Thermal error characteristic analysis and modeling for machine tools due to time-varying environmental temperature

- The thermal error transfer function of a workpiece considering the influence of environment temperature is established.
- The thermal error transfer function of the machine tools is built using the principle of dimension chain and the thermal error transfer function.
- Thermal error transfer function in in time domain and frequency domain is implemented to analyze the thermal characteristics of machine tool.
- The thermal error model structure is determined according to the thermal error dimension chain, which can save time in identifying structure parameters of thermal error transfer function.

The accuracy of machine tools is affected by both internal heat sources and time-varying environmental temperature. Therefore, the thermal deformation caused by environmental temperature variation is an important factor, which requires attention during thermal error modeling. In order to analyze the influence of time-varying environmental temperature on the thermal error of the machine tool, this paper proposed a thermal error modeling approach by using the thermal error transfer function of the machine tool. The approach was implemented in the following three steps. First, the thermal time constant of major components was calculated, according to structural parameters. Then, the thermal error transfer function of the components was derived. Finally, the thermal error transfer function of the whole machine was built based on the construction relationship. The analytical approaches of time domain and frequency domain were applied to obtain the thermal characteristics of machine tools based on the thermal error transfer function. Numerical simulations and the Z-axis operating experiment of three-axis milling machine were performed to verify the accuracy and effectiveness of the thermal error predicted model. The result shows that the proposed model is versatile and general with a clear modeling mechanism, which would provide a useful tool for the analysis and optimization design of machine tools with good thermal robustness.