Int. J. Vehicle Design, Vol. 34, No. 4, 2004
Optimal design of vehicle components using topology design and optimisation Ali Rıza Yildiz, Necmettin Kaya and Ferruh Öztürk* University of Uluda÷, Mechanical Engineering Department, Bursa 16059, Turkey Fax: (0224) 442 80 21 E-mail:
[email protected] E-mail:
[email protected] *Corresponding author
Orhan Alankuú TOFAù-FIAT, Yalova Yolu, R&D Department, Bursa 16369, Turkey Abstract: An important problem in automotive industry is how to achieve better design concepts by considering structure performance and manufacturing cost in the early stages of product development. The topology design and optimisation provide an initial design concept for downstream applications, which leads to achieving better design by using computer-aided techniques. In this research, engine mount bracket design is presented to illustrate the application of topology optimisation approach for optimal design of vehicle components under dynamic loading conditions. The objective of the proposed research is to create an initial design concept, which has optimal structural layout. The effectiveness and verification of proposed approach are demonstrated with experimental results. Keywords: topology optimisation; shape optimisation; fatigue analysis; vehicle components. Reference to this paper should be made as follows: Yildiz, A.R., Kaya, N., Öztürk, F. and Alankuú, O. (2004) ‘Optimal design of vehicle components using topology design and optimisation’, Int. J. Vehicle Design, Vol. 34, No. 4, pp.387–398. Biographical notes: Ali Rıza Yildiz is a Research Assistant in the Mechanical Engineering Department at Uludag University. He follows a Ph.D. postgraduate program in the Mechanical Engineering Department at Uludag University. His research focuses on computer aided design and optimisation. Dr. Necmettin Kaya is a Lecturer in the Mechanical Engineering Department at Uludag University. He received his Ph.D. degree in Mechanical Engineering from Uludag University. His research focuses on computer aided design, fixture design and optimisation. Dr. Orhan B. Alankuú is Director of Research and Development (R&D) Department of TOFAù-FIAT Automotive Factory in Bursa/Turkey. He received a Ph.D. in Mechanical Engineering from Imperial College of Science and Technology in London/UK. Before joining TOFAù-FIAT in 1984, Copyright © 2004 Inderscience Enterprises Ltd.
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A.R. Yildiz et al. he worked in England on a project related to the development of a new multi-processor CNC systems to be applied to machine and robots. His major research interests include manufacturing engineering, CIM, robotics, new organisational system and modern technology. Dr. Ferruh Öztürk is a Lecturer and Head of the Mechanical Engineering Department at Uludag University. He is Director of CAD/CAE/CAM Laboratory at the Faculty of Engineering and Architecture at Uludag University. He has a Ph.D. in Mechanical and Manufacturing Systems Engineering from Bradford University, UK. Before joining Uludag University in 1986, he had worked with the TOFAù-FIAT automotive company in Bursa, Turkey. His research interests include vehicle design and dynamics, computer aided design and optimisation, neural networks, genetic algorithms.
1
Introduction
The final product structure is very dependent on the initial design concept that affects the cost and performance of a new vehicle. In order to meet today’s vehicle design requirements and to improve the cost and fuel efficiency, there is an increasing interest to design light-weight and cost-effective vehicle components. Therefore, an important problem in automotive industry is how to achieve better product design by considering product performance and manufacturing cost in the early design stages of product development. Major shortcomings are usually due to: 1
no priori knowledge about product layout
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highly depend on designer experience, creativity and heuristics and
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over design and conflicting objectives.
To overcome these deficiencies, topology design and optimisation approaches have to be employed to determine product layout and to reduce the weight by yet satisfying stiffness and dynamic performance requirements of a component. The optimisation methods are used to design products, which are light-weight to improve the cost and fuel efficiency, without sacrificing strength and performance. During the optimisation, the shape and size of structure can be changed, but the topology of the structure is not changed. Therefore, optimisation techniques have to be considered in the conceptual design phase to create an optimal initial design layout. Topology of a new component is determined in the conceptual stage of the design. The designer may consider many alternative topologies and one of them is chosen as being final component layout. It is a trial-and-error approach and highly depends on designer’s experience, creativity and heuristics. This procedure may result with final component layout, which is often non-optimal. However, in topology optimisation approach, designer does not have to choose optimal topology among alternatives and no priori knowledge about topology is required. The other problem is due to over design and conflicting objectives. There are usually several conflict objectives such as reducing the weight and increasing the stiffness. In topology optimisation approach, the objectives are usually to minimise the compliance or to maximise the fundamental frequency of the structure. In this research, several practical examples are carried out to determine the effects of compliance and vibration objectives on the topology of the structure. Although
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multiobjective criteria objectives are used by some authors, the single objective topology optimisation either compliance or vibration is usually considered in practical applications in literature. In this research, significant consideration is given to show the effects of compliance and frequency objectives on the product layout design. It is also shown that optimal layout of engine mount bracket can be obtained using topology optimisation approach without a priori knowledge about product topology in the conceptual design phase. Objectives of this paper are: 1
to introduce an efficient cost-effective initial optimal layout design process for conceptual design phase
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to use optimal material distribution method to reduce the weight of the vehicle components under dynamic loading conditions and
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to use design analysis techniques to avoid over design and to shorten product development time.
