The selection of temperature-sensitivity points based on K-harmonic means clustering and thermal positioning error modeling of machine tools

  • Yang Li
  • Ji Zhao
  • Shijun Ji
  • Fusheng LiangEmail author


In the thermal error compensation technology of CNC machine tools, the core is to establish a mathematical model of thermal error with high predictive accuracy and strong robustness. The prerequisite for the error model is to select the optimum temperature-sensitivity points, which can inhibit the multi-collinearity problem among temperature points and improve the predictive accuracy and robustness of the error model. In this paper, K-harmonic means (KHM) clustering is introduced for the first time to select the temperature-sensitivity points in the field of error modeling. In statistical numerical experiments, it is verified that KHM clustering is very stable and requires relatively small number of iterations to converge comparing with the common clustering methods such as K-means (KM) clustering and fuzzy C-means clustering (FCM). Then, the effect of KHM clustering on the selection of temperature-sensitivity points is validated in the actual experiments. Multiple linear regression model combined with KHM clustering (MLR-KHM) is adopted to construct the thermal error model of positioning error. The experimental results demonstrate that the predictive accuracy and robustness of MLR-KHM error model can conform with the requirements of the error compensation.


CNC machine tools Thermal error Temperature-sensitivity point selection K-harmonic means clustering 


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Funding information

This work is supported by the National Key Basic Research and Development Program (973 Program) of China (grant no. 2011CB706702), Natural Science Foundation of China (grant no. 51135006 and 51305161), Jilin province science and technology development plan item (grant no. 20130101042JC), and Project 2017140 supported by Graduate Innovation Fund of Jilin University (grant no. 2017140).

Supplementary material

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical Science and EngineeringJilin UniversityChangchunChina

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