A Comparison of Basis Functions for Thermal Error Compensation based on Regression Analysis - A Simulation Based Case Study

It is a well-known problem of milling machines, that waste heat from motors, friction effects on guides, the environment and the milling process itself greatly affect positioning accuracy and thus production quality. An economic and energy-efficient method of correcting this thermo-elastic positioning error is to gather sensor data (temperatures, axis positions, etc.) from the machine tool and the process and to use that information to predict and correct the resulting tool center point displacement using regression analysis. This paper compares multilinear characteristic diagrams, B-spline characteristic diagrams, Radial Basis Function fitting and Wavelet fitting in general and also in the context of thermal error compensation. The demonstrations are made using FEM simulation data from a machine tool demonstrator. The results show that all of the above kernel types if properly used, are able to create good compensation models. However, high-dimensional multivariate analysis usually only works by adding grid structures and regularization.