Skip to main content
SpringerLink
Log in

Geometric error sensitivity analysis for a 6-axis welding equipment based on Lie theory

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

Abstract

The influence of geometric errors on the accuracy of machine tools tends to attract more attention to the increasing demand for high-precision machining. In this paper, geometric error modeling and sensitivity analysis are employed to quantify the importance of geometric error for a new efficient and automatic 6-axis welding equipment. The geometric error model of the 6-axis welding equipment with 36 geometric error components is established based on Lie theory. Based on the geometric error model, the new sensitivity analysis method, in which the deviation of the welding torch pose is treated as a distance metric in SE(3), is proposed to evaluate the influences of geometric errors on the accuracy of the welding torch. And the sensitivity coefficient of each geometric error is derived by considering the basic value of geometric errors. Numerical simulations of a typical welding trajectory for intersecting pipes are conducted to analyze the sensitivity of geometric errors by the new method. The simulation results verified the validity of the sensitivity analysis method and the dominant geometric errors affecting the accuracy of the welding equipment were identified. Compared with the previous sensitivity analysis method, the proposed sensitivity analysis method considers the orientation error and position error of the welding torch simultaneously, which is more convenient and effective, and can also be applied in precision design and geometric error compensation of machine tools.

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

Similar content being viewed by others

References

  1. Huang T, Li Y, Tang G, Li S, Zhao X, Xianping L (2002) Error modeling, sensitivity analysis and assembly process of a class of 3-DOF parallel kinematic machines with parallelogram struts. Sci China Ser E-Technol Sci 45:467–476. https://doi.org/10.1360/02ye9054

  2. Schwenke H, Knapp W, Haitjema H, Weckenmann A, Schmitt R, Delbressine F (2008) Geometric error measurement and compensation of machines-an update. CIRP Ann-Manuf Technol 57(2):660–675. https://doi.org/10.1016/j.cirp.2008.09.008

  3. Lin Y, Shen Y (2003) Modelling of Five-Axis Machine Tool Metrology Models Using the Matrix Summation Approach . Int J Adv Manuf Technol 21:243–248. https://doi.org/10.1007/s001700300028https://doi.org/10.1007/s001700300028

  4. Fu G, Fu J, Xu Y, Chen Z (2014) Product of exponential model for geometric error integration of multi-axis machine tools. Int J Adv Manuf Technol 71:1653–1667. https://doi.org/10.1007/s00170-013-5586-5https://doi.org/10.1007/s00170-013-5586-5

  5. Chen J-x, Lin S-w, Zhou X-l (2016) A comprehensive error analysis method for the geometric error of multi-axis machine tool. Int Mach Tools Manuf 106:56–66. https://doi.org/10.1016/j.ijmachtools.2016.04.001https://doi.org/10.1016/j.ijmachtools.2016.04.001

  6. Díaz-Tena E, Ugalde U, De Lacalle LL, De la Iglesia A, Calleja A, Campa FJ (2013) Propagation of assembly errors in multitasking machines by the homogenous matrix method. Int J Adv Manuf Technol 68:149–164. https://doi.org/10.1007/s00170-012-4715-x

  7. Zhang X, Zhang Y, Pandey MD (2015) Global sensitivity analysis of a CNC machine tool: application of MDRM. Int J Adv Manuf Technol 81:159–169. https://doi.org/10.1007/s00170-015-7128-9

  8. Cheng Q, Zhao H, Zhang G, Gu P, Cai L (2014) An analytical approach for crucial geometric errors identification of multi-axis machine tool based on global sensitivity analysis. Int J Adv Manuf Technol 75:107–121. https://doi.org/10.1007/s00170-014-6133-8

  9. Cheng Q, Feng Q, Liu Z, Gu P, Zhang G (2016) Sensitivity analysis of machining accuracy of multi-axis machine tool based on POE screw theory and Morris method. Int J Adv Manuf Technol 84:2301–2318. https://doi.org/10.1007/s00170-015-7791-x

  10. 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):1–11. https://doi.org/10.1016/j.precisioneng.2010.09.004

