Abstract
High-speed electric spindle is an important part of computer numerical control (CNC) machining equipment. The thermal displacement generated by the electric spindle during operation is the main reason that affects the machining stability and machining accuracy of the electric spindle. Compensating the thermal error of the high-speed electric spindle can effectively improve the CNC machining. Improve equipment processing performance. Therefore, it is particularly important to establish the accuracy of the thermal error prediction model. Taking the A02 high-speed electric spindle as the research object, ANSYS is used to analyze the thermal characteristics of the electric spindle, and the temperature and thermal displacement monitoring points of the electric spindle are arranged according to the simulation results, and the temperature and thermal displacement data of the monitoring points under different rotational speeds are collected; using K-means to classify temperature measurement points, uses the gray relation analysis degree to determine the correlation between the temperature measurement point and the thermal displacement data, and selects 4 temperature-sensitive points from 10 temperature measurement points. Finally, particle swarm optimization (PSO) is used to optimize the penalty factor and kernel function of support vector machine (SVM), and the PSO-SVM prediction model is established to compare with the neural network prediction model of SVM and genetic algorithm (GA) optimized SVM. The results show that PSO-SVM has better robustness, stability, and generalization ability.
Similar content being viewed by others
Data availability
Data is contained within the article.
References
Liu K, Han W, Wang YQ, Liu HB, Song L (2021) Review on thermal error compensation for axes of CNC machine tools. J Mech Eng 57:156–173
Li Y, Yu ML, Bai YM, Hou ZY, Wu WW (2021) A review of thermal error modeling methods for machine tools. Appl Sci 11(11):5216
Wang HT, Li TM, Wang LP, Li FC (2015) Review on thermal error modeling of machine tools. J Mech Eng 51:119–128
Dai Y, Tao XS, Li ZL, Zhan SQ, Li Y, Gao YH (2022) A review of key technologies for high-speed motorized spindles of CNC machine tools. Machines 10(2):145
Yue HT, Guo CG, Li Q, Zhao LJ, Hao GB (2020) Thermal error modeling of CNC milling machine tool spindle system in load machining: based on optimal specific cutting energy. J Braz Soc Mech Sci Eng 42(9):1–12
Yang J, Shi H, Feng B, Zhao L, Ma C, Mei XS (2015) Thermal error modeling and compensation for a high-speed motorized spindle. Int J Adv Manuf Technol 77(5):1005–1017
Liu JY, Cai YH, Zhang QJ, Zhang HF, He H, Gao XD, Ding LT (2021) Thermal error analysis of taurenEDM machine tool based on FCM fuzzy clustering and RBF neural network. J Intell Fuzzy Syst 1–12
Fu GQ, Gong HW, Gao HL, Gu TD, Cao ZQ (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):2039–2055
Huang Z, Liu YC, Du L, Yang H (2020) Thermal error analysis, modeling and compensation of five-axis machine tools. J Mech Sci Technol 34(10):4295–4305
Cui L, Wang QS (2018) Thermal properties analysis of compact motorized spindle considering fluid-solid thermal coupling. IOP Conf Ser Mater Sci Eng 389(1):012004
Chen B, Guan X, Cai DC, Li HL (2022) Simulation on thermal characteristics of high-speed motorized spindle. Case Stud Therm Eng 102144
Li YF, Zhang YJ, Zhao YQ, Shi XJ (2021) Thermal-mechanical coupling calculation method for deformation error of motorized spindle of machine tool. Eng Fail Anal 128:105597
Liu YC, Li KY, Tsai YC (2021) Spindle thermal error prediction based on LSTM deep learning for a CNC machine tool. Appl Sci 11(12):5444
Liu PL, Du ZC, Li HM, Deng M, Feng XB, Yang JG (2021) Thermal error modeling based on BiLSTM deep learning for CNC machine tool. Adv Manuf 9(2):235–249
Wu CY, Xiang ST, Xiang WS (2021) Spindle thermal error prediction approach based on thermal infrared images: a deep learning method. J Manuf Syst 59:67–80
Zhou HM, Wang Z (2021) Cooling prediction of motorized spindle based on multivariate linear regression. J Phys Conf Ser 1820(1):012196
Zhu MR, Yang Y, Feng XB, Du ZC, Yang JG (2022) Robust modeling method for thermal error of CNC machine tools based on random forest algorithm. J Intell Manuf 1–14
Liu Y, Wang XF, Zhu XG, Zhai Y (2021) Thermal error prediction of motorized spindle for five-axis machining center based on analytical modeling and BP neural network. J Mech Sci Technol 35(1):281–292
Li ZL, Zhu B, Dai Y, Zhu WM, Wang QH, Wang BD (2021) Research on thermal error modeling of motorized spindle based on BP neural network optimized by beetle antennae search algorithm. Machines 9(11):286
Guo QJ, Fan S, Xu RF, Cheng X, Zhao GY, Yang JG (2017) Spindle thermal error optimization modeling of a five-axis machine tool. Chin J Mech Eng 30(3):746–753
Li ZL, Zhu B, Dai Y, Zhu, WM, Wang QH, Wang BD (2022) Thermal error modeling of motorized spindle based on Elman neural network optimized by sparrow search algorithm. Int J Adv Manuf Technol 1–18
Dai Y, Yin XM, Wei WQ, Wang G, Zhan SQ (2020) Thermal error modeling of high-speed motorized spindle based on ANFIS. Chin J Sci Instrum 41(6):50–58
Yue HT, Guo CG, Li Q, Zhao LJ, Hao GB (2020) Thermal error modeling of CNC milling machining spindle based on an adaptive chaos particle swarm optimization algorithm. J Braz Soc Mech Sci Eng 42:1–13
Funding
This research was funded by the National Natural Science Foundation of China (grant number [52075134]).
Author information
Authors and Affiliations
Contributions
All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Zhaolong Li, Wenming Zhu, Bo Zhu, Qinghai Wang, and Baodong Wang. The first draft of the manuscript was written by Wenming Zhu and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher's note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Li, Z., Zhu, W., Zhu, B. et al. Thermal error modeling of electric spindle based on particle swarm optimization-SVM neural network. Int J Adv Manuf Technol 121, 7215–7227 (2022). https://doi.org/10.1007/s00170-022-09827-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-022-09827-4