Skip to main content
SpringerLink
Log in

Product-of-exponential formulas for precision enhancement of five-axis machine tools via geometric error modeling and compensation

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

Abstract

This paper proposes the precision enhancement of five-axis machine tools using product-of-exponential (POE) formulas through geometric error modeling and compensation. Firstly, two issues of geometric error Denavit–Hartenberg (D-H) models for five-axis machine tools are discussed for further improvement: models of squareness errors and position of rotary axes. Three D-H models of squareness errors and three expressions of position of rotary axes are represented and analyzed. Secondly, POE formulas are established to solve the two problems and to realize the modeling and compensation. The rotation twists and rotation POE formulas of rotary axes are established with the help of the clear geometric meaning of twists to describe their positions and motions. Then, corresponding POE formulas of squareness errors are established by analyzing their geometric definition. All motion POE formulas, rotation POE formulas, and error POE formulas are multiplied in certain order to obtain the final geometric error POE formula of five-axis machine tools. In addition, Jacobian of twists is calculated easily and reasonably with the twists of each axis for the geometric error compensation. Thirdly, experiments are conducted on one SmartCNC500 five-axis machine tool in order to verify the effectiveness of error POE formula and corresponding compensation.

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

Similar content being viewed by others

References

  1. Uddin MS, Ibaraki S, Matsubara A, Matsushita T (2009) Prediction and compensation of machining geometric errors of five-axis machining centers with kinematic errors. Precis Eng J Int Soc Precis Eng Nanotechnol 33(2):194–201

    Google Scholar 

  2. 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(9–12):2525–2534

    Article  Google Scholar 

  3. 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

    Article  Google Scholar 

  4. Lin Y, Shen Y (2003) Modelling of five-axis machine tool metrology models using the matrix summation approach. Int J Adv Manuf Technol 21(4):243–248

    Article  Google Scholar 

  5. 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

    Article  Google Scholar 

  6. Khan A, Chen W (2011) A methodology for systematic geometric error compensation in five-axis machine tools. Int J Adv Manuf Technol 53(5–8):615–628

    Article  Google Scholar 

  7. Kong LB, Cheung CF (2012) Prediction of surface generation in ultra-precision raster milling of optical freeform surfaces using an Integrated Kinematics Error Model. Adv Eng Softw 45(1):124–136

    Article  Google Scholar 

  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. The International Journal of Advanced Manufacturing Technology:1–15

  9. 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 Tool Manuf 52(1):24–29

    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 Tool Manuf 42(10):1153–1162

    Article  Google Scholar 

  11. Hsu YY, Wang SS (2007) A new compensation method for geometry errors of five-axis machine tools. Int J Mach Tool Manuf 47(2):352–360

    Article  Google Scholar 

  12. Wang J, Guo J (2012) Research on volumetric error compensation for NC machine tool based on laser tracker measurement. Sci China Technol Sci 55(11):3000–3009

    Article  Google Scholar 

  13. Chen GS, Mei XS, Li HL (2013) Geometric error modeling and compensation for large-scale grinding machine tools with multi-axes. Int J Adv Manuf Technol 69(9–12):2583–2592

    Article  Google Scholar 

  14. Lee RS, She CH (1997) Developing a postprocessor for three types of five-axis machine tools. Int J Adv Manuf Technol 13(9):658–665

    Article  Google Scholar 

  15. 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

    Article  Google Scholar 

  16. Lei WT, Sung MP (2008) NURBS-based fast geometric error compensation for CNC machine tools. Int J Mach Tool Manuf 48(3–4):307–319

    Article  Google Scholar 

  17. Chen J, Lin S, He B (2014) Geometric error compensation for multi-axis CNC machines based on differential transformation. Int J Adv Manuf Technol 71(1–4):635–642

    Article  Google Scholar 

  18. Lei WT, Hsu YY (2003) Accuracy enhancement of five-axis CNC machines through real-time error compensation. Int J Mach Tool Manuf 43(9):871–877

    Article  Google Scholar 

  19. Huang Y, Du L, Huang M (2010) Screw theory based error modeling method of robot mechanisms. J Harbin Inst Technol 42(3):484–489

    Google Scholar 

  20. Li Y, Zhu MC, Li YC (2006) IEEE, Kinematics of reconfigurable flexible-manipulator using a local product-of-exponentials formula. WCICA 2006: Sixth World Congress on Intelligent Control and Automation, Vols 1–12, Conference Proceedings. New York: IEEE. 9022–9026

  21. Tao PY, Yang G, Sun YC, Tomizuka M, Lai CY (2012) Product-of-exponential (POE) model for kinematic calibration of robots with joint compliance. In: Advanced Intelligent Mechatronics (AIM), 2012 IEEE/ASME International Conference on

  22. He RB, Zhao YJ, Yang SN, Yang SZ (2010) Kinematic-parameter identification for serial-robot calibration based on POE formula. IEEE Trans Robot 26(3):411–423

    Article  Google Scholar 

  23. Chen IM, Yang GL, Tan CT, Yeo SH (2001) Local POE model for robot kinematic calibration. Mech Mach Theory 36(11–12):1215–1239

    Article  MATH  Google Scholar 

  24. Tian WJ, He BY, Huang T (2011) Universal geometric error modeling of the CNC machine tools based on the screw theory, in Fourth International Seminar on Modern Cutting and Measurement Engineering, J. Xin, L. Zhu, and Z. Wang, Editors. Spie-Int Soc Optical Engineering: Bellingham.

  25. Yu Z, Tiemin L, Xiaoqiang T (2011) Geometric error modeling of machine tools based on screw theory. Procedia Eng 24:845–849

    Article  Google Scholar 

  26. Moon SK, Moon YM, Kota S, Landers RG (2001) Screw theory based metrology for design and error compensation of machine tools. In: Proceedings of DETC

  27. 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(9–12):1653–1667

    Article  Google Scholar 

  28. Okafor AC, Ertekin YM (2000) Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics. Int J Mach Tool Manuf 40(8):1199–1213

    Article  Google Scholar 

  29. 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 Tool Manuf 89:170–181

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The State Key Lab of Fluid Power Transmission and Control, Department of Mechanical Engineering, Zhejiang University, Hangzhou, 310027, China

    Guoqiang Fu, Jianzhong Fu, Hongyao Shen, Yuetong Xu & Yu’an Jin

Authors
  1. Guoqiang Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianzhong Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongyao Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yuetong Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yu’an Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jianzhong Fu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fu, G., Fu, J., Shen, H. et al. Product-of-exponential formulas for precision enhancement of five-axis machine tools via geometric error modeling and compensation. Int J Adv Manuf Technol 81, 289–305 (2015). https://doi.org/10.1007/s00170-015-7035-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-015-7035-0

Keywords

Search

Navigation