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Literature review
Over the past, various research works are carried out in the area of topology design and shape optimisation [1–15]. Although, a substantial number of works have been presented in the topology design, two major methods are widely used by researchers, which are homogenisation method and density method. Most of the topology optimisation applications in literature rely on either homogenisation or density methods. Bendsoe and Kikuchi [16] presented homogenisation method for the topology optimisation of continuum structures to minimise the fixed initial design domain. This method transforms the topological optimisation problem into an optimal material distribution problem. Bendsoe and Kikuchi used the homogenisation method to compute the macroscopic material properties with the assumption that a structure is full of microvoids. The optimisation process is then used to obtain the optimal topology. Several papers were presented using the homogenisation method [17–20]. For a comphrensive review on the structural topology optimisation, the reader is referred to Bendsoe [21]. The formulation and mathematical background of technique are outlined in this book. It also covers a review of world research about this subject. In homogenisation method, material density is treated as design variables and objective is to minimise the mean compliance that is equivalent to maximising the structural global stiffness or to maximise the fundamental natural frequency while satisfying the constrains specified (volume reduction, etc.). Another method, which becomes popular, is density function approach which is introduced by Yang and Chuang [22]. In this method, material density is selected as design variable, and objective is the same as homogenisation method. The density of each finite element is chosen as the design variable and its relationship that Young’s modulus is expressed by an empirical formula. This approach employs the relationship between the density and the material properties without considering their microstructures. They used density approach for the determination of structural topology. The objectives are considered: one is to maximise the stiffness of the structure and the other is to maximise the lowest eigenvalue.
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A review paper which discusses FE-based generalised shape optimisation, which can be classified with respect to the types of topologies involved in the paper by Rozvany [9]. Considering in detail the most important class of topologies, the computational efficiency of various solution strategies are compared. Olhoff et al. [23] developed an interactive computer aided design based structural topology and design optimisation system. It is stated that topology optimisation gives rough outer and inner boundaries that should be modified by the designer to meet practical requirements, before the more detailed shape optimisation is performed. The actual shape optimisation model is generated by drawing the initial structure on top of the generated topology. One of the earliest works on structural optimisation under dynamic loads is presented in the paper by Fox and Kapoor [24]. Another paper that includes finding optimal topology under dynamic loads presented in Min et al. [25]. Ma et al. [26] used topology design approach for vibrating structures. In literature, that there are only few works related to topology optimisation under dynamic loading conditions. Most of the work is related to static loading conditions. The topology and shape optimisation of continuum structures have been active research area in literature since last two decades. Recently, topology optimisation has received increasing interest by researchers and engineers in industry because of its powerful ability to define optimal product outlines [27–29]. It is seen that most of the systems are focused on topology optimisation with either compliance or vibration. The minimum compliance and maximum fundamental frequency are usually used as single objective in the topology optimisation problems. The constraint is taken as the amount of material allowed in the specified design domain. The topology optimisation is usually implemented to single objective optimisation systems. There are some research works, which use both objectives in topology optimisation problems. However, most of them deal with optimisation of two-dimensional structures.
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Topology design and optimisation
Design performance is highly depending on the initial design intent, which is based on the experience and intuition of the designer. Traditional design procedure is an iterative process. It starts with an initial concept design that is based on the experience, knowledge and intuition of the designer. Analysis and redesign steps are carried out to evaluate and modify the product layout. This is time consuming and inefficient procedure that can create sub-optimal structure layouts since starting topology is not optimal. To improve the design process, design optimisation is introduced into the design process. The aim of design optimisation is to find the best possible or optimal structure layout for a product without sacrificing functionality and manufacturability conditions. Topology optimisation has been proven very effective in determining the topology of initial design structure for component development in the conceptual design phase. Different approaches for structural layout design have been proposed for structural optimisation in literature. Two types of structural optimisation methods are widely used in literature: shape optimisation and topology optimisation. The shape optimisation approach is different from topology optimisation since the structural changes are only related to the boundaries of the design domain.
