Thermal Conductance Correlations of Static Lubricated Ball Bearings

Abstract Ball bearings are commonly used to reduce the friction in rotating mechanical components. The present work reports improved numerical approaches to model bearing thermal conductance in the absence of convection. We start by modeling the thermal pathway across a single ball-to-race pathway for a simplified geometry, an azimuthally symmetric ball in contact with a flat surface (ball-on-flat). A first-principles approach is used to calculate the static lubricant meniscus shape using a custom-developed Python code. We apply the finite element method (FEM) to extract total thermal conductance of the lubricated ball-on-flat system. Using similar methods, we also present a three-dimensional numerical model of the lubricant meniscus in a static angular contact ball bearing section (ball-on-race). By generating thermal conductance correlations for Yovanovich's classic lubricated model and two- and three-dimensional multiphysics models, we enable facile comparisons among the models and also identify four- and six-parameter correlations with improved fidelity of the meniscus and three-dimensionality. To compare them, parametric studies are conducted to illustrate the effect of lubricant volume and applied load on the total thermal conductance for each model and correlation. The hierarchical methodology reported here improves both the fidelity of tribo-thermo-mechanical modeling and establishes a reference for the accuracy of commonly used geometric approximations for thermal transport in spacecraft ball bearings.