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Actuators Placement for Active Damping of Vibration on Two Dimensional Clamped Plate Peter Šolek

15

1 / 2011

Journal published by Faculty of Mechanical Engineering

The Technical University of Košice

M. nUMAN dURAKBASA & P. Herbert osanna

Intelligent Design and Metrology for Higher Quality, Accuracy and Improving Production Efficiency Peter Bigoš Increasing of Power Output of Racing Motorcycle Engine using of Exhaust System Optimisation Feliks Stachowicz Instantaneous Plastic Flow Properties of Thin Brass Sheets Under Uniaxial and Biaxial Testing Emil Spišák Joining Car Body Steel Sheets Using the Clinching Method Domnita Florina Fratila Assessment of Cutting Area Temperature to the Face Milling using Several Cooling Methods


Excellent Personality of the Faculty of Mechanical Engineering, Technical University of Košice

prof. Ing. Peter Bigoš, CSc. Head of Department of machine design, transport and logistics Scientific Orientation:

Optimization of Material Flows Identification and Simulation of Logistic Interrelations in the Production and Supply Processes

Operational Abilities of Manipulation Equipment with regard to their Kinematical and Dynamical Dispositions Development of new Concepts for Technically Improved Transport and Handling Machines with a high-level of Reliability Experimental Verification of Dynamical Characteristics of Manipulation Machinery, taking into Consideration their Reliability and Residual Durability


VOLUME 15 No. 1 / 2011

Journal published by Faculty of Mechanical Engineering

Published Since 1996

web.tuke.sk/actamechanica

The Technical University of Košice

ISSN 1335-2393


ACTA MECHANICA SLOVACA Journal PublishEd By Faculty of Mechanical Engineering, The Technical University of Košice Editorial Office:

Acta Mechanica Slovaca, Faculty of Mechanical Engineering, Technical University of Košice, Letná 9, 042 00 Košice, tel.: + 421 55/602 3216, fax: + 421 55/602 2716, e-mail: actamechanica@tuke.sk

Editorial board: CHAIRMAN: Dr.h.c. prof. Ing. Miroslav BADIDA, PhD., Technical University of Košice, Slovakia  SCIENTIFIC EDITOR: Dr.h.c. prof. PhDr. Ing. Štefan KASSAY, DrSc., I.D.C. Holding, a.s., of Bratislava, Slovakia  EDITOR-IN-CHIEF: Ing. Miriama PIŇOSOVÁ, Technical University of Košice, Slovakia  SECRETARY: Valéria KOŇOVÁ, Technical University of Košice, Slovakia  Language Editor: Ing. Melichar KOPAS, Technical University of Košice, Slovakia Associate Editors:

prof. Dr. Fodor János, DSc., John von Neumann Faculty of Informatics, Budapest, Tech. Budapest, Hungary  prof. Dipl. -Ing. Dr. Techn. Dr.h.c., mult. Herbert Mang, PhD., Institute for Mechanics of Materials and Structures University of Technology, Vienna, University of Technology, Austria  prof. Dr. Mirka Miller, The University of Newcastle, Australia  D.h.c. Acad. prof. Ilija Mamuzič, B.Sc., D.Sc., Faculty of Metalurgy University of Zagreb, Sisak, Croatia  Dr.h.c. prof. MUDr. Ján Slezák, DrSc. Slovak Academy of Science, Slovakia  prof. Dr. hab. Inz. Feliks Stachowicz Politechnika Rzeszowska, Rzeszow, Poland  prof. dr. Patkó Gyula, University of Miskolc, Hungary  prof. Dr. Richard L. Magin University of Illinois Chicago, USA  prof. Pascal Verdonck, University of Gent, Belgium  prof. Annradi M. Dr. Padr, University of Dublin, Ireland  Dr.h.c. mult. prof. Ing. František Trebuňa, CSc., Technical University of Košice, Slovakia  Dr.h.c. prof. Ing. Jozef Živčák, PhD. Technical University of Košice, Slovakia  Dr.h.c. prof. Ing. Michal Besterci, DrSc., SAV Košice, Slovakia,  Dr.h.c. mult. prof. Dr. Stanislav Adamcziak, Politechnika Swietokrizska, Kielce, Poland  Dr.h.c. prof. Dr. Janko Hodolič, University of Novi Sad, Serbia  Dr.h.c. mult. prof. Dr. Branko Katalanič, Technical University of Wien, Austria  prof. Dr. EBerhardt Schmidt, University of Wuppertal, Germany

2 VOLUME 15, No. 1, 2011


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

Contents

4 Editorial Turning Research into Education and Practice

6 M. Numan Durakbasa (A), P. Herbert Osanna (A) Intelligent Design and Metrology for Higher Quality, Accuracy and Improving Production Efficiency

12 Janette Brezinová (SK), Anna Guzanová (SK), Branislav Hadzima (SK) Evaluation of the Quality of the Renovation Layers Applied by Thermal Spraying Technology

22 Feliks Stachowicz (PL) Instantaneous Plastic Flow Properties of Thin Brass Sheets Under Uniaxial and Biaxial Testing

28 Emil Spišák (SK), Ľuboš Kaščák (SK) Joining Car Body Steel Sheets Using the Clinching Method

36 Arkadiusz Tofil (PL), Zbigniew Pater (PL) Wasteless Splitting of Metal Round Bars Basing on Cross-Wedge Rolling Process

44 Jozef Svetlík (SK), Peter Demeč (SK) Curved rotary module for modular construction of motion structures

50 Domnita Florina Fratila (RO) Assessment of Cutting Area Temperature to the Face Milling using Several Cooling Methods

56 Ján Slolta (SK), Emil Spišák (SK) Determination of Forming - Limit Diagrams Considering Various Models for Steel Sheets

64 Peter Šolek (SK), Martin Horínek (SK) Actuators Placement for Active Damping of Vibration on Two Dimensional Clamped Plate

70 Peter Bigoš (SK), Michal Puškár (SK) Increasing of Power Output of Racing Motorcycle Engine using of Exhaust System Optimisation

98 Jan Fuxa (CZ), František Fojtík (CZ) The Boundary States Investigation of the Proportional Loaded Materials Using the Multiaxial Strength Criteria

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Editorial Turning Research into Education and Practice prof. Ing. Jozef Bocko, CSc.

Head of the Department of applied mechanics and mechatronics

Research, education, and cooperation with industry are three cornerstones of university. However, if we want to have university that hosts world-class studying, teaching and research activities we should joint them together and form an integrated complex institution.

The mechanical engineering is a field where collaborative research traditionally has proven to be fruitful. Mechanical engineer touches many problems of mathematics, physics, chemistry, design, technology, environmental sciences, management, economy, and so on and often there is a need to consult people who are specialists in these areas. Acta Mechanica Slovaca, journal of Faculty of Mechanical Engineering, Technical University of Košice should serve as a base for exchange of information and skill enhancement in aspects being important for teaching and research. According to our law, education and research are two main activities of university and the journal reflects both sides of university life. However, it is not sometime easy to tie them together meaningfully in order to achieve a powerful synergetic effect. “Pure scientists” and “pure teachers” are categories of humans that can be, may be due to our history, met very often. Rather than seeing the relationship between education and research as opposite positions, as has sometimes traditionally been the case, there is a growing body of researchers across a number of disciplines who take education as part of their research. They involve students directly into their research activities, or present them results of their original research work. That’s probably the best way the research can be bring into student community and invoke there avid interest to learn more about essence of things and phenomenon. But it is not all we have to take into account. Similarly, as there is not possible to have only „l´art pour l´art“, the science has to be applied in practice. The more, the better. In certain sense and broad meaning the students can be considered to be our “products” and “application” of research in practice. Of course, that is not enough, and by 4 VOLUME 15, No. 1, 2011


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

most of us our role of engineer prevails role of tutor with feeling that practice should product something that is “more material” and “market-oriented” and we search applications of our research in collaboration with companies. Results of such work belong then to set of things that enrich our mind. Acta Mechanica Slovaca is a platform for contact of three above-mentioned areas – research, education and practice. We hope that you enjoy our journal, that you find it informative, and most of all that it stimulates you to get involved and find out more. Do not hesitate to contact us for ideas and suggestions.

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Intelligent Design and Metrology for Higher Quality, Accuracy and Improving Production Efficiency M. Numan Durakbasa (A) durakbasa@mail.ift.tuwien.ac.at P. Herbert Osanna (A)

BIOGRAPHICAL NOTES

M. Numan Durakbasa, prof. Dr. Dipl. -Ing. Prof.h.c. (born in 1955) Head of the Department for Interchangeable Manufacturing and Industrial Metrology (Austauschbau und Messtechnik / Produktionsmesstechnik & Qualität) of the Institute for Production Engineering and Laser Technology, and Nanotechnology Laboratory and vice head of the Department for Certification of Quality Professional at Vienna University of Technology, with long-standing international practical experience as “Quality System Auditor”, Austrian expert in the international technical Committee ISO/TC 213 “Geometrical Product Specifications and Verification”, as well as ISO/TC 176 “Quality Management and Quality Assurance”, chairman of the Austrian Standard Committee ON-K 031 “Anforderungen und Prüfungen der geometrischen Produktspezifikation; Technische Produktdokumentation“ and expert of the Austrian Standard Committees ON-K 129 “Quality Management Systems” and “Environmetal Management Systems”. Research Interests: metrology, quality management, geometrical product specifications and verification - GPS, nanometrology, CAQ, environmental management, interchangeable manufacturing, industrial metrology, measurement technique, precision engineering, calibration, accreditation, certification, standardisation. Publications: 9 books, more than 280 scientific papers.

KEY WORDS

Intelligent metrology, Design, GPS, Accuracy, Quality, Production Efficiency

ABSTRACT

Adequate knowledge in the areas of intelligent metrology and design are important presuppositions to achieve waste free production and low costs of manufacturing and accuracy at the same time within the sophisticated production systems. This is of extreme importance in present time of worldwide international competition in industry and production engineering and at the same time increasingly higher costs of energy and raw material. The prescription and consumption of material and energy to achieve the necessary and required workpiece accuracy in series manufacturing depends to a great extent from the (geometrical) workpiece tolerances of any kind (roughness, form, positional, dimensional) which are prescribed for the production and the fulfillment of these tolerances and therefore for the function of the produced workpieces and their fitness for practical application and none the less of the economy of production altogether. This requirement is of great importance at the time being which is characterized as described above.

1 Accuracy, Efficiency and High Quality in Production The problematic of the high accuracy of the work pieces in modern industrial production technique gained in the last years more and more importance through constantly

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Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

increasing demands on the quality of the produced parts. The necessity faces to the additional outlay caused through that in the entire manufacturing process, to produce due to the world wide competition fight’s and it price pressure’s resultant from that maximally economical and to strive for cost savings and efficiency increasing in production. If the workpiece geometry of machined parts is considered as a whole there exist interactions between the different features forming the periphery of the part. But also within the surface of every single feature there exist interactions between geometrical deviations of different kind and different order. If we take these deviations of dimensions, roughness, form and position collectively the existing interactions are significant for the accuracy, high quality and the functions of the parts that should be accomplished during practical application. The most important parameters in determining the suitability of a technical part are its compatibility, functionality, performance and corrosion resistance. The precise assessment of wear, friction and miniaturization demands creation of nanometer scaled surface structures, surfaces with thin film deposition and ultra precision surface treatment with the utilization of new manufacturing and measurement instrumentation and techniques. These include micro and nanofabrication of surface patterns and topographies by the use of laser machining, photolithographic techniques, and electron beam and colloidal lithography to produce controlled structures on technical surfaces in size ranging from 10 nm to 100nm. At the time being 3D surface measurement is already proved to be an important tool in several areas of surface analysis including wear, indentation, topography, contact problems and functional behavior of surfaces (see Fig. 1). The needs of the industry for ultra-high precision engineering and workpieces with a surface roughness less than few nanometers call for measurement instrumentation that can be applied reliably in modern production processes, together with international standards defining parameters and tolerances in the nanometer scale. The requirements on the measurement systems and the measurement strategy to determine suitable parameters, time, costing and the guarantee of a predetermined process stability by means of measurable and correlated parameters come into focus.

Fig. 1 3D Measurement of a high precision machined alloy specimen

2 Production Engineering and Production Metrology - from Past to Future Since 1970 we see increasing importance of modern metrology as means to control and improve industrial manufacturing and the quality of all kinds of products and processes to test technical products with high accuracy on the basis of geometrical product specifications and verification. At the same time precision engineering developed as important trend in instrumentation and metrology. As the tolerances of workpieces and their features decrease, the interaction and correlation between dimensional tolerances and surface finish becomes more important [1]. To achieve surface finishes and part tolerances in the sub-micrometer and nanometer level, it is necessary to incorporate very sophisticated instrumentation and metrology into the design [2]. In the same period the standards governing product design and manufacturing have undergone basic international harmonisation. Focal points of interest included workpiece microgeometry [3] and geometrical deviations [4], as well as tolerancing principles according to the principle of independence [5]. In many countries, the above-mentioned international standards have been adopted also on a national level, similar as the new international standards about quality management [6, 7 ,8]. In this respect the general term “Geometrical Product Specifications and Verification GPS” has become recently well-known for the area of mechanical engineering. It defines on a technical drawing the shape (geometry), dimensions and surface characteristics of the workpiece under discussion. In this way the optimal function of the respective part is supposed to be guaranteed considering certain manufacturing tolerances. Nevertheless workpieces will be produced, which do not fulfill these require-

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ments. Therefore workpieces are measured in order to compare them with the specifications. There is a need to relate between actual workpieces and: the workpiece imagined by the designer, the workpiece as manufactured, the knowledge about the workpiece as measured. In order to establish this relationship between design, production and measurement and to clarify the mutual importance, standards have been developed in the area of Geometrical Product Specifications and Verification. Comprehensive knowledge in this area is an important presupposition to achieve economic design, construction, production, metrology and quality management (see Fig. 2).

Fig. 2 Geometrical Tolerances and Tolerances of Dimension and Geometrical Properties of the Surface

measurement standards in this area. The concept of GPS is represented in Fig. 3, showing four different types of GPS standards and designated as the “GPS-matrix-model” (see Fig. 2) [9]. The Global GPS standards General GPS Matrix

The Fundamental GPS Standards

General GPS chains of standards The Total run-out The Size chain of chain of standards standards The Distance chain The Datum chain of standards of standards The Roughness The Radius chain chain of standards of standards The Angle chain of The Waviness profile chain of standards The Form of a line standards The Primary The Form of a profile chain of surface standards The Orientation The Surface chain of standards The Location chain defects chain of standards of standards The Edges chain The Circular runof standards out chain of standards

Complementary GPS Matrix Complementary GPS chains of standards Process specific tolerance standards Machine element geometry standards

Fig. 3 The GPS-matrix-model - GPS Masterplan - Overview

As already mentioned above this set of requirements concerning the geometry of the workpiece (or of an assembly of several workpieces) is known as “GPS” covering requirements of size and dimension, geometrical tolerances and geometrical properties of the surface. A feasible approach to new international measurement standards for roughness and toleration on the nanometer scale would be the adaptation and transfer of the GPS (Geometrical Product Specifications and Verification) to nano metrology. The GPS Technical Committee of ISO was established in June 1996 with the aim to create a “Masterplan” which summarizes all existing geometric standards [9]. In this masterplan there are the 18 most important geometric parameters listed, each of them with the appropriate standards. Similar to this approach in conventional geometric metrology, a masterplan for the most important geometric parameters in nano metrology could be designed and then serve as the basis for the definition of new international

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Geometrical Product Specifications are a means to transform function dependent demands into produced workpieces and parts based on: mathematical rules and methods, consideration of macro and micro geometry, possibilities for measuring of quantities and especially toleranced quantities and evaluation of uncertainty, etc.

3 Co-ordinate Metrology in Modern Production Environment An important development as far as workpiece metrology is concerned is the big general advance of coordinate metrology which also happened in the same period of time as computer-aided metrology and “GPS” in general. Three dimensional coordinate measuring machines (3D-CMMs) allow to measure deviations of dimensions, form and position very accurately with only one measuring device [10,11]. For 3D measure-


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

ments it is often more advantageous to use a CMM. Such Nano-CMMs have been recently introduced achieving an uncertainty of 100 nm or better and enabling three-dimensional measurements as well as scanning of high precision parts. Besides measuring accuracy the number of workpieces to be measured is important when choosing the measuring device. Especially when workpiece tolerances are more accurate than tolerance grade IT5 (e.g. 11nm for 50mm it is necessary to make use of coordinate metrology. This is also possible for big series of workpieces. CMMs are referred to as those measuring instruments giving physical representations of a three dimensional rectilinear Cartesian coordinate system. The nature of coordinate metrology can be defined as: The geometrical features of the workpiece to be measured are touched in several measuring points using a coordinate measuring device. The coordinates of the measuring points are used to compute the mathematical geometry of the workpiece with help of the control computer of the CMM. At the time being coordinate metrology is a very important tool to solve problems of production metrology of nearly any kind especially when high flexibility and high accuracy are demanded at same type of workpiece. One of the essential requirements in coordinate metrology is the computation of associated features from the probed contact points. When we consider as an example the measurement of a bore hole, we can distinguish between conventional measurements and the application of coordinate metrology. A two-point-measurement has to be done by means of the strategy trying to get the maximum value perpendicular to the axis and then finding the minimum in the axial section (see Fig. 4). The bore diameter is given by the condition that these two diameter values are equal.

Fig. 4 Conventional Metrology and Coordinate Metrology

In this context it is distinguished between: nominal geometry, real geometry and substitute geometry. This follows the way of parts from design to manufacturing and quality control (see Fig. 5).

Tecnical drawing

Nominal geometry

Manufacturing

Real geometry

Co-ordinate metrology

Measuring points

Evaluation of measuring results Substitute geometry

Fig. 5 Principle of the Workpiece evaluation in the Frame of Geometrical Product Specifications and Verification

4 Intelligent Metrology with Coordinate Measuring Machines The course of the steps, which are necessary for a measurement, is always identical independent of the kind of the programming. Choosing the stylus combination is an essential step for the measurement. It must occur on the one hand so that all geometrical features to be measured can be touched, on the other hand too complicated and particularly too long stylus combinations are to be avoided since an additional source of errors arises from their bending. The steps which are needed for the automated measurement of workpieces are shown in Fig. 6. The measurement results obtained with several or even many different probes is then as that obtained with a single probe tip with the diameter zero. By

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using an automatic stylus-exchanging-unit every combination needs to be calibrated only once if there are not any extremely high demands on the uncertainty of measurement. CNC programming

Preparation e.g. probe combination, calibration, clamping of measuring object etc.

Nominal value from technical drawing Nominal and actual value

Probe combination e.g. from stylus exchanging unit Set-up of workpiece co-ordinate system Geometrical elements by probing Geometrical elements calculated by measuring results Conversion of measuring results for related elements Geometrical deviations Report

Fig. 6 Flow Diagram for the Measurement Steps on CMMs

5 Outlook to Future Developments The ideas presented in this publication explain in principal the correlation between different geometrical deviations and the manufacturing conditions. This can help to achieve lower manufacturing costs and at the same time higher quality, accuracy and efficiency in present production. The results of the presented study can be seen as a further step in the direction of a comprehensive analysis of workpiece geometry and it is fully in line with research work already carried out in the past [11]. By the described successful application of co-ordinate metrology for the solution of measurement problems of various kinds also new challenges are put onto precision production measurement technology especially in the area of GPS.

6 References [1] Osanna, P. H., Durakbasa, M.N., Kräuter, L., 2008, “Industrial Metrology and Interchangeable Manufacturing under the Viewpoint of Nanotechnology and Nanometrology”, Bulgarian Academy of Sciences, Problems of Engineering Cybernetics and Robotics, Vol. 59, pp.60-73 [2] D. Whitehouse, “Comparison between stylus and optical methods for measuring surfaces”,

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Annals CIRP, 37(2), pp. 649-653, 1988 [3] ISO 4287 Geometrical Product Specifications (GPS) - Surface texture: Profile method - Terms, definitions and surface texture parameters (ISO 4287:1997+Cor 1:1998+Cor 2:2005+Amd 1:2009) [4] EN ISO 1101-2006: Geometrical Product Specifications (GPS) - Geometrical Tolerancing - Tolerances of Form, Orientation, Location and Run-out; EN ISO 1101/A1: 2010 Geometrical Product Specifications (GPS) - Geometrical tolerancing-Tolerances of form, orientation, location and run-out- Amendment 1: Representation of specifications in the form of a 3D model [5] ISO 8015 - 2011: Geometrical product specifications (GPS) - Fundamentals - Concepts, principles and rules [6] EN/ISO 9001 - 2008: Quality Management Systems - Requirements. 2008-12 [7] EN/ISO 14001 - 2009: Environmental management systems - Requirements with guidance for use (ISO 14001:2004 + Cor. 1:2009) [8] EN/ISO 9004 - 2009: Managing for the sustained success of an organization - A quality management approach [9] ISO/TR 14638: Geometrical product specification (GPS) - Masterplan [10] ISO/TR 10360-1-1993, Part 1: Coordinate Metrology - Part 1: Definitions. Applications of the Fundamental Geometrical Principals. 1993 [11] P.H. Osanna, N.M. Durakbasa e.a.: Global Competitive Manufacturing on the Basis of Intelligent Metrology and Quality Management as Important Tools. Proceedings of the International Symposium “Tools and Methods of Competitive Engineering - TMCE’2002” (Editor: Horvath, I. e.a.), Wuhan, China, April 2002, ISBN 7-5609-2682-7, 837/844


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

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Evaluation of the Quality of the Renovation Layers Applied by Thermal Spraying Technology Janette Brezinová (SK) janette.brezinova@tuke.sk Anna Guzanová (SK) anna.guzanova@tuke.sk Branislav Hadzima (SK) branislav.hadzima@fstroj.uniza.sk

BIOGRAPHICAL NOTES

Janette Brezinová, assoc. prof. Ing. PhD. (born in 1968) is currently associate professor and associate dean for education at the Technical University of Košice, Faculty of Mechanical Engineering, Department of Materials and Technology. She graduated in Welding and Surface Treatment (1991), obtained the Ph.D. in the field of degradation in abrasive blast cleaning at the Technical University of Košice in 2003 and in 2008 was habilitated in the field of Mechanical Engineering and Materials. In her research work she focuses on surface treatment and materials, degradation phenomena during abrasive blast cleaning and shot peening, corrosion of metals, corrosion protection of metals, evaluation of organic and inorganic coatings, renovation of worn surfaces. J. Brezinová is the member of Slovak Metal Science Society. She is the author of more than 100 scientific works presented in journals and in proceeding from many international scientific conferences. Anna Guzanová, Ing. PhD. (born in 1974) is currently assistant professor at the Technical University of Košice, Faculty of Mechanical Engineering, Department of Materials and Technology. She graduated in Welding and Surface Treatment (1997), obtained the Ph.D. in the field of abrasive blast cleaning using ecological types of blasting abrasives at the Technical University of Košice in 2003. In her research work she focuses on surface treatment and materials, shot peening, abrasive blast cleaning, wear of materials and coatings, evaluation of quality the various types of blasting abrasives, evaluation of thermal sprayed coatings. A. Guzanová is the member of Slovak Metal Science Society. She is the author of more than 80 scientific works presented in journals and on many international scientific conferences. Branislav Hadzima, assoc. prof. Ing. PhD. (born in 1976) is currently a research scientist at the University of Žilina, Faculty of Mechanical Engineering, Department of Materials Engineering. He graduated in Materials science (1999), obtained the Ph.D. in the field of Threshold states of Materials at the University of Žilina in 2003 and in 2009 was habilitated in the field of Materials engineering. In his research work he focuses on corrosion of metals and corrosion protection of metals mainly on corrosion of light metals alloys. B. Hadzima spent his research stays at the University of Technology in Clausthal, Germany and at the Charles University in Prague, Czech Republic. He is the author of the book entitled “Basics of electrochemical corrosion of metals” and more than 110 scientific publications, which were cited more than 160 times.

