Address for Correspondence ¹Professor, Department of Mechanical Engineering, Nehru Institute of Engineering and Technology, Coimbatore

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1 Research Paper A STUDY OF MODELING AND FINITE ELEMENT ANALYSIS OF AUTOMOTIVE VEHICLE WHEEL RIM ASSEMBLY FOR THE DEFORMATION AND VARIOUS STRESS DISTRIBUTION Thangarasu Subramaniam¹, Dhandapani Velliangiri² *, Sureshkannan Gurusamy 3 Address for Correspondence ¹Professor, Department of Mechanical Engineering, Nehru Institute of Engineering and Technology, Coimbatore Professor, Department of Mechanical Engineering, Karpagam College of Engineering, Coimbatore Associate Professor, Department of Mechanical Engineering, Coimbatore Institute of Technology, Coimbatore ABSTRACT This paper which deals with wheel rim modelling and finite element analysis of various stress distribution. When the human race starting to use the log to transport heavy objects. The original wheels were the round slices of a log and it was gradually re in-forced and used in this form for centuries on both carts and wagons. The distribution of stresses from the wheel hub and wheel rim is properly distributed to entire portion of wheel rim. The net result of larger deformation and more stress in a one particular area, due do this failure occur. This failure can be avoided by introducing the wedge band between the hub and rim. During the finite element analysis of the wedge band, the net result of the stress distribution within the standard and recommended value of throughout the wheel rim with minimum deformation. The main objective is to determine the stress distribution and deformation on each part of the wheel rim assembly under radial load condition with linear and non - linear analysis and find out the factor of safety of the wheel rim. KEYWORDS: Vehicle, wheel rim, FEA, Stress distribution, ANSYS simulation. 1.1 INTRODUCTION TO WHEEL RIM The wheel is a device that enables efficient movement of an object across a surface where there is a force pressing the object to the surface. Wheels are components working under a cyclic loading where it heavily undergoes both static loads as well as fatigue loads as wheel rim travels different load profile or terrain. Wheel is defined as a rotating loadcarrying member between the tire and the hub. The main components of a wheel are the rim, the tire, the disc or the spokes. The importance of wheel and tires in the automobile cannot be challenged. Without engine, vehicle may tow but without the wheels, this is not possible. The wheel with tires takes full load condition and reduces friction and provides cushioning effects by absorbing vibration due to road surface unevenness and assist in steering control Literature Review This review deals with the expert members, As discussed by Awoto Y., Ikeda M., Manville S.K. and Nishikawa [1] regarding automotive suspension design and analysis. Bayarakceken H., Tasgetiren S. and Yavuz, Conle F. A. and Chu C I [2, 3] explained about the two cases of failure in the power transmission system of vehicles a universal joint yoke and a drive shaft. Points discussed by Hobbacher A Jiang Y., Hertel O. and Vormwald M [4, 5], Recommendations for fatigue strength of welded components. Experimental evaluation of three critical plane multi axial fatigue criteria. Lagoda L., Macha E. and Nieslony A [6], study about the fatigue life calculation by means of the cycle counting and spectral methods under multi axial random loading. Discussed by E Pedersen M.M, Mouritsen O.Ø., Hansen M.R., Andersen J.G. and Wenderby J [7, 8], Re-analysis of fatigue data for welded joints. Xiaofeng W, Zhao L, Xiaoge Z [8], finite element analysis of a wheel based on the wheel dynamic cornering fatigue test. Ramamurty Raju P, Satyanarayana B, Ramji K, Suresh Badu K [9], study about the Evaluation of fatigue life of aluminum alloy wheels under radial loads. M.V.Prabha and Pendyala veera raju[10,11], explained design and development of aluminum alloy wheels. MacCormack C & Monghan J, Journal of Mater Process Technology. Bil H & Tekkaya A E & Kilic S E, 2D finite element analysis [13], Study about the modeling of Machining A Comparison of Different Approaches with Experiments. As explained about Asnafi N, Vazquez V & Altan [14, 15], design and analysis of wheel rim assembly. 1.2 WHEEL RIM WITH DIMENSIONS 1.3 3D MODEL OF WHEEL RIM Figure 1.1: Assembly of wheel rim Steps: 1. Go to assembly mode in CATIA. Click on existing component icon and click on product in the specification tree. Now select wheel rim base. 2. Wheel rim base is imported. Fix the component. 3. Now get the bead seat band and apply to assemble wheel rim base and bead seat band. 4. Now get the back flange and apply

