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Geometric accuracy enhancement of five-axis machine tool based on error analysis

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Abstract

The characteristics of geometric error affect both the positions and orientations of a five-axis machine tool, which are very important for precision manufacturing. It is necessary to conduct quantitative analysis for the above characteristics to improve the precision of the five-axis machine tool. In this paper, the synthetic volumetric error model of the five-axis machine tool with a turntable-tilting head has been established, which describes the effect of 43 geometric error terms on position and orientation error vector intuitively. The multidimensional output of geometric error vectors in the workspace of the machine tool is sufficiently taken into account, and global quantitative sensitivity analysis is introduced to determine the effect of each geometric error on the precision of the machine tool. The results showed that geometric errors of the rotary axes are dominant sensitivity factors, reaching 59.32 and 51.59% of sensitivity indices of the position and orientation error vector, respectively. Furthermore, geometric error terms that are noncritical and critical are extracted according to the result of mutual information analysis. Those geometric errors were removed from the geometric error compensation model, which are at the same time insensitivity errors and nonsignificant geometric errors. The geometric error compensation results show that the accuracy of the machined parts with complex curved surfaces was improved 56.22% after error compensation based on sensitivity and mutual information analysis. This research provides a feasible methodology for analyzing the effect of geometric errors and determining the compensation values of the machine tool.

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References

  1. Chen YT, More P, Liu CS, Cheng CC (2019) Identification and compensation of position-dependent geometric errors of rotary axes on five-axis machine tools by using a touch-trigger probe and three spheres. Int J Adv Manuf Technol. https://doi.org/10.1007/s00170-019-03413-x

    Article  Google Scholar 

  2. Ding S, Wu WW, Huang XD, Song AP, Zhang YF (2019) 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(5):1715–1724. https://doi.org/10.1007/s00170-018-3086-3

    Article  Google Scholar 

  3. Yang H, Huang XD, Ding S, Yu CY, Yang YM (2018) Identification and compensation of 11 position-independent geometric errors on five-axis machine tools with a tilting head. Int J Adv Manuf Technol 94(1–4):533–544

    Article  Google Scholar 

  4. Ni J (1997) CNC machine accuracy enhancement through real-time error compensation. J Manuf Sci Eng Trans ASME 119(4):717–725

    Article  Google Scholar 

  5. Ibaraki S, Knapp W (2013) Indirect measurement of volumetric accuracy for three-axis and five-axis machine tools: a review. Int J Autom Technol 6(2):110–124

    Article  Google Scholar 

  6. Lee KI, Yang SH (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(4):45–52

    Article  Google Scholar 

  7. 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(68):11–20

    Article  Google Scholar 

  8. Wang JD, Guo JJ (2013) Algorithm for detecting volumetric geometric accuracy of NC machine tool by laser tracker. Chin J Mech Eng-EN 26(1):166–175

    Article  Google Scholar 

  9. Cheng Q, Zhao HW, Zhang GJ, Gu PH, Cai LG (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

    Article  Google Scholar 

  10. Liu K, Liu HB, Li T, Liu Y, Wang YQ (2019) Intelligentization of machine tools: comprehensive thermal error compensation of machine-workpiece system. Int J Adv Manuf Technol. https://doi.org/10.1007/s00170-019-03495-7

    Article  Google Scholar 

  11. Inasaki I, Kishinami K, Sakamoto S (1997) Shaper generation theory of machine tools—its basis and applications, Yokendo, Tokyo

  12. Guo SJ, Jiang GD, Zhang DS, Mei XS (2017) Position-independent geometric error identification and global sensitivity analysis for the rotary axes of five-axis machine tools. Meas Sci Technol 28(4):045006

    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(8):771–780

    Article  Google Scholar 

  14. Xiang ST, Yang JG, 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

    Article  Google Scholar 

  15. Chen DJ, Dong LH, Bian YH, Fan JW (2015) Prediction and identification of rotary axes error of non-orthogonal five-axis machine tool. Int J Mach Tools Manuf 94:74–87

    Article  Google Scholar 

  16. Lasemi A, Xue DY, Gu PH (2016) Accurate identification and compensation of geometric errors of 5-axis CNC machine tools using double ball bar. Meas Sci Technol 27(5):055004

    Article  Google Scholar 

  17. Guo JK, Beaucamp A, Ibaraki S (2017) Virtual pivot alignment method and its influence to profile error in bonnet polishing. Int J Mach Tools Manuf 122:18–31

    Article  Google Scholar 

  18. Yang SH, Lee HH, Lee KI (2019) Identification of inherent position-independent geometric errors for three-axis machine tools using a double ballbar with an extension fixture. Int J Adv Manuf Technol. https://doi.org/10.1007/s00170-019-03409-7

