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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
iii
To my beloved parents and my dear brother and sister, for their endless support and
encouragement.
iv
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.
v
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.
vi
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
viii
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
x
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
xi
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
xii
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
4
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.
6
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.
75
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