OPTIMIZATION PROCESS FOR LIGHTWEIGHT MODULAR AUTOMOTIVE

COMPONENTS

EHSAN SHAHBAZI

A project report submitted in partial fulfilment of the

requirements for the award of the degree of

Master of Engineering (Mechanical)

Faculty of Mechanical Engineering

Universiti Teknologi Malaysia

JUNE 2014

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To my beloved parents and my dear brother and sister, for their endless support and

encouragement.

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ACKNOWLEDGEMENTS

First and foremost, I would like to express heartfelt gratitude to my

supervisor Prof. Dr. Mohd Nasir Tamin, for his patience, advice and constant

support throughout this project. Without his continuous support and patience this

thesis would not have been the same as presented here.

The Last but not the least a warm gratitude and sincere appreciation to my

beloved family and peers for their endless support.

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ABSTRACT

This research is based on a design process flow, which deals with the

improvement of the current way of using computer based topology and shape

optimization techniques. The objective is to integrate Topology and Shape

optimization with the numerical optimization techniques in order to obtain superior

designs. To this purpose an improved design process is introduced to overcome the

limitations of the current trend in design. The effectiveness of the proposed design

process is evaluated through a design problem in which a selected automotive

component is chosen to be optimized for weight and stiffness. It is seen that

following the proposed approach in design can result in better solutions thanks to

the invaluable gradient information that the numerical optimization part of the

design process provides.

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ABSTRAK

Kajian ini adalah berdasarkan aliran proses reka bentuk, yang

memperkatakan tentang kaedah semasa penggunaan topologi berasaskan komputer

dan teknik pengoptimuman bentuk. Objektifnya adalah untuk mengintegrasikan

Topologi dan Bentuk pengoptimuman dengan teknik-teknik pengoptimuman

berangka untuk mendapatkan reka bentuk yang lebih baik. Untuk tujuan ini, satu

proses reka bentuk yang lebih baik diperkenalkan bagi mengatasi keterbatasan dari

trend semasa dalam reka bentuk. Keberkesanan proses reka bentuk yang

dicadangkan itu dinilai melalui satu kajian masalah reka bentuk di mana sebuah

komponen automotif dipilih untuk dioptimumkan bagi mengurangkan berat badan

dan ketegangan. Hasil menunjukkan bahawa kaedah yang dicadangkan memberikan

penyelesaian yang lebih baik kerana hasil maklumat yang tidak ternilai disediakan

oleh pengoptimuman berangka proses reka bentuk.

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TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENTS iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF FIGURES x

LIST OF TABELS xii

1. INTRODUCTION 1

1.1 Introduction 1

1.2 Background of the study 1

1.3 Statement of the problem 3

1.4 Objective 4

1.5 Scopes of the study 4

1.6 Importance of the study 5

1.7 Structure of the thesis 5

2. LITERATURE REVIEW 7

2.1 Introduction 7

2.2 Modularization 7

2.3 Lightweight Materials 9

2.3.1 Advanced and Ultra High Strength Steels (AHSS, UHSS) 11

2.3.2 Aluminum Alloys 13

2.3.3 Polymer Composites 15

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2.3.3.1 Plastic/Steel Hybrid 15

