξi ≥ 0, ξi ' ≥ 0, i = 1,..., N . (11)

C determines the trade-off between the error and the complexity of the solution. The hyper-parameter C can be regarded as a penalty parameter that penalizes excessive divergence (larger than ε). For higher values of C, the objective function is more sensitive to the slack variables, so in the optimum solution the value of the slack variables remains low, and the function will be a reasonable approximation of the learning points, while a low value of C can result in a function that runs at a considerable distance from certain learning points. According to the standard dualization method [15], we introduce the Lagrange function: L(w, b, λ , λ' , α, α' ) = =

N N 1 T w ⋅ w + C ∑ (ξi + ξi' ) − ∑ ( λiξi + λi'ξi' ) − 2 i =1 i =1 N

(

)

(

)

−∑ α i' ε + ξi' + ∆W (di ) − (w T ⋅ t (di ) + b) , i =1

(12)

) ( ) ⋅ t (d )

(

i =1

(13)

−ε ∑ (α i + α i ') + ∑ (α i − α i ') ∆W (di ) subject to:

∑ (α i =1

− α i ') = 0 and α i ,α i' ∈ [0, C ]. (14)

Solving the dual problem, we obtain:

f (t (d)) = ∑ (α i − α i ') t (d)T ⋅ t (di ) + b, (15) i =1

that is, the solution (regression function) is a linear combination of kernel functions ki ( d ) = t (d)T ⋅ t (di ). This form of f says that the explicit form of w does not need to be computed. Furthermore, it can be proved that for the learning points inside the ε-tube αi – αi' = 0, that is f is determined only by the learning points having non-vanishing coefficients. These pairs are called support vectors. Which learning points play the parts of support vectors depends on the choice of parameter ε (Fig. 5). The wider the band, the smoother the solution. Otherwise, the model will attempt to fit the solution more accurately to the learning points, and the function will change more rapidly. The fact that the solution is determined by support vectors is a consequence of using the special error function (Eq. (5)). It is known that the solution of the problem discussed above is a regression function, which can be written as a linear combination of kernel functions ki, i = 1, ..., N having the form of Eq. (3), so we are not involved with the transformation function t. This fact leads to the following idea: choosing a suitable kernel function, an appropriate solution of the regression problem can be achieved. In accordance with our calculation experience and the research results in this field, the Gaussian kernel function:

−∑ α i ε + ξi + (w T ⋅ t (di ) + b) − ∆W (di ) − i =1

1 N ∑ (α i − α i ' ) α j − α j ' t d i 2 i , j =1

ki (d) = e

− γ d −di

, (16)

belonging to the class of radial basis functions (RBF) provides the best solution to our problem, where γ is a parameter controlling the form of the kernel function. In the calculation, the Gaussian function Eq. (16) is chosen as a kernel function. Since it depends only on

Mankovits, T. – Szabó, T. – Kocsis, I. – Páczelt, I.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 61-71

the distances d − di , i = 1,.., N , the learning points behave as a kind of centre when the Gaussian kernel functions are applied. The value of the regression function is fundamentally determined by the nearby known values (learning points). In the following, the regression function obtained from the SVR model is denoted by ΔWSVR, that is: ∆WSVR (d) = f (t (d)). (17)

It is easy to see that the accuracy of the regression provided by the SVR method depends on γ and C. An optimum choice of the hyper-parameters (γ,C) leads to the error of the learning process: N

δ1 =

∑ ( ∆W i =1

i FEM

i − ∆WSVR

∑ ( ∆W ) i FEM

i =1

)

≤ δ1* , (18)

i i where ∆WSVR = ∆WFEM (di ) = ∆WSVR (di ) and ∆WFEM are the values of the objective function determined by the finite element calculation. δ1* can be specified by the user according to the expected accuracy. A successful combination of hyper-parameters can be achieved when the error remains within the specified limit δ1*. In our examples, the hyper-parameters are chosen by the following steps: • the initial values of the hyper-parameters γmin, Cmin are predefined; • while keeping C = Cmin at a constant value, we are considering the error δ1 as a function of γ and looking for the parameter γ = γopt, where δ1 is minimal; • hen keeping the parameter γopt at a constant value, we are considering the error δ1 as a function of C and looking for the parameter C = Copt, where δ1 is within the specified limit δ1*; • values of γopt and Copt mean the hyper-parameters satisfy the requirements in Eq. (18) and determine the regression function used in the last part of the shape optimization process. Considering a set:

{

D = d ,..., d

} ⊂ Ω, (19)

according to technology limitations the minimum of ΔWSVR on D is determined numerically.

2 PRODUCING THE LEARNING POINTS BY THE FEM Rubber bumpers may undergo large deformations under load, which in itself shows non-linear behaviour. The changing contact range between the parts and the incompressibility of the rubber increases this nonlinear behaviour further. In order to be able to use the SVR method, the spring characteristics have to be produced by the finite element code within the optimization range, and then the difference of the work values has to be calculated for the learning points to be written. There is no generally accepted rule concerning the learning points. Their number may depend on the expected accuracy and the type of the problem, among other factors. In determining the learning points, the objective was that they should properly cover the optimization range. For rubber, the material models are generally given by the strain energy density function [16]. The energy density function of nearly incompressible materials can be divided into a volume-changing and a volume-preserving part. The strain energy density resulting from the change in volume U(J) is given in the following form:

U (J ) =

1 ⋅ κ ⋅ ( J − 1) 2 , (20) 2

where J is the Jacobian, κ is the bulk modulus, which is a real material characteristic and in the finite element investigations can be interpreted as a penalty parameter. If an incompressible material is examined, then U(J) is zero, for ν = 0.5. It is to be noted that rubber bumpers may be regarded as nearly incompressible materials due to additives. Accordingly, the Poisson ratio is between 0.49 < ν < 0.5. A compression test according to the standard ISO 7743 is performed to determine the stressstrain curve of the rubber part. A number of material models can be found in the literature for the volumepreserving member of strain energy density. Since the deformation is relatively small in our investigations, the two-parameter Mooney-Rivlin material model is sufficient to describe the material behaviour, where the strain energy density is expressed using the scalar invariants:

(C ) = µ ⋅ ( I I − 3) + µ ⋅ ( I II − 3). (21) W 10 01

The Mooney-Rivlin material constants μ10 and μ0 are determined from the results of the compression test using FEM computations [7]. I I and I II are the scalar invariants of the volume preserving member of the Cauchy-Green strain tensor of the right C [16].

Optimization of the Shape of Axi-Symmetric Rubber Bumpers

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 61-71

The program developed uses the combined technique, which is based on the following functional:  (C  )dV + U ( J )dV + Π (u, J , p ) = ∫ W ∫ V

1 + ∫ p ⋅ ( J − J )dV + ∫ c ⋅ g n2 dA − Π extt (u), (22) 2 Ac V

where the displacement field u is approximated using the quadratic tensor product space, the volume change J and the hydrostatic pressure p are approximated using linear functions independently of each other, U( J ) is the penalty parameter member, J can be indirectly derived from the displacement and is independent of J , c is the penalty parameter of the contact, gn is the gap function, Πext(u) is the potential of the external forces, V is the volume of the rubber and Ac is the contact surface. To discretize the functional, nine-node isoparametric axi-symmetric finite elements are used. Applying the Total-Lagrange description to the variation equations of functional Eq. (22) according to u, J , p [16], after finite element discretization, and the Newton-Raphson iteration equation [17] is finally obtained:

K T ∆u = ∆f , (23)

where KT is the structural tangent stiffness matrix, Δu is the vector of nodal point displacement increment and Δf is the unbalanced load vector. The validation and calibration of our program (mesh, material constants and finite element input data) were performed according to [18]. For the finite element code, a data generation program (mesh, boundary conditions, loads and finite element input data) has also been developed.

δ2 =

∆ WFEM (d opt ) − ∆ WSVR (d opt ) ∆ WFEM (d opt )

In the course of the optimization process, the geometry of the initial design, the results of the compression testing, and the specified characteristics are known. As the first step, the finite element model is built, and then the Mooney-Rivlin material constants (μ10, μ01) are determined with consideration of the measurement results. In order to decrease the running time, the clearest mesh is found at which the required calculation accuracy can be preserved. For the same specified material characteristics (μ10, μ01, κ and c), the learning points are created. The learning points are used to test the error δ1 of the regression function produced by the software

≤ δ 2* , (24)

is checked, where the limit is specified by the user. If Eq. (24) is fulfilled, the optimization is considered to be completed. Fig. 6 shows the flowchart of the shape optimization problem. 4 NUMERICAL EXAMPLES 4.1 Two-Dimensional Shape Optimization The rubber part investigated is the bumper of an air spring used in buses. The meridian section of the air spring containing the rubber bumper is shown in Fig. 1. The air springs are designed so that the buses can “kneel” at bus stops, and the air spring goes flat. The rubber bumper rests against the bumper plate at that time. In current practice, when a softer or a harder rubber bumper is needed, this is achieved by changing the rubber composition. Our task is to enable the described rubber bumper to produce a 15% harder characteristic under operating conditions. This is to be achieved by changing the shape of the rubber bumper. Table 1. FEM input data Mooney-Rivlin constant (μ10)

3 OPTIMIZATION PROCESS

optimizing the hyper-parameters γ and C. If the error δ1 is within the specified limit δ1* the regression function is accepted and is used for further calculation. The minimum of ΔWSVR on D defined in Eq. (19) is calculated. The finite element calculation is performed again with the optimum design parameter vector determined using SVR method and the condition:

Mooney-Rivlin constant (μ01) Bulk modulus (κ)

Penalty parameter of contact (c) Prescribed disp. inc. (Δu)

Number of load steps (m)

0.63 N/mm² 0.1575 N/mm² 1000 N/mm² 1000 N/mm² 1 mm 13

In Fig. 1, it can be seen that the rubber bumper comes into contact with the top plate and the pin even under a small compression. The displacements are known on the lower and upper surfaces. The finite element code was developed so that it would be suitable to also consider normal contact. The shape optimization problem is two-dimensional in this case. The finite element input data are given in Table 1, the initial geometry of the rubber bumper and the

Mankovits, T. – Szabó, T. – Kocsis, I. – Páczelt, I.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 61-71

deformed shape of the original geometry are shown in Fig. 7.

the hole diameter D1 and the height of the part h should not change.

Fig. 8. The spring characteristics

In the shape optimization, the inequalities d2 ≥ Db0 and d1 > d2 are specified, so that the design parameters in mm are defined according to the following conditions: d1 ∈ {82, 83,...,102} and d1 > d2. d = (d1, d2), where   d 2 ∈ {74, 75,..., 90} Thus, the optimization range and the learning points chosen can be seen in Fig. 9.

Fig. 6. Flowchart of the shape optimization

Fig. 9. The optimization region and the learning points

Table 2. Input data of the optimization process

Fig. 7. The initial and the deformed geometry

The initial and the specified characteristics are shown in Fig. 8. Taking the production technology and application technology limitations into consideration, the two design parameters are the largest diameter d1 = Dk and the external diameter of the bumper surface d2 = Db. It is a fundamental requirement that

SVR parameter (ε)

0.01

SVR parameter (γmin)

0.1

SVR parameter (Cmin)

Tolerance (δ1*) Tolerance (δ2*)

1 0.01 0.05

The manufacturing accuracy for the two design parameters is 1 mm. Under the specified accuracy, the number of possible solutions is P = 312, which can be determined from the predefined conditions on design

Optimization of the Shape of Axi-Symmetric Rubber Bumpers

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 61-71

parameters and manufacturing accuracy. The number of learning points is N = 24. The input data of the optimization process are collected in Table 2. After reading in the learning points on the basis of the hyper-parameter search (Figs. 10 and 11), the following parameters are considered to be optimal in the SVR program: γopt =1.5, Copt = 1.5, where δ1 = 0.008429. The goodness of learning is shown in Fig. 12.

The results obtained by the teaching using the optimal hyper-parameters are collected in Table 3. Table 3. Results of the SVR teaching No. 1 2 3 4 … 23 24

d1 [mm] 82 82 86 86 … 102 102

d2 [mm] 74 78 74 78 … 86 90

ΔWFEM [Nm] 9.94111 8.72711 8.16311 6.93211 … 4.26789 5.55889

ΔWSVR [Nm] 9.799091 8.669142 8.135446 6.959917 … 4.284846 5.531014

On the basis of the calculation, the minimum work difference of the possible solutions is ΔWSVR(dopt) = 0.368536 Nm, for which the optimum design parameters are d1opt = 94 mm and d2opt = 88 mm. The optimization results are summarized in Table 4. Fig. 10. Determination of γopt (Cmin = const.)

