Front Cover

Computational Methods and Production Engineering: Research and Development

Copyright

Contents

List of contributors

About the editor

Preface

Chapter 1: Parallel direct solver for finite element modeling of manufacturing processes

1.1. Introduction

1.2. Brief review of standard gauss elimination

1.2.1. Skyline matrix storage

1.2.2. Gauss elimination

1.2.2.1. Factorization of the system matrix and reduction of the right-hand side vector

1.2.2.2. Division of right-hand side vector by system matrix diagonals

1.2.2.3. Backward substitution

1.3. Structure of the parallel direct solver

1.3.1. Parallel region

1.3.2. Main loop

1.3.3. Core loop

1.3.3.1. Reduction of off-diagonal terms, diagonal term, and right-hand side vector (case: jh>2)

1.3.3.2. Reduction of diagonal term and right-hand side vector (case: jh=2)

1.3.3.3. Source code

1.3.4. Utilization as preconditioner of iterative solvers

1.4. Test cases and evaluation parameters

1.4.1. Benchmark test case

1.4.2. Resistance welding test case

1.4.3. Evaluation parameters for parallelization

1.5. Results and discussion

1.5.1. Solution time of different solvers

1.5.2. Accuracy of direct and iterative solvers

1.5.3. Performance of the parallel direct solver

1.5.4. Performance of the parallel direct solver in resistance welding

1.6. Conclusions

Appendix

Acknowledgments

References

Chapter 2: Optimal inspection/actuator placement for robust dimensional compensation in multistage manufacturing processes

2.1. Introduction

2.2. State-space approach for modeling multistage assembly processes

2.2.1. Stage-level model

2.2.2. System-level model

2.3. Feed-forward predictive control

2.4. Optimal inspection/actuator placement for feed-forward control

2.4.1. Step 1: Optimal placement of actuators

2.4.2. Step 2: Optimal placement of inspection stations

2.5. Case study

2.6. Conclusions

Appendix

Derivation of matrices Γi,Ψi, and Ωi

Derivation of the unconstrained optimal control action

Derivation of the constrained optimal control action

Derivation of final state after control implementation

References

Chapter 3: Numerical optimization strategies for springback compensation in sheet metal forming

3.1. Introduction

3.2. Springback compensation strategies

3.3. Modeling strategies

3.3.1. Metamodeling optimization: Response surface methodology

3.3.1.1. First-order model: MLR

3.3.1.2. Second-order model: Polynomial regression (P.2)

3.3.1.3. Universal kriging (U.K.)

3.3.2. Finite element model updating

3.4. Evaluation strategies

3.4.1. Cost function formulation

3.4.2. FEA software

3.4.3. Experimental analysis

3.5. Optimization algorithms

3.5.1. Generalized reduced gradient

3.5.2. Direct search algorithm

3.5.3. Least-squares gradient-based algorithm

3.6. Parameterization strategies

3.7. Case study: U-rail

3.8. Results and discussion

3.8.1. Sensitivity analysis

3.8.2. Modeling strategies and evaluation

3.8.2.1. Metamodels

3.8.2.2. FEMU versus metamodels

3.8.3. Optimization

3.8.4. Parameterization

3.9. Conclusions

Acknowledgments

References

Chapter 4: Finite element modeling of hot rolling: Steady- and unsteady-state analyses

