Design Improvement of Steering Knuckle Component Using Shape Optimization

Transcription

1 International Journal of Advanced Computer Science, Vol. 2, No. 2, pp , Feb Design Improvement of Steering Knuckle Component Using Shape Optimization Wan Mansor Wan Muhamad, Endra Sujatmika, Hisham Hamid, & Faris Tarlochan Manuscript Received: 2,Oct., 2011 Revised: 16,Dec., 2011 Accepted: 16,Jan., 2011 Published: 15,Mar.,2012 Keywords Shape Optimization, Steering Knuckle Component Abstract Reducing mass of vehicle components will contribute towards overall mass reduction of a vehicle, lower its energy consumption demand, therefore, will improve its fuel efficiency. Material resources will be saved too. The objective of this research is reduce mass of an existing steering knuckle component of a local car model by applying shape optimization technique. A finite element software, HyperWorks which contains several modules, is used to achieve this objective. HyperMesh was used to prepare the finite element model while HyperMorph was utilized for defining shape variables. For optimization purpose, OptiStruct was utilized. The improved design achieves 8.4% reduction of mass. Even though there are volume reduction and shape changes, maximum stress has not change significantly. This result is satisfactory considering using optimization in shape only, with limited design space given and no change in material properties. 1. Introduction In this investigation, steering knuckle was used as component for study. Suspension system in any vehicle uses different types of links, arms, and joints to let the wheels move freely; front suspensions also have to allow the front wheels to turn. Steering knuckle/spindle assembly, which might be two separate parts attached together or one complete part, is one of these links [1]. Mass or weight reduction is becoming important issue in car manufacturing industry. Weight reduction will give substantial impact to fuel efficiency, efforts to reduce emissions and therefore, save environment. Weight can be reduced through several types of technological improvements, such as advances in materials, design and analysis methods, fabrication processes and optimization techniques, etc. Another tool had been developed beside the CAD Wan Mansor Wan Muhamad, Endra Sujatmika, & Hisham Hamid are with Mechanical and Manufacturing Section, Malaysia France Institute (MFI), Universiti Kuala Lumpur (UniKL), Seksyen 14, Jalan Teras Jernang Bandar Baru Bangi, Selangor, MALAYSIA dr.wmansor@mfi.unikl.edu.my Faris Tarlochan is with Mechanical Engineering Department, College of Engineering, Universiti Tenaga Nasional (UniTEN), Kajang, Selangor, MALAYSIA software which is CAE. The needs of the CAE in industrial field are reported by Yoshio Kojima [1]. Car s components are subjected to many types of loadings; those components are designed and manufactured to meet the requirements for strength and safety. Optimization methods were developed to have lighter, less cost and may have better strength too. Many optimization types, methods and tools are available nowadays due to the revolution of the high speed computing and software development. There are four disciplines for optimization process [2]: a. Topology optimization: it is an optimization process which gives the optimum material layout according to the design space and loading case. b. Shape optimization: this optimization gives the optimum fillets and the optimum outer dimensions. c. Size optimization: the aim of applying this optimization process is to obtain the optimum thickness of the component. d. Topography: it is an advanced form of shape optimization, in which a design region is defined and a pattern of shape variable will generate the reinforcements. Shape optimization was developed using optimization techniques such as Genetic Algorithms (GAs) [3]. Shape optimization is applied to many fields such as Computational Fluid Dynamics (CFD) especially aerodynamics [4]-[5] and electrical engineering field [6] as well as mechanical engineering, for example: strain gauge load cell [7], a cantilever beam [8] and cam [9]. Finite element method used for many type of analysis, such as linear analysis, nonlinear analysis, fatigue analysis and another types. FE analysis was developed to solve the optimization process such as OptiStruct linear solver [2], TopShape [10]. 2. Objective This research aims to contribute to the development of structural design and mass reduction of vehicle components using shape optimization by the gradient based method. Optimization process for this work was conducted using OptiStruct solver in order to reduce the mass of the component which will reduce the cost with respect to the mass production process.