Table 4. Design solutions obtained with the SVR No. 174 296 175 297 280 235 …

d1 [mm] 94 102 94 102 101 98 …

d2 [mm] 88 74 89 75 75 81 …

ΔWSVR [Nm] 0.368536 0.388816 0.389079 0.411857 0.415206 0.44596 …

Fig. 11. Determination of Copt (γopt = const.)

Fig. 13. The spring characteristics

Fig. 12. SVR best fit

The characteristics obtained for the control finite element calculation run for the optimum design variable and the specified characteristics are shown in Fig. 13, where ΔWFEM(dopt) = 0.385546 Nm, so the tolerance is δ2 = 0.04412. The optimal shape is shown in Fig. 14. Mankovits, T. – Szabó, T. – Kocsis, I. – Páczelt, I.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 61-71

Table 5. FEM input data Mooney-Rivlin constant (μ10) Mooney-Rivlin constant (μ01) Bulk modulus (κ)

0.5 N/mm² 0.125 N/mm² 1000 N/mm²

Prescribed disp. inc. (Δu)

Number of load steps (m)

2 mm 10

Fig. 14. The optimum shape

4.2 Multi-Dimensional Shape Optimization Although the prescribed characteristics can be achieved by changing two or three design parameters in engineering practice, it may be considered that more design variables are needed to describe the specific feature. The shape optimization using SVR is suitable for handling even more design parameters. In the following example, the efficiency of this method is presented using a five-dimensional shape optimization problem. The outer skirt of the rubber bumper investigated is described by means of a cubic spline in five control points. These control points are the design parameters. The finite element input data are given in Table 5; the initial geometry of the rubber bumper and the deformed shape for the original geometry are shown in Fig. 15. The initial and the desired loaddisplacement curves can be seen in Fig. 16.

Fig. 16. The spring characteristics

In the investigation, the design parameters in [mm] are defined according to the following conditions:  d1 ∈ [ 40, 56]   d 2 ∈ [ d1 − 4, d1 + 4]  d = (d1, d2, d3, d4, d5), where  d3 ∈ [ d 2 − 2, d 2 + 2]  d ∈ [ d − 2, d + 2] 3 3  4 d5 ∈ [ d 4 − 2, d 4 + 2] and d1, d2, d3, d4, d5, are even numbers. Under the specified accuracy, the number of possible solutions is P = 1215. The number of learning points is N = 10. The input data of the optimization process are included in Table 6. Table 6. Input data of the optimization process SVR parameter (ε)

0.01

SVR parameter (γmin)

0.05

SVR parameter (Cmin)

Tolerance (δ1

Tolerance (δ˝2*)

Fig. 15. The initial and the deformed geometry

0.02 0.05

After reading in the learning points on the basis of the hyper-parameters search, the following parameters are considered to be optimum in the SVR program: γopt = 0.1, Copt = 20, where δ1 = 0.013775. The goodness of learning is shown in Fig. 17. On the basis of the calculation, the minimum work difference of the possible solutions is ΔWSVR(dopt) = 0.432812 Nm, for which the optimum design parameters are d1opt = 52 mm, d2opt = 48

Optimization of the Shape of Axi-Symmetric Rubber Bumpers

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 61-71

mm, d3opt = d4opt = d5opt = 54 mm. The results of the optimization are summarized in Table 7. The characteristics obtained for the control finite element calculation run for the optimum design variable and the specified characteristics are shown in Fig. 16, where ΔWFEM(dopt) = 0.41267 Nm, so the tolerance is δ2 = 0.04878. A deformed shape for the optimal geometry is shown in Fig. 18.

Fig. 17. SVR best fit Table 7. Design solutions obtained with the SVR No. 837 861 828 836 852 860 …

[mm] 52 52 52 52 52 52 …

[mm] 48 50 48 48 50 50 …

[mm] 54 54 52 54 52 54 …

[mm] 54 52 54 54 52 52 …

[mm] 54 54 54 52 54 52 …

ΔWSVR [Nm] 0.43281 0.43344 0.45588 0.4559 0.45601 0.46177 …

5 CONCLUSIONS Rubber bumpers that are built into vehicles and structures have to meet several requirement as a result of their function. In this paper, bumpers with predefined load-displacement curves were achieved via shape optimization. The characteristics of the rubber bumpers of different shapes were determined with the help of the finite element method. In the investigations, the SVR was used by means of open-source software to perform the optimization task. Combining the above two methods into one system, two shape optimization problems were solved to prove the efficiency of the presented procedure for axi-symmetric rubber bumpers. The SVR method requires relatively few timeconsuming learning points to treat non-linear multidimensional optimization problems. Naturally, the learning points should cover the optimization range. The density of the points may depend on the complexity of the problem. The teaching procedure producing a small number of learning points and carried out by using the finite element method can be regarded as short. After the teaching procedure, the software provides a remarkably strong prediction for further multitude of parameters by dispensing with the time-consuming finite element calculations and relying on engineering intuition. For both two and five design parameters, the novel shape optimization procedure proved to be fast and accurate (see the examples presented in 4.1 and 4.2, respectively). This regression process results in an approximation value of the objective function. The goodness of the calculation can be checked by finite element computation. Experimental measurements on bumper shapes obtained by numerical simulations would be justified, but this was not part of the current project. It may be considered that further work is needed on multi-objective optimization including total mass or life cycle number, etc. 6 REFERENCES

Fig. 18. Deformed shape of the optimal geometry

[1] Gáspár, P., Szászi, I., Bokor, J. (2003). Design of robust controllers for active vehicle suspension using the mixed synthesis. Vehicle System Dynamics, vol. 40, no. 4, p. 193-228. [2] Luo, R.K., Wu, W.X. (2006). Fatigue failure analysis of antivibration rubber spring. Engineering Failure Analysis, vol. 13, no. 1, p. 110-116.

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Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 61-71

[3] Li, Q., Zhao, J., Zhao, B. (2009). Fatigue life prediction of a rubber mount based on test of material properties and finite element analysis. Engineering Failure Analysis, vol. 16, no. 7, p. 2304-2310. [4] Oman, S., Fajdiga, M., Nagode, M. (2010). Estimation of air-spring life based on accelerated experiments. Materials and Design, vol. 31, no. 8, p. 3859-3868. [5] Oman, S., Nagode, M. (2013). On the influence of the cord angle on air-spring fatigue life. Engineering Failure Analysis, vol. 27, p. 61-73. [6] Wang, L.R., Wang, J.C., Hagiwara, I. (2005). An integrated characteristic simulation method for hydraulically damped rubber mount of vehicle engines. Journal of Sound and Vibration, vol. 286, no. 4-5, p. 673-696. [7] Kim, J.J., Kim, H.Y. (1997). Shape design of an engine mount by a method of parameter optimization. Computers and Structures, vol. 65, no. 5, p. 725-731. [8] Choi, K.K., Duan, W. (2000). Design sensitivity analysis and shape optimization of structural components with hyperelastic material. Computer Methods in Applied Mechanics and Engineering, vol. 187, p. 219-243. [9] Ramachandran, T., Padmanaban, K.P., Nesamani, P. (2012). Modeling and analysis of IC engine mount using finite element method and RSM. Procedia Engineering, vol. 38, p. 1683-1692.

[10] Lee, J.S., Kim, S.C. (2007). Optimal design of engine mount rubber considering stiffness and fatigue strength. Journal of Automobile Engineering, vol. 221, no. 7, p. 823-835. [11] Drucker, H., Bruges, C.J.C., Kaufman, L., Smola, A.J., Vapnik, V. (1997) Support vector regression machines. Advances in Neural Information Processing System, vol. 9, p. 155-161. [12] Andrés, E., Salcedo-Sanz, S., Monge, F., Pérez-Bellido, A.M. (2012). Aerodynamic design through evolutionary programming and support vector regression algorithm. Expert Systems with Applications, vol. 39, no. 12, p. 10700-10708. [13] Haykin, S. (2009). Neural networks and learning machines. Pearson Prentice Hall, Upper Saddle River. [14] Karatzoglou, A., Meyer, D., Hornik, K. (2006). Support vector machines in R. Journal of Statistical Software, vol. 15, no. 9, p. 1-28. [15] Boyd, S., Vandenberghe, L. (2009). Convex Optimization. Cambridge University Press, Cambridge. [16] Bonet, J., Wood, R.D. (1997). Nonlinear continuum mechanics for finite element analysis. Cambridge University Press, Cambridge, p. 248. [17] Bathe, K.J. (1996). Finite Element Procedures. Prentice Hall, New Jersey. [18] Mankovits, T., Szabó, T. (2012). Finite element analysis of rubber bumper used in air-spring. Procedia Engineering, vol. 48, p. 388-395.

Optimization of the Shape of Axi-Symmetric Rubber Bumpers

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 72-74 List of reviewers

List of reviewers who reviewed manuscripts in 2013

Abdi Meisam, UK Abu Bakar Abd Rahim, Malaysia Adams Mike, UK Ahmadi Iman, Iran Aladag Cagdas Hakan, Turkey Almeida Luis F., Brazil Ambrož Miha, Slovenia Arkar Ciril, Slovenia Arslan Kamil , Turkey Arslan Kamil, Turkey Astakhov Viktor P., USA Babnik Aleš, Slovenia Baer Sebastian, Germany Baginski Frank E., USA Bajić Dražen, Croatia Balestrassi Pedro P., Brazil Balič Jože, Slovenia Barkey Mark E., USA Bauer Branko, Croatia Baykara Cemal, Turkey Bazaras Žilvinas, Lithuania Beckman Scott P., USA Belingardi Giovanni, Italy Bergada Josep M., Spain Bergant Anton, Slovenia Berger Gerald, Austria Bibb Richard, UK Biermann Dirk, Germany Biluš Ignacijo, Slovenia Bobovnik Gregor, Slovenia Bolarinwa Emmanuel, USA Bolmsjö Gunnar, Sweden Boltežar Miha, Slovenia Bordinassi Éd Claudio, Brazil Borkowski Przemyslaw, Poland 72

Boulougris Evangelos, UK Bourell David L., USA Brajlih Tomaž, Slovenia Brandao Lincoln Cardoso, Brazil Brezovnik Simon, Slovenia Brojan Miha, Slovenia Brunčko Mihael, Slovenia Bück Andreas, Germany Buendía Juana Abenójar, Spain Butala Peter, Slovenia Cardon Ludwig, Belgium Carrera Erasmo, Italy Castaño Ramón Barber, Spain Ceccarelli Marco, Italy Chandrashekhara K., USA Chen Gang, Denmark Chen Yikai, China Chierichetti Maria, USA Cogun Can, Turkey Costa Mario, Portugal Cumunel Gwendal, France Čep Robert, Czech Republic Čepon Gregor, Slovenia Čirić-Kostić Snežana, Serbia Čudina Mirko, Slovenia Čuš Franci, Slovenia Debevec Mihael, Slovenia Di Puccio Francesca, Italy Diaci Janez, Slovenia Dick Andrew J., USA Diniz Anselmo Eduardo, Brazil Domazet Željko, Croatia Donevski Božin, R. of Macedonia Dražumerič Radovan, Slovenia Dubé Jean François, France

Emri Igor, Slovenia Erickson Paul A., USA Erklig Ahmet, Turkey Ersoy Hakan, Turkey Escaler Xavier, Spain Fajdiga Matija, Slovenia Fang Mingjing, China Fefer Dušan, Slovenia Felde Imre, Hungary Fetvaci Cuneyt, Turkey Ficko Mirko, Slovenia Filipič Bogdan, Slovenia Flašker Jože, Slovenia Flores Paulo, Portugal Fondón García Irene, Spain Franco Patricio, Spain Friesenbichler Walter, Austria Frontini Patricia, Argentina Gambarotta Agostino, Italy García Andrés Gabriel, Argentina Gašperšič Rok, Slovenia Glodež Srečko, Slovenia Golpira Hiwa, Iran Gómez Jáuregui Valentín, Spain Gotlih Karel, Slovenia Graizzaro Alessandro, Italy Green Daniel E., Canada Grimberg Raimond, Romania Grum Janez, Slovenia Gu Junjie, Canada Gusel Leo, Slovenia Gutiérrez Eugenio, Italy Guven Aybars, Turkey Habak Malek, France Hansen Niels, Denmark

