Modeling, Simulation and Optimization Analysis on Steering Knuckle Component For Purpose of Weight Reduction

Transcription

1 Modeling, Simulation and Optimization Analysis on Steering Knuckle Component For Purpose of Weight Reduction W. M. Wan Muhamad 1, E. Sujatmika 1, Hisham Hamid 1 and Faris Tarlochan 2 1 UniKL Malaysia France Institute, Universiti Kuala Lumpur, Bandar Baru Bangi, Selangor, Malaysia 2 Mechanical Engineering Department, Universiti Tenaga Nasional, Kajang, Selangor, Malaysia Abstract - Reducing weight of vehicle components will contribute towards overall weight 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 weight of an existing steering knuckle component of a local car model by applying shape optimization technique. A finite element modeling and analysis 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 used. The improved design achieves 8.4% reduction of weight while meeting the strength requirement. This result can be considered satisfactory in view of using optimization in shape only, with limited design space given and no change in material properties. Keywords: Simulation, Optimization, CAD/CAE, Vehicle Component, Weight Reduction 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]. 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 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 weight reduction of vehicle components using shape optimization by the gradient based method.

2 Optimization process for this work was conducted using OptiStruct solver in order to reduce the weight of the component which will reduce the cost with respect to the weight production process. 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. Using HyperMesh as one of the application, solid model was imported for finite element modeling which is loads and constraints applied. Shape optimization process requires shape definition for design variables and HyperMorph can be used to conduct such purposes. 4 Modeling and Optimization Processes 4.1 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). Start Import CAD Model Mesh 3D Model Linear FE Modeling (Bulk Data) Initial Model and Results No Execute Linear Static Analysis Shape Optimization Optimized Model 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. 4.2 Finite Element Model Finite element model for the knuckle is shown in Fig. 3 below. Compare with Initial Model Validate? Yes Stop Fig. 1: Design Optimization Flowchart. Furthermore, Hyperview and Hypergraph were used to display and plot the data for results interpretation.

3 Fig. 3: Finite Element Model of Knuckle Material properties and loading conditions are shown in Table 1 and Table 2 respectively. 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 Table 2: Loads Conditions Description Magnitude Force (2.8G) Moment N.mm Total number of nodes Total number of elements (Tetra) There are two type loads that applied to 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. 4.3 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; 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. Where x is the vector of nodal coordinates, x o is the vector of nodal coordinates of the initial design, PV i is the perturbation vector associated to the design variable DV i. 4.4 Shape Optimization Parameters An general optimization or a mathematical programming problem can be stated as follows [11]. Find (X) = subject to the constraints gj (X) 0, j = 1, 2,...,m lj (X) = 0, j = 1, 2,..., p which minimize f(x) where X is an n-dimensional vector called the design vector, f (X) is termed the objective function, and g j (X) and l j (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 Simulation Results and Discussions For the optimization process, eight shape variables were defined and optimized considering stress constraint. Figures 4 (a), (b), (c) and (d) show the shape optimization results that obtained using OptiStruct solver. Using the basis vector approach, the structural shape is defined as a linear combination of basis vectors. The basis vectors define nodal locations. x = DV i. BV i (1) Where x is the vector of nodal coordinates, BV i is the basis vector associated to the design variable DV i. 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 = x o + DV i. PV i (2)

4 The design region that was defined to have three shapes changing (1, 2 and 3) had the most reduction among all shapes as shown in Fig. 4(a). Second design region is shown in Fig. 4(b), and it was defined to have the (4th, 5th) shape variables and it has less changing than that in Fig. 4(a). Fig. 4(c) and 4(d) show the optimization of shapes (6, 7 and 8) and all of them have less shape changing than that in Fig. 4(a). (a) The objective of the research is to reduce the weight (represented by reduction volume) using shape optimization, Fig. 5 shows the graph of volume minimization versus the iteration of the shape optimization process. The weight reduction for the front knuckle was 8.37%. The weight reduction was not too much because of the original design already sufficient. Nevertheless, more reduction is possible to be achieved if there is more design space through redesigning of assembly layout. (b) Fig. 5: Objective vs. Iteration Summary of the results is shown in table 3. Table 3: Results Summary (c) (d) Fig. 4: (a) Shape 1, Shape 2 and Shape 3, (b) Shape 4 and Shape 5, (c) Shape 6 and Shape 7, (b) Shape 8 6 Conclusions Optimization method used in this study succeeded in reducing the weight of existing knuckle component to 8.4% while meeting the strength requirement. 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 weight using shape

5 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. [12] Rao S.S., Engineering Optimization Theory and Practice, John Wiley & Sons, Inc.,(2009), 4th edition. 7 References [1] Zurofi M. "Manufacturing Process Effects on Fatigue Design and Optimization of Automotive Components An Analytical and Experimental Study", The University of Toledo, Ph.D. thesis, [2] Kojima,Y. Mechanical CAE In Automotive Design, R & D review of Toyota CRLD, Vol 35, No. 4, [3] "Altair Hyperworks 9". Altair Engineering Inc., India, [4] Goldberg DE. "Genetic Algorithms In Search, Optimization And Machine Learning". Addison-Wesley, Reading, MA, [5] Obayashi S. Pareto. "Genetic algorithm for aerodynamic design using the Navier-Stokes equations". In: Genetic Algorithms And Evolution Strategies In Engineering And Computer Science, Wiley, Chichester, England, [6] Obayashi S, Tsukahara T. Comparison Of Optimization Algorithms For Aerodynamic Shape Design. 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, [8] Robinson GM. "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. London, [9] Richards RA. "Zeroth-Order Shape Optimization Utilizing A Learning Classifier System". PhD Dissertation, Mechanical Engineering Department, Stanford University, [10] Lampinen J. Cam Shape Optimisation By Genetic Algorithm, Journal of Computer-Aided Design, Vol. 35, pp , [11] Harzheim L., Graf G., Topshape: An Attempt To Create Design Proposals Including Manufacturing Constraints, International Journal of Vehicle Design, Vol. 28, No. 4, pp , 2002.