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Sensitivity analysis using a variance-based method for a three-axis diamond turning machine

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Abstract

It is of great interest to determine which of the numerous sources of error in an ultra-precision diamond turning machine has the greatest influence on the machining inaccuracy. Global sensitivity analysis is a well-known mathematical technique that is able to quantify the contribution of each error source to the machining inaccuracy. The present study employs a variance-based sensitivity analysis method to comprehensively investigate the influence of each error source in a three-axis diamond turning machine on the machining inaccuracy. The procedure for establishing a volumetric error model based on multi-body system theory in conjunction with a homogeneous transformation matrix is first described in detail. The basic working principle and relevant estimation process of the Sobol method is then explained, and the Sobol method is employed to quantify the sensitivity index of each error source based on the volumetric error model. Finally, simulation testing is conducted to comprehensively investigate the main geometric error sources contributing to machining errors along the X, Y, and Z directions, and with respect to comprehensive volumetric errors. After the main geometric error sources are identified, some measures are taken to improve the identified error sources, and a flat surface cutting experiment is conducted to verify the effectiveness of the proposed sensitivity method. The results show that the proposed sensitivity method is effective for identifying the most crucial geometric errors, the form error of flat surface is improved by approximately 50% after modifying parts of these errors, and these errors should then be the subjects of careful scrutiny in the precision design, error compensation, and precision processing stages. The method is of significant guidance for on-machine and real-time online error compensation.

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References

  1. Zhou L, Cheng K (2009) Dynamic cutting process modelling and its impact on the generation of surface topography and texture in nano/micro cutting. P I Mech Eng B-J Eng:247–266. doi:10.1243/09544054JEM1316

  2. Huo D, Cheng K, Wardle F (2010) Design of a five-axis ultra-precision micro-milling machine-UltraMill. Part 1: holistic design approach, design considerations and specifications. Int J Adv Manuf Technol 47:867–877. doi:10.1007/s00170-009-2128-2

    Article  Google Scholar 

  3. Huo D, Cheng K, Wardle F (2010) Design of a five-axis ultra-precision micro-milling machine-UltraMill. Part 2: integrated dynamic modelling, design optimisation and analysis. Int J Adv Manuf Technol 47:879–890. doi:10.1007/s00170-009-2129-1

    Article  Google Scholar 

  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 Tool Manuf 40:1235–1256. doi:10.1016/S0890-6955(00)00009-2

    Article  Google Scholar 

  5. Ramesh R, Mannan MA, Poo AN (2000) Error compensation in machine tools—a review: part II: thermal errors. Int J Mach Tool Manuf 40:1257–1284. doi:10.1016/S0890-6955(00)00010-9

    Article  Google Scholar 

  6. Yang SH, Kim KH, Park YK, Lee SG (2004) Error analysis and compensation for the volumetric errors of a vertical machining centre using a hemispherical helix ball bar test. Int J Adv Manuf Technol 23:495–500. doi:10.1007/s00170-003-1662-6

    Article  Google Scholar 

  7. 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 62:1261–1272. doi:10.1007/s00170-011-3860-y

    Article  Google Scholar 

  8. Liu X, Zhang X, Fang F, Zeng Z, Gao H, Hu X (2015) Influence of machining errors on form errors of microlens arrays in ultra-precision turning. Int J Mach Tool Manuf 96:80–93. doi:10.1016/j.ijmachtools.2015.05.008

    Article  Google Scholar 

  9. Gao H, Fang F, Zhang X (2014) Reverse analysis on the geometric errors of ultra-precision machine. Int J Adv Manuf Technol 73:1615–1624. doi:10.1007/s00170-014-5931-3

    Article  Google Scholar 

  10. Li J, Xie F, Liu X (2016) Geometric error modeling and sensitivity analysis of a five-axis machine tool. Int J Adv Manuf Technol 82:2037–2051. doi:10.1007/s00170-015-7492-5

    Article  Google Scholar 

  11. Yao H, Li Z, Zhao X, Sun T, Dobrovolskyi G, Li G (2016) Modeling of kinematics errors and alignment method of a swing arm ultra-precision diamond turning machine. Int J Adv Manuf Technol. doi:10.1007/s00170-016-8451-5

  12. 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. doi:10.1007/s00170-013-4874-4

    Article  Google Scholar 

  13. Xie F, Liu X, Chen Y (2013) Error sensitivity analysis of novel virtual center mechanism with parallel kinematics. J Mech Eng 49:85–91. doi:10.3901/JME.2013.17.085