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 72-74

Harl Boštjan, Slovenia Horvat Darja, Slovenia Hriberšek Matjaž, Slovenia Hu Zhong, USA Ibaraki Soichi, Japan Ihalainen Petri, Finland Israr Mohammad, India Jauregui Juan Carlos, Mexico Jenko Marjan, Slovenia Jerman Boris, Slovenia Jezeršek Matija, Slovenia Jošt Dragica, Slovenia Jozić Sonja, Croatia Kabele Karel, Czech Republic Kalin Mitjan, Slovenia Kamnik Roman, Slovenia Kaplunov Julius, UK Karacali Ozdogan, Turkey Karadžić Uroš, Montenegro Karger-Kocsis József, Hungary Katrašnik Tomaž, Slovenia Kegl Marko, Slovenia Kessler Franz, Austria Khader Iyas, Germany Kirstein N. Kaspar, Denmark Kitazaki Satoshi, USA Kivak Turgay, Turkey Klančnik Simon, Slovenia Klemenc Jernej, Slovenia Klit Peder, Denmark Kljajin Milan, Croatia Klocke Fritz, Germany Koc Pino, Slovenia Kopač Janez, Slovenia Kosel Tadej, Slovenia Köveš Arpad, Slovenia Krajnik Peter, Slovenia Kramar Davorin, Slovenia Kramberger Janez, Slovenia Krella Alicja, Poland Krese Gorazd, Slovenia Kristl Živa, Slovenia Kušar Janez, Slovenia

Kyratsis Panagiotis, Greece Lam Jasmine, Singapore Lebar Andrej, Slovenia Leppert Tadeusz, Poland Lerher Tone, Slovenia Li Xiaochun, USA Liu Huibin, USA Liu Zhiqiang, China Liu Zhong-Liang, China Lojen Gorazd, Slovenia Lovrec Darko, Slovenia Lozina Željan, Croatia Lu Hongbing, USA Lübben Thomas, Germany Magyar Balázs, Germany Majdič Franc, Slovenia Mazal Pavel, Czech Republic Menezes Luís Filipe, Portugal Merkuriev Yuri, Latvia Mešter Gyula, Hungary Mignosa Paolo, Italy Mihalić Tihomir, Croatia Miličević Miroslav, Serbia Milinović Momčilo, Serbia Ming Xu, China Mirzaei Majid, Iran Mole Nikolaj, Slovenia Molfino Rezia, Italy Monno Michele, Italy Morina Ardian, UK Motorcu Ali Riza, Turkey Možina Janez, Slovenia Muthukannan Duraiselvam, India Nagode Marko, Slovenia Nastac Laurentiu, USA Natesan Kanthavelkumaran, India Ng Adolf, Canada Nikas George, UK Nikitakos Nikitas, Greece Nikolić Saša S., Serbia Nikonov Anatolij, Slovenia Nurmikolu Antti, Finland Okorn Ivan, Slovenia

Oman Simon, Slovenia Ozturk Sabri, Turkey Palpacelli Matteo-Claudio, Italy Paunescu Doru, Romania Pavić Miloš, Serbia Pavlou Dimitrios, Greece Peddieson John, USA Pehan Stanislav, Slovenia Peng Peng, USA Peperko Aljoša, Slovenia Perkovič Marko, Slovenia Persson Karin, Sweden Petersen Eric, USA Pevec Miha, Slovenia Pietrusiak Damian, Poland Plančak Miroslav, Serbia Podgornik Bojan, Slovenia Pogrebnyak Aleksander, Ukraine Polach Pavel, Czech Republic Popović Vladimir, Serbia Postawa Przemyslaw, Poland Potočnik Primož, Slovenia Potrč Iztok, Slovenia Pouzada Antonio, Portugal Precup Radu-Emil, Romania Prezelj Jurij, Slovenia Prvulović Slavica, Serbia Przybyla Craig, USA Pustaić Dragan, Croatia Pušavec Franci, Slovenia Radkowski Stanisław, Poland Rahnejat Homer, UK Rauchs Gaston, Luxembourg Ravnik Jure, Slovenia Razfar Mohammad, Iran Rihtaršič Janez, Slovenia Sadilek Marek, Czech Republic Sagade Atul, India Salacinski Tadeusz, Poland Santos Rafael, Belgium Scavuzzo Rudolph, USA Scheidl Rudolf, Austria Schöppner Volker, Germany 73

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, 72-74

Schuöcker Dieter, Austria Schuschnigg Stephan, Austria Senegačnik Andrej, Slovenia Simani Silvio, Italy Slabe Janez Marko, Slovenia Slavič Janko, Slovenia Smutny Jaroslav, Czech Republic Soares Carlos, Portugal Solis Adriano, Canada Spindler Lea, Slovenia Stanković Tino, Switzerland Starbek Marko, Slovenia Stiemer Marcus, Germany Su Changqing, China Sun Guifang, USA Šajn Viktor, Slovenia Šeruga Domen, Slovenia Šitum Željko, Croatia Škraba Andrej, Slovenia

Štok Boris, Slovenia Šturm Roman, Slovenia Tapaninen Ulla, Finland Tavčar Jože, Slovenia Tibullo Vincenzo, Italy Toppila Esko, Finland Totis Giovanni, Italy Tušek Janez, Slovenia Udiljak Toma, Croatia Ulaga Samo, Slovenia Uysal Alper, Turkey Uzunsoy Erdem, Turkey Valentinčič Joško, Slovenia Voloshin Arkady, USA Vosoughifar Hamid Reza, Iran Vrabič Rok, Slovenia Vuherer Tomaž, Slovenia Vukašinović Nikola, Slovenia Wang Chao, USA

Wang Gongyao, USA Weber Gerhard-Wilhelm, Turkey Willner Kai, Germany Winczek Jerzy, Poland Winner Hermann, Germany Xiaohong Zhang, China Yan Xinping, China Yazici Murat, Turkey Yeh Rong-Hua, Taiwan Yesilce Yusuf, Turkey Zhang Jie, UK Zhang Qin He, China Zupanič Franc, Slovenia Zvoncan Marek, Slovak Republic Žavbi Roman, Slovenia Žerovnik Pavel, Slovenia Žlajpah Leon, Slovenia Župerl Uroš, Slovenia

The Editorial would like to thank all the reviewers in participating in reviewing process. We appreciate the time and effort and greatly value the assistance as a manuscript reviewer for Strojniški vestnik – Journal of Mechanical Engineering.

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1 Vsebina

Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 60, (2014), številka 1 Ljubljana, januar 2014 ISSN 0039-2480 Izhaja mesečno

Uvodnik

SI 3

Razširjeni povzetki člankov Darja Steiner Petrovič, Roman Šturm: Drobna morfologija silicijeve elektropločevine po laserskem površinskem legiranju s prahom Sb Wei Teng, Feng Wang, Kaili Zhang, Yibing Liu, Xian Ding: Zaznavanje jamičenja na prenosniku vetrne turbine z empirično dekompozicijo oblik Pavel Žerovnik, Dušan Fefer, Janez Grum: Ocenjevanje integritete površin iz časovnih zakasnitev napetostnih signalov magnetnega Barkhausnovega šuma Govindaraj Elatharasan, Velukkudi Santhanam Senthil Kumar: Korozijska analiza aluminijeve zlitine AA 7075, varjene z gnetenjem Tomaž Berlec, Janez Kušar, Janez Žerovnik, Marko Starbek: Optimiranje velikosti serij izdelkov Jijun Yi, Tao Zeng, Jianhua Rong: Optimizacija topologije v kontinuumu ob upoštevanju omejitve globalnega pomika Tomasz Trzepieciński, Hirpa G. Lemu: Študija tornih lastnosti pločevine iz aluminijeve zlitine AA5251 s simulatorjem zavorne letve in numeričnimi metodami Tamás Mankovits, Tamás Szabó, Imre Kocsis, István Páczelt: Optimizacija oblike osnosimetričnih gumijastih blažilnikov Osebne vesti Doktorske disertacije, znanstveno magistrsko delo, diplomske naloge

SI 5 SI 6 SI 7 SI 8 SI 9 SI 10 SI 11 SI 12 SI 13

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1 Uvodnik

Uvodnik

60 let

Od leta 1955: Strojniškega vestnika - Journal of Mechanical Engineering Jubilejni uvodnik pišem na zadnji dan leta 2013, torej na Silvestrovo, ko si zaželimo veliko dobrih želja v prihajajočem letu, ter se ob tem ozremo v preteklost in razmislimo o uspehu in učinkovitosti našega delovanja in ustvarjanja. Ponovno je minilo zelo uspešno in naporno leto uredniškega dela revije, rojene v letu 1955. Vstopamo v 60. leto delovanja, že zdavnaj smo torej zapustili najstniška leta, kljub temu so ta še vedno prisotna v naših srcih in aktivnostih pri delu. Toda iz leta v leto revija postaja zrelejša. Relativna mladost nam vpliva nova upanja in cilje ter zagotavlja potrebno energijo in zanos. Strojniški vestnik – Journal of Mechanical Engineering (SV-JME) je vplivna in kakovostna revija od samega začetka leta 1955, ko se je porodila zamisel za izdajanje tehniške besede v tiskani obliki za povezovanje čedalje večje raznolikosti raziskav v strojništvu. V začetku namenjena predvsem ožji domovini, z razvojem pa tudi mednarodni javnosti, SV-JME vseskozi deluje v okviru skromnih možnosti majhnosti. Vendar tudi majhnost lahko omogoča signifikantno mednarodno odmevnost. Naj mi bo dovoljeno izpostaviti zgodovinsko gledano pomembnega človeka, očeta naše revije, ustanovnega in dolgoletnega urednika zaslužnega prof. dr. h.c. Bojana Krauta.

angleškem jeziku, v letu 1997 se v kolofonu revije prvič pojavijo imena mednarodnih članov uredniškega odbora, od leta 1998 je SV-JME v bazi Science Citation Indeks (SCI) ter od leta 2010 izhajajo članki samo v angleškem jeziku z enostranskim povzetkom v slovenskem jeziku. Mednarodni ugled revije se iz leta v leto povečuje, v letu 2012 je revija prešla v drugo četrtino kakovosti (Q2).

K temu uspehu poleg avtorjev člankov in uredništva prispevajo tudi naši recenzenti (spisek recenzentov za leto 2013 je objavljen na straneh 72 do 74). Ob tej priložnosti se ponovno zahvaljujemo vsem recenzentom za njihov cenjeni čas in požrtvovalno pripadnost reviji, kar omogoča, da so članki pravočasno in kakovostno recenzirani. Priliv člankov se iz leta v letu povečuje, v letu 2013 smo jih v uredništvo prejeli 454, objavljena pa je približno petina člankov.

Revija se je v 60. letih spreminjala tako oblikovno kakor vsebinsko, pa tudi jezikovno. Z 38. zvezkom so bili članki v celoti objavljeni v slovenskem in SI 3

SV-JME ima sedaj faktor vpliva 0.883 (2012) kar je tesno povezano z našo citiranostjo. Na spletni strani revije je brezplačno na voljo njena elektronska različica, letak z objavljenimi članki v preteklih dveh letih, kakor tudi vsi zvezki od leta 2005, tiskano revijo pa je potrebno kupiti.

pri vse večjem obsegu uredniškega dela ter uredniku spletnih strani, g. Darku Švetku za skrb za kakovostno spletno urejanje. Posebna iskrena zahvala gre Javni agenciji za raziskovalno dejavnost Republike Slovenije (ARRS) za sofinanciranje revije, kar trajnostno omogoča izboljševanje nivoja le-te, saj z gotovostjo lahko trdimo, da brez finančne podpore ARRS, revija ne bi obstala. Hvala vsem, ki ste v 60 letih izdajanja revije kakorkoli prispevali k rasti ugleda revije in njeni prepoznavnosti v svetu. Zaželimo reviji srečno pot tudi v letu 2014, pri čemer ne pozabimo: le s skupnimi prizadevanji majhni postajajo veliki. V imenu uredništva vam želim uspešno in znanstveno kreativno leto 2014, prebiranje zanimivih raznolikih člankov v mesečnih izdajah naše revije, čim več uspešnih temeljnih raziskav, odmeven razvoj naprednih tehnologij in interdisciplinarnih odkritij ter novih znanstvenih spoznanj, ki bodo objavljena v naši reviji. Zaupajte nam, mi zaupamo vam! Vincenc Butala Glavni in odgovorni urednik VIRI

Ob visokem jubileju se želim zahvaliti članom Mednarodnega uredniškega odbora ter članom Izdajateljskega sveta SV-JME za njihov doprinos in neomajnost k uresničitvi strateških ciljev naše revije. V septembru 2013 je bil za predsednika Izdajateljskega sveta izvoljen g. prof. dr. Branko Širok, spremembe pa doživlja tudi Mednarodni uredniški odbor. Posebno pozornost in zahvalo posvečam dosedanjemu predsedniku Izdajateljskega sveta g. prof. dr. Jožefu Duhovniku, odlično in kreativno sodelovanje je obrodilo številne sadove. Zahvala tehnični urednici revije ga. Piki Škraba za neumornost in predanost

SI 4

[1] Butala, V. (2010). Strojniški vestnik – Journal of Mechanical Engineering: 55 let. Kalin M. (ur.) Zgodovina strojništva in tehniške kulture na Slovenskem. Univerza v Ljubljani, Fakulteta za strojništvo, Ljubljana, p. 95-105. [2] Butala, V. (2011). Uvodnik, Poglejmo naše dosežke in izkoristimo našo različnost. Strojniški vestnik – Journal of Mechanical Engineering, vol. 57, no. 12, p. 867-868. [3] ISI Web of Knowledge, Thomson Reuters (2013). available at: http://apps.webofknowledge.com/ CitationReport.do?product=WOS&search_mode=Citat ionReport&SID=S2XZVoOpVxW19Y8YuBL&page=1 &cr_pqid=1&viewType=summary accessed 2014-0102.

