Modeling and compensation of the axial thermal error of electric spindles based on HHO-GRU method

As the core component of precision CNC machine tools, a lot of heat is generated from the internal heat source of electric spindles during operation, resulting in thermal deformation and thermal errors that affect machining accuracy. Thermal error compensation is an economical method for reducing thermal errors, through which the impact of thermal errors on machining accuracy can effectively decrease. Taking a high-speed electric spindle as the research object, the temperature measurement points are selected as its front and rear bearing seat, as well as some positions far from the heat source. The temperature changes at the front and rear bearing as well as in the environment are monitored, then the thermal errors are measured using a Lion spindle rotation accuracy instrument. The optimal training parameters of the gated recurrent unit (GRU) network are optimized utilizing the global optimization ability of a Harris Hawks optimizer (HHO). Finally, the thermal error prediction model of the GRU electric spindle optimized using the Harris Hawks optimizer (HHO-GRU) is established, based on which axial thermal error compensation experiments are conducted. The results show that using the HHO-GRU prediction model for compensation, the axial thermal errors of the electric spindle can be reduced by more than 80%, which can be controlled within 5 μm.