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Shape optimisation is a technique that seeks to determine an optimum design. Optimal design should meet all specified requirements but with a minimum expense of certain factors such as weight, surface area, volume, stress, cost, etc. A good survey on shape optimisation presented by Haftka and Grandhi [3]. The goal of topology optimisation is to find the best use of material for a component. It provides an initial design concept for subsequent applications following design such as shape optimisation, machining etc. For example, the topology optimisation of an example part to minimise the compliance with a constraint on 60% volume reduction is shown in Figure 2. Sample cantilever beam is subjected loads and constraints as shown in Figure 1. The results of topology optimisation in terms of density contours are given in Figure 2. Figure 1
Load and boundary conditions
Figure 2
Optimal topology layout
In general, there are three topology optimisation methods in literature as homogenisation method, material distribution method and evolutionary method. In this section, homogenisation and material distribution methods, which are widely used in the area of design optimisation, are briefly explained. The homogenisation method first presented by Bendsoe and Kikuchi [16]. According to this method, the optimal material distribution within elastic design domain by using the stiffness-density relationship is obtained by the homogenisation of a cellular microstructure. The porosity of a microstructure is represented by a rectangular hole in a microstructure. A microstructure is classified as void which constrains no material (hole size = 1), solid medium which constraints isotropic material (hole size = 0), and the generalised porous medium which constraints orthotropic material (0 < hole size < 1). The distribution of void, solid, and porous microstructures indicates the shape and topology of structure. In homogenisation method, a structure is assumed to be composed of periodic microstructures, and the equivalent material properties are estimated by limiting process that involves diminishing the microscopic size. The elastic material properties of a structure can be defined by the dimensions and orientation of
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micro structural holes. During the optimisation, microstructures changes between void and the solid. The material distribution method presented by Yang and Chuang [22]. In material distribution method, the material density of each finite element treated as the design variable as being different from homogenisation method. The structural formulation of topology optimisation is usually considered as minimising the objective function of compliance while subject to a constraint on the mass reduction of the structure. Since vehicle component design is usually considered to meet the stiffness and dynamic performance requirements, in this research, the compliance and vibration based topology design is proposed to generate optimal layouts. Two subsequent topology optimisation procedures are employed to determine best possible topology instead of single traditional approaches in most of the practical industrial applications. In this research, topology and shape optimisation approaches are used together to design light-weight component with shorter lead time. This approach does not require trial-anderror methods to define initial design concept. Engine mount bracket design example is presented to evaluate the proposed optimum design method.
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Optimum structural design of engine mount bracket
Traditionally, mount brackets are often designed by iterative methods. They are optimised under non-optimal topologies and often based on static loading conditions. Vehicle elements such as engine mount brackets generally face with dynamic loading during working conditions. Therefore, in this research, the optimal layout of an engine mount bracket under dynamic loading conditions is determined using topology and shape optimisation approach. Fatigue life analysis is also considered to evaluate the fatigue behaviour of the optimised structure. The following optimisation stages are carried out to obtain the optimal layout of bracket.
4.1 Stage 1: define the initial design domain and FE model The design domain of bracket is given in Figure 3. The finite element model of design domain is generated which contains 17,064 elements and 26,729 nodes. Youngs’s modulus (E), Poission’s ratio (ν) and density (ρ) for the material of bracket are taken as 2.1 × 105 N/mm2, 0.3 and 7.82 × 10–6 kg/m3, respectively. Figure 3
Design domain and finite element model of engine mount bracket
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4.2 Stage 2: topology optimisation The goal of topological optimisation is often to minimise the energy of structural compliance or maximise the fundamental natural frequency while satisfying the volume reduction constraint. Minimising the compliance is equivalent to maximising the global structural stiffness. In topological optimisation, the material distribution function over a design domain serves as the optimisation parameter. In this study, optimum design of engine mount bracket is performed using topology optimisation based on a material distribution method. In topology optimisation, objective functions chosen as 1 2
to minimise the compliance and to maximise the natural frequency with a 75% material usage constraint imposed The topological optimisation procedure consists of following main steps: Step 1: define optimisation functions Step 2: define objective and constraints Step 3: initialise the optimisation parameters Step 4: execute the topological optimisation Step 5: review the results.
In this case study, the density of each element is selected as the design variable and above given steps are carried out using ANSYS software. The material distribution for rough outlines of initial engine mount bracket design for 75% material usage is obtained as shown in Figure 4. Figure 4
Material distribution of engine mount bracket design domain
The lighter density colours represent the material, which should be removed and the darker density colours represent the material, which should be kept as shown in Figure 4. A sample finite element model of topology after material removed is given in Figure 5.
