Skip to main content
SpringerLink
Log in

Precision allocation optimization modeling of large-scale CNC hobbing machine based on precision reliability

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

Reducing manufacturing cost is the main goal of machine tool precision allocation under the condition of meeting precision design requirements. The previous studies generally took “ensuring machining errors completely within the allowable range of design precision” as constraint. Due to the strict constraint, the cost reduction effect is limited. This paper proposes a new method of precision allocation based on precision reliability. The probability that the machining errors are within the design precision allowable range is taken as the measurement index of precision reliability, and the optimization model constraint is relaxed to “that the machining errors are within the allowable range of design precision with predefined precision reliability”, so as to obtain lower manufacturing cost under tolerable precision loss risk. The case study of a large-scale gear hobbing machine shows that this method can effectively reduce the manufacturing cost, and the precision allocation is more economical and reasonable.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

S x, S y, S z :

Displacements of X, Y and Z-axis

θ A, θ C, θ M :

Rotation angles of A, C and M-axis

\(\left. {\matrix{{_X{\delta _x}\left({{S_x}} \right){,_X}{\delta _y}\left({{S_x}} \right){,_X}{\delta _z}\left({{S_x}} \right)} \cr {_X{\varepsilon _x}\left({{S_x}} \right){,_X}{\varepsilon _y}\left({{S_x}} \right){,_X}{\varepsilon _z}\left({{S_x}} \right)} \cr}} \right\}\) :

Errors of X-axis at Sx

\(\left. {\matrix{{_Y{\delta _x}\left({{S_y}} \right){,_Y}{\delta _y}\left({{S_y}} \right){,_Y}{\delta _z}\left({{S_y}} \right)} \cr {_Y{\varepsilon _x}\left({{S_y}} \right){,_Y}{\varepsilon _y}\left({{S_y}} \right){,_Y}{\varepsilon _z}\left({{S_y}} \right)} \cr}} \right\}\) :

Errors of Y-axis at Sy

\(\left. {\matrix{{_Z{\delta _x}\left({{S_z}} \right){,_Z}{\delta _y}\left({{S_z}} \right){,_Z}{\delta _z}\left({{S_z}} \right)} \cr {_Z{\varepsilon _x}\left({{S_z}} \right){,_Z}{\varepsilon _y}\left({{S_z}} \right){,_Z}{\varepsilon _z}\left({{S_z}} \right)} \cr}} \right\}\) :

Errors of Z-axis at Sz

\(\left. {\matrix{{_A{\delta _x}\left({{\theta _A}} \right){,_A}{\delta _y}\left({{\theta _A}} \right){,_A}{\delta _z}\left({{\theta _A}} \right)} \cr {_A{\varepsilon _x}\left({{\theta _A}} \right){,_A}{\varepsilon _y}\left({{\theta _A}} \right){,_A}{\varepsilon _z}\left({{\theta _A}} \right)} \cr}} \right\}\) :

Errors of A-axis at θA

\(\left. {\matrix{{_C{\delta _x}\left({{\theta _C}} \right){,_C}{\delta _y}\left({{\theta _C}} \right){,_C}{\delta _z}\left({{\theta _C}} \right)} \cr {_C{\varepsilon _x}\left({{\theta _C}} \right){,_C}{\varepsilon _y}\left({{\theta _C}} \right){,_C}{\varepsilon _z}\left({{\theta _C}} \right)} \cr}} \right\}\) :

Errors of C-axis at θc

\(\left. {\matrix{{_M{\delta _x}\left({{\theta _M}} \right){,_M}{\delta _y}\left({{\theta _M}} \right){,_M}{\delta _z}\left({{\theta _M}} \right)} \cr {_M{\varepsilon _x}\left({{\theta _M}} \right){,_M}{\varepsilon _y}\left({{\theta _M}} \right){,_M}{\varepsilon _z}\left({{\theta _M}} \right)} \cr}} \right\}\) :

Errors of M-axis at θM

\(_X^C{\delta _x},_X^C{\delta _y},_X^C{\delta _z},_X^C{\varepsilon _x},_X^C{\varepsilon _y},_X^C{\varepsilon _z}\) :

Errors between X-C axes

\(_Z^X{\delta _x},_Z^X{\delta _y},_Z^X{\delta _z},_Z^X{\varepsilon _x},_Z^X{\varepsilon _y},_Z^X{\varepsilon _z}\) :

Errors between Z-X axes

\(_A^Z{\delta _x},_A^Z{\delta _y},_A^Z{\delta _z},_A^Z{\varepsilon _x},_A^Z{\varepsilon _y},_A^Z{\varepsilon _z}\) :

Errors between A-Z axes

\(_Y^A{\delta _x},_Y^A{\delta _y},_Y^A{\delta _z},_Y^A{\varepsilon _x},_Y^A{\varepsilon _y},_Y^A{\varepsilon _z}\) :

Errors between Y-A axes

\(_M^Y{\delta _x},_M^Y{\delta _y},_M^Y{\delta _z},_M^Y{\varepsilon _x},_M^Y{\varepsilon _y},_M^Y{\varepsilon _z}\) :

