Dynamics analysis on the MDOF model of ball screw feed system considering the assembly error of guide rails

The dynamics of the ball screw feed system is very important in high-precision machining of CNC machine tools. However, the existing literatures rarely study the dynamic behaviors of the coupled feed system and didn't take the influence of the assembly error of the guide rails into consideration. Because the stiffness of the feed system is mainly affected by the ball screw, linear guide and ball bearings, this paper presents the fourteen degree-of-freedom dynamic model of the feed system by deriving the nonlinear restoring force functions of the screw nut, linear guide and ball bearings and the screw shaft's stiffness. An algorithm of combining the Newmark Method and the Monte Carlo simulation is proposed to numerically solve for the vibration responses of the feed system, and the proposed dynamic model is experimentally verified. Based on the established dynamic model, the effects of the excitation amplitude, system parameters and assembly error on the dynamic characteristics of the feed system are discussed by means of the amplitude-frequency curve and 3-D frequency spectrum, which demonstrate that the vibration responses of the feed system for the fourteen degrees of freedom influence each other, and the assembly error affects the nonlinear dynamic characteristics of the feed system.