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Thermal error prediction of ball screws based on PSO-LSTM

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Abstract

Thermal error of ball screws seriously affects the machining precision of computerized numerical control (CNC) machine tools especially in high speed and precision machining. Compensation technology is one of the most effective methods to address the thermal issue, and the effect of compensation depends on the accuracy and robustness of the thermal error model. Traditional modeling approaches have major challenges in time series thermal error prediction. In this paper, a novel thermal error model based on long short-term memory (LSTM) neural network and particle swarm optimization (PSO) algorithm is proposed. A data-driven model based on LSTM neural network is established according to the time series collected data. The hyperparameters of LSTM neural network are optimized by PSO, and then a PSO-LSTM model is established to precisely predict the thermal error of ball screws. In order to verify the effectiveness and robustness of the proposed model, two thermal characteristic experiments based on step and random speed are conducted on a self-designed test bench. The results show that the PSO-LSTM model has higher accuracy compared with the radial basis function (RBF) model and back propagation (BP) model with high robustness. The proposed method can be implemented to predict the thermal error of ball screws and provide a foundation for thermal error compensation.

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All data generated or analyzed in this study are included in the present article.

References

  1. Yun WS, Kim SK, Cho DW (1999) Thermal error analysis for a CNC lathe feed drive system. Int J Mach Tools Manuf 39:1087–1101

    Article  Google Scholar 

  2. Bryan J (1990) International status of thermal error research. CIRP Ann Manuf Technol 39:645–656

    Article  Google Scholar 

  3. Tsai PC, Cheng CC, Hwang YC (2014) Ball screw preload loss detection using ball pass frequency. Mech Syst Signal Process 48:77–91

    Article  Google Scholar 

  4. Xu ZZ, Liu XJ, Kim HK, Shin JH, Lyu SK (2011) Thermal error forecast and performance evaluation for an air-cooling ball screw system. Int J Mach Tools Manuf 51:605–611

    Article  Google Scholar 

  5. Xu ZZ, Liu XJ, Choi CH, Lyu SK (2012) A study on improvement of ball screw system positioning error with liquid-cooling. Int J Precis Eng Manuf 13:2173–2181

    Article  Google Scholar 

  6. Shi H, He B, Yue Y, Min C, Mei X (2019) Cooling effect and temperature regulation of oil cooling system for ball screw feed drive system of precision machine tool. Appl Therm Eng 161:114150

    Article  Google Scholar 

  7. Gao XS, Qin ZY, Guo YY, Wang M, Zan T (2019) Adaptive method to reduce thermal deformation of ball screws based on carbon fiber reinforced plastics. Materials 12:3113

    Article  Google Scholar 

  8. Guo YY, Gao XS, Wang M, Zan T (2020) Bio-inspired graphene-coated ball screws: novel approach to reduce the thermal deformation of ball screws. Proc Inst Mech Eng C J Mech Eng Sci 235(5):789–799

    Article  Google Scholar 

  9. Yang S, Yuan J, Ni J (1996) The improvement of thermal error modeling and compensation on machine tools by CMAC neural network. Int J Mach Tools Manuf 36:527–537

    Article  Google Scholar 

  10. Yang JG, Yuan JX, Ni J (1999) Thermal error mode analysis and robust modeling for error compensation on a CNC turning center. Int J Mach Tools Manuf 39:1367–1381

    Article  Google Scholar 

  11. Zhao HT, Yang JG, Shen JH (2007) Simulation of thermal behavior of a CNC machine tool spindle. Int J Mach Tools Manuf 47:1003–1010

    Article  Google Scholar 

  12. Zhu J, Ni J, Shih AJ (2008) Robust machine tool thermal error modeling through thermal mode concept. J Manuf Sci E T ASME 130(6):061006

    Article  Google Scholar 

  13. Li TJ, Zhao CY, Zhang YM (2018) Adaptive real-time model on thermal error of ball screw feed drive systems of CNC machine tools. Int J Adv Manuf Technol 94:3853–3861

    Article  Google Scholar 

  14. Shi H, Ma C, Yang J (2015) Investigation into effect of thermal expansion on thermally induced error of ball screw feed drive system of precision machine tools. Int J Mach Tools Manuf 97:60–71

    Article  Google Scholar 

  15. Ramesh R, Mannan MA, Poo AN (2003) Thermal error measurement and modelling in machine tools: Part I. Influence of varying operation condition. Int J Mach Tools Manuf 43:391–404

    Article  Google Scholar 

  16. Ramesh R, Mannan MA, Poo AN, Keerthi SS (2003) Thermal error measurement and modelling in machine tools: Part II. Hybrid Bayesian Network - Support vector machine model. Int J Mach Tools Manuf 43:405–419

    Article  Google Scholar 

  17. Wu H, Zhang HT, Guo QJ, Wang XS, Yang JG (2008) Thermal error optimization modeling and real-time compensation on a CNC turning center. J Mater Process Technol 207:172–179

    Article  Google Scholar 

  18. Zhang Y, Yang JG, Jiang H (2012) Machine tool thermal error modeling and prediction by grey neural network. Int J Adv Manuf Technol 59:1065–1072

    Article  Google Scholar 

  19. Wang HT, Wang LP, Li TM, Han J (2013) Thermal sensor selection for the thermal error modeling of machine tool based on the fuzzy clustering method. Int J Adv Manuf Technol 69:121–126