2 66 3. Methodology Shape optimization was applied to reduce volume of steering knuckle model. OptiStruct was used to perform the process. The approach is shown in Fig. 1. All of the optimization processes use some application software that included in the HyperWorks (HW). Using HyperMesh as one of the application in HW, finite element model was established from importing model until applying loads and boundary conditions. The model can be either solid model (e.g. IGES, Catia, ProE, STEP, etc) or other Finite element software (e.g. Radioss, Nastran, Abaqus, Ansys, etc). The model is linear finite element model or bulk data. Preliminary analysis was conducted to the initial model using OptiStruct to get initial required information (stress distribution, displacement, maximum stress, etc). That information would be used as reference for optimization process setting and compared to the optimized model for assessing optimization process performance. Shape optimization process requires shape design variables. HyperMorph application in HW is dedicated to define shapes by altering geometry of the model and saving them as shapes. Furthermore, each shape will become a design variable. Minimizing the model is an objective of the optimization process while maximum stress is a constraint that must be satisfied. There are some iterations and evaluations during the optimization process to achieve an optimized model. Validation process is important step in this design optimization. The optimized model s performance is compared with initial models. If the result is not satisfactory, shapes redefinition is required to explore others possible design space. Furthermore, Hyperview and Hypergraph were used to display and plot the data for results interpretation. International Journal of Advanced Computer Science, Vol. 2, No. 2, Pp , Feb Initial Model and Results No Compare with Initial Model Start Import CAD Model Mesh 3D Model Linear FE Modeling (Bulk Data) Execute Linear Static Analysis Shape Optimization Optimized Model Validate? Yes Stop Fig. 1: Design Optimization Flowchart. 4. Model and Numerical Analysis A. Model Boundary Condition The boundary condition and loading condition were set following conditions for testing purpose in one automotive manufacturing company. The boundary conditions were defined by fixing all the hub bolt holes except the pair of bolt holes A (see Fig. 2). Those holes were released in the horizontal direction and coincided with the plane of moment, while any moving was not allowed for the other bolt holes B, C and D. In the vehicle, pair of holes A are attached to lower control arm, hole B is connected to steering system by a tie rod while holes C and D are connected the strut joints of suspension system (MacPherson-strut front suspension). Fig. 2: Free Body Diagram of the model Force and moment were applied through the holder that was attached to top of the model. Load of 2.8 G were charged continuously in the other end of the holder. That load was represented by a force and moment that worked on top of the model.

3 Wan Mansor Wan Muhamad et al.: Design Improvement of Steering Knuckle Component Using Shape Optimization. B. Finite Element Model Finite element model for knuckle is shown in Fig. 3 below, those are the basis vector approach and the perturbation approach. Those approaches refer to the definition of the structural shape as a linear combination of vectors. Using the basis vector approach, the structural shape is defined as a linear combination of basis vectors. The basis vectors define nodal locations. x = DVi. BVi Where x is the vector of nodal coordinates, BVi is the basis vector associated to the design variable DVi. Using the perturbation vector approach, the structural shape change is defined as a linear combination of perturbation vectors. The perturbation vectors define changes of nodal locations with respect to the original finite element mesh. x = xo + DVi. PVi 67 Fig. 3: Finite Element Model of Knuckle TABLE 1: MATERIAL PROPERTIES Young modulus Mpa Poisson ratio 0.29 Density 7.85 E-09 tone/mm 3 Ultimate Tensile Stress 522 Mpa Yield Stress Mpa This model has material properties as shown in Table 1 above. Young modulus, Poisson ratio and density are included when material is defined. Property definition requires material properties and type of element. TABLE 2: LOADS CONDITIONS Description Magnitude Force (2.8G) Moment N.mm Total number of nodes Total number of elements (Tetra) The model is divided into D solid elements (volume tetra element) There are two type loads that were applied to the knuckle, those are force and moment. The knuckle has two constraints that restraint them on all direction (x, y, z translation and xx, yy and zz rotation) and one constraint that allow it translate to z direction. C. Design Variables for Shape Optimization The vector of nodal coordinates (x) is used to define the shape of steering knuckle structure in finite elements model. Changes of the boundary in model structure will translate to interior of mesh to avoid distortion of the elements when shapes change. During shape optimization, there are two approaches that can be used to account for mesh changes; Where x is the vector of nodal coordinates, xo is the vector of nodal coordinates of the initial design, PVi is the perturbation vector associated to the design variable DVi. D. Shape Optimization Parameters An general optimization or a mathematical programming problem can be stated as follows [11]. Find (X) = { ( (x_1@x_2 )} which minimize f(x) subject to the constraints gj (X) 0, j = 1, 2,...,m lj (X) = 0, j = 1, 2,..., p where X is an n-dimensional vector called the design vector, f (X) is termed the objective function, and gj (X) and lj (X) are known as inequality and equality constraints, respectively. In this paper, the objective function of shape optimization problem is as implicit function that is to minimize volume and subject to maximum stress of the elements as constraint. Design variables were determined using Hypermorph. There are 8 shapes were defined (shape 1, shape 2, shape 3, shape 4, shape 5, shape 6, shape 7 and shape 8) as design variables. 5. Results and Discussions For the optimization process, eight shape variables were defined and optimized considering stress constraint. Figures 4 (a) - (f) show the shape optimization results that obtained using OptiStruct solver. The design region that was defined to have three shapes (1, 2 and 3) had the most volume reduction among all shapes as shown in Fig. 4(c). Second design region is shown in Fig. 4(d), which has shape 4 and 5, has less volume change compared to that of Fig. 4(c). Fig. 4(e) and 4(f) show the optimized shapes (6, 7 and 8) and all of them have less shape change than that in Fig. 4(c).

