Mechanism Analysis of Time-Dependent Characteristic of Dynamic Errors of Machine Tools

Abstract

The Dynamic Errors (DEs) of individual axes present Time-dependent Characteristics (TDCs) because the setpoints, as the input of the servo feed system, change in velocity, acceleration and jerk during the feed motion. Deep insight into the TDC contributes to the effective control of DEs. However, up to now, mechanism analysis about the TDCs of DEs are indistinct and inadequate due to a lack of analysis on the TDC of setpoint frequency. So, in this study, the mechanism of the TDC of DE is investigated by extracting the TDC of setpoint frequency. Firstly, the servo dynamics model is established for presenting the DE and its respective components, the Dynamic Error Inside Servo-loop (DEIS) (tracking error) and the Dynamic Error Outside Servo-loop (DEOS) under to and fro motions. Secondly, time–frequency analysis is carried out on the setpoints of the to and fro motions to present a TDC of setpoint frequency which is described as the Time-dependent Setpoint Bandwidth (TDSB) and the Time-dependent Potential Excitation (TDPE). Finally, the correlation between the TDSBs and DEISs and the correlation between the TDPEs and DEOSs are investigated, respectively. On these bases, the mechanism of the TDC of DE is analyzed. The results show that the TDSB, which is related to the acceleration of setpoints, accounts for the TDC of the DEIS; that the TDPE, which is related to the jerk of setpoints, accounts for the TDC of the DEOS in vibration-form; and that the TDC of transient-form DEOS is determined by the change in acceleration of the setpoints.