The vibration analysis of the CNC vertical milling machine spindle system considering nonlinear and nonsmooth bearing restoring force

Abstract The performance improvement of the computer numerically controlled (CNC) vertical milling machine is constrained by limited understanding of the dynamic behaviors of the spindle system. In order to study the dynamic characteristics of the CNC vertical milling machine spindle system under unbalanced force, the lumped mass method is applied to propose a novel dynamic model. In this comprehensive model, Hertz contact, radial clearance and time-varying stiffness of rolling bearings are considered. According to the contact behaviors of rolling bearings supporting the spindle, restoring force is a nonsmooth and nonlinear function of displacements and bearing radial clearance. Then, governing differential equations of the eighteen-degree-of-freedom system are derived using the Lagrange equation. In addition, the effectiveness of this dynamic model is verified by experiments. The influences of spindle speed and the bearing parameters on the vibration behaviors and stability of the spindle are analyzed by amplitude-frequency curve, bifurcation diagram, time domain waveform, spectrum diagram, trajectory and Poincare. Moreover, we discussed how the dynamics of the spindle are affected by the eccentricity of the belt pulley, the extended length of the milling tool, and the position of the intermediate bearing set. The research results can benefit the structural design of the spindle, optimize the bearings selection, as well as improve the machining accuracy.