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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 94
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
Edited by: B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru and M.L. Romero
Paper 81

Mathematical Modelling of Load and Stress Distribution in a Ball Bearing

T. Lazovic, A. Marinkovic, N. Trisovic and C. Mitrovic

Faculty of Mechanical Engineering, Belgrade University, Serbia

Full Bibliographic Reference for this paper
T. Lazovic, A. Marinkovic, N. Trisovic, C. Mitrovic, "Mathematical Modelling of Load and Stress Distribution in a Ball Bearing", in B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru, M.L. Romero, (Editors), "Proceedings of the Seventh International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 81, 2010. doi:10.4203/ccp.94.81
Keywords: ball bearing, load distribution, stress distribution, mathematical model.

Summary
The ball bearings are the most common and important machine elements of almost all forms of rotating machinery. The reliability and service life of rotating machines depends on the reliability and service life of applied ball bearings. Ball bearing performance, as well as its service life depends on the load distribution between rolling elements [1].

The load distribution is a basic input in mechanical and mathematical modelling with the purpose of analysis of machine parts under operating conditions from different aspects: durability, stiffness, reliability and stability [2]. The modelling of load distribution is a very important and difficult task.

The mathematical model developed in this paper establishes a correlation between elastic deformations of the bearing contacting parts, internal radial clearance and external radial load and their influence on load distribution between balls.

In load transfer from the shaft to the housing, the ball engagement is unequal. The degree of inequality of the external load transfer depends on external load, contact stiffness of the bearing parts, accuracy of their sizes and form and internal radial clearance. The factor of load distribution between balls shows the degree of participation of each ball in an external load transfer through the bearing [3]. The load distribution factor is the ratio between contact load transferred by ball and external radial load. This factor is the original value which considers all relevant influences on the load distribution in the rolling bearing: bearing internal geometry (dimensions of ball and raceways, number of rolling elements, internal radial clearance) and external load [4]. The mathematical model developed can be also applied to cylindrical roller bearings [5].

Based on the load distribution factor the expression for contact stress between balls and raceways is derived. Based on the finite element analysis a new mathematical model of load and stress distribution presented in this paper can be successfully verified [6].

References
1
T. Lazovic, R. Mitrovic, M. Ristivojevic, "Influence of internal radial clearance on the ball bearing service life", 3rd International Conference Power Transmissions '09, Chalkidiki, Greece, 2009.
2
T.A. Harris, "Rolling Bearing Analysis", John Wiley and Sons, New York, 1984.
3
T. Lazovic, M. Ristivojevic, R. Mitrovic, "Mathematical model of load distribution in rolling bearing", FME Transactions, 36, 189-196, 2008.
4
T. Lazovic, "Influence of internal radial clearance of rolling bearing on load distribution between rolling elements", J. of Mechanical Engineering Design, 4(1), 25-32, 2001.
5
T. Lazovic, R. Mitrovic, M. Ristivojevic, "Load distribution between rolling elements of ball and roller bearings", Proceedings of 3rd International Conference Research and Development in Mechanical Industry - RADMI'03, Herceg Novi, 1807-1810, 2003.
6
A. Marinkovic, T. Lazovic, "Modelling and simulation of rolling bearings using advance software tools", 6th Vienna Conference on Mathematical Modelling - MATHMOD 09, Vienna, Austria, 2009.

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