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A status review of volumetric positioning accuracy prediction theory and static accuracy design method for multi-axis CNC machine tools

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Abstract

The volumetric positioning accuracy of multi-axis CNC machine tools indicates the deviation from desired to actual position of the tool; it directly influences the machining accuracy of the workpiece, and it is also one of the important indicators to measure the performance of the machine tool. The volumetric positioning accuracy of machine tools is supported to be fundamentally improved. The accuracy design methods for machine tools currently include a robust design method for machining accuracy and static geometric accuracy. The robust design method for machining accuracy is set up based on the effective evaluation of the volumetric positioning accuracy of machine tools, and the geometric error elements are used as the analysis variables without directly directing the tolerance design. The joint surface tolerance of key components is used as the analysis variable in the design method for static geometric accuracy, which is supported to be optimized according to the accuracy design requirements of different machine tools. The present paper summarizes and analyzes the aspects including the volumetric accuracy modeling, identification of geometric error elements for axis of motion, robust design method for machining accuracy, tolerance modeling, and design method for static geometric accuracy of machine tools, and analyzes the key problems to be solved in the method of improving the volumetric positioning accuracy of multi-axis CNC machine tools, and then a feasible research idea to improve the volumetric positioning accuracy of multi-axis CNC machine tools is proposed.

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References

  1. Xie Z, Xie F, Liu XJ, Wang J, Mei B (2021) Tracking error prediction informed motion control of a parallel machine tool for high-performance machining. Int J Mach Tools Manuf 164 (Prepublish)

  2. Wu H, Zheng H, Li X, Wang W, Xiang X, Meng X (2020) A geometric accuracy analysis and tolerance robust design approach for a vertical machining center based on the reliability theory. Measurement 161 (Prepublish) https://doi.org/10.1016/j.measurement.2020.107809

  3. Wu H, Li X, Sun F, Zheng H, Zhao Y (2022) Optimization design method of machine tool static geometric accuracy using tolerance modeling. Int J Adv Manuf Technol 118(5–6):1793–1809

    Article  Google Scholar 

  4. Aguilar JJ, Velazquez J, Aguado S, Santolaria J, Samper D (2016) Improving a real milling machine accuracy through an indirect measurement of its geometric errors. J Manuf Syst 40:26–36

    Article  Google Scholar 

  5. Haitjema H, Schwenke H, Schmitt R, Weckenmann A, Knapp W, Delbressine F (2008) Geometric error measurement and compensation of machines - an update. CIRP Ann 57:660–675

    Article  Google Scholar 

  6. Nojehdeh MV, Arezoo B (2016) Functional accuracy investigation of work-holding rotary axes in five axis CNC machine tools. In Parallel kinematic machines with parallelogram struts. Sci China (Ser E Technol Sci) 45(5):67–476

    Google Scholar 

  7. Li J, Xie F, Liu X, Mei B, Dong Z (2017) Analysis on the research status of volumetric positioning accuracy improvement methods for five-axis NC machine tools. J Mech Eng 53:113–128

  8. Xiang S, Altintas Y (2016) Modeling and compensation of volumetric errors for five-axis machine tools. International Journal of Machine Tools & Manufacture: Design, Research and Application 101: 65–78

  9. Huang T，Li Y，Tang B, Zhao X (2002) Error modeling，sensitivity analysis and assembly process of a class of 3-DOF parallel kinematic machines with parallelogram struts. Science in China(Series E:Technological Sciences) 45(5)67–476

  10. Huang P (2011) Research on the accuracy assurance of a class of special parallel manipulators with 3-DOF. Tsinghua University Publishing, Beijing

    Google Scholar 

  11. Su S (2002) Study on the methods of precision modeling and error compensation for multi-axis CNC machine tools. Doctor of Philosophy in Changsha National University of Defense

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

  13. ISO 230–4 (2005) Test code for machine tools-Part 4: Circular tests for numerically controlled machine tools

  14. Lee K, Yang S (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 Des Res Appl 70:45–52

    Article  Google Scholar 

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

    Article  Google Scholar 

  16. 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

    Article  Google Scholar 

  17. Vahebi M, Arezoo B (2018) Accuracy improvement of volumetric error modeling in CNC machine tools. Int J Adv Manuf Technol 95(5):2243–2257

    Article  Google Scholar 

  18. Aguado S, Santolaria J, Samper D, Aguilar JJ, Velázquez J (2016) Improving a real milling machine accuracy through an indirect measurement of its geometric errors. J Manuf Syst 40:26–36

    Article  Google Scholar 

  19. Wang K, Sun C, Qian F, Zheng W (2010) Position accuracy measuring and error compensation method of NC machine tool based on laser interferometer. Aeronaut Manuf Technol 21:90–93. https://doi.org/10.16080/j.issn1671-833x.2010.21.018