Prejeto v recenzijo: 2013-07-26 Prejeto popravljeno: 2013-09-30 Odobreno za objavo: 2013-10-30

Drobna morfologija silicijeve elektropločevine po laserskem površinskem legiranju s prahom Sb Steiner Petrovič, D. – Šturm, R. Darja Steiner Petrovič1,* – Roman Šturm2 1 Inštitut

za kovinske materiale in tehnologije, Ljubljana, Slovenija v Ljubljani, Fakulteta za strojništvo, Slovenija

2 Univerza

Neorientirane elektropločevine so mehkomagnetni materiali, ki jih izdelujemo iz silicijevih jekel. Silicijeva jekla so strateškega pomena v evropskem in globalnem merilu za vrsto panog s področja energetike in proizvodnje električnih naprav, saj omogočajo optimalno kombinacijo za prenos in distribucijo električne energije. Lastnosti, ki jih zahtevamo od teh materialov so visoka permeabilnost in indukcija, nizke izgube pri magnetenju in nizka magnetostrikcija. Dandanes lahko višjo dodano vrednost teh proizvodov omogoči njihova kakovost, predvsem visoka permeabilnost in odlične magnetne lastnosti. Magnetenje elektropločevin je močno odvisno od kemijske sestave jekla, pa tudi od njihove nanoteksture, mikrostrukture in teksture. Namen pričujoče raziskave je bil preučiti izvedljivost modifikacije „po meri“ masovnega proizvoda. Glavni cilj raziskave je razviti nove visokokakovostne elektropločevine z odličnimi lastnostmi po meri, za kar smo uporabili nekonvencionalno, a dobro definirano kombinacijo eksperimentalnih metodologij: industrijsko gotovo neorientirano elektropločevino smo lasersko površinsko legirali s prahom površinsko aktivnega elementa antimona (Sb). Za karakterizacijo modificirane elektropločevine smo uporabili metalografsko analizo (svetlobno mikroskopijo, vrstično elektronsko mikroskopijo z energijsko disperzijsko spektroskopijo) in meritve mikrotrdote. Strjevanje silicijevega jekla smo opisali s termodinamičnimi izračuni z računalniško aplikacijo Thermo-Calc. Izdelali smo simulacijo termodinamičnih ravnotežij v modificiranem silicijevem jeklu. Rezultati kažejo, da je uporaba laserskega površinskega legiranja primerna za modifikacijo silicijeve pločevine z Sb. Izbrani parametri laserskega površinskega legiranja omogočajo legiranje silicijevega jekla z Sb do globine približno 0,1 mm. Lastnosti izbranega postopka in ohlajevalni pogoji ustvarita edinstvene pogoje strjevanja, ki zagotavljajo drobno strukturirano morfologijo strjevalne mikrostrukture. V legirani površinski plasti smo izmerili tudi višjo trdoto jekla. Ta predhodna študija predstavlja nov pristop k modifikaciji masovnega proizvoda, to je gotove elektropločevine. Največjo omejitev postopka prestavlja pokanje legirane površinske plasti, kar pa bi bilo mogoče odpraviti z optimizacijo uporabljenih procesnih parametrov. Kombinacija modifikacije površine jekla z laserskim legiranjem s površinsko aktivnim elementom omogoča drobno strukturirano morfologijo strjevalne mikrostrukture. Ti izsledki lahko v prihodnje pozitivno vplivajo na nadaljnji razvoj novih mehkomagnetnih materialov pridobljenih iz silicijevega jekla. Ključne besede: Antimon, lasersko površinsko legiranje, neorientirana elektropločevina, silicijeva jekla, morfologija, mikrostruktura, strjevanje

*Naslov avtorja za dopisovanje: Inštitut za kovinske materiale in tehnologije, Ljubljana, Lepi pot 11, 1000 Ljubljana, Slovenija, darja.steiner@imt.si

SI 5

Prejeto v recenzijo: 2013-07-04 Prejeto popravljeno: 2013-08-31 Odobreno za objavo: 2013-09-27

Zaznavanje jamičenja na prenosniku vetrne turbine z empirično dekompozicijo oblik

Teng, W. – Wang, F. – Zhang, K.L. – Liu, Y.B. – Ding, X. Wei Teng1,2,* – Feng Wang1 – Kaili Zhang1 – Yibing Liu1 – Xian Ding1 1 Severnokitajska univerza za elektroenergetiko, Fakulteta za energetiko in strojništvo, Kitajska 2 Taiyuan

tehnološka univerza, Ministrstvo za izobraževanje, Kitajska

V mnogih vetrnih poljih po svetu se dogaja, da prenosnik odpove le nekaj tisoč ur po zagonu vetrne turbine, doba uporabnosti pa je mnogo krajša od načrtovane. Prenosnik vetrne turbine je sestav, ki pretvarja nizko vrtilno hitrost rotorja turbine v visoko hitrost generatorja, njegova konstrukcija pa je lahko zelo zapletena. Zato skušamo poiskati inteligentno metodo za zaznavanje okvare prenosnika ter postaviti mehanizem za ohranitev visoke učinkovitosti vetrne turbine. Empirična dekompozicija oblik (EMD) je uporabno časovno-frekvenčno orodje za adaptivno dekompozicijo signala vibracij v zbirko funkcij lastnih nihajnih oblik (IMFs), v tem članku pa je uporabljena za razkrivanje jamičenja v visokohitrostni stopnji prenosnika vetrne turbine. Postopek EMD je bil uporabljen za obdelavo signala vibracij na prenosniku dejanske vetrne turbine z imensko izhodno močjo 600 kW. Postopek EMD je bil za ponazoritev inteligentnega učinka primerjan s konvencionalno Hilbertovo demodulacijsko analizo. Na nizko- in visokohitrostno stopnjo prenosnika vetrne turbine so bili prilepljeni štirje merilni pretvorniki pospeška, štirje signali vibracij pa so bili nato analizirani po postopkih Hilbertove demodulacije in EMD. V eni uri je bilo vsako minuto zajetih 57 skupin podatkov o vibracijah iz drugega merilnega pretvornika ter obdelanih po postopkih EMD in Hilbertove demodulacije. Hilbertova demodulacija lahko zazna vrtilno frekvenco gredi s poškodovanim zobnikom, ki je hkrati tudi modulacijska frekvenca, pri tej metodi pa je potreben človeški poseg za izbiro resonančnega območja za frekvenčni pas filtra v spektru gostote moči. Postopek EMD lahko nasprotno razkrije okvare prenosnika vetrne turbine tudi brez človeških posegov in je hkrati prilagodljivejši. Rezultati analize kažejo visoko stopnjo jamičenja na zobniškem paru visokohitrostne stopnje, ki se ujema z rezultati vizualne kontrole skozi okence v prenosniku vetrne turbine. Članek podaja inteligentno metodo za zaznavanje jamičenja v prenosniku vetrne turbine na podlagi postopka EMD, ki pa ne omogoča ugotavljanja stopnje okvarjenosti. Kvantitativni kazalnik stopnje okvarjenosti zobnikov v prenosniku vetrne turbine bi bil ključnega pomena za napovedovanje odpovedi in odločanje o vzdrževanju. Prenosniki vetrnih turbin pa delujejo v zahtevnih pogojih spreminjajočih se obremenitev zaradi vetrnih turbulenc in v prihodnjih raziskavah bi veljalo preučiti kvantitativni kazalnik stopnje okvarjenosti prenosnika vetrne turbine, ki bi lahko izključil moteče vplive vetrnih turbulenc. Naša ekipa preučuje ustrezne teme, o katerih bomo poročali v prihodnjih prispevkih. Uporaba EMD za diagnostiko okvar v objavljeni literaturi kaže na dobre možnosti pri obdelavi nestacionarnih signalov vibracij. Ti uspešni primeri pa uporabljajo predvsem simulirane signale testnih sistemov, ki se precej razlikujejo od dejanske situacije. V članku je prikazana uporaba postopka EMD za obdelavo signalov vibracij prenosnika dejanske vetrne turbine, učinkovitost postopka EMD pa je ponazorjena s primerjavo s Hilbertovo demodulacijsko analizo. Ključne besede: empirična dekompozicija oblik, Hilbertova demodulacijska analiza, adaptivnost, odkrivanje napak, vetrna turbina, prenosnik

SI 6

*Naslov avtorja za dopisovanje: Severnokitajska univerza za elektroenergetiko, Fakulteta za energetiko in strojništvo, Peking, 102206, Kitajska, tengw@ncepu.edu.cn

Prejeto v recenzijo: 2012-12-11 Prejeto popravljeno: 2013-03-11 Odobreno za objavo: 2013-07-05

Ocenjevanje integritete površin iz časovnih zakasnitev napetostnih signalov magnetnega Barkhausnovega šuma Žerovnik, P. – Fefer, D. – Grum, J. Pavel Žerovnik1 – Dušan Fefer2 – Janez Grum1,* 1 Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija 2 Univerza v Ljubljani, Fakulteta za elektrotehniko, Slovenija

V članku je predstavljena metoda vrednotenja napetostnih signalov magnetnega Barkhausnovega šuma, ki temelji na časovnih zakasnitvah napetostnih signalov glede na sinusoido magnetilnega toka. Z metodo lahko primerjamo mikrostrukturo in mehanske lastnosti po hladni deformaciji in po toplotni obdelavi. Mikromagnetna metoda je zelo primerna tudi za neporušno testiranje jekel v različnih stanjih, kakor tudi za neporušno določanje zaostalih napetosti. Fizikalno ozadje magnetne metode na osnovi Barkhausnovega šuma temelji na dejstvu, da vsak feromagnetni material pri magnetenju z določeno magnetilno frekvenco in magnetilnim tokom vsebuje majhna magnetna področja, imenovana magnetne domene. Med procesom magnetenja se premikajo stene magnetnih domen, kar povzroča sunkovito naraščanje gostote magnetnega pretoka. Z ustrezno senzorsko enoto lahko pri tem zajemamo inducirane napetostne sunke. Večino jekel uvrščamo med feromagnetne materiale, ki imajo različne mehanske lastnosti oziroma so izpostavljeni različnim zunanjim mehanskim vplivom. Omenjene spremembe vplivajo na intenzivnost in dinamiko nastajanja magnetnih domen, oziroma na premikanje sten magnetnih domen. Tako dobimo različne signale magnetnega Barkhausnovega šuma, ki so značilni za določen material oziroma za določeno stanje materiala. Za uspešno raziskovalno delo pri analizi stanja materiala z obravnavano mikromagnetno metodo, kakor tudi za uspešno uvajanje te metode v avtomatizirano proizvodnjo, sta razen razvoja senzorske tehnike zelo pomembna tudi obdelava in vrednotenje zajetih napetostnih signalov. Razen izbire prave značilke, določene iz napetostnega signala, je treba postaviti tudi nivojske kriterije za oceno kakovosti oziroma stanja površine. V prispevku so bile iz poteka napetostnega signala magnetnega Barkhausnovega šuma določene ovojnice, ki jih oblikujemo s pomočjo računalniškega programa. Za izris ovojnice je treba določiti začetek in konec signala, ki ga razdelimo na n enakih delov. Na vsakem n-tem delu nato določimo povprečno amplitudno vrednost napetostnih impulzov. Dobljene točke s pomočjo geometrične regresije popišejo ovojnico zajetega napetostnega signala. Najvišja točka na ovojnici predstavlja osrednji del zajetega napetostnega signala. Časovne zamike smo določili in izmerili od točke, ki predstavlja presečišče sinusoide toka magnetenja z abscisno osjo in osrednjim delom zajetega napetostnega signala magnetnega Barkhausnovega šuma. Primerjave časovnih zakasnitev napetostnih signalov so bile opravljene na poboljšanih vzorcih z visokim popuščanjem pri različnih temperaturah. Izbrani sta bili dve ravni temperatur visokega popuščanja, in sicer ∆T1 = 10 °C ter ∆T2 = 25 °C. Majhne razlike v temperaturi popuščanja med dvema sosednjima vzorcema posledično vplivajo tudi na majhne razlike v doseženi trdoti materiala. S Studentovim t-testom je bila ocenjena zanesljivost napovedovanja trdote z izbrano metodo iz značilke napetostnega signala, to je časovne zakasnitve signala. Primerjalni rezultati merjenja mikrotrdote po Vickersovi metodi in na osnovi časovnih zakasnitev magnetnega Barkhausenovega šuma so znotraj 16 enot po Vickersu. Test je potrdil, da je izbrana mikromagnetna metoda vrednotenja signalov zelo hitra, ponovljiva in zanesljiva, kar ustreza današnjim zahtevam v avtomatizirani proizvodnji. Ključne besede: mikromagnetna metoda, Barkhausnov šum, časovna zakasnitev napetostnih signalov, trdota, Studentov t-test, zanesljivost

