Skip to main content
SpringerLink
Log in

An efficient geometric error modelling algorithm of CNC machine tool without interference of higher-order error terms

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

Abstract

Higher-order error terms (HOET) occur inevitably during the geometric error modelling and compensation of a machine tool using both screw theory and multi-body system (MBS) theory. Though the HOET has little influence on machining accuracy, it will make analysis and compensation of geometric errors complicated and tedious. Especially, it is necessary to eliminate the higher-order error terms artificially when deriving the analytical expressions for geometric error compensation. Hence, a novel geometric error modelling and compensation algorithm without the interference of HOET is proposed in this paper. Taking a three-axis CNC machine tool as an example. A new summation operation rule for geometric error modelling was defined according to the homogeneous transformation matrix (HTM) method, which has no multiplication between error matrices. And the analytical expressions of motion-axis commands for error compensation could be calculated directly according to the new modelling algorithm without manual deletion of HOET. Active elimination of HOET can simplify the process of geometric error modelling and compensation and can significantly improve efficiency. The results show that the acquisition efficiency of symbolic compensation expressions can be improved by at least 70% compared to the traditional actual inverse kinematics. Moreover, the HOET are automatically eliminated and has a small influence on the compensation accuracy. Finally, a cutting experiment was conducted and analyzed to verify the high efficiency and effectiveness of the proposed method.

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

Similar content being viewed by others

Data availability

Not applicable.

Code availability

Not applicable.

References

  1. Ni J (1997) CNC Machine accuracy enhancement through real-time error compensation. J Manuf Sci Eng 119:717–725. https://doi.org/10.1115/1.2836815

    Article  Google Scholar 

  2. Zhang JT, Lian BB, Song YM (2019) Geometric error analysis of an over-constrained parallel tracking mechanism using the screw theory. Chin J Aeronaut 32(6):1541–1554. https://doi.org/10.1016/j.cja.2018.08.021

    Article  Google Scholar 

  3. Ding S, Zhang H, Wu WW, Guo EK, Zhang YF, Song AP (2021) A digital and structure-adaptive geometric error definition and modeling method of reconfigurable machine tool. Int J Adv Manuf Technol 112(7):2359–2371. https://doi.org/10.1007/s00170-020-06435-y

    Article  Google Scholar 

  4. Wu CJ, Fan JW, Wang QH, Chen DJ (2018) Machining accuracy improvement of non-orthogonal five-axis machine tools by a new iterative compensation methodology based on the relative motion constraint equation. Int J Mach Tool Manuf 124:80–98. https://doi.org/10.1016/j.ijmachtools.2017.07.008

    Article  Google Scholar 

  5. Gao HM, Fang FZ, Zhang XD (2014) Reverse analysis on the geometric errors of ultra-precision machine. Int J Adv Manuf Technol 73(9–12):1615–1624. https://doi.org/10.1007/s00170-014-5931-3

    Article  Google Scholar 

  6. Esmaeili SM, Mayer JRR (2021) CNC table based compensation of inter-axis and linear axis scale gain errors for a five-axis machine tool from symbolic variational kinematics. CIRP Ann-Manuf Technol 70(1):439–442. https://doi.org/10.1016/j.cirp.2021.04.042

    Article  Google Scholar 

  7. Cheng L, Zhang L, Li JX, Ke YL (2021) Modelling and compensation of volumetric errors for a six-axis automated fiber placement machine based on screw theory. Proc Inst Mech Eng Part C: J Mech Eng Sci 235(23):6940–6955. https://doi.org/10.1177/09544062211017163

    Article  Google Scholar 

  8. Liang RJ, Wang ZQ, Chen WF, Ye WH (2021) Accuracy improvement for RLLLR five-axis machine tools: a posture and position compensation method for geometric errors. J Manuf Processes 71:724–733. https://doi.org/10.1016/j.jmapro.2021.09.037

    Article  Google Scholar 

  9. Fu GQ, Fu JZ, Xu YT, Chen ZC, Lai JT (2015) Accuracy enhancement of five-axis machine tool based on differential motion matrix: geometric error modelling, identification and compensation. Int J Mach Tool Manuf 89:170–181. https://doi.org/10.1016/j.ijmachtools.2014.11.005

    Article  Google Scholar 

  10. Huang ND, Jin YQ, Bi QZ, Wang YH (2015) Integrated post-processor for 5-axis machine tools with geometric errors compensation. Int J Mach Tool Manuf 94:65–73. https://doi.org/10.1016/j.ijmachtools.2015.04.005

    Article  Google Scholar 

  11. Peng FY, Ma JY, Wang W, Duan XY, Sun PP, Yan R (2013) Total differential methods based universal post processing algorithm considering geometric error for multi-axis NC machine tool. Int J Mach Tool Manuf 70:53–62. https://doi.org/10.1016/j.ijmachtools.2013.02.001

