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Topology Optimization of Alloy Wheel

BGN Satya prasad M Anil kumar Deputy Manager Assistant Manager Hyundai Motor India Engineering Hyundai Motor India Engineering Hyderabad-82, INDIA. Hyderabad-82, INDIA.

Key Words: Alloy wheel, optimization, fatigue, automobile ABSTRACT India is one of the largest automotive industries in the world and one of the fastest growing globally. Now all automakers are concentrating on India for the promising growth in the sector. So competition in this industry is very high. Hence, there is a need to focus more on product development. The development of the product needs to be started from conceptual design with low cost, high performance and quality. There is a large scope for reducing the mass of aluminum wheel. In this paper the application of topology optimization to reduce the mass of aluminum wheel is discussed.

Introduction

Wheel is one of the most important components of an automobile. It supports and bears the entire vehicle

load. It suffers not only the vertical force but also the irregular forces resulting from the car’s ride, braking,

cornering, road bumps, and all uneven shocks in the process of moving on road. Due to high speed

rotation, its quality has a huge impact on wheel stability, handling and other characteristics.

Fig. Schematic diagram of (1) Cornering fatigue test simulation of alloy wheel (2) Fig : Percentage reduction

in mass (3) Radial fatigue test simulation of alloy wheel

Cornering Fatigue Test and Radial Fatigue Test are performed on any road wheel. It is observed that the

FEA result of the above two tests shows that the maximum stress being induced in the wheel is much less

than the allowable stress of aluminum alloy. Here comes the scope for further optimization of these wheels.

Structural optimization is aimed at to minimize the mass of wheel without compromising the strength of

wheel. In many instances, the results of equivalent stress, equivalent elastic strain and total deformation are

found similar to the results before optimization.

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Thus with some modifications in spoke design, mass of wheel can be decreased maintaining the

characteristic behavior of the wheel intact. Finally, the ultimate goal of this project is to reduce the mass of

wheel, thereby reducing the cost of wheel.

In the current study, the road wheel used an alloy wheel with 8 spokes and approximately 6.73 kg mass is

considered for optimization. HyperMesh, and OptiStruct is used for the purpose of modeling and analysis. A

total of 350gm mass reduction per wheel is achieved through optimization.

Alloy wheel Design Criteria

Alloy wheels are automobile (car, truck) wheels which are made from an alloy of aluminum or magnesium.

They are typically lighter for the same strength and provide better heat conduction and improved cosmetic

appearance than "normal" wheels.

Cornering Fatigue Test

Wheels are subjected to high stress during cornering. Static analysis is performed on the wheel to analyze

its characteristics while cornering. Bending moment is applied keeping the inboard rim flange region

constrained, to simulate the real time conditions. The stresses in critical zones are noted. The wheel is

checked to pass the min. no. of cycles considering the factor of safety

CFT RFT

Radial Fatigue test

Wheels are subjected to compressive loads during operation. Static analysis is performed to study the

wheel behavior to vertical loading. Load is applied normally, fixing the wheel centre. The stresses in critical

zones are noted. The wheel is checked to pass the min. no. of cycles considering the factor of safety.

Dynamic Stiffness Test

Wheels are to be checked for dynamic stiffness. Here FRF and normal mode analysis are used to extract

the frequency values using which the dynamic stiffness of the wheel are found out.

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Impact test

One of the critical conditions any wheel is subjected to is Impact. It is a general saying that a wheel which

passes the requirements for impact also passes all other requirements like Cornering Fatigue Test, Radial

Fatigue Test, Dynamic stiffness test and normal mode analysis. Impact is well established during accidents.

To study the performance of wheel for impact, static analysis is performed wherein huge impact load at an

angle of 13 degrees to the face of wheel is applied. Stresses induced are found out and checked for safety.

The set up shown below is defined as per SAE J175 Reaffirmed SEP2003.

Introduction to Optimization Finite element-based optimization techniques were first developed by UCLA Professor, Lucien Schmit in the 1960s (Schmit 1960). Schmit recognized the potential of combining optimization techniques with finite element analysis (FEA) for structural design. Today, three types of finite element based optimization approaches are available within commercial FEA softwares: parameter optimization, shape optimization, and topology optimization. Parameter optimization uses physical properties as design variables. This approach strives to find the optimum value of these properties in the constitutive elements of the structure. Typically, cross-sectional parameters are used as design variables.

Fig: Design and non design area of alloy wheel

These parameters include thickness, area, and moment of inertia, among others. Shape optimization involves determining the optimal profile or boundary of the structure. Two of the most common approaches for shape optimization are: the basis vector and the grid perturbation approach. The basis vector approach requires the definition of different trial designs called the basis vectors. The design variables are the weighting parameters that define the participation of each basis vector in the design process. On the other hand, the grid perturbation approach requires the definition of perturbation vectors. These vectors perturb or deform the boundary of the design domain. The design variables are the values that determine the amount of the perturbation during the optimization process. The work in this paper makes use of the grid perturbation approach. Topology optimization is being used more frequently in recent studies to find preliminary, and sometimes completely innovative, structural configurations that meet specific conditions (i.e., objective function and constraints).