    Article  Google Scholar 

  19. Tian WJ, Gao WG, Zhang DW, Huang T (2014) A general approach for error modeling of machine tools. Int J Mach Tools Manuf 79(4):17–23

    Article  Google Scholar 

  20. Zhong XM, Liu HQ, Mao XY, Li B, He SP, Peng FY (2018) Volumetric error modeling, identification and compensation based on screw theory for a large multi-axis propeller-measuring machine. Meas Sci Technol 29(5)

    Article  Google Scholar 

  21. Fu GQ, Fu JZ, Xu YT, Chen ZC (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 

  22. Guo JK, Li BT, Liu ZG, Hong J, Zhou Q (2016) A new solution to the measurement process planning for machine tool assembly based on Kalman filter. Precis Eng 43:356–369

    Article  Google Scholar 

  23. Lee KI, Lee DM, Yang SH (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

    Article  Google Scholar 

  24. Li ZH, Feng WL, Yang JG, Huang YQ (2018) An investigation on modeling and compensation of synthetic geometric errors on large machine tools based on moving least squares method. Proc Inst Mech Eng B J Eng Manuf 232(3):412–427

    Article  Google Scholar 

  25. Tang H, Duan JA, Lan SH, Shui HY (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

    Article  Google Scholar 

  26. Fan JW, Tao HH, Wu CJ, Pan R, Tang YH, Li ZS (2018) Kinematic errors prediction for multi-axis machine tools’ guideways based on tolerance. Int J Adv Manuf Technol 98(5):1131–1144

    Article  Google Scholar 

  27. He GY, Sun GM, Zhang HS, Huang C, Zhang DW (2017) Hierarchical error model to estimate motion error of linear motion bearing table. Int J Adv Manuf Technol 93(5–8):1915–1927

    Article  Google Scholar 

  28. Mir YA, Mayer JRR, Fortin C (2002) Tool path error prediction of a five-axis machine tool with geometric errors. Proc Inst Mech Eng B J Eng Manuf 216:697–712

    Article  Google Scholar 

  29. Qiao Y, Chen YP, Yang JX, Chen B (2017) A five-axis geometric errors calibration model based on the common perpendicular line (CPL) transformation using the product of exponentials (POE) formula. Int J Mach Tools Manuf 118–119:49–60

    Article  Google Scholar 

  30. Yang JX, 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 

  31. Ibaraki S, Kimura Y, Yu N, Nishikawa S (2015) Formulation of influence of machine geometric errors on five-axis on-machine scanning measurement by using a laser displacement sensor. J Manuf Sci Eng Trans ASME 137(2):021013

    Article  Google Scholar 

  32. Chen JX, Lin SW, He BW (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 

  33. Jiang ZX, Song B, Zhou XD, Tang XQ, Zheng SQ (2015) On-machine measurement of location errors on five-axis machine tools by machining tests and a laser displacement sensor. Int J Mach Tools Manuf 95:1–12

    Article  Google Scholar 

  34. Jiang XG, Cripps RJ (2016) Geometric characterisation and simulation of position independent geometric errors of five-axis machine tools using a double ball bar. The Int J Adv Manuf Technol 83(9):1905–1915

    Article  Google Scholar 

  35. Cheng Q, Feng QN, Liu ZG, Gu PH, Zhang GJ (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(9–12):2301–2318

    Article  Google Scholar 

  36. He ZY, Fu JZ, Zhang LC, Yao XH (2015) A new error measurement method to identify all six error parameters of a rotational axis of a machine tool. Int J Mach Tools Manuf 88:1–8

    Article  Google Scholar 

  37. Saltelli A, Annoni P (2011) Sensitivity Analysis. International encyclopedia of statistical science. Springer, Berlin

    Google Scholar 

  38. Zargarbashi SHH, Mayer JRR (2006) Assessment of machine tool trunnion axis motion error, using magnetic double ball bar. Int J Mach Tools Manuf 46(14):1823–1834

    Article  Google Scholar 

  39. Cheng Q, Zhao HW, Zhao YS, Sun BW, Gu P (2015) Machining accuracy reliability analysis of multi-axis machine tool based on Monte Carlo simulation. J Intell Manuf 29(1):191–209

    Article  Google Scholar 

  40. Ibaraki S, Goto S, Tsuboi K, Saito N, Kojima N (2018) Kinematic modeling and error sensitivity analysis for on-machine five-axis laser scanning measurement under machine geometric errors and workpiece setup errors. Int J Adv Manuf Technol 96(9–12):4051–4062

