Topology Optimization of Gear shifter Housing and Contact Benchmarks

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Topology Optimization of Gear shifter

Housing and Contact Benchmarks.

Naresh Kalidindi

Mohamad Fardmoshiri

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Topology Optimization of Gear shifter Housing and Contact

Benchmarks.

Naresh Kalidindi

Mohamad Fardmoshiri

This thesis work is performed at Jönköping Institute of Technology within the subject area Product Development and Materials Engineering. The work can also be a part of the master’s degree.

The authors are responsible for the given opinions, conclusions and results. Supervisor: Niclas Strömberg

Credit points: 30 ECTS credits Date: 26/08/2010

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Abstract

1

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Acknowledgement

1

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List of figures

2

Summary

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List of figures

3

List of figures

Figure 01: Geometry, boundary conditions and draw direction. 10

Figure 02: Optimized component . 11

Figure 03: Color contour of element density. 11

Figure 04: Geometry extracted from OptiStruct. 12

Figure 05: Geometry and boundary conditions and draw direction. 13

Figure 06: Manufacturing constraint with no draw direction (left) 14

and with draw direction (right).

Figure 07: Flow chart diagram of optimization process [1]. 16

Figure 08: A system of two linear elastic bodies in unilateral contact [12]. 17

Figure 09: Housing top layer. 21

Figure 10: Housing bottom layer with design (blue) and non-design (red). 22

Figure 11: Housing rigid links (red) surrounding the hole. 22

Figure 12: Constrained at rigid links inside the hole in (x, y and z) in all 23

directions.

Figure 13: Manufacturing constraints (z-axis). 24

Figure 14: Geometry benchmark 1. 25

Figure 17: Housing bottom layer optimized. 27

Figure 18: Optimized bottom layer IGES. 27

Figure 19: Solid layer of component CAD model 28

(two layers one component).

Figure 20: Bottom view of CAD model (two layers one component). 28

Figure 21: Solid layer of component (two layers one component). 29

Figure 22: Stress analysis of optimized component. 29

Figure 23: Bottom view of stress analysis of optimized component. 30

Figure 24: Displacement of optimized component. 30

Figure 25: Benchmark 01 2-D symmetry geometry [12], TOPO4ABQ, 31

symmetry no contact condition, load case:1 (vertically downwards).

Figure 26: Benchmark 01 2-D HyperWorks, no contact condition, 31

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List of figures

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Figure 27: Benchmark 01 2-D TOPO4ABQ, symmetry [12], 32

contact condition, load case: 1 (vertically downwards).

Figure 28: Benchmark 01 2-D HyperWorks, contact condition 32

load case:1 (vertically downwards).

Figure 29: Benchmark 02 2-D TOPO4ABQ [12], no contact condition, 33

load case: 2 (vertically downwards and upwards).

Figure 30: Benchmark 02 2-D HyperWorks, no contact condition, 33

load case: 2 (vertically downwards and upwards)

Figure 31: Benchmark 02 2-D TOPO4ABQ [12], contact condition, 34

Figure 32: Benchmark 02 2-D HyperWorks, contact condition, 34

Figure 23: 2-D TOPO4ABQ [12], contact condition, 35

load case: 1 (vertically downwards).

Figure 34: 2-D HyperWorks, contact condition, 35

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List of tables

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List of Tables

Table 1: Magnesium material properties. 21

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Table of Contents

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Topology Optimization of Gear shifter Housing and Contact

Benchmarks. ... 1

Acknowledgement ... 1

Summary ... 2

Key words ... 2

List of figures ... 3

List of Tables ... 5

1 Introduction ... 8

1.1 BACKGROUND ... 8

1.2 PURPOSE AND AIMS ... 8

1.3 DELIMITS ... 8

1.4 OUTLINE ... 8

2 Theoretical background ... 9

2.1 OPTIMIZATION PROBLEM ... 9

2.1.1 Design variables for topology optimization [13] ... 10

MANUFACTURABILITY FOR TOPOLOGY OPTIMIZATION... 12

2.2.1 Minimum member size control [13] ... 12

2.2.2 Maximum member size control [13] ... 13

2.2.3 Draw direction constraints for topology optimization [13] ... 13

2.3 RESPONSES ... 14

2.3.1 Weighted compliance [13]... 14

2.3.2 Combined compliance index [13] ... 14

2.3.3 Move limit adjustments [13] ... 14

2.4 GRADIENT-BASED OPTIMIZATION METHOD ... 15

2.4.1 Iterative solution [1] ... 15

3 Contact formulation for TOPO4ABQ

[12]

_{... 16}

3.1 CONTACT PROBLEM DEFINITION[12] ... 17

3.2 CONTACT OPTIMIZATION PROBLEM[12] ... 18

3.3 PENALTY CONTACT IN HYPERWORKS[12] ... 19

4 Implementation ... 21

4.1 TOPOLOGY OPTIMIZATION OF GEAR SHIFTER HOUSING: ... 21

4.1.1 Optimization ... 23 4.2 CONTACT BENCHMARKS ... 24 4.2.1 TOPO4ABQ ... 24 4.2.2 OptiStruct... 25 4.2.3 Benchmark problems ... 25

5 Results ... 27

5.1 CONTACT ... 31

6 Conclusions and discussions ... 36

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Table of Contents

7

8 References ... 37

9 Total proccess ... 38

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Introduction

8

1 Introduction

1.1 Background

1.2 Purpose and aims

1.3 Delimits

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Theoretical background 9

2 Theoretical background

2.1 Optimization problem

Subjected to

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Theoretical background

10

2.1.1 Design variables for topology optimization [13]

, p

[N]

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11

Figure 02: Optimized component .

