Capacitance calculation of unloaded rolling elements -- Comparison of analytical and numerical methods

TL;DR

This paper compares analytical, semi-analytical, and numerical methods for calculating the capacitance of unloaded rolling elements in bearings, highlighting the accuracy and limitations of each approach.

Contribution

It introduces a new semi-analytical method that improves capacitance estimation for unloaded point contacts and compares multiple existing methods.

Findings

Semi-analytical approximation overestimates capacitance compared to numerical simulations.

Effective radii method captures trend but lacks accuracy.

New semi-analytical approach yields better results for point contacts.

Abstract

Various methods for calculating the capacitance of unloaded rolling elements are compared to improve the electric characterization of rolling element bearings. Semi-analytical approximations and finite element simulations are applied and a closed-form analytical two-dimensional solution is derived for comparison. The results show that the most common semi-analytical approximation, which uses effective radii to express the contact geometry, reproduces the trend from numerical and analytical calculations, but overestimates the results derived from numerical simulations. Another semi-analytical approach is presented that delivers better results for the capacitance of unloaded point contacts.