Segmented modeling and compensation of thermal error of gear grinding machine spindle based on variable thermal hysteresis.

Thermal error is the main factor that affects the machining accuracy of the machine tools. Error compensation is a convenient and efficient method to reduce the effect of thermal error, and the compensation effect largely depends on the performance of the thermal error model. It is found that the thermal error has an obvious thermal hysteresis effect, and the current thermal error is affected by the previous temperature. Therefore, the thermal hysteresis effect is considered in the thermal error modeling. In this paper, the segmented modeling of the thermal error with variable lag order is studied. Firstly, the thermal characteristics of the spindle system of the gear grinding machine are analyzed and the X-directional thermal hysteresis of the gear grinding machine is theoretically demonstrated. Secondly, according to the temperature-thermal error relationship sketch combined with fuzzy cluster means (FCM) and correlation coefficient, the temperature sensitive points are selected. Thirdly, considering the variable lag order of thermal hysteresis, the lag orders of the heating and cooling processes in every cycle are calculated by particle swarm optimization (PSO). Fourthly, the distributed lag (DL) calculated by the PSO and multiple linear regression (MLR) is used to establish the model in different states, respectively. The S-PSO-DL model is obtained by combining all the segmented models. Compared with the segmented DL model established by mean lag order of inflection point (S-MLO-DL), the segmented back propagation neural network (S-BPNN), the segmented MLR model (S-MLR), and the no-segmented PSO-DL, the maximum residual of the prediction result of S-PSO-DL reduces by 40.8%, 60.0% and 72.8%, 46.3%. Finally, the thermal error of the gear grinding machine spindle is compensated, and the compensation rate of the model reaches 74.3%. [ABSTRACT FROM AUTHOR]