Skip to main content
SpringerLink
Log in

A general identification method for position-dependent geometric errors of rotary axis with single-axis driven

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

Abstract

Position-dependent geometric errors (PDGEs) of rotary axis affect the accuracy of the multi-axis machine tool. However, many PDGE identification methods were not general enough and not applicable when the structure of the machine tool was limited or changed. In this paper, a general PDGE identification method with single-axis driven was proposed. Firstly, the comprehensive length change model of the double-ball bar (DBB) was established. The simplification was conducted through the constraint condition to obtain the identification matrix. Then, the effect of the installation errors of the DBB was analyzed and eliminated. Simulations were carried out to validate the correctness of the proposed method when considering the installation errors. Next 10 measurement patterns were determined according to the structure limitation of the small-size 5-axis machine tool. Totally 364 combinations with full rank identification matrix are available. Finally, the prediction experiments and analysis for standard deviation were conducted to further validate the effectiveness of the proposed method. It turned out that the small condition number of the identification matrix can more likely achieve high accuracy. And an improved combination using 5 patterns was proposed with the same accuracy achieved compared to that using a total of 10 patterns.

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

Similar content being viewed by others

Data availability

The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

PDGEs:

Position-dependent geometric errors

PIGEs:

Position-independent geometric errors

DBB:

Double-ball bar

MADM:

Multi-axis driven method

SADM:

Single-axis driven method

P 0(x w, y w, z w):

Initial position of the workpiece ball center

P i(x i, y i, z i):

Theoretical position of the workpiece ball center

P(x, y, z):

Actual position of the workpiece ball center

Q(x t, y t, z t):

Position of the tool ball center

T i :

Theoretical motion transformation matrix

T :

Actual motion transformation matrix

Δx, Δy, Δz :

Deviation components of the workpiece ball center

E XC, E YC, E ZC :

Translational PDGEs of C-axis along X-, Y-, and Z-axes

E AC, E BC, E CC :

Angular PDGEs of C-axis around X-, Y-, and Z-axes

E XOC, E YOC :

Translational PIGEs of C-axis along X- and Y-axes

E AOC, E BOC :

Angular PIGEs of C-axis around X- and Y-axes

r :

Standard radius of double-ball bar

Δr :

Length change of the DBB considering the PDGEs

ΔR :

Length change of the DBB considering the PDGEs, PIGEs, and installation error

E :

PDGEs in matrix form

K :

Identification matrix

Δr :

Length change in matrix form

δ xt, δ yt, δ zt :

Installation errors on the side of tool ball

δ xw, δ yw, δ zw :

Installation errors on the side of workpiece ball

E(pre):

Pre-set PDGEs in the simulation

E(set):

PDGEs set in the simulation

E(cal):

PDGEs calculated

E(ref):

PDGEs referred

σ:

Standard deviations of identified PDGEs

m :

Measurement times

n :

Total number of measured points

References

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

    Article  Google Scholar 

  2. K. Xu, G. Li, K. He, X. Tao (2020) Identification of position-dependent geometric errors with non-integer exponents for linear axis using double ball bar, International Journal of Mechanical Sciences, 170

  3. Tsutsumi M, Tone S, Kato N, Sato R (2013) Enhancement of geometric accuracy of five-axis machining centers based on identification and compensation of geometric deviations. Int J Mach Tools Manuf 68:11–20

    Article  Google Scholar 

  4. Yang J, 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

    Article  Google Scholar 

  5. ISO 230-1, Test code for machine tools—part 1: geometric accuracy of machines operating under no-load or quasi-static conditions, 2012

  6. ISO 230-7, Test code for machine tools-part 7: geometric accuracy of axes of rotation, ISO, 2006

  7. Abbaszadeh-Mir, Y., Mayer, J.R.R., Cloutier, G., Fortin, C, Theory and simulation for the identification of the link geometric errors for a five-axis machine tool using a telescoping magnetic ball-bar, International Journal of Production Research, 40(18):4781–4797