    Article  Google Scholar 

  12. Ding S, Huang XD, Yu CJ, Wang W (2016) Actual inverse kinematics for position-independent and position-dependent geometric error compensation of five-axis machine tools. Int J Mach Tool Manuf 111:55–62. https://doi.org/10.1016/j.ijmachtools.2016.10.001

    Article  Google Scholar 

  13. Xia CJ, Wang SL, Wang SB, Ma C, Xu K (2021) Geometric error identification and compensation for rotary worktable of gear profile grinding machines based on single-axis motion measurement and actual inverse kinematic model. Mech Mach Theory 155:104042. https://doi.org/10.1016/j.mechmachtheory.2020.104042

    Article  Google Scholar 

  14. Yang JX, Mayer JRR, Altintas Y (2015) A position independent geometric errors identification and correction method for five-axis serial machines based on screw theory. Int J Mach Tools Manuf 95:52–66. https://doi.org/10.1016/j.ijmachtools.2015.04.011

    Article  Google Scholar 

  15. Liu Y, Wan M, Xing WJ, Xiao QB, Zhang WH (2018) Generalized actual inverse kinematic model for compensating geometric errors in five-axis machine tools. Int J Mech Sci 145:299–317. https://doi.org/10.1016/j.ijmecsci.2018.07.022

    Article  Google Scholar 

  16. Zhong XM, Liu HQ, Mao XY, Li B (2019) An optimal method for improving volumetric error compensation in machine tools based on squareness error identification. Int J Precis Eng Manuf 20(10):1653–1665. https://doi.org/10.1007/s12541-019-00191-0

    Article  Google Scholar 

  17. Cheng Q, Sun BW, Liu ZF, Feng QN, Gu PH (2018) Geometric error compensation method based on Floyd algorithm and product of exponential screw theory. Proc Inst Mech Eng Part B: J Eng Manuf 232(7):1156–1171. https://doi.org/10.1177/0954405416663537

    Article  Google Scholar 

  18. Tian WJ, Mou MW, Yang JH, Yin FW (2019) Kinematic calibration of a 5-DOF hybrid kinematic machine tool by considering the ill-posed identification problem using regularisation method. Robot Comput-Integr Manuf 60:49–62. https://doi.org/10.1016/j.rcim.2019.05.016

    Article  Google Scholar 

  19. Fu GQ, Gong HW, Fu JZ, Gao HL, Deng XL (2019) Geometric error contribution modelling and sensitivity evaluating for each axis of five-axis machine tools based on POE theory and transforming differential changes between coordinate frames. Int J Mach Tool Manuf 147:103455. https://doi.org/10.1016/j.ijmachtools.2019.103455

    Article  Google Scholar 

  20. Guo SJ, Tang SF, Zhang DS (2019) A recognition methodology for the key geometric errors of a multi-axis machine tool based on accuracy retentivity analysis. Complexity 2019:8649496. https://doi.org/10.1155/2019/8649496

    Article  Google Scholar 

  21. Zhong XM, Liu HQ, Mao XY, Li B, He SP, Peng FY (2018) Volumetric error modeling, identification and compensation based on screw theory for a large multi-axis propeller-measuring machine. Meas Sci Technol 29(5):055011. https://doi.org/10.1088/1361-6501/aaaef3

    Article  Google Scholar 

  22. Liu YT, Ding F, Li D, Wu YG, Xue JD, Wang W, Qiao Z, Wang B (2020) Machining accuracy improvement for a dual-spindle ultra-precision drum roll lathe based on geometric error analysis and calibration. Precis Eng 66:401–416. https://doi.org/10.1016/j.precisioneng.2020.08.005

    Article  Google Scholar 

  23. Lee DM, Yang SH (2010) Mathematical approach and general formulation for error synthesis modelling of multi-axis system. Int J Mod Phys B 24(15–16):2737–2742. https://doi.org/10.1142/S0217979210065556

    Article  MATH  Google Scholar 

  24. Bi QZ, Huang ND, Sun C, Wang YH, Zhu LM, Ding H (2015) Identification and compensation of geometric errors of rotary axes on five-axis machine by on-machine measurement. Int J Mach Tool Manuf 89:182–191. https://doi.org/10.1016/j.ijmachtools.2014.11.008

    Article  Google Scholar 

  25. Fan KG, Yang JG, Yang LY (2015) Unified error model based spatial error compensation for four types of CNC machining center: part I-singular function based unified error model. Mech Syst Signal Process 60–61:656–667. https://doi.org/10.1016/j.ymssp.2014.12.023

    Article  Google Scholar 

  26. Xiang ST, Yang JG, Fan KG, Lu HX (2016) Multi-machine tools volumetric error generalized modelling and Ethernet-based compensation technique. Proc Inst Mech Eng Part B: J Eng Manuf 230(5):870–882. https://doi.org/10.1177/0954405414564407

