SpringerLink
Log in

Synthetic positioning error modeling for a linear feed system based on GA-SVR algorithm

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

The positioning error of the linear feed system has a great impact on the fabrication quality of the parts. The main error sources contain the geometric error fundamentally determined by the machining capacity and the assembly performance and the thermal error resulted from the temperature rise caused by internal and external heat sources in the manufacturing process. The error compensation method is an effective and economical way to improve the positioning accuracy whose core issue is to establish an error mathematical model with high prediction accuracy and strong robustness. In this paper, a genetic algorithm parameter-optimized support vector machine regression (GA-SVR) modeling method is used to map an intrinsic relationship between location and temperature rise as inputs and synthetic positioning error as output, in which the positioning error collected by a laser interferometer is decomposed into geometrical error and thermal error that is employed to sift the temperature-sensitive points with hierarchical clustering method and gray correlation analysis. The thermal characteristic experiments at different feed speeds were carried out to validate the developed synthetic positioning error model of the X-axis feed system in the machining center. The results showed that the model can accurately reflect the synthetic positioning error change trend of the feeding axis under various operating conditions and has practical availability to perform real-time synthetic error compensation.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

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

Similar content being viewed by others

References

  1. Bryan J (1990) International status of thermal error research. CIRP Ann Manuf Technol 39(2):645–656. https://doi.org/10.1016/S0007-8506(07)63001-7

    Article  Google Scholar 

  2. Postlethwaite SR, Allen JP, Ford DG (1999) Machine tool thermal error reduction—An appraisal. Proc Inst Mech Eng Part B J Eng Manuf 13(1):1–9. https://doi.org/10.1177/095440549921300101

    Article  Google Scholar 

  3. Ferreira PM, Liu CR (1986) An analytical quadratic model for the geometric error of a machine tool. J Manuf Syst 5(1):51–63. https://doi.org/10.1016/0278-6125(86)90067-1

    Article  Google Scholar 

  4. Donmez MA, Blomquist DS, Hocken RJ, Liu CR, Barash MM (1986) A general methodology for machine tool accuracy enhancement by error compensation. Precis Eng 8(4):187–196. https://doi.org/10.1016/0141-6359(86)90059-0

    Article  Google Scholar 

  5. Zhong G, Wang C, Yang S, Ge Y (2015) Position geometric error modeling, identification and compensation for large 5-axis machining center prototype. Int J Mach Tool Manuf 89:142–150. https://doi.org/10.1016/j.ijmachtools.2014.10.009

    Article  Google Scholar 

  6. Yun WS, Kim SK, Cho DW (1999) Thermal error analysis for a CNC lathe feed drive system. Int J Mach Tool Manuf 39(7):1087–1101. https://doi.org/10.1016/S0890-6955(98)00073-X

    Article  Google Scholar 

  7. 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 Tool Manuf 51:605–611. https://doi.org/10.1016/j.ijmachtools.2011.04.001

    Article  Google Scholar 

  8. Jiang SY, Mao HB (2010) Investigation of variable optimum preload for a machine tool spindle. Int J Mach Tool Manuf 50:19–28. https://doi.org/10.1016/j.ijmachtools.2009.10.001

    Article  Google Scholar 

  9. Turek P, Jdrzejewski J, Modrzycki W (2010) Methods of machine tool error compensation. J Mach Eng 10(4):5–25

    Google Scholar 

  10. Yang S, Yuan J, Ni J (1996) Accuracy enhancement of a horizontal machining center by real-time error compensation. J Manuf Syst 15(2):113–124. https://doi.org/10.1016/0278-6125(96)82336-3

    Article  Google Scholar 

  11. Mou J (1997) A method of using neural networks and inverse kinematics for machine tool error estimation and correction. ASME Trans J Manuf Sci Eng 119:247–254

    Article  Google Scholar 

  12. Zapłata J, Pajor M (2019) Piecewise compensation of thermal errors of a ball screw driven CNC axis. Precis Eng 60:160–166. https://doi.org/10.1016/j.precisioneng.2019.07.011

