Explicit solution of ball-disc oil film capacitance and its extensions

An explicit analytical method is proposed for calculating oil film capacitance in ball-on-disc systems based on the potential distribution of an eccentric spherical shell. The method is versatile, extending to a range of complex scenarios such as air capacitance, Hertz deformation in EHD lubrication condition, cylinder-disc line contact, and lubricant-film resistance in conductive lubricants. The extended models are validated against FEM simulations, showing high accuracy and flexibility across a wide range of conditions. Experiments using a custom ball–ring–disc setup further validate the capacitance model. The framework also accommodates asymmetric oil-reservoir geometries under dynamic rolling–sliding conditions. This work provides a unified and efficient approach for real-time estimation of capacitance and resistance, offering a robust tool for electrical monitoring of lubrication performance.