Data-driven thermal error compensation of linear x-axis of worm gear machines with error mechanism modeling

Abstract

To increase the machining accuracy of worm gear machines, the thermal error compensation was carried out from the view of X-axis's error mechanism of worm gear machines. The spatial motion error of the worm hob caused by X-axis's positioning error is derived, and then the necessity for the reduction of the positioning error is proved. The memory behaviors of the thermal error are revealed, and finally, the applicability of self-recurrent wavelet (SRW) neural networks to the error modeling is demonstrated. Then the genetic algorithm (GA) is used to optimize the number of neurons in the wavelet and product layers and weights of SRW neural networks, and the error models are established with the GA-SRW, SRW, and back propagation (BP) neural networks. The results show that the predictive performance of the error models based on GA-SRW, SRW, and BP neural networks decreases in turn. Moreover, the precision improvement ratios for the average normal error of tooth surfaces of the GA-SRW neural network error model are more than 21.8% and 43.7% compared to the SRW and BP neural networks error models, respectively. Besides, the predictive performance of the GA-SRW neural network model is better than that of the regression models.