    Article  Google Scholar 

  13. Mareš M, Horejš O, Havlík L (2020) Thermal error compensation of a 5-axis machine tool using indigenous temperature sensors and CNC integrated Python code validated with a machined test piece. Precis Eng 66:21–30. https://doi.org/10.1016/j.precisioneng.2020.06.010

    Article  Google Scholar 

  14. Shik YA, Han YX, Rong ZJ, Lee C-Y, Hsieh W-H (2018) DOE-FEM based design improvement to minimize thermal errors of a high speed spindle system. Therm Sci Eng Prog 8:525–536. https://doi.org/10.1016/j.tsep.2018.10.011

    Article  Google Scholar 

  15. Thiem X, Kauschinger B, Ihlenfeldt S (2019) Online correction of thermal errors based on a structure model. Int J Mach Tools Manuf 2(1):49–62. https://doi.org/10.1504/IJMMS.2019.097852

    Article  Google Scholar 

  16. Ma C, Liu J, Wang S (2020) Thermal error compensation of linear axis with fixed-fixed installation. Int J Mech Sci 175(2):105531. https://doi.org/10.1016/j.ijmecsci.2020.105531

    Article  Google Scholar 

  17. Liu J, Ma C, Wang S (2020) Data-driven thermal error compensation of linear x-axis of worm gear machines with error mechanism modeling. Mech Mach Theory 153:104009. https://doi.org/10.1016/j.mechmachtheory.2020.104009

    Article  Google Scholar 

  18. Liu J, Ma C, Wang S (2020) Data-driven thermally-induced error compensation method of high-speed and precision five-axis machine tools. Mech Syst Signal Process 138(2):106538. https://doi.org/10.1016/j.ymssp.2019.106538

    Article  Google Scholar 

  19. Li Y, Zhao J, Ji S (2018) Thermal positioning error modeling of machine tools using a bat algorithm-based back propagation neural network. Int J Adv Manuf Technol 97(5–8):2575–2586. https://doi.org/10.1007/s00170-018-1978-x

    Article  Google Scholar 

  20. 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):2333–2348. https://doi.org/10.1007/s00170-018-2793-0

    Article  Google Scholar 

  21. Sun J, Xu Y, Liu X (2014) Thermal error compensation and modeling for CNC boring and milling center. Adv Mater Res 945–949:1665–1668

    Article  Google Scholar 

  22. Pahk H, Lee SW (2002) Thermal error measurement and real time compensation system for the CNC machine tools incorporating the spindle thermal error and the feeding axis thermal error. Int J Adv Manuf Technol 20(7):487–494. https://doi.org/10.1007/s001700200182

    Article  Google Scholar 

  23. Fu J, Chen Z (2004) Research on modeling thermal dynamic errors of precision machine based on fuzzy logic and artificial neural network. J Zhejiang Univ Sci 38(6):742–746

    Google Scholar 

  24. Lin W, Fu J, XuChen Y (2008) Thermal error modeling & compensation of numerical control machine tools based on on-line least squares support vector machine. Jisuanji Jicheng Zhizao **tong Comput Integr Manuf Syst 14(2):295–299

    Google Scholar 

  25. 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. https://doi.org/10.1007/s00170-013-5229-x

    Article  Google Scholar 

  26. Lin CJ (2001) On the convergence of the decomposition method for support vector machines. IEEE Trans Neural Netw 12(6):1288–1298. https://doi.org/10.1109/72.963765

    Article  Google Scholar 

  27. Vapnik V, Golowich SE, Smola A (2008) Support vector method for function approximation, regression estimation, and signal processing. Adv Neural Inf Process Syst 9:281–287

    Google Scholar 

  28. Shen H, Fu J, He Y, Yao X (2012) On-line Asynchronous Compensation Methods for static/quasi-static error implemented on CNC machine tools. Int J Mach Tool Manuf 60:14–26. https://doi.org/10.1016/j.ijmachtools.2012.04.003

