Evolution of lower-order vibration mode of the slender ball screw feed system

Dynamic performance characterized by lower-order natural frequency and lower-order vibration mode is vital for the dynamic positioning accuracy of the ball screw feed system. This paper focuses on the evolution between the lateral vibration mode and the axial vibration mode of the slender ball screw feed system (SBSFS). Firstly, it is proved the first-order vibration mode transformation of the SBSFS is subject to the position of the nut based on an elastodynamic model. This model is established using substructure synthesis method considering the axial, torsional, and lateral deformation of the screw simultaneously through dealing with the screw as Timoshenko Beam elements. By comparing with the experimental results, the validity and accuracy of the established dynamic model are verified. The effects of the stiffness of the kinematic joints on the dynamic performance of SBSFS are then analyzed. The results demonstrate that the dynamic behavior evolution of the SBSFS undergoes the coupling effects from the kinematics joints' stiffness. Furthermore, a dynamic index (R-SP) is proposed considering the evolution of the first-order vibration mode. On the basis of R-SP, three optimization schemes are illustrated. The results show that the R-SP can be used to evaluate the dynamic performance of the SBSFS considering the vibration mode.