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A reconstructed variable regression method for thermal error modeling of machine tools

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Abstract

For the thermal error model of computer numerical control (CNC) machine tools based on empirical modeling method, selecting the appropriate temperature-sensitive points is very important. Owing to the existence of multi-collinearity among temperature variables, the accuracy and robustness of the error model are degraded. Therefore, a reconstructed variable regression (RVR) algorithm is presented firstly in this paper. The reconstructed variable is derived from representative temperature points which are selected from the raw temperature data through fuzzy C means (FCM) clustering method. Then, the reconstructed variable is utilized to build the thermal error model based on regression analysis. Meanwhile, a criterion is proposed to find out the optimal cluster result from the whole results of clustering. RVR algorithm was validated through the thermal error experiments of positioning error on a 3-axis machine tool. The number of temperature measuring points could be reduced from 9 to 2. The results of experiments showed that the fitting accuracy of RVR model could reach 92 % and the prediction accuracy could reach about 90 %. It is verified that the RVR model is of high prediction accuracy and strong robustness which is a great choice for thermal error modeling.

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Authors and Affiliations

  1. School of Mechanical Science and Engineering, Jilin University, Changchun, 130025, China

    Yang Li, Ji Zhao & Shijun Ji

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  1. Yang Li
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  2. Ji Zhao
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  3. Shijun Ji
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Correspondence to Ji Zhao.

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Li, Y., Zhao, J. & Ji, S. A reconstructed variable regression method for thermal error modeling of machine tools. Int J Adv Manuf Technol 90, 3673–3684 (2017). https://doi.org/10.1007/s00170-016-9648-3

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  • DOI: https://doi.org/10.1007/s00170-016-9648-3

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