Comparison of basis functions for thermal error compensation based on regression analysis – a simulation based case study
More details
Hide details
Fraunhofer Institute for Machine Tools and Forming Technology IWU Chemnitz, Germany
Acceptance date: 2020-10-15
Online publication date: 2020-11-29
Publication date: 2020-12-18
Journal of Machine Engineering 2020;20(4):28–40
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.
BONSE R., McKEOWN P., WECK M., HERBST U., 1995, Reduction and Compensation of Thermal Errors in Machine Tools, Annals of the CIRP, 44/2, 589–598.
BRYAN J.B., 1990, International Status on Thermal Error research, Annals of the CIRP, 39/2, 645–656.
POSTLETHWAITE S., ALLEN J., FORD D., 1999, Machine Tool Thermal Error Reduction – an Appraisal, Proceed. of the Institution of Mech. Engineers, part B: Journal of Engineering Manufacture, 213/1, 1–9.
ESS M., 2012, Simulation and Compensation of Thermal Errors of Machine Tools, Dissertation, ETH Zurich.
LEE J.H., YANG S.H., 2002, Statistical Optimization and Assessment of a Thermal Error Model for CNC Machine Tools, International Journal of Machine Tools and Manufacture, 42, 147–155.
CHEN J.S., YUAN J., NI J., 1996, Thermal Error Modelling for Real-Time Error Compensation, International Journal of Advanced Manufacturing Technology, 12, 266–275.
YANG H., NI J., 2005, Dynamic Neural Network Modeling for Nonlinear, Nonstationary Machine Tool Thermally Induced Error, International Journal of Machine Tools and Manufacture, 45/4–5, 455–465.
BRECHER C., HIRSCH P., WECK M., 2004, Compensation of Thermo-Elastic Machine Tool Deformations Based on Control Internal Data, CIRP Annals Manufacturing Technology, 53/1, 299–304.
YANG S., YUAN J., NI J., 1996, Accuracy Enhancement of a Horizontal Machining Center by Real-Time Error Compensation, Journal of Manufacturing Systems, 15/2, 113–124.
NAUMANN C., RIEDEL I., IHLENFELDT S., PRIBER U., 2016, Characteristic Diagram Based Correction Algorithms for the Thermo-Elastic Deformation of Machine Tools, Proceedings of the 48th CIRP Conference on Manufacturing Systems (CMS), 41, 801–805.
FENG W.L., YAO X.D., AZAMAT A., YANG J.G., 2015, Straightness Error Compensation for Large CNC Gantry Type Milling Centers on B-Spline Curves Modeling, International Journal of Machine Tools & Manufacture, 88, 165–174.
TAN K.K., HUANG S., SEET H.L., 2000, Geometrical Error Compensation of Precision Motion Systems Using Radial Basis Functions, IEEE Transactions on Instrumentation and Measurement, 49/5, 984–991.
JIN C., WU B., HU Y., 2015, Temperature Distribution and Thermal Error Prediction of a CNC Feed System Under Varying Operating Conditions, Internat. Journal of Advanced Manufacturing Technology, 77, 1979–1992.
CHEN J.S., YUAN J., NI J., WU S.M., 1992, Thermal Error Modelling for Volumetric Error Compensation, Sensors and Signal Processing for Manufacture, 55, 113–125.
NAUMANN C., THIEM X. et al., 2016, Implementation and Demonstration of Characteristic Diagram as well as Structure Model Based Correction of Thermo-Elastic Tool Center Point Displacements, Journal of Machine Engineering, 16/3, 88–101.
PRIBER U., 2003, Smoothed Grid Regression, 13th Workshop Fuzzy Systems.
PRAUTZSCH H., BOEHM W., PALUSZNY M., 2002, Bézier and B-Spline Techniques, Springer.
SCHOENBERG I.J., 1967, On Spline Functions, Inequalities, Academic Press, 255–291.
CHEN C.S., HON Y.C., SCHABACK R.A., 2005, Scientific Computing with Radial Basis Functions, Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS 39406.
ZHANG X., ZHENG J., GAO H., 2001, Curve Fitting Using Wavelet Transform for Resolving Simulated Overlapping Spectra, Analytica Chimica Acta, 443, 117–125.
HERZOG R., RIEDEL I., 2015, Sequentially Optimal Sensor Placement in Thermoelastic Models for Real Time Applications, Optimization and Engineering, 1–30.
NAUMANN C., PUTZ M., 2019, A New Multigrid Based Method for Characteristic Diagram Based Correction of Thermo-Elastic Deformations in Machine Tools, Journal of Machine Engineering, 19/4, 42–57.