Analytical solution of ball-disc oil film capacitance for various lubrication conditions

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Accurately solving the electrical impedance in various conditions is fundamental in monitoring the lubrication conditions of rolling bearings with electrical impedance method. In the present study, an analytical solution using Legendre polynomials for the capacitance of ball-disc contact is proposed, accounting for the clearance, oil reservoir angle, oil-solid contact angle, Hertz deformation, air capacitance, and extending to dynamic oil reservoir. The analytical results show good agreement with the numerical simulation results from finite element model and ball-disc experiment with specific oil reservoirs and dynamic conditions. Parametric studies reveal that the oil reservoir angle, indicating the oil supply condition, should be considered, especially for larger film thickness and fully-flooded lubrication. The capacitance contributed by air should be involved because the dielectric constants of oil and air are generally close, while the effect of contact angle is negligible for common practical conditions.