Skip to main content
SpringerLink
Log in

A method of identifying geometric errors for machine tools with 3 axes based on a set of sine functions using double ballbar

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

Abstract

Geometric error is an important error source of machine tools. Quick, accurate, and convenient measurement of machine tool geometric errors is an urgent need to improve the accuracy of machine tools. Based on the ballbar’s circular trajectory test principle, this paper proposes a machine tool error identification method based on a collection of sine functions. Based on the multi-body system theory and the homogeneous coordinate transformation method, a mathematical model of the circular path error and geometric error of the machine tool with 3 axes is established. Using a collection of sine functions to fit geometric errors has a higher fitting accuracy than traditional polynomial function fitting methods. By designing five circular motion trajectories of the same radius with different centers in the test area, and assuming that each geometric error is a collection of sine functions, a parametric identification model for machine tool geometric errors based on the circular trajectory is derived. The particle swarm algorithm is used to search and solve the various parameters of the sine function collection, and finally, 9 linear errors and 5 angular errors of the machine tool are obtained. In order to verify the effectiveness of the method, simulation and test comparison experiments were carried out. The experimental results show that 4 linear errors and 1 angular error of the machine tools can be effectively obtained. The verification experiment results show that, compared with the measurement results of the laser interferometer, the maximum deviation of the measurement and identification results proposed in this paper is within 2.5 μm.

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

Similar content being viewed by others

Data availability

The datasets generated and analyzed during the current study are available upon reasonable request.

References

  1. Xia HJ, Peng WC, Ouyang XB et al (2017) Identification of geometric errors of rotary axis on multi-axis machine tool based on kinematic analysis method using double ball bar. Int J Mach Tools Manuf 122:161–175

    Article  Google Scholar 

  2. Zhengchun DU, Jianguo YANG, Qibo FENG (2017) Research status and trend of geometrical error measurement of CNC machine tools. Aeronaut Manuf Technol 60(6):34–44

    Google Scholar 

  3. Xia C, Wang S, Xu K et al (2020) Geometric error identification of rotary axes based on uniaxial motion measurement of double ball bar. Chinese J Sci Instrum 41(07):19–28

    Google Scholar 

  4. Guangsheng C, Haolin L (2013) Fast geometric error measurement and identification of rotary table for multi-axis CNC machining tools. Chinese J Sci Instrum 34(11):2499–2505

    Google Scholar 

  5. Jiang X, Wang L, Liu C (2019) Geometric accuracy evaluation during coordinated motion of rotary axes of a five-axis machine tool. Measurement 146(11):403–410

    Article  Google Scholar 

  6. Florussen GHJ, Delbressine FLM, Van de Molengraft MJG et al (2001) Assessing geometrical errors of multi-axis machines by three-dimensional length measurements. Measurement 30(4):241–2554

    Article  Google Scholar 

  7. Zhang H, Zhou Y, Tang X et al (2002) Error identification and compensation of CNC machining centers using Renishaw ballbar. Chinese J Mech Eng 10(2002):108–113

    Google Scholar 

  8. Tian W, Guo L, Liu H (2016) Rapid identification method for geometric errors of CNC machine tools. J Tianjin Univ (Sci Technol) 49(02):171–177

    Google Scholar 

  9. Xu K, Li G, He K et al (2020) Identification of position-dependent geometric errors with non-integer exponents for Linear axis using double ball bar. Int J Mech Sci 170:105326

    Article  Google Scholar 

  10. Lei WT, Hsu YY (2002) Accuracy test of five-axis CNC machine tool with 3D probe–ball. Part I: design and modeling. Int J Mach Tools Manuf 42(2002):1153–1162

    Article  Google Scholar 

  11. Lei WT, Hsu YY (2002) Accuracy test of five-axis CNC machine tool with 3D probe-ball. Part II: errors estimation. Int J Mach Tools Manuf 42(2002):1163–1170

    Article  Google Scholar 

  12. Kaiguo F (2012) Comprehensive compensation and application for multi-error elements on CNC machine. Shanghai Jiao Tong University

  13. FAN Z, YANG J, LI Z (2009) The polynomial order selection for the geometric errors modeling of NC machine tool. Mach Tool Hydraul 37(10):49–50

    Google Scholar 

  14. Guo R, Fu G, Sun L et al (2015) Chebyshev polynomials based parametric modeling of geometric errors for CNC machine tools. Trans Chinese Soc Agric Mach 46(05):336–343

    Google Scholar 

  15. Leng S, Liu Z, Wang X et al (2017) Legendre polynomials based parametric modeling of geometric errors for machining center. Comput Integr Manuf Syst 23(11):2491–2496

    Google Scholar 

  16. Fu G (2016) Research pm geometric error modeling and compensation of CNC machine tools based on the product-of-exponential theory and transforming differential changes between coordinate frames. Zhejiang University

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Guangsheng Chen, Yue Zhang & Bu Yuan

Authors
  1. Guangsheng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yue Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bu Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Guangsheng Chen: methodology, software, writing (original draft preparation), experiment and data processing; Yue Zhang: conceptualization, methodology, writing (review and editing), supervision, project administration; Bu Yuan: format checking, modification of figures and text.

Corresponding author

Correspondence to Guangsheng Chen.

Ethics declarations

Ethics approval

Not applicable.

Consent to participate

Not applicable.

Consent for publication

All the co-authors consent to the publication of this work.

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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, G., Zhang, Y. & Yuan, B. A method of identifying geometric errors for machine tools with 3 axes based on a set of sine functions using double ballbar. Int J Adv Manuf Technol 121, 559–571 (2022). https://doi.org/10.1007/s00170-022-09342-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-022-09342-6

Keywords

Search

Navigation