2 to assemble wheel rim base and bead seat band and back flange. 5. Now get the wedge band and apply to assemble wheel rim base, bead seat band, back flange and wedge band. 1.4 LINEAR STATIC ANALYSIS In linear analysis, the behavior of the structure is assumed to be completely reversible; that is, the body returns to its original deformed state upon the removal of applied loads and solutions for various load cases can be superimposed. The assumptions in linear analysis are: 1) Displacements are assumed to be linearly dependent on the applied load. 2) A linear relationship is assumed between stress and strain. 3) Changes in geometry due to displacement are assumed to be small and hence ignored. 4) Loading sequence is not important and the final state is not affected by the load history. The load is applied in one go with no iterations. 1.5 NON LINEAR STATIC ANALYSIS In many engineering problems, the behavior of the structure may depend on the load history or may result in large deformations beyond the elastic limit. The assumptions/ features in nonlinear analysis are: 1) The load-displacement relationships are usually nonlinear. 2) In problems involving material nonlinearity, the stress-strain relationship is a nonlinear function of stress, strain, and/or time. 3) Displacements may not be small; hence an updated reference state may be needed. 4) The behavior of the structure may depend on the load history; hence the load may have to be applied in small increments with iterations performed to ensure that equilibrium is satisfied at every load increment. 1.6 ANALYSIS OF WHEEL RIM The wheel rim modeled in CATIA is saved as an.iges file. It is then imported into ANSYS using the import file command. The import file command in ANSYS can import models from CATIA in the.iges file mode. The element type used for the model is chosen as 8 nodded tetra elements from ANSYS element menu. The model is then assigned the material properties like Young s Modulus (E=2.1X10 5 N/mm 2 ), Poisson s ratio (µ=.33) and Density of steel (ρ=7.85xe -6 N/mm 2 ). The meshing is done with the mesh tool option in ANSYS. The total number of elements created as a result of the meshing process is Then the loading and the boundary conditions are applied to the model. The model is restrained in all degrees of freedom. 1.7 LINEAR ANALYSIS A linear FEA analysis is undertaken when a structure is expected to behave linearly, i.e. obeys Hook s Law. The stress is proportional to the strain, and the structure will return to its original configuration once the load has been removed. A structure is a load bearing member and can normally be classified as a bar, beam, column, or shaft. Geometry: Figure 1.2: Geometry of wheel rim The model created in CATIA is imported to ANSYS. 1.7 MESHING: Figure 1.3: Wheel rim after meshing Now, the model is meshed. LOADING: Figure 1.4: Wheel rim after application of load Rotational velocity 0.275rad/sec is applied at the center of wheel rim and the pressure 0.395Mpa is applied to EQUIVALENT STRESS: Figure 1.5: Equivalent stress at wheel rim Equivalent stress at the wheel rim is mpa maximum and mpa minimum. TOTAL DEFORMATION: Figure 1.6: Total deformation of wheel rim Maximum deformation at the wheel rim is mm and minimum deformation is mm. 1.8 Non Linear Analysis A non-linear FEA is used to predict the behavior of a structure that is loaded beyond the elastic limits of the material of interest. The structure experiences Plastic deformation and will not return to its original configuration or shape.

3 GEOMETRY: Figure 1.7: Geometry The model created in CATIA is imported to ANSYS and spring is inserted between wheel rim center to road surface to find out stiffness and critical damping. MESHING: The deformation takes place in Z-Direction is mm maximum and mm minimum. Calculation Material Properties Table 1.1: Material properties Structured steel grade Material used II C1002 BEML standard Yield strength 350MPa Tensile strength 540MPa Modulus of elasticity 2X10 5 N/mm Density 7850 Kg/m 3 Mass and mass distribution: Net Vehicle Mass 74,000kg Rated Pay Load 91,500kg Gross Vehicle Mass 1, 65,500kg Table 1.2: Mass distribution Mass Distribution Empty Loaded Front Axle, kg 34,780 54,450 Rear Axle, kg Free body diagram: W = KN (47%) 39,220 (53%) (33%) 1,11,050 (67%) Figure 1.8: Wheel rim after meshing Now, the model is meshed. LOADING: Figure 1.9: Wheel rim with loading Loads are applied at the center of the wheel rim and it is acting downwards and at the road and is acting upward. EQUIVALENT STRESS: H=0 V=0 Resolving Vertical Forces: R B X =0 R B X3720 = R B = R B = KN To find R A : R A +R B = 0 R A = R A = KN DIAGRAM: Figure 2.0: Wheel rim with loading Equivalent stress at the wheel rim is Mpa maximum and Mpa minimum. Directional deformation: Figure 2.1: Total deformation Gross vehicle mass of the dump truck is kg and it is acted at the centre of the axle the rear axle carries 67% of the load when it is fully loaded. So R B = X0.67 R B = kg Two wheel on each side of the wheel end so divide by 2. R B = R B = kg R B = X9.81 R B = N TO FIND VELOCITY: The maximum speed of the BH100 ton rear dump truck is 60km/hr

