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Temperature-sensitive point selection and thermal error modeling of spindle based on synthetical temperature information

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Abstract

Thermal errors are the important factors that affect machining accuracy. It is effective to improve the accuracy by establishing the error model and compensating for the errors. In this paper, a temperature-sensitive point selection method based on synthetical temperature information (STI) is proposed, and the thermal error model using support vector regression (SVR) optimized by the whale optimization algorithm (WOA) is established. Firstly, the STI matrix is constructed by combining the temperature value information, the temperature shape information, and the relationship between temperatures and errors. Multiple cluster validity indexes (CVI) are used to determine the optimal number of clusters. Secondly, the STI matrix and the optimal number of clusters are used for fuzzy C-means clustering (FCM), and the correlation coefficient is used to select the temperature-sensitive points. Thirdly, the SVR model optimized by the WOA based on STI (S-WOA-SVR) is established. Finally, the S-WOA-SVR model is verified at different speeds and compared with other traditional methods, such as the SVR model optimized by the WOA based on the traditional clustering method (T-WOA-SVR) and the SVR model optimized by the GA based on STI (S-GA-SVR). The results show that the S-WOA-SVR model has higher accuracy and robustness. Compared with the T-WOA-SVR model and the S-GA-SVR model, the RMSE of the S-WOA-SVR model is reduced by 52.3% and 46.6% for the thermal elongation in Z direction δz, respectively.

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References

  1. Mayr J, Jedrzejewski J, Uhlmann E, Alkan Donmez M, Knapp W, Härtig F, Wendt K, Moriwaki T, Shore P, Schmitt R, Brecher C, Würz T, Wegener K (2012) Thermal issues in machine tools. CIRP Ann 61(2):771–791

    Article  Google Scholar 

  2. Liu K, Sun M, Zhu T, Wu Y, Liu Y (2016) Modeling and compensation for spindle's radial thermal drift error on a vertical machining center. Int J Mach Tools Manuf 105:58–67

    Article  Google Scholar 

  3. En-ming M, Ya-yun G, Lian-chun D, Ji-chao M (2014) Temperature-sensitive point selection of thermal error model of CNC machining center. Int J Adv Manuf Technol 74(5-8):681–691

    Article  Google Scholar 

  4. Yang B, Liu Z (2020) Thermal error modeling by integrating GWO and ANFIS algorithms for the gear hobbing machine. Int J Adv Manuf Technol 109(9-12):2441–2456

    Article  Google Scholar 

  5. Li Y, Zhao J, Ji S, Liang F (2019) The selection of temperature-sensitivity points based on K-harmonic means clustering and thermal positioning error modeling of machine tools. Int J Adv Manuf Technol 100(9-12):2333–2348

    Article  Google Scholar 

  6. Liu H, Miao E, Zhuang X, Wei X (2018) Thermal error robust modeling method for CNC machine tools based on a split unbiased estimation algorithm. Precis Eng 51:169–175

    Article  Google Scholar 

  7. Zhang T, Ye W, Shan Y (2016) Application of sliced inverse regression with fuzzy clustering for thermal error modeling of CNC machine tool. Int J Adv Manuf Technol 85(9-12):2761–2771

    Article  Google Scholar 

  8. Liu Z, Yang B, Ma C, Wang S, Yang Y (2020) Thermal error modeling of gear hobbing machine based on IGWO-GRNN. Int J Adv Manuf Technol 106(11-12):5001–5016

    Article  Google Scholar 

  9. Tan F, Yin M, Wang L, Yin G (2018) Spindle thermal error robust modeling using LASSO and LS-SVM. Int J Adv Manuf Technol 94(5-8):2861–2874

    Article  Google Scholar 

  10. Tan F, Deng C, Xiao H, Luo J, Zhao S (2020) A wrapper approach-based key temperature point selection and thermal error modeling method. Int J Adv Manuf Technol 106(3-4):907–920

    Article  Google Scholar 

  11. Fu G, Gong H, Gao H, Gu T, Cao Z (2019) Integrated thermal error modeling of machine tool spindle using a chicken swarm optimization algorithm-based radial basic function neural network. Int J Adv Manuf Technol 105(5-6):2039–2055

    Article  Google Scholar 

  12. Miao E, Liu Y, Liu H, Gao Z, Li W (2015) Study on the effects of changes in temperature-sensitive points on thermal error compensation model for CNC machine tool. Int J Mach Tools Manuf 97:50–59

    Article  Google Scholar 

  13. Liu H, Miao E, Wei X, Zhuang X (2017) Robust modeling method for thermal error of CNC machine tools based on ridge regression algorithm. Int J Mach Tools Manuf 113:35–48

    Article  Google Scholar 

  14. Ma C, Zhao L, Mei X, Shi H, Yang J (2017) Thermal error compensation of high-speed spindle system based on a modified BP neural network. Int J Adv Manuf Technol 89(9-12):3071–3085

    Article  Google Scholar 

  15. Huang Y, Zhang J, Li X, Tian L (2014) Thermal error modeling by integrating GA and BP algorithms for the high-speed spindle. Int J Adv Manuf Technol 71(9-12):1669–1675