    Article  Google Scholar 

  20. Wang J, Guo J (2016) Geometric error identification algorithm of numerical control machine tool using a laser tracker. Proc Inst Mech Eng Part B J Eng Manuf 230:2004–2015

    Article  Google Scholar 

  21. Fan J, Tian Y, Song G (2000) Technology of NC machine error parameter identification based on fourteen displacement measurement line. J Beijing Polytech Univ 26(2):11–15

    Google Scholar 

  22. Yang X, Huang Y, Zhu D, Bao B (2009) A method to measure vertical axis roll angular errors of machine tool based on laser interferometer. China Mech Eng 12:1399–1402

    Google Scholar 

  23. Chen G, Yuan J, Ni J (2001) A displacement measurement approach for machine geometric error assessment. Int J Mach Tools Manuf 41:149–161

    Article  Google Scholar 

  24. Zhang L, Huang Y, Qiao Y (2008) Interferometer measurement and errors compensation of straightness for parallel axis with straight-line motion. Chin J Mech Eng 44(9):220–224

    Article  Google Scholar 

  25. Chen S (2016) Research on the geometric error measurement method of the numerical control machine tools based on twelve line. Huazhong University of Science & Technology Dissertation

  26. Sun K, Shen X (2009) Technology of NC machine error parameter identification based on 22 displacement measurement line. Mech Eng 3:120–121

    Google Scholar 

  27. Chen J, Lin S, Zhou X (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 

  28. Lau K, Ma Q, Chu X, Liu Y, Olson S (1999) An advanced 6-degree-of-freedom laser system for quick CNC machine and CMM error mapping and compensation. Laser Metrol Mach Perform IV 23:14

    Google Scholar 

  29. Li J, Xie F, Liu X, 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 87:2269–2283

    Article  Google Scholar 

  30. Zhu SW, Ma SW, Yan KY, Ding GF, Qin SF (2013) Workpiece locating error prediction and compensation in fixtures. Int J Adv Manuf Technol 67:1423–1432

    Article  Google Scholar 

  31. Wan M, Liu Y, Zhang W (2016) A new algorithm for the identification of CNC geometric errors. Procedia CIRP 56:293–298

    Article  Google Scholar 

  32. Lee K, Yang S (2016) Compensation of position-independent geometric errors of an index table by linear axes circular tests at different angular positions. Int J Adv Manuf Technol 84:981–988

    Google Scholar 

  33. Lee K, Yang S (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 

  34. Wenjie T, Guang Y, Lina W, Fuwen Y, Weiguo G (2018) The application of a regularization method to the estimation of geometric errors of a three-axis machine tool using a double ball bar. J Mech Sci Technol 32:4871–4881

    Article  Google Scholar 

  35. Wu H, Zheng H, Wang W, Xiang X, Rong M (2020) A method for tracing key geometric errors of vertical machining center based on global sensitivity analysis. Int J Adv Manuf Technol 106:3943–3956

    Article  Google Scholar 

  36. Cai Y, Sang Q, Lou Z, Fan K (2019) Error analysis and compensation of a laser measurement system for simultaneously measuring five-degree-of-freedom error motions of linear stages. Sensors 19:3833

    Article  Google Scholar 

  37. Liu J, Zhao Y, Lai T, Li F, Liu K (2022) Identification of geometrical error on multi-axis machine tools based on a laser tracker. J Phys Conf Ser 2185(1)

    Article  Google Scholar 

  38. Chang’an H, Shutong L, Wanze L, Dongyan C, Jiangang L (2021) Application of laser tracker in the industrial measurement field. J Phys Conf Ser 1820

  39. Zhong X, Liu H, Mao X, Li B, He S, Peng F (2018) Volumetric error modeling, identification and compensation based on screw theory for a large multi-axis propeller-measuring machine. Meas Sci Technol 29:055011

    Article  Google Scholar 

  40. Aguado S, Santolaria J, Samper D, Velazquez J, Aguilar JJ (2016) Empirical analysis of the efficient use of geometric error identification in a machine tool by tracking measurement techniques. Meas Sci Technol 27:035002

    Article  Google Scholar 

  41. Tannous M, Caro S, Goldsztejn A (2014) Sensitivity analysis of parallel manipulators using an interval linearization method. Mech Mach Theory Dyn Mach Syst Gears Power Transm Robots Manip Syst Comput-Aided Des Methods 71:93–114

    Google Scholar 

  42. He Z, Fu J, Zhang L, Yao X (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 

  43. 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 

  44. Hong C, Ibaraki S (2013) Non-contact R-test with laser displacement sensors for error calibration of five-axis machine tools. Precis Eng 37:159–171

