Dynamic linearization modeling approach for spindle thermal errors of machine tools

Conventional model-based prediction (MBP) methods for spindle thermal errors have three serious contradictions: those between unmodeled dynamics and robustness, between model precision and model complexity, and between partial linearization and overall complexity. To avoid these contradictions, a new data-driven prediction (DDP) approach is applied to the dynamic linearization modeling for spindle thermal errors. In this model, the current thermal errors are predicted by history temperature data without the information of physical mechanisms. Four points along the spindle front bearing circle (left, right, front and back sides) are selected, whose temperatures are recorded in real time via thermocouples, and the average values are calculated. Then the temperature gradients of these four points are selected as the input to predict the axial and radial offsets and the tilt angle errors. The hysteresis phenomenon between temperature and deformation is determined via thermal characteristic tests, and the time interval for data input is identified. Furthermore, sufficient experimental tests verify that the DDP model is significantly better than the general model-based method in terms of accuracy and robustness.