2.3.3.2 Long Fiber Thermoplastic (LFT) 15

2.3.3.3 Stamping Mold 16

2.3.3.4 Injection-Molded Polypropylene Reinforced

by Long Glass Fibers 16

2.3.3.5 High-Strength Plastic Reinforced by Liquid

Crystal Polymers (LCP) 16

2.3.4 Mixed Material Concept 17

2.4 Optimization 17

2.4.1 Mathematical Optimization (Vanderplaats, 1984) 18

2.4.1.1 Minimization of Unconstrained Single Variable

Functions 23

2.4.1.2 Minimization of Constrained Multi Variable

Functions 26

2.5 Structural Optimization 31

2.5.1 Sizing Optimization 32

2.5.2 Shape Optimization 32

2.5.3 Topology Optimization 33

2.5.3.1 SIMP Method: 34

2.5.3.2 Homogenization method 37

2.5.3.3 Checkerboard Pattern 38

2.6 The necessity of this study 39

3. RESEARCH METHODOLOGY 41

3.1 Introduction 41

3.2 Research Methodology and Procedure 41

3.2.1 Design Concept Generation 43

3.2.2 Topology/Shape Optimization 44

3.2.2.1 Appropriate Loading and Boundary Conditions 45

3.2.2.2 Appropriate Objective and Constraint definition for

Topology/Shape Optimization 49

3.2.3 Result interpretation 50

3.2.4 Deriving mathematical models for numerical optimization 51

3.2.5 Complementary Finite Element Analysis 52

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3.2.6 Prototyping 53

3.3 Establishment of the process flow 54

4. RESULTS AND DISCUSSION 55

4.1 Introduction 55

4.2 Component Selection 55

4.3 Conceptual Design of a modular joint 56

4.4 Topology/ Shape Optimization of the Chosen Concept 58

4.4.1 Loading and B.Cs of the problem 58

4.4.2 Defining Objectives and Constraints of the Topology

Optimization 61

4.5 Interpretation of Topology Optimization results 62

4.6 Numerical Optimization 67

4.7 Complementary Finite Element Analysis 68

4.7.1 Stiffness Analysis of the Optimum Design 68

4.7.1.1 Axial Stiffness of the Optimum Design 69

4.7.1.2 Bending Stiffness of the Optimum Design 70

4.7.1.3 Torsional Stiffness of the Optimum Design 71

4.7.2 Durability Analysis of the Optimum Design 72

4.8 Prototyping 72

5. CONCLUSION 73

REFERENCES 75

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LIST OF FIGURES

FIGURE NO. TITLE PAGE

1.1 Conceptual Design of a Modular Chassis (Designer Mr ALI

FAROKHINEJAD, Founded by RUG Flagship Project 00G42) 3

2.1 Strength plotted against density (yield strength for metals and polymers,

compressive strength for ceramics, tear strength for elastomers and tensile

strength for composites) (Ashby, 2005) 10

2.2 Schematic of AHSS steels (shown in color) compared to low strength steels

(dark grey) and traditional HSS (light grey) (Keeler & Kimchi, 2014) 13

2.3 Usable-Feasible Search Direction 22

2.4 Geometric interpretation of Kuhn-Trucker necessary conditions for optimality 23

2.5 Schematic illustration of golden section method 25

2.6 Schematic illustration of the general concepts behind the method of feasible

directions 27

2.7 Effect of the push off factor on search direction 28

2.8 Schematic of imposing bound on the magnitude of search direction 30

2.9 Sizing Optimization 32

2.10 Shape Optimization 32

2.11 Topology Optimization 33

2.12: The effect of penalization factor on the stiffness matrix 35

2.13 The computation process flow for topology optimization using the Method of

Moving Asymptotes (MMA) (Bendsøe & Sigmund, 2003) 37

2.14 Two common composite microstructures used in homogenization method

a) Hole-in-cell and b) Layered microstructure 38

2.15 Checker board pattern commonly encountered in topology optimization 39

3.1 Established design process flow 43

3.2: Conceptual design of the specified tool 44

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3.3 Appropriate Boundary Conditions to isolate individual components 45

3.4 Transferring the Coordinate system to the Center of Area 46

3.5 Separation of the nodal forces into x, y, and z components 46

3.6 Separation of a varying amplitude load into an average constant amplitude

load and corresponding moments 47

3.7 Objects with the same Topology 49

3.8 Deming’s cycle 54

4.1 Selected Component of a Conceptual Design of a Modular Chassis (Designer

Mr. ALI FAROKHINEJAD, Founded by RUG Flagship Project 00G42) 56

4.2 Final conceptual design of a modular joint 57

4.3 Isolating the joint by cutting the neighbouring components 58

4.4 Separation of a varying amplitude load into an average constant amplitude

load and corresponding moments 59

4.5 The internal equivalent loads and moments acting on the cross sections 59

4.6 Final Boundary Conditions for designing the joint 60

4.7 Strength plotted against density (yield strength for metals and polymers,

compressive strength for ceramics, tear strength for elastomers and tensile

strength for composites) (Ashby, 2005) 60

4.8 FE model of the topology optimization problem 62

4.9 Topology optimization results (volume = 10%) and the interpreted conceptual

design 63

4.10 Preliminary FE analysis of the interpreted conceptual design 64

4.11 Topology optimization results (volume = 20%) and the interpreted conceptual

design 64

4.12 Topology optimization results of the new concept 65

4.13 Topology optimization results of the modified concept 65

4.14 Final Conceptual Design of the Modular Joint and the preliminary FEA 66

4.15 Geometry parameterization of the final conceptual design (First Part) 66

4.16 Topology optimization results and the final parameterized conceptual design 67

4.17 Stress distribution under Axial Loading (Axial Stiffness evaluation) 69

4.18 Stress distribution under Bending Loading (Bending Stiffness evaluation) 70

4.19 Stress distribution under Torsional Loading (Torsional Stiffness evaluation) 71

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LIST OF TABELS

TABLE NO. TITLE PAGE

5-1 Overal Mechanical Characteristics of the two Design Conceps 74

CHAPTER 1

1. INTRODUCTION

1.1 Introduction

Optimization technique –having been used successfully in many science and

engineering problems– is a specialized mathematical method which aids scientists in

achieving optimum results more efficiently. Mechanical engineering in general is

one of the fields in which this technique is widely used to achieve optimum designs.

