A general method for the modeling of spindle-bearing systems

In this paper we outline a general method that can be used to model spindle assembly, which consists of spindle shaft, angular contact ball bearings and housing. The spindle shaft and housing are modeled as Timoshenko's beam by including the centrifugal force and gyroscopic effects. The bearing is modeled as a standard nonlinear finite element based on Jones' bearing model that includes the centrifugal force and gyroscopic effects from the rolling elements of bearings. By applying cutting forces to the spindle for a given preload, the stiffness of the bearings, contact forces on bearing balls, natural frequencies, time history response, and frequency response functions of the spindle assembly can be evaluated. In the paper we provide details of the mathematical model supported by experimental results obtained from an instrumented test spindle.