A proposal of models for thermal compensation in machine tools based on a formulation for in-series heat transfer

Machine tools need to possess excellent positioning accuracy to meet increasingly stringent dimensional tolerances and geometric specifications for producing parts. The accuracy is significantly affected by distortions caused by irregular thermal distribution throughout the machine’s structure, with the motorized spindle being a major source of heat. In this study, through finite element analysis, the influence of the spindle’s heating on other machine components is examined, revealing that the air inside the protection cover acts as one of the main mediums for heat transfer from the spindle to other components far from the spindle. A thermal error compensation model is proposed, considering the in-series heat transfer through the air inside the protection cover, leading to a higher-order thermal expansion curve. Additionally, the thermal errors caused by ball screws are addressed using a first-order exponential model. Testing the two models on a CNC turning center shows a considerable reduction in radial thermal error when combined with inputs from the CNC and temperature sensors strategically placed on the machine.