Prediction and compensation of geometric error for translational axes in multi-axis machine tools

  • Changjun Wu
  • Jinwei Fan
  • Qiaohua Wang
  • Ri Pan
  • Yuhang Tang
  • Zhongsheng Li


This paper proposes an integrated geometric error prediction and compensation method to eliminate the positioning inaccuracy of tool ball for a double ball bar (DBB) caused by the translational axes’ geometric errors in a multi-axis machine tool (MAMT). Firstly, based on homogeneous transform matrix (HTM) and multi-body system (MBS) theory, the positioning error model only considering the translational axes of a MAMT is established. Then, an integrated error parameter identification method (IEPIM) by using a laser interferometer is proposed. Meanwhile, the identification discrete results of geometric error parameters for the translational axes are obtained by identification experiments. According to the discrete values, the optimal polynomials of 18 position-dependent geometric errors (PDGEs) are founded. As a basis, an iterative compensation method is constructed to modify the NC codes generated with the ordinary compensation method in self-developed compensation software. Finally, simulation verification is conducted with these two compensation methods. Simulation results show the positioning errors for test path of tool ball calculated with the iterative compensation method that are limited within 0.001 mm, and its average accuracy and accuracy stability are improved by 79.5 and 52.2%, respectively. In order to further verify the feasibility of the presented method, a measuring experiment is carried out in XY plane of a five-axis machine tool by using DBB. The experiment results show that the maximum circularity error with the iterative compensation method is reduced about 40.4% than that with the ordinary compensation method. It is therefore reasonable to conclude that the proposed method in this paper can avoid the influence of the translational axes’ geometric errors on rotary ones during a DBB test.


Translational axes Geometric error Positioning error Integrated error parameter identification method Iterative compensation method The optimal polynomials 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


Funding information

This work is financially supported by the National Natural Science Foundation of China (Nos. 51775010 and 51705011) and the Science and Technology Major Projects of High-end CNC Machine Tools and Basic Manufacturing Equipment of China (No. 2014ZX04011031). The authors appreciate the support from the Key Scientific Research Project for Henan Province Higher School of China (No. 18A460036).


