Skip to main content
Log in

An analytical approach for crucial geometric errors identification of multi-axis machine tool based on global sensitivity analysis

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

Abstract

Geometric errors directly affect the tool tip position, reduce machining accuracy, and are one of the most important errors of multi-axis machining tool. However, the geometric errors are intercoupling, and the measured values at different points vary and are stochastic. The identification of the most crucial geometric errors and the determination of a method to control them is a key problem to improve the machining accuracy of machine tool. To achieve this goal, a new analytical method, to identify crucial geometric errors for a multi-axis machine tool is proposed here based on multibody system (MBS) theory and global sensitivity analysis. The volumetric error modeling of multi-axis machine tool has been given by MBS theory, which describes the topological structure of multibody system simply and conveniently in a matrix. The stochastic characteristic of geometric errors is taken into consideration and Sobol global sensitivity analysis method is introduced to identify crucial geometric errors of machine tool. A vertical machining center is selected as an illustration example. The analysis results reveal that the analytical method presented in this paper can identify the crucial geometric errors and are helpful to improve the machining accuracy of multi-axis machine tool.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Sartori S, Zhang GX (1995) Geometric error measurement and compensation of machines. CIRP Ann Manuf Technol 44(2):599–609

    Article  Google Scholar 

  2. Ahn KG, Cho DW (2000) Analysis of the volumetric error uncertainty of a three-axis machine tool by beta distribution. Int J Mach Tools Manuf 40(15):2235–2248

    Article  Google Scholar 

  3. Cheng Q, Wu C, Gu PH, Chang WF, Xuan DS (2013) An analysis methodology for stochastic characteristic of volumetric error in multi-axis CNC machine tool. Math Probl Eng 2013, 863283. doi:10.1155/2013/863283

    Google Scholar 

  4. Wu CW, Tang CH, Chang CF, Shiao YS (2012) Thermal error compensation method for machine center. Int J Adv Manuf Technol 59:681–689

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. 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 Tools Manuf 40:1199–1213

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. Tarantola S, Saltelli A (2003) SAMO 2001: methodological advances and innovative applications of sensitivity analysis. Reliab Eng Syst Saf 79(2):121–122

    Article  Google Scholar 

  11. Nojedeh MV, Habibiand M, Arezoo B (2011) Tool path accuracy enhancement through geometrical error compensation. Int J Mach Tools Manuf 51(6):471–482

    Article  Google Scholar 

  12. Rao N, Bedi S, Buchal R (1996) Implementation of the principal-axis method for machining of complex surfaces. Int J Adv Manuf Technol 11(4):249–257

    Article  Google Scholar 

  13. Rahman M, Heikkala J, Lappalainen K (2000) Modeling measurement and error compensation of multi-axis machine tools. Int J Mach Tools Manuf 40(10):1535–1546

    Article  Google Scholar 

  14. Eman K (1987) A generalized geometric error model for multi-axis machines. CIRP Ann Manuf Technol 36(1):253–256

    Article  Google Scholar 

  15. Xie J, Zhou RM, Xu J, Zhong YG (2010) Form-truing error compensation of diamond grinding wheel in CNC envelope grinding of free-form surface. Int J Adv Manuf Technol 48(9):905–912

    Article  Google Scholar 

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

    Article  Google Scholar 

  17. Jha BK, Kumar A (2003) Analysis of geometric errors associated with five-axis machining centre in improving the quality of Cam profile. Int J Mach Tools Manuf 43(6):629–636

    Article  Google Scholar 

  18. Kong LB, Cheung CF, To S, Lee WB, Du JJ, Zhang ZJ (2008) A kinematics and experimental analysis of form error compensation in ultra-precision machining. Int J Mach Tools Manuf 48(12):1408–1419

    Article  Google Scholar 

  19. 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 

  20. Xu C, Gertner G (2007) Extending a global sensitivity analysis technique to models with correlated parameters. Comput Stat Data Anal 51(12):5579–5590

    Article  MathSciNet  MATH  Google Scholar 

  21. Karkee M, Steward BL (2010) Local and global sensitivity analysis of a tractor and single axle grain cart dynamic system model. Biosyst Eng 106(4):352–366

    Article  Google Scholar 

  22. Chhatre S, Francis R, Zhou YH, Titchener-Hooker N, King J, Keshavarz-Moore E (2008) Global sensitivity analysis for the determination of parameter importance in bio-manufacturing processes. Biotechnol Appl Biochem 51(2):79–90