    Article  Google Scholar 

  14. Fan KC, Wang H, Zhao JW, Chang TH (2003) Sensitivity analysis of the 3-PRS parallel kinematic spindle platform of a serial-parallel machine tool. Int J Mach Tool Manuf 43:1561–1569. doi:10.1016/S0890-6955(03)00202-5

    Article  Google Scholar 

  15. Harper EB, Stella JC, Fremier AK (2011) Global sensitivity analysis for complex ecological models: a case study of riparian cottonwood population dynamics. Ecol Appl 21:1225–1240. doi:10.1890/10-0506.1

    Article  Google Scholar 

  16. Pianosi F, Sarrazin F, Wagener T (2015) A Matlab toolbox for global sensitivity analysis. Environ Model Softw 70:80–85. doi:10.1016/j.envsoft.2015.04.009

    Article  Google Scholar 

  17. Cheng Q, Sun B, Liu Z, Li J, Dong X, Gu P (2016) Key geometric error extraction of machine tool based on extended Fourier amplitude sensitivity test method. Int J Adv Manuf Technol. doi:10.1007/s00170-016-9609-x

  18. Zhang M, Djurdjanovic D, Ni J (2007) Diagnosibility and sensitivity analysis for multi-station machining processes. Int J Mach Tool Manuf 47:646–657. doi:10.1016/j.ijmachtools.2006.04.011

    Article  Google Scholar 

  19. Chhatre S, Francis R, Newcombe AR, Zhou Y, 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 51:79. doi:10.1042/BA20070228

    Article  Google Scholar 

  20. Qiu Q, Li B, Feng P, Gao Y (2014) Decomposition method of complex optimization model based on global sensitivity analysis. Chin J Mech Eng-En 27:722–729. doi:10.3901/CJME.2014.0516.096

    Article  Google Scholar 

  21. Cukier RI, Fortuin CM, Shuler KE, Petsche AG, Schaibly JH (1973) Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I Theory. J Chem Phys 59:3873. doi:10.1063/1.1680571

    Article  Google Scholar 

  22. Sobol IM (1993) Sensitivity analysis for non-linear mathematical models. Math Model Comput 1:407–414

    MATH  Google Scholar 

  23. 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. doi:10.1007/s00170-014-6133-8

    Article  Google Scholar 

  24. Zhang X, Zhang Y, Pandey MD (2015) Global sensitivity analysis of a CNC machine tool: application of MDRM. Int J Adv Manuf Technol 81:159–169. doi:10.1007/s00170-015-7128-9

    Article  Google Scholar 

  25. 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 Tool Manuf 105:45–57. doi:10.1016/j.ijmachtools.2016.03.001

    Article  Google Scholar 

  26. 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. doi:10.1007/s00170-016-8580-x

    Article  Google Scholar 

  27. Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55:271–280. doi:10.1016/S0378-4754(00)00270-6

    Article  MathSciNet  MATH  Google Scholar 

  28. Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M et al (2008) Global sensitivity analysis—the primer. Wiley, Chichester

    MATH  Google Scholar 

  29. Soboĺ IM (1990) Quasi-Monte Carlo methods. Prog Nucl Energy 24:55–61. doi:10.1016/0149-1970(90)90022-W

    Article  Google Scholar 

  30. Saltelli A, Annoni P, Azzini I, Campolongo F, Ratto M, Tarantola S (2010) Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Comput Phys Commun 181:259–270. doi:10.1016/j.cpc.2009.09.018

    Article  MathSciNet  MATH  Google Scholar 

  31. International Organization for Standardization. (2014) ISO230 Test code for machine tools—part 2: determination of accuracy and repeatability of positioning of numerically controlled axes

  32. International Organization for Standardization (2012) ISO230 Test code for machine tools—part 1: geometric accuracy of machines operating under no-load or quasi-static conditions

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Authors and Affiliations

  1. Center for Precision Engineering, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Xicong Zou, Xuesen Zhao, Zengqiang Li & Tao Sun

  2. Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang, 621900, People’s Republic of China

    Guo Li

Authors
  1. Xicong Zou
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  2. Xuesen Zhao
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  3. Guo Li
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  4. Zengqiang Li
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  5. Tao Sun
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Corresponding author

Correspondence to Xuesen Zhao.

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Zou, X., Zhao, X., Li, G. et al. Sensitivity analysis using a variance-based method for a three-axis diamond turning machine. Int J Adv Manuf Technol 92, 4429–4443 (2017). https://doi.org/10.1007/s00170-017-0394-y

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