Comparison of analytic and numeric methods to calculate ball bearing capacitance

The electrical characteristics of rolling bearings become increasingly important. This work examines various methods for calculating the capacitance and contributes to a deeper understanding of the electric behavior of the rolling bearing. The focus is on the peripheral zone outside the Hertzian area of loaded as well as unloaded rolling elements. Semi-analytical approximations and finite element simulations are applied and a closed-form analytical two-dimensional solution is derived for comparison. The rolling contact of radially loaded deep groove ball bearings serves as an application example. The results show that the semi-analytical approximations reproduce the trend from numerical and analytical calculations, but show significant quantitative differences. Particularly the contribution of unloaded rolling elements to the total capacitance has been underestimated so far.