The vibration frequency analysis of the screw feeding system with spring supports

Ball screw feeding system has wide application in machine tools, and its dynamic research is very important. The drive screw can be seen as a rotating Timoshenko beam under the pre-tension force. Considering the bearing stiffness, the boundary condition of the screw is spring supported. Also, considering the contact deformation between the screw and the worktable and the worktable moving, the screw is added an intermediate moving spring-mass system. Using boundary conditions and continuity conditions, the lateral and longitudinal frequency equations of the screw feeding system are derived considering the effect of gyroscope, the pre-tension force, the bearing stiffness, the contact between the worktable and the screw and the moving of the worktable. The effect of the system parameters on the natural frequency is studied. The diameter, the pre-tension force, the bearing stiffness, the contact stiffness and the rotational speed of the screw have effect on the vibration frequency and the frequency varies when the worktable moves along the screw from the left to the right end. This work supplies a base for designing the drive system to avoid resonance and to improve the stability of the system.