Multiple-Criteria Optimization of a Cold Heading Optimization of a Cold Heading Process using Finite Element Analysis and a ... DESIGN PARAMETERS IN COINING ... MAXIMUM PRINCIPAL STRESS

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  • Multiple-Criteria Optimization of a Cold Heading Process using Finite Element Analysis and a

    Taguchi Approach

    by

    Christine EI-Lahham

    Department of Mechanical Engineering McGill University Montreal, Canada

    A Thesis submitted to McGill University in partial fulfillment of the requirements for the degree of

    Master of Engineering

    Under the supervision of: Professor J.A. Nemes

    McGill University

    Christine EI-Lahham October, 2003

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  • Abstract

    The current work aims at modeling a three-stage cold heading process of an industrial

    boIt, and presents a methodology for the optimization of preform die geometries.

    The process is modeled using finite element simulations and potential defects in the

    heading process are analyzed using external and internaI crack criteria. The preform

    geometries are then optimized with respect to external cracking in the blank and forming

    die load. The conventional Taguchi approach is first applied on each criterion separately.

    Three optimal solutions are generated. It is found that sorne parameters have conflicting

    optimal solutions.

    The single criterion approach is therefore extended to multiple-criteria approaches by the

    use of overall evaluation criteria within the Taguchi method. Two methodologies are

    proposed, namely, the additive utility function method and the TOPSIS decision-making

    mode!. It is found that the performances of the two methods are comparable.

    1

  • Rsum

    Le prsent travail vise modliser un processus trois tapes de formage froid d'un

    boulon industriel, et prsente une mthodologie permettant d'optimiser la gomtrie des

    matrices servant la prforme.

    Le processus est modlis numriquement par la mthode de simulation des lments

    finis. Les dfauts potentielles de ce processus de formage sont analyss par des critres

    de fissuration internes et externes. La gomtrie des matrices servant la prforme est

    alors optimise en considrant la fissuration externe des boulons ainsi que la charge

    externe des matrices. L'approche conventionnelle de Taguchi est d'abord applique sur

    chaque critre sparment permettant d'obtenir trois solutions optimales. Les rsultats

    obtenus indiquent que certains paramtres ont des solutions optimales contradictoires.

    L'approche d'un seul critre est donc remplac par des approches critres multiples en

    utilisant 'un critre d'valuation globale' au sein de la mthode de Taguchi. Deux

    mthodologies sont alors proposes, la mthode de fonction utilitaire additive et le

    modle de prise de dcision TOPSIS. On constate que les performances de ces deux

    mthodes sont comparables.

    II

  • Acknowledgements

    1 would like to first thank my supervisor, Professor James A. Nemes, for his guidance and

    encouragement.

    The supporters of this project are also greatly acknowledged: the Natural Sciences and

    Engineering Research Council of Canada (NSERC), Le Fonds Quebecois de Recherche

    sur la Nature et les Technologies (FQRNT) and Ivaco Rolling Mills.

    For his advice and invaluable insight for this work, 1 would like to thank my colleague,

    Abbas S. Milani.

    Finally, 1 thank my family and friends for their love and support.

    III

  • Table of Contents

    Abstract

    Rsum

    A cknowledgements

    Table of contents

    List of Figures

    List of Tables

    1. INTRODUCTION

    1.1 Literature Review 1.1.1 Simulation of the cold heading process 1.1.2 Ductile fracture criteria 1.1.3 Optimization techniques for fonning processes

    1.1.3.1 Single criterion approach 1.1.3.2 Multiple criteria approach

    2. MATHEMATICAL BACKGROUND

    2.1 Constitutive Equation

    2.2 Failure Criteria 2.2.1 External Cracks 2.2.2 InternaI Cracks

    2.2.2.1 Initiation of localization 2.2.2.2 Defonnation adiabatic shear band fonnation (DASB) 2.2.2.3 Transfonnation adiabatic shear band fonnation (TASB)