    Article  Google Scholar 

  16. Guo Q, Xu R, Yang T, He L, Cheng X, Li Z, Yang JG (2016) Application of GRAM and AFSACA-BPN to thermal error optimization modeling of CNC machine tools. Int J Adv Manuf Technol 83(5-8):995–1002

    Article  Google Scholar 

  17. Miao E, Gong Y, Niu P, Ji C, Chen H (2013) Robustness of thermal error compensation modeling models of CNC machine tools. Int J Adv Manuf Technol 69(9-12):2593–2603

    Article  Google Scholar 

  18. Yao X, Hu T, Yin G, Cheng C (2020) Thermal error modeling and prediction analysis based on OM algorithm for machine tool’s spindle. Int J Adv Manuf Technol 106(7-8):3345–3356

    Article  Google Scholar 

  19. Xiang S, Yao X, Du Z, Yang J (2018) Dynamic linearization modeling approach for spindle thermal errors of machine tools. Mechatron 53:215–228

    Article  Google Scholar 

  20. Yang J, Zhang D, Feng B, Mei X, Hu Z (2014) Thermal-induced errors prediction and compensation for a coordinate boring machine based on time series analysis. Math Probl Eng 2014:1–13

    Google Scholar 

  21. Zhang Y, Wang P, Liu T, Gao W, Chang W, Tian Y, Zhang D (2018) Active and intelligent control onto thermal behaviors of a motorized spindle unit. Int J Adv Manuf Technol 98(9-12):3133–3146

    Article  Google Scholar 

  22. Li Q, Li H (2019) A general method for thermal error measurement and modeling in CNC machine tools’ spindle. Int J Adv Manuf Technol 103(5-8):2739–2749

    Article  Google Scholar 

  23. Liu K, Li T, Liu H, Liu Y, Wang Y (2020) Analysis and prediction for spindle thermal bending deformations of a vertical milling machine. IEEE Trans Ind Inform 16(3):1549–1558

    Article  Google Scholar 

  24. Arbelaitz O, Gurrutxaga I, Muguerza J, Pérez JM, Perona I (2013) An extensive comparative study of cluster validity indices. Pattern Recognit 46(1):243–256

    Article  Google Scholar 

  25. Wang W, Zhang Y (2007) On fuzzy cluster validity indices. Fuzzy Sets Syst 158(19):2095–2117

    Article  MathSciNet  Google Scholar 

  26. Rizman Žalik K (2010) Cluster validity index for estimation of fuzzy clusters of different sizes and densities. Pattern Recognit 43(10):3374–3390

    Article  Google Scholar 

  27. Bezdek JC (1974) Numerical taxonomy with fuzzy sets. J Math Biol 1(1):57–71

    Article  MathSciNet  Google Scholar 

  28. Fukuyama Y, Sugeno M (1989) A new method of choosing the number of clusters for the fuzzy c-means method. 5th Fuzzy Systems Symposium 1989:247-250

  29. Xie X, Beni G (1991) A validity measure for fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence,13(8):841-847

  30. Kwon SH (1998) Cluster validity index for fuzzy clustering. Electron Lett 34(22):2176–2177

    Article  Google Scholar 

  31. Zahid N, Limouri M (1999) Essaid A (1999) A new cluster-validity for fuzzy clustering. Pattern Recognit 32(7):1089–1097

    Article  Google Scholar 

  32. Wang L, Wang H, Li T, Li F (2015) A hybrid thermal error modeling method of heavy machine tools in z-axis. Int J Adv Manuf Technol 80(1-4):389–400

    Article  Google Scholar 

  33. Lei M, Jiang G, Yang J, Mei X, Xia P, Shi H (2018) Improvement of the regression model for spindle thermal elongation by a boosting-based outliers detection approach. Int J Adv Manuf Technol 99(5-8):1389–1403

    Article  Google Scholar 

  34. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67

    Article  Google Scholar 

  35. Aljarah I, Faris H, Mirjalili S (2018) Optimizing connection weights in neural networks using the whale optimization algorithm. Soft Comput 22(1):1–15

    Article  Google Scholar 

  36. ISO 230-3 (2007) Test code for machine tools part 3: determination of thermal effects. ISO copyright office, Switzerland

  37. Miao E, Lv X, Miao J, Dang L (2015) Selection of optimum spindle speed to thermal error compensation of machine tools. Optics and Precision Engineering 23(11):3176–3182 (in Chinese)

    Article  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, China

    Zheyu Li, Guolong Li, Kai Xu, Xiaodong Tang & Xin Dong

Authors
  1. Zheyu Li
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  2. Guolong Li
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  3. Kai Xu
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  4. Xiaodong Tang
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  5. Xin Dong
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Correspondence to Guolong Li.

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Li, Z., Li, G., Xu, K. et al. Temperature-sensitive point selection and thermal error modeling of spindle based on synthetical temperature information. Int J Adv Manuf Technol 113, 1029–1043 (2021). https://doi.org/10.1007/s00170-021-06680-9

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  • DOI: https://doi.org/10.1007/s00170-021-06680-9

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