Vibration analysis of a high-speed spindle under the action of a moving mass

The dynamic response of a high-speed spindle subject to a moving mass is studied. The system under investigation consists of a ball screw and a moving nut; both of which are key components of a high-speed feed drive system for a machine tool. The ball screw is modelled as a high-speed rotating shaft using Timoshenko beam theory and the nut is modelled as a moving concentrated mass. The system dynamic equation and the corresponding transient response are obtained through Lagrangian approach and Runge–Kutta method, respectively. Influences of parameters on the transient response of the system such as the mass moving speed, the Rayleigh coefficient and the mass ratio are discussed. Results show that the inertia effect caused by the moving nut influences the deflection in the orthogonal direction of the moving nut much more than that in the transverse direction. The maximum deflection in the orthogonal direction under the moving nut could be several times larger than that under the equivalent force for a short and stubby rotating shaft. Moreover, the moving nut reduces the critical frequencies of the spindle. Therefore, the critical frequencies of a ball screw could be seriously overestimated if the ball screw system is modelled either as a shaft subjected to a moving force or as a shaft alone with the moving nut excluded.