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Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of KoĹĄice

KEY WORDS

BOF - Basic Oxygen Furnace, Thermal Spraying, EIS - Electrochemical Impedance Spectroscopy, Microhardness, Erosive Wear, Mass Loss

ABSTRACT

This contribution deals with research results focused on analysis of renovative layers applied by thermal spraying. There were two types of sprayed wires used - formerly used S-NiCro 80/20 and new cored wire marked DURMAT. Micro hardness of thermally sprayed coatings was measured by Vickers indenter, wear resistance of coatings was checked by erosion test, simulated by abrasive grit blasting. EDX analysis proved the presence of particular structural phases. Higher micro hardness values were found in DURMAT coating and this property led to higher wear resistance of this coating in comparison with previously used S-NiCro 80/20 coating. Test results showed that new coating marked DURMAT-AS-7641 has better properties in comparison with previously used coating from perspective of chemical composition, micro hardness and also erosive wear evaluation. Part of the experimental work was to determine the electrochemical characteristics of blasted surfaces using the EIS (electrochemical impedance spectroscopy) method.

INTRODUCTION Shortage of raw materials in world market and its more difficult and more expensive procuring raises efforts to increase products’ lifetime and saving of raw materials and energy. Industrial development is connected mainly with development of material-technical basis with its technology and technical modernization and with substantial advance in labour productivity. Economic reasons of maximal exploitation of materials in mechanical and metallurgical production are actual topics of scientific research nowadays. The most frequent causes of parts and construction failures are tribology processes occurring on functional surfaces. Tribological characteristics of used materials are of great importance for correct operation of parts and construction nodes. Interaction of functional surfaces during their mutual motion causes undesirable changes on surface layers giving birth to wear. In term of material loss prevention, the most important concern should

be active surface protection technology in friction nodes. In steel production, inner parts of oxygen converter hood are subject to extreme wear. Converter hood material is exposed to set of unique factors related to temperature and gas rate variation, dust particles load etc. In addition to extensive heat increase, the material is subject to cyclic load and overheating. With high probability, overheating is the main reason of cracking problem as a result of thermal fatigue caused by thermal cycles from one heat campaign to other, along with differences in converter wall temperature during cooling. Other important degradation factor is erosion caused by oxides of iron, calcium, magnesium, silicium and other elements occurring in exhaust gas. As a result of the inner wall material mass loss by erosion, wall thickness is reduced. For inner hood side protection there are various types of protective coatings used with aim to enlarge hood lifespan. [1,2,3,4,5,6,7]. Suitable surface pretreatment significantly affects the quality of subsequently applied thermal sprayed coatings. Abrasive blast cleaning is appropriate and preferentially used technology in practice for obtaining a clean surface with the desired microgeometry. Blasted surface creates conditions for perfect anchoring of subsequently applied coatings, however, it is characterized by high surface activity. In real conditions, its activity rapidly decreases because of the chemical adsorption of gases from the atmosphere and oxidation. The consequence is an electrode potential reduction of metal and the adhesion of applied coatings. One of the modern methods of corrosion monitoring for determination of electrochemical properties of the surface is electrochemical impedance spectroscopy (EIS) [8,9,10,11]. EIS is suitable technique for the measurement of low conducted or complex layers and coatings on the surface of a basic metal. One of the advantages of EIS method is small influence of the measured surface in comparison with voltametric (e.g. potentiodynamic) techniques. EIS resulted in polarization resistance value of the layer on metal surface, which characterizes its corrosion resistance. This report deals with research results focused on analysis of renovative layers applied by thermal spraying. Part of the experimental work was to determine the electrochemical characteristics of blasted surfaces using the EIS method.

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1 Materials and Methods The specimens for electrochemical measurements have a cylindrical shape (φ11,3 x 20mm) and were manufactured by turning and then they were finished with standard metallographic procedure. The faces of the samples were blasted with mineral blasting material and for comparison also by the glass beads. Pre-treatment was realised on laboratory air blast equipment TVJP - 320 at a pressure of 0,4 MPa until surface saturation. Electrochemical characteristics of the surfaces were evaluated using EIS on VoltaLab 10 laboratory measuring device. The measurements were performed using PGZ 100 measurement unit and CTV 101 control unit of rotating electrode. Corrosive environment consisted of 0,1 M NaCl solution. Stabilisation time at the free electrode potential of sample in the electrolyte was 5 min., 1, 4 and 8 hours. The frequency varied in the range from 100 kHz to 10mHz with change in frequency 20 times per decade. Amplitude of the AC voltage was 20 mV. The temperature during measuring was 22°C ± 1°C. During the measurement, the sample rotated on the rotating electrode at 70 min-1. Determination and calculation of the polarization resistance Rp was performed from measured EIS courses using circular regression of Nyquist diagrams. For analysis of the measured curves equivalent circuit given in (Fig. 1), was used. The values of parameters that characterize the individual components in the equivalent circuit were determined using VoltaMaster 4 software analysis program. Connection and measurement principle is given in [8].

Experimental protective layers were applied on the base material of STN 41 2021 (ISO 2605) - heat-resistant carbon steel with specific properties, used for making pipes for energy and chemical equipment, operating at high temperatures. [12] Mechanical properties of base material: Tensile strength: Rm=340-370 MPa Notch toughness KCU 3: 69J.cm-2 Yield strength at 20°C: 235 MPa Brinell hardness: max. 147HB Elongation A5: min. 25% Modulus of elasticity E at 20°C: min.206GPa Chemical composition of base material is shown in (Tab. 1). C

Mn

Si

Cr

0,07-0,15

0,35-0,60

0,77-0,35

max. 0,25

Ni

Cu

P

S

max. 0,25

max. 0,25

max. 0,04

max. 0,04

Tab. 1 Chemical composition of base material (wt-%)

There were two types of cladding layers applied by thermal spraying technology on this base material. Characteristics of applied materials: 1. S - NiCro 80/20 in form of ø 1,6 mm wire, manufactured by Zander Schweisstechnik, applied by thermal flame-spraying technology. Chemical composition is shown in (Tab. 2). This cladding material was applied in two layers. C

Si

Mn

S

Cr

0,036

1,19

0,29

0,002

19,8

Tab. 2 Chemical composition of S - NiCro 80/20 (wt-%)

2. DURMAT - AS - 761 in form of cored wire ø 1,6 mm, manufactured by DURUM Verschleiβschutz GmbH, applied by wire arc spraying technology. Chemical composition is shown in (Tab. 3). Fig. 1 Equivalent circuit of a simple corrosion system

Surface pre-treated using angular blasting medium is characterised by a lot of sharp notches, its morphology is suitable for coating application, because it allows sufficient anchoring effect. Therefore, for the pretreatment before applying coatings angular blasting medium - brown corundum was selected.

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C

Si

Cr

Ni

B

WSC

0,35

4,10

10,60

33,15

1,80

50

Tab. 3 Chemical composition of DURMAT - AS - 761 (wt-%)

Before coatings application, test samples were pretreated by pneumatic abrasive blast cleaning: blasting medium - brown corundum, grain size 0,71 mm, blasting angle 75°, air pressure 0,6 MPa, distance


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testing sample - 250 mm blasting nozzle. The surface roughness of blasted samples was evaluated by contact roughness tester Surftest SJ - 301, Mitutoyo, according to STN EN ISO 4287 - Profile method. Following roughness parameters were evaluated in mean line measuring system: Ra (arithmetical mean deviation of the profile), Rz (maximum height of profile), Rq (root mean square deviation), Rt (total height of profile), RSm (mean width of the profile elements). Roughness measuring parameters were chosen as follows: sampling length l ( λc ) =2,5mm, number of sampling lengths N = 5, measured profile: R (mean line measuring system), filter used: Gauss, evaluation length ln =12,5 mm. Vickers microhardness test of cladding and also base material was evaluated on metallographic crosssections according to STN EN ISO 6507, testing equipment DUH 202 SHIMADZU, (Fig. 2).

0,9 mm. Circumferential velocity of blasting wheel 51,0 m.s-1, output velocity of abrasive grains - 70,98 m.s-1. One erosive cycle equals to 5 cycles of blasting medium in blasting equipment.

2 Results Surface of base material after grit blasting with angular blasting medium is characterized by typical morphology - undirected, isotropy surface. This morphology is suitable for functional coating application, because it provides higher adhesion to substrate. Blasted surface roughness parameters are shown in (Tab. 4). Figure 3 shows appearance of the surface blasted by brown corundum. Impact of large number of blasting grains gives rise to very rugged surface. Its nature depends on several factors. The main factors influencing the nature of the blasted surface are the shape and size of blasting grains, surface coverage degree, parameters of blasting machine and material characteristics of the basic material and the blasting material used. R - profile

mmc (mm)

2,5

Rq (nm)

14,3

N

5

Rt (nm)

93,1

Ra (nm)

11,42

RSm(10%)

392

Rz (nm)

72,89

Tab. 4 Surface roughness parameters of blasted surface

Fig. 2 Pattern of microhardness measurement

Microstructure of evaluated coatings was observed by SEM FEI Quanta 400. Chemical composition of applied coatings was analysed by EDX analysis. Tested coating was exposed to erosive wear simulated by abrasive grit blasting with aim to simulate operating conditions. The equipment used for this aim was laboratory blasting equipment KP-1, which enables to control number of blasting cycles. After each blasting cycle, weight of tested samples was evaluated. Mass loss of tested samples was monitored at two blasting angles: 45° and 75°. Used blasting medium - brown corundum with grain size

Blasted surface belongs to the undirected, isotropic surfaces, which means that the value of surface roughness in the longitudinal and perpendicular direction is not significantly different. The blasted surface is characterized by sharp deep hacks. It is mainly used to obtain the desired surface roughness in the pre-treatment and surface cleaning. From (Fig. 3) it is clear that the surface was completely covered with the notches after blasting grain impact, i.e. the degree of surface coverage equals 1. The figure also shows remains of blasting grains wedged in the surface. Nyquist diagrams of steel surface after blasting by glass beads and corundum are reported in (Fig. 4). Polarisation resistance in this form of the measured curves equals to the diameter of the semicircle in Nyquist plot. There was the presence of only one layer recorded.

15


after 4 hours of exposure is due to release of corrosion products, which were partially protective in nature, causing the formation of new surfaces and the further development of active corrosion process. Corrosive products are better able to adhere to the blasted surface, and if disrupted faster corrosion processes and the creation of new partially protective corrosion products on the exposed surface occur. The increase in total resistance at the interface of material - electrolyte is due to the increase in resistance of the porous layer.

Fig. 3 3D view on surface blasted by corrundum

a)

b) Fig. 4 EIS curves of S235JRG1 steel in 0.1 M NaCl solution after blasting by a - glass beads, b - corundum

The value of polarization resistance Rp increased with the exposure time of samples in the electrolyte, (Fig. 5). Higher values of Rp were measured after application of glass beads, which may be related to the size of the assessed blasted area, but especially to the lower surface roughness of the surface blasted by glass beads and also to lower energy transmitted by impinging particles of glass beads compared to angular brown corundum grit. The maximum value of Rp was recorded for both blasting media after 4 hour exposure of samples in corrosive environment. With the increasing value of Rp corrosion rate decreases. Decrease in polarization resistance

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Fig. 5 Diagrams of polarization resistance for the surfaces blasted by different types of blasting media

Experimentally determined microhardness of base material was 281 HV 0.01. Figure 7 shows ferrite - pearlite structure of base material. Microhardness of coating made of DURMAT-AS-761 was higher (810 HV 0.5) in comparison with S - NiCro 80/20 coating (775 HV 0.5), resulting from material properties, chemical composition and structure of particular materials, (Fig. 6). It is possible to assume that higher microhardness values provide higher wear resistance of coatings.

Fig. 6 Microhardness of evaluated coating


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Fig. 7 Structure of base material Fig. 10 Interlayer under-coating S - NiCro 80/20

Fig. 8 Cross-section of coating S - NiCro 80/20

Fig. 9 Cross-section of coating DURMAT- AS - 761

Microscopic analysis proved characteristic sandwich structure of both evaluated coatings, (Fig. 8, 9). Chemical composition of present phases and interlayers was determined by EDX analysis, (Fig. 13). It is possible to observe impinged particle deformation and porosity of coatings. Figures 10 and 11 show interlayer under-coatings formed by Ni, Fe, Cr.

Fig. 11 Interlayer under-coating DURMAT- AS - 761

Utilization of tubular cored wires seems to be suitable for protective coatings, in cases when corrosion and wear occur together. Characteristic feature of the wires is higher melting power and consequently higher coating making productivity. Melting rate of tubular wire depends on current density and wire unwinding rate. Figure 12a shows mass loss Wh (g) of samples coated by DURMAT-AS-761 at blasting angle 75° and 45°, (Fig.12b) shows wear process of S - NiCro 80/20 coating at mentioned blasting angles. Lower wear of both coating was achieved at 75° blasting angle. Lower blasting angle = more intensive material wear. Notched abrasive grain can cause crack generation and failure of coatings, resulting in stress concentration and coating separation. Erosive wear test was carried out up to 5 cycles, when coating was completely removed. DURMAT-AS-761 coating showed high wear resistance resulting from its material properties, chemical composition and material structure along with its microhardness.

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a)

b)

Fig. 12 Mass loss of samples coated by a) DURMAT-AS-761, b) S – NiCro 80/20

Fig. 13 EDX analysis of coating a) S - NiCro 80/20, b) DURMAT- AS – 761

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3 Conclusion Analysis of Nyquist diagrams and the measured polarization resistance show that the higher value of Rp was present in material blasted by glass beads, which corresponds to a lower corrosion rate. This is in line with the obtained surface morphology. The surface created after blasting with glass beads is composed of spherical indentations after the impact of beads and partly of notches created by fragments of blasting particles. Decrease in polarisation resistance is due to the releasing of corrosion products, which are protective in nature. The rate of corrosion reactions has practical significance in terms of temporary protection of surfaces pre-treated by abrasive blast cleaning until the application of protective and functional coatings. Experimental work has proved that the use of EIS as a modern non-destructive method presents new opportunities of quick way how to quantitatively describe the local corrosion process, course of corrosion processes and their controlling. It represents the future in industrial monitoring of corrosion. Problems related to actual need for increasing the lifetime of oxygen converter hood gave rise to this report. During steel making, there is combined wear of cooling hood pipes occurring. Exposed parts of hood are exploited by high-temperature corrosion along with erosive and abrasive wear by flowing particles consisting of iron, oxides of iron etc. Thermally sprayed coatings are applied to increase lifetime of cooling pipes and to protect the base material. The aim of this report was to analyse currently used S - NiCro 80/20 coating and compare it with new DURMAT-AS-761 coating. Tested samples were cut out of functional hood parts. Microscopic analysis proved typical sandwich structure on both of the evaluated coatings. EDX analysis determined chemical composition of present phases and interlayers. Experimentally determined microhardness of the base material was 281 HV 0.01. Microhardness of new tested coating, DURMAT-AS-761, was higher (810 HV 0.5), in comparison with S - NiCro 80/20 coatings (775 HV 0.5); and it results from their material characteristics, chemical composition and structure. It can be assumed that higher microhardness values provide higher wear resistance of coatings. Erosive wear test proved lower mass loss at 75° blasting angle for both of evaluated coatings.

Lower blasting angle causes more intensive material reduction. At places of abrasive impact, some cracks and coating failures can appear resulting in stress concentration and coating separation. Achieved results showed, that new coating marked DURMAT-AS-761 has better properties in comparison with previously used coating from perspective of chemical composition, microhardness and also erosive wear evaluation.

4 Acknowledgement This contribution is the result of the project implementation: „Unique equipment for evaluation of tribocorrosion properties of the mechanical parts surfaces“ (ITMS: 26220220048) supported by the Research & Development Operational Programme funded by the ERDF and project No.1/0510/10 supported by grant agency VEGA.

5 References [1] Rigney, D. W., Viguie, R., Wortman, D. J., Skelly, D. V.: Thermal barrier coatings applications and process development for aircraft engines. Journal of thermal spray technology 6, 1997, pp. 167-175 [2] Diekmann, H., Gramberg U.: The Role of Tantalum as a Construction Material in the Chemical Industry. Annual Symposium of the Tantalum International Study Center, Wien, Oct. 4 - 6, 1994 [3] Vasen, R., Pracht, G., Stover, D.: New thermal barrier coating systems with a graded ceramic coating. ITSC 2002, Essen 2002 [4] Pershin, V., Lufitha, M., Mostaghimi, J., Chandra, S.: Effect of substrate temperature on nickel coating adhesion. Proceedings from Materials solutions 2001, Thermal spray symposium, Ottawa 2001 [5] Cherico, S., Toth, R.: Survey of various protective coatings and deposition technology to exhaust cover BOF lifespan extension. Cleveland, Ohio, 2006 [6] Ambrož, O., Kašpar, J.: Plasma sprayed coatings and their utilization in industry. Brno, 1990, 320 s [7] Amada, S., Hirose, T.: Influence of grit blasting pre-treatment on the adhesion strength of plasma sprayed coatings: fractal analysis of roughness. Surface and Coatings Technology, 102, 1998, s.132-137

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[8] Škublová, L. – Mráziková, R. – Škorík, V.: Vplyv elektroerozívne upraveného povrchu na koróznu odolnosť titánovej zliatiny Ti6Al4V. Transfer inovácií, č.17/2010, 2010, pp. 116-119 [9] Nauer, G. E.: Modern electrochemical surface treatments for automotive applications, Kplus ECHEM, University of Viena, 2008 [10] Raja, V.S. et al.: Electrochemical impedance behavior of graphite-dispersed electrically conducting acrylic coating on AZ31 magnesium alloy in 3.5 wt.% NaCl solution. Progress in Organic Coatings, Volume 67, Issue 1, January 2010, Pages 12-19 [11] http://www.gamr y.com/App_Notes/EIS_ Primer/EIS_Primer.htm#Model2 [12] Egri, M.: Application of specific surface treatments with aim of extension of mechanical parts lifespan. Diploma thesis. Technical university of Košice, 2008

20 VOLUME 15, No. 1, 2011


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Instantaneous Plastic Flow Properties of Thin Brass Sheets Under Uniaxial and Biaxial Testing Feliks Stachowicz (PL) stafel@prz.edu.pl

BIOGRAPHICAL NOTES

Feliks Stachowicz, prof. DSc, PhD, Eng. (born in 1951) graduate of the Faculty of NonFerrous Metals at AGH University of Science and Technology in Kraków (1975), he specializes in evaluating metals usability for cold forming processes (especially forming limits of thin sheet metal) and analyses of basic parameters concerning technological forming processes of sheet metal, pipes and structural profiles as ell as recycling processes. In 1981 he defended PhD degree, in 1991 obtained DSc degree and in 2000 he was awarded the professor’s degree. Member of the Section of Plastic Forming Processes Theory in Committee on Metallurgy at Polish Academy of Science. In years 1999-2002 and 2005-2008 dean of Faculty of Mechanical Engineering and Aeronautics, since 2008 vice rector for general affairs of Rzeszow University of Technology.

KEY WORDS

Plastic Anisotropy, Strain Hardening, Strain State, Forming Limit, Sheet Metal

ABSTRACT

In the prediction of formability of sheet metals, it is necessary to determine material properties which are normally evaluated on the data obtained by performing simple tests. The most important parameters affecting the value of limit strains of a sheet metal are the strain hardening exponent (n) and plastic anisotropy ratio (r). It was established that especially the value of n-parameter of brass sheets strongly depend on the specimen elongation and stress/strain state. The effect of instantaneous (differential) nt - value and rt - value on the forming limit curve was computed theoretically.

INTRODUCTION There is still great interest in the workability prediction of a material during sheet metal forming. This type of processing involves complex sequences of stress and strain states, and the material workability cannot be evaluated through simple procedures such as simple tension testing [1]. Some materials form better than others. Moreover, a material that has the best formability for one stamping may behave very poorly in a stamping of another configuration. For these reasons, extensive test programs are often carried out in an attempt to correlate material formability with value of some mechanical properties. The formability of sheet metal has frequently been expressed by the value of: strain hardening exponent n, and plastic anisotropy ratio r. The stress-strain and hardening behaviour of a material is very important in deter-

22 VOLUME 15, No. 1, 2011


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were measured and recorded continuously up to specimen failure.

2 Plastic Anisotropy Ration Normal anisotropy value represents the ratio of the natural width deformation in relation to the thickness deformation of a strip specimen elongated by uniaxial tensile stress:

r = fw ft

(1)

The r-value at a given elongation, usually 15 pct (f=0,14) has been used for many years as a quality control indicator of drawability. More recently, there has been interest in the effect of strain on the plastic ratio, while acknowledging that the changes in the crystallographic texture occurred with increasing strain. For plasticity studies, the basic definition of r-value has been replaced with the instantaneous rt - value, which is defined as:

rt = dfw dft

(2)

1,7

anisotropy factor

mining its resistance to plastic instability. In sheet forming operation biaxial as well as uniaxial stress state exists. Thus, one must known and understands material hardening behavior as a function of stress state [2,3,4,5,6,7,8]. Additionally the value of the n and r parameters depend on the grain size of the material [9] and changes as plastic deformation accumulates. Since experimental determination of the forming limit diagram of a sheet metal is very timeand material-consuming, the knowledge of the above mentioned relations could be very useful in the theoretical calculations of the limit strains of a sheet under different strain state. We might to expect that calculations of the forming limit diagram using instantaneous (elongation dependent, instantaneous) value of the normal anisotropy ratio rt and strain hardening exponent nt enable to achieve better correlation between calculated and experimental results. Experimental studies of formability of various materials have, however, revealed basic differences in behavior, such as the “brass-type” and the “steeltype” [10], exhibiting respectively, zero and positive dependencies on forming limit upon the strain ratio. Such results cannot be reconciled without proper attention to the details of strain hardening behaviors of these materials, particularly as functions of strain and strain ratio. Modern universal testing machines with appropriate measuring systems for length-width variations allow the usual characteristic values to be ascertained together with r and n values, both rationally and with a high accuracy.