  1. 1.
    Khan AW, Chen W (2010) A methodology for error characterization and quantification in rotary joints of multi-axis machine tools. Int J Adv Manuf Technol 51(9–12):1009–1022. CrossRefGoogle Scholar
  2. 2.
    Zhu J (2008) Robust thermal error modeling and compensation for CNC machine tools[D]. University of Michigan, Ann ArborGoogle Scholar
  3. 3.
    Chen D, Dong L, Bian Y, Fan J (2015) Prediction and identification of rotary axes error of non-orthogonal five-axis machine tool. Int J Mach Tool Manu 94:74–87. CrossRefGoogle Scholar
  4. 4.
    Ramesh R, Mannan MA, Poo AN (2000) Error compensation in machine tools—a review part I: geometric, cutting-force induced and fixture-dependent errors. Int J Mach Tools Manuf 40(9):1235–1256. CrossRefGoogle Scholar
  5. 5.
    Tsutsumi M, Saito A (2003) Identification and compensation of systematic deviations particular to 5-axis machining centers. Int J Mach Tools Manuf 43(8):771–780. CrossRefGoogle Scholar
  6. 6.
    Lee K II, Lee D-M, Yang S-H (2012) Parametric modeling and estimation of geometric errors for a rotary axis using double ball-bar. Int J Adv Manuf Technol 62(5–8):741–750. CrossRefGoogle Scholar
  7. 7.
    Lee K II, 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 Tool Manu 70:45–52. CrossRefGoogle Scholar
  8. 8.
    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 Tool Manu 103:1–12. CrossRefGoogle Scholar
  9. 9.
    Xiang S, Yang J, Zhang Y (2014) 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(9–12):2071–2082. CrossRefGoogle Scholar
  10. 10.
    Hsu YY, Wang SS (2007) A new compensation method for geometry errors of five-axis machine tools. Int J Mach Tool Manu 47(2):352–360. CrossRefGoogle Scholar
  11. 11.
    Zhang H, Yang J, Zhang Y, Shen J, Wang C (2011) Measurement and compensation for volumetric positioning errors of CNC machine tools considering thermal effect. Int J Adv Manuf Technol 55(1–4):275–283. CrossRefGoogle Scholar
  12. 12.
    Schwenke H, Knapp W, Haitjema H, Weckenmann A, Schmitte R, Delbressine F (2008) Geometric error measurement and compensation of machines-an update. CIRP Ann Manuf Technol 57(2):660–675. CrossRefGoogle Scholar
  13. 13.
    Ibaraki S, Knapp W (2012) Indirect measurement of volumetric accuracy for three-axis and five-axis machine tools: a review. Int J Autom Technol 6(2):110–124.  10.20965/ijat.2012.p0110 CrossRefGoogle Scholar
  14. 14.
    Du S, Hu J, Yu Z, Hu C (2017) Analysis and compensation of synchronous measurement error for multi-channel laser interferometer. Meas Sci Technol 28(5):055201–055207CrossRefGoogle Scholar
  15. 15.
    Ngoi BKA, Chin CS (2000) Self-compensated heterodyne laser interferometer. Int J Adv Manuf Technol 16(3):217–219CrossRefGoogle Scholar
  16. 16.
    Zhang G, Lu B, Ouyang R, Hocken R, Veale R, Donmez A (1988) A displacement method for machine geometry calibration. CIRP Ann Manuf Technol 37(1):515–518. CrossRefGoogle Scholar
  17. 17.
    Liu YW, Liu LB, Zhao XS, Zhang Q, Wang SX (1998) Investigation of error compensation technology for NC machine tool. China J Mech Eng 9(12):48–52 (in Chinese)Google Scholar
  18. 18.
    Fan J, Tian Y, Song G, Huang X, Kang C (2000) Technology of NC machine error parameter identification based on fourteen displacement measurement line. J Beijing Polytech Univ, China 26(6):11–15 (in Chinese)Google Scholar
  19. 19.
    Chen G, Yuan J, Ni J (2001) A displacement measurement approach for machine geometric error assessment. Int J Mach Tool Manu 41(1):149–161. CrossRefGoogle Scholar
  20. 20.
    Su S, Li S, Wang G (2002) Identification method for errors of machining center based on volumetric error model. Chin J Mech Eng 38(7):121–125 (in Chinese)CrossRefGoogle Scholar
  21. 21.
    Li J, Xie F, Liu XJ, Li W, Zhu S (2016) Geometric error identification and compensation of linear axes based on a novel 13-line method. Int J Adv Manuf Technol 87(5–8):2269–2283. CrossRefGoogle Scholar
  22. 22.
    Cui G, Lu Y, Li J, Gao D, Yao Y (2012) Geometric error compensation software system for CNC machine tools based on NC program reconstructing. Int J Adv Manuf Technol 63(1–4):169–180. CrossRefGoogle Scholar
  23. 23.
    Ding S, Huang X, Yu C, Liu X (2016) Novel method for position-independent geometric error compensation of five-axis orthogonal machine tool based on error motion. Int J Adv Manuf Technol 83(5–8):1069–1078. CrossRefGoogle Scholar
  24. 24.
    Khan AW, 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. CrossRefGoogle Scholar
  25. 25.
    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. CrossRefGoogle Scholar
  26. 26.
    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(1–4):107–121. CrossRefGoogle Scholar
  27. 27.
    Guo S, Zhang D, Xi Y (2016) Global quantitative sensitivity analysis and compensation of geometric errors of CNC machine tool. Math Probl Eng 2016:1–12Google Scholar
  28. 28.
    Cheng Q, Zhang Z, Zhang G, Gu P, Cai L (2015) Geometric accuracy allocation for multi-axis CNC machine tools based on sensitivity analysis and reliability theory. Proc IMechE C J Mech Eng Sci 229(6):1134–1149. CrossRefGoogle Scholar
  29. 29.
    Fan JW, Guan JL, Wang WC, Luo Q, Zhang XL, Wang LY (2002) A universal modeling method for enhancement the volumetric accuracy of CNC machine tools. J Mater Process Technol 129(1–3):624–628. CrossRefGoogle Scholar
  30. 30.
    Zhu S, Ding G, Qin S, Lei J, Zhang L, Yan K (2012) Integrated geometric error modeling, identification and compensation of CNC machine tools. Int J Mach Tool Manu 52(1):24–29. CrossRefGoogle Scholar
  31. 31.
    He Z, Fu J, Zhang X, Shen H (2016) A uniform expression model for volumetric errors of machine tools. Int J Mach Tool Manu 100:93–104. CrossRefGoogle Scholar
  32. 32.
    Jung J-H, Choi J-P, Lee S-J (2006) Machining accuracy enhancement by compensating for volumetric errors of a machine tool and on-machine measurement. J Mater Process Technol 174(1–3):56–66. CrossRefGoogle Scholar
  33. 33.
    Bringmann B, Besuchet JP, Rohr L (2008) Systematic evaluation of calibration methods. CIRP Ann Manuf Technol 57(1):529–532. CrossRefGoogle Scholar
  34. 34.
    Lasemi A, Xue D, Gu P (2016) Accurate identification and compensation of geometric errors of 5-axis CNC machine tools using double ball bar. Meas Sci Technol 27(5):055004–055021. CrossRefGoogle Scholar
  35. 35.
    Huang N, Jin Y, Bi Q (2015) Integrated post-processor for 5-axis machine tools with geometric errors compensation. Int J Mach Tool Manu 94:65–73. CrossRefGoogle Scholar
  36. 36.
    Lee J-H, Liu Y, Yang S-H (2006) Accuracy improvement of miniaturized machine tool: geometric error modeling and compensation. Int J Mach Tool Manu 46(12-13):1508–1516. CrossRefGoogle Scholar
  37. 37.
    Cheng Q, Wu C, Peihua G, Chang W, Xuan D (2013) An analysis methodology for stochastic characteristic of volumetric error in multiaxis CNC machine tool. Math Probl Eng 2013:1–12Google Scholar
  38. 38.
    Lee K II, 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(2):231–239. CrossRefGoogle Scholar
  39. 39.
    ISO 230-1 (2012) Test code for machine tools—part 1: geometric accuracy of machines operating under no-load or quasi-static conditions 1–11Google Scholar
  40. 40.
    Sharma MJ, Jin YS (2015) Stepwise regression data envelopment analysis for variable reduction. Appl Math Comput 253:126–134MathSciNetzbMATHGoogle Scholar
  41. 41.
    Liu Y, Fan J, Miao W (2013) Soft compensation for CNC crankshaft grinding machine tool. Adv Mech Eng 2013:1–11Google Scholar
  42. 42.
    Akaike H (1978) A Bayesian analysis of the minimum AIC procedure. Ann Inst Stat Math 30(1):9–14. MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Wu C, Fan J, Wang Q, Chen D (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 Tools Manuf 124(1):80–98. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2017

Authors and Affiliations

  1. 1.College of Mechanical Engineering & Applied Electronics TechnologyBeijing University of TechnologyBeijingPeople’s Republic of China
  2. 2.School of Mechanical and Electrical EngineeringZhengzhou University of Light IndustryZhengzhouPeople’s Republic of China

Personalised recommendations