    Article  Google Scholar 

  41. 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(9–12):1261–1272

    Article  Google Scholar 

  42. Chen JX, Lin SW, Zhou XL (2016) A comprehensive error analysis method for the geometric error of multi-axis machine tool. Int J Mach Tools Manuf 106:56–66

    Article  Google Scholar 

  43. Lei WT, Wang WC, Fang TC (2014) Ballbar dynamic tests for rotary axes of five-axis CNC machine tools. Int J Mach Tools Manuf 82–83(4):29–41

    Article  Google Scholar 

  44. Liu XL, Zhang XD, Fang FZ, Liu SG (2016) Identification and compensation of main machining errors on surface form accuracy in ultra-precision diamond turning. Int J Mach Tools Manuf 105:45–57

    Article  Google Scholar 

  45. Li QZ, Wang W, Jiang YF, 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(5–8):1791–1805

    Article  Google Scholar 

  46. Zou XC, Zhao XS, Li G, Li ZQ, Sun T (2017) Sensitivity analysis using a variance-based method for a three-axis diamond turning machine. Int J Adv Manuf Technol 92(9–12):4429–4443

    Article  Google Scholar 

  47. Du ZC, Wang J, Yang JG (2017) Geometric error modeling and sensitivity analysis of single-axis assembly in three-axis vertical machine center based on Jacobian-Torsor model. ASME J Risk Uncertainty Part B 4(3):031004

    Google Scholar 

  48. ISO 230-1 (2012) Test code for machine tools. Part 1. Geometric accuracy of machines operating under no-load or quasi-static conditions. ISO.

  49. Huang ND, Jin YQ, Bi QZ, Wang YH (2015) Integrated post-processor for 5-axis machine tools with geometric errors compensation. Int J Mach Tools Manuf 94:65–73

    Article  Google Scholar 

  50. Ibaraki S, Nagai Y (2017) Formulation of the influence of rotary axis geometric errors on five-axis on-machine optical scanning measurement-application to geometric error calibration by “chase-the-ball” test. Int J Adv Manuf Technol 92(9):4263–4273

    Article  Google Scholar 

  51. ISO 10791-6 (2014) Test conditions for machining centers—part 6: accuracy of speeds and interpolations. ISO.

  52. Zhu SW, Ding GF, Qin SF, Lei J, Zhuang L, Yan K (2012) Integrated geometric error modeling, identification and compensation of CNC machine tools. Int J Mach Tools Manuf 52(1):24–29

    Article  Google Scholar 

  53. Li J, Xie FG, Liu XJ, Li WD, Zhu SW (2016) Geometric error identification and compensation of linear axes based on a novel 13-line method. Int J Adv Manuf Technol 87(5):2269–2283

    Article  Google Scholar 

  54. Guo SJ, Jiang GD, Mei XS (2017) Investigation of sensitivity analysis and compensation parameter optimization of geometric error for five-axis machine tool. Int J Adv Manuf Technol 93(9–12):3229–3243

    Article  Google Scholar 

  55. Jiang L, Ding GF, Li Z, Zhu SW, Qin SF (2013) Geometric error model and measuring method based on worktable for five-axis machine tools. Proc Inst Mech Eng B J Eng Manuf 227(1):32–44

    Article  Google Scholar 

  56. Kalpakjian S (2010) Manufacturing engineering and technology: machining. Prentice Hall, New Jersey

    Google Scholar 

  57. Ding WD, Zhu XC, Huang XD (2016) Effect of servo and geometric errors of tilting-rotary tables on volumetric errors in five-axis machine tools. Int J Mach Tools Manuf 104:37–44

    Article  Google Scholar 

  58. Garciacabrejo O, Valocchi A, Soares CG (2014) Global sensitivity analysis for multivariate output using polynomial chaos expansion. Reliab Eng Syst Saf 126:25–36

    Article  Google Scholar 

  59. Wei PF, Lu ZZ, Song JW (2015) Variable importance analysis: a comprehensive review. Reliab Eng Syst Saf 142:399–432

    Article  Google Scholar 

  60. Herman G, Zhang B, Wang Y, Ye GT, Chen F (2013) Mutual information-based method for selecting informative feature sets. Pattern Recogn 46(12):3315–3327

    Article  Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China (No. 11502122), National Key R&D Program of China (No. 2016YFB1102500), and Program for Changjiang Scholars and Innovative Research Team in University of the Ministry of Education of China (No. IRT_15R54).

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Correspondence to Gedong Jiang.

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Guo, S., Mei, X. & Jiang, G. Geometric accuracy enhancement of five-axis machine tool based on error analysis. Int J Adv Manuf Technol 105, 137–153 (2019). https://doi.org/10.1007/s00170-019-04030-4

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