Estimation of Axial Displacement in High-speed Spindle Due to Rotational Speed

This paper presents an estimation procedure for axial displacement in spindle equipped with angular contact ball bearings due to rotational speed. High-speed spindle-bearing system experiences axial displacement due to thermal expansion and rotational speed-dependent characteristics of angular contact ball bearings. This paper deals with the axial displacement caused by the rotational speed-dependent effects such as centrifugal force and gyroscopic moments. To this end, a bearing dynamic model is established that includes all the static and dynamic properties of angular contact ball bearing. An analytical formula to calculate the axial displacement based on contact angles between ball and races is derived to discuss the physics regarding the axial displacement in spindle. The proposed dynamic model is compared with a reference and a commercial program. Numerical examples are presented to show the effects of centrifugal force and gyroscopic moment on the axial displacement. The proposed model is also validated with an experimental result.