On the effects of bearing settings on the dynamic performance of a three-bearing machine tool spindle assembly

An analytical investigation of the response characteristics of a spindle unit supported by three angular contact ball bearings is presented in this paper. A general system of equations is presented utilizing the Hertzian equation for representing the non-linear elastic deformation of the rolling elements. The system of non-linear ordinary differential equations is integrated using the Runge-Kutta Fehlberg technique in Matlab. The model is used to study the effects of bearing settings and preload on the variable-compliance vibrations. The study shows that a three-bearing spindle is characterized by a beat-type mode of response with families of sidebands around the main frequency components. The modulations of the carrier and the spacing of the sidebands are shown to be affected by change in the bearing settings. This type of response is not evident in the conventional two- or four-bearing spindle units.