1,4

1,1

0,8 0

0,1

0,2

0

0,1

0,2

1 Material and Mechanical Testing

0,3

1,7

anisotropy factor

The tests were carried out on the 1,0 mm thick 80-20 and 0,5 mm thick 63-37 brass sheets in annealed state. The tensile specimens of 50 mm gauge length and 12,5 mm width, were prepared from strips cut at 0°, 45° and 90° according to the rolling direction of the sheet. The experiments were carried out using a special device which recorded simultaneously the tensile load, the current length and width of specimen, using a microcomputer. In order to determine the flow properties of a material in biaxial stretching, the bulge test was carried out, using hydraulic bulge apparatus with a circular die aperture of 100 mm diameter. The bulging pressure and the curvature of the pole

strain

1,4

1,1

0,8

strain

0,3

Fig. 1 Variation of rt - value with strain for the 63-37 brass sheet specimens cut at 0° (upper) and 45° (lower) according to rolling direction

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According to the latest experimental results [2,9,11,12] no systematic increase or decrease of rtvalue with strain was observed, in contrast to previous reports in the literature. The test results for different materials and for different specimen orientation (Fig. 1) have shown that in the case of the 80-20 and 63-37 brass sheets no clear correlation between plastic anisotropy ratio and specimen elongation exists. And because of that the r-value of brass sheet was determined using [13] method (Fig. 2), and it could be treated as a reasonable representation of anisotropic behaviour over a wide range of elongation. r=0,941

dv = Knfn - 1 = v n df f

-0,06

(4)

-0,12

which results in: -0,12

-0,06

0

thickness strain

Fig. 2 Plastic anisotropy ratio of the 63-37 brass sheets determined by Welch et al. method

3 Strian Hardening Exponent For many years strain hardening laws such as those from Ludwig, Hollomon, Voce, Swift and Krupkowski has been used to describe the plastic behaviour of polycrystalline metals and alloys. The Hollomon law in the form of: n

v = Kf

(3)

has been used the most frequently. The parameters involved in this laws, particularly n-value has been, and continue to be, correlated to changes in the microstructure of a material and in some way represents processes which occur during deformation. They have also been used extensively to characterize the formability of sheet material. The value of strain hardening exponent n is usually determined from the double logarithmic plot of the true stress and true strain by linear regression. When copper and brass sheets are concerned the logarithmic strain-stress relation is not a straight line - and that was observed in the case of 80-20 brass sheet under both the uniaxial and biaxial straining. The n-value is strain dependent what

24 VOLUME 15, No. 1, 2011

nt = dv f df v strain hardening exponent

-0,18 -0,18

(5)

0,5 0,4 0,3 0,2 0,1 0

0,1

0,2

0,3

0,4

effective strain 0,5

strain hardening exponent

width strain

0

resulted from the changes in the crystallographic texture [13,14]. Because of this the mean n-value (which describe the strain hardening of the whole strain range) and instantaneous nt - value were determined on the base of the results of uniaxial and biaxial testing. Equation (3) assumes a constant n-value and the average n-value is measured at a given strain range or can be determine for the whole range of straining from double logarithmic stress-strain data by a least squares approach. To examine the true strain hardening behaviors the instantaneous nt - value should be determined. taking the derivative from equation (3) yields:

0,4 0,3 0,2 0,1 0

0,1

0,2

0,3

effective strain

Fig. 3 Variation of nt - value with strain for the 80-20 brass sheet, under uniaxial (upper) and equibiaxial testing (lower)


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4 Forming Limit Diagram The forming limit diagram (FLD) is today a generally accepted measure of sheet metal formability. It is extensively used in both scientific research and industrial practice. The FLD defines the extent to which a sheet can be strained before a sharp neck and final failure occur. The diagram presents the forming limit for a range of deformation modes ranging from deep drawing (negative minor strains, uniaxial tension) to stretch forming (positive minor strains, biaxial tension). The FLDs of the brass sheets were calculated basing on the M-K theory [17] - a sheet element was divided into two parts, region A with no material defects and region B, softened due to a presence of surface dimples and internal defects. The solution to the M-K problem was achieved in straight-forward incremental numerical procedure of calculations. In our calculations of the FLD we have used no fitting parameters to describe the inhomogeneity of a material, but we have based on experimentally obtained relations [18] which describe the material softening and strain localization processes. When the influence of plastic anisotropy ratio on the FLD brass sheets is concerned, the following calcula-

tions were performed:

calculations of the FLD using the value of mean

normal anisotropy ratio r, calculations of the FLD using two different type of instantaneous rt-value and elongation relation - the increasing and decreasing function.

major strain

0,4 0,3 0,2

r - increasing r - const. r - decreasing

0,1 0 0

0,1

0,2

0,3

minor strain

Fig. 4 Effect of instantaneous anisotropy ratio changes (increasing and decreasing function of elongation) on the forming limit curve position

The FLD calculations using instantaneous rt - value as a two types of function of elongation (Fig. 4) has shown that in the f2 > 0 region increasing function of rt - value resulted in decreasing of limit strains while when using the decreasing function the limit strains increase. This effect was the most visible for the equibiaxial stretching.

major strain

The results presented in Fig. 3 show clearly that there is no unique constant n-value which may characterize hardening process in both uniaxial and biaxial deformation of brass sheets. The intensity of strain hardening depends on the true strain [15]. In the case of materials tested instantaneous nt - value varies continuously with strain-increases rapidly at small strains and at higher strains falls again somewhat less rapidly. It was established [16] that at large strains (above 0,10) stress is controlled by the cell size. This observation suggested that there is a change in the accommodation process from the grain level at low strains to the cell level at large strains - what resulted in a change in the strain hardening process. Variation of the nt - value is strain and strain state dependent (Fig. 3). In the case of uniaxial testing of the 80-20 brass sheet the nt-value riches its maximum at f = 0,15, while in the case of biaxial stretching at f = 0,10. These points could be treated as the beginning of quasistatical range of deformation process. The strain value of f = 0,36 and f = 0,26, for uniaxial and biaxial testing respectively, are the limit strains.

0,4 0,3 0,2

differential n-value mean n-value

0,1 0 -0,2

-0,1

0

0,1

0,2

0,3

minor strain Fig. 5 Effect of instantaneous anisotropy ratio changes (increasing and decreasing function of elongation) on the forming limit curve position

As it was mentioned above the second important parameter affected the FLD is the strain hardening

25


exponent. The knowledge of the differences in the hardening process during deformation seemed to be very useful in FLD calculations. Theoretically determined FLD presented in Fig. 5 demonstrate that forming limit curves calculated using both mean n-value and instantaneous nt - value are different in the shape. The FLD calculated using instantaneous strain hardening exponent as a function of effective strain Fig. 3 is more flat than that of the FLD calculated using mean n - value - however the position of these two FLD is very close.

4 Conclusion The two most important material parameters - plastic anisotropy ratio (r) and especially strain hardening exponent (n) of brass sheets strongly depend on the strain state. Both the n and r parameters are strain dependent, so in some cases instantaneous nt and rt value more precisely represent a material properties. These remarks should be taken into account in predicting sheet metal formability (forming limit diagram) as well as in numerical modeling of sheet metal forming processes.

5 References [1] Pereira I.M., Rubim G., Acselrad O., Cetlin P.R., Comparison of the experimental and the numerically predicted mechanical damage in the sheet forming of steel, Journal of Materials Processing Technology, vol. 203, 2008, p. 13-18 [2] Doucet A.B., Wagoner R.H., Transient tensile behavior of Intersitial-Free steel and 70/30 brass following plane-strain deformation. Metallurgical Transactions, vol. 20A, 1989, p.14831493 [3] Vial C., Yield locus of 70-30 brass sheets, International Journal of Mechanical Science, vol. 30, No. 2, 1988, p. 137-145 [4] Shi M.F., Strain hardening and forming limits of automotive steels, SAE Transactions, vol.104, 1995, p. 571-577 [5] Mahmudi R., Stress-state dependence of workhardening behavior in aluminium alloy sheet, Journal of Materials Processing Technology, vol. 72, 1997, p. 302-307 [6] An Y.G., Vegter H., Elliot L., A novel and simple method for the measurement of plane strain work hardening, Journal of Materials Processing Technology, vol. 155-156, 2004, p. 16161622

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[7] Slota J., Spiťak E., Determination of flow stress by the hydraulic bulge test, Metalurgija, vol. 47, no. 1, 2008, p. 13-17 [8] Dournaux J.L., Bouvier S., Aouafi A., Vacher P., Full-field measurement technique and its application to the analysis of materials behaviour under plane strain, Materials Science and Engineering A, vol. A 500, 2009, p. 47-62 [9] Stachowicz F., On the mechanical and geometric inhomogeneity and formability of aluminium and aluminium alloy sheets. Archives of Metallurgy, vol. 41, no. 1, 1996, p. 61-75 [10] Ghosh A.K. Plastic flow properties in relation to localized necking in sheets. In D.P. Koistinen & N-M. Wang (ed.), Mechanics of sheet metal forming, Plenum Press. New York 1978, p. 287312 [11] Rao K.P., Mohan E.V.R., A unified test for evaluating material parameters for use in the modelling of sheet metal forming, Journal of Materials Processing Technology, vol. 113, 2001, p. 725-731 [12] Chamanfar A., Mahmudi R., Compensation of elastic strains in the determination of plastic strain ratio (R) in sheet metals, Materials Science and Engineering A, vol. A 397, 2005 [13] Welch P.I., Ratke L., Bunge H-J., Consideration of anisotropy parameters in polycrystalline metals, Zeitschrift fßr Metallkunde, vol. 74, 1983, p. 233-237 [14] Hill R., J.W. Hutchinson, Instantaneous hardening in sheet metal under biaxial loading: A theoretical framework, Journal of Applied Mechanics, vol. 59, 1992, p. S1-S9 [15] Ding Hao, Ding Hua, Song D., Tang Z., Yang P., Strain hardening behavior of a TRIP/TWIP steel with 18,8% Mn, Materials Science and Engineering A, vol. A 528, 2011, p. 868-873 [16] Gracio J.J., Fernandez J.V., Schmitt J.H., Effect of grain size on substructural evolution and plastic behavior of copper. Materials Science and Engineering A, vol. A 118, 1989, p. 97-105 [17] Marciniak Z., Kuczyński K., Limit strain in the process of stretch forming of sheet metals, International Journal of Mechanical Science, vol. 9, No, 1967, p. 609-624 [18] Stachowicz F., Effect of material inhomogeneity on forming limits of 85-15 brass sheets, Archives of Metallurgy, vol. 36, no. 2, 1991, p. 223-242


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Joining Car Body Steel Sheets Using the Clinching Method Emil Spišák (SK) emil.spisak@tuke.sk Ľuboš Kaščák (SK) lubos.kascak@tuke.sk

BIOGRAPHICAL NOTES

Emil Spišák, prof. CSc. (born in 1955) is professor of Department of Technologies and Materials, Faculty of Mechanical Engineering, Technical University of Košice. He is head of the Department of Technologies and Materials and Vice-Rector for Development and Construction of the University. He served as Vice-Dean for 4 years and Vice-Rector for 8 years. He works in the area of evaluating of material properties, material failures, analysis and quantification of production factors influence in production of thin steel sheet stamping parts, modelling and simulation of technological processes, mainly forming processes. He is national secretary and a member of International DeepDrawing Research Group. He is author of 5 monographs and more than 200 publications in journals and conference proceedings at Slovakia and abroad. His published works were cited 115 times. He has been worked on 60 grant projects, research tasks and 47 projects solved for industry. Ľuboš Kaščák, Ing. PhD. (born in 1974) is an assistant professor at the Department of Technology and materials. He received scientific degree PhD. in 2004 in the field of properties evaluation of joined deep drawn sheets. He is an author of more than 70 publications in journals and conference proceeding in Slovakia and abroad. He has worked on several grant projects and research tasks.

KEY WORDS

Clinching, Car Body Sheets, Evaluation of Properties

ABSTRACT

The paper deals with joining steel sheets for automotive industry using the clinching method. This method is a relatively new technique in joining car body sheets and it is beginning to find its place in the automotive industry as an alternative to resistance spot welding, especially in joining materials of different qualities or materials with different surface treatment. Combination of three hot-dip galvanized steel sheets: microalloyed steel sheet H220PD with the thickness of 0,8 mm, TRIP steel 40/70+Z100MBO with the thickness of 0,77 mm and drawing grade sheet DX51D+Z with the thickness of 0,9 mm were used for the experiments. The tensile test and metalographical analysis were used for the evaluation of the clinched joints properties. We observed the influence of the sheets’ position during clinching (taking into consideration the materials and the active parts of the tool - punch and die) on the carrying capacity of the joint.

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Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of KoĹĄice

INTRODUCTION Contemporary automotive industry is a challenging business. It is required not only to respond to environmental concerns such as greenhouse gases and fuel economy, but also to meet customer expectations [1]. The car body consists of a combination of several materials, which is a result of material and energy saving trends applied in car body production. The production of vehicles with lower weight and consequently also lower fuel consumption is responding to ecological demands of reduction of emissions into the environment. There is a need to join different materials - materials of various thicknesses, qualities, surface treatments [2]. Such practice in car body production opens new possibilities for designers in optimal utilization of properties of various materials, which can be combined into one construction. For example, the cheapest materials can be situated in the common parts of pressing in car body, good-quality sheets can be situated in the critical places of deformation and high-strength sheets can be used in the exposed places due to demands of construction - deformation zones [3]. These demands lead to research in the area of material joining with the emphasis mainly on carrying capacity of joints, quality of joints and corrosion resistance. It is not always possible to achieve the required quality of joints in automotive industry when classical methods of joining like resistance spot welding and laser brazing are used. There is a need to conduct research into alternative methods of material joining. One of the alternative joining methods used in automotive industry is clinching [4]. Clinching is a joining method in which sheet metal parts are deformed locally without the use of any additional elements [5]. It is mechanical press joining by local forming, which can be widely applied in manufacture of thin-walled structures, especially in the automotive industry. It consists in clamping together several sheet metals by an impact extrusion between a punch and a die [6]. Another clinching method used in the automotive field is self-piercing riveting with the semi-tubular rivets [7]. The paper evaluates joints made by clinching the following materials: microalloyed steel HSLA H220PD, TRIP steel 40/70+Z100MBO and drawing grade steel DX51D+Z.

Fig. 1Clinching tool and the mechanism of joint creation [10]

1 Clinching Process The clinching process is a combination of drawing and forming that locks together sheets metal layers [8]. The blanks are plastically deformed and the shape of the tools remains theoretically unchanged during the clinching processes. The punch is movable, whereas the fixture and the die are fixed during the process (Fig. 1). The punch force needed for the joining process depends on the thickness and the strength of the materials to be joined, the size of the tools and friction coefficient usually varies from 10 to 100kN [9]. The technology has many advantages, such as no pre-drilled hole requirement, capability to join a wide range of similar or dissimilar materials and combinations of materials (Fig. 2 and Fig. 3), no fume emissions etc. However, the process is limited by the inability to change process parameters such as rivet size or die configuration “on the fly� between successive joint positions on a vehicle structure. This leads to potential increasing costs and limits the application of the technology [1].

29


This method should be used as an alternative to resistance spot welding, especially in joining of combination of materials. Comparisons of carrying

capacities between joints made by clinching and resistance spot welding were published mainly in [10-12].

Fig. 2 Combination of materials used in car body of Volvo V70

Fig. 3 Range of materials used in car body production (VW Jetta)

2 Materials and Experiments The following steel sheets were used for experimets: microalloyed steel HSLA H220PD with the thickness of 0,8 mm, TRIP 40/70+Z100MBO with the thickness of 0,77mm and DX51D+Z with the thickness of 0,9 mm. Their basic mechanical properties and chemical composition are shown in Tabs. 1 and 2. Properties of DX51D steel were specified by producer. According to the orientation of punch and die to the position of upper and lower joined material, following combinations of steel sheets for press joining were used:

30 VOLUME 15, No. 1, 2011

Samples A: H220PD (a0 = 0,80 mm) and TRIP (a0

= 0,77 mm)* Samples B: TRIP (a0 = 0,7 mm) and H220PD (a0 = 0,80 mm)* Samples C: H220PD (a0 = 0,80 mm) and H220PD (a0 = 0,80 mm) Samples D: TRIP (a0 = 0,77 mm) and DX51D (a0 = 0,90 mm)* Samples E: DX51D (a0 = 0,90 mm) and TRIP (a0 = 0,77 mm)* (*sheet on the die side of press joining tool) The samples of 40 x 90 mm dimensions with the length of lapping 30 mm according to STN 05


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of KoĹĄice

1122 standard were used for the experiments. Six samples were prepared for every combination of sheets. Beacuse of the used joining method, it was not necessary to clean the surfaces of samples before clinching. Material

Rp0,2 [MPa]

Rm [MPa]

A80 [%]

n90

H220PD

238

382

36

0,228

TRIP 40/70

450

766

26

0,278

450*

23*

DX51D

Clinching was performed on the tension machine ZD 40 made by Werkotoffrufmaschinen Leipzig Company with the loading range of 40 kN. The force needed for joining was 30 kN. The force for blankholder was 8 kN. The carrying capacities of joints made with clinching were evaluated according to standard STN 05 1122 - Tensile test of spot welded joints. This test was used for measuring the maximum carrying capacities Fmax of pressed joints. The test was carried out on the testing machine for determination of strength of metals TIRAtest 2300 made by VEB TIW Rauenstein with the loading speed of 8 mm/ min. The metallographical analysis was used for the evaluation of pressed joints quality.

Tab. 1 Basic mechanical properties of used steels (*specified by producer) Material

Chemical composition in [%] wt C

Mn

Si

P

S

Al

Cu

Ni

Cr

Ti

H220PD

0,004

0,415

0,100

0,042

0,004

0,035

0,011

0,017

0,310

0,037

TRIP 40/70

0,204

1,683

0,198

0,018

0,003

1,731

0,028

0,018

0,055

0,009

DX51D

0,15*

0,040*

0,040*

V

Nb

Mo

Zr

H220PD

0,002

0,026

0,005

0,001

TRIP 40/70

0,004

0,004

0,008

0,007

Tab. 2 Chemical composition of used steel sheets (*specified by producer) Number of sample 1

Carrying capacity Fmax [N] Samples A

Samples B*

Samples C

Samples D*

Samples E

939

--

980

--

1087

2

985

--

1008

--

1584

3

1016

--

956

--

1334

4

1080

--

924

--

1834

5

1093

--

973

--

1973

6

937

--

978

--

1658

Tab. 3 Measured values of carrying capacities of the clinched samples (*joints were not made)

3 Analysis of Results The measured values of carrying capacities of clinched joints after tensile test are shown in Tab. 3. The carrying capacities of samples B and samples D were not measured, because clinched joints were not made. The upper sheets of both samples (TRIP 40/70 steel) were cut off in the place of the joint and then pressed to the lower sheet (Fig. 4 and Fig. 5). No cracks were observed on the lower part of

sheet on the die side of samples B and D. The average value of carrying capacities of samples A was 1008 N. The cracks in the TRIP steel of the die side were observed (Fig. 6), which could possibly have a negative effect, especially during dynamic load. The cracks can even decrease the joints’ corrosion resistance. The values of carrying capacity of samples A are similar to the values measured in clinched joints of the common drawing grade steel sheets as was published in [2].

31


The average value of carrying capacity of samples E was 1578 N. The cracks in the TRIP steel of the die side were observed, similar to those in sample A (Fig. 8).

H220PD Fig. 4 Sample B without creating a clinched joint

TRIP Fig. 8 Sample E after tensile test with cracks in the joint

DX51D Fig. 5 Sample D without creating a clinched joint

TRIP Fig. 6 Sample A after tensile test with cracks in the joint

The measured values of carrying capacity of samples E are higher than values of samples A and C, which is probably caused by the thicker material of the upper sheet in the joint (DX51D of 0,9 mm). The results of metallographical analysis and the critical areas of clinched joints are shown in Fig. 9 - 11. Critical area is the area with the most significant thinning in the joint. Failures occured in these areas during tensile tests of samples A, C and D, and during the clinching process in samples B and D. The metallographical analysis confirmed the occurrence of cracks in the TRIP steel on the die side of the joints in the round part (Fig. 9).

Critical area

The average value of carrying capacity of samples C was 970 N. No cracks occurred in the place of the joint from the side of die (Fig. 7). The carrying capacity values of samples C are similar to the values measured in clinched joints of the common drawing grade steel sheets.

Fig. 9 Sample A with the critical area and the cracks in TRIP steel on the die side

Fig. 7 Sample C after tensile test

32 VOLUME 15, No. 1, 2011

Figure 10 shows sample C of two H220PD steels. There are no cracks or failures in the joint. Figure 11 shows the critical area of the clinched joint of sample E, which is different from the criti-


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

cal area of sample C. It is caused by using the joint’s upper sheet with a different thickness, which is in accordance with the values of carrying capacity measured during tensile test.

Carrying capacities of these samples were on sufficient level and metallographical analysis confirmed no occurrence of cracks or failures in the area of clinched joints.

4 Acknowledgement

Fig. 10 Sample C with the critical area of the joint

This paper is the result of the project implementation: Center for research of control of technical, environmental and human risks for permanent development of production and products in mechanical engineering (ITMS:26220120060) supported by the Research & Development Operational Programme funded by the ERDF.

5 References

Fig. 11 Sample E with the critical area of the joint

3 Conclusion The paper focused on the evaluation of clinched joints of various material combinations. Microalloyed steel HSLA H220PD, TRIP steel 40/70+Z100 MBO and DX51D+Z steel were used for the experiments. The influence of the orientation of joined materials regarding the position of punch and die of the tool was also observed. The material combinations of TRIP 40/70 with H220PD as well as TRIP 40/70 with DX51D, where TRIP steel is oriented towards the punch, are not suitable for joining by clinching, because the joints are not created. Failures in the critical areas of joints occur during the clinching process. The same material combinations, where TRIP steel is oriented towards the die, are not suitable for joining by clinching, even though the joints are successfully created, because there occur cracks in TRIP steel, which could negatively affect the joint, especially during dynamic load. The cracks can even decrease the corrosion resistance of the joints. Only the combination of the same materials H220PD is suitable for joining by clinching.