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

SI 7

Prejeto v recenzijo: 2012-07-24 Prejeto popravljeno: 2013-04-22 Odobreno za objavo: 2013-05-13

Korozijska analiza aluminijeve zlitine AA 7075, varjene z gnetenjem Elatharasan, G. – Senthil Kumar, V.S. Govindaraj Elatharasan – Velukkudi Santhanam Senthil Kumar* Univerza Anna, Tehniški kolidž Guindy, Oddelek za strojništvo, Indija

Prispevek pri tem raziskovalnem delu je bila preučitev vpliva procesnih parametrov na korozijsko obstojnost aluminijeve zlitine AA7075, varjene z gnetenjem. Varjenje z gnetenjem (FSW) je v primerjavi z navadnim laserskim varjenjem, ki spada med talilne postopke, okolju prijaznejša in energijsko varčnejša tehnologija. Varjenje z gnetenjem je bilo uporabljeno tudi v eksperimentih in analizah izboljševanja korozijske obstojnosti. Aluminijeva zlitina AA7075 (Al–Zn–Mg–Cu) je ena od najmočnejših aluminijevih zlitin, ki se danes uporablja v industriji. Zaradi dobrega razmerja med trdnostjo in težo ter njenih značilnosti naravnega staranja je lahko primerna za številne dele letalskih konstrukcij. Pri postopku varjenja z gnetenjem se plastično stanje kovine doseže s posebej zasnovanim valjastim orodjem z ramenskim delom in varilnim čepom malega premera, ki se vrti med dvema sočelno staknjenima površinama in tako ustvari močan zvarni spoj. Proces spajanja se dogaja pri temperaturah pod tališčem materiala, tvorijo pa se tri značilna območja mikrostrukture: leča, termomehansko vplivana cona (TMAZ) in toplotno vplivana cona (HAZ). Leča nastane v območju, skozi katerega gre čep orodja ter je podvrženo visoki stopnji deformacije in vplivu toplote. Sestavljena je iz finih enakoosnih zrn, ki nastanejo s polno rekristalizacijo. Termomehansko vplivana cona zraven leče je območje, kjer je kovina plastično deformirana in ogreta, kar pa ne zadošča za rekristalizacijo. Toplotno vplivana cona je podvržena samo vplivu segrevanja, do mehanskih deformacij pa ne pride. Tehnike obdelave površine lahko izboljšajo korozijsko obstojnost zlitine tako, da ji spremenijo mehanske lastnosti. Parametri orodja imajo ključno vlogo pri določanju lastnosti spoja. Čeprav se na površini aluminija tvori tanek zaščitni oksidni sloj, se lahko le-ta v agresivnem okolju poškoduje in posledično pride do korozije. Zlasti v okolju, kjer je prisotna sol (NaCl), nastajajo aluminijevi kloridi, ki zmanjšujejo učinkovitost oksidnega sloja pri preprečevanju korozije. Zato je bil preučen vpliv parametrov varjenja z gnetenjem na korozijske lastnosti zvara. Primerjane so bile lastnosti elektromehanske korozivnosti za material zvara in osnovni material. Delovna elektroda iz zlitine AA7075 je bila uporabljena v običajnem trielektrodnem sestavu s platinastim filmom kot protielektrodo in nasičeno kalomelovo elektrodo (SCE) kot referenčno elektrodo. Korozijske lastnosti, ki so bile ugotavljane s polarizacijo in elektrokemično impedančno spektroskopijo v 3,5 % NaCl, je mogoče izboljšati z različnimi strategijami (zlasti z uravnavanjem vrtilne hitrosti in hitrosti pomika orodja). Mikrostruktura na različnih mestih po debelini plošče iz aluminijeve zlitine je bila ugotovljena ob različnih vrednostih parametrov kot sta vrtilna hitrost in hitrost pomika. Toplotno vplivana cona zvara je najdovzetnejša za interkristalno korozijo. Iz rezultatov je mogoče povzeti, da je varjenje z gnetenjem primerno za izdelavo trdnih zvarov zlitine AA7075. Korozijska obstojnost se zmanjša ob povečanju hitrosti pomika iz 0,37 na 0,76 mm/s pri vrtilni hitrosti 800 vrt/ min. Korozijska obstojnost pri vrtilni hitrosti 1000 vrt./min. je manjša kot pri 1200 vrt./min. Korozijsko obstojnost je mogoče izboljšati tudi z razbijanjem in topljenjem intermetalnih delcev. Prihodnje raziskave bodo obravnavale spajanje dveh toplotno utrjevalnih aluminijevih zlitin AA6061 in AA7075 po postopku varjenja z gnetenjem ter vrednotenje njihove korozijske obstojnosti v 3,5 % raztopini NaCl. Ključne besede: varjenje z gnetenjem, mikrostruktura, topljenje intermetalnih delcev, aluminijeva zlitina, AA7075, korozija

SI 8

*Naslov avtorja za dopisovanje: Univerza Anna, Tehniški kolidž Guindy, Oddelek za strojništvo, Chennai 600025, Tamilnadu, Indija, vsskumar@annauniv.edu

Prejeto v recenzijo: 2013-01-28 Prejeto popravljeno: 2013-06-27 Odobreno za objavo: 2013-08-23

Optimiranje velikosti serij izdelkov

Berlec, T. – Kušar, J. – Žerovnik, J. – Starbek, M. Tomaž Berlec* – Janez Kušar – Janez Žerovnik – Marko Starbek Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija

Pri vstopu na svetovni trg se podjetja srečujejo z več težavami, med katerimi ima pomembno mesto tudi določanje optimalne velikosti serij izdelkov. V osnovi obstajata dve možnosti planiranja velikosti serij izdelka, in sicer planiranje velikih serij izdelka v dolgih časovnih presledkih ter planiranje majhnih serij izdelka v krajših časovnih presledkih. Prednosti pri planiranju velikih serij izdelka so: cenovna prednost naročanja velike serije izdelka (nizka cena, varnost pred dvigom cene, količinski rabat), prihranek stroškov zaradi manjšega obsega administrativnih operacij, prihranek stroškov preizkusov in odpreme, ter majhno tveganje prekinitve proizvodnje zaradi velike zaloge. Slabosti so: velika vezava kapitala ter veliki stroški skladiščenja zaloge izdelka. Prednosti planiranja pri majhnih serijah izdelka so: majhna vezava kapitala, majhni stroški skladiščenja zaloge ter velika fleksibilnost z ozirom na spremembe količin pri dobaviteljih in kupcih, slabosti pa so: stroški pogostega naročanja in veliko tveganje prekinitev proizvodnje zaradi majhne zaloge izdelka. Med planiranjem velikih in majhnih serij izdelka pa se nahaja stroškovno optimalna velikost serije izdelka, torej velikost serije, pri kateri bodo stroški na enoto izdelka minimalni. V članku predstavljamo pot določitve stroškovno optimalne velikosti serije izdelka po osnovnem modelu, ki upošteva stroške menjave serije (stroški izdelave dokumentacije, stroški kontrole in vhoda blaga, stroški plač delavcev, stroški delovnih sredstev med pripravo ter stroški izdelave vzorcev) in skladiščne stroške (stroški obresti na vezani kapital in stroški skladiščenja). Optimalna velikost naročila pri osnovnem modelu xOpt bo tista velikost, pri kateri bo vsota letnih stroškov menjave naročil in skladiščnih stroškov minimalna. Do optimalne velikosti naročila za osnovni model se pride v štirih korakih: 1. korak: Določitev letnih stroškov menjave naročila. 2. korak: Določitev letnih skladiščnih stroškov. 3. korak: Določitev vsote letnih stroškov menjave naročila in skladiščnih stroškov – osnovni model. 4. korak: Določitev stroškovno optimalne velikosti naročila xOpt – osnovni model. Poleg osnovnega modela je prikazan še razširjeni model, ki razen stroškov menjave serije in skladiščnih stroškov upošteva tudi stroške vezave kapitala v proizvodnji, torej stroške izvedbe operacij naročila v proizvodnji in stroške odlaganja – prehodov. Optimalna velikost naročila pri razširjenem modelu bo tista, pri kateri bo vsota letnih stroškov menjave naročila, skladiščnih stroškov, stroškov izvedbe operacij naročila in stroškov prehodov minimalna. Do optimalne velikosti naročila za razširjeni model se pride v zaporedju šestih korakov: 1. korak: Določitev letnih stroškov menjave naročila. 2. korak: Določitev letnih skladiščnih stroškov. 3. korak: Določitev letnih stroškov zaradi časov obdelave naročila. 4. korak: Določitev letnih stroškov zaradi časov odlaganja – prehodov. 5. korak: Določitev vsote letnih stroškov – razširjeni model. 6. korak: Določitev stroškovno optimalne velikosti naročila – razširjeni model. Članek se zaključi s primerom določanja optimalne velikosti serij izdelkov po osnovnem in razširjenem modelu v slovenskem podjetju, ki dobavlja komponente proizvajalcu osebnih vozil, ter z ugotovitvami, kdaj uporabiti osnovni in kdaj razširjeni model določanja optimalne velikosti serij izdelkov. Za optimalne velikosti serij so izračunani tudi pretočni časi serij, pripadajoči stroški vezave kapitala na kos ter razlika v stroških na kos pri uporabi osnovnega in razširjenega modela določanja optimalne velikosti serij. Na osnovi izračuna optimalnih velikosti serij je bilo v podjetju ugotovljeno, da izračunane optimalne velikosti serij močno odstopajo od trenutno uporabljenih velikosti serij, kar ima za posledico velike skladiščne stroške in dolge pretočne čase. Vodstvo podjetja se je odločilo, da projektni tim izvede še JE-analizo toka vrednosti pri obstoječih velikostih serij izdelkov. Po prehodu na optimalne serije bo projektni tim ponovil analizo toka vrednosti za ista dva izdelka in ugotovil prihranke pri pretočnih časih. Ključne besede: optimalna serija, vezava kapitala, skladiščni stroški, čas na enoto mere, pripravljalni čas, pretočni čas, čas izvedbe, čas prehoda *Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, tomaz.berlec@fs.uni-lj.si

SI 9

Prejeto v recenzijo: 2013-01-02 Prejeto popravljeno: 2013-05-23 Odobreno za objavo: 2013-11-12

Optimizacija topologije v kontinuumu ob upoštevanju omejitve globalnega pomika Yi, J.J. – Zeng, T. – Rong, J.H. Jijun Yi1,2,* – Tao Zeng2 – Jianhua Rong1

2 Univerza

1 Univerza srednjega juga, Fakulteta za strojništvo in elektrotehniko, Kitajska za znanost in tehnologijo Changsha, Fakulteta za avtomobilsko tehniko in strojništvo, Kitajska