4 N = 60km/hr N = m/sec V = 16.67m/sec AREA OF THE WHEEL RIM: Area = Area of (wedge band + rim base + bead seat band + back flange) Area = Area = mm 2 TO FIND PRESSURE: P =... (6.1) Curve 1.2: Fatigue: Stress Vs Time P = P = 0.395N/mm 2 TO FIND THE ROTATIONAL VELOCITY: V = R... (6.2) = = = rad/sec TO FIND THE STIFFNESS (K): F = K... (1.1) Curve 1.3: Cyclic Load Where K is stiffness, F = load, = displacement, minimum displacement assumed is 50mm N/mm TO FIND CRITICAL DAMPING (C C ): C c = 2... (1.2) C c = 2 C c = N-s/mm TO FIND STIFFNESS (K):... (1.3) Where = 80mm assumed maximum displacement of tire N/mm Find the factor of safety: Yield strength of the material is 350Mpa Working stress of the material is Mpa FOS = 350 / 64 FOS = 5.4 Dump trucks are heavy structure, so according to standard the FOS should be 1. For static analysis the factor of safety should be more than 4 2. For dynamic analysis the factor of safety in between 1.5 to 2.5 The factor of safety should be above four so the wheel rim is safe. Curve 1.1: Deformation and stress distribution Curve 1.4: S N curve CONCLUSION This paper was discussed about the linear and non linear finite element analysis of wheel rim assembly was carried out by using FEA package. The 3D model of wheel rim assembly was designed and created by using CATIA software. Then the 3D model was imported into ANSYS in IGES format. The analysis was performed in a static condition. The model is constrained in all degree of freedom and boundary and loading conditions are applied on the wheel rim. In linear finite element analysis, the obtained total deformation of wheel rim is mm and the obtained maximum equivalent stress is Mpa. In non linear finite element analysis, the obtained equivalent stress at the wedge band is Mpa and the obtained equivalent stress at the wheel rim is Mpa. So the stress at the wedge band is equally distributed to all parts of the wheel rim. The obtained working stress from the analysis is Mpa and deformation 27.3 mm. The obtained factor of safety from the analysis is 5.4 for the structured steel grade II material. According to ISO standard for static analysis FOS should be more than 4 and for dynamic analysis FOS should be lies 1.5 to 2.5. So the wheel rim is safe. REFERENCES 1. Awoto Y., Ikeda M., Manville S.K. and Nishikawa A. Automotive suspension design and analysis, Engineering Failure Analysis, Vol. 15 pp , Bayarakceken H., Tasgetiren S. and Yavuz I. Two cases of failure in the power transmission system of vehicles a universal joint yoke and a drive shaft, International Journal of Engineering Failure Analysis, Vol. 14, pp , 2007.

5 3. Conle F. A. and Chu C, Fatigue Analysis of Local Stress strain Approach in Complex Vehicular Structures, Inter J of Fatigue, Vol. 19, pp , Hobbacher, Recommendations for fatigue strength of welded components, Inter J of Fatigue, Vol. 31, pp , Jiang Y., Hertel O. and Vormwald M., A Experimental evaluation of three critical plane multi axial fatigue criteria, International Journal of Fatigue Analysis, Vol.29, pp , Lagoda L., Macha E. and Nieslony A., Fatigue life calculation by means of the cycle counting and spectral methods, Fatigue and Fracture of engineering materials and structures, Vol. 28, pp , Pedersen M.M, Mouritsen O.Ø., Hansen M.R., Andersen J.G. and Wenderby J., Re-analysis of fatigue data for welded joints using the notch stress approach, International Journal of Fatigue, Vol. 32, pp , Xiaofeng W, Zhao L, Xiaoge Z, (2007) Finite element analysis of a wheel based on the wheel dynamic cornering fatigue test, volume 34, number Ramamurty Raju P, Satyanarayana B, Ramji K, Suresh Badu K, (2007) Evaluation of fatigue life of aluminum alloy wheels under radial loads. Failure analysis, volume 14, page M.V.Prabha and Pendyala veera raju, Department of Mechanical, Godavari institute of engineering college, Rajahmundry, A.P, India. December 2012 Design and development of aluminum alloy wheels. 11. Kobayashi S & Oh S I & Altan T, Metal forming and the finite element method (Oxford University Press), MacCormack C & Monghan J, J Mater Process Technol, 117 (2001) Bil H & Tekkaya A E & Kilic S E, 2D Modeling of Matchining : A Comparison of Different Approaches with Experiments, 14. Asnafi N, Engineering Failure Analysis,6 (1999) MacCormack C & Monaghan J, Journal of Mater Process Technology, 118(2001)