    Article  Google Scholar 

  20. Miao EM, Gong YY, Dang LC, Miao JC (2014) Temperature-sensitive point selection of thermal error model of CNC machining center. Int J Adv Manuf Technol 74:681–691

    Article  Google Scholar 

  21. Miao EM, Gong YY, Niu PC, Ji CZ, Chen HD (2013) Robustness of thermal error compensation modeling models of CNC machine tools. Int J Adv Manuf Technol 69:2593–2603

    Article  Google Scholar 

  22. Yang J, Shi H, Feng B, Zhao L, Ma C, Mei X (2014) Applying neural network based on fuzzy cluster pre-processing to thermal error modeling for coordinate boring machine. Procedia CIRP 17:698–703

    Article  Google Scholar 

  23. Abdulshahed A, Longstaff AP, Fletcher S, Myers A (2013) Comparative study of ANN and ANFIS prediction models for thermal error compensation on CNC machine tools. In Lamdamap 10th International Conference. EUSPEN

  24. Abdulshahed AM, Longstaff AP, Fletcher S (2015) The application of ANFIS prediction models for thermal error compensation on CNC machine tools. Appl Soft Comput 27:158–168

    Article  Google Scholar 

  25. Liu H, Miao EM, Wei XY, Zhuang XD (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 

  26. Santos MOD, Batalha GF, Bordinassi EC, Miori GF (2018) Numerical and experimental modeling of thermal errors in a five-axis CNC machining center. Int J Adv Manuf Technol 96:2619–2642

    Article  Google Scholar 

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

    Article  Google Scholar 

  28. Rojek I, Kowal M, Stoic A (2017) Predictive compensation of thermal deformations of ball screws in CNC machines using neural networks. Teh Vjesn 24:1697–1703

    Google Scholar 

  29. Li B, Zhang Y, Wang L, Li X (2019) Modeling for CNC machine tool thermal error based on genetic algorithm optimization wavelet neural networks. J Mech Eng 55:215–220 (in Chinese)

    Article  Google Scholar 

  30. Sagheer A, Kotb M (2019) Time series forecasting of petroleum production using deep LSTM recurrent networks. Neurocomputing 323:203–213

    Article  Google Scholar 

  31. Zhang YZ, Xiong R, He HW, Pecht MG (2018) Long short-term memory recurrent neural network for remaining useful life prediction of lithium-ion batteries. IEEE Trans Veh Technol 67:5695–5705

    Article  Google Scholar 

  32. Zhang JF, Zhu Y, Zhang XP, Ye M, Yang JZ (2018) Developing a long short-term memory (LSTM) based model for predicting water table depth in agricultural areas. J Hydrol 561:918–929

    Article  Google Scholar 

  33. Qin Y, Xiang S, Chai Y, Chen HZ (2020) Macroscopic–microscopic attention in LSTM networks based on fusion features for gear remaining life prediction. IEEE Trans Ind Electron 67:10865–10875

    Article  Google Scholar 

  34. Lecun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521:436–444

    Article  Google Scholar 

  35. Zhao R, Yan RQ, Chen ZH, Mao KZ, Wang P, Gao RX (2019) Deep learning and its applications to machine health monitoring. Mech Syst Signal Process 115:213–237

    Article  Google Scholar 

  36. Yang R, Singh SK, Tavakkoli M, Amiri N, Yang Y, Karami MA, Rai R (2020) CNN-LSTM deep learning architecture for computer vision-based modal frequency detection. Mech Syst Signal Process 144:106885

    Article  Google Scholar 

  37. Sun RB, Yang ZB, Yang LD, Qiao BJ, Chen XF, Gryllias K (2020) Planetary gearbox spectral modeling based on the hybrid method of dynamics and LSTM. Mech Syst Signal Process 138:106611

    Article  Google Scholar 

  38. Greff K, Srivastava RK, Koutnik J, Steunebrink BR, Schmidhuber J (2017) LSTM: a search space odyssey. IEEE Trans Neural Netw Learn Syst 28:2222–2232

    Article  MathSciNet  Google Scholar 

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Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by the National Natural Science Foundation of China (grant numbers: 51875008, 51505012, and 51575014).

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Authors and Affiliations

  1. Beijing Key Laboratory of Advanced Manufacturing Technology, Faculty of Materials and Manufacturing, Beijing University of Technology, No. 100 Pingleyuan, Chaoyang District, Beijing, 100124, China

    Xiangsheng Gao, Yueyang Guo, Dzonu Ambrose Hanson, Zhihao Liu, Min Wang & Tao Zan

Authors
  1. Xiangsheng Gao
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  2. Yueyang Guo
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  3. Dzonu Ambrose Hanson
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  4. Zhihao Liu
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  5. Min Wang
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  6. Tao Zan
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Contributions

Xiangsheng Gao conceived the experiment and modeling and wrote the manuscript as well. Yueyang Guo conducted the experiment and modeling. Dzonu Ambrose Hanson conducted the data analysis and the English editing. Zhihao Liu conducted the experiment. Min Wang and Tao Zan supervised this work and revised the manuscript.

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Correspondence to Xiangsheng Gao.

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Gao, X., Guo, Y., Hanson, D.A. et al. Thermal error prediction of ball screws based on PSO-LSTM. Int J Adv Manuf Technol 116, 1721–1735 (2021). https://doi.org/10.1007/s00170-021-07560-y

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  • DOI: https://doi.org/10.1007/s00170-021-07560-y

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