Cilj topološke optimizacije konstrukcij v kontinuumu je iskanje najboljše porazdelitve razpoložljivega materiala po vnaprej opredeljeni konstrukcijski domeni ob izpolnjevanju določenih pogojev. Cilj večine metod za optimizacijo topologije je določitev konstrukcij z maksimalno togostjo, ki pa je povezana z globalnim pomikom in še zlasti z maksimalnim pomikom konstrukcije. Maksimalni pomik je potrjen, ko je konstrukcija zasnovana in se išče konstrukcija z želenim maksimalnim pomikom. Na podlagi spremenljivke gostote vozlišč ter interpolacijske sheme racionalne aproksimacije materialnih lastnosti (RAMP) je bila razvita nova topološka metoda za globalni pomik in zmanjšanje prostornine konstrukcije. Predlagan je nov pristop k nadzorovanju maksimalnega pomika konstrukcije. Metoda za predstavitev ekvivalentnega maksimalnega pomika uporablja pomik s p-normo, s čimer se izognemo neodvedljivosti funkcije maksimuma. Razvita je nova optimizacija topologije za natančen nadzor globalnega maksimalnega pomika. Obravnavan je vpliv parametra p in dokazano je, da poljubno izbrana vrednost parametra p ne vpliva na končni maksimalni pomik. Postavljen je tudi enakovreden model optimizacije s spremenljivimi omejitvami pomika s pomočjo razvoja v Taylorjevo vrsto okrog trenutne točke. Prava ciljna funkcija je zamenjana s kvadratnim približkom. Model dobro predstavlja izvirni model v t.i. območju zaupanja. Območja zaupanja zagotavljajo robustnost iteracij ter pripomorejo k izvedljivosti in doseganju optimuma. Problem optimizacije je končno pretvorjen v reševanje dvojnega problema programiranja s teorijo dvojnosti. V nasprotju s postopkom na osnovi elementov je gostota vozlišč konstrukcijska spremenljivka, ki se v katerikoli točki interpolira s Shepardovimi funkcijami. S to tehniko se izognemo kockastemu vzorcu in odvisnosti mreže za končne elemente nizkega reda. Z omejitvijo globalnega pomika je mogoče dobiti optimalno konstrukcijo z želenimi deformacijami, pri čemer ni treba poznati mesta maksimalnega pomika. Predlagana metoda je zelo uporabna za praktične inženirske naloge in predstavljenih je več primerov, ki potrjujejo uporabnost predlagane metode pri doseganju konvergentnih optimalnih rešitev za konstrukcije z omejenim globalnim pomikom. Ko je uporabljena ista mreža, je strošek računanja optimizacije topologije na osnovi od elementov neodvisne gostote vozlišč večji kot pri pristopu na osnovi elementov. To je glavni vzrok za veliko število vozlišč v domeni vpliva. Ločljivost topologije na osnovi predlaganega pristopa je večja kot pri pristopu na osnovi elementov. Za izboljšanje učinkovitosti predlaganega pristopa bi bilo analizo po metodi končnih elementov in postopek optimizacije mogoče izvesti s tehniko paralelnega programiranja. S takšnim pristopom je mogoče izkoristiti paralelizacijo brez potrebe po večjih spremembah kode. Ključne besede: optimizacija topologije, omejitev globalnega pomika, spremenljivka gostote vozlišč, pomik s p-normo

SI 10

*Naslov avtorja za dopisovanje: Univerza srednjega juga, Fakulteta za strojništvo in elektrotehniko, Changsha, Kitajska, jijunyi@gmail.com

Prejeto v recenzijo: 2013-07-12 Prejeto popravljeno: 2013-09-30 Odobreno za objavo: 2013-10-22

Študija tornih lastnosti pločevine iz aluminijeve zlitine AA5251 s simulatorjem zavorne letve in numeričnimi metodami Trzepieciński, T. – Lemu, H.G. Tomasz Trzepieciński1 – Hirpa G. Lemu2,*

1 Tehniška

2 Univerza

univerza v Rzeszowu, Oddelek za oblikovanje, Poland v Stavangerju, Oddelek za strojništvo in materiale, Norveška

Članek podaja rezultate raziskave vpliva površinske hrapavosti pločevine, pogojev mazanja in orientacije preskušanca na vrednost koeficienta trenja v območju zavorne letve pri postopkih preoblikovanja pločevine. Študija obravnava dva glavna problema: eksperimentalno raziskavo tornih pogojev pri pločevini iz aluminijaste zlitine s tornim preskusom v simulatorju zavorne letve, ter numerične simulacije na osnovi rezultatov tornega preskusa. Torni pogoji pločevine so bili preučeni s simulatorjem torne letve, ki je bil zgrajen po pristopu avtorja Nine (Nine, 1978). Različne tribološke razmere so bile ustvarjene s pomočjo valjev različne površinske hrapavosti. Za preskusni material je bila uporabljena aluminijeva zlitina AA5251, pripravljena z različnimi postopki toplotne obdelave. Glavni standardni 3D-parametri površinske hrapavosti so bili izmerjeni z inštrumentom Alicona InfiniteFocus. Numerični model zavorne letve je bil ustvarjen v programu Msc. MARC Mentat 2010 in opravljenih je bilo več simulacij za preučitev napetostno/deformacijskega stanja v raztegnjenem vzorcu pri preskusu v simulatorju zavorne letve. V simulacijah so bili uporabljeni izotropni von Misesovi modeli in dva anizotropna (Hill1948 in Barlat1991) modela materiala, ki upoštevajo orientacijo preskušanca glede na smer valjanja pločevine. Za mreženje pločevinastega materiala so bili uporabljeni elementi lupine quad4 s petimi integracijskimi točkami po debelini lupine. Za izboljšanje upogibnih lastnosti elementov je bila uporabljena privzeta formula za deformacije. Rezultati eksperimentov razkrivajo več odvisnosti, ki dokazujejo vpliv površinskega profila in mazanja na vrednost koeficienta trenja. Na osnovi eksperimentalnih meritev je mogoče povzeti, da so orientacija preskušanca in pogoji mazanja pomembne spremenljivke, ki vplivajo na koeficient trenja. Za preučitev učinkovitosti mazanja pločevine je bil uveden indeks L. Ugotovljeno je bilo, da je predlagani indeks L v nelinearni odvisnosti od vrednosti parametra hrapavosti. Rezultati simulacij kažejo, da je porazdelitev napetosti pri obeh orientacijah podobna, medtem ko orientacija vzorca vpliva na absolutno vrednost napetosti. Vrednosti strižnih napetosti za Hillovo funkcijo tečenja so bistveno manjše kot pri drugih modelih in enakomernejše predvsem v srednjem delu analizirane širine vzorca. Kriterij tečenja močno vpliva na porazdelitev normalnih in strižnih napetosti. Občutljivost mreže in potrjene rezultate bi bilo treba preučiti z elementi zidaki. Uporabljeni lupinasti elementi niso primerni, če je polmer zavorne letve majhen, pločevina pa debela. Vrednost normalnih napetosti se spreminja po širini pločevine. Zato je potrebna analiza občutljivosti vpliva širine preskušanca ne deformacijo pločevine pri tornem preskusu s simulatorjem zavorne letve. V članku je predstavljen nov numerični pristop k ugotavljanju vrednosti koeficienta trenja pri tornem preskusu v simulatorju zavorne letve. V numeričnih modelih je bila upoštevana anizotropija materiala ter orientacija preskušanca glede na smer valjanja pločevine. Analiza napetostnega stanja je pokazala, da je za reprezentančne rezultate numeričnih simulacij tornega preskusa po Nineu nujna 3D-simulacija modela zavorne letve. Ključne besede: koeficient trenja, zavorna letev, simulacija MKE, trenje, preoblikovanje pločevine

*Naslov avtorja za dopisovanje: Univerza v Stavangerju, N-4036 Stavanger, Norveška, Hirpa.g.lemu@uis.no

SI 11

Prejeto v recenzijo: 2013-07-15 Prejeto popravljeno: 2013-09-11 Odobreno za objavo: 2013-09-25

Optimizacija oblike osnosimetričnih gumijastih blažilnikov Mankovits, T. – Szabó, T. – Kocsis, I. – Páczelt, I. Tamás Mankovits1,* – Tamás Szabó2 – Imre Kocsis1 – István Páczelt2 1 Univerza v Debrecenu, Tehniška fakulteta, Madžarska 2 Univerza

v Miskolcu, Fakulteta za strojništvo in informatiko, Madžarska

Gumijasti blažilniki, vgrajeni v sisteme zračnega vzmetenja avtobusov, opravljajo vrsto pomembnih nalog, konstruiranje gumijastih blažilnikov pa je zato precej zahtevno. V članku je predstavljena nova, praktično uporabna rešitev za zagotavljanje zahtevane karakteristike gumijastih osnosimetričnih blažilnikov. Prava karakteristika podajanja pod obremenitvijo je osnovna zahteva pri snovanju gumijastih blažilnikov. Avtomobilska industrija mehkejšo ali tršo izvedbo gumijastih blažilnikov običajno zagotavlja s spremembo sestave gume. Cilj optimizacije je doseganje zahtevane karakteristike z geometrijsko obliko gumijastega blažilnika ob nespremenjenih lastnostih materiala. Namen raziskave je določanje vedenja gumijastih blažilnikov pri različnih delovnih pogojih. Gumijasti blažilniki se ne upravljajo aktivno, zato je zahtevano karakteristiko mogoče doseči z optimizacijo oblike. Uporabljen je bil postopek z analizo po metodi končnih elementov (MKE) in regresija z metodo podpornih vektorjev (SVR). Za hiter in razmeroma natančen izračun karakteristike gumijastih blažilnikov je bila uporabljena koda končnih elementov, ki so jo avtorji razvili na osnovi funkcionala treh polj. Program za analizo po metodi končnih elementov omogoča preučevanje osnosimetričnih gumijastih delov in se ga lahko prilagodi za optimizacijo oblik. Optimizacija se začne s karakteristiko obstoječega blažilnika znane konstrukcije, formulirati pa jo je mogoče kot problem minimizacije v dani domeni. Ciljna funkcija podaja površino med želeno karakteristiko in krivuljo, pridobljeno po metodi končnih elementov za specifično obliko gumijastega blažilnika. Namen optimizacije oblike je iskanje take geometrije, kjer je razlika dela pod določeno mejno vrednostjo. Ker se uporabljajo numerične metode, dá proces približno vrednost optimuma. Orodje za optimizacijo je metoda SVR, ki daje regresijsko funkcijo za razliko dela. Čeprav že obstajajo rezultati uporabe modelov SVR na področju tehnike, pa se ta metoda še ni uveljavila v inženirski optimizaciji. Prednost uporabe metode SVR pri nelinearnih modelih je v tem, da lahko transformacijska funkcija med vhodnim prostorom in t.i. prostorom značilnosti ostane skrita, primerna regresijska funkcija pa se poišče s postopki strojnega učenja. Naloga optimizacije z metodo SVR je bila opravljena z odprtokodno programsko opremo. Z združitvijo obeh metod v en sistem sta bila rešena dva problema optimizacije oblike, s čimer je bila dokazana uporabnost predlaganega postopka za osnosimetrične gumijaste blažilnike. Metoda SVR potrebuje razmeroma malo časovno zamudnih točk učenja za obravnavo nelinearnih večrazsežnostnih optimizacijskih problemov. Točke učenja morajo seveda pokrivati območje optimizacije, gostota točk pa je odvisna od zahtevnosti problema. Postopek učenja, ki dá majhno število točk učenja in se izvede po metodi končnih elementov, lahko šteje za kratkega. Programska oprema lahko po učenju dobro napoveduje več parametrov, pri čemer odpadejo časovno zamudni izračuni po metodi končnih elementov in se lahko zanašamo le na inženirsko intuicijo. V članku sta predstavljena dva praktična primera z dvema in petimi konstrukcijskimi parametri, ki dokazuje hitrost in natančnost novega postopka optimizacije oblike. Kakovost izračuna je mogoče preveriti z izračunom po metodi končnih elementov. Upravičene bi bile tudi eksperimentalne meritve oblik blažilnikov, ki so bile določene z numeričnimi simulacijami, vendar to ni bil del tega projekta. Prihodnje raziskave bi lahko bile usmerjene v večciljno optimizacijo, ki vključuje tudi skupno maso ali številko življenjskega cikla. Ključne besede: optimizacija oblike, gumijast blažilnik, regresija z metodo podpornih vektorjev, metoda končnih elementov, karakteristična krivulja, funkcija jedra

