Analytical and numerical analysis of load distribution in a thin walled flexible race ball bearing

Abstract

Flexible race ball bearings (FRB) are generally used in power transmitting for precision drives. The flexion of the FRB provides deformation even at no load condition in case of precision drive. FRB design allows for accurate and smooth movement where low loads, low speed, precise degrees of rotation are necessary, and are mainly used for radial loads. The present research aims to map the load distribution between balls in flexible race bearings by considering the contact deformations at each contact point and the thin walled race deformation. Furthermore, the analysis also shows the effect of race thickness of the bearing on the developed radial stress, deformation and flexibility. Given that all components of the bearing are designed to be elastic, the study aims to provide a comprehensive analysis of these effects. For this purpose, a closed form analytical method is considered assuming a mechanics of solids approach. A 2D numerical model is used to analyze the deformation of the bearing under an applied radial load. A comparative study between analytical and numerical analysis is conducted to provide insight in to the optimal race thickness for minimizing stress and enhancing bearing flexibility and performance. The results of contact forces show the maximum value at 0th ball position are 40.20 and 41.93 N, corresponding to maximum radial deformations of 0.0204 and 0.0189 mm respectively. While showing the effect of flexibility on radial stress, the maximum radial deformation of 0.0207 mm and a radial stress of 182.97 MPa for race thickness of 1.651 mm without failure with static loading is observed. Consequently, the design shows the influence of race thickness when race flexibility is functional, in order to calculate maximum bearing deformation without failure. This study shows an improvement in radial load carrying capacity of flexible race thin walled ball bearing.