Skip to main content
Log in

Sensitivity analysis of machining accuracy of multi-axis machine tool based on POE screw theory and Morris method

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

Abstract

The geometric errors have a significant effect on the machining accuracy of multi-axis machine tool. Because of their complex inter-coupling, the process to control these geometric errors and then to improve the machining accuracy on this basis is recognized as a difficult problem. This paper proposes a method based on the product of exponential (POE) screw theory and Morris approach for volumetric machining accuracy global sensitivity analysis of a machine tool. When a five-axis machine tool is chosen as an example, there are five screws to represent the six basic error components of each axis (in an original way) according to the geometric definition of the errors and screws. This type of POE model is precise and succinct enough to express the relation of each of the components as the Morris method is based on the elementary effect (EE). The method can compare incidence of these errors and be used to describe the nonlinear relationship by less calculated amount in a global system. Based on the POE modelling, the Morris method is adopted to identify the key geometric errors which have a greater influence on the machining accuracy by global sensitivity analysis. Finally, according to the results obtained from analysis, suggestions, and guidelines are provided to adjust and modify the machine tool components to improve the machining accuracy economically.

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. Kvrgic V, Dimic Z, Cvijanovic V, Ilic D, Bucan M (2012) A control algorithm for a vertical five-axis turning centre. Int J Adv Manuf Technol 61(5-8):569–584

    Article  Google Scholar 

  2. Cheng Q, Feng Q, Liu Z, Gu P, Cai L (2014) Fluctuation prediction of machining accuracy for multi-axis machine tool based on stochastic process theory. Proc Inst Mech Eng C J Mech Eng Sci 0954406214562633

  3. 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 

  4. Liu H, Li B, Wang X, Tan G (2011) Characteristics of and measurement methods for geometric errors in CNC machine tools. Int J Adv Manuf Technol 54(1-4):195–201

    Article  Google Scholar 

  5. Schwenke H, Knapp W, Haitjema H, Weckenmann A, Schmitt R, Delbressine F (2008) Geometric error measurement and compensation of machines—an update. CIRP Ann-Manuf Technol 57(2):660–675

    Article  Google Scholar 

  6. Ziegert JC, Kalle P (1994) Error compensation in machine tools: a neural network approach. J Intell Manuf 5(3):143–151

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. 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

    Article  Google Scholar 

  9. Lamikiz A, De Lacalle LL, Ocerin O, Díez D, Maidagan E (2008) The Denavit and Hartenberg approach applied to evaluate the consequences in the tool tip position of geometrical errors in five-axis milling centres. Int J Adv Manuf Technol 37(1-2):122–139

    Article  Google Scholar 

  10. de Lacalle NL, Mentxaka AL (Eds.) (2008) Machine tools for high performance machining. Springer Science & Business Media

  11. Kvrgic V, Dimic Z, Cvijanovic V, Vidakovic J, Kablar N (2014) A control algorithm for improving the accuracy of five-axis machine tools. Int J Prod Res 52(10):2983–2998

    Article  Google Scholar 

  12. Tian W, Gao W, Zhang D, Huang T (2014) A general approach for error modeling of machine tools. Int J Mach Tools Manuf 79:17–23

    Article  Google Scholar 

  13. 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 

  14. 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 

  15. Eman KF, Wu BT, DeVries MF (1987) A generalized geometric error model for multi-axis machines. CIRP Ann-Manuf Technol 36(1):253–256

    Article  Google Scholar 

  16. Schiehlen W (1997) Multibody system dynamics: roots and perspectives. Multibody Syst Dyn 1(2):149–188

    Article  MathSciNet  MATH  Google Scholar 

  17. 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):624–628

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  19. 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, 1;697–707

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

    Article  Google Scholar 

  21. 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 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  24. Shahsavani D, Grimvall A (2011) Variance-based sensitivity analysis of model outputs using surrogate models. Environ Model Softw 26(6):723–730

    Article  Google Scholar 

  25. Nossent J, Elsen P, Bauwens W (2011) Sobol’sensitivity analysis of a complex environmental model. Environ Model Softw 26(12):1515–1525

    Article  Google Scholar 

  26. 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 

  27. Cheng Q, Wu C, Gu P, Chang W, Xuan D (2013) An analysis methodology for stochastic characteristic of volumetric error in multiaxis CNC machine tool. Math Probl Eng 2013

  28. Morris MD (1991) Factorial sampling plans for preliminary computational experiments. Technometrics 33(2):161–174

    Article  Google Scholar 

  29. Campolongo F, Cariboni J, Saltelli A (2007) An effective screening design for sensitivity analysis of large models. Environ Model Softw 22(10):1509–1518

    Article  Google Scholar 

  30. King DM, Perera BJC (2013) Morris method of sensitivity analysis applied to assess the importance of input variables on urban water supply yield–a case study. J Hydrol 477:17–32

    Article  Google Scholar 

  31. Touhami HB, Lardy R, Barra V, Bellocchi G (2013) Screening parameters in the Pasture Simulation model using the Morris method. Ecol Model 266:42–57

    Article  Google Scholar 

  32. Ruano MV, Ribes J, Seco A, Ferrer J (2012) An improved sampling strategy based on trajectory design for application of the Morris method to systems with many input factors. Environ Model Softw 37:103–109

    Article  Google Scholar 

  33. Herman JD, Kollat JB, Reed PM, Wagener T (2013) Technical note: method of Morris effectively reduces the computational demands of global sensitivity analysis for distributed watershed models. Hydrol Earth Syst Sci 17(7):2893–2903

    Article  Google Scholar 

  34. Li Y, Zhu M, Li Y (2006) Kinematics of reconfigurable flexible-manipulator using a local product-of-exponentials formula. In Intelligent Control and Automation, 2006. WCICA 2006. The Sixth World Congress on, 2; 9022-9026. IEEE

  35. He R, Zhao Y, Yang S, Yang S (2010) Kinematic-parameter identification for serial-robot calibration based on POE formula. Robot IEEE Trans 26(3):411–423

    Article  Google Scholar 

  36. Liu W, Liang M (2008) Multi-objective design optimization of reconfigurable machine tools: a modified fuzzy-Chebyshev programming approach. Int J Prod Res 46(6):1587–1618

    Article  MATH  Google Scholar 

  37. Zhang G, Ouyang R, Lu B, Hocken R, Veale R, Donmez A (1988) A displacement method for machine geometry calibration. CIRP Ann-Manuf Technol 37(1):515–518

    Article  Google Scholar 

  38. Chen G, Yuan J, Ni J (2001) A displacement measurement approach for machine geometric error assessment. Int J Mach Tools Manuf 41(1):149–161

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhifeng Liu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheng, Q., Feng, Q., Liu, Z. et al. 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 (2016). https://doi.org/10.1007/s00170-015-7791-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-015-7791-x

Keywords

Navigation