Thermal error compensation for a fluid-cooling ball-screw feed system

Thermal deformation resulted from the heat generated by the motor and the frictional behavior between the moving pairs significantly reduces the positioning accuracy of feed systems and thus influences the machining quality of parts. The internal cooling ball screw takes advantage of the cooling liquid to strengthen the convection heat transfer actively and suppress the temperature rise. Owing to the intermittent starting and stopping operation modes of the cooling machine, the heat flux arising from various heat sources cannot be completely removed by the coolant; consequently, thermal errors still exist. In this study, K-means++ clustering and correlation analyses were used to select thermal key points. A difference equation model of the thermal error was established to describe the transient change relationship between the temperatures of the thermal key points and the ball-screw shaft elongation, which was separated from the thermal characteristic experimental data according to the linear superposition principle of geometric and thermal errors to constitute the positioning error. The model parameters were identified using the least-squares method, and a thermal error compensation strategy based on the origin offset method was implemented. Experiments comparing the thermal error compensation of the three models under different working conditions were conducted to confirm that the thermal error difference equation model can be applied to reduce the thermal error of the feed system effectively and maintain excellent robustness.