Abstract This study presents an innovative transmission model to investigate the nonlinear dynamic interaction between friction and backlash in a feed drive system. The model consists of two equivalent masses, dual LuGre friction models, and a spring element to represent the elastic characteristics between the two masses. The ball screw drive system comprising a motor, screw, and table is divided into two subsystems: the motor-screw and the screw-table. Each subsystem is modeled using an equivalent mass and a LuGre friction model, while the elastic coupling between the two masses is represented by a linear spring. The LuGre model is employed to simulate the nonlinear behavior at the contact surfaces, and backlash is represented as the elastic deformation of the spring within the feed drive system. The contact mechanism between the two masses is divided into five stages, enabling a deeper understanding of the dynamic characteristics during velocity reversal. Model parameters are identified experimentally. A servo control loop is incorporated to evaluate tracking errors caused by friction and backlash. Comparisons between simulation and experimental results show that the proposed model achieves a maximum error of approximately 3.7%. Furthermore, the model offers physical insight into the tracking errors induced by friction and backlash.
Jian et al. (2025) studied this question.