Errors between M-Y axes

\(\left. {\matrix{{{M_{1,2}},{M_{2,3}},{M_{3,4}}} \hfill \cr {{M_{4,5}},{M_{5,6}},{M_{6,7}}} \hfill \cr}} \right\}\) :

Motion transformation matrices

\(\left. {\matrix{{E_{1,2}^m,E_{2,3}^m,E_{3,4}^m} \hfill \cr {E_{4,5}^m,E_{5,6}^m,E_{6,7}^m} \hfill \cr}} \right\}\) :

Motion axis error transformation matrices

\(\left. {\matrix{{E_{1,2}^P,E_{2,3}^P,E_{3,4}^P} \hfill \cr {E_{4,5}^P,E_{5,6}^P} \hfill \cr}} \right\}\) :

Inter axis error transformation matrices

M 1,7 :

Ideal motion transformation matrix

\(M_{1,7}^e\) :

Motion transformation matrix with errors

E :

Comprehensive error matrix of machine

δx, δy, δz, εx, εy, εz :

Comprehensive errors of machine

I δx, I δy, I δz, I εx, I εy, I εz :

Precisions design requirements

F X, F Y, F Z, F A, F C, F M, FA ij :

Fuzzy manufacturing costs

a,b,c,d,m ij :

Precision-cost function coefficients

F (Error):

Fuzzy cost optimization objective

Motion axis errors :

Errors caused by manufacturing and servo positioning control of motion axes

Assembly errors :

Errors caused by motion axes assembly

Comprehensive errors :

Relative pose errors between tool and workpiece caused by motion axis errors and assembly errors

Precision allocation :

Allocate the precision of each moving part according to the performance design requirements of the machine tool

Precision-cost function :

Relationship function between machine tool precision and manufacturing cost

Precision reliability :

Probability of machine tool machining precision meeting design requirements

References

  1. M. Hallmann, B. Schleich and S. Wartzack, From tolerance allocation to tolerance-cost optimization: a comprehensive literature review, The International Journal of Advanced Manufacturing Technology, 107(1) (2020) 1–54.

    Google Scholar 

  2. R. J. Hocken, J. A. Simpson, B. Borchardt, J. Lazar, C. Reeve and P. Stein, Three dimensional metrology, Journal of Ann. CIRP, 26(2) (1977) 403–408.

    Google Scholar 

  3. P. Dufour and R. Groppetti, Computer aided accuracy improvement in large NC machine tool, Proc. of the 21st International Machine Tool Design and Research conference, Palgrave, London (1981) 611–618.

    Chapter  Google Scholar 

  4. V. Kiridena and P. M. Ferreira, Mapping the effects of positioning errors on the volumetric precision of five-axis CNC machine tools, Int. J. Mach. Tools Manuf., 33(3) (1993) 417–437.

    Article  Google Scholar 

  5. V. T. Portman, A universal method for calculating the precision of mechanical devices, J. Sov. Eng. Res., 1(7) (1982) 11–15.

    Google Scholar 

  6. X. Zhong, Research on the modelling, identification of volumetric error considering error coupling and traceability of multi-level geometric errors for CNC machine tool, Doctoral Thesis, Huazhong University of Science and Technology, China (2019).

    Google Scholar 

  7. G. Fu, Research on geometric error modeling and compensation of CNC machine tools based on the product-of-exponential theory and transforming differential changes between corrdinate frames, Doctoral Thesis, Zhejiang University, Hangzhou, China (2016).

    Google Scholar 

  8. J. Chen and S. Lin, Geometric error decoupling for multi-axis CNC machines based on differential transformation, China Mechanical Engineering, 25(17) (2014) 2290–2294.

    Google Scholar 

  9. S. Wang, J. Yun and Z. Zhang, Modeling and compensation technique for the geometric errors of five-axis CNC machine tools, Chin. J. Mech Eng., 16 (2003) 197–201.

    Article  Google Scholar 

  10. W. Ding et al., Study on accuracy design of multi-axis machine tools oriented to remanufacturing, J. Basic Sci. Eng. (4) (2007) 559–568.

  11. E. L. Bohez et al., Systematic geometric rigid body error identification of 5-axis milling machines, Int. J. Comp. Aided Des., 39(4) (2007) 229–244.

    Article  Google Scholar 

  12. G. Zhang et al., Precision analysis for planar linkage with multiple clearances at turning pairs, Chinese J. Mec. Eng., 21(2) (2008) 36–41.

    Article  Google Scholar 

  13. S. Zhu et al.,, Integrated geometric error modeling, identification and compensation of CNC machine tools, Int. J. Mach. Tools Manuf., 52 (2012) 24–29.

    Article  Google Scholar 

  14. Q. Cheng et al., An analysis methodology for stochastic characteristic of volumetric error in multiaxis CNC machine tool, Math. Prob. Eng., 2013 (2013) 1–12.

    Google Scholar 

  15. X. Shi, H. Liu, H. Li, C. Liu and G. Tan, Comprehensive error measurement and compensation method for equivalent cutting forces, Int. J. Adv. Manuf. Technol., 85(1–4) (2016) 149–156.

    Article  