4 68 International Journal of Advanced Computer Science, Vol. 2, No. 2, Pp , Feb (a) The objective of the research is to reduce the mass (represented by reduction volume) using shape optimization. Fig. 5 shows the graph of volume minimization versus the iteration of the shape optimization process. The mass reduction for the front knuckle was found to be 8.37%, compared to the currently used model. This result is satisfactory considering using optimization in shape only, with limited design space given and no change in material properties. More reduction is possible, though may not be much, is expected to be achieved if there is more design space through redesigning of the whole assembly. (b) (c) (d) (e) Fig. 5: Objective vs. Iteration Figure 6 shows simulation results of initial model and optimized model. Shape optimization process succeeds to reduce volume of the component. It is noted that mass reduction of the original model does not occur in the critical regions (region which having maximum stress which is shown in red color) so that there is no significant stress change in the said region. Fig. 6 (a) and 6 (b) show the comparison between before and after optimization process. This optimization process also gives small change on the displacement. It means that change of volume and shapes doesn t influence significantly to stiffness of the structure. Summary of the results is shown in table 3. TABLE 3: RESULTS SUMMARY (f) Fig. 4: (a) initial shape of model (b) optimized model shape (c) Shape 1, shape 2 and shape 3, (d) Shape 4 and shape 5, (e) Shape 6 and shape 7, (f) Shape 8

5 Wan Mansor Wan Muhamad et al.: Design Improvement of Steering Knuckle Component Using Shape Optimization. optimization. Therefore, the overall weight of the vehicle can be reduced to achieve savings in costs and materials, as well as, improve fuel efficiency and reduce carbon emissions to sustain the environment. 69 Fig. 6: (a) Stress contour of initial model, (b) Stress contour of optimized model, (c) Displacement contour of initial model, (d) Displacement contour of optimized model 6. Conclusions Optimization method used in this study succeeded in reducing the mass of existing knuckle component to 8.4%. Even though there are volume reduction and shape changes, maximum stress has not change significantly. This result is satisfactory considering using optimization in shape only, with limited design space given and no change in material properties. Other vehicle components, similarly, have the potential to be reduced with respect to mass using shape (a) (b) (c) (d) Acknowledgments This research was sponsored by Ministry of Science, Technology and Innovation (MOSTI) Malaysia TechnoFund Grant. The authors would also like to thank PROTON for its support. References [1] M. Zurofi, Manufacturing Process Effects on Fatigue Design and Optimization of Automotive Components An Analytical and Experimental Study, The University of Toledo, Ph.D. thesis, [2] Y. Kojima, "Mechanical CAE in automotive design," (2000) R & D review of Toyota CRLD, vol. 35, no. 4. [3] Altair Hyperworks 9, Altair Engineering Inc., (2009), India. [4] Goldberg, D.E. Genetic algorithms in search, optimization and machine learning. Reading, MA: Addison-Wesley, 1989, ISBN [5] Obayashi, S. Pareto genetic algorithm for aerodynamic design using the Navier-Stokes equations. In: Quagliarella D, Pe riaux J, Poloni C, Winter G, editors. Genetic algorithms and evolution strategies in engineering and computer science. Chichester, England: Wiley; 1997, p ISBN [6] S. Obayashi & T. Tsukahara "Comparison of optimization algorithms for aerodynamic shape design," (1997) AIAA Journal, vol. 35, no. 8, pp [7] Pe riaux J, Sefrioui M, & Mantel P. GA multiple objective optimization strategies for electromagnetic backscattering. In: Quagliarella D, Pe riaux J, Poloni C, Winter G, editors. Genetic algorithms and evolution strategies in engineering and computer science. 1997, p ISBN [8] Robinson G.M. Genetic algorithm optimisation of load cell geometry by finite element analysis. PhD Thesis. City University, Measurement and Instrumentation Centre, Department of Electrical, Electronic and Information Engineering, School of Engineering. 1995, London (UK). [9] Richards R.A. Zeroth-order shape optimization utilizing a learning classifier system. PhD Dissertation, Mechanical Engineering Department, Stanford University, [10] J. Lampinen "Cam shape optimisation by genetic algorithm," (2003) Journal of Computer-Aided Design, vol. 35, pp [11] L. Harzheim & G. Graf "Topshape: an attempt to create design proposals including manufacturing constraints," (2002) International Journal of Vehicle Design, vol. 28, no. 4, pp [12] Rao, S.S., Engineering Optimization Theory and Practice, John Wiley & Sons, Inc., 2009, 4th edition.