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Statistical optimization and assessment of a thermal error model for CNC machine tools
Authors:Jin-Hyeon Lee  Seung-Han Yang  
Affiliation:1. Inspire AG, Technoparkstrasse 1, 8005 Zürich, Switzerland;2. Institute of Machine Tools and Manufacturing (IWF), ETH Zürich, 8092 Zürich, Switzerland
Abstract:The objective of a thermal error compensation system for CNC machine tools is improved machining accuracy through real time error compensation. The compensation capability depends on the accuracy of the thermal error model. A thermal error model can be obtained using an appropriate combination of temperature variables. In this study, the thermal error modeling is based on a correlation grouping and a successive linear regression analysis. During the successive regression analysis, the residual mean square is minimized using a judgement function, which, although simple, is effective in the selection of variables in the error model. When evaluating the proposed thermal error model, the multi-collinearity problem and computational time are both improved through the correlation grouping, and the linear model is more robust against measurement noises than the engineering judgement model, which includes variables with higher order terms. The modeling method used in this study can be effectively and practically applied to real-time error compensation because it includes the advantages of simple application, reduced computational time, sufficient model accuracy, and model robustnesss.
Keywords:Thermal error model  Correlation grouping  Regression analysis  Multi-collinearity  Judgement function  Robustness
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