Skip to main content
SpringerLink
Log in

Spindle unit thermal error modeling and compensation based on digital twin

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

The thermal error in the spindle unit is substantial and necessitates mitigation. Current models, being predominantly static in nature, have limited efficacy in error control. Integrating digital twin technology for modeling and controlling spindle unit thermal error holds promise in enhancing the machining accuracy of machine tools. Yet, the notion of a digital twin system specifically tailored for spindle unit thermal characteristics remains uncharted territory. To navigate these challenges, this study introduces a novel digital twin system tailored for spindle unit thermal characteristics. This system is poised to revolutionize thermal error modeling and compensation by harnessing the capabilities of digital twin technology. Within this digital twin framework, both the thermal error control model and the analytical thermal characteristic model are seamlessly integrated. The control model is devised as an exponential function, utilizing operational time, inherent time constants, and both initial and equilibrium thermal errors as parameters. Delving deeper, the analytical thermal characteristic model for the spindle system is rooted in a thermal resistance network approach. This leads to a closed-loop thermal characteristic modeling process, culminating in the derivation of a steady-state thermal error. Intricate heat transfer dynamics between spindle components are dissected, and a comprehensive thermal equilibrium equation set is formulated for the spindle unit. This equation set comprehensively accounts for dynamic variations in key parameters such as preload, lubricant viscosity, thermal load intensity, thermal contact resistance, and convective coefficients. To ascertain the time constant, a meticulously designed set of thermal characteristic experiments is executed. Subsequently, the digital twin system embarks on predictive modeling of thermal errors across varied operational conditions. This prediction then forms the foundation for thermal error compensation. With the integration of the present model into the digital twin system, the results are impressive: the absolute average and maximum deviations in thermal elongation, post-error control, stand at approximately 0.40 μm and 1.24 μm, respectively.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27

Similar content being viewed by others

References

  1. Cao H, Zhang X, Chen X (2017) The concept and progress of intelligent spindles: a review. Int J Mach Tool Manu 112(1):21–52. https://doi.org/10.1016/j.ijmachtools.2016.10.005

    Article  Google Scholar 

  2. Mayr J, Jedrzejewski J, Uhlmann E, Donmez MA, Knapp W, Härtig F, Moriwaki T, Shore P, Schmitt R, Brecher C, Würz T, Wegener K (2012) Thermal issues in machine tools. CIRP Ann-Manuf Techn 61(2):771–791. https://doi.org/10.1016/j.cirp.2012.05.008

    Article  Google Scholar 

  3. Li H, Shin YC (2004) Integrated dynamic thermo-mechanical modeling of high speed spindles, part 1: model development. J Manuf Sci E-T ASME 126(1):148–158. https://doi.org/10.1115/1.1644545

    Article  Google Scholar 

  4. Chien CH, Jang JY (2008) 3-D numerical and experimental analysis of a built-in motorized high-speed spindle with helical water cooling channel. Appl Therm Eng 28(17):2327–2336. https://doi.org/10.1016/j.applthermaleng.2008.01.015

    Article  Google Scholar 

  5. Liu J, Ma C, Wang S, Wang S, Yang B, Shi H (2018) Thermal-structure interaction characteristics of a high-speed spindle-bearing system. Int J Mach Tool Manu 137:42–57. https://doi.org/10.1016/j.ijmachtools.2018.10.004

    Article  Google Scholar 

  6. Ma C, Yang J, Zhao L, Mei X, Shi H (2015) Simulation and experimental study on the thermally induced deformations of high-speed spindle system. Appl Therm Eng 86:251–268. https://doi.org/10.1016/j.applthermaleng.2015.04.064

    Article  Google Scholar 

  7. Ma C, Mei X, Yang J, Zhao L, Shi H (2015) Thermal characteristics analysis and experimental study on the high-speed spindle system. Int J Adv Manuf Tech 79(1):469–489. https://doi.org/10.1007/s00170-015-6821-z

    Article  Google Scholar 

  8. Ma C, Zhao L, Shi H, Mei X, Yang J (2017) Experimental and simulation study on the thermal characteristics of the high-speed spindle system. P I Mech Eng C-J Mec 231(6):1072–1093. https://doi.org/10.1177/0954406216631573

    Article  Google Scholar 

  9. Pouly F, Changenet C, Ville F, Velex P, Damiens B (2010) Power loss predictions in high-speed rolling element bearings using thermal networks. Tribol T 53(6):957–967. https://doi.org/10.1080/10402004.2010.512117