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12

Figure 04: Geometry extracted from OptiStruct.

Manufacturability for topology optimization

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13

2.2.2 Maximum member size control [13]

2.2.3 Draw direction constraints for topology optimization [13]

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14

Figure 06: Manufacturing constraint with no draw direction (left) and with draw direction (right).

2.3 Responses

2.3.1 Weighted compliance [13]

2.3.2 Combined compliance index [13]

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15

2.4 Gradient-based optimization method

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16

Figure 07: Flow chart diagram of optimization process [13].

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17

Figure 08: A system of two linear elastic bodies in unilateral contact [12].

3.1 Contact problem definition

[12]

≥

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3.2 Contact optimization problem

[12]

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Implementation

21

4 Implementation

4.1 Topology optimization of gear shifter housing:

Magnesium mechanical properties

Young’s Modulus (MPa) 45000

Poisson’s Ratio 0.35

Yield Strength (MPa) 140

Density (Tonne/mm3) 1.89E-9

Table 1: Magnesium material properties.

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Implementation

22

Figure 10: Housing bottom layer with design (blue) and non-design (red).

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Implementation

23

Figure 12: Constrained at rigid links inside the hole in (x, y and z) in all translation and rotation.

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Implementation

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Figure 13: Manufacturing constraints (z-Axis).

4.2 Contact benchmarks

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Implementation

25

4.2.2 OptiStruct

4.2.3 Benchmark problems

Steel material properties

Young’s modulus 2.1E5 [N]

Poisson’s ratio 0.3

Table 2: Steel material properties.

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Implementation

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Figure 15: Geometry benchmark 2.

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Results

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5 Results

Figure 17: Housing bottom layer optimized.

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Results

28

Figure 19: Solid layer of component CAD model (two layers one component).

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Results

29

Figure 21: Solid layer of component (two layers one component).

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Results

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Figure 23: Bottom view of stress analysis of optimized component.

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Results

31

5.1 Contact

Figure 25: Benchmark 01

2-D symmetry geometry [12]

TOPO4ABQ elements: 7800 symmetry no contact condition

Figure 26: Benchmark 01 [12]

2-D HyperWorks elements: 15,600 no Contact condition

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Results

32

2-D TOPO4ABQ elements: 7800 symmetry [12]

contact condition

2-D HyperWorks elements: 15,600 contact condition

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Results

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2-D TOPO4ABQ[12] elements: 35560

no contact condition

2-D HyperWorks elements: 34 928 no contact condition

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Results

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2-D TOPO4ABQ[12] elements: 35,560

contact condition

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Results

35

2-D TOPO4ABQ [12] elements: 35,560

contact condition

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Conclusions and discussions

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6 Conclusions and discussions

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References

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8 References

1. L.A. Schmit, Structural design by systematic synthesis, Proc. 2nd ASCE Conf. Electronic Computation (ASCE, New York, 1960) 105-132.

R.L. Fox, Constraint surface normals for structural synthesis techniques, AIAA J. 3 (8) (1965) 1517-1518.

W. Prager and J.E. Taylor, Problems of optimal structural design, J. Appl. Mech. 35 (1968) 102-106.

W. Prager, A note on discretized Michell structures, Comput. Methods Appl. Mech. Engrg. 3 (3) (1974)349-355.

K. Svanverg, Optimal geometry in truss design, in: A.J. Morris, ed., Foundations of Structural Optimization. A Unified Approach (Wiley, New York, 1982) Chapter 14, 513-544.

G.I.N. Rozvany, Optimal Deisgn of Fiexural Systems (Pergamon, Oxford, 1976).

N. OIhoff, Optimal design with respect to structural eigenvalues, Proc. 15th Internat. Congress of Theoretical and Applied Mechanics, Toronto (1890) 133-149.

M.P. Bendsoe and N. Kikuchi, Generating optimal topologies in structural design using a homogenization. method, Comput. Methods Appl. Mech. Engrg. 71 (2) (1988) 197-224.

K.T. Cheng and N. Olhoff, An investigation concerning optimal design of solid elastic plates, Internat. J.Solids and Structures 17 (1981) 305-323. M.P. Bendsoe, Optimal shape design as a material distribution problem, Structural Optimization 1 (4) (1989) 193-202.

G.I.N. Rozvany, Structural Design via Optimality Criteria (Kluwer Academic Publishers, Dordrecht, 1989).

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Attachments

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