On the Free Vibration Modeling of Spindle Systems: A Calibrated Dynamic Stiffness Matrix

Abstract

The effect of bearings on the vibrational behavior of machine tool spindles is investigated. This is done through the development of a calibrated dynamic stiffness matrix (CDSM) method, where the bearings flexibility is represented by massless linear spring elements with tuneable stiffness. A dedicated MATLAB code is written to develop and to assemble the element stiffness matrices for the system’s multiple components and to apply the boundary conditions. The developed method is applied to an illustrative example of spindle system. When the spindle bearings are modeled as simply supported boundary conditions, the DSM model results in a fundamental frequency much higher than the system’s nominal value. The simply supported boundary conditions are then replaced by linear spring elements, and the spring constants are adjusted such that the resulting calibrated CDSM model leads to the nominal fundamental frequency of the spindle system. The spindle frequency results are also validated against the experimental data. The proposed method can be effectively applied to predict the vibration characteristics of spindle systems supported by bearings.