    2.3 The Taguchi Approach 2.3.1 Design of Experiments 2.3.2 Producing an optimum solution 2.3.3 The predictive equation and verification of additivity 2.3.4 ANOY A analysis on Taguchi results

    2.4 Multiple-Criteria Optimization 2.4.1 The MODM approach

    2.4.1.1 The utility function method 2.4.2 The MADM approach

    2.4.2.1 Solution method (TOP SIS)

    IY

    1

    II

    III

    IV

    VI

    IX

    1

    2 2 6 8 8

    10

    12

    12

    14 14 16 16 17 19

    20 20 21 23 24

    25 27 27 29 30

  • 3. NUMERICAL ANAL YSIS

    3.1 Description of Simulation

    3.2 Assessment of Potential Defects 3.2.1 External Cracking 3.2.2 InternaI Cracking 3.2.3 Analysis of a harder steel

    3.3 Summary

    4. SINGLE CRITERIA OPTIMIZATION

    4.1 Experiments: the L-9 Orthogonal Array

    4.2 Convention al Taguchi Optimization 4.2.1 Factor Plots 4.2.2 Additivity of the method 4.2.3 ANOV A Analysis

    4.3 Discussion

    5. MULTIPLE CRITERIA OPTIMIZATION

    5.1 Selected Methods

    34

    34

    40 40 41 44 47

    48

    50

    55 55 56 57

    57

    61

    62

    5.2 Utility Function Methods 62 5.2.1 Weight 5 as an illustrative example 64 5.2.2 Sensitivity to changes in weights and breakdown point 68 5.2.3 Compatibility with single criterion optimization 68 5.2.4 Extent ofparameter level differentiation 69 5.2.5 Pareto frontiers 70

    5.3 A new OEC approach within the Taguchi method: TOPSIS 71 5.3.1 The TOPSIS method compared to the additive utility function method 73

    5.4 Sensitivity to outlier points 78

    6. CONCLUSIONS AND FUTURE WORK 79

    REFERENCE LIST 82

    v

  • List of Figures

    FIGURE 1-1: SCHEMATIC OF A FOUR-STATION BOLT-MAKlNG MACHINE ............................. 3

    FIGURE 1-2: THREE BASIC RULES FOR UPSET FORGING ....................................................... 4

    FIGURE 1-3: ALLOWABLE LIMITS IN UPSETTING ................................................................. 5

    FIGURE 1-4: DESIGN PARAMETERS IN COINING STAGES ..................................................... 8

    FIGURE 2-1 : TEST SPECIMEN BETWEEN UPPER AND LOWER DIES ...................................... 15

    FIGURE 2-2: ONS ET OF LONGITUDINAL CRACKING ON HEAD SURFACE ............................ 15

    FIGURE 2-3: INTERNAL CRACK RESUL TING FROM SHEAR LOCALIZATION ......................... 17

    FIGURE 2-4: DEFORMATION ADIABATIC SHEAR BAND CRITERION .................................... 18

    FIGURE 2-5: A TRANSFORMATION SHEAR BAND .............................................................. 19

    FIGURE 2-6: A REPRESENTATION OF AN MADM DECISION MA TRIX ............................... 34

    FIGURE 3-1: THE COMMON BOLT THAT IS MODELED ......................................................... 37

    FIGURE 3-2: SCHEMATIC OF A THREE-STAGE COLD HEADING PROCESS ............................. 37

    FIGURE 3-3: COLD HEADING SIMULATION STEPS ............................................................... 37

    FIGURE 3-4: TEMPERATURE CHANGE FOR TWO THICKNESSES WITHIN THE DEFORMED BLANK, DURING UNLOADING STAGES .................................................................................. 38

    FIGURE 3-5: SCHEMATIC OF THE FINITE ELEMENT MODEL. ................................................. 38

    FIGURE 3-6: TENSILE TEST CURVE FITTING FOR DETERMINATION OF JOHNSON-COOK P ARAMETERS ....................................................................................................................... 39

    FIGURE 3-7: EVOLUTION OF PLASTIC STRAIN IN THE BLANK ............................................. 39

    F