  8. Abbaszadeh-Mir Y, Mayer JRR, Fortin C (2003) Methodology and simulation of the calibration of a five-axis machine tool link geometry and motion errors using polynomial modelling and a telescoping magnetic ball-bar. WIT Trans Eng Sci 44:527–543

    Google Scholar 

  9. Lee K-I, Yang S-H (2013) Robust measurement method and uncertainty analysis for position-independent geometric errors of a rotary axis using a double ball-bar. Int J Precis Eng Manuf 14:231–239

    Article  Google Scholar 

  10. Xiang S, Yang J (2014) Using a double ball bar to measure 10 position-dependent geometric errors for rotary axes on five-axis machine tools. Int J Adv Manuf Technol 75:559–572

    Article  Google Scholar 

  11. R. Zhou, B. Kauschinger, S. Ihlenfeldt, Path generation and optimization for DBB measurement with continuous data capture, Measurement, 155 (2020)

  12. Zhong X, Liu H, Mao X, Li B, He S (2019) Influence and error transfer in assembly process of geometric errors of a translational axis on volumetric error in machine tools[J]. Measurement 140:450–461

    Article  Google Scholar 

  13. Tsutsumi M, Saito A (2003) Identification and compensation of systematic deviations particular to 5-axis machining centers. Int J Mach Tools Manuf 43:771–780

    Article  Google Scholar 

  14. Xiang S, Yang J, Zhang Y (2013) Using a double ball bar to identify position-independent geometric errors on the rotary axes of five-axis machine tools. Int J Adv Manuf Technol 70:2071–2082

    Article  Google Scholar 

  15. Fu G, Fu J, Xu Y, Chen Z, Lai J (2015) Accuracy enhancement of five-axis machine tool based on differential motion matrix: geometric error modeling, identification and compensation. Int J Mach Tools Manuf 89:170–181

    Article  Google Scholar 

  16. Zhong L, Bi Q, Wang Y (2017) Volumetric accuracy evaluation for five-axis machine tools by modeling spherical deviation based on double ball-bar kinematic test. Int J Mach Tools Manuf 122:106–119

    Article  Google Scholar 

  17. Lee K-I, Yang S-H (2015) Compensation of position-independent and position-dependent geometric errors in the rotary axes of five-axis machine tools with a tilting rotary table. Int J Adv Manuf Technol 85:1677–1685

    Article  Google Scholar 

  18. Lee K-I, Yang S-H (2013) Measurement and verification of position-independent geometric errors of a five-axis machine tool using a double ball-bar. Int J Mach Tools Manuf 70:45–52

    Article  Google Scholar 

  19. Ding S, Wu W, Huang X, Song A, Zhang Y (2018) Single-axis driven measurement method to identify position-dependent geometric errors of a rotary table using double ball bar. Int J Adv Manuf Technol 101:1715–1724

    Article  Google Scholar 

  20. Zargarbashi SHH, Mayer JRR (2006) Assessment of machine tool trunnion axis motion error, using magnetic double ball bar. Int J Mach Tools Manuf 46:1823–1834

    Article  Google Scholar 

  21. Zargarbashi SHH, Angeles J (2014) Identification of error sources in a five-axis machine tool using FFT analysis. Int J Adv Manuf Technol 76:1353–1363

    Article  Google Scholar 

  22. Xiang S, Li H, Deng M, Yang J (2018) Geometric error analysis and compensation for multi-axis spiral bevel gears milling machine. Mech Mach Theory 121:59–74

    Article  Google Scholar 

  23. Xiang Sitong. Volumetric error measuring, modeling and compensation technique for five-axis machine tools, PhD Thesis, Shanghai Jiao Tong University

  24. Liu Y, Wan M, Xing W-J, Xiao Q-B, Zhang W-H (2018) Generalized actual inverse kinematic model for compensating geometric errors in five-axis machine tools. Int J Mech Sci 145:299–317

