Feedback control of the mechanical spindle thermal error based on thermal simulation with bearing heat sources analysis

The thermal error stability (STE) of the spindle seriously affects the machining accuracy of a machine tool, however existing empirical heating model-based active cooling strategies mainly focus on suppressing the spindle’s overall thermal deformation and cannot effectively stabilize the thermal error. This study regards the “active cooling-spindle” system as a feedback control system and employs a data-driven thermal error model to provide feedback. Thus, the spindle thermal error can be stabilized for a long time owing to the homeostasis of the feedback control system under disturbance. A mechanical spindle with an external cooling scheme is taken as the study object. Bearings are the primary heat sources of the mechanical spindle; thus, the angular contact ball-bearing heat generation is precisely modeled based on local heat sources analysis of bearing components, elastohydrodynamic lubrication, and micro-contact theory. Thermal simulation of the spindle under varying-coolant temperature cooling is conducted to pre-validate the thermal error suppression and variation trend influencing effect, and obtain the Reference Input of Thermal Error (RITE) for the feedback control under different work conditions. Subsequently, a spindle thermal error feedback control system is developed, including computation, cooling, and real-time monitoring modules with inter-communication. Finally, the thermal error feedback control strategy is applied on the mechanical spindle, and experimental comparisons with constant coolant temperature cooling show that the thermal equilibrium time is advanced by 61.46%, 59.16%, 40.51%, and 58.08%. The thermal error variation range (TEVR) after the preheating stage is reduced to1.92, 1.52, 1.91, and 1.69 μm, respectively. The significant reduction in TEVR validated the effectiveness of the proposed strategy for spindle thermal error stabilization.