Thermal error compensation on a computer numerical control machine tool considering thermal tilt angles and cutting tool length

The present error compensation technology of computer numerical control machine tools ignores radial thermal tilt angle errors of the spindle, while the thermal-induced offset is closely related to the tilt angle and the handle length. To solve this problem, three models of spindle thermal errors are proposed for the thermal yaw, pitch angles and elongation, and error compensation is performed based on the thermal tilt angles and cutting tool length. A five-point method was applied to measure the spindle thermal drifts at different speeds by eddy current sensors, which could effectively analyse the changes in the position-pose of the errors. Fuzzy clustering and correlation analysis were applied to group and optimise the temperature variables and select the variables sensitive to thermal errors in order to depress the multicollinearity of the temperature variables and improve the stability of the model. Finally, the thermal offset compensation was conducted in three directions. The results indicate that back propagation has a better capability for nonlinear fitting, but its generalisation is far less than that of time series. While the structure of multiple linear regression analysis is simple, its prediction accuracy is not satisfied. Time series adequately reflects the dynamic behaviours of the thermal error, and the prediction accuracy can reach 94%, with excellent robustness under different cutting conditions. The thermal error compensation equation that includes thermal tilt angles and cutting tool length is suitable for actual conditions and can accurately describe the space-pose of the thermal deformation and improve the machining accuracy.