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Fig: Optimization output

Topology optimization involves the optimal distribution of material within a design domain. Initially, the design domain is comprised of a large number of (finite) elements. The topology optimization process selectively removes unnecessary elements from the domain. Novell optimum structures are usually obtained using this technique. The design variables in topology optimization depend on the type of material model used in the finite element analysis. The nature of these design variables characterizes distinct methods. Two of the most commonly referenced topology optimization methods are the homogenization approach and the density approach. The alloy road wheel is selected for the purpose of optimization for it has huge scope for mass reduction and it falling under the category of unsprung mass. The purpose of this work is to use a topology analysis to synthesize a structure for the alloy road wheel with the intention of decreasing weight keeping the stiffness intact.

Fig: Design changes from base to case4

Design Domain The creation of design domain is a key aspect in performing a successful topology optimization analysis and requires a good deal of preparation. To create the design domain for the alloy road wheel, the existing wheel design is utilized to establish the necessary design and non-design regions. The design regions are areas in which material can be removed during the design synthesis. Non-design regions are areas where material cannot be removed, usually to keep important geometries intact, and thus the elements in these areas are excluded from the optimization process. The entire component was modeled as one part file with the inclusion of the non-design regions in order to save time when working in OptiStruct. For this TA wheel we have done the following changes with topology optimization. Here mass is taken as the design variable for minimizing the volume. Here the inner side of spokes is considered as design area while the regions comprising the hub contacting face and rim are taken to be non-design region. Four appropriate cases are

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considered to reach the objective. Cornering fatigue test, Radial fatigue test, modal analysis, Impact test and Dynamic stiffness are performed for the two models. Here, frequency above 400Hz for first rim mode; Safety factor of 1.0 for CFT, RFT are taken as minimum considerations. This process is a CAE driven design using topology optimization. Topology Optimization is performed to reduce the mass without affecting its performance.

Fig: Design changes (slot in case4) Results & Discussions On trying different cases with varying dimensions, one model is finally reached at with a total of 5% (350gm) mass reduction without compromising its performance. The wheel on subjection to Cornering Fatigue Test, Radial Fatigue Test, Normal mode analysis, Dynamic stiffness test and impact test, is observed to pass through all the requirements.

Fig: Mass reduction (case by case) In Cornering and Radial fatigue tests, the alloy wheel is observed to have a safety factor of greater than 1.5 which is a very safe value, the minimum requirement for safety factor in case of CFT and RFT being 1.0.

Fig: Safety factor

Item Base Optimized Target

Mass(Kg) 6.73 6.39 (5%↓) Minimum

Freq(Hz) 547 517 >400 Hz

S.F. 2.08 1.54 > 1.5

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On performing the normal mode analysis the first rim mode of the wheel is observed at a frequency of 517Hz. The minimum frequency for a safe run of the wheel being 400Hz, this wheel is confirmed for good performance in modal point of view.

Fig: 1st rim mode frequencies

Dynamic stiffness of the wheel rim is calculated with the inputs from normal mode analysis The dynamic stiffness of rim is calculated to be 6895 kgf/mm. With the dynamic stiffness values of the alloy wheel under consideration are far above the limitation, this wheel is considered to be safe and reliable. The wheel when subjected to impact loading ,safety factor is 1.09, it is confirmed that the alloy wheel under consideration is strong enough to sustain impact loads.

Fig: Impact test simulation Conclusion The alloy wheel, having passed all the tests with proper margin for safety, can be sent for production. Here a mass reduction of 340gm per wheel is achieved which mounts to 1.7kg per car considering the spare wheel. This mass reduction results in two benefits. Decrease in total weight of the car and decrease in cost of production. Optimization techniques help largely in reducing the mass of solid components which results in overall body weight reduction and thus lesser cost. Lesser weight in turn gives better performance and better fuel efficiency. These result in many indirect benefits to mankind which includes conservation of natural resources to some extent, reduction in air pollution and so on.

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ACKNOWLEDGEMENTS We thank our Head of the Department, Mr. Won Sang Lee and all our team members for their continuous support and cooperation throughout the study. REFERENCES 1. SAE J175 Reaffirmed SEP2003 2. www.nafems.com 3. HyperWorks help, topology optimization 4. K.J. Bathe, “Finite Element Procedures in Engineering Analysis”, Prentice-Hall, Inc. 5. Design Guide and Procedures, Hyundai Motor Corporation. 6. Nitin S. Gokhale, “Practical Finite Element Analysis”, Finite To Infinite.