A semi-mechanical thermal error model for motorized spindle of high-speed dry hobbing machine considering electro-mechanical-thermal coupling effects

Motorized spindle (MS), serving as a pivotal component of the high-speed dry hobbing (HSDH) machine, exerts a profound influence on machining accuracy. However, it remains challenging to develop an accurate thermal error model for spindle system owing to the complex electro-mechanical-thermal (EMT) coupling effects and unclarified thermal deformation mechanism. To tackle the gap, this research introduces a novel semi-mechanical thermal error model for MS of HSDH machine considering EMT coupling effects, in which the proposed approach extracts the merits from the ongoing mechanism and data-driven thermal error models. Firstly, according to the mechanism analysis, the thermal energy balance equation for MS system that contains thermal error and EMT variable items is constructed. Then, a thermal error model that pertains to EMT variables, namely, power, rotational speed, cutting load, temperature/temperature difference, etc., is derived. Furthermore, the undetermined coefficients acquisition is transformed into an optimization problem, and the optimal solutions can be derived using a hybrid PSO-GA (HPSO-GA) algorithm combining experimental EMT data. Finally, an accurate thermal error model is obtained and the model performance is validated by a case study conducted on HSDH machine. This study provides an essential foundation for spindle thermal error prediction, thermal error compensation, and optimization of thermal balance control strategies.