    Article  Google Scholar 

  10. Pouly F, Changenet C, Ville F, Velex P, Damiens B (2010) Investigations on the power losses and thermal behaviour of rolling element bearings. P I Mech Eng J-J Eng 224(9):925–933. https://doi.org/10.1243/13506501JET695

    Article  Google Scholar 

  11. Takabi J, Khonsari MM (2013) Experimental testing and thermal analysis of ball bearings. Tribol Int 60:93–103. https://doi.org/10.1016/j.triboint.2012.10.009

    Article  Google Scholar 

  12. Shi H, He B, Yue Y, Min C, Mei X (2019) Cooling effect and temperature control of oil cooling system for ball screw feed drive system of precision machine tool. Appl Therm Eng 161(10):114150. https://doi.org/10.1016/j.applthermaleng.2019.114150

    Article  Google Scholar 

  13. Liu T, Gao W, Zhang D, Zhang Y, Chang W, Liang C, Tian Y (2016) Analytical modeling for thermal errors of motorized spindle unit. Int J Mach Tool Manu 112:53–70. https://doi.org/10.1016/j.ijmachtools.2016.09.008

    Article  Google Scholar 

  14. 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 Tool Manu 43(4):405–419. https://doi.org/10.1016/S0890-6955(02)00264-X

    Article  Google Scholar 

  15. Wang L, Wang H, Li T, Feng Li (2015) A hybrid thermal error modeling method of heavy machine tools in z-axis. J Adv Manuf Tech 80:389–400. https://doi.org/10.1007/s00170-015-6988-3

    Article  Google Scholar 

  16. 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 Tool Manu 105:58–67. https://doi.org/10.1016/j.ijmachtools.2016.03.006

    Article  Google Scholar 

  17. Mayr J, Müller M, Weikert S (2016) Automated thermal main spindle & B-axis error compensation of 5-axis machine tools [J]. CIRP Ann-Manuf Techn 65(1):479–482. https://doi.org/10.1016/j.cirp.2016.04.018

    Article  Google Scholar 

  18. Ramesh R, Mannan MA, Poo AN (2003) Thermal error measurement and modelling in machine tools: part I. Influence of varying operating conditions. Int J Mach Tool Manu 43(4):391–404. https://doi.org/10.1016/S0890-6955(02)00263-8

    Article  Google Scholar 

  19. Liu H, Miao E, Wei X, Zhuang X (2016) Robust modeling method for thermal error of CNC machine tools based on ridge regression algorithm. Int J Mach Tool Manu 113:35–48. https://doi.org/10.1016/j.ijmachtools.2016.11.001

    Article  Google Scholar 

  20. 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(7):158–168. https://doi.org/10.1016/S0890-6955(02)00263-8

    Article  Google Scholar 

  21. 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. J Adv Manuf Tech 89(3071–3085):1–15. https://doi.org/10.1007/s00170-016-9254-4

    Article  Google Scholar 

  22. Ma C, Zhao L, Mei X, Shi H, Yang J (2017) Thermal error compensation based on genetic algorithm and artificial neural network of the shaft in the high-speed spindle system. P I Mech Eng B-J Eng. 231(5):753–767. https://doi.org/10.1177/0954405416639893

    Article  Google Scholar 

  23. Tan B, Mao X, Liu H, Li B, He S, Peng F, Yin L (2014) A thermal error model for large machine tools that considers environmental thermal hysteresis effects. Int J Mach Tool Manu 82–83(7):11–20. https://doi.org/10.1016/j.ijmachtools.2014.03.002

    Article  Google Scholar 

  24. Feng W, Li Z, Gu Q, Yang J (2015) Thermally induced positioning error modelling and compensation based on thermal characteristic analysis. Int J Mach Tool Manu 93(6):26–36. https://doi.org/10.1016/j.ijmachtools.2015.03.006

    Article  Google Scholar 

  25. Yang H, Ni J (2005) Dynamic neural network modeling for nonlinear, nonstationary machine tool thermally induced error. Int J Mach Tool Manu 45(4–5):455–465. https://doi.org/10.1016/j.ijmachtools.2004.09.004

    Article  Google Scholar 

  26. Liu J, Ma C, Gui H, Wang S (2021) Thermally-induced error compensation of spindle system based on long short term memory neural networks. Appl Soft Comput 102:107094. https://doi.org/10.1016/j.asoc.2021.107094

