Analysis of the transient backlash error in CNC machine tools with closed loops

•Backlash error in full-closed loop type CNC machine tools is studied.•A general model of closed loop with backlash is developed.•A greatly simplified feed drive model is proposed.•Formulations of the transient backlash errors are derived.•A sensor-less method is proposed for the measurement of backlash width.

Backlash is one of the most commonly encountered nonlinear phenomena in feed drives, which degrades the contouring accuracy of machine tools. The full-closed loop could suppress the adverse effects of backlash significantly. However, a transient backlash error (TBE) remains. Unfortunately, the mechanism of the TBE is completely different from that of the conventional backlash error. The purpose of this paper is to reveal the mechanism of the TBE. First, for the demonstration of the TBE, a general model is derived from an industrial feed drive with the closed loop control. Subsequently, the model is simplified further. Based on the simplified model, the mechanism is described and clarified in detail, and furthermore, the analytical formulations of TBEs are derived for the cases of straight line and circle, respectively. Finally, several simulations and experiments are given to validate the proposed models and formulations.