Thanks to this superior technique, mechanical engineers are able to more

scientifically study the problems and achieve noble solutions which are very difficult

or even impossible to get if these techniques are not to be used.

This method has provided engineers with a reliable tool to cut the expenses

and time of design process through achieving the final designs with less experimental

trial and error.

This chapter would provide the interested reader with a background of the

study, statement of the research problem, objectives, scopes, and finally the

importance of the study.

1.2 Background of the study

The automobile industry has recently succeeded in building lighter vehicles

which can be equipped with more energy efficient engines in order to meet the legal

2

requirements in reducing fuel consumption. Considerable reduction in fuel

consumption and CO2 emission is the immediate outcome of such developments. On

the other hand, increasing demand for Electric and Hybrid Vehicles during the last

few years has derived more attention to development of lightweight automotive

structures (SUN Hongtu, et al 2010).

Modularization and common part strategy is another concept which has

gained considerable attention nowadays. It is widely recognized as a cost saving and

production tool in automotive and airline industry. Modularization in product design

was introduced to address the customer’s great tendency towards ordering

personalized cars. Automotive manufacturers also show a clear tendency in

providing their customers with a full product range to respond to changes in demand

and reduce the risk of being threatened by the possible collapse of one market

segment. Although the variety of products is a desired effect, there are some

undesired side effects which the old-fashioned approach of production cannot

address them. Modern modularization concepts, in contrast, suggest building more

complex modules which can be widely used in many different vehicles (Parry &

Graves, 2008).

In order to address both lightness and modularization issues, a conceptual

design of a lightweight modular chassis for an electric car was designed by Ali

Farokhinejad as part of the RUG Flagship Project 00G42 (Figure 1.1). Since the

chassis is intended to be used in an electric car, the lightness of the structure is of

greatest importance which is the main purpose of this project.

In addition to lightness and modularization issues, efficient design of the

structure and automotive components is a key factor in improving the performance of

a vehicle. There are a number of factors which shall be considered in the design of

automotive components. A chassis frame, for example, shall provide rigidity for

accurate handling, mounting points for suspensions, seating for occupants, steering

mechanism, etc. While the required functions are fulfilled, these components should

be light enough to reduce inertia and provide desired performance. These

components should be designed strong enough to resist fatigue loads also.

3

Figure 1.1 Conceptual Design of a Modular Chassis (Designer Mr ALI

FAROKHINEJAD, Founded by RUG Flagship Project 00G42)

Efficient design of the structure and automotive components is best achieved

through optimization techniques. Due to geometry and occasionally material

complexities, numerical and finite element techniques are widely used in the design.

Although mathematical modelling of the optimization problem is usually a great

challenge, it is worth being worked on for the invaluable gradient information it

provides. Since there are some complexities regarding the geometry and material, a

more accurate optimization model is achieved if the derived model is coupled with

the FE solver in case finite element analysis provides more accurate solutions.

In this project, a process flow for optimization of lightweight automotive

components will be established and validated through optimizing a lightweight

modular joint.

1.3 Statement of the problem

In any optimization problem the main challenge is efficiently optimizing the

objectives to find the optimum set of variables. In optimization of lightweight

modular automotive components the problem is even more complicated; here

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optimization is only part of the problem and maybe the most straight forward part of

the problem. There are several other important issues which need to be considered

before the optimization phase is started including modularity and lightweight

concepts which need to be overcome in the design process.

The modularity concept is the first issue to address. First we need to identify

modules which are necessary and can be found in all product versions. Since

modularization is situation specific, it cannot be described in process and would be

considered in a case study.

Lightness of the components is the second issue to consider. Lightweight

materials with high strength to weight ratio have great potential in achieving this

goal. However, the problem is finding the optimum material which can only be

achieved through optimization techniques.

The last but not the least is combining different optimization techniques to

achieve the required objective which is the lightest component.

1.4 Objective

The objective of this project is introducing a validated process flow for

lightweight modular automotive components.