    Article  Google Scholar 

  45. Zhang Y, Fu J, Chen Z (2013) Machining tests to identify kinematic errors of machine tool table rotation axis based on sensitive directions. Int J Adv Manuf Technol 67:495–500

    Article  Google Scholar 

  46. Jiang Z, Bao S, Zhou X, Tang X, Zheng S (2015) Identification of location errors by a touch-trigger probe on five-axis machine tools with a tilting head. Int J Adv Manuf Technol 81:149–158

    Article  Google Scholar 

  47. Ibaraki S, Ota Y (2014) A machining test to calibrate rotary axis error motions of five-axis machine tools and its application to thermal deformation test. Int J Mach Tools Manuf 86:81–88

    Article  Google Scholar 

  48. Hong C, Ibaraki S, Oyama C (2012) Graphical presentation of error motions of rotary axes on a five-axis machine tool by static R-test with separating the influence of squareness errors of linear axes. Int J Mach Tools Manuf 59:24–33

    Article  Google Scholar 

  49. Bi Q, Huang N, Sun C, Wang Y, Zhu L, Ding H (2015) Identification and compensation of geometric errors of rotary axes on five-axis machine by on-machine measurement. Int J Mach Tools Manuf 89:182–191

    Article  Google Scholar 

  50. Su Z, Wang L (2015) Latest development of a new standard for the testing of five-axis machine tools using an S-shaped test piece. Proc Inst Mech Eng Part B J Eng Manuf 229:1221–1228

    Article  Google Scholar 

  51. Lee K, Lee D, Yang S (2012) 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 

  52. 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 

  53. Wang W, Jiang Z, Li Q, Tao W (2015) A new test part to identify performance of five-axis machine tool-Part II validation of S part. Int J Adv Manuf Technol 79:739–756

    Article  Google Scholar 

  54. Hong C, Ibaraki S, Matsubara A (2010) 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 

  55. Huang N, Jin Y, Li X, Liang L, Wu S (2019) Identification of integrated geometric errors of rotary axis and setup position errors for 5-axis machine tools based on machining test. Int J Adv Manuf Technol 102:1487–1496

    Article  Google Scholar 

  56. Tsutsumi M, Ihara Y, Saito A, Mishima N (2008) Yonetani T (2008) A18 Standardization of testing methods for kinematic motion of five-axis machining centers: draft proposal for ISO standard. Proc Manuf Mach Tool Conf 7:95–96

    Google Scholar 

  57. 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

    Article  Google Scholar 

  58. Liu X, Zhang X, Fang F, Liu S (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 

  59. Guo S, Tang S, Zhang D, Wang Q (2019) A recognition methodology for the key geometric errors of a multi-axis machine tool based on accuracy retentivity analysis. Complexity. https://doi.org/10.1155/2019/8649496

    Article  Google Scholar 

  60. Li D, Feng P, Zhang J, Yu D, Wu Z (2014) An identification method for key geometric errors of machine tool based on matrix differential and experimental test. Proc Inst Mech Eng C J Mech Eng Sci 228:3141–3155

    Article  Google Scholar 

  61. 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

    Article  Google Scholar 

  62. Abdessalem AB, El-Hami A (2014) Global sensitivity analysis and multi-objective optimisation of loading path in tube hydroforming process based on metamodelling techniques. Int J Adv Manuf Technol 71:753–773

    Article  Google Scholar 

  63. 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

    Article  Google Scholar 

  64. Marziale M, Polini W (2011) A review of two models for tolerance analysis of an assembly: Jacobian and torsor. Int J Comput Integr Manuf 24(1)

    Article  Google Scholar 

  65. Marziale M, Polini W (2009) A review of two models for tolerance analysis of an assembly: vector loop and matrix. Int J Adv Manuf Technol 43:1106–1123

    Article  Google Scholar 

  66. Ngoi BKA, Teck OC (1997) A tolerancing optimisation method for product design. Int J Adv Manuf Technol 13:290–299

    Article  Google Scholar 

  67. Desrochers A, Ghie W, Laperriere L (2003) Application of a unified Jacobian—Torsor model for tolerance analysis. J Comput Inf Sci Eng 3(1):2–14

    Article  MATH  Google Scholar 

  68. Ghie W, Laperrière L, Desrochers A (2010) Statistical tolerance analysis using the unified Jacobian-Torsor model. Int J Prod Res 48(15)

    Article  MATH  Google Scholar 

  69. Ghie W, Laperrière L, Desrochers A (2007) Re-design of mechanical assemblies using the unified Jacobian-Torsor model for tolerance analysis. Models Comput Aided Tolerancing Des Manuf 15:95–104. https://doi.org/10.1007/1-4020-5438-6_11

    Article  MATH  Google Scholar 

  70. Hambleton JP, Sloan SW (2013) A perturbation method for optimization of rigid block mechanisms in the kinematic method of limit analysis. Comput Geotech 48:260–271