4.1. Introduction

4.1.1. Flat hot rolling

4.1.2. Finite element method

4.1.3. FEA of hot rolling process

4.2. Thermomechanical analysis of hot rolling: An overview

4.3. Work-roll and workpiece interface behavior

4.3.1. Interfacial heat transfer coefficient

4.3.2. Friction coefficient

4.4. Constitutive equation for material model

4.5. Basic steps of FEM

4.6. Different approaches in FEM

4.6.1. Lagrangian approach

4.6.2. Eulerian approach

4.6.3. Arbitrary Lagrangian-Eulerian (ALE) approach

4.7. Solution methods

4.8. Steady- and unsteady-state analyses of hot rolling

4.8.1. Initial geometry

4.8.1.1. Steady-state analysis

4.8.1.2. Unsteady-state analysis

4.8.2. Mesh generation

4.8.2.1. Steady-state analysis

4.8.2.2. Unsteady-state analysis

4.8.3. Mesh update

4.8.4. Boundary conditions

4.8.4.1. Thermal boundary

4.8.4.2. Mechanical boundary

4.8.5. Governing equation

4.8.5.1. Equilibrium equations

4.8.5.2. Constitutive equation

4.8.5.3. Yield function

4.8.6. Conservation laws

4.8.6.1. Lagrangian formulation

4.8.6.2. ALE formulation

4.8.7. Constitutive equation for material model

4.8.8. Finite element formulation

4.8.8.1. Deformation analysis

4.8.8.2. Thermal analysis

4.8.9. Type of solver

4.8.10. Computing environment

4.8.11. Mesh sensitivity study

4.8.12. Temperature distribution

4.8.13. Stress and strain distributions

4.8.14. Rolling load and rolling torque

4.9. Concluding remarks

References

Chapter 5: Numerical modeling methodologies for friction stir welding process

5.1. Introduction to FSW

5.1.1. Lexicon of FSW

5.2. Modeling of FSW: Requirement and complexities

5.3. General steps for modeling a process

5.3.1. Complexity level and analysis type

5.3.2. Geometric modeling and assembly

5.3.3. Material properties and constitutive equation

5.3.3.1. Jonson-Cook material model

5.3.3.2. Sheppard and Wright model

5.3.4. Contact interaction

5.3.4.1. Mechanical interactions

5.3.4.2. Thermal interaction

5.3.5. Boundary conditions

5.3.6. Mesh generation

5.3.7. Simulation control and solver

5.3.7.1. Lagrangian analysis

5.3.7.2. Eulerian analysis

5.3.7.3. Arbitrary Lagrangian-Eulerian analysis

5.3.7.4. Coupled Eulerian-Lagrangian analysis

5.3.8. Capabilities of software

5.4. Modeling of FSW with Lagrangian analysis

5.4.1. Geometric modeling and material model

5.4.2. Mesh generation

5.4.2.1. Mesh refinement study

5.4.2.2. Remeshing technique

5.4.3. Contact interaction

5.4.4. Boundary conditions and assumptions for the model

5.4.5. Governing equation

5.4.6. Solvers and iterative method

5.4.7. Results and discussion

5.4.7.1. Temperature and plastic strain distribution

5.4.7.2. Evolution of force and torque during FSW

5.5. Modeling of FSW with Eulerian analysis

5.5.1. Geometric modeling and boundary condition

5.5.2. Material model

5.5.3. Governing equation

5.5.4. Heat generation

5.5.5. Mesh generation and solver

5.5.6. Results and discussion

5.6. Modeling of FSW with coupled Eulerian-Lagrangian (CEL) analysis

5.6.1. Geometric modeling and material model

5.6.2. Mesh generation

5.6.2.1. Mesh refinement study

5.6.3. Contact interaction

5.6.4. Boundary conditions

5.6.5. Governing equations

5.6.6. Results and discussion

5.7. Comparison of modeling methods

5.8. Conclusion

References

Chapter 6: Modeling of hard machining

6.1. Introduction to hard machining

6.1.1. Hard turning

6.1.2. Hard milling

6.1.3. Other hard machining processes

6.1.4. Phenomena occurring during hard machining processes

6.2. Numerical modeling of hard machining

6.2.1. Thermal models

6.2.2. Thermomechanical models

6.2.3. Thermomechanical models with flow stress incorporating initial hardness

6.2.4. Thermomechanical models with microstructure-related prediction capabilities

6.3. Soft computing and statistical methods modeling of hard machining

6.3.1. Artificial neural networks

6.3.2. Fuzzy logic models

6.3.3. Response surface methodology

6.4. Conclusions

References

Chapter 7: Multiresponse optimization in wire electric discharge machining (WEDM) of HCHCr steel by integrating response ...

7.1. Introduction

7.2. Experimental work

7.3. Response surface methodology

7.4. Results and discussion

7.4.1. Analysis of surface roughness (Ra)

7.4.2. Analysis of material removal rate (MRR)

7.4.3. Analysis of tool wear rate (TWR)

7.4.4. X-ray diffraction analysis

7.4.5. Machined surface topography and EDX analysis

7.5. Differential evolution (DE) optimization

7.5.1. Overview

7.5.2. Development of DE optimization for WEDM characteristics

7.6. Conclusions

References

Index

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