    Article  Google Scholar 

  23. Cossarini G, Solidoro C (2008) Global sensitivity analysis of a trophodynamic model of the Gulf of Trieste. Ecol Model 212(1):16–27

    Article  Google Scholar 

  24. Wang KH, Ke JB, Lee WC (2007) Reliability and sensitivity analysis of a repairable system with warm standbys and R unreliable service stations. Int J Adv Manuf Technol 31(11):1223–1232

    Article  Google Scholar 

  25. Sudret B (2008) Global sensitivity analysis using polynomial chaos expansions. Reliab Eng Syst Saf 93(7):964–979

    Article  Google Scholar 

  26. Tsutsumi M, Saito A (2004) Identification of angular and positional deviations inherent to 5-axis machining centers with a tilting-rotary table by simultaneous four-axis control movements. Int J Mach Tools Manuf 44(12):1333–1342

    Article  Google Scholar 

  27. 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

    Article  Google Scholar 

  28. 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 

  29. Chen GD, Liang YC, Sun YZ, Chen WQ, 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 

  30. Deng C, Xie SQ, Wu J, Shao XY (2014) Position error compensation of semi-closed loop servo system using support vector regression and fuzzy PID control. Int J Adv Manuf Technol 71(5–8):887–898

    Article  Google Scholar 

  31. Saltelli A, Ratto M, Tarantola S, Campolongo F, Commission E, Ispra JRC (2006) Sensitivity analysis practices: strategies for model-based inference. Reliab Eng Syst Saf 91(10–11):1109–1125

    Article  Google Scholar 

  32. Abdessalem AB, El-Hami A (2014) Global sensitivity analysis and multi-objective optimization of loading path in tube hydroforming process based on meta modelling techniques. Int J Adv Manuf Technol 71(5–8):753–773

    Article  Google Scholar 

  33. Lagerwall G, Kiker G, Munoz-Carpena R, Wang NM (2014) Global uncertainty and sensitivity analysis of a spatially distributed ecological model. Ecol Model 275:22–30

    Article  Google Scholar 

  34. Miro S, Hartmann D, Schanz T (2014) Global sensitivity analysis for subsoil parameter estimation in mechanized tunneling. Comput Geotech 56:80–88

    Article  Google Scholar 

  35. Kim K, Kim MK (1991) Volumetric accuracy analysis based generalized geometric error model in multi-axes machine tools. Mech Mach Theory 26(2):207–212

    Article  Google Scholar 

  36. Soons JA, Theuws FC, Schellenkens PH (1992) Modeling the errors of multi-axis machines: a general methodology. Precis Eng 14(1):5–19

    Article  Google Scholar 

  37. 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 

  38. Rahman M, Heikkala J, Lappalainen K (2000) Modeling, measurement and error compensation of multi-axis machine tools. Part I: theory. Int J Mach Tools Manuf 40(10):1535–1546

    Article  Google Scholar 

  39. Shin YH (1991) Characterization of CNC machining centers. J Manuf Syst 10(5):407–421

    Article  Google Scholar 

  40. Lee DK, Zhu ZK, Lee KI, Yang SH (2011) Identification and measurement of geometric errors for a five-axis machine tool with a tilting head using a double ball-bar. Int J Precis Eng Manuf 12(2):337–343

    Article  Google Scholar 

  41. Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55(1–3):271–280

    Article  MathSciNet  MATH  Google Scholar 

  42. Homma T, Saltelli A (1996) Importance measures in global sensitivity analysis of nonlinear models. Reliab Eng Syst Saf 52(1):1–17

    Article  Google Scholar 

  43. Slamani M, Mayer R, Balazinski M, Zargarbashi SHH, Engin S, Lartigue C (2010) Dynamic and geometric error assessment of an XYC axis subset on five-axis high-speed machine tools using programmed end point constraint measurements. Int J Adv Manuf Technol 50(9–12):1063–1073

    Article  Google Scholar 

  44. Zhang HT, Yang JG, Zhang Y, Shen JH, Wang C (2011) Measurement and compensation for volumetric positioning errors of CNC machine tools considering thermal effect. Int J Adv Manuf Technol 55(1):275–283

    Article  Google Scholar 

  45. Helton JC, Davis FJ (2003) Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab Eng Syst Saf 81(1):23–69

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Guojun Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheng, Q., Zhao, H., Zhang, G. et al. 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 (2014). https://doi.org/10.1007/s00170-014-6133-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-014-6133-8

Keywords

Navigation