Comparison of Loading Functions in the Modelling of Automobile Aluminium Alloy Wheel under Static Radial Load
Affiliation(s)
1 Mechanical Engineering Department, Ambrose Alli University, Ekpoma, Nigeria. 2 Mechanical Engineering Department, University of Ibadan, Ibadan, Nigeria.
1 Mechanical Engineering Department, Ambrose Alli University, Ekpoma, Nigeria. 2 Mechanical Engineering Department, University of Ibadan, Ibadan, Nigeria.
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 0.3, 0.15 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 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 13 and 12MPa respectively. The CLF, BLF and the Sherwood values are the same at about 6 and 3 MPa at 0.15 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, hence 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.
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 0.3, 0.15 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 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 13 and 12MPa respectively. The CLF, BLF and the Sherwood values are the same at about 6 and 3 MPa at 0.15 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, hence 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.
Cite this paper
Igbudu, S. and Fadare, D. (2015) Comparison of Loading Functions in the Modelling of Automobile Aluminium Alloy Wheel under Static Radial Load. Open Journal of Applied Sciences, 5, 403-413. doi: 10.4236/ojapps.2015.57040.
Igbudu, S. and Fadare, D. (2015) Comparison of Loading Functions in the Modelling of Automobile Aluminium Alloy Wheel under Static Radial Load. Open Journal of Applied Sciences, 5, 403-413. doi: 10.4236/ojapps.2015.57040.
References
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http://dx.doi.org/10.1016/j.engfailanal.2008.12.010 [13] Baeumel, A. and Seeger, T. (1990) Materials Data for Cyclic Loading. Elsevier Service, Amsterdam. [14] Shang, R., Li, N., Altenhof, W. and Hu, H. (2004) Dynamic Side Impact Simulation of Aluminium Wheels Incorporating Material Property Variations, Aluminum. The Minerals, Metals & Materials Society. [15] Blake, A. (1990) Practical Stress Analysis in Engineering Design. McGraw-Hill, New York, 363-367. [16] Wang, X.F. and Zhang, X.G. (2010) Simulation of Dynamic Cornering Fatigue Test of a Steel Passenger Car Wheel. International Journal of Fatigue, 32, 434-442. [17] Reipert, P. (1985) Optimization of an Extremely Light Cast Aluminum Alloy Wheel Rim. International Journal of Vehicle Design, 6, 509-513. [18] Mizoguchi, T., Nishimura, H., Nakata, K. and Kawakami, J. (1982) Stress Analysis and Fatigue Strength Evaluation of Sheet Fabricated 2-Piece Aluminum Alloy Wheels for Passenger Cars. Research & Development, 32, 25-28. [19] Sakyaan, V. and Lectuere, G. (2006) Note on Theory of Elasticity. Department of Mechanical Engineering, Federal University of Technology, Minna. [20] Sherwood, J.A. and Fussel, B.K. (1995) Study of the Pressure on an Aircraft Tire-Wheel Interface. Journal of Aircraft, 32, 921-928.
[1] Mohd, I.B.B. Simulation Test of Automotive Alloy Wheel Using Computer Aided Engineering Software. http://umpir.ump.edu.my/143/11. 31/03/11 [2] Stearns, J.C. (2000) An Investigation of Stress and Displacement Distribution in Aluminium Alloy Automobile Rim. PhD Thesis, University of Akron, Akron. [3] Garrett, T.K., Newton, K. and Steeds, W. (2000) Chapter 41 Wheels and Tyres. Journal of Motor Vehicle, 13, 1085- 1108. http://dx.doi.org/10.1016/B978-075064449-5/50042-0 [4] Kruse, G. and Mahning, F.A. (1976) Comprehensive Methods for Wheel Testing by Stress Analysis. SAE Tecnical Paper Series # 760042. http://dx.doi.org/10.4271/760042 [5] Muhammet, C. (2010) Numerical Simulation of Dynamic Side Impact Test for an Aluminium Alloy Wheel. Scientific Research and Essays, 5, 2494-2710. [6] Raju, R., Satyanrayana, B., Ramji, K. and Suresh, B.K. (2007) Evaluation of Fatigue Life of Aluminium Alloy Wheels under Radial Loads. Engineering Failure Analysis, 14, 791-800. http://dx.doi.org/10.1016/j.engfailanal.2006.11.028 [7] JISD 4103 (1989) Japanese Industrial Standard. Disc Wheel for Automobiles. [8] Kocabicak, U. and Firat, M. (2001) Numerical Analysis of Wheel Cornering Fatigue Tests. Engineering Failure Analysis, 8, 39-54. http://dx.doi.org/10.1016/S1350-6307(00)00031-5 [9] Tonuk, E., Samim, Y. and Unlusoy, Y. (2001) Pediction of Automobile Tire Cornering Force Characteristics by Finite Element Modelling Analysis. Computers, 1219-1232. [10] Carvalho, C., Voorwald, H. and Lopes, C. (2001) Automobile Wheels—An Approach for Structural Analysis and Fatigue Life Prediction. SAE Paper No. 2001-01-4053. [11] Kouichi, A. and Ryoji, I. (2002) Shortening Design and Trial Term for Aluminium Road Wheel by CAE. Casting Technology, 74, 533-538. (In Japanese) [12] Chang, C.-L. and Yang, S.-H. (2009) Simulation of Wheel Impact Test Using finite Element Method. Engineering Failure Analysis, 16, 1711-1719.
http://dx.doi.org/10.1016/j.engfailanal.2008.12.010 [13] Baeumel, A. and Seeger, T. (1990) Materials Data for Cyclic Loading. Elsevier Service, Amsterdam. [14] Shang, R., Li, N., Altenhof, W. and Hu, H. (2004) Dynamic Side Impact Simulation of Aluminium Wheels Incorporating Material Property Variations, Aluminum. The Minerals, Metals & Materials Society. [15] Blake, A. (1990) Practical Stress Analysis in Engineering Design. McGraw-Hill, New York, 363-367. [16] Wang, X.F. and Zhang, X.G. (2010) Simulation of Dynamic Cornering Fatigue Test of a Steel Passenger Car Wheel. International Journal of Fatigue, 32, 434-442. [17] Reipert, P. (1985) Optimization of an Extremely Light Cast Aluminum Alloy Wheel Rim. International Journal of Vehicle Design, 6, 509-513. [18] Mizoguchi, T., Nishimura, H., Nakata, K. and Kawakami, J. (1982) Stress Analysis and Fatigue Strength Evaluation of Sheet Fabricated 2-Piece Aluminum Alloy Wheels for Passenger Cars. Research & Development, 32, 25-28. [19] Sakyaan, V. and Lectuere, G. (2006) Note on Theory of Elasticity. Department of Mechanical Engineering, Federal University of Technology, Minna. [20] Sherwood, J.A. and Fussel, B.K. (1995) Study of the Pressure on an Aircraft Tire-Wheel Interface. Journal of Aircraft, 32, 921-928.