Dynamics analysis of a slender ball

For a slender ball-screw feed system, the position of the screw–nut joints will change greatly when the moving worktable moves along its whole stroke. Therefore, the compression/tension and torsion stiffness of the screw-shaft on both sides of the screw–nut joints will change. Thus, the system transmission stiffness will also vary and affect its dynamics. In this article, considering the changes of the worktable position and using hybrid element method, a dynamic model was established for the slender ball-screw feed system, and a calculation method of the system stiffness and mass matrix was provided. The experiments on the slender ball-screw feed system with different positions were also performed to verify the proposed dynamic model. Finally, the influences of length, screw-tension force, pitch, nominal diameter of screw and rated dynamic load of screw-nut joints on the slender ball-screw feed system’s natural frequency along its whole stroke were studied. The results showed that the slender ball-screw feed system possesses obvious position-dependent variable dynamics along its whole stroke; the ratio of length to diameter of the screw (Lf/d0) would be better designed smaller than 50 in order to obtain the relative uniformity of the system dynamics when manufacturing large machine tools