SI 12

*Naslov avtorja za dopisovanje: Univerza v Debrecenu, Tehniška fakulteta, 2-4 Ótemető, 4028 Debrecen, Madžatska, tamas.mankovits@eng.unideb.hu

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)1, SI 13-17 Osebne objave

Doktorske disertacije, magistrsko delo, diplomske naloge

DOKTORSKE DISERTACIJE Na Fakulteti za strojništvo Univerze v Ljubljani so obranili svojo doktorsko disertacijo: ● dne 2. decembra 2013 Andrej PIRC z naslovom: »Aktivna energetska omrežja s sistemi sočasne proizvodnje toplote in električne energije in vodikovimi tehnologijami« (mentor: izr. prof. dr. Mihael Sekavčnik); V delu je obravnavano numerično načrtovanje aktivnih energetskih omrežij. Na začetku so predstavljeni vplivni dejavniki ter njihovi medsebojni vplivi. Načrtovanje poteka po pet-koračni odločitveni metodi, ki poteka od definiranja porabnika in virov energije preko določitve možnih konfiguracij omrežja ter odločitvenega parametra do optimalne konfiguracije. Kvazi dinamičen model testnega primera omrežja je sestavljen iz porabnika energije, proizvodnih enot in hranilnih kapacitet. Obratovanje posameznih komponent se vrši preko modula za upravljanje omrežja, ki deluje po matričnem načelu. Celoten model je bil izveden z uporabo programskega paketa Matlab Simulink-a. Model omogoča poleg simulacije obratovanja tudi optimizacijo posameznih konfiguracij po WSM metodi in občutljivostno analizo različnih scenarijev; ● dne 9. decembra 2013 Henrik ZALETELJ z naslovom: »Napovedovanje zdržljivosti zvarnih spojev v področju malocikličnega obremenjevanja« (mentor: izr. prof. dr. Gorazd Fajdiga, somentor: izr. prof. dr. Janez Kramar); Natančno poznavanje materialnih lastnosti in odziva materiala na različna obremenitvena stanja je pri določevanju dobe trajanja izdelkov ključnega pomena. Posebno pozornost moramo nameniti izdelkom, ki so v obdobju obratovanja obremenjeni z različnimi sestavljenimi obremenitvami kot je naprimer termomehansko obremenitveno stanje. V nalogi je predstavljen primer določevanja utrujenostnih lastnosti materiala z oznako 1.4512 (EN 10088-2) tako za malociklično kot za velikociklično področje pri različnih temperaturah, s čimer je določeno širše območje zdržljivosti materiala. Kot vpliv na zdržljivost je obravnavan var, ki predstavlja zaradi težnje po zmanjševanju mase izdelka vse pogostejši postopek spajanja dveh delov v celoto. Zaradi vplivov med postopkom varjenja var zmanjša zdržljivost osnovnemu materialu. Dodatno je kot vpliv na zdržljivost obravnavano staranje, ki se pojavi pri izpostavljenosti materiala določeni temperaturi v določenem časovnem obdobju. Izvedena

je analiza eksperimentalnih rezultatov in določene krivulje zdržljivosti za področje malocikličnega in velikocikličnega obremenjevanja. Posebna pozornost je namenjena malocikličnemu obremenjevanju in obdobju utrujenostne rasti razpoke, katere zakonitost pri dimenzioniranju izdelkov s čim manjšo maso ob poznavanju obremenitvenih pogojev predstavlja bistven pomen; ● dne 10. decembra 2013 Domen STADLER z naslovom: »Avtomatska geometrijska optimizacija lopatice vodilnika reverzibilne vodne turbine« (mentor: prof. dr. Franc Kosel); V nalogi je bila izdelana avtomatska geometrijska optimizacija vodilne lopatice z uporabo numeričnih metod. Z namenom, da se skrajša računski čas optimizacije, je bilo izdelano novo optimizacijsko ogrodje na podlagi genetskega algoritma, optimiranja z uporabo nadomestnih modelov in principa deli in vladaj. Opravljen je bil test ogrodja na matematičnih funkcijah, ki se uporabljajo za primerjavo optimizacijskih algoritmov. Metoda za deformiranje računskih mrež je bila uporabljena, da bi bila optimizacija popolnoma avtomatska. Predstavljeni sta dve novi metodi, ki sta hitrejši od že poznanih metod, in temeljita na umetnih nevronskih mrežah ter na delitvi območja računske mreže; ● dne 12. decembra 2013 Ana BIŽAL z naslovom: »Napovedovanje zdržljivosti tlačno litih izdelkov« (mentor: prof. dr. Matija Fajdiga, somentor: izr. prof. dr. Jernej Klemenc); Aluminijeve zlitine imajo zaradi širokega spektra dobih lastnosti velik potencial v avtomobilski industriji. Njihovo uporabnost pa ovira dovzetnost za pojav napak v materialu. Napake v ulitku, kot sta poroznost in vključki, imajo velik vpliv na funkcionalnost in zanesljivost izdelka. V doktorski nalogi je predstavljena metodologija za napovedovanje dobe trajanja in njenega raztrosa za ulite izdelke z nehomogenostmi. Metoda temelji na eksperimentalnih podatkih in rezultatih numeričnih analiz napetostno-deformacijskega stanja ulitkov z nehomogenostjo. Značilnost metode je, da dobo trajanja napove na podlagi zdržljivostnih krivulj homogenega materiala in statistične porazdelitve preiskovane nehomogenosti. Primernost metodologije je bila najprej preverjena na primeru zdržljivostnih testov poroznih preskušancev, potem je bila aplicirana še na preskušance z vključki. S predlagano metodologijo je mogoče dobro oceniti red velikosti dobe trajanja ulitkov s prisotno nehomogenostjo. Njene glavne prednosti so, da za napoved uporablja SI 13

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lastnosti homogenega materiala ter da je časovno izjemno efektivna; ● dne 19. decembra 2013 Miha PIRNAT z naslovom: »Vibro-akustična karakterizacija sestavljenih struktur« (mentor: prof. dr. Miha Boltežar); Raziskava predstavi vibro-akustično karakterizacijo sistema komora-plošča, ki je geometrijsko in fizikalno analogen energetskemu transformatorju. Najprej je predstavljen in validiran pristop k modeliranju lastne dinamike lamelirane strukture, ki v primeru energetskega transformatorja predstavlja enega izmed glavnih izvorov hrupa. Za primer danega notranjega akustičnega vzbujanja je razvit vibro-akustični model sistema komora-plošča, ki omogoča določitev akustičnega in strukturnega odziva sistema, ter temelji na zaporedni uporabi pristopa modalnega sklapljanja in metode robnih elementov. Razviti vibro-akustični model je tudi uspešno eksperimentalno validiran na namensko izdelanem preizkuševališču. Z uporabo validiranega modela so v zadnjem delu raziskave analizirane nekatere modifikacije sistema komora-plošča z namenom izboljšanja njegovih vibro-akustičnih lastnosti; ● dne 20. decembra 2013 Gabrijel PERŠIN z naslovom: »Zaznavanje in lokalizacija poškodb v mehanskih pogonih s tehnikami zlivanja informacij« (mentor: prof. dr. Jožef Vižintin, somentor: prof. dr. Đani Juričić); Predstavljena teza se osredotoča na zaznavanje poškodb na mehanskih pogonih, pri čemer upošteva več možnih načinov spremljanja stanja naprav. Iz neodvisnih analiz vibracij in olja je moč potegniti delne zaključke o stanju stroja, ki jih lahko uporabimo za izvedbo kombiniranega postopka, ki temelji na incidenčni tabeli. Ta tabela vsebuje obsežen popis relacij med napakami in za napake značilnimi odčitki z merilcev stanja olja in vibracij, ki jih uporabljamo za končno oceno verjetnosti za pojavitev napake. Analiza parametrov olja temelji na zaznavanju sprememb trendov in njihovem kvalitativnem analiziranju, kar nam omogoča vpogled v naravo zaznanih sprememb. Ko prepoznamo spremembo v parametrih olja, ki nakazuje možnost napake, izvedemo oceno verjetnosti le-te. Vibracijska analiza temelji na uporabi spektralnega kurtozisa in filtriranja, s katerim nestacionarne, za napake značilne komponente ločimo od šuma ozadja. Filitriran vibracijski signal nato uporabimo za izpeljavo diagnostičnih značilk, s pomočjo katerih izvedemo zaznavanje poškodbe, ki temelji na k-means rojenju in razvrščanju k-najbližjih sosedov. SI 14

* Na Fakulteti za strojništvo Univerze v Mariboru so obranili svojo doktorsko disertacijo: ● dne 13. decembra 2013 Tomaž BRAJLIH z naslovom: »Razvoj metode prilagajanja parametrov selektivnega laserskega sintranja oblikovnim značilnostim izdelkov« (mentor: izr. prof. dr. Igor Drstvenšek); V delu je predstavljen razvoj metode za prilagajanje izdelovalnih parametrov pri tehnologiji selektivnega laserskega sintranja. Dimenzijska natančnost kosov je eden izmed glavnih problemov pri izdelavi s selektivnim laserskim sintranjem. Glavni vzrok za pogreške pri izdelavi je skrček materiala in velikost vplivnega območja laserskega žarka. V prvem delu disertacije je postavljena teza, da na velikosti skrčkov in vplivnega območja laserskega žarka vplivajo oblikovne značilnosti izdelkov. Postavljen je tudi način opisa oblikovnih značilnosti izdelka s številskimi dejavniki. Z analizo variance več-faktorskega preizkusa je dokazana teza in vpliv dejavnikov oblikovnih značilnosti. V drugem delu je predstavljen način postavitve modela prilagajanja izdelovalnih parametrov, ki so namenjeni korekciji skrčkov in vplivnega območja laserskega žarka. Uporabljeni sta metodi skupinske inteligence in nevronske mreže. V zaključku so predstavljene sposobnosti napovedovanja modelov. Predstavljen je tudi način uporabe modelov pri izdelavi poljubnega izdelka v praksi. Napovedane vrednosti so preizkušene na poljubnem izdelku. Obravnavan je vpliv uporabe predlagane metode na dosegljivo natančnost izdelave in podane smernice za prihodnje raziskave; ● dne 17. decembra 2013 Jernej ŠENVETER z naslovom: »Razvoj metode za inteligentno napovedovanje tehnoloških parametrov upogibanja pločevine v dveh stopnjah« (mentor: prof. dr. Jože Balič); V doktorskem delu je znanstveno opisano doslej slabo poznano in raziskano upogibanje v dveh stopnjah za kot 90° ali več v večstopenjskih progresivnih orodjih. Omenjeno upogibanje je proces, pri katerem v prvi fazi pločevino preddeformiramo do pred-upogibnega kota ter nato v drugi stopnji upogibanja pločevino upognemo do končnega kota upogiba. Osrednji del naloge zavzema razvoj ter implementacija metode za inteligentno napovedovanje tehnoloakih parametrov. Za uspeano uporabe inteligentne metode, smo preučili postopke upogibanja ter podrobneje raziskali in analizirali upogibanje v dveh stopnjah. Pomemben vidik za zadovoljivo uporabo metode je tudi razvito in izdelano testno orodje za upogibanje pločevine. Na testnem