    Article  Google Scholar 

  29. Li Z, Li G, Xu K, Tang X, Dong X (2021) Temperature-sensitive point selection and thermal error modeling of spindle based on synthetical temperature information. Int J Adv Manuf Technol 113(3–4):1–15. https://doi.org/10.1007/s00170-021-06680-9

    Article  Google Scholar 

  30. Shi Y, Li Q, Meng X, Zhang T, Shi J (2020) On time-series InSAR by SA-SVR algorithm: prediction and analysis of mining subsidence. J Sensors. https://doi.org/10.1155/2020/8860225

    Article  Google Scholar 

  31. Guo Q, Xu R, Yang T, He T, Cheng X, Li Z (2016) Application of GRAM and AFSACA-BPN to thermal error optimization modeling of CNC machine tools. Int J Adv Manuf Technol 83:995–1002. https://doi.org/10.1007/s00170-015-7660-7

    Article  Google Scholar 

  32. 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 71:1669–1675. https://doi.org/10.1007/s00170-014-5606-0

    Article  Google Scholar 

  33. 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 89:3071–3085. https://doi.org/10.1007/s00170-016-9254-4Q2

    Article  Google Scholar 

  34. Miao E, Niu P, Fei Y, Yan Y (2011) Selecting temperature-sensitive points and modeling thermal errors of machine tools. J Chin Soc Mech Eng Trans Chin Inst Eng Ser C 32(6):559–565

    Google Scholar 

  35. ** L, Liu N, Chen Y, Liu Q (2017) The selection of key temperature measuring points for the compensation of thermal errors of CNC machining tools. Int J Manuf Res 12(3):338–350. https://doi.org/10.1504/IJMR.2017.086177

    Article  Google Scholar 

  36. Gholami R, Fakhari N (2017) Chapter 27—Support vector machine: principles, parameters, and applications. Handbook of neural computation. Academic Press, pp 515–535

    Chapter  Google Scholar 

  37. ISO230-3 (2020) Test code for machine tools—part 3: determination of thermal effects. ISO copyright office, Switzerland

  38. ISO230-2 (2014) Test code for machine tools—part 2: determination of accuracy and repeatability of positioning numerically controlled axes. ISO copyright office, Switzerland

Download references

Funding

This work is supported by the National Natural Science Foundation of China (No. 51775432) and Shaanxi Province Major Science and Technology Project (No. 2018ZDZX01-02-01).

Author information

Authors and Affiliations

  1. Key Lab of Mechanical Manufacturing Equipment of Shaanxi Province, **’an, 710048, China

    Yan Li, Quanan Chen, Feng Gao & **n Kou

  2. School of Mechanical and Precision Instrument Engineering, **’an University of Technology, **’an, 710048, China

    Yan Li, Quanan Chen, Feng Gao & **n Kou

  3. Qinchuang Machine Tool & Tool Group Corp., Baoji, 710018, China

    Yao Liu

  4. Shandong Deed Machinery Tool Co., Ltd., **ing, 272100, China

    **aoqing Wei

Authors
  1. Yan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Quanan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Feng Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. **n Kou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. **aoqing Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

YL contributed to conceptualization, methodology, supervision, and writing—original draft. QC contributed to methodology, software, formal analysis, and experiment. FG contributed to writing—review and editing, project administration, and funding acquisition. XK contributed to experiment, formal analysis, and investigation. YL contributed to data curation. XW contributed to visualization.

Corresponding author

Correspondence to Yan Li.

Ethics declarations

Competing interests

The authors declare that they have no competing interests.

Consent for publication

The manuscript has not been published before and is not being considered for publication elsewhere. All authors have contributed to the creation of this manuscript for important intellectual content and approved the final manuscript.

Additional information

Technical Editor: Rogério Sales Gonçalves.

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

Li, Y., Chen, Q., Gao, F. et al. Synthetic positioning error modeling for a linear feed system based on GA-SVR algorithm. J Braz. Soc. Mech. Sci. Eng. 45, 85 (2023). https://doi.org/10.1007/s40430-023-04019-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40430-023-04019-x

Keywords

Search

Navigation