    Article  Google Scholar 

  71. Liu W, Liu J, Ning R, Jiang K (2011) Unified dimension and tolerance modeling for mechanical precision predicting. Int J Adv Manuf Technol 57:307–323

    Article  Google Scholar 

  72. Mao J, Zong Y (2015) Assembly tolerance modeling based on generalized directed graph. Procedia CIRP 27:318–323

    Article  Google Scholar 

  73. Saravanan A, Jerald J, Rani ADC (2020) An explicit methodology for manufacturing cost–tolerance modeling and optimization using the neural network integrated with the genetic algorithm. Artif Intell Eng Des Anal Manuf 34(3):430–443

    Article  Google Scholar 

  74. Chen L, Pasquale F, Zhijie M, Dariusz C (2020) A framework for tolerance modeling based on parametric space envelope. J Manuf Sci Eng 142(6):061007

    Article  Google Scholar 

  75. Mu X, Sun Q, Sun W, Wang Y, Wang C, Wang X (2018) 3D tolerance modeling and geometric precision analysis of plane features for flexible parts. Eng Comput 35(7):2557–2576

    Article  Google Scholar 

  76. Peng H, Lu W (2018) Modeling of geometric variations within three-dimensional tolerance zones. J Harbin Inst Technol (New Ser) 25:41–49

    Google Scholar 

  77. Dorndorf U, Kiridena VSB, Ferreira PM (1994) Optimal budgeting of quasistatic machine tool errors. J Eng Ind 116(1):42–53

    Article  Google Scholar 

  78. Krishna AG, Rao KM (2006) Simultaneous optimal selection of design and manufacturing tolerances with different stack-up conditions using scatter search. Int J Adv Manuf Technol 30:328–333

    Article  Google Scholar 

  79. Jin S, Zheng C, Kuigang Yu, Lai X (2010) Tolerance design optimization on cost–quality trade-off using the Shapley value method. J Manuf Syst 29:142–150

    Article  Google Scholar 

  80. Yu ZM, Liu ZJ, Ai YD, Xiong M (2013) Geometric error model and precision distribution based on reliability theory for large CNC gantry guideway grinder. Chin J Mech Eng 49:142–151

    Article  Google Scholar 

  81. 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 Inst Mech Eng Part C J Mech Eng Sci 229:1134–1149

    Article  Google Scholar 

  82. Cai L, Zhang Z, Qiang C, Liu Z, Gu P, Yin Q (2016) An approach to optimize the machining accuracy retainability of multi-axis NC machine tool based on robust design. Precis Eng 43:370–386

    Article  Google Scholar 

  83. Zhang Z, Liu Z, Cai L, Cheng Q, Qi Y (2017) An accuracy design approach for a multi-axis NC machine tool based on reliability theory. Int J Adv Manuf Technol 91:1547–1566

    Article  Google Scholar 

  84. Zhang Z, Cai L, Cheng Q, Liu Z, Gu P (2019) A geometric error budget method to improve machining accuracy reliability of multi-axis machine tools. J Intell Manuf 30:495–519

    Article  Google Scholar 

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Funding

The authors wish to thank the major technological innovation projects in Chengdu (2019-YF08-00162-GX) and the open fund project of Sichuan provincial key laboratory of pattern recognition and intelligent information processing, Chengdu University (MSSB-2022–09), which supported the research presented in this paper.

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Authors and Affiliations

  1. School of Electronic Information and Electrical Engineering, Chengdu University, No. 2025 Chengluo Avenue, Chengdu, Sichuan, 610106, China

    Haorong Wu & Yongxin Zhao

  2. Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, Chengdu University, No. 2025 Chengluo Avenue, Chengdu, Sichuan, 610106, China

    Haorong Wu

  3. School of Mechanical Engineering, Chengdu University, No. 2025 Chengluo Avenue, Chengdu, Sichuan, 610106, China

    Xiaoxiao Li & Fuchun Sun

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  1. Haorong Wu
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  2. Xiaoxiao Li
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  4. Yongxin Zhao
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Contributions

Haorong Wu: Conceptualization, Methodology, Software, Investigation, Writing- original draft, Writing–review and editing. Xiaoxiao Li: Validation, Formal analysis, Visualization. Fuchun Sun: Validation, Formal analysis, Visualization, Software. Yongxin Zhao: Validation, Formal analysis, Visualization.

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Correspondence to Haorong Wu.

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Wu, H., Li, X., Sun, F. et al. A status review of volumetric positioning accuracy prediction theory and static accuracy design method for multi-axis CNC machine tools. Int J Adv Manuf Technol 122, 2139–2159 (2022). https://doi.org/10.1007/s00170-022-10015-7

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