Dynamic Analysis of a Rotating Shaft Subject to the Double Cutting Force and Time-varying Mass Effects of the Rod

This paper investigates the dynamic behaviors of a rotating shaft subjected to the double cutting force and time-varying mass effects. The Timoshenko beam theory is used to model the rotating shaft, and the general boundary condition is assumed as the clamped-hinged supports. This system is used to simulate the manufacture process of the double turret CNC lathes, and the mass of the rod which is reduced gradually in cutting process. The system equations of motion are derived based on the global assumed mode method, and the dynamic responses of the system are obtained by Runge-Kutta numerical method. The transformation matrix is derived to make the equation of motion completing the boundary geometric constraints. The numerical results compare the dynamic response in different moving speeds and skew angles of the cutting forces with/without the time-varying mass effects. Additionally, this paper compares the response with single cutting force and double force. The results show that the double moving force system can reduce not only the machining time but also the amplitude of shaft vibration.