    Article  Google Scholar 

  27. Fan JW, Tao HH, Pan R, Chen DJ (2020) An approach for accuracy enhancement of five-axis machine tools based on quantitative interval sensitivity analysis. Mech Mach Theory 148:103806. https://doi.org/10.1016/j.mechmachtheory.2020.103806

    Article  Google Scholar 

  28. Fan JW, Wang PT, Ren XF (2022) A novel sensitivity analysis of translational axis operation considering key component tolerances. Int J Adv Manuf Technol 118(3):1255–1268. https://doi.org/10.1007/s00170-021-07932-4

    Article  Google Scholar 

  29. Tao HF, Chen R, Xuan JP, Xia Q, Yang ZY, Zhang X, He S, Shi TL (2020) Prioritization analysis and compensation of geometric errors for ultra-precision lathe based on the random forest methodology. Precis Eng 61:23–40. https://doi.org/10.1016/j.precisioneng.2019.09.012

    Article  Google Scholar 

  30. Chen QD, Li W, Jiang C, Zhou ZX, Min SK (2021) Separation and compensation of geometric errors of rotary axis in 5-axis ultra-precision machine tool by empirical mode decomposition method. J Manuf Process 68:1509–1523. https://doi.org/10.1016/j.jmapro.2021.06.057

    Article  Google Scholar 

  31. Kvrgic VM, Ribic AI, Dimic Z, Zivanovic ST, Dodevska ZA (2022) Equivalent geometric errors of rotary axes and novel algorithm for geometric errors compensation in a nonorthogonal five-axis machine tool. CIRP J Manuf Sci Technol 37:477–488. https://doi.org/10.1016/j.cirpj.2022.03.001

    Article  Google Scholar 

  32. Jia PZ, Zhang B, Zheng FJ, Feng QB (2022) Comprehensive measurement model of geometric errors for three linear axes of computer numerical control machine tools. Meas Sci Technol 33(1):015202. https://doi.org/10.1088/1361-6501/ac2dbb

    Article  Google Scholar 

  33. Liu XL, Zhang XD, Fang FZ, Liu SG (2016) Identification and compensation of main machining errors on surface form accuracy in ultra-precision diamond turning. Int J Mach Tool Manuf 105:45–57. https://doi.org/10.1016/j.ijmachtools.2016.03.001

    Article  Google Scholar 

  34. Guo SJ, Zhang DS, Xi Y (2016) Global quantitative sensitivity analysis and compensation of geometric errors of CNC machine tool. Math Probl in Eng 2016:2834718. https://doi.org/10.1155/2016/2834718

    Article  Google Scholar 

  35. Chen GH, Zhang L, Wang C, Xiang H, Tong GQ, Zhao DZ (2022) High-precision modelling of CNCs’ spatial errors based on screw theory. SN Appl Sci 4(2):1–15. https://doi.org/10.1007/s42452-021-04929-2

    Article  Google Scholar 

  36. Liu YW, Liu LB, Zhao XS, Zhang Q, Wang SX (1998) Investigation of error compensation technology for NC machine tool. China Mech Eng 9(12):48–51. https://doi.org/10.3321/j.issn:1004-132X.1998.12.015(inChinese)

    Article  Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China (Grant no. 51905470), the Qing Lan Project support program from Yangzhou University, the China Postdoctoral Science Foundation (No. 2020M671617), Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant no. 19KJB460029) and Research Fund of DMIECT (Grant no. DM201701).

Author information

Authors and Affiliations

  1. College of Mechanical Engineering, Yangzhou University, Yangzhou, Jiangsu, 225127, People’s Republic of China

    Shuang Ding, Zhanqun Song, Zhiwei Chen, Weiwei Wu & Aiping Song

  2. Jiangsu Key Laboratory of Digital Manufacturing for Industrial Equipment and Control Technology, Nanjing, Jiangsu, 211816, People’s Republic of China

    Shuang Ding

Authors
  1. Shuang Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhanqun Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhiwei Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Weiwei Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Aiping Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Shuang Ding: conceptualization, methodology, validation, writing—review and editing, investigation, visualization, supervision, project administration, and funding acquisition. Zhanqun Song: methodology, writing—original draft, writing—reviewing and editing, and software. Zhiwei Chen: software, writing—reviewing and editing, and validation. Weiwei Wu: writing—reviewing and editing, and investigation. Aiping Song: writing—reviewing and editing, and supervision.

Corresponding author

Correspondence to Shuang Ding.

Ethics declarations

Ethics approval

The article follows the guidelines of the Committee on Publication Ethics (COPE) and involves no studies on human or animal subjects.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

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

Ding, S., Song, Z., Chen, Z. et al. An efficient geometric error modelling algorithm of CNC machine tool without interference of higher-order error terms. Int J Adv Manuf Technol 126, 3353–3366 (2023). https://doi.org/10.1007/s00170-023-11297-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-023-11297-1

Keywords

Search

Navigation