Comparison of Loading Functions in the Modelling of Automobile Aluminium Alloy Wheel under Static Radial Load

Abstract

Formulation of exact loading function for radial loading situation has been a major challenge in wheel modeling. Hence, approximate loading functions such as Cosine, Boussinesq, Eye-bar, Polynomial, Hertzian etc., have been developed by different researchers. In this paper, analysis of different loading functions—Cosine (CLF), Boussinesq (BLF) and Eye-bar (ELF) at deferent inflation pressure of 0.3MPa, 0.15 MPa and 0 MPa at specified radial load of 4750N is carried out on a selected aluminium with ISO designation (6JX14H2; ET 42). The 3-D computer model of the wheel is generated and discretised into 3785 hexahedral elements and analysed with Creo Elements/Pro 5.0. Loading angle of 90 degree symmetric with the point of contact of the wheel with the ground is used for ELF, while 30 degrees contact angle is employed for both CLF and BLF. Von Mises stress is used as a basis for comparison of the different loading functions investigated with the experimental data obtained by Sherwood et al while the displacement values (as obtained from the FEM tool) are used as a basis for comparison of the different loading functions, as displacement is not covered by Sherwood et al. Results show that at 0.3MPa inflation pressure, the maximum stress value of CLF approaches the Sherwood value of about 14 MPa and that the CLF function values coincide with Sherwood values at three points along the curve, with values of about 13.8 MPa, 13 MPa and 6.4 MPa at about 0 degree, 15 degree and 20 degree respectively. The BLF value coincides with the Sherwood value at about 18 degree with a magnitude of about 10.6 MPa, while ELF equals the Sherwood value at magnitude of about 6.2 MPa at about 22 degree. At 0.15 MPa and 0 MPa inflation pressure, values CLF, BLF and ELF deviate significantly from the Sherwood values (due to under inflation) with the maximum CLF stress value approaching a value of about 13MPa and 12MPa respectively. The CLF, BLF and the Sherwood values are the same at about 6 MPa and 3 MPa at 0.15 MPa and 0 MPa inflation pressure respectively. The displacement values for ELF are lesser than those of CLF and BLF for all range of values. The different loading functions values being equal the Sherwood values (used as refernce) at different points, with the CLF having more coincident points along the curve. Higher stress and displacement magnitudes are clustered between 0 degree and about 35 degree. Although, the CLF and BLF offer greater stress and displacement values than ELF, it is of the view that the type of loading function adapted for any analysis depends on the type of tyres to be fitted on the wheel. CLF and BLF offers greater prospect for non run flat tyres, while ELF is most suited for run flat tyres. In all cases the right inflation pressure as specified by the tyre manufacture should be employed in any analysis.