CNC machine tool thermal error robust state space model based on algorithm fusion

Thermal error is one of the main sources of errors in CNC machine tools. The thermal error characteristics of CNC machine tools will change with changes in machine temperature and machine operating parameters. An excellent thermal error model should have good prediction accuracy and prediction robustness on the premise of high-precision fitting of thermal error. Based on the Leaderway-V450 CNC machine tool, 18 batches of thermal error measurement experiments are conducted in different periods and rotating speeds throughout the year. Moreover, the change in the thermal error law caused by the coupling of temperature change and spindle rotating speed change is studied. After an in-depth analysis of the ridge regression and state space algorithms, a robust state space model (RSSM) is proposed by combining the advantages of the ridge regression algorithm in eliminating collinearity between independent variables on model robustness and that of the state space algorithm in describing system internal structure and characteristics. RSSM is compared with the multiple linear regression model (MLRM), ridge regression model (RRM) and state space model (SSM). RSSM based on the algorithm fusion is proven to realise the comprehensive description of the relationship between the thermal error of machine tool, temperature increase of temperature sensitive point and spindle speed. Moreover, RSSM has superior model accuracy and prediction robustness under the influence of change in temperature and spindle speed. The mathematical model is ultimately used to accurately describe engineering phenomena and laws. In engineering application, different algorithm features should be extracted according to the laws of engineering objects to integrate them, thereby meeting the actual engineering laws, so that the established model can have sufficient prediction accuracy and also meet the engineering needs of robustness. This research systematically studied the realisation of the RRM and SSM algorithm fusion for the accurate and robust thermal error prediction of CNC machine tools, thereby providing important theoretical reference for the application of algorithm fusion in engineering.