    Article  Google Scholar 

  25. Chen J, Lin S, Zhou X, Gu T (2016) A ballbar test for measurement and identification the comprehensive error of tilt table. Int J Mach Tools Manuf 103:1–12

    Article  Google Scholar 

  26. Lee K-I, Yang S-H (2014) Circular tests for accurate performance evaluation of machine tools via an analysis of eccentricity. Int J Precis Eng Manuf 15:2499–2506

    Article  Google Scholar 

  27. Zhu S, Ding G, Qin S, Lei J, Zhuang L, Yan K (2012) Integrated geometric error modeling, identification and compensation of CNC machine tools. Int J Mach Tools Manuf 52:24–29

    Article  Google Scholar 

  28. Hong C, Ibaraki S, Matsubara A (2011) Influence of position-dependent geometric errors of rotary axes on a machining test of cone frustum by five-axis machine tools. Precis Eng 35:1–11

    Article  Google Scholar 

  29. Ibaraki S, Oyama C, Otsubo H (2011) Construction of an error map of rotary axes on a five-axis machining center by static R-test. Int J Mach Tools Manuf 51:190–200

    Article  Google Scholar 

  30. Xia H, Peng W, Ouyang X, Chen X, Wang S, Chen X (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 

  31. Chen J, Lin S, He B (2014) Geometric error measurement and identification for rotary table of multi-axis machine tool using double ballbar. Int J Mach Tools Manuf 77:47–55

    Article  Google Scholar 

  32. Xiang S, Altintas Y (2016) Modeling and compensation of volumetric errors for five-axis machine tools. Int J Mach Tools Manuf 101:65–78

    Article  Google Scholar 

  33. Liu Y, Wan M, Xing W-J, Zhang W-H (2018) Identification of position independent geometric errors of rotary axes for five-axis machine tools with structural restrictions. Robot Comput Integr Manuf 53:45–57

    Article  Google Scholar 

  34. Jiang X, Cripps RJ (2015) A method of testing position independent geometric errors in rotary axes of a five-axis machine tool using a double ball bar. Int J Mach Tools Manuf 89:151–158

    Article  Google Scholar 

  35. Xiang S, Li H, Deng M, Yang J (2018) Geometric error identification and compensation for non-orthogonal five-axis machine tools. Int J Adv Manuf Technol 96:2915–2929

    Article  Google Scholar 

  36. RENISHAW PLC. Renishaw ball bar help. Ball bar 5HPS software. Version 5.09.09. [Computer Software]

  37. Lee K-I, Lee D-M, Yang S-H (2011) Parametric modeling and estimation of geometric errors for a rotary axis using double ball-bar. Int J Adv Manuf Technol 62:741–750

    Article  Google Scholar 

Download references

Funding

This work was supported by the National Key Research and Development Program of China (No. 2019YFB1703700).

Author information

Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, China

    Kai Xu, Guolong Li, Zheyu Li, Xin Dong & Changjiu Xia

Authors
  1. Kai Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guolong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zheyu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xin Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Changjiu Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Kai Xu proposed the identification method and wrote the manuscript. Guolong Li contributed significantly to analysis and manuscript preparation. Zheyu Li performed the experiment. Xin Dong helped perform the analysis with constructive discussions. Changjiu Xia performed the data analyses.

Corresponding author

Correspondence to Guolong Li.

Ethics declarations

Ethical approval

Not applicable.

Consent to participate

Not applicable.

Consent to publish

Yes.

Competing interests

The authors declare that they have 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

Xu, K., Li, G., Li, Z. et al. A general identification method for position-dependent geometric errors of rotary axis with single-axis driven. Int J Adv Manuf Technol 112, 1171–1191 (2021). https://doi.org/10.1007/s00170-020-06530-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-020-06530-0

Keywords

Search

Navigation