    Article  Google Scholar 

  27. Liu J, Gui H, Ma C (2023) Digital twin system of thermal error control for a large-size gear profile grinder enabled by gated recurrent unit. J Amb Intel Hum Comp 14:1269–1295. https://doi.org/10.1007/s12652-021-03378-4

    Article  Google Scholar 

  28. Wang J, Niu X, Gao RX, Huang Z, Xue R (2023) Digital twin-driven virtual commissioning of machine tool. Robot Cim-Int Manuf 81:102499. https://doi.org/10.1016/j.rcim.2022.102499

    Article  Google Scholar 

  29. Liu J, Wen X, Zhou H, Sheng S, Zhao P (2022) Digital twin-enabled machining process modeling. Adv Eng Inform 54:101737. https://doi.org/10.1016/j.aei.2022.101737

    Article  Google Scholar 

  30. Liu S, Bao J, Zheng P (2023) A review of digital twin-driven machining: from digitization to intellectualization. J Manuf Syst 67:361–378. https://doi.org/10.1016/j.jmsy.2023.02.010

    Article  Google Scholar 

  31. Tao F, Xiao B, Qi Q, Cheng J, Ji P (2022) Digital twin modeling. J. Manuf Syst 64:372–389. https://doi.org/10.1016/j.jmsy.2022.06.015

    Article  Google Scholar 

  32. Wei Y, Hu T, Dong L, Ma S (2023) Digital twin-driven manufacturing equipment development. Robot Cim-Int Manuf 83:102557. https://doi.org/10.1016/j.rcim.2023.102557

    Article  Google Scholar 

  33. Creighton E, Honegger A, Tulsian A, Mukhopadhyay D (2010) Analysis of thermal errors in a high-speed micro-milling spindle. Int J Mach Tool Manu 50(4):386–393. https://doi.org/10.1016/j.ijmachtools.2009.11.002

    Article  Google Scholar 

  34. Kim KD, Kim MS, Chung SC (2004) Real-time compensatory control of thermal errors for high-speed machine tools. P I Mech Eng B-J Eng 218(8):913–924. https://doi.org/10.1243/095440504148616

    Article  Google Scholar 

  35. ISO 230–3 (2007) Test code for machine tools part 3: determination of thermal effects, ISO copyright office, Switzerland. https://www.iso.org/standard/39188.html

  36. 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):763–771. https://doi.org/10.1115/1.2976148

    Article  Google Scholar 

  37. Zimmermann N, Müller E, Lang S, Mayr J, Wegener K (2023) Thermally compensated 5-axis machine tools evaluated with impeller machining tests. CIRP J Manuf Sci Tec 46:19–35. https://doi.org/10.1016/j.cirpj.2023.07.005

    Article  Google Scholar 

  38. Zhao H, Yang J, Shen J (2007) Thermal error optimization modeling and real-time compensation on a CNC turning center. Int J Mach Tool Manu 207:172–179. https://doi.org/10.1016/j.jmatprotec.2007.12.067

    Article  Google Scholar 

Download references

Funding

This research was supported by the National Natural Science Foundation of China (Grant numbers 52275474 and 51905057), the China Postdoctoral Science Foundation (2022M720565), the Natural Science Foundation Project of Chongqing, Chongqing Science and Technology Commission, China (Grant number cstc2019jcyj-msxmX0050), the Fundamental Research Funds for the Central Universities, China (Grant number 2020CDJQY-A036), the Venture & Innovation Support Program for Chongqing Overseas Returnees (Grant number cx2019054), and State Key Laboratory for Manufacturing Systems Engineering, China (Grant number sklms2020016).

Author information

Authors and Affiliations

  1. College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing, 400044, China

    Jialan Liu, Chi Ma & Qiang Yuan

  2. State Key Laboratory of Mechanical Transmission for Advanced Equipment, Chongqing University, Chongqing, 400044, China

    Jialan Liu, Chi Ma & Qiang Yuan

Authors
  1. Jialan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chi Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qiang Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Jialan Liu, Chi Ma, and Qiang Yuan. The first draft of the manuscript was written by Jialan Liu, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Chi Ma.

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 (e.g. a society or other partner) 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.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, J., Ma, C. & Yuan, Q. Spindle unit thermal error modeling and compensation based on digital twin. Int J Adv Manuf Technol 132, 1525–1555 (2024). https://doi.org/10.1007/s00170-024-13445-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-024-13445-7

Keywords

Search

Navigation