Effects of spindle speed-dependent dynamic characteristics of ball bearing and multi-modes on the stability of milling processes

To predict the stable cutting regions of high speed milling, one needs to know the frequency response function of tool tip, which is usually obtained by the modal test or finite element from a static spindle. The dynamic characteristics of high speed spindle which is commonly supported by ball bearing, however, change dramatically during high speed rotation. In this paper, the speed dependent dynamic characteristics of ball bearings are investigated and the speed-dependent variable bearing stiffness's are determined. By considering the effects of speed-dependent dynamic characterisitics, and then the influences on the modal parameters of tool tip, a set of differential equations with variable mass, stiffness, and damping is set up to describe the dynamics of a multiple mode milling system in two orthogonal directions. Semi-discretization method is used to determine the stability boundaries related to chatter. Results indicate that the effects of variable bearing stiffness and higher order modes of spindle cannot be ignored to predict the stability of the milling processes.