1.5 Scopes of the study

The scope of this project includes the following aspects:

Modularization Concepts in designing automotive components

Lightweight structural materials (HSS, Al, FRP Composites)

General Optimization Problems

5

Structural Optimization techniques used in the Design Process

Detailed 3G Optimization of a Modular Joint

1.6 Importance of the study

Lightweight Modular Automotive structure is not a new concept but it has

gain considerable attention nowadays due to environmental issues and fuel crises.

No one questions the fact that the lightest possible structure is achieved if and only if

advanced design techniques are used. Optimization techniques which have proved

their great potential in achieving optimum solutions are an important part of the

advanced design processes, through which one can achieve a lightweight structure

more efficiently. Although optimization techniques have been widely used in

structural optimization for many years, it seems that the current way of using

available optimization techniques needs to be reconsidered and a more efficient

process flow needs to be established. It is hoped that this research would help

mechanical and automotive engineers in getting familiar with the modularization

concepts and lightweight materials. It is also expected that this research would

provide a better understanding of the importance of optimization techniques as a

reliable tool in Mechanical Engineering.

1.7 Structure of the thesis

After an introduction to the current problem, chapter 2 involves some of the

literatures reviewed and provides the reader with a general understanding of the

modularization and lightness concepts, general optimization problems, structural

optimization techniques, and some case studies in which the mentioned concepts

were used. After some of the theories behind optimization are introduced in

chapter 2, the methodology used in this research and the established process flow for

optimization of lightweight modular automotive components is explained in

chapter 3.

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For illustration purposes of the established process flow, a joint of the

conceptual chassis presented in Figure 1.1 is chosen. Then the modularity concepts

besides optimization for maximum stiffness and lightest design which satisfies

design requirements, based on the process flow is presented in chapter 4.

Finally a conclusion is made in chapter 5 through comparison of the

mechanical characteristics of the new lightweight modular joint with the old design.

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6. REFERENCES

Aluminium Automotive Manual. (n.d.). Retrieved from www.eaa.net/aam

Ashby, M. F. (2005). Materials Selection in Mechanical Design (Third ed.). Elsevier.

Bartz, W. (1993). Aluminium materials technology for automobile construction.

London: Mech.Eng.Publ.

Bendsøe, M. P. (1995). Optimization of Structural Topology, Shape, and Material.

Verlag Berlin Heidelberg: Springer.

Bendsøe, M. P., & Kikuchi, N. (1988). Generating Optimal Topologies in Structural

Design using a Homogenization Method. Computer Methods in Applied

Mechanics and Engineering, Vol. 71, No. 2, pp.197-224.

Bendsøe, M. P., & Sigmund, O. (2003). Topology Optimization, theory, methods and

applications. Springer.

Cantor, B., Grant, P., & Johnston, C. (2008). Automotive Engineering: Lightweight,

Functional, and Novel Materials. CRC Press, Taylor & Francis Group.

Cantor, B., Grant, P., & Johnston, C. (2008). Automotive Engineering: Lightweight,

Functional, and Novel Materials. CRC Press, Taylor & Francis Group.

Cheng, H.-C., Kikuchi, N., & Ma, Z.-D. (1994). Generalized Shape/Topology

Designs of Plate/Shell Structures for Eigenvalue Optimization Problems.

Proceeding of ASME International Mechanical Engineering Congress and

Exposition , PED, Vol 682, pp. No. 2, pp. 483-492.

Diaz, A. R., & Sigmund, O. (1995). Checkerboard Patterns in Layout Optimization.

Structural Optimization, vol. 10, pp. 40-45.

Eschenauer, H. A., & Olho, N. (2001). Topology optimization of continuum

structures: A review. Appl. Mech., vol 54, No.4, pp. 331-390.

Eskildsen, K. (2011). Modularization. International Technology Management.

Copenhagen: Aalborg Universtity.

Fonseca, J. (1997). Design of Microstructures of Periodic Composite Materials.

Ph.D. Thesis, The University of Michigan.

76

Frecker, M., Ananthasuresh, G., Kikuchi, N., & Kota, S. (1997). Topological

synthesis of compliant mechanisms using multi-criteria optimization. Journal

of Mechanical Design, ASME Transactions, Vol. 119, No.2, pp. 238-245.

Hirsch, J. (n.d.). Automotive Trends in Aluminium - The European Perspective. (J.

M. Nie, Ed.) ICAA9, 1, pp. 15-23.

Hirsch, J., Bassan, D., Lahay, C., & Goede, M. (n.d.). Aluminum in innovative light-

weight car design. Lightweight Vehicle Structure Conference.

