The study on the position-dependent dynamic characteristics of a vertical ball screw feed system without counterweight is an important step in the enhancement of the structural performance of mini-type vertical milling machines. The ball screw is generally driven by a servomotor, which converts a rotary motion into a linear motion through a screw–nut pair. To assess the position-dependent dynamic characteristics of a vertical ball screw feed system subjected to the influence of the screw–nut joint stiffness, a variable-coefficient lumped parameter model of the system is developed. This model is established taking into account the screw–nut joint stiffness under three different strategies: (1) considering the preload and the weight of the spindle system, (2) considering the elastic deformation but ignoring the effect of the weight, and (3) a perfectly rigid model. The differences between the three models in predicting the position-dependent dynamic characteristics of the system are compared, revealing that the stiffness of screw–nut joint greatly affects the vibratory behavior of the spindle system in the transmission direction. A set of conducted experimental results demonstrate that the stiffness model under the preload and the weight of the spindle system is the most accurate model for the prediction of the position-dependent natural frequency and displacement response of the system with the spindle system position. Therefore, it is more suitable for structure design, performance simulation, and evaluation of a vertical ball screw feed system without counterweight.

No abstract

The distinguishing feature of a vertical ball screw feed system without counterweight is that the spindle system weight directly acts on the kinematic joints. Research into the dynamic characteristics under acceleration and deceleration is an important step in improving the structural performance of vertical milling machines. The magnitude and direction of the inertial force change significantly when the spindle system accelerates and decelerates. Therefore, the kinematic joint contact stiffness changes under the action of the inertial force and the spindle system weight. Thus, the system transmission stiffness also varies and affects the dynamics. In this study, a variable-coefficient lumped parameter dynamic model that considers the changes in the spindle system weight and the magnitude and direction of the inertial force is established for a ball screw feed system without counterweight. In addition, a calculation method for the system stiffness is provided. Experiments on a vertical ball screw feed system under acceleration and deceleration with different accelerations are also performed to verify the proposed dynamic model. Finally, the influence of the spindle system position, the rated dynamic load of the screw-nut joint, and the screw tension force on the natural frequency of the vertical ball screw feed system under acceleration and deceleration are studied. The results show that the vertical ball screw feed system has obviously different variable dynamics under acceleration and deceleration. The influence of the rated dynamic load and the spindle system position on the natural frequency under acceleration and deceleration is much greater than that of the screw tension force.