Study on Temperature Measurement Point Optimization and Thermal Error Modeling of NC Machine Tools

Shuo Fan, Qianjian Guo*
School of Mechanical Engineering, Shandong University of Technology, Zibo 255000, China

© 2017 Fan and Guo.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the School of Mechanical Engineering, Shandong University of Technology No.12, Zhangzhou Road, Zhangdian District, Zibo City, Shandong Province, China; Tel: 18353363136; E-mails:;



In precision machining, thermal error is the main source of machine tool error. And thermal error compensation is an effective method to reduce thermal error.


In order to improve the prediction accuracy and computational efficiency of thermal error model, a new optimization method used for the selection of temperature measurement point is proposed.


This method is based on stepwise regression. According to the results of partial-F statistic, new variable is selected one by one, unapparent variables are deleted, and optimization selection of temperature measurement point is fulfilled, thermal error model of the NC machine tool is presented.


The new modeling method was used on NC machine tool, which reduced the temperature point number from 24 to 5. Moreover, model residual was less than 5µm after compensation.


The result shows that the new thermal error model has higher prediction accuracy and less temperature variables.

Keywords: NC machine tool, Stepwise regression method, Measurement point optimization, Thermal error modeling.