Keeler, S., & Kimchi, M. (2014). Advanced High-Strength Steels: Application

Guidelines Version 5.0. WorldAutoSteel.

Kelkar, A. (2000). Analysis of Aluminum in Auto Body Designs and its Strategic

Implications for the Aluminum Industry.

Kikuchi, N., Nishiwaki, S., Fonseca, J., & Silva, E. (1998). Design Optimization

Method for Compliant Mechanisms and Material Microstructure. Computer

Methods in Applied Mechanics and Engineering, Vol. 151, pp. 401-417.

Kikuchi, N., Suzuki, K., & Fukushima, J. (1991). Layout optimization using the

homogenization method: generalized layout design of three-dimensional

shells for car bodies. in: Rozvany, G. I. N., ed., Optimization of Large

Structural Systems, NATO-ASI Series (Berchtesgaden) 3, pp. 110-126.

Klarbring, A., & Christensen, P. W. (2009). An Introduction to Structural

Optimization. Solid Mechanics and its Applications. Springer Science +

Business Media B.V.

Kragtwijk, N. (1998). The Application of Steel and Aluminum in a New Lightweight

Car Body Design.

Lahaye, C., Hirsch J., Bassan D., Criqui B., Urban P., Goede M. (2008). Aluminium

Alloys, Their Physical and Mechanical Properties. In Hirsch J. et.al (Ed.),

ICAA11, (pp. 236-237). Aachen.

Ma, Z.-D., Kikuchi, N., & Cheng, H.-C. (1995). Topological Design for Vibrating

Structures. Computer Methods in Applied Mechanics and Engineering, Vol.

121, pp. 259-280.

Ma, Z.-D., Kikuchi, N., & Hagiwara, I. (1993). Structural Topology and Shape

Optimization for a Frequency Response Problem. Computational Mechanics,

Vol. 13, No. 3, pp. 157-174.

77

Ma, Z.-D., Kikuchi, N., Cheng, H.-C., & Hagiwara. (1995). Topological

Optimization Technique for Free Vibration Problems. ASME Journal of

Applied Mechanics, Vol. 62, pp. 200-207.

Mills, A. (2002). Development of a Carbon Fibre Composite Ultra Lightweight

Vehicle Structure for the Aero-Stable Carbon Car – Fastframes.

Nikkei Mechanical. (1998). Vol. 12, No. 531, 17.

Nishiwaki, S., Frecker, M., Min, S., & Kikuchi, N. (1998). Topology Optimization of

Compliant Mechanisms Using the Homogenization Method. International

Journal for Numerical Methods in Engineering, Vol. 42, pp. 535-559.

Ota. (1995). Total Life Cycle Conference & Exposition.

Parry, G., & Graves, A. (2008). Build to order: the road to the 5-day car. Springer.

Rozvany, G. I. (2000). Aims, scope, methods, history and unified terminology of

computer aided topology optimization in structural mechanics. Struct.

Multidisc. Optim., Vol. 21, pp. 90-108.

Rozvany, G. I. (2009). A critical review of established methods of structural

topology optimization. Struct. Multidisc. Optim., Vol. 37, pp. 217-237.

Sigmund, O., & Petersson, J. (1998). Numerical instabilities in topology

optimization: A survery on procedures dealing with checkerboards, mesh-

dependencies and local minima. Structural Optimization, Vol. 16, pp. 68-75.

Silva, E., Nishiwaki, S., Fonseca, J., & Kikuchi, N. (1999). Optimization Methods

Applied to Material and Flextensional Actuator Design Using the

Homogenization Method. Compt. Methods Appl. Mech. Engrg., Vol. 172, pp.

241-271.

SUN Hongtu, H., MA, N., SHEN, G., & LIU, B. (2010). Application of Hot Forming

High Strength Steel Parts on Car Body in Side Impact.

Suzuki, K., & Kikuchi, N. (1991). A homogenization method for shape and topology

optimization. Comput. Methods Appl. Mech. Energ., Vol. 93, pp. 291-318.

Tachibana, M. e. (2002). Plastic Bolster (Radiator Core Support). Nissan Technical

Review, No. 50, pp. 47–50.

Tochioka, T. e. (2002). Development of module carriers by injection molding with

glass fiber reinforced polypropylene. JSAE, No. 31-02, pp. 5–8.

ULSAB organization. (1997). Data distributed by the ULSAB organization. ULSAB.

Vanderplaats, G. N. (1984). Numerical optimization techniques for enineering design

with applications. McGraw-Hill.

78

Zoutendijk, G. (1960). Methods of Feasible Directions. Amsterdam: Elsevier.