Effect of the screw–nut joint stiffness on the position-dependent dynamics of a vertical ball screw feed system without counterweight

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.