[1] Han L., Thornton M., Shergold M., A comparison of the mechanical behaviour of selfpiercing riveted and resistance spot welded aluminium sheets for the automotive industry, Materials and Design, 31, 2010, p. 1457-1467 [2] Kaščák Ľ., Spišák E., Tlakové spájanie oceľových plechov pre automobilový priemysel, PROTECH-MA 2005, Progressive Technologies and Materials, Rzeszów – Bezmiechowa 2005, p. 76 - 81 [3] Spišák E., Kaščák Ľ., Spájanie oceľových plechov v automobilovom priemysle, In: MAT/TECH automobilového priemyslu, 2005, p. 97 - 102 [4] Kaščák Ľ., Nové metódy tlakového spájania materiálov, Transfer inovácií, 8/2005, p. 99-100 [5] Varis J.P., Lepistö J., A simple testing-based procedure and simulation of the clinching process using finite element analysis for establishing clinching parameters, Thin-Walled Structures, 41, 2003, p. 691-709 [6] Oudjene M., Ben-Ayed L., On the parametrical study of clinch joining of metallic sheets using the Taguchi method, Engineering Structures, 30, 2008, p. 1782-1788 [7] Mucha J., The influence of shape of tool die and blankholder on effect of deformation joint elements and rivetion load values, In: Acta Mechanica Slovaca, 3-A/2008, p. 279-286 [8] Shiming G., Lothar B., Mechanism of mechanical press joining. Journal of Mechanical Tools Manufacturer, 34, 1993, p. 641-657 [9] Varis J.P., Ensuring the integrity in clinching process. Journal of Materials Processing Technology, 174, 2006, p. 275-277 [10] Kaščák Ľ., Spišák E., Joints of thin sheets made

33


by forming and resistance spot welding: evaluations of properties, IDDRG 2007 – Forming the future, Györ, Maďarsko, p. 545-550 [11] Kaščák Ľ., Spišák E., Evaluations of properties of clinching and resistance spot welding, In: Scientific Bulletins of Rzeszów University of Technology : Mechanics 73, no. 253, 2008, p. 161-166 [12] Spišák E., Kaščák Ľ., Únosnosť spájaných pozinkovaných oceľových plechov Zinkohal 350, In: Acta Mechanica Slovaca, 2-B/2006 – Protechma, p. 393-398

34 VOLUME 15, No. 1, 2011


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

35


Wasteless Splitting of Metal Round Bars Basing on Cross-Wedge Rolling Process Arkadiusz Tofil (PL) atofil@pwsz.chelm.pl Zbigniew Pater (PL) z.pater@pollub.pl

BIOGRAPHICAL NOTES

Arkadiusz Tofil, Ing. PhD. (born in 1975) Assistant professor in the Department of Computer Modeling and Metal Forming Technologies at the Lublin University of Technology and Vice-Rector for Development and International Relations at the State School of Higher Education in Chełm. He graduated from the faculty of Mechanical Engineering at the Lublin University of Technology in 2001. Professional specialization it is mainly forming of metals, technology of cross-wedge rolling, bar cropping without waste, modelling and computer simulation.

KEY WORDS

Bar Splitting, Cross-Wedge Rolling, Experiment

ABSTRACT

This paper presents research works on a new method of wasteless splitting of metal round bars. This method is connected with rolling on the bar circumference of a groove in the shape of letter V, and, later, on repeated rotary bending of the bar separate part, leading to the metal cracking. Special tools sets, in which a flat-wedged rolling mill LUW-2 used at the Lublin University of Technology was equipped with, were applied in the splitting process. A typical set includes: mounting, cutting knife and bending pad. Laboratory tests confirmed the effectiveness of the worked out splitting method. This process was also analyzed theoretically, basing on finite element method (FEM). In calculations, the influence of process basic parameters on the cracking process was analyzed: knife forming angle, rolled groove depth, bending angle and length of the cut bar part. The possibility of brittle fracture (on the basis of Saint-Venant hypothesis) and ductile fracture (on the basis of Cockroft-Latham) presence was analyzed.

INTRODUCTION Different kinds of devices are used for round metal bars cutting, depending on production and metal type. Basically applied cutting methods can be divided into cutting with waste and without waste. In recent years, at the Department of Computer Modeling and Metal Forming at Lublin University of Technology, research works [1,2] on a new method of wasteless splitting of round metal bars have been carried out. This method is connected with making on the bar circumference of a V-groove, and later, on repeated rotary bending of the bar separate part, leading to metal cracking. Cross-wedge rolling process in cold conditions (CWR) was used for V-groove making on the bar circumference. Detailed description of research works dealing with this

36 VOLUME 15, No. 1, 2011


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

process is presented in paper [2]. Due to a research stand for CWR, research works were limited to rolling method by means of flat wedges. Two ways of groove forming (Fig. 1) were considered. In the first way (Fig. 1a), called free CWR, contact with metal is only in the area of the formed necking. In the second way (Fig. 1b), called CWR with compression, tools contact with the billet also outside the forming zone. Additionally in Fig. 1, the most important parameters of the analyzed process CWR were shown. a) γ

∆r

d0

dn

α

material is on the billet whole width);

strains in the groove area are of laminar charac-

ter (in form of ring layers) and reach maximal values in external surfaces; during free CWR metal is upset before the wedge, which leads to the increase of the rolled bar diameter. The upsetting value depends on the applied forming angle a; forming forces value depends on CWR process parameters. Forces undergo reduction together with the application of larger angles a and smaller reduction ratio 3r; CWR process stability can be limited in the result of uncontrolled slip and rolled bar rupture presence. The best forming conditions, in order to avoid the mentioned earlier distur-bances, are obtained when the applied tools have forming angles a=45°. This paper discusses the results of the further research stage dealing with bars cracking during splitting without waste. The research scope included laboratory tests of splitting of bars from steel C45 and numerical analysis basing on finite element method (FEM).

1 Laboratory tests of wasteless splitting process

b)

α d

∆r d0

γ Fig. 1 Analyzed within the scope of research works method of cross rolling of V-grooves on the workpiece circumference: a) local contact (free CWR), b) contact on the tool whole length (CWR with compression)

On the basis of the conducted research works it was stated that: the application of the CWR in cold allows for forming of V-groove on the bar circumference; the rolling process can be realized by means of two ways: free CWR method (contact between tools and material is only in the area of formed necking) and CWR method with compression (contact tool-

Experimental research of the splitting without waste process of round metal bars were done at Lublin University of Technology using flat-wedge rolling mill LUW-2 (Fig. 2). For the research needs, tools sets with the length 500 mm and width 120 mm were made (shown schematically in Fig. 3). Each tool set consists of a knife (wedge) and a bending pad which are placed in mounting. The knife is used for rolling of V-groove on the bar circumference. However, bending pads are responsible for rotary bending of the bar split part of length l. In Fig. 3 main parameters of the splitting without waste process are also presented: bending angle i, forming angle a, reduction ratio 3r. In research processes knives with angles a = 45° and 60° were used, which cut into the bar at the depth 3r = 2 mm. Two sets of bending pads were also used for which i = 45° and 3°. Bars with diameters ø 20 mm and length 200 mm were split. The conducted research concerned splitting of bars from steel C45 type. On the basis of compression tests, a curve of the used steel type was determined and described by means of the following dependency:

37


v p = 1041 . 4{0i . 201

(1)

where vp - yield stress φi - effective strain.

Fig. 2 Laboratory stand LUW-2 for CWR with two flat wedges

the container and tools were also backtracked, and again after billet positioning the splitting process was repeated. In the result of stand tests the rightness of the analyzed conception of round metal bars splitting was confirmed - Fig. 4. It was stated that application of this method allows for splitting from bar of parts with minimal length 1.3 bar diameter d0. Two characteristic zones at the splitting surface can be distinguished: external (shiny) - appearing during rolling of V-groove and internal (mat) - appearing during metal cracking. Moreover, on the basis of conducted laboratory stand tests it was stated that metal cracking has a spiral character (from the external to the bar axis) - Fig. 4. Yet, the largest the bending angle i value, the smaller the number of bar rotation (at the bending stage) is required for metal splitting.

Upper tool

θ bar α ∆r Bottom tool

Fig. 3 Schema of analyzed process of wasteless splitting

On the basis of tensile tests the following parameters of the applied steel C45 were deter-mined: tensile strength Rm = 697 MPa, yield point Re = 439 MPa, unit elongation A10 = 19,1%. Yet, basing on ring-sample upsetting, the friction factor for friction pair steel C45-tool steel was determined and it was equal m = 0,5. Experimental research were realized at rolling tools spacing 20 mm. The splitting test course was as follow: the billet together with sleeve was placed in the rolling mill feeder. Next, tools were put into motion (with linear velocity o = 0,1 m/s) and splitting process was realized at given parameters (i, a) and reduction ratio 3r = 2 mm. In the case when the bar did not undergo splitting, it was removed from

38 VOLUME 15, No. 1, 2011

Fig. 4 C45 steel grade elements obtained during wasteless splitting process at: a=45°, 3r=2 mm, i=2° (upper figure) or i=3° (bottom figure)


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

2 Numerical analysis of metal cracking in splitting process Numerical analysis of metal cracking in splitting without waste process was made applying the commercial software MSC.SuperForm 2005 basing on FEM. Calculations were made assuming that split bars were of steel C45 type. It was assumed that material model of the formed metal is described by the dependency (1). In the analysis

Billet Holder Starting situation

Uchwyt

thermo - mechanical schema of calculations was used, assuming that bar and tools temperature was the same as the environment temperature 20°C. At the same time, it was assumed that heat exchange coefficient between tools and metal was 20 kW/m2K and between metal and environment 0,2 kW/m2K. In simulations, model of shear friction was used, which depends on the metal slip vs. tool and is determined by friction factor m = 0,5.

Bottom tool Narzędzie dolne

Sytuacja początkowa

Top tool Narzędzie górne z z

x y x

Finishing situation

Fig. 5 FEM model of wasteless splitting process realized at 3r = 2 mm, a=45°, d0=20 mm and i = 3°

Numerical analysis was made assuming the following simplifications: tools behave as perfect rigid body, tools edges rounding is not important in splitting process and it can be omitted, friction factor on material-tools surface of contact is constant and does not change during the process. After considering of the mention above simplifications several FEM models of splitting without waste process were worked out, one of them is shown in Fig. 5. Each model consists of a bar from steel C45 (with diameter d0 = 20 mm), two tools sets moving in the opposite directions with velocities o = 0,1 m/s - upper and lower, and mounting device positioning bar during rolling. In calculations the following parameters were changed: forming angle (a = 45°; 50° and 60°), bending angle (i = 2°; 3° and 4°), reduction ratio

(3r = 1,5 mm; 2,0 mm and 2,5 mm) and rolling length (l = 20 mm; 30 mm; and 57,5 mm). Remeshing was not used in calculations due to retaining of full information about state of strain in nodes. The rightness of finite element method application in the analysis of cross-wedge rolling process (including CWR of V-groove in cold conditions) was confirmed by results of tests verifying calculations, made in laboratory and industrial conditions [1]. It can be then assumed that this method will be also adequate for the analysis of splitting without waste process. This is confirmed by comparison of tangent forces (directed according to tools movement), calculated by FEM and measured in laboratory conditions, shown in Fig. 6 and considering one of the analysed splitting cases. This comparison shows good qualitive and quantitive conformity between the noticed forces distributions.

39


Influence of state of stress on cracking is described by condition of brittle fracture as in the equation [3]:

(2)

30000

FEM

25000

Experiment

15000 10000 5000

0

100

200

300

400

500

Displacement of tool [mm]

Fig. 6 Comparison of tangential loads (acting in tools movement direction) in wasteless splitting process of C45 steel bar, at: d0=20 mm, 3r=2 mm, a=45° and i=3°

In the above equation Rm means tensile strength, vzr - reduced stress that can be defined e.g on the basis of hypothesis of the largest elongation as: σV stress in node A [MPa]

800 600 400 200 0 -200 0

0

1000

1 ∆r=1.5 mm

1000

2 ∆r=2.0 mm

3

4

5

Time t [s]

∆r=2.5 mm

800 600 400 200 0 0

1

2

3

4

5

Time t [s]

Fig. 8 Influence of bending angle i on vV during wasteless splitting process of C45 steel bar at: d0 = 20 mm, 3r = 2 mm, l = 57,5 mm and a = 45° - in nodes A & B

vzr = vV = v1 - o (v2 + v3)

(3)

800 600 400 200 0 -200 0

σV stress in node B [MPa]

1000

20000

σV stress in node B [MPa]

Tangential load Fx [N]

vzr = Rm

σV stress in node A [MPa]

3 Brittle fracture

1000

1

2 α=50°

α=45°

3

4

5

4

5

Time t [s]

α=60°

800 600 400 200 0 0

1

2

3

Time t [s]

Fig. 7 Influence of forming angle a on vV during wasteless splitting process of C45 steel bar at: d0 = 20 mm, 3r = 2 mm, l = 57,5 mm and i = 3° - in nodes A & B

40 VOLUME 15, No. 1, 2011

where: vv - de Saint-Venant stress, v1, v2, v3 - first, second and third main stress respectively, o - Poisson’s coefficient [3]. On the basis of calculations, the values of reduced stress in two nodes A (at the beginning placed at r = 7,5 mm from the bar axis) and B (for which r = 2,5 mm) placed in the plane of the formed necking were analyzed. The obtained distributions of stress vv in the function of analyzed splitting parameters (angles a and i), reduction ratio 3r, length l and time t are shown in Figs. 7,8,9,10. On the basis of calculations it was stated that the change of forming angle a (Fig. 7) influences reduced stress vv only in V-groove rolling phase, that is for t < 2 s. However, in the rotary bending phase (t > 2 s) distributions of vv calculated for angles a = 45°; 50° and 60° are almost the same. Hence, it can be concluded that the value of angle a does not influence splitting metal cracking course. Concerning the influence of applied bending angle i on reduced stress vv (Fig. 8) it was stated that the increase of i causes considerable increase of


Acta Mechanica Slovaca

σV stress in node A [MPa]

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

σV stress in node A [MPa]

stress vv, both in external layers (point A) and in layers close to axis (point B). However, differences between values vv for various i increase at the further stages of bending. The change of this parameter has, of course, no influence on stress vv, noticed at rolling stage of V-groove. The increase of reduction ratio 3r causes considerable increase of reduced stress vv (Fig. 9) both in nodes A and B. This effect is well visible in the whole process, that is during rolling of V-groove and rotary bending. Analysis of diagrams shown in Fig. 10 provides interesting information concerning the influence of length l of split billet on reduced stress vv. The shortening of length l causes reduction of stress vv. In the case of billet of length l = 20 mm the observed stresses vv (in both analyzed points) did not reach tensile strength value Rm = 697 MPa, obtained in tensile test. Hence, in this case the metal will not crack, which was confirmed in experimental tests. Probably, for short billets (l < 1,3.d0) a different schema of deformation is present, in the result of which bending process is replaced by rotary compression with elongation in axial direction.

800 600 400 200 0 -200

σV stress in node B [MPa]

0 1000

1 l=20 mm

2 l=30 mm

3

4

5

Time t [s]

l=57.5 mm

800 600 400 200 0 0

1

2

3

4

5

Time t [s]

Fig. 10 Influence of length l of separated element on vV during wasteless splitting process of C45 steel bar at: d0 = 20 mm, i = 3°, 3r = 2 mm and a = 45° - in nodes A & B

1000

4 Ductile fracture

800

In the analysis of discards presence, CrocfortLatham criterion was used, defined by the dependency:

600 400 200

{*

# v d{ = C

0

1

-200

(4)

0

0

σV stress in node B [MPa]

1000

1000

1 θ=2°

2 θ=3°

3

4

5

Time t [s]

θ=4°

800 600 400 200 0 0

1

2

3

4

5

Time t [s]

Fig. 9 Influence of rolling depth 3r on vV during wasteless splitting process of C45 steel bar at: d0 = 20 mm, i = 3° , l = 57,5 mm, a = 45° and - in nodes A & B

where v1 - first main stress, {* - limiting strain of cracking, {i – effective strain, C - material constant value. Conducting of calculations required determining material constant value C which describes the material cracking moment. In order to do this, authors’ method was applied. This method was based on simulation by means of finite element method of tensile test of sample from steel C45 type. Calculations were made till the moment at which relative elongation reached the value 19,1% (in experimental research at such elongation billets rupture appeared). Next, the value of integral (4) in nodes in critical section was analyzed. Mean results for particular nodes allowed for determining the material constant value which was C = 0,69.

41


Cockroft-Latham integral in node B

Cockroft-Latham integral in node A

0.10 ∆r=1,5 mm

0.08

∆r=2,0 mm

∆r=2,5 mm

0.06 0.04 0.02 0.00 0

1

2

3

4

0

1

2

3

4

5

Time t [s]

0.12 0.10 0.08 0.06 0.04 0.02 0.00 5

Time t [s]

Fig. 11 Influence of rolling depth 3r on Cockroft - Latham integral during wasteless splitting process of C45 steel bar at: i = 3°, l = 57,5 mm and a = 45°- in nodes A & B

42 VOLUME 15, No. 1, 2011

Cockroft-Latham integral in node A Cockroft-Latham integral in node B

In order to state how the integral Cockroft-Latham value changes in the analyzed splitting process, its distributions in nodes A and B were determined, in which previously values of reduced stress vv were analyzed. Some of the obtained distributions were presented in Figs. 11, 12. Analysis of calculations results showed that in many cases values of integral (4) not only does not increase during splitting but also decrease. It happens when v1 has negative values. Then, according to equation (4) integral values will decrease. Present in this situation state of 3D compression is favorable for eliminating of micro cracks. Concerning values of integral calculated for nodes A and B it was stated that in any of the analyzed cases it did not exceed the limiting value 0,2. Hence, in bar cross sections, determined by these points placement unfavorable conditions for metal ductile fracture presence appear. The influence of forming angle a, reduction ratio 3r (Fig. 11) and length l of the bar split part on values of integral accumulated in nodes A and B is irregular (difficult to determine). Among the analyzed parameters only increasing of bending angle i (Fig. 12) causes considerable increase of integral values, which is observed at the whole stage of bending (t > 2 s).

0.10 0.08 0.06 0.04 0.02 0.00 0

1

2

3

4

5

Time t [s]

0.10 θ=2°

0.08

θ=4°

θ=3°

0.06 0.04 0.02 0.00 0

1

2

3

4

5

Time t [s]

Fig. 12 Influence of bending angle i on Cockroft - Latham integral during wasteless splitting process of C45 steel bar at: 3r = 2 mm, l = 57,5 mm and a=45°- in nodes A & B

5 Conclusions On the basis of research works the following conclusions were drawn: method of wasteless splitting, basing on crosswedge rolling of V-groove and next, rotary bar bending, allow for successful splitting from round metal bar of its part with length l larger than 1.3 bar diameter d0; bar splitting in the analyzed process of splitting without waste takes place in the result of brittle fracture of metal. State of stress present in the material and strains favors the appearance of ductile rupture; metal brittle fracture in the process of splitting without waste of round metal bar can be intensified by increasing of bending angle i and/or reduction ratio 3r; modelling of wasteless splitting process, based on FEM in conditions of 3D state of strain allows for verification of technological and designing parameters of the assumed variants of splitting process; research works should be continued in order to fully determine technological possibilities of the proposed wasteless splitting process and to work out of an industrial equipment.


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

6 References [1] Pater Z., Tofil A. Experimental and theoretical analysis of the cross - wedge rolling process in cold forming conditions. Archives of Metallurgy and Materials 2007 vol. 52, Issue 2 s. 289 - 297 [2] Tofil A. Research of process of mechanical splitting without waste of round metal bars. Ph. D. Thesis, Lublin University of Technology, Lublin 2008 (in Polish) [3] Pełczyński W. T., Pełczyński T. A. Teoria procesów obróbki plastycznej. Część I Mechanika obróbki plastycznej. Warsaw University of Technology, Warsaw 1982 (in Polish)

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Curved rotary module for modular construction of motion structures Jozef Svetlík (SK) jozef.svetlik@tuke.sk Peter Demeč (SK) peter.demec@tuke.sk

BIOGRAPHICAL NOTES

Jozef Svetlík, Ing. PhD. (born in 1977) assistant professor at the Department of Manufacturing Engineering and Robotics (since 2003) at the Faculty of Mechanical Engineering in TU Košice (SjF, TUKE). Graduate TUKE SjF 2000, scientific degree of Doctor of Philosophy (PhD) defended at Technical University of Košice in 2004. Internal PhD. student SjF TUKE (2000-2003). Member of the editorial board of “Journal of Applied Statistics. Research interests of construction machinery and modular robotics. Co-author of the script “modules for the construction of production machinery” and “Robotics - Technical equipment for automated workplaces: inter-operational handling. Winner of “Siemens Excellence Award 2004” for the dissertation. The holder of an honorary recognition of the International Engineering Fair 2003 in Nitra Agrokomplex for “intelligent modular assembly system”. Team member “SjF Tuke robotics”, which is several times European champion and world champion from 2010 in robotic soccer. Author of a utility model “rotary module for modular construction machinery” and patent “contactless transmission of electrical power for modular machines” (in the approval process). Author of over 60 scientific and professional articles in journals and contributions to scientific and professional conferences. Peter Demeč, prof. Ing. PhD. (born in 1952) professor of Production machinery and equipment (since 2003) at the Faculty of Mechanical Engineering TU of Košice (SjF, TUKE). Graduate SjF TUKE in 1975, scientific degree Candidate of Sciences (CSc / PhD.) defended the STU in Bratislava in 1984, Associate Professor of habilitated SjF TUKE 1994. SjF TUKE prodean (1993-1996), Head of Department of Manufacturing Technology (1997-2002), Deputy Head of the Department of Production Systems and Robotics (2003-present). Member of scientific advice SjF TUKE, Faculty of Environmental and Manufacturing Technology University in Zvolen, Faculty of Special Technology and University of Alexander Dubček in Trenčín, a member of the Society for machine tools, the Czech Republic, Club President of the Slovak Association of Mechanical Engineers for SjF TUKE, Member of Editorial Board, and MM Science Journal Technologist. Research interests of construction, virtual prototyping, and precision machine tools. Author of the memoir „The accuracy of machine tools and its mathematical modeling“ (Košice: Vienala 2001) and over 130 scientific and professional articles in journals and contributions to scientific and professional conferences.

