Development and Experimental Verification of a Thermal Elongation Prediction Model for Electric Spindles

Thermal elongation in high-speed motorized spindles constitutes a major source of machining error in five-axis machine tools, critically impacting machining precision. This study aims to develop and validate a cumulative thermal error compensation model for predicting spindle thermal elongation, subsequently enabling effective compensation via a dedicated control algorithm. Key thermal error factors, primarily spindle speed and cumulative thermal error, were identified through analysis. An innovative numerical prediction model incorporating these factors was established. Its performance was evaluated through experiments utilizing eddy-current displacement sensors for high-speed, high-precision thermal elongation measurement. The validation results demonstrated the model’s strong predictive capability: During spindle startup, prediction errors exhibited minor transients, stabilizing near zero once the operating speed was reached. Under dynamic speed changes, the maximum prediction error was only 1.28 μm, with the overall maximum residual error recorded at 2.04 μm. These findings confirm the model’s high accuracy. Furthermore, the model exhibits excellent generalization capability, delivering significant compensation effectiveness across diverse variable-speed operating conditions. This work successfully developed a highly accurate numerical model and a practical compensation strategy, significantly enhancing the positioning accuracy of high-speed spindles against thermal disturbances. The proposed approach offers substantial engineering utility for thermal error compensation in precision machining applications.