Thermally affected stiffness matrix of angular contact ball bearings in a high-speed spindle system

Abstract

Bearing stiffness directly affects the dynamic characteristics in a high-speed spindle system and plays an important role in terms of manufacturing quality. We developed a new approach for predicting the thermal behavior of a high-speed spindle, calculated the thermal expansion, and generated a bearing stiffness matrix for angular contact ball bearings. The heat convection of spindle housing in air, the balls in lubricant, the spindle shaft in quiescent air, and the bearing inner ring surfaces were determined. Heat sources such as bearing friction, and the heat contributed by the built-in motor, were simulated using an analysis systems (ANSYS) steady-state thermal model. The results were imported into a static ANSYS structural model. Ball thermal expansion was calculated based on changes in the coordinates of nodal points on the ball surface. Finally, a thermally affected bearing stiffness matrix was generated by applying the Newton–Raphson technique. Decreases in the bearing radial, axial, angular, and coupling stiffness values as rotational spindle speed increased were calculated. Also, the stiffness coefficients at a specific speed increased significantly caused by the thermal effects. Finally, for validation, the bearing stiffness was compared to that calculated using an earlier thermal network approach.