Closed-form analytical solutions for calculation of loads and contact pressures for roller and ball bearings.pdfVIP

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Closed-form analytical solutions for calculation of loads and contact pressures for roller and ball bearings.pdf

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Closed-form analytical solutions for calculation of loads and contact pressures for roller and ball bearings.pdf

Tribology International 103 (2016) 187–196 Contents lists available at ScienceDirect Tribology International journal homepage: /locate/triboint Closed-form analytical solutions for calculation of loads and contact pressures for roller and ball bearings Jaewon Lee, Jwo Pan n Mechanical Engineering, The University of Michigan, Ann Arbor, MI 48109-2125, United States article info Article history: Received 2 April 2016 Received in revised form 15 June 2016 Accepted 28 June 2016 Available online 29 June 2016 Keywords: Roller load Contact pressure Bearing design Bearing fatigue abstract Closed-form load distribution solutions for calculation of the loads exerted by the rolling elements on the outer raceway in cylindrical and spherical roller bearings under radial loading are proposed. The analytical solutions are derived from the non-conforming contact solution of Hertz and the conforming contact solution of Persson. The maximum pressures due to the maximum loads of the rolling elements calculated from the analytical solutions are within a few percents of the results from the corresponding two-dimensional and three-dimensional ?nite element analyses. A simple method to estimate the fatigue lives of bearings based on the analytical solutions is also presented for engineers to compare the fatigue performance of bearings with different designs. 2016 Elsevier Ltd. All rights reserved. 1. Introduction Bearings are essential components in machines and vehicles allowing relative motions of components with minimal friction. The fatigue lives of bearings in machines and vehicles are expected to outlast the lives of the machines and vehicles themselves. However, large cyclic service loads will tend to shorten the lives of the bearings. For use in vehicles, bearings should be designed to withstand both the constant load due to the vehicle weights and the service loads caused by the operation of vehicles. A bearing should be designed such that the mechanical stresses due to these lo