Thermal error is one of the main reasons for the loss of accuracy in lathe machining. In this study, a thermal deformation compensation model is presented that can reduce the influence of spindle thermal error on machining accuracy. The method used involves the collection of temperature data from the front and rear spindle bearings by means of embedded sensors in the bearing housings. Room temperature data were also collected as well as the thermal elongation of the main shaft. The data were used in a linear regression model to establish a robust model with strong predictive capability. Three methods were used: (1) Comsol was used for finite element analysis and the results were compared with actual measured temperatures. (2) This method involved the adjustment of the parameters of the linear regression model using the indicators of the coefficient of determination, root mean square error, mean square error, and mean absolute error, to find the best parameters for a spindle thermal displacement model. (3) The third method used system recognition to determine similarity to actual data by dividing the model into rise time and stable time. The rise time was controlled to explore the accuracy of prediction of the model at different intervals. The experimental results show that the actual measured temperatures were very close to those obtained in the Comsol analysis. The traditional model calculates prediction error values within single intervals, and so the model was divided to give rise time and stable time. The experimental results showed two error intervals, 19µm in the rise time and 15µm in the stable time, and these findings allowed the machining accuracy to be enhanced.

Over the years, machine tool manufacturers have moved steadily towards the enhancement of machining accuracy to improve the quality of finished products. In this study, the thermal deformation of a machine spindle, which has a profound effect on machining accuracy, was investigated. The temperatures of the front and rear spindle bearings, and of the environment as well as the Z-axis displacement on a model MC4200BL CNC lathe (Hybrid Sphere) were measured under long-term operating conditions. Measurements were carried out at spindle speeds of 1000, 1500, 2000, 2500, and 3000 rpm, and the data were used to establish a model for the prediction of spindle displacement. A back propagation neural network (BPNN) was used to establish the model and explore adjustments of the training function, the data training ratio, and the number of neurons in the hidden layer. Results of the experiments showed that the coefficient of determination (R 2) of the prediction model derived from the best parameters can be up to 0.9948. This was much better than the 0.8273 achieved by the partial least squares regression method.