Tribological Models for Advanced Ball Bearing Simulation

Abstract

Advanced ball bearing simulations require the use of accurate tribological models, starting with the calculation of the ball-race contact load and pressure in potentially truncated contacts. Ball—cage and cage—guiding ring contact stiffness models are suggested using the Hertzian contact stiffness and/or a structural stiffness. The central ball-race film thickness, a hydrodynamic rolling force, and normal load increase are calculated using relationships respecting miscellaneous lubrication regimes, including iso-viscous-rigid or piezo-viscous-elastic. A drag force acting at the ball center is included, and its magnitude discussed for claiming that the contribution from drag to the final rolling resistance is smaller than the one from hydrodynamic rolling acting at the ball-race contact. The central film thickness and sliding speed are used for defining shear rate, shear stress, and, hence, final sliding force, using a nonlinear visco-elastic-plastic lubricant rheological model including viscosity, elastic lubricant shear modulus, and limiting shear stress, which are all functions of the pressure and temperature. Elastic effects are approximated using a simple nonlinear visco-plastic model with apparent viscosity. The temperature is defined as the sum of the operating temperature and several other sources of temperature increase. It is observed that when adopting Roelands viscosity model and a simple nonlinear visco-plastic model, the final lubricant traction coefficient and its gradient with respect to sliding speed decrease as the rolling speed increases, mostly reducing the need for a lubricant elastic shear modulus. Appropriate experimental results are highlighted to support these analytical models.

Keywords:

• Rolling bearings
• ball bearings
• EHL
• traction
• rolling friction

Acknowledgements

The authors would like to thank Smart Manufacturing Technology for permission to publish this work, in particular, Paul Langlois and Tom Harvey who provided useful discussions and support for this project.