Closed-loop thermal error control with a physical-based ensemble model for the precision spindle of a machine tool

Overall, a rapid increase in the thermal error of the spindle can seriously deteriorate the machining accuracy of the machine tool. A closed-loop thermal error control system was presented to stabilize the thermal error in machining processes. The closed-loop system employed an active cooling system as the actuator and relies on a thermal error model to provide feedback. Thermal measurements of the spindle can be severely disturbed by the temperature-varying coolant recirculation, leading to the invalidity of the data-driven regression models. A physical-based model that can accurately reflect the combined effect of the cooling and heating sources was established via a thermal resistance-capacity network. A modified AdaBoost framework with a statistics-based weights updating mechanism was used to train physical-based models and ensemble them into an optimal model, which is translucent to be empirically supervised. Through thermal testing experiments, it was shown that the physical-based ensemble model provided satisfactory feedback for the closed-loop control system, where the thermal error variation ranges were less than 1.5 μm throughout the experimental processes. Furthermore, employing the proposed closed-loop control system and with the use of the physical-based ensemble model, the total machining error was reduced by 70.33% compared to that of the constant temperature cooling. The study findings demonstrate that the method of closed-loop spindle thermal error control employing the physical-based ensemble model is effective and feasible for enhancing machining accuracy.