Dynamic modeling and vibration analysis of ball recirculation system considering return device assembly error

This study proposes a dynamic model of the ball recirculation system (BRS) that explicitly incorporates return device assembly error (RDAE). The model captures the dynamics of the return device (RD), the nut, the balls, and the segment of the screw raceway engaged with the nut. Model predictions are validated by vibration tests on a BRS test bench; the predicted ball-pass frequency (BPF) agrees closely with the experimental measurements. We analyze the load distribution under combined loads and the transient variations of elastic forces as balls pass through the RD. Based on the modeling of RDAE, we quantify the relationship between RDAE and the BRS dynamic response, evaluate the sensitivity of the response to variations in screw rotational speed at several representative RDAE magnitudes, and analyze the impact of asymmetry in the assembly errors of the RD’s inlet and outlet on the dynamic characteristics of the BRS. The results provide guidance for optimizing high-precision, low-vibration ball screw transmission in precision grinding machines and inform the design and assembly of the RD.