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orodju so bili opravljeni preizkusi, ki smo jih izvedli z različnimi vrstami pločevin. Pri spremljanju procesa upogibanja pločevine, smo merili oziroma beležili naslednje parametre: pred-upogibni kot, zamik matrice pri drugem upogibu, debelino pločevine, mejo plastičnosti, natezno trdnost ter končni kot upogiba. Po temeljiti analizi ter overitvi izmerjenih parametrov smo z uporabo umetne inteligencenevronske mreže implementirali inteligentne metode za napovedovanje končnega kota upogiba, zamika matrice pri drugem upogibu ter pred-upogibnega kota pri postopku upogibanja v dveh stopnjah. Inteligentna metoda povečuje kakovost uporabe postopka in zmanjauje atevilo preizkusov. Na osnovi metode za napovedovanje tehnoloakih parametrov je moč postopek enostavno uporabiti v večstopenjskih progresivnih orodjih za preoblikovanje pločevine. Razvita inteligentna metoda napovedovanja končnega kota upogiba, zamika matrice pri drugem upogibu ter pred-upogibnega kota uporabnikom omogoča učinkovito ekonomsko in tehnično enostavno uporabo postopka; ● dne 19. decembra 2013 Peter SEVER z naslovom: »Raziskava selektivnih prostorskih struktur in razvoj analitičnega modela lahkih nosilcev« (mentor: izr. prof. dr. Igor Drstvenšek); Predložena doktorska disertacija obravnava aktualno področje slojevitih tehnologij, s poudarkom na tehnologiji selektivnega laserskega sintranja. Selektivne prostorske strukture predstavljajo inovativni koncept generiranja lahkih izdelkov, ki z odprto-celično ali zaprto- celično strukturo izkoriščajo potencial ponujene geometrijske svobode V okviru izvajanja eksperimenta je bilo določeno izvedljivo območje premerov nosilcev prostorskih struktur, ki so omejene med 3-kratnik in 8-kratnik nazivnega premera laserskega žarka. Uvodne meritve na epruvetah z masivno strukturo in na epruvetah z izdelano prostorsko strukturo so izkazale izrazito tehnološko anizotropijo, kjer je razvidna razlika med natezno trdnostjo epruvet izdelanih v Z smeri in trdnostmi epruvet izdelanih v X in Y smeri. Analiza prelomnih mest epruvet je razkrila, da je vzrok za identificirano tehnološko anizotropijo predvsem v nepopolnih spojih med posameznimi izdelavnimi plastmi v smeri izdelave oziroma rasti izdelka, ki so, kot ugotovljeno na podlagi izvedenih simulacij z metodo končnih elementov, predvsem posledica premajhnih vnosov energije. Segmentacija epruvete na osrednji in vprijemni del je omogočila tehnološko vzdržen selektivni vnos energije, kjer so bile poprej uporabljene epruvete vnovič izdelane s povišanim vnosom energije v osrednjem delu z izdelano prostorsko strukturo. Ponovitev meritev nateznih trdnosti je potrdila, da

lahko zaradi intenzivnejšega hlajenja selektivnih prostorskih struktur, ki so v procesu izdelave obdane z izdelavnim materialom v praškasti obliki, že zgolj s spremembo vnosa energije bistveno prispevamo k izboljšavi vezi med posameznimi sloji, s čimer minimiziramo tehnološko anizotropijo. Alternativno, je na nivoju izdelka s podrejeno oblikovano osnovno celico v eksperimentu prikazana rešitev, ki v funkciji osnovnega gradnika prostorske strukture z inverzno anizotropnimi lastnostmi izniči vpliv tehnoloških parametrov in tehnološko anizotropijo. Minimizirana in v nekaterih primerih celo izničena tehnološka anizotropija, je v okviru naloge omogočila oblikovanje analitičnega modela za napovedovanje nateznih napetosti v odvisnosti od raztezka, ki potrjuje zadano tezo in predstavlja končni rezultat te doktorske disertacije. ZNANSTVENO MAGISTRSKO DELO Na Fakulteti za strojništvo Univerze v Ljubljani je z uspehom zagovarjal svoje magistrsko delo: ● dne 24. decembra 2013 Uroš POGAČNIK z naslovom: »CAM za nove izdelke s področja embalaže farmacevtskih proizvodov« (mentor: prof. dr. Janez Kopač). DIPLOMSKE NALOGE Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 19. decembra 2013: Blaž BRECELJ z naslovom: »Zaščita oči pri varjenju s taljenjem z različnimi viri toplote« (mentor: prof. dr. Janez Tušek); Bojan GRAČNAR z naslovom: »Varjenje z gnetenjem aluminijeve zlitine z bakrom« (mentor: doc. dr. Damjan Klobčar, somentor: prof. dr. Janez Tušek); Jože ŠPEHAR z naslovom: »Sanacija poškodovanih orodij za tlačno litje z varjenjem« (mentor: prof. dr. Janez Tušek, somentor: izr. prof. dr. Primož Mrvar); Tom PLESKOVIČ z naslovom: »Eksperimentalna analiza vpliva nočnega znižanja temperature vode v ogrevalnem sistemu daljinskega ogrevanja« (mentor: izr. prof. dr. Ivan Bajsić); Matej FRANKOVIČ z naslovom: »Vzorčenje cevi toplotnih izmenjevalcev v jedrskih elektrarnah« (mentor: doc. dr. Joško Valentinčič, somentor: prof. dr. Mihael Junkar); SI 15

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Franci GOLOB z naslovom: »Analiza vpliva geometrijskih parametrov na globoki vlek škatlastega izdelka« (mentor: izr. prof. dr. Tomaž Pepelnjak). * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 19. decembra 2013: Borut VAŠ z naslovom: »Razvoj in izdelava robotske celice za nameščanje kartonskih kotnikov« (mentor: prof. dr. Miran Brezočnik, somentor: dr. Simon Brezovnik); Andraž HLASTEC z naslovom: »Uporaba servo pogonov v stiskalnicah z omejeno potjo« (mentor: izr. prof. dr. Ivan Pahole, izr. prof. dr. Karl Gotlih). * Na Fakulteti za strojništvo Univerze v Mariboru je pridobil naziv magister inženir strojništva: dne 6. decembra 2013: Sašo BERIĆ z naslovom: »Optimizacija SCR sistema« (mentor: prof. dr. Breda Kegl, somentor: izr. prof. dr. Marko Kegl); dne 18. decembra 2013: Gregor ČREŠNIK z naslovom: »Napoved karakteristik vetrne turbine« (mentor: prof. dr. Aleš Hribernik, somentor: dr. Matej Zadravec); Mitja MATJAŽ z naslovom: »Primer modeliranja CNC obdelovalnih strojev v virtualnih obdelovalnih sistemih« (mentor: prof. dr. Jože Balič, somentor: dr. Simon Klančnik); Danijel POGOREVC z naslovom: »Uvedba sistema kanban za proizvodnjo odtočnih ventilov tipa 280 v podjetju Geberit - Sanitarna tehnika d.o.o.« (mentor: izr. prof. dr. Borut Buchmeister, somentor: doc. dr. Iztok Palčič); dne 19. decembra 2013: Uroš CVELBAR z naslovom: »Numerična simulacija toplotno - tokovnih razmer v UniPor celični strukturi« (mentor: prof. dr. Matjaž Hriberšek, somentor: izr. prof. dr. Matej Vesenjak); Simon URBAS z naslovom: »CFD simulacija curka več-komponentnega bencinskega goriva« (mentor: prof. dr. Matjaž Hriberšek). * Na Fakulteti za strojništvo Univerze v Mariboru je pridobil naziv magister gospodarski inženir: dne 18. decembra 2013: Vito STRAŠEK z naslovom: »Vpliv uvajanja vitke proizvodnje na kakovost procesov v podjetju« SI 16

(mentor: prof. dr. Bojan Ačko, somentorici: doc. dr. Nataša Vujica Herzog, prof. dr. Polona Tominc); dne 19. decembra 2013: Jan JURJEC z naslovom: »Tehnično - poslovni preračun energijske izrabe perutninskega perja in postavitev sistema za soproizvodnjo toplotne in električne energije« (mentor: prof. dr. Niko Samec, somentorja: viš. pred. dr. Filip Kokalj, doc. dr. Igor Vrečko); * Na Fakulteti za strojništvo Univerze v Mariboru je pridobil naziv diplomirani inženir strojništva (UN): dne 19. decembra 2013: Tadej PIŠOTEK z naslovom: »Vpliv parametrov selektivnega laserskega taljenja (SLM) na mehanske lastnosti izdelka« (mentor: izr. prof. dr. Igor Drstvenšek, somentor: mag. Tomaž Brajlih). * Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva: dne 5. decembra 2013: Uroš BLAŽEVIČ z naslovom: »Tehnološki načrt obdelave izstopne komore ventila« (mentor: prof. dr. Janez Kopač); Jan KRAJGER z naslovom: »Shranjevalnik toplote in hladu z uporabo fazno spremenljive snovi za ogrevanje in hlajenje prostorov« (mentor: prof. dr. Vincenc Butala, somentor: doc. dr. Uroš Stritih); Matej ČEMAŽAR z naslovom: »Uporaba reverzne osmoze za pripravo kotlovske napajalne vode« (mentor: prof. dr. Iztok Golobič, somentor: izr. prof. dr. Andrej Senegačnik); Miro JANČAR z naslovom: »Dvonosilčni mostni žerjav« (mentor: doc. dr. Boris Jerman); Marko PEČARIČ z naslovom: »Preverjanje geometrijske natančnosti trosnega vertikalnega obdelovalnega stroja« (mentor: izr. prof. dr. Ivan Bajsić); Domen ŽIBERNA z naslovom: »Uvedba projektnega vodenja v podjetju« (mentor: izr. prof. dr. Janez Kušar, somentor: prof. dr. Marko Starbek); dne 6. decembra 2013: Igor GAŠPAROVIĆ z naslovom: »Načrtovanje tehnologije montaže posebnih gradbenih panelnih elementov« (mentor: izr. prof. dr. Niko Herakovič); Anže GRILC z naslovom: »Izboljšanje energetske učinkovitosti pečice z izbiro izolacije« (mentor: izr. prof. dr. Andrej Kitanovski, somentor: prof. dr. Alojz Poredoš); Jef De POORTERE z naslovom: »Razvoj sistema omaric za potrebe distribucije blaga / Engineering

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design of boxes for distribution of goods« (mentor: izr. prof. dr. Jože Tavčar, somentor: prof. dr. Jožef Duhovnik). * Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva (VS): dne 5. decembra 2013: Jure LESKOVEC z naslovom: »Lasersko oplastenje aluminijeve zlitine s keramičnimi sestavinami« (mentor: izr. prof. dr. Roman Šturm); Andrej TOMAŽIČ z naslovom: »Energijski pregled poslovne stavbe in predlagani sanacijski ukrepi« (mentor: prof. dr. Vincenc Butala); Gašper TRATNIK z naslovom: »Razvoj ventila ročke na kavnem avtomatu« (mentor: izr. prof. dr. Jože Tavčar, somentor: prof. dr. Jožef Duhovnik); Tomaž TRČEK z naslovom: »Vpliv povečanja mase kolesnega sklopa na vertikalno dinamiko vozila ter na sile v kolesnem ležaju« (mentor: izr. prof. dr. Robert Kunc, somentor: prof. dr. Ivan Prebil).

* Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva: dne 19. decembra 2013: Darko BELČIĆ z naslovom: »Postopek prostega upogibanja pločevine v matrici in vpliv upogibnega polmera na razvito mero pločevine« (mentor: izr. prof. dr. Ivan Pahole, somentor: doc. dr. Mirko Ficko); Gregor FERENČAK z naslovom: »Povečanje moči motorja z notranjim zgorevanjem z uporabo tlačnega polnjenja« (mentorica: prof. dr. Breda Kegl, somentor: izr. prof. dr. Stanislav Pehan); Zlatko MIŠKO z naslovom: »Izboljšave procesa razvoja izdelkov narejenih z rotacijskim litjem polimerov« (mentor: izr. prof. dr. Stanislav Pehan); Andraž ŠIFRER z naslovom: »Visokotrdnostna jekla v vozilih - uporaba reševalnega orodja za razrez visokotrdnostnih jekel v vozilih« (mentor: izr. prof. dr. Ivan Pahole, somentor: doc. dr. Mirko Ficko).

SI 17

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

http://www.sv-jme.eu

60 (2014) 1

Strojniški vestnik Journal of Mechanical Engineering

Since 1955

Contents

Papers

Darja Steiner Petrovič, Roman Šturm: Fine-structured Morphology of a Silicon Steel Sheet after Laser Surface Alloying of Sb Powder

Pavel Žerovnik, Dušan Fefer, Janez Grum: Surface Integrity Characterization Based on Time-Delay of the Magnetic Barkhausen Noise Voltage Signal

Govindaraj Elatharasan, Velukkudi Santhanam Senthil Kumar: Corrosion Analysis of Friction Stirwelded AA 7075 Aluminium Alloy

Tomaž Berlec, Janez Kušar, Janez Žerovnik, Marko Starbek: Optimization of a Product Batch Quantity

43 Jijun Yi, Tao Zeng, Jianhua Rong: Topology Optimization for Continua Considering Global Displacement Constraint 51

Tomasz Trzepieciński, Hirpa G. Lemu: Frictional Conditions of AA5251 Aluminium Alloy Sheets Using Drawbead Simulator Tests and Numerical Methods

Tamás Mankovits, Tamás Szabó, Imre Kocsis, István Páczelt: Optimization of the Shape of Axi-Symmetric Rubber Bumpers

Journal of Mechanical Engineering - Strojniški vestnik

12 Wei Teng, Feng Wang, Kaili Zhang, Yibing Liu, Xian Ding: Pitting Fault Detection of a Wind Turbine Gearbox Using Empirical Mode Decomposition

1 year 2014 volume 60 no.