KEY WORDS

Modular Machine, Rotation Module, Robotic Manipulator, Curved Rotary Module, Modular Construction, Robot Workspace, Serial Robot

ABSTRACT

The article deals with the mechanics of modular machines and examines in detail the parameters of the principle of joining newly designed curved rotary modules into

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Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

homogeneous serial kinematical chain with five degrees of freedom of movement. The result of analysis is generated workspace built on the basis of 60° curved rotary module with unlimited rotation for a serial kinematical structure with homogeneous 5DOF.

INTRODUCTION The idea of modular principle of machines is not new [6]. In the past there have been many creative

and innovative ideas from which the amount of time is transformed into a real functioning machine. In the field of motion structures with modular serial construction, there are some innovative solutions to many well-known and unknown companies, for example.: SCHUNK, Epson, Yamaha. These concepts give a chance to build machines for the handling, processing and other tasks as seen in Fig. 1.

Fig. 12 Modular serial structures

Known modular systems also offer a range of modular motion units. These modules are characterized by different attributes, parameters and sizes. Modules can be translational, rotational, and other rare cases. The main weaknesses of these modules include the limitation of rotational movement and greater complexity of design. From these facts suggest limiting it to the prescribed limits of the range of motion (rotation in the range max. 270 degrees, translational motion in the range of 350 mm, and so on). The resulting movement possibilities of cinematic chain composed of these modules have a limited range of rotational movement. This eliminates the shortcomings hereinafter referred rotation module for the construction of modular machines.

ing plate, which performs a rotational movement over the body, as seen in Figs. 2, 3. In the body of a rotary module is stored servomotor and reducer. Servomotor is equipped with incremental encoder and an electromagnetic brake.

1 Principle of Design Solutions

Fig. 2 Sketch the basic layout of the internal rotation module

Rotation module, designed for modular construction machinery, allows merge these modules and the creation of kinematic chain with theory of any number of degrees of freedom of movement, able to perform controlled motion [1]. Its internal structure consists of a body, interlink and clamp-

Clamping plate of rotation module is attached to the body through a rotary motion tie of one degree of freedom of movement and it is located on the clamping mechanism for connecting interlink

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to the next module (modules in the chain). This rotary motion linkage is unlimited range of motion [11]. Interlink of rotation module is geometrically curved and includes a bayonet fixing mechanism for connecting of clamping plate of the previous module (modules in the chain). Angle of curvature determines the scope and characteristics of the working space of the modular machine assembled from these modules. Homogeneous kinematic structure of a modular concept consists of several identical or identical type (eg. size or curvature of the diverging) rotary motion modules [12].

Example of 3D display modular manipulator with 6 degrees of freedom of movement is shown in Fig. 5, when is used the extension part [9]. This part serves to increase the reach of kinematic chain and has no internal drive system. It is inserted between the modules and in this way, adjusts the characteristics of the working space and also reachability positioning member in the end of it. Except the extension member are also used rotating different modules with varying degrees of curvature. This method achieves a high flexibility and variability of working space and reachability of location is a function of mutual selection and arrangement of appropriate modules and extension parts.

?

Fig. 3 Modification of 3D models of a separate rotary module of varying degrees of curvature

Links between all internal parts of the module and also between the individual modules are fixed (except rotary links between the body and clamping plate), sufficiently rigid and unable to pass the required mechanical load. Communication equipment intended for control are proposed as a wireless, eg.: WiFi, Bluetooth and so on. Electronic communications modules with accessories should be positioned into the body of the module. Connection of individual modules should be realize in terms of flexibility by bayonet method. Example of 3D display modular manipulator with 6 degrees of freedom of movement is shown in Fig. 4, which are used to build basic rotary modules. This series homogenous structure is characterized by its simplicity and not the most appropriate reachability within your workspace. To achieve the desired position to be extensive rotationing of many modules, which is relatively energy consuming.

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Fig. 4 3D model of the modular machine, assembled from rotary motional basic modules, with 6 degrees of freedom of movement

Fig. 5 3D model with a modular machine using an extension part and adapted the basic modules with 6DOF


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

2 Mathematical Description of Structure For the mathematical description of a serial kinematic chain is best to use Denavit-Hartenberg principle of deployment of joint chain to the coordinate systems [2]. This deployment will achieve particulate transformation matrices (1). This transformation matrix “Ab0” describes the position and rotation of the first couple coordinate systems, thus the current position of the base “b” and the first module “0” in Fig. 6, where q1 and q5 are common variables. In our case, the steering angles of rotary modules and take their values in the interval (0, 2π). Variables lx1 and lx2 represent distance of local coordinate systems according to the principle

of D-H principle. Variable “a” represent the angle of curvature of the module used in this case was used 60° angle. Further transformation matrices in order of the other members of the kinematic chain are analogous to the shape and functions are gradually variables q2 and q5. In order to get the overall transformation matrix is necessary transformation matrix between neighboring coordinate system multiplied “Ab0” and “A01”, resulting in a total transformation matrix of great complexity. Relationship (2) reflects the partial transformation matrix between the base “b” and the second movable member in order-rotating module, “1”. After multiplying all the sub-transformation matrices of type “A” there

Fig. 6 3Composition of homogeneous serial kinematical structures with 5DOF  cos q1 − sin q1. cos a sin q1. sin a l x1. cos q1     sin q1 cos q1. cos a − cos q1. sin a l x1. sin q1  Ab 0 (q1 , q2 , q3 , q4 , q5 , q6 ) =  lx 2  0 sin a cos a     0 0 0 1  

(1)

Tb1 (q1 , q2 , q3 , q4 , q5 , q6 ) = Ab 0 (q1 , q2 , q3 , q4 , q5 , q6 ).A01 (q1 , q2 , q3 , q4 , q5 , q6 ) =  3. cos( q1 − q 2 ) cos( q1 + q 2 )  + 4 4   3. sin( q1 − q 2 ) sin( q1 + q 2 ) +  4 4  3. sin q 2   2  0 

3. sin q1 cos q1 . sin q 2 cos q 2 . sin q1 + − 4 2 4 cos q1 . cos q 2 3. cos q1 sin q1 . sin q 2 − + 4 4 2 3.(cos q 2 + 1) 4 0

3. cos q1 . sin q 2 3. sin q1 3. cos q 2 . sin q1 − − 2 4 4 3. cos q1 3. cos q1 . cos q 2 3. sin q1 . sin q 2 + + 2 4 4 1 3. cos q 2 − 4 4 0

3 Identification of Workspace To identify the shape and scope of workspace was necessary to define transformation matrices in a MathCAD program [3, 8] and also define the geometrical parameters: the curvature module a=π/3rad, module length l1=100mm, width mod-

 150. cos q1 + 75. sin q1 + 150. cos q1 . cos q 2 + 75. sin q1 . sin q 2    150. sin q1 − 75. cos q1 − 74. cos q1 . sin q 2 + 150. cos q 2 . sin q1    25. 3.(3. sin q 2 + 1)   1 

(2)

ule l2=100mm. The distance between the coordinate system is defined as a variable Lx1 and Lx2 (3, 4). It is necessary to define the scope of the local variable q1…q5 is from the interval (0, 2π) and the step number is ½ rad.

47


Fig. 7 Workspace of modular serial kinematic structures with 5DOF the curvature of the building module 60°

l x1 = 0,5.l1.(1 − cos a )

l x 2 = l2 +

l1. sin a 2

(3) (4)

Formularization of the overall transformation matrix and the gradual substitution of the general variables q1 until q5 the specified steps to get around 33000 points. These points represent the final position in the end coordinate system rotating module. Their display in a suitably chosen Cartesian coordinate system we will likely shape, size and scope of workspace. Workspace of homogeneous serial kinematic structure of Fig. 6 is reproduced in Fig. 7.

4 Conclusion The overall result of the described technical solution is a modular system for the building of modular machines assembled from identical or identical type (eg diverging of size or curvature) rotary motion units with unlimited rotation range of motion [7]. It is necessary to make more extensive analysis and find the best angle of curvature of the building module. This angle should be provide for widest possible range of workspace and also a good reachability of desired point in this workspace . On the other side should be provide the safe operation of that in any position of the kinematic chain can happen to self-collision kinematic structure [4]. It is probable that the varying degree of freedom of movement should always choose a different angle

48 VOLUME 15, No. 1, 2011

of curvature of the basic module [5]. Similarly it is probable that application-specific angle of curvature may be appropriate basic module other than that which is derived simulation in virtual terms [10,13].

5 References [1] Svetlík, J., Demeč, P., Turisová, R., Rotačný modul na stavbu modulárnych strojov: úžitkový vzor: prihláška č. 99-2010, Banská Bystrica: ÚPV SR, 2010. 12 s [2] Mostýn V., Skařupa J., Teorie prúmyslových robotú, In: Vienala pre Edíciu vedeckej a odbornej literatúry Strojníckej fakulty TU v Košiciach, 146s, 2000, ISBN 80-88922-35-6 [3] Kreheľ, R., Dobránsky, J., Uplatnenie simulačného systému v procese experimentálneho merania, 2009. In: Jemná mechanika a optika., Vol. 54, no. 11-12 , p. 329-331., ISSN 0447-6441 [4] Baron, P., Kočiško, M: Aplikácia počítačovej podpory katastra rizík technických zariadení. In: Zborník z vedeckej konferencie Nové smery vo výrobných technológiách, FVT Prešov, 2004, s. 410 – 413, ISBN 80–8073–136–5 [5] Khouri, S., Kyseľová, K., Al-Zabidi, D.: Restructuring an enterprise by implementing a complex information system as a tool for securing its further prosperity, 2009. In: Ekonomika ir vadyba: aktualijos ir perspektyvos., Vol. 14, no. 1, p. 152-158., ISSN 1648-9098 [6] Svetlík, J., Fedorčáková, M.: Progresívne typy robotov. In: Transfer inovácií. č. 11, SjF TU v


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

Košiciach, 2008, str. 216-218, ISSN 1337-7094 [7] Lešková, A., Švač, V.: Aplikácia modulových stavebnicových systémov pri realizácii skúšobných stendov. In: Transfer inovácií: Špecializovaná publ., vedecko-technické výstupy grantových úloh. Košice: TU-SjF, 2003, s. 18-19 [8] Kočiško, M: Výskum v oblasti počítačovej podpory výrobných technológií. In: Strojárstvo, Media/ST, Žilina, 5/2007, s.141, ISSN 1335-2938 [9] Marcinčin, J. N., Zajac, J., Kočiško, M., Baron, P.: Solid Edge v19+v20, FVT TU Prešov, 2008, 312 s., ISBN 978-80-553-0050-4 [10] Šebo, J., Fedorčáková, M., Jurčišin, R.: Basic indicators of measuring productivity and their application on machinery production orders, In: Intercathedra: Annual scientific bulletin of plant- economic department of the european technology university studies. no. 2009, str. 132-136, ISSN 1640-3622 [11] Dobránsky, J.: Automatizácia procesu dopravy vstupnej suroviny do linky v technológii balenia tavených syrov. In: Automation in production planning and manufacturing, SjF TU Žilina, 2006, s. 27-32, ISBN 80-8070-537-2 [12] Fedorčáková, M.: Logistické racionalizačné technológie, In.: Inovatívne projektovanie demontážnych procesov a systémov, zborník študijných materiálov 2009, TU v Košiciach, 978-80-553-0275-1 [13] Naščáková, J., et al.: Appcom as a flexible industry solution for managing modern IT infrastructure, In: Annals of MTeM for 2007 and proceedings of the 8th international conference Modern Technologies in Manufacturing., Cluj-Napoca: MTeM, 2007, p. 299-302, ISBN 9739087833

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Assessment of Cutting Area Temperature to the Face Milling using Several Cooling Methods Domnita Florina Fratila (RO) domnita.fratila@tcm.utcluj.ro

BIOGRAPHICAL NOTES

Domnita Fratila, Assoc.prof. Dr. Eng. (born in 1972) is an associated professor at the Technical University of Cluj-Napoca, Machine Building Faculty, Department of Manufacturing Engineering, Romania. She graduated at the Technical University of Cluj-Napoca, Machine Building Faculty, in 1996. Her professional orientation is focused on the manufacturing technologies, environment friendly techniques, eco-design, as well as microfabrication and micro-assembly. She is a member of the „Young Researches’ and Scientists’ Committee” in the framework of the „DAAAM International Association” and also member of the „Academic Association for Manufacturing Engineering.”

KEY WORDS

Cooling Effect, Near Dry Machining, Face Milling, Dry Cutting

ABSTRACT

This paper analyzes the temperature variations in the cutting zone under flood cooling (FC), near dry machining (NDM) and dry cutting (DC) conditions. The research compares the dual effects of air-oil mixture in near-dry machining with the cooling effect to dry cutting and flood cooling in terms of the reduction of cutting temperature through the cooling effect, as well as the reduction of heat generation through the lubricating effect to face milling.

INTRODUCTION Nowadays in the competition context manufacture no costs related to manufacturing processes can be ignored. When machining operations are performed, one of them is the cost related to use, maintenance and disposal of cutting fluids. Is it known the non-value added costs associated with flood coolants - parts cleaning, frequent floor cleaning, coolant additives such as biocides, chip cleaning, etc. The metal machining companies are currently under increasing pressure of competition, environmental regulation, and supply chain demand for improved environmental performance as presenred in [6], [7], [10]. Conventional production knowledge has three levels consisting on: idea (design of new products), CAD (Computer Aided Design) and CAM (Computer Aided Manufacturing). As an alternative, the sustainable production put all these components on the same level defining the sustainable product based on sustainable principles as presented in Fig.1. The environmentally friendly production techniques and the rapid growth of cutting fluid disposal costs have justified the demand for an alternative to machining processes using fluids. Thus, dry machining (DM) and Minimum Quantity Lubricant (MQL) machining have become the focus of attention of researchers and technicians in the field of machining as an alternative to traditional fluids as shown in [2], [4]. The

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Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

most logical measure that could be considered to eliminate the cutting fluids from cutting processes is DM. To DM no cutting fluid is used, it means that there is more friction and adhesion between work piece and tool, and at the same time the thermal load of tool and work piece are greater. With NDM, also known as Minimal Quantity Lubrication, there are no flood coolants. Just a small amount of sprayed cutting fluid is applied directly to the cutting interface. Typical fluid consumption is on the order of 50-100 ml/hour per nozzle and the chips are almost dry, having about 0,2% oil con-

tent. In conventional machining the cutting fluids are needed (cooling lubrication fluids - CLF and cleaning emulsion-CE). Compared the environmentfriendly techniques have some potential benefits like: Sustainable machining through lower flow rates of CLF, providing better cooling and lubrication mechanisms; Decreasing the cutting tool-chip contact length, resulting in lower cutting forces and lower tool wear; Extension of machining parameters operational range, resulting in increased process productivity.

CA

D

(E De ngin sig eer n) ing

Manufacturing costs

DE SI GN

(Id ea s)

Personal health

KNOWLEDGE BASE

Sustainable product

CAM (Manufacturing Engineering )

Energy consumption

Operational safety

Waste management Environmental impact

Fig. 1 Components of sustainable production

In the MQL the media feed in the cutting area in small quantities (as mentioned above) is generally the oil, but in some application the emulsion and water are used. MQL or NDM is the use of a minimal amount of cutting fluid mixed with air as an aerosol to provide controlled lubrication and reduce friction at the cutting-edge zone. The transportation medium is usually air or the droplets are formed and feed to the cutting zone in the way of aerosol spray in the case of the airless system. Although some MQL-technology suppliers claim that any cutting fluid can be used with the technique, most shops use highly refined vegetable oil or ester oil. These high-performance oils have excellent lubricity and natural dissolving properties, and they are environmentally friendly [5], [8]. With the increasing trends in the achieving sustainable machining, dry and near-dry techniques are emerging as

viable and more sustainable alternatives to flood cooling in the machining processes. Principally, every cutting and non-cutting process is convertible from closed circuit cooling with coolant lubricant to dry machining or minimal quantity lubrication. Due to the techniques flexibility, there are suitable individual solutions for a wide variety of manufacturing processes. MQL is used in almost every form of mechanical metal removal processes: sawing, turning, milling, high speed milling, boring, deep drilling, tapping, broaching, drill finishing with single and multiple edge cutting tools, and having still limited use in grinding [1, 3, 8, 9].

1 Cooling Effect By NDM NDM by meaning the use of MQL and DM applications are growing continuously due to the following reasons: High costs of cutting fluids, in the range of 8-20% of manufacturing cost;

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Personal health, work safety, waste disposal,

chip recycling; Progressive innovation in development of cutting tools involving advanced solutions. NDM refers to the condition of applying cutting fluid at relatively low flow rates, as opposed to the conventional way of using either a large quantity, typically of about 10 l/min, as in wet machining; or no fluid at all, as in dry machining. One main expectation of applying fluids is to control the cutting temperature, which is an important parameter for tool life and part dimensional accuracy in machining processes. In this context, it is of interest, the study of cutting temperature variation corresponding to the NDM and lubrication. 1.1 NDM influencing variables The experiments planning aims the understanding of the NDM operations in the terms of major machining performance (cutting forces, surface roughness, surface accuracy) under the range of tool geometry, tool material, work piece material, cutting conditions, chips forms as shown in Fig. 2. There are several variables influencing the environment-friendly machining. These are presented in Fig. 3. By experimental research, the temperature variations have been determined in the cutting area under flood cooling (FC), near dry cooling and DC conditions.

The research compares the dual effects of air-oil mixture in NDM, DC and FC in terms of the reduction of cutting temperature through the cooling effect, as well as the reduction of heat generation through the lubricating effect. 1.2 Experimental setup Experiments have been performed on the HAAS TM-1CNC Milling machine. The experiment setup is schematically presented in Fig. 4. The variable process parameters were considered: coolant flow rate Q[ml/min], cutting speed vc[m/min], cutting depth ap[mm]. The experiments have been planned as presented in Tab. 1. Emulsion 15% and vegetable oil (raps oil) have been used as cutting fluids for FC- respectively MQL milling. The cutting fluid flow rate of 0 ml/min correspods to the dry machining.

Fig. 4 Experimental setup

Fig. 2 General experiments planning

The first of the recorded parameters was the cutting area temperatures. In this sense it was used an non contact infrared thermometers XTempLS, that allow to appoint the cutting temperature in a range of -35°C to 900°C. The device has a temperature resolution of 0,1°C and the IR accuracy ±0,75°C. The recording interval, equal with diagram resolution, has been set to 20msec. For comparison purpose, the other checked output parameter of the face milling process was the power consumption, directly indicated on the CNC milling machine display.

2 Results and Disscussions Fig. 3 Variables influencing DM and NDM

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The results of experiments are summarized in the Tab. 1 too (last column). Concerning the power consumption the results show a 25% usage of tool


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

machine power capacity in case of DC and 15% to MQL and FC. The temperature ongoing in each case of the above mentioned parameters variation was recorded using the appropriate device software OptrisConnect. Three kind of temperatures were simultaneous measured: object (cutting area) temperature, internal temperature, and the external one. Some of

these diagrams are shown in the Figs. 5, 6, 7. The cooling effect depends obviously of the cooling technique. For the same cooling lubrication method, the coolant flow rate do not have a significant influence on the temperatures developed in the cutting zone. FC provides a high stability of milling process by keeping constant the temperature in the cutting zone.

Cutting speed [m/min]

Cutting depth [mm]

Coolant flow rate [ml/min]

Maximal temperature [°C] Obj

Ext

Int

150

2

0

86,1

22,2

25,2

150

2,5

25

42,8

22,6

25

200

2

25

48

22,1

24,9

200

2,5

50

49,7

22,3

25,8

250

2

0

123

21

26

250

2,5

50

54,3

25

21,8

150

2,5

1000

20,2

24,2

22,3

200

2,5

1000

21,4

24,8

22,8

250

2,5

1000

22,4

22,4

21,6

Fig. 1 Components of sustainable production

Fig. 5 Cutting area temperature to MQL milling (vc=250 m/min, ap=2.5 mm, Q=50 ml/min)

Fig. 7 Cutting area temperature to FC milling (vc=150m/ min, ap=2.5mm, Q= 1 l/min)

3 Conclusions The evaluation of the environment-friendly techniqies was undertaken to understand the likely impacts of theis use on sustainability performance measures. The results are more than an experimental method for supporting design of technology but also an instrument for supporting decisionmaking in the case of gear milling. This reseach supports technology policy and encourages the adoption and the application of NDM in industry. Fig. 6 Cutting area temperature to DC milling (vc=250 m/ min, ap=2.5 mm, Q=0 ml/min)

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4 References [1] Brockhoff T., Walter, A., Fluid minimization in cutting and grinding. Journal of Abrasive Engineering Society, Oct-Nov 1998, Butler, Pa [2] Dunlap C., Should you Try Dry? Cutting Tool Engineering, vol. 49, no.1, 1997, p. 22-33 [3] Kelly J.F., Cotterell M.G., Minimal lubrication machining of aluminum alloys. Journal of Material Processing Technology, no.12, 2002, Little Island, Cork, Ireland [4] Machado A.R., Diniz, A.E., Advantages and disadvantages of the use of the cutting fluids. Machining Congress, São Paulo, Brazil, 2000 [5] Marksberry PW, Jawahir IS. A comprehensive tool-wear/tool-life performance model in the evaluation of NDM for sustainable manufacturing. International Journal of Machine Tools and Manufacture, vol. 48, no 7-8, 2008, p. 878886 [6] Pusavec F, Krajnik P, and Kopac J. Transition to sustainable production – Part I: application on machinig technologies. Journal of Cleaner Production, vol. 18, no. 2, 2008, p.174-184 [7] Pusavec F, Kramar D, et al., Transitioning to sustainable production – part II: evaluation of sustainable machining technologies. Journal of Cleaner Production. In Press, DOI:10.1016/j. jclepro.2010.01.015 [8] Rahman M., Kumar A.S., Salam MU, Experimental evaluation on effect of minimal quantity lubricant in milling. International Journal of Machine Tools & Manufacture, no. 42, 2002, p. 539-547 [9] Weinert K, Inasaki I, et al. Dry machining and minimum quantity lubrication. CIRP Annals– Manufacturing Technology, vol. 53, no. 3, 2004, p. 511-537 [10] Westkämper E, et al. Life Cycle management and assessment: approaches and visions towards sustainable manufacturing. CIRP Annals - Manufacturing Technology, vol. 49, no. 2, p. 501-502

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Determination of Forming - Limit Diagrams Considering Various Models for Steel Sheets Ján Slota (SK) jan.slota@tuke.sk Emil Spišák (SK) emil.spisak@tuke.sk

BIOGRAPHICAL NOTES

doc. Ing. Ján Slota, PhD. (born 1974) is associated professor of Department of Technologies and Materials, Faculty of Mechanical Engineering, Technical University of Košice. He is graduated on Faculty of Mechanical Engineering, TU in Košice, where he received also scientific degree PhD and where he habilitated at the field of mechanical engineering processes and materials. From 2004, he has been head of section of Computer Aided of Production Engineering on the Department. His research works are mainly focused on the area of computer simulations in deep-drawing processes. He is a member of International Deep-Drawing Research Group. He is author of three university textbooks and more than 70 publications in journals and conference proceedings at Slovakia and abroad. He has been worked on several grant projects, research tasks and many projects solved for industry. prof. Ing. Emil Spišák, CSc. (born 1955) is professor of Department of Technologies and Materials, Faculty of Mechanical Engineering, Technical University of Košice. He is head of the Department of Technologies and Materials and Vice-Rector for Development and Construction of the University. He served as Vice-Dean for 4 years and ViceRector for 8 years. He works in the area of evaluating of material properties, material failures, analysis and quantification of production factors influence in production of thin steel sheet stamping parts, modelling and simulation of technological processes, mainly forming processes. He is national secretary and a member of International Deep-Drawing Research Group. He is author of 5 monographs and more than 200 publications in journals and conference proceedings at Slovakia and abroad. His published works were cited 115 times. He has been worked on 60 grant projects, research tasks and 47 projects solved for industry.