4.3 Stage 3: material removal process According to results of topology optimisation, the bracket structure is redefined as being based on material distribution (Figures 6 and 7). This is the initial optimal topology of engine mount bracket which is used for shape optimisation and fatigue behaviour evaluation.
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Figure 5
Finite element model of topology after material removed for compliance minimisation
Figure 6
Engine mount bracket outlines for frequency maximisation
Figure 7
Engine mount bracket outlines for compliance minimisation
4.4 Stage 4: shape optimisation In shape optimisation, the objective is to minimise the mass of structure and constraint is maximum stress. The shape optimisation procedure consists of following main steps: Step 1: build the parametric model Step 2: choose optimisation method Step 3: specify optimisation looping controls Step 4: define optimisation variables and limits Step 5: define objective function Step 6: define constraint function and its upper limit Step 7: initiate optimisation analysis Step 8: review the results.
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Final shape of the engine mount bracket is checked for stress constraint and fatigue life evaluation as shown in Figure 8. Comparison of topological and shape optimisation results are presented in terms of compliance, displacement, stress and volume parameters for compliance and frequency objectives (Table 1). Figure 8
Table 1
Evaluation of the final shape of engine mount bracket for stress and displacements
Comparison of topology and shape optimisation results for compliance and frequency objectives Compliance minimisation
Frequency maximisation
Non-optimal topology
Topology optimisation
Shape optimisation
Topology optimisation
Shape optimisation
Natural frequency (Hz)
133.499
122.403
119.556
230.248
228.782
Compliance (Nmm)
0.132
0.0659
0.07085
0.084
0.0608
Max. stress (N/mm2)
0.599
2.469
2.594
2.274
3.165
Max. displ. (mm)
1.2 E–4
4.18 E–4
4.19 E–4
5.04 E–4
5.01 E–4
Volume (mm3)
1,333,800
281,591
273,025
317,264
316,197
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4.5 Fatigue life evaluation Fatigue is the phenomenon which is caused by repeated (cyclic) loading. The fatigue damage and life evaluation of I-DEAS computer aided engineering program is considered to evaluate whether the design will remain viable for the specified life criteria. Fatigue life results are used to evaluate engine mount bracket optimum design for specified load repetitions (Figure 9). Figure 9
Evaluation of engine mount bracket models for fatigue life
The life results are unitless scalars which represent the number of occurrences of an event to failure. Fatigue life behaviour of engine mount bracket is obtained as shown in Figure 9. Fatigue life is found as 5 E+19 cycles for 1,000,000 repetitions of load which is greater than 10 E+6 cycles of infinite life. Therefore, if required, re-design of component can be considered for the fatigue life results and criteria that designer specify. It is seen that compliance and frequency objectives provide alternative models with different volume, stress, displacement, frequency results. Comparison of the two design models showed that the designer can select the best model which satisfies the required product design specifications. Therefore, designer must select the optimal design, which meets the objective function criteria and constraints. If required, further design improvements on product can be carried out using optimisation techniques.
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Conclusions
In this research, topology design and shape optimisation approach is presented to create an initial design concept which has optimal structural layout. Both compliance and vibration conditions are considered together to achieve an optimal topology. The shape optimisation and fatigue evaluation is also considered to obtain optimal product design layout. It is seen that single objective approach can lead to non-efficient design outlines. The effectiveness and verification of proposed approach is demonstrated with experimental results. The topology based design is used in the conceptual design phase and then, the shape optimisation is subsequently employed using initial optimal topology. The optimal design
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decisions must be employed in the early phases of the design since initial design layout is generated in the conceptual design phase. Design optimisation methods can lead to sub-optimal products since they do not start with optimal topology for initial design intent. The automotive industry is one of the most competitive and technologically challenging industries. In order to meet today’s global market requirements, there is a need to introduce advanced design and manufacturing technologies to produce higher quality products at less cost with shorter development times. Recently, computer aided design and analysis scenarios (design-build-test) are widely employed in automotive industry and savings in development time and cost reduction are obtained. In this research, it is seen that there is a crucial need to consider structural optimisation techniques to support the innovative design and further to reduce development time and cost. Therefore, the optimal structural design of components is of great importance in the area of automotive industry. The primary goal in future research directions is to automate the proposed design approach with the integration of topology, shape and fatigue analysis in an integrated approach. An intelligent system can be developed to automate the proposed approach and re-design process in case of over-design.
Acknowledgments The authors acknowledge the support of R&D Department of TOFAù-FIAT automobile factory for this research.
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