  11. Lee RS, Lin YH (2012) Applying bidirectional kinematics to assembly error analysis for five-axis machine tools with general orthogonal configuration. Int J Adv Manuf Technol 62:1261–1272. https://doi.org/10.1007/s00170-011-3860-y

  12. 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. https://doi.org/10.1016/j.ijmachtools.2014.11.005https://doi.org/10.1016/j.ijmachtools.2014.11.005

  13. Khan AW, Wuyi C (2010) Systematic geometric error modeling for workspace volumetric calibration of a 5-axis turbine blade grinding machine. Chin J Aeronaut 23(5):604–615. https://doi.org/10.1016/S1000-9361(09)60261-2

  14. Chen G, Liang Y, Sun Y, Chen W, Wang B (2013) Volumetric error modeling and sensitivity analysis for designing a five-axis ultra-precision machine tool. Int J Adv Manuf Technol 68:2525–2534. https://doi.org/10.1007/s00170-013-4874-4

  15. Tang H, Duan J-a, Lan S, Shui H (2015) A new geometric error modeling approach for multi-axis system based on stream of variation theory. Int J Mach Tools Manuf 92: 41–51. https://doi.org/10.1016/j.ijmachtools.2015.02.012

  16. Shi L, Tian X, Zhang C (2015) Automatic programming for industrial robot to weld intersecting pipes. Int J Adv Manuf Technol 81:2099–2107. https://doi.org/10.1007/s00170-015-7331-8

  17. Li Q, Wang W, Jiang Y, Li H, Zhang J, Jiang Z (2018) A sensitivity method to analyze the volumetric error of five-axis machine tool. Int J Adv Manuf Technol 98:1791–1805. https://doi.org/10.1007/s00170-018-2322-1

  18. Park FC (1995) Distance Metrics on the Rigid-Body Motions with Applications to Mechanism Design. ASME J Mech Des 117(1):48–54. https://doi.org/10.1115/1.2826116

  19. Wang Y (2006) An incremental method for forward kinematics of parallel manipulators. In 2006 IEEE Conference on Robotics, Automation and Mechatronics, pp 1–5

  20. Li J, Xie F, Liu X (2016) Geometric error modeling and sensitivity analysis of a five-axis machine tool. Int J Adv Manuf Technol 82:2037–2051. https://doi.org/10.1007/s00170-015-7492-5

  21. Fu G, Gong H, Fu J, Gao H, Deng X (2019) Geometric error contribution modeling 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 Tools Manuf 147. https://doi.org/10.1016/j.ijmachtools.2019.103455

  22. Murray RM, Li Z, Sastry SS (1994) A mathematical introduction to robotic manipulation. CRC press, Boca Raton

  23. Craig JJ (2009) Introduction to robotics: mechanics and control, 3/E. Pearson Education India

  24. Guo S, Zhang D, Xi Y (2016) Global Quantitative Sensitivity Analysis and Compensation of Geometric Errors of CNC Machine Tool. Math Probl Eng 2016. https://doi.org/10.1155/2016/2834718https://doi.org/10.1155/2016/2834718

  25. Shi L, Tian X (2015) Automation of main pipe-rotating welding scheme for intersecting pipes. Int J Adv Manuf Technol 77:955–964. https://doi.org/10.1007/s00170-014-6526-8

Download references

Funding

The authors received research funding by the National Key Research and Development Plan of China under Grant No.2017YFB13035 and the Shandong Provincial Key Research and Development Program (Major Scientific and Technological Innovation Project) under Grant No. 2019JZZY010441.

Author information

Authors and Affiliations

  1. Center for Robotics, School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Weihua Fang & Xincheng Tian

  2. Engineering Research Center of Intelligent Unmanned System, Ministry of Education, Jinan, 250061, China

    Weihua Fang & Xincheng Tian

Authors
  1. Weihua Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xincheng Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xincheng Tian.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Author’s contributions

Weihua Fang was a major contributor in writing the manuscript. All authors read and approved the final manuscript.

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

Fang, W., Tian, X. Geometric error sensitivity analysis for a 6-axis welding equipment based on Lie theory. Int J Adv Manuf Technol 113, 1045–1056 (2021). https://doi.org/10.1007/s00170-020-06527-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-020-06527-9

Keywords

Search

Navigation