KEY WORDS

Forming-Limit Diagrams, Prediction Models, Sheet Metal Forming

ABSTRACT

In this paper a comparative investigation of three mathematical models (Marciniak - Kuczynski model, Swift-Hill model and Sing-Rao model) as well as on an empirical model proposed by the North American Deep Drawing Research Group (NADDRG) has been carried out. The yield criterion proposed by Hill is used for the calculation of

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Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

the limit strains in connection with the Swift’s instability condition for diffuse necking and by using the Marciniak - Kuczynski analysis. The emphasis of this investigation is to consider these different approaches to predicting the FLD. Experimental results has been carried out for low carbon steel sheets of drawing quality as well as rephosphorised, TRIP and micro-alloyed steels. It was compared, which theoretical model showing good correlation with experiment, thus, which model is suitable for materials mentioned above.

INTRODUCTION The concept of forming limit diagrams (FLDs) was introduced by Keeler (1964) and Goodwin (1968) and represents the first safety criterion for deep drawing operations. Marciniak and Kuczynski (M– K) have proposed a mathematical model for the theoretical determination of FLDs that suppose an infinite sheet metal to contain a region of local imperfection where heterogeneous plastic flow develops and localizes. The implementation of different yield criteria in the M–K model has been investigated by several authors [1,2]. Because of the complexity of the experimental determination of the FLD, a number of theoretical calculating models have been set up on the basis of the classical or modified Swift and Hill instability criteria [3,4]. In recent years, the knowledge and principles of damage mechanics, plastic mechanics of porous materials, and microscopic materials science combined with the finite-element method (FEM) have also been introduced into the theoretical predictions of the FLD [5,6,7]. These results have significantly enriched and improved the understanding and application of the FLD. However, there has not been a general model that can be applied for various steel sheets until now and, furthermore, the still-too-complex calculations for predicting the FLD will limit their use in practical applications. This investigation was carried out for a better understanding of the forming behaviour of selected steel sheets by means of the experimental determination and theoretical predication of the FLD.

1 Theoretical FLC Models 1.1 The Marciniak-Kuczynski model One of the most accurate models for predicting the failure strains during biaxial stretching of thin sheets is the M–K model. However, this accuracy

requires a considerable number of arithmetic operations and if the M-K model is used in finite element method codes to guard against the failure strains, leading to a significant increase of the simulation time. The M-K model assumes that the strain localization appears in the region of a material or geometrical inhomogeneity. The initial groove or trough is assumed develop when proportional loading is applied outside the groove. The force equilibrium ensures that the strain level within the groove will grow faster than the strain outside, until eventually a plane strain condition is reached with in the groove [8]. At this point, the material is assumed to lose its capability for carrying additional load, and localized necking occurs. The M-K method has been used widely in predicting forming limits of sheet metals (e.g., [9,10,11]). The model presented in this paper assumes the existence of a geometric non-homogeneity in the form of notch (zone b) perpendicular to the direction of the maximum principal stress v1. The initial thickness of the sheet metal ta0 is greater than the initial thickness in the region which contains an imperfection tb0 (see Fig. 1). The sheet-metal is stretched by the principal stresses v1 and v2.The current value of the inhomogeneity coefficient (Eq. 1) is expressed by the relationship:

f0 = ` tb j ta

(2)

where ta and tb are the current values of the thickness in the regions a and b, respectively.

Fig. 1 Schematic of the M–K model on prediction of FLD For each of the two regions of the sheet following the Levy-Mises equations and Hollomon’s equation, respectively, are valid. The model is completed with two equations the link between regions a and b. Equation (2) express ing the equilibrium of the along the interface of the two regions:

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σ 1a .ta = σ 1b .tb

(2)

Equation (3) expressing the fact that the strains parallel to the notch are equal in both regions

d ε 2 a = d ε 2b

(3)

1.2 The Swift-Hill model Swift and Hill based their analyses on the maximum force principle: the sheet metal fails when the applied force begins to decrease, that is, at failure the force reaches its maximum. When coupled with other assumption upon the deformation process, this principle can lead to an analytic expression for the particular case of proportional loading. It has been proven that a good simulation of the forming limit strains can be given on the basis of the Swift diffuse instability theory and the Hill localized instability theory [12, 13], and where Swift’s and Hill’s theories are used to calculate the forming limit strains on the left according to eq. (4) and (5) and the right side (eq. (6) and (7)), respectively, of the FLD. Assuming that the stress–strain relationship of sheets can be expressed by Hollomon’s equation. According to Swift’s and Hill’s criterion, the formulae calculating the forming-limit strains can be written as follows, with a=v2/v1 for f2 < 0

ε1 =

1 + (1 − α )rm n 1+ α

(4)

for f2 > 0

ε2 =

α − (1 − α )rm n 1+ α

(5)

2r   1 + rm (1 − α )  . 1 − m α + α 2  1+ r   n ε1 =  1 + 4r + 2r 2  (6) 2 m m α +α  (1 + α )(1 + rm ) 1 − 2 (1 + r )   2r   (1 + rm ) α − rm  . 1 − m α + α 2  1+ r   ε2 = n  1 + 4r + 2r 2  (7) 2 m m α +α  (1 + α )(1 + rm ) 1 − 2 (1 + r )  

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1.3 The SING-RAO model According to the original Sing-Rao proposition the forming limit stress curve FLSC could be obtained using the linear regression technique based on the results of calculation using below mentioned scheme taking into account mean plastic anisotropy ratio [14,15]. On the base of flow rule the surface limit strains (eq. (8) and (9)) for different stress (or strain) ratio (eq. 10) could be calculated as:

ε1 = (1 + 2rm )(σ 1 − σ 2 ) + (σ 1 + σ 2 )  λ

(8)

ε 2 =  − (1 + 2rm )(σ 1 − σ 2 ) + (σ 1 + σ 2 )  λ

(9)

where

λ=

εe 2 (1 + rm ) σ e

(10)

1.4 The NADDRG model For simplifying the experimental and theoretical determination of the FLD and utilizing the FLD more easily in the press workshop, the North American Deep Drawing Research Group (NADRG) introduced an empirical equation for predicting the FLD in practise. [16] According to this model, the FLD is composed of two lines through the point f10 in the plane-strain state. The slopes of the lines located on the left and right side of FLD respectively are about 45° and 20°. The equation for calculation the forming limit strain f10 in term of engineering strain can be expressed as:

ε10 =

( 23,3 + 14,13t0 ) n 0, 21

(11)

where t0 is the sheet thickness in mm and n is strain hardening exponent.

2 Experimental Work The materials used in the present investigation are listed in Tab. 1 along with their mechanical properties, thickness and flow curve parameters applied in the theoretical calculations of FLDs. The DX 53D is low carbon deep drawable steel sheet. ZStE 220 P is the rephosphorised drawing quality steel that exhibits a capacity for a significant increase in strength through work hardening during


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

Steel

Thickness [mm]

YS [MPa]

UTS [MPa]

A80 [%]

rm

n

Ag

DX 53D+Z

1,0

232

324

36,7

1,515

0,154

15,0

ZStE 220 P

0,8

234

380

34,2

1,676

0,197

20,4

QStE 340 TM

1,25

386

483

25,6

1,076

0,165

-

TRIP

0,75

444

766

26,3

0,816

0,29

24,0

Tab. 1 Mechanical properties, thickness and flow curve parameters of the materials C

Mn

P

S

Ti

Si

Al

Cr

Ni

Nb

Mo

DX 53D+Z

Steel

0,04

0,2

0,015

0,012

-

0,01

0,03

-

-

-

-

ZStE 220 P

0,06

0,7

0,08

0,03

-

0,03

0,02

-

-

-

-

QStE 340 TM

0,12

1,3

0,025

0,01

0,10

-

0,015

-

-

0,08

0,06

TRIP

0,2

1,68

0,018

0,003

0,009

0,2

1,73

0,055

0,018

0,004

0,008

Tab. 2 Chemical composition of the material studied (mass %) part formation. The QStE 340TM is high-strength low alloy steel (HSLA) for cold-forming, thermomechanically-rolled. The steel with transformation induced plasticity (TRIP) RAK 40/70 have been investigated too. All steel sheets have been hot dip galvanised with 100 g/m2 on both sides. All of the steels are produced industrially. The chemical composition of the different steel is given in Tab. 2. The experiments determining the FLDs for all the sheets studied have been carried out in an Erichsen 145-60 universal materials testing machine with specimens of different width and shape. Specimens were deformed by a rigid punch with hemispherical shape. The limit strains have been determined from a circular grid pattern. The flow curves have been determined by means of the conventional tensile test. In this investigation, all tests were carried out at room temperature.

ing region with higher strain and extremely higher limit strains in the drawing region with higher strain. Fig. 1 also shows the extreme differences among sheets in strain path, which may contribute to differences in forming behavior.

3 Results and Discussion

Comparison between the theoretical and experimental FLDs A comparison among the experimental forminglimit curves for steel sheets of drawing quality, rephosphorised steel, high-strength low alloy steel and TRIP steel is shown in Fig. 2. The limit strains in the plane-strain state and the nearby region for TRIP, ZStE 220 P and QStE 340TM steels are much lower than for DX53D steel, which may be associated with its higher strength and different thicknesses of sheets, respectively. However, TRIP steel shows comparable formability in the stretch-

Fig. 2 The experimental forming-limit diagram of materials studied Figs. 3, 4, 5 and 6 show the comparisons between the theoretical predictions based on the different models mentioned above and the experimental FLDs, for all the steel sheets studied. Generally speaking, there exists no one model that can beused for every material. Because of adequacy examination, the FLDs obtained by predicted mathematical models have been necessary compared with experiment.

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Fig. 3 The theoretical and experimental FLD for DX 53D The simple empirical model developed by NADDRG no gives very good predications of the FLDs for all studied steels which belong to the groups of deep-drawable or high strength steel. For DX 53D this model has lower boundary of the FLDS and for ZStE 220P, QStE 340TM and TRIP steel just upper boundary than those experimental results.

Fig. 5 The theoretical and experimental FLD for QStE 340TM The method proposed by Sing and Rao seems to be in good correlation with experimental results for QStE 340TM. However, for materials such DX 53D, TRIP and ZStE 220P, the predictions by this model have slightly lower and upper boundaries respectively, than experiment.

Fig. 4 The theoretical and experimental FLD for ZStE 220P The predictions by the Hillâ&#x20AC;&#x201C;Swift model based on Hollomonâ&#x20AC;&#x2122;s equation seem to give a lower boundary of the FLDs for DX 53D. The FLD calculated according to method proposed by Hill and Swift seemed to be in good correlation with experimental results only on left-hand side for ZStE 220P and TRIP. The right-hand side is much lower against experiment. This prediction seems to be able for micro-alloyed steel QStE 340TM.

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Fig. 6 The theoretical and experimental FLD for TRIP The worst correlation between calculated and experimental results was obtained in the case of calculation according to Marciniak-Kuczynski method. The predictions by this model do not show a good coincidence with the experimental results.The predicted FLD are much lower than the measured values. Only in case of the ZStE 220P steel and the QStE 340TM steel was a satisfactory agreement


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with the experimental FLDs observed, at greater deformations in biaxial stretching especially. Figs. 3 - 6 shows the major limit strains based on M-K method increase rapidly and monotonically from the plane-strain state up to the equi-biaxial stress state, whereas the major limit strains based on the Hill-Swift method increase somewhat slowly and finally decrease near to equi-biaxial stress state. The major difference between models lies in the applied strain-hardening models for material. It is obvious that the theoretical FLDs differ greatly with the strain-hardening model, and for same model the predicted accuracy varies with different materials. On the other hand, although the flow rule can represent very well the stress-strain relationships in uniaxial tension materials, the theoretical predictions still show large deviations from the experimental FLDs. This implies that an appropriate calculating method depends only on the understanding of the flow behaviour of materials, but also on the assumptions for instability criteria and perhaps on further material properties and experimental factors.

4 Conclusion In this paper a comparative investigation of three mathematical models (Marciniak-Kuczynski model, Hill-Swift model, Sing-Rao model) as well as on an empirical model proposed by the North American Deep Drawing Research Group (NADDRG) and experimental results has been carried out for different steel sheets. None of the models can predict the forming-limit diagram reliably. The FLD0 value is met by the empirical NADDRG model and the modified Swift– Hill model with sufficient accuracy for ferritic steels. The classical Swift–Hill and M-K models deliver too-small FLD0 values. The method proposed by Sing and Rao seems to be in good correlation with experimental results for some steel sheets. The forming-limit diagram is affected by the thickness, the yield and tensile strength, and the strain hardening and plastic anisotropy. In order to understand the influence of the material properties and make effective use of the materials, there is a need for adopting mathematical models for analysis the interacting factors as a whole, with due consideration to the practical manufacturing process constrains. Based on the formability prediction

models, the analytical influence of the basic material properties have been investigated, and have been compared with experimental data.

5 Acknowledgement This paper is the result of the project implementation: Center of research of control of technical, environmental and human risks for permanent development of production and production and products in mechanical engineering (ITMS:26220120060) supported by the Research & Development Operational Programme funded by the ERDF.

6 References [1] Barlat, F., Lian, J. (1989). Plastic behavior and stretchability of sheet metals. Part I. A yield function for orthotropic sheets under plane stress condition. Int. J. Plasticity, vol. 5, pp. 5166 [2] Banabic, D. (1996). Forming limit diagrams predicted by using the New Hill’s criterion. Proceedings of the Numisheet ’96, pp. 240-245 [3] Banabic, D., Dannenmann, E. (2001) Prediction of influence of yield locus on the limit strain in sheet metals. Journal of mat. Porc. Technology, vol. 109, pp. 9-12 [4] Djavanroodi, F., Derogar, A. (2010). Experimental and numerical evaluation of forming limit diagram for Ti6Al4V titanium and Al6061-T6 aluminum alloys sheets. Materials & Design, vol. 31, pp. 4866-4875 [5] Ganjiani, M., Assempour, A. (2007). An improved analytical approach for determination of forming limit diagrams considering the effects of yield functions. Journal of Materials Processing Technology, vol. 182, no. 1-3, pp. 598-607 [6] Ganjiani, M., Assempour, A. (2008). Implementation of a robust algorithm for prediction of forming limit diagrams. Journal of Materials Engineering and Performance, vol. 17, no. 1, pp. 1-6 [7] Korhonen, A.S., Manninen, T. (2008). Forming and fracture limits of austenitic stainless steel sheets. Materials Science and Engineering AStructural Materials Properties Microstructure and Processing, vol. 488, no. 1-2, pp. 157-166 [8] Sowerby, R., Duncan, J.L. (1971). Failure in sheet metal in biaxial tension. Int. J. Mech. Sci.,

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vol. 30, pp. 217-229 [9] Eyckens, P., Van Bael, A., Van Houtte, P. (2009). Marciniak-Kuczynski type modelling of the effect of Through-Thickness Shear on the forming limits of sheet metal. International Journal of Plasticity, vol. 25, no. 12, pp. 2249-2268 [10] Evangelista, S.H., Lirani, J., Al-Qureshi, H.A. (2002). Implementing a modified Marciniakâ&#x20AC;&#x201C; Kuczynski model using the finite element method for the simulation of sheet metal deep drawing. Journal of Materials Processing Technology, vol. 130-131, pp. 135-144 [11] Banabic, D., Comsa, S., Jurco, P., Cosovici, G., Paraianu, L., Julean, D. (2004). FLD theoretical model using a new anisotropic yield criterion. Journal of Materials Processing Technology, vol. 157-158, pp. 23-27 [12] Wang, L., Lee, T.C. (2006). The effect of yield criteria on the forming limit curve prediction and the deep drawing process simulation.International Journal of Machine Tools and Manufacture, vol. 46, no. 9, pp. 988-995. [13] Rees, D.W.A., Power, R.K. (1994). Forming limits in a clad steel. J. Mater. Process. Technol. , vol. 45, pp. 571-575 [14] Sing, W.M., Rao, K.P. (1997). Role of strain-hardening laws in the prediction of forming limit curves. Journal of Materials Processing Technology, vol. 63, no. 1-3, pp. 105-110 [15] FrÄ&#x2026;cz W., Stachowicz F.: Determination of the forming limit diagram by Sing-Rao method, Acta Mechanica Slovaca, 3 (1999), str. 35-40 [16] Levy, S.B.: A comparison of empirical forming limit curves for low carbon steel with theoretical forming limit curves of Ramaekers and Bongaerts, IDDRG WG3, Ungarn, (1996)

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Actuators Placement for Active Damping of Vibration on Two Dimensional Clamped Plate Peter Šolek (SK) peter.solek@stuba.sk Martin Horínek (SK) martin.horinek@stuba.sk

BIOGRAPHICAL NOTES

Peter Šolek, prof. Ing. PhD. he graduated from Slovak Technical University in Bratislava, Instrumentation field of study, Regulation and automation technology. After graduation he became an internal aspirants at Department of Technical Mechanics Faculty of Mechanical Engineering STU and defended his dissertation in 1978. In 1992 he defended his habilitation work and became an Associate Professor in Applied Mechanics. Since 2007, acts as head of the Institute of Applied Mechanics and Mechatronics Engineering at University of Technology in Bratislava. Is a member of trade union committees in the fields of study Mechatronics and Manufacturing machinery and equipment. He is a member of several professional organizations at home and is Chairman of the National Committee for the IFTOMM. He is the author of one monographs and co-author of nine CC publications. As a responsible person and deal with addresses APVT and VEGA projects and working in an international project CEEPUS between EU and U.S. universities. In 2010 he became Professor of Mechatronics. Martin Horínek, Ing. graduated at Slovak Technical University in Bratislava, Faculty of mechanical engineering. Bachelor degree in mechatronics, master degree in applied mechanics. Currently PhD student in field mechatronics.

KEY WORDS

Actuator Placement, Controllability, Norms, Two-Dimensional Flexible System

ABSTRACT

This article deals with the investigation of optimal actuator placement for two dimensional systems. In this article the two dimensional system is represented by a clamped plate. The intention of optimal actuator placement is to place actuators in minimal number of actuators to ensure controllability of the system. In this article is compared placement of force actuators and piezoelectric actuators. The approach proposed in this article is based on the evaluation of the H2 and H∞ norms. The optimal actuator placement satisfies the condition of controllability.

INTRODUCTION For the target of improving the performance control of flexible structures, it is useful to investigate various actuators and sensors location. The first purpose of the investigation is to determine the minimal number of actuators and sensors and to meet requirements of controllability, observability and spillover prevention. Second purpose is that the minimal subset of actuators and sensors has the same controllability and observability properties as the original set. The importance of actuator and sensor placement

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is supported in many investigations and contributions. The articles [1, 2] used the norms H2, H∞ and Hankel singular values for the actuator and sensor placement. The contributions [3, 4] use observability and controllability grammians for the actuator and sensor placement. Next big group of articles use the various formulations of optimization problems [5, 6] for the solution of the actuator and sensor placement the flexible structures. Conrollability and observability A structure is controllable if the applied actuators excite all its structural modes. A structure is observable if the realized sensors detect the motion of all the modes. This information is limited, and answers of mode excitation or detection are in terms yes or no. The alternative approach uses grammians to determine the system properties. Grammians express the controllability and observability properties qualitatively and they are nonnegative matrices. The definitions of the controllability and observability grammians are in the form: Where (A, B, C) is the state-space representation

AT Wo + WoA + C T C = 0

(7)

Norms System norms serve as a measure of intensity of its response to standard excitations, such as unit impulse or white noise of unit standard deviations. The standardized response allows comparing different systems. For flexible structures the H2 norm has an additive property - this property is a root-meansquare sum of the norms of individual modes. All norms of a mode with multiple inputs (outputs) can be decomposed into the rms sum of norms of a mode with a single input (output). When (A, B, C) is a system state-space representation of a linear system and let G(ω) = C(jωI-A)-1 is the transfer function. The H2 norm is formulated in form (8)

G

2 2

=

1 2π

∫ tr (G(ω ) G(ω ))dω *

(8)

−∞

A suitable way to determine the H2 norm is using the formula (9)

t

Wc(t ) = ∫ exp ( Aτ ) BBT exp( AT τ )dτ

(1)

0 t

Wo(t ) = ∫ exp ( AT τ )C T C exp( Aτ )dτ

(2)

0

of a time continuous system. We can express the controllability and observability grammians conveniently from the next differential equations (3) and (4)

 = AWc + WcAT + BBT Wc

(3)

 = AT Wo + WoA + C T C Wo

(4)

The solutions Wc(t) and Wo(t) are time-varying matrices. For a stable system, we obtain the stationary solutions of the above equations by assuming

 = Wo  =0 Wc

(5)

G

2

= tr (C T CWc) = tr ( BBT Wo)

(9)

where Wc a Wo are the controllability and observability grammians. The H∞ norm is formulated as (10)

G

= sup

y (t ) u (t )

2

(10)

2

where y(t) is the system output and u(t) is the system input. Actuator placement Actuators and sensors placement are solved independently and both procedures are similar. Indicate by G the transfer function with all S candidate actuators. The index of placement v2ki that evaluates the k-th actuator at the i-th mode in terms of the H2 norm is defined with respect to all the modes and all admissible actuators (11).

Gki

Now the differential equations (6) and (7) are replaced with the algebraic equations, called Lyapunov equations

σ 2 ki = wki

AWc + WcAT + BBT = 0

where wki ≥ 0 is the weight assigned to the k-th actuator and the i-th mode, n is the number of modes, Gki is the transfer function of the i-th mode and k-th

(6)

G

2

(11)

2

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actuator. The index of placement v∞ki evaluates the k-th actuator at the i-th mode in terms of the H∞ norm. This index is defined for all modes and all admissible actuators (12).

Gki

σ ∞ki = wki

G

(12)

When a force actuator for suppressing an amplitude of vibration is used shown in Fig. 3, then it is needed to be placed perpendicularly to the surface of the plate for damping the motion. Using the above presented H∞ norm placement technique finds the best place for actuators functioning in direction perpendicular to the surface of the plate to control the first, second, third, and fourth own mode and to control simultaneously first four modes.

The matrix of placement gives an insight into the placement properties of each actuator because the index of placement of the k-th actuator is defined as the rms sum of the k-th column. In case of the H2 norm, it is the rms sum of the k-th sensor indices over all modes (13).

σ sk =

n

∑σ i =1

2 ik

(13)

And in the case of H∞ norm it is (14).

σ sk = max(σ ik )

(14)

i

1 Example Using H∞ and H2 norms for determining optimal actuator placement is presented in the following example dealing with a clamped plane plate which is shown in Fig. 1. Calculation of natural frequencies and modes of the plate was done using finite element methods in program Ansys. Analyzed model of plate has six degrees of freedom in each node: displacements in directions x, y, z and rotations around these directions. The length of the plate is 50 cm, width is 40 cm and its thickness is 2,5 mm.

Fig. 2 Eigenmodes of the clamped plate presentation. a) first mode, b) second mode, c) third mode, d) fourth mode

Fig. 3 Applying force on the structure Fig. 1 Scheme of the clamped plate

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first four modes. Using v2,1234i we obtain indices with two maxima on shorter free edge, and these places are the most suitable for the actuator placement, shown in Fig. 5b).

Fig. 4 Actuator placement H∞ / H2 indices as a function of actuator location. a) for the first four modes of norm H∞, b) for the first four modes of norm H2

Fig. 4 Actuator placement indices as a function of actuator locations: a) for the first mode, b) for the second mode, c) for the third mode, d) for the fourth mode

We obtain H∞ norm Gki∞ for the kth mode (k = 1, 2, 3, 4) and ith actuator location. From these norms we obtain the actuator placement indices for each mode from (12), using weight such that maxi (v∞ki) = 1. The plots of v∞ki are shown in Fig. 4. The plot of the actuator placement indices for the first mode in Fig. 4a) shows the maximum in the middle of the shorter free edge, and that indicates that an actuator shall be placed at that place. The same situation appears in the third mode, although the first and third modes are different which is shown in Fig. 4c). In Fig. 4b) and 4d) indices for second mode and fourth mode reach their maximal values on two free corners of the plate. Next, we determine the indices for actuator placing for controlling first four modes according to (14) v∞1234i = max(v∞1i, v∞2i, v∞3i, v∞4i), we obtain three maxima on free edge of the plate, which is shown in Fig. 5 a). For determining the best actuator placement, the H2 norm vki2 for the kth mode (k = 1, 2, 3, 4) and ith actuator location was used for solving this example as well. From these norms and using (11) we obtain indices for each individual mode and from the equation (13) we determine the indices for the

Also piezoelectric actuators are suitable for using in active vibration suppression. This kind of actuator is shown in Fig. 6. Such a piezoelectric actuator acts against deformation on an outer layer of the structure during vibration.

Fig. 6 Applying piezoelectric actuator on the structure

In Fig. 7 there are shown maximal strain during first four single own modes of the plate clamped on one edge. These maximal strains are indices for placing actuators for decreasing a strain during vibration. As we can see actuator placement indices are maximal in the clamped edge but for every mode in a different place. For the first mode which is shown in Fig. 7 a) the maximal index for actuator placement is in the middle of a clamped edge. In Fig. 7 b), c), d) is shown that indices for actuator placement for second, third, and fourth mode are approximately on the same places on the clamped edge.

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Fig. 7 Actuator placement indices as a function of actuator locations: a) for the first mode, b) for the second mode, c) for the third mode, d) for the fourth mode

H∞ norm for first four modes according to v∞1234i = max(v∞1i, v∞2i, v∞3i, v∞4i) shows in Fig. 8a) three places are on clamped edge for piezoelectric actuator placing. For the H2 norm using v2,1234i there are indices with two maxima on a clamped edge, so these places are the most suitable for the actuator placement which is shown in Fig. 8b).

tric actuators there are different location for optimal actuators placement in this boundary condition. For clamped plate, actuators shall be placed on the clamped edge because clamped boundary condition caused maximal strain of outer layer of the plate just on that edge. Evaluated actuator placement according to norm H∞ when piezoelectric actuators are used there are three places for actuating and for using norm H2 there are two places.

3 Acknowledgement Authors acknowledge the support by the Slovak Grant Agency VEGA -1/4128/07.

4 References

Fig. 8 Actuator placement H∞ / H2 indices as a function of actuator location. a) for the first four modes of norm H∞, b) for the first four modes of norm H2

2 Conclusion When force actuators for decreasing amplitude of vibration are placed according to indices of the norm H∞ for the first four modes, then there are three actuators on the plate on the free edge. In case of actuator placement according to indices of the norm H2 for the first four modes then we have only two actuators on the free corner. For piezoelec-

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[1] Gawronski W. K.: Advanced Structural Dynamics and Active Control of structures. Springer Verlag, New York, 2004 [2] Liu, Wei, Hou, Zhokun, Demetrion, Michael A.: A computationa scheme for the optimal sensor/actuator placement of flexible structures using spatial H2 measures. Mechanical Systems and Signal processing. Volume 20,4, 2006, pp. 881-895 [3] Hiramot K., Doki H., Obinata G: Optimal sensor/actuator placement for active vibration control. Journal of Sound and Vibrations. Volume 229,5,2000, pp. 1057-1075 [4] DeLorenzo M.L.: Sensor and actuator selsction for large space structure control. Journal of Guidance, Control and Dynamics. Vol.13, 1990, pp. 249-257 [5] Kim Y., Junkins J. L.: Measure of control-


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

lability for actuator placement. Journal of Guidance,Control and Dynamics. Vol. 14, 1991, pp. 895-902 [6] Pulthasthan, Suwit, Pota, Hemanshu R.: Oprimal actuator-sensor placement for acoustic cavity. Poceedings of the IEEE Conference on Decision and Control, CDC, 2006, pp. 16841689

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Increasing of Power Output of Racing Motorcycle Engine using of Exhaust System Optimisation Peter Bigoš (SK) peter.bigos@tuke.sk Michal Puškár (SK) michal.puskar@tuke.sk

BIOGRAPHICAL NOTES

Peter Bigoš, prof. Ing. CSc. Is a university professor nominated in the branch of science “Transport and Handling Engineering”. He is a head of the Department of Machine Design, Transport and Logistics at the Faculty of Mechanical Engineering, Technical University of Košice. He graduated at the Faculty of Mechanical Engineering of the former Technical College in Košice (1973). Dissertation thesis he defended in 1980 and in 1983 he was designated as a docent (associate professor). In 1991 he defended his inaugural dissertation at the Technical University of Košice. In the framework of his study stages he visited TU Miskolc, VH Dresden (1981), Polytechnika Rzeszowska (1983), Ruhr Universität Bochum (1989), Imperial College London (1993), TU Budapest (1997). He is a vice-chairman of the “Common professional commission for PhD.-study” in the branch of study “Transport Machines and Machinery” and he is a member of professional commission in the branch “Forensic Engineering”, too. He is also member of several advisory boards of domestic and foreign professional journals, as well as he is a guarantor of international and domestic conferences about transport machines and logistics. Michal Puškár, Ing. PhD. Is a researcher at the Department of Machine Design, Transport and Logistics at the Faculty of Mechanical Engineering, Technical University of Košice. He graduated at the mentioned Department in 2005 and the PhD.-degree received in 2008 with theme of his dissertation thesis: Rising of Power Parameters of Single-Track Transport Means. His current fields of research interest are single-track transport means, piston combustion engines and increasing of their power output and reliability.

KEY WORDS

Temperature of Exhaust System, Engine Output Performance

ABSTRACT

An exhaust gas system of a two-stroke piston combustion engine has a significant impact on its maximal power output and speed characteristics. In the first part of this paper there is described an impact of the exhaust gas pipeline system on the output speed characteristics. In the second part is analysed a relation between temperature of exhaust gases and speed characteristics, as well as there is determined an optimal temperature for achievement of the best output characteristics. Results presented in this paper enable to optimise curve of the speed characteristics for application in various kinds of single-track vehicles.

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INTRODUCTION AND AIMS An exhaust system is the important supplement of the all engines. It has got the determining influence on engine outgoing parameters for the engines with two-stroke operating cycle. Gas flow in an exhaust system is controlled by means of the difficult principles of non-stationary convection with very difficult calculation. Although the existing special software reached the certain voluminous results, the main merits of work are still in the verification of calculated values on a testing engine. In practice, in most motorcycle firms which are the leaders for development, there are designed several modifications of exhaust systems according to generally known rules. These modified systems are tested and consequently improved with output brake engine tests. One exhaust system is suitable theoretically only for one value of engine speed. It is rather small speed range in practice. The final modification of exhaust system is accommodated to the most using speed values considering the operation possibility in its other modes. In a cylinder on a piston top edge there is an impulse created by means of the opening of exhaust port. It causes an overpressure wave which is spreading into an exhaust manifold in existing environment with sound speed. In an exhaust manifold there is the sound speed much higher than in the open air. Exhaust manifold gases are step by step exposed the pressure wave influence. In consequence of this fact the gases begin to move outwards from an engine. But there is a reflection back of pressure wave from the opposite cone (Fig.1) what causes the gas oscillation following a longitudinal axle of an exhaust stroke. The aim of the correct dimensioned exhaust system is to improve exhaust of gases from a cylinder and this way to improve the scavenging process. During scavenging of working space with overflowing streams there is the certain mixing of combustion products and fresh fuel-air mixture. The part of fresh fuel-air mixture leaks out into an exhaust port. A fuel-air mixture and combustion products mixing continues there. Close by an engine the gas mixture contains rather few combustion products [3]. That is why there is the effort dimensionally to dispose the exhaust system so that the back movement occurs in the final phase. This back movement comes into existence by reason of the oscillation and again there is the return of off-take gases into the cylinder working space [2].

Fig. 1 Parts of Exhaust System: 1-exhaust pipe, 2- expansion cone, 3-rezonator, 4- opposite cone, 5- fishtail

The fuel-air mixture, which contains lower percentage of combustion products, can be used at combustion. In the Fig.1 there is the design of exhaust system with two-stroke engine in the section [4]. The aim of this article was established in consequence of the described theoretical knowledge about combustion products oscillation in an exhaust system: “to increase the output of two-stroke combustion engine by means of exhaust system optimization with keeping its main technical parameters (a diameter of diffuser in carburator, a shape of ignition curve, an origin mould of engine bloc and a compression ratio)” The following steps are connected to this main aim: analysis of exhaust system length influence on a maximum engine output and a range of exploitable engine speed, analysis of combustion product temperature influence in an exhaust system on a maximum engine output and its position in engine speed range.

1 Experimental Models and Devices That is very difficult to develop theoretically the individual components and then to demonstrate the components influence on the output parameters and torque of two-stroke petrol engine. Although there is software for modelling of processes which are operating inside a cylinder and an exhaust system during the combustion, the real results are performed seriously. That is why the experiment was used to achieve the main aim. It is necessary to choose the experimental model for experimental measurements. The development was realised with this experimental model. Further it is a need to develop the measurement devices (to provide feed back, to give information about a real output proposition for concrete change in an exhaust system). 1.1 Experimental Models The motorcycle Aprilia RS 125 was used as the first experimental model. This single-track vehicle is equipped with the two-stroke engine ROTAX 122

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(Fig.2). In Tab.1 there are the technical parameters of serial version for this engine (specified by producer). Output parameters of our engine ROTAX 122 are higher because we used some racing parts (cylinder, head of cylinder and other parts). But these parts doesn’t have an influence on results of this experiment.

mum output is higher. 1.2 Experimental Devices Two testing and measuring devices were developed for a need of experimental measurements.

Fig. 3 Output (Engine) Brake

Fig. 2 Engine ROTAX 122 Type

a single-cylinder, a two-stroke engine, liquid cooled, membrane filled, an electrical-controlled exhaust power valve

Capacity

124,8 cm3

Bore x Stroke

54 x 54,5 mm

Compression ration

12,5 ± 0,5:1

Max. output

21,8 kW (29,3 HP) – 11 000 rpm

Max. torque

19,1 Nm (1,95 kpm) – 10 000 rpm

Carburator

Dell‘Orto PHBH 28 BD

Tab. 1 Technical Parameters of Engine ROTAX

The motorcycle Honda RS 125R was used as the second experimental model. The second singletrack vehicle is equipped with the engine Honda 125. The principle of filling and scavenging of this engine is similar as that is for the engine ROTAX 122. The technical parameters of serial version of this motorcycle are also similar. Only the diameter of carburator diffuser (39 mm) in the shape of an ignition curve is different and that is why a maxi-

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engine brake

motorcycle sensor balance-wheel convertor PC+ software output and torque Fig. 4 Block Diagram of Engine Brake

Output Engine Brake That is a starting dynamic brake (Fig.3). Its advantage is a possibility to obtain an output–moment characteristic during several seconds. A measurement is performed in place that is why a testing ring is not needed. In Fig. 4 there is the block diagram for data measurement, data operating and data evaluating. The principle consists in an accelerating of constant mass (balance-wheel) which has got a constant moment of inertia. The sensor, which is set on the brake frame, scans every revolution of the balance-wheel and time when the revolution is done. The program determines an average of times from the certain number of revolutions. The time-lag between individual averages is pro-


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portional to an output increment. The operating period of one measurement is relative short (circa several seconds). After what the measurement is finished, the software calculates the functional relation among engine output, torque and engine revolutions (Fig. 6). Engine Watch and Control System â&#x20AC;&#x201C; EWaC That is a data-recording system, i.e. a device which scans and stores information during a motorcycle ride (in real conditions, in real loading). This device makes possible to diagnose parameters of a twostroke combustion engine: an output, a torque and their behaviours, a temperature of exhaust system and its behaviour, detonating strokes and their number per time unit and other characteristics. A number and a kind of scanned parameters are related to the types and a number of sensors which are installed on the two-stroke. The block diagram for data measurement, operating and evaluation is similar as output engine brake is but there is a difference of its output. The engine activity record in dependence on time is the result of this system.

Fig. 5 Engine Watch and Control System

The principle of EWaC system is in the measurement of the engine instantaneous speed, an instantaneous temperature of exhaust system and scanning of active speed gear or further parameters. The system does a functional record of engine activity on the base of scanned and entered data (a wheel circumference, gear ratios of individual speed gears, a curve of air resistance and a motorcycle weight). This record is stored in the memory of EWaC system. After finishing of the measurement, it is possible to copy the record by mean of parallel port into PC (Fig. 5). On PC display (Fig.10) there is the record of engine activity in

dependence on a time axis graphically presented (by means of the software which is a component of EWaC system). Every point of the record covers an instantaneous speed, detonating strokes, a temperature of exhaust system and an output at a crank shaft end [5, 6].

2 Experimental Results 2.1 Analysis of Exhaust System Length Influence on Output Characteristic The performed measurements are intent on the analysis of an exhaust system length influence with an output characteristic in consideration of the defined aim. The motorcycle Aprilia RS 125 was used as an experimental model. Aprilia RS 125 is equipped with the engine ROTAX 122 (Fig. 2). A standard exhaust system, used in the motorcycle Aprilia RS 125, was applied for the first measurement APR1. The second measurement (APR2) was performed with the same exhaust system which had the 5-mm-trimmed exhaust pipe (Fig.1). For the realisation of APR3 measurement there was the exhaust system again shortened. The system had the 10-mm-trimmed exhaust pipe. The measurement device was used the output engine brake (Fig. 3). In Fig. 6, 7, 8 there are illustrated graphically the measured dependences of an output and a torque on engine speed with using of various exhaust system variants. An upper curve represents the dependence an output on revolutions; a bottom curve represents the behaviour of torque. In Fig. 9 there is the comparison of these measurements. The range of exploitable speed, i.e. revolutions in which there is constantly kept the high value of instantaneous output (over 22,4 kW, i.e. 30 HP) and the torque (over 19,6 Nm, i.e. 2 kpm.), is the most important parameter in term of the practical application. In Tab.2 there are the measurement results and the individual ranges of exploitable engine speed displayed. Axis: x - axis revolutions per minute, y - axis (left) output [HP], i.e. x0,7457[kW], z - axis (right) torque [kpm], i.e. x9,81[Nm], This system operates only with HP and kpm. Upper legend in the graphs: MOTOR - engine, VYFUK exhaust port, KARB. - carburettor, ZAPAL. - ignition, Q.S.K. - capacity of combustion space, STRB. - distance between the piston and head, TLAK - pressure, TEPL - temperature, VLHK. - humidity, BENZ. -

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petrol, Pmax = 34.2/11318 rpm, Mkmax = 2.22/10723 rpm

Fig. 9 Comparison of Output Behaviours with Using of All Three Exhaust Systems Speed range with the output over 22,4 kW (30 HP) n [rpm]

Speed range with the torque over 19,6 Nm (2 kpm) n [rpm]

Standard exhaust system

1200

2000

5-mm-trimmed standard exhaust system

1250

2000

10-mm-trimmed standard exhaust system

1500

2000

Fig. 6 Output and Torque Behaviour with Using of Standard Exhaust System (APR1)

Tab. 2 Measurement Results

Fig. 7 Output and Torque Behaviour with Using of 5-mmtrimmed Exhaust System (APR2)

2.2 Analysis of Combustion Products Temperature Influence in Exhaust System for Output Characteristic When the exhaust system length is shortened the maximum output and the maximum torque are moved into higher operating speed of the twostroke combustion engine. That is valid at a constant temperature and a constant pressure . And similarly the sonic wave rate of spread depends on a pressure and a temperature (1) according to the undulatory theory [1,2]. C = KĂ&#x2014;

Fig. 7 Output and Torque Behaviour with Using of 5-mmtrimmed Exhaust System (APR2)

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R Ă&#x2014;T M

(1)

where: C sonic waves rate of spread; K ratio of specific heats; R gas constant; T temperature; M molar mass A sonic wave rate of spread increases with an accumulative temperature in the exhaust system (1). A maximum and minimum temperature exists theoretically for every exhaust system, defined shape


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and dimensions. The output and torque behaviours increase the most effectively in this thermal interval because the scavenging of two-stroke engine cylinder is optimized by means of the exhaust system. With regard to above-mentioned assumption, the experimental measurements were performed on the base of this prediction and these measurements were intent on the explanation of combustion products temperature in an exhaust system for an output characteristic of two-stroke combustion engine. The measuring device was the Engine Watch and Control System (EWaC system) (Fig. 5). The motorcycle Honda RS 125R was used as an experimental model. The aim of measurements was defined for the optimal operating thermal interval to achieve a maximum output for used exhaust system. Three thermal states were used for the measurement in the exhaust system: 1. Thermal interval from 440 to 540°C (Fig. 10) 2. Thermal interval from 520 to 620°C (Fig. 11) 3. Thermal interval from 600 to 720°C (Fig. 12) The temperature values were measured at points where the temperature of exhaust system reaches the maximum, i.e. in the area of exhaust pipe, approximately 150 mm from the upper edge of exhaust port (Fig.1). In the outputs from EWaC system there are displayed the record of engine activity in dependence on time. That is illustrated by means of an upper curve. The concrete section, delimited with both sides, is selected from this curve. In this section there are performed the output analysis (left smaller window) and the temperature analysis of combustion products in an exhaust system (the curve in the middle of the picture). This system operates only with HP and Nm.

Fig. 11 Activity Record and Output Behaviour of TwoStroke Engine in 2nd Thermal State

Fig. 12 Activity Record and Output Behaviour of TwoStroke Engine in 3rd Thermal State

An sonic waves rate of spread increases with accumulative temperature (1). In the exhaust system a back wave returns quicker and so the back scavenging process of a cylinder is accelerated. Theoretically, an exhaust system is shortened. An exhaust system temperature hast to rise with the increasing revolutions of optimal adjusted engine therefore the exhaust system is theoretically shorter at higher speed and theoretically longer (with lower temperature) at lower engine speed. The maximum output and the range of exploitable speed, i.e. revolutions with high value of instantaneous output is constantly kept (over 22,4 kW, i.e. 30 HP), are important parameters for the practical use. In Tab. 3 there are the measurement results, the maximum outputs and the ranges of exploitable speed in the individual thermal intervals.

Fig. 10 Activity Record and Output Behaviour of TwoStroke Engine in 1st Thermal State

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Maximum output P [kW (HP)] / n [rpm]

Range of exploitable speed n [rpm]

1. Thermal interval: from 440 to 540°C

31,3 (42) / 13000

2700

2. Thermal interval: from 520 to 620°C

32,1 (43) / 12000

3000

3. Thermal interval: from 600 to 720°C

26,1 (35) / 12500

1100

Tab. 3 Measurement Results

3 Conclusions According to the measurement results analysis in last section the shortening of exhaust system length in the area of exhaust pipe induces the transfer of a maximum output and a maximum torque to the higher operating speed of twostroke combustion engine. Simultaneously the range of operating speed (i.e. revolutions, in which the engine reaches the constant high output, over 22,4 kW, i.e. 30 HP) is wider. The next contribution is the more fluent increasing of an output and a torque what provides better steering control. This knowledge makes possible the variability of output curve according to the concrete necessity of given single-track vehicle. According to the measurement results analysis, the <520; 620°C> is the optimal interval of operating temperatures in an exhaust system for this twostroke combustion engine. The engine reaches the perfect output 32,1kW (43 HP) at 12 000 rpm and the range of exploitable speed is 3000 rpm. However, the conditions are not so optimal in this interval of limited values 520°C and 620°C. The highest output is reached if the temperature converges in an exhaust system to the mean value of interval, i.e. 570°C. The temperature in an exhaust system increased with an output what is characteristic for an optimal adjustment. In thermal interval <440; 540°C> there was the maximum engine output lower and the range of exploitable speed decreased as well. The exhaust system was overcooled thus theoretically shorter. That is valid predominately for the temperature 440°C. The exhaust manifold is theoretically shortened toward an upper limit of interval and the en-

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gine characteristics are improved significantly. In thermal interval <600; 720°C> there was the maximum engine output the lowest and there was the range of exploitable speed practically unavailable. That is valid predominately for the temperature 720°C. In lower limit of interval 600°C there are good output characteristics. The output parameters make significantly worse with the increasing temperature. The system is overheated and theoretically the exhaust manifold is excessively shortened. In the exhaust manifold the low temperature means that there is an overrich mixture (fuel redundancy) and it follows an imperfect burning. In the exhaust manifold the high temperature means that there is a weak mixture, it smoulders out in the exhaust manifold, the combustion process takes longer time (fuel lack). In the exhaust manifold the optimal temperature means that the composition of mixture is optimal and heat is changed into mechanical energy with the high efficiency. It follows that a temperature in an exhaust system has got a cardinal influence on an engine output characteristic. That is why it is necessary to ensure its optimal interval. It will be important for this thermal interval where the temperature increases proportionately with an operating engine speed and an engine load. It causes theoretically the lengthening (for lower operating engine speed) and theoretically the shortening (for higher operating engine speed) of an exhaust system. This effect provides a higher output in the whole regime of revolutions and decreases a production of emission because there is more perfect combustion here. Now, the highest efficiency of two-stroke combustion engine will be provided.

