Citation: Liu, H.; Miao, E.; Zhang, L.;
Tang, D.; Hou, Y. Correlation Stability
Problem in Selecting Temperature-
Sensitive Points of CNC Machine
Tools. Machines 2022, 10, 132.
https://doi.org/10.3390/
machines10020132
Academic Editor: Dan Zhang
Received: 4 January 2022
Accepted: 5 February 2022
Published: 12 February 2022
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Article
Correlation Stability Problem in Selecting
Temperature-Sensitive Points of CNC Machine Tools
Hui Liu
1
, Enming Miao
2,
*, Liyin Zhang
1
, Dafeng Tang
1
and Yinlong Hou
1
1
School of Automation, Xi’an University of Posts & Telecommunications, Chang’an West St. Chang’an District,
Xi’an 710121, China; liuhui@xupt.edu.cn (H.L.); zhangliyin@xupt.edu.cn (L.Z.);
tdflyy2019@xupt.edu.cn (D.T.); houyinlong@xupt.edu.cn (Y.H.)
2
College of Mechanical Engineering, Chongqing University of Technology, Chongqing 400054, China
* Correspondence: miaoem@cqut.edu.cn
Abstract:
In the thermal-error compensation of CNC machine tools, temperature-sensitive points
(TSPs) are used for predicting thermal error and need to have a high correlation with the thermal
error. The stability of the correlation between TSPs and the thermal error is the key to long-term
prediction accuracy. In this paper, the uncertainty-calculation method of the correlation coefficient is
proposed to measure the stability of the correlation, and the reasons that affect the stability of the
correlation of TSPs are analyzed. Then, the uncertainty-correlation coefficient is proposed, which
can comprehensively evaluate the correlation and the stability of the correlation between TSPs and
the thermal error. Through long-term experimental verifications, compared with the current TSP
selection algorithm, the uncertainty-correlation coefficient can help to select a more stable TSP and
improve the long-term prediction accuracy of the thermal error.
Keywords:
correlation stability; uncertainty; temperature-sensitive points; machine tools; thermal error
1. Introduction
During the working process of the CNC machine tool, the thermal deformation of
the structure will cause the tools to move, resulting in thermal error. The influence of
the thermal error on machine-tool accuracy cannot be ignored [
1
,
2
]. Thermal-error com-
pensation is a widely used method for solving the thermal error problem. The principle
is to send the thermal error into the CNC system as a feedback signal. Then the CNC
system controls the tool to move the same value in the opposite direction of the thermal
error to achieve compensation [
3
]. The origin offset function is a built-in module of the
CNC system of the machine tool that can automatically complete the entire compensation
process without affecting the normal processing of the machine tool [
4
,
5
]. Therefore, the
focus of thermal-error compensation is how to obtain accurate thermal error values during
machining. In the machining process of machine tools, it is difficult to install sensors
to measure high-speed rotating tools, and it is necessary to use temperature to predict
thermal error. Therefore, how to establish an accurate model between the temperature and
thermal error is the key to thermal-error compensation. Typically, the model is called a
thermal-error-compensation model.
The thermal error originates from the thermal deformation of the machine tool’s
structure, so some studies have used FEM to simulate thermal deformation. Through FEM
simulation, Ni [
6
] found that, if a constraint is imposed on the front end of the spindle
(near the tool), and the rear end is kept free to expand, the thermal deformation can be
guided to the rear end of the spindle, thereby reducing the thermal deformation at the
tool position. Wang [
7
] analyzed the spindle deformation caused by cutting force and
temperature through FEM simulation and found that thermal deformation accounts for
90%, so the thermal error is the main error source of the machine tool. Wei [
8
] analyzed
the thermal deformation of the shaft components in the axial direction and found that the
Machines 2022, 10, 132. https://doi.org/10.3390/machines10020132 https://www.mdpi.com/journal/machines
