A thermal error model for large machine tools that considers environmental thermal hysteresis effects

Environmental temperature has an enormous influence on large machine tools with regards to thermal deformation, which is different from the effect on ordinary-sized machine tools. The thermal deformation has hysteresis effects due to environmental temperature, and the hysteresis time fluctuates with seasonal weather. This paper focused on the hysteresis nonlinear characteristic, analyzing the thermal effect caused by external heat sources. Fourier synthesis, time series analysis and the Newton cooling law were combined to build a time-varying analytical model between environmental temperature and the corresponding thermal error for a large machine tool. A multiple linear regression model based on the least squares principle was used to model the internal heat source effects simultaneously. The two models were united to make up a synthetic thermal error prediction model called the environmental temperature consideration prediction model (ETCP model). A series of experiments were performed using a large gantry type machine tool to verify the accuracy and efficiency of the predicted model under random environments, random times and random machining conditions throughout an entire year. The proposed model showed high robustness and universality, with over 85% thermal error, with up to 0.2 mm was predicted. The mathematical model was easily integrated into the NC system and could greatly reduce the thermal error of large machine tools under ordinary workshop conditions, especially for long-period cycle machining.