4 Acknowledgement At the present time the problem of increasing for output parameters of combustion engine is solved in the framework project VEGA 1/0356/11 Innovative processes in construction of driving units applied in transport means, machines and optimisation of material flows and logistics in order to save energy and to increase reliability with regard to application purposes in the practice.

5 References [1] BLAIR, G. P.: Further Developments in Scav-


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Journal published by Faculty of Mechanical Engineering - Technical University of Košice

[2] [3]

[4] [5] [6]

enging Analysis for Two-Cycle Engines. SAE 800038,1980 KOŽOUŠEK, J.: Teorie spalovacích motorů, SNTL/ALFA, Praha, 1971 (“Theory of Combustion Engines”) MURÁNSKY, J., BADIDA, M.: Enviromental Compatibility of Mechanical Engineering Products (MEP-s), Acta Mechanica Slovaca, 1/2010, str.72-75, ISSN 1335-2393 PLOHBERGER, D., MIKULIC, L. A.,LANDFAHRER, K.: Development of a Fuel Injected Two-Stroke Gasoline Engine, SAE 880170,1988 SINAY, J., HOEBORN, G., MAJER, I.: Risks in Mechatronical Systems, Acta Mechanica Slovaca, 1/2009, str.58-63, ISSN 1335-2393 ŽIVČÁK, J., KAŤUCH, P., HUDÁK, R.: New Applications of Industrial Computed Tomography in Biomedical Engineering, Acta Mechanica Slovaca, 1/2009, str.50-57, ISSN 1335-2393

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The Boundary States Investigation of the Proportional Loaded Materials Using the Multiaxial Strength Criteria Jan Fuxa (CZ) jan.fuxa@vsb.cz František Fojtík (CZ) frantisek.fojtik@vsb.cz

BIOGRAPHICAL NOTES

prof. Ing. Jan Fuxa, CSc. (born 1947) is employed on 60% part-time as research-pedagogical senior lecturer on the department of Mechanics of Materials at VŠB – TU Ostrava, which has headed until retirement. After the graduation in 1970 on Faculty of Mechanical Engineering VŠB-TU Ostrava professor Fuxa worked as an engineer and computational engineer in ŽĎAS (Machine works and Foundries in Žďár nad Sázavou), in VÚHŽ (Research institute of iron metallurgy in Dobrá near Frýdek-Místek), where has according to his projects and patents built laboratory of plasticity. Since 1986 he works on VŠB-TU Ostrava, where has been in 1991 habilitated as docent with research work “Stress state of conveyor belt cylinders”. In 2001 he has been appointed as professor. Professor Fuxa had participated on establishment of study course “Applied mechanics” for which has instituted two subjects – Theory of plasticity and Creep and thermal loading. He has also actively participated on building of cathedral laboratories, especially designs of test devices and methodics of material testing by multi-axial static and fatigue loading. Professor Fuxa has been the head of Academic senate of Faculty of Mechanical Engineering VŠB-TU Ostrava over two innings. After retirement he actively applies oneself to fine art, especially graphics, photo-graphics and oil painting. Additional informations are mentioned on page 152 in encyclopedia “Who I who – personalities of Czech present – 5000 biographies”, 5. publication, 2005, Micheal Třeštík – editorial, ISBN 80-902586-9-7. Ing. František Fojtík, Ph.D (born 1978) is a Deputy Head on the department of Mechanics of Materials at VŠB – TU Ostrava, Faculty of Mechanical Engineering. Ing. Fojtík graduated at VŠB – TU Ostrava, Faculty of Mechanical Engineering in 2002, in the branch of applied mechanics. Afterwards, he started to study a Ph.D. course in branch of applied mechanics and graduated in 2007. At the same time, he has worked as research and scientific staff member at VŠB – TU Ostrava, Faculty of Mechanical Engineering, department of Mechanics of Materials. Since 2005 he has worked as an assistant professor at VŠB – TU Ostrava, Faculty of Mechanical Engineering, department of Mechanics of Materials. His professional specialization is especially computational prediction and experimental verification of multiaxial fatigue analysis of materials as well as experimental stress analysis in the field of elastic and plastic deformations by means of strain gage method and finite element method. He also specializes on measurements of residual stresses, design of force and torque transducers. He is an author

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and coauthor of many industrial and functional designs and other 40 conference publications and periodical papers.

KEY WORDS

Experiment in Multiaxial Fatigue, Combined Loading, High-Cycle Fatigue, Multiaxial Analysis

ABSTRACT

The contribution describes the experimental results obtained from the combined loading of the specimens in the field of high-cycle fatigue. Those specimens were manufactured from common construction steel 11523. The following experiments were performed: The first set of the specimen was loaded by the alternating torque amplitude. The second set was loaded by the alternating amplitude of the bending moment. The next set was loading by alternating amplitude of the torque and bending moment. This experiment was performed for two loading levels applied in the same phase. The results were evaluated by the conjugated strength criterion and another generally used multiaxial fatigue criteria. The stress-strain analysis of the specimens by FEM was performed to determine parameters (constants) of particular strength criteria.

terial loading. The experimental data obtained at the fatigue limit were judged primarily, i.e. for specimens which were not damaged after 107 cycles. The bellow presented methodology is made for this lifetime. Those experiments were performed under co-phase loading with the testing frequency of 25Hz. The loading amplitude (soft cycle) with sinus shape was controlled in the experiments. The obtained data were used to determine the constants of conjugated strength criterion whose application can be suitable even for prediction of boundary cycle number in the field of lifetime strength.

1 Experimental Material The experiments were performed on the hollow specimens (Fig. 1) manufactured from low carbon steel CSN 411523.1 melting T31052. Those specimens were polished on the outer diameter. The chemical content and basic mechanical properties of this material are summarized in Tab. 1 and Tab. 2.

INTRODUCTION Although the material failure phenomenon in the conditions of multiaxial fatigue is investigated for many years by world-known research institutes, the reliable mathematical description making possible to describe this boundary state was not introduced yet. Hence, it is still necessary to perform expensive prototype verification [1]. The evidence of this fact is number of laboratories especially in aircraft and automotive industry. We bring another build-stone into the mosaic of this interesting technical field in this contribution. Number of fatigue experiments using both the reconstructed and new proposed devices [2], were performed at the Department of Mechanics of Matierial, VSB-TU Ostrava. The aim was to verify the ability of the conjugated strength criterion [3] proposed at our department and to use it for coupling of static and fatigue [4] multiaxial strength criterion. Our contribution describes certain findings obtained from four different types of mechanical ma-

Fig. 1 Testing specimen C%

Mn %

Si %

P%

S%

Cu %

0,18

1,38

0,4

0,018

0,006

0,05

Tab. 1 Chemical properties of the specimen material Ultimate tensile strength [MPa]

Tensile yield stress [MPa]

Elongation at fracture [%]

Reduction of area at fracture [%]

560

400

31,1

74,0

Tab. 2 Mechanical properties of specimen material The following material parameters were experimentally found out for the setting of bellow mentioned fatigue criteria. ď&#x20AC;źtensile modulus: E = 2,06.105 MPa,

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Poisson’s ratio: n = 0,3. Other material parameters determined via experiment for given material and melting which are necessary for setting of given fatigue criteria: fatigue limit in fully reversed torsion: t-1 = 149,1 MPa, fatigue limit in fully reversed plane bending: f-1 = 311 MPa, fatigue limit in repeated bending: f0 = 380 MPa, tensile true fracure strength: vf = 979,2 MPa, torsion true fracure strength: xf = 516,6 MPa.

where coefficients aS and bS are defined as:

aS =

f-1 t-1

f f b S = 6 $ -1 - 3 $ -1 f0 t-1

(4)

where f0 is fatigue limit in repeated bending vH,m mean value of hydrostatic stress during load history, other parameters in the equation are defined as in the case of Crossland Method.

2 Used Multiaxial Fatigue Methods

5 McDiarmid Method

The following generally used fatigue strength criteria were used for the analysis of performed experiments. The results obtained in experimental way for given loading combination on the fatigue limit will be judged by those criteria.

This criterion is widely used. On the base of number of experiments McDiarmid proposed the following shape of the criterion:

3 Crossland Method Crossland published his results in the 50th of previous century. His criterion uses the square root from the second invariant of stress tensor. This invariant is determined from the stress amplitude. Another term added to the equation is the hydrostatic stress calculated from maximal stress values [5].

aC $ ^ J2 ha + bC $ vH,max # f-1

(1)

f-1 f $ Ca + -1 $ Nmax # f-1 tAB 2 $ Su

where Ca is shear stress amplitude on an examined plane, f-1 is fatigue limit in fully reversed axial loading, Nmax is maximum normal stress on the plane examined, Su is tensile strength, tAB is fatigue limit in fully reversed torsion with crack in A or B system. The crack parallel with the surface is typical for the type A. The crack leading inside down from the surface is typical for type B [7].

6 Papadopoulos Method

where coefficients aC and bC are defined as:

aC =

f-1 t-1

bC = c3 -

(2)

f-1 m t-1

other parameters in the equation are: J2 second invariant of stress tensor deviator, f-1 fatigue limit in fully reversed axial loading (in tension, in bending or in rotating bending), vH,max maximum value of hydrostatic stress during load history, t-1 fatigue limit in fully reversed torsion.

4 Sines Method Sines published his results in the same period as Crossland. The formulation of both criteria as similar, they differ in the determination of hydrostatic stress. Sines calculate this stress from mean stress values [6].

aS $ ^ J2 ha + bS $ vH,m # f-1 80 VOLUME 15, No. 1, 2011

(5)

(3)

The Papadopoulos method is based on the Dang Van Criterion. However this method integrates the input variables in all planes. The method can be found in following shape [8].

a p $ ]T 2 ag + b p $ vH,max # f-1

(6)

where:

5 $$ ll22 aa pp = =5 bb pp = 33 $$ ll =3 - 3 f-1 ll = = f-1 tt--11 7 Papuga PCr Method Papuga proposed the criterion on the base of long-term studies of multiaxial fatigue criteria in following shape (7) [9]. According to his research embodies this criterion the most accurate results


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Journal published by Faculty of Mechanical Engineering - Technical University of Košice

for wide range of materials.

aC $ C 2 a + bC $ Na + t-1 $ Na # f-1 f0

tical value as the octaedric normal stress and can be written as:

(7)

It is valid for following ratio of fatigue limits:

l1

l$

AN = ] AO + AC g / 2 + ] AO - AC g / 2 $ (12) cos ^r $ ]log N /log NC gah ... N 1 1, NC 2

l4 - l2 , bC = fn 2

AO is the constant of the static reference strength criterion and can be determined based on the torsion test:

4 , 1 . 155 3

2 8 $ f-1 $ l2 $ ]4 - l2g aC = b 4 $ l 2 l, bC = ]4 + l2g2 4+l

AO = 31 / 2 $ x f

All mentioned criteria according to the results from (1, 3, 5, 6, 7) judge if the component is able to transfer the infinity of loading cycles. To judge of those criteria the fatigue index error DFI is used. It shows the rate of deviation from the ideal equilibrium of the left and right hand sides of mentioned criterion relations [10].

DFI =

LHS]load g - f-1 $ 100 % f-1

(8)

where LHS is the left hand side of the equation. The relation LHS(load) ≤ f-1 has to be fulfilled. If LHS is greater, the component can fail.

8 Conjugates Strength Criterion This criterion was proposed by Fuxa [3]. For the crack initiation in N-th cycle it can be written in following shape:

Sv = AN - BN $ vR

(9)

where Sv marks the stress intensity and is defined as:

Sv = 1 $ 2

(11)

where v1, v2, v3 are the principal stresses. The value AN can be considered as dependent on the cycle number N and is written as:

4 , 1 . 155 3

2 aC = l + 2

vR = ]v1 + v2 + v3g / 3

]v1 - v2g2 + ]v2 - v3g2 G (10) = +]v3 - v1g2

vR is the reference stress value producing the iden-

(13)

AC the stress intensity at the fatigue limit in torsion, NC number of cycles at the fatigue limit, a material constant, BN is the constant equal to:

BN = 3 $ ^ 3 $ x f / v f - 1h

(14)

where vf is the value of true fracure strength in tension and xf is the value of true fracure strength in torsion. The absolute value of mean relative error of the used approximation can be determined as follows:

CHF = ABS]Svi - SvFig / Svi $ 100 0 0

(15)

where Svi are the calculated values of the stress intensities stated in the appropriate table and SvFi are the calculated values according to the Fuxa’s approximation.

9 First Experiment - Alternating Torsion The first set of specimens was loaded by the nominal amplitude of the torque. In the case of first specimen the proper amplitude was set and the number of cycles until failure was registered. In case of other specimens was this amplitude stepwise reduced until the fatigue limit - 107 cycles was reached. The experiments were performed at the frequency 25 Hz. The experimental results are summarized in Tab. 3 where va is the stress amplitude in bending and xa is the stress amplitude in torsion. The result stress was obtained via stress/

81


strain analysis using FEM in the software ANSYS. The limit stress intensity in Nf cycles is depicted in Fig. 2. It is calculated from obtained stress values. Nf [-]

Nr.

va [MPa]

xa [MPa]

Nf [-]

1

376,9

0

89 700

2

352,4

0

196 635

3

336,8

0

2144 30

Nr.

va [MPa]

xa [MPa]

1

0

181,0

92 200

4

324,8

0

1 262 300

2

0

162,7

351 800

5

319,0

0

5 037 000

3

0

156,2

749 450

4

0

151,4

1 944 600

6

311,0

0

11631000

5

0

149,1

11 001 000

Notes

No crack generated

Notes

No crack generated

Tab. 4 Experimental results for alternating bending

Tab. 3 Experimental results for alternating torsion

Fig. 3 S-N curve for alternating bending Fig. 2 S-N curve for alternating torsion

10 Second Experiment - Alternating Bending The second set of specimens was loaded by the nominal amplitude of the bending moment. In the case of first specimen the proper amplitude was set and the number of cycles until failure was registered. In case of other specimens was this amplitude stepwise reduced until the fatigue limit - 107 cycles - was reached. The experiments were performed at the frequency 25 Hz again. The experimental results are summarized in Tab. 4 where va is the stress amplitude in bending and xa is the stress amplitude in torsion. The result stress was obtained via stress/strain analysis using FEM in the software ANSYS. The limit stress intensity leading to the crack initiation in Nf cycles is depicted in Fig. 3. It is calculated from obtained stress values. The data are approximated according to (9).

11 Third Experiment - Alternating Bending and Torsion The third set of specimens was loaded by the nominal amplitude of the bending moment and nominal amplitude of the torque. The loading was

82 VOLUME 15, No. 1, 2011

performed with zero phase shifts. The experiments were performed at the frequency 25 Hz again. The process was the same as in previous cases. The experimental results are summarized in Tab. 5. The limit stress intensity leading to the crack initiation in Nf cycles is depicted in Fig. 4.

12 Fourth Experiment - Alternating Bending and Torsion The fourth set of specimens was loaded by the nominal amplitude of the bending moment and nominal amplitude of the torque. The different ratio of both amplitudes than in previous case was chosen. The process was the same as in previous cases. The experimental results are summarized in Tab. 6. The limit stress intensity leading to the crack initiation in Nf cycles is depicted in Fig. 5. It is determined from measured values which were transformed into the stress state in the critical spot of the specimen.

13 Experimental Results Analysis The obtained experimental results from all described experiments were used for the analysis of above mentioned fatigue stress criterions. The software Pragtic [10] was used for the analysis. It


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of KoĹĄice

contains all mentioned criteria with the exception of Conjugated stress criterion which was proposed at the authorsâ&#x20AC;&#x2122; laboratory. The program in MicroNr.

va [MPa]

xa [MPa]

Nf [-]

1

224,3

150,4

2

203,5

136,5

3

199,6

4

189,7

5 6

soft Office Excel was created for the analysis of this criterion. The results of this study are depicted in Tab. 7. Nr.

va [MPa]

xa [MPa]

Nf [-]

56 100

1

341,7

76,4

33100

290 400

2

321,0

71,7

108600

133,9

821 400

3

318,0

71,1

114900

127,2

1 069 800

4

293,4

65,6

657500

184,2

123,5

4 005 000

5

175,6

117,7

2827300

175,6

117,7

10146000

6

269,5

60,3

11819000

Notes

No crack generated

Notes

No crack generated

Tab. 5 Experimental results for alternating torsion and alternating bending

Tab. 6 Experimental results for alternating torsion and alternating bending

Fig. 4 S-N curve for alternating torsion and alternating bending

Fig. 5 S-N curve for alternating torsion and alternating bending DFI (%), CHF (%)

Nr.

va [MPa]

xa [MPa]

Crossland

Sines

McDiarmid

Papadopouos

Papuga PCr

Fuxa

1

0

149,1

0,0

0,0

0,0

0,0

0,0

0,15

2

311,0

0

0,0

20,5

18,2

0,0

0,0

7,9

3

318,0

71,1

-7,3

4,3

-11,0

-7,3

-4,4

1,1

4

269,5

60,3

-5,8

12,0

6,9

-5,8

5,0

2,7

Tab. 7 Experimental results analysis

14 Conclusion The often used multiaxial fatigue criteria of the authors Crosland [5], Sines [6], McDiarmid [7], Papadopoulos [8], Papuga [9] and the conjugated strength criterion [3] proposed by the authors of this contribution with the aim to couple static and fatigue multiaxial criterion were described. This approach enables the prediction of the fatigue crack initiation even in the field of lifetime strength. The four sets of experiments on hollow, thin-

walled specimens manufactured from the steel 11523.1 according to the CSN were proposed and performed at the laboratory of the Department of mechanics of materials, VSB - TU Ostrava for the verification of the mentioned criteria. The different stress states were generated in the specimens during the loading - torsion, bending, torsion and bending at different ratios of shear and normal stress. The stress states in the critical spot were determined from the measured data using FEM.

83


The good prediction ability of the developed conjugated strength criterion is obvious from the summarizing Tab. 7.

15 Acknowledgement The paper was created under support of GACR, project no: 101/08/P141.

16 References [1] Trebuňa, F., Šimčák, F. (2004). Odolnosť prvkov mechanických sústav. Emilena, Košice [2] Fuxa, J., Fojtík, F., Kubala, R. (2007). Torque machine fit for high cycle fatigue of material testing. Experimental Stress Analysis, Hotel Výhledy [3] Fuxa, J., Kubala, R., Fojtík F. (2006). Idea of Conjugated Strength Criterion. Acta Mechanica Slovaca, vol. 1, pp. 125-130 [4] Fuxa, J., Poruba, Z., Fojtik, F. (2006). Conjugated Stress Criterion. New Method of Damage and Failure Analysis of Structural Parts, Ostrava, pp. 245-258 [5] Crossland, B. (1956). Effect of large hydrostatic pressure on the torsional fatigue strength of an alloy steel. Proc. Int. Conf. on Fatigue of Metals, Institution of Mechanical Engineers, London, pp. 138-149 [6] Sines, G. (1959). Behavior of metals under complex static and alternating stresses. Metal Fatigue. Red. G. Sines a J.L. Waisman, New York, McGraw Hill, pp. 145-469 [7] McDiarmid, D.L. (1991). A general criterion for high cycle multiaxial fatigue failure. Fatigue Fract. Engng. Mater. Struct., vol. 14, no. 4, pp. 429-453 [8] Papadopoulos, I.V., Davoli, P., Gorla C., Filippini M., Bernasconi A. (1997). A comparative study of multiaxial high-cycle fatigue criteria for metals. Int. J. Fatigue, vol. 19, no. 3, pp. 219-235 [9] Papuga, J., Růžička, M. (2008). Two new multiaxial criteria for high cycle fatigue computation. Int. J. Fatigue, vol. 30, no. 1, pp. 58-66 [10] Papuga, J. (2008). Program PragTic in research, engineering practice and competitive environment. Kunovice, Evektor, s.r.o., http://www. pragtic.com/ docu/PragTicA_Intro.pdf

84 VOLUME 15, No. 1, 2011


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

85


Journal Content Focus actuators Placement for active Damping of Vibration on two Dimensional clamped Plate Peter Šolek

15

1 / 2011

Journal published by Faculty of Mechanical Engineering

The Technical University of Košice

m. nUman DUrakBasa & P. herBert osanna

intelligent Design and metrology for Higher Quality, Accuracy and Improving Production Efficiency Peter Bigoš Increasing of Power Output of Racing Motorcycle Engine using of Exhaust System Optimisation Feliks stachowicz Instantaneous Plastic Flow Properties of Thin Brass Sheets Under Uniaxial and Biaxial Testing emil sPišák Joining Car Body Steel Sheets Using the Clinching Method Domnita Florina Fratila Assessment of Cutting Area Temperature to the Face Milling using Several Cooling Methods

86 VOLUME 15, No. 1, 2011

Journal provides a spaces for publishing scientific and professional articles in the field of basic and applied research in branches such as machine elements and mechanisms, transport machines and equipment, production machines and equipment, energetic machines and equipment, mechanical technology and materials, technical systems safety and work safety, automatization and control, applied mechanics, bionics and biomechanics, production quality engineering, judicial engineering, mineralogy and environmentally engineering, mechatronics, material engineering and limiting conditions.


Acta Mechanica Slovaca

Journal published by Faculty of Mechanical Engineering - Technical University of Košice

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Actuators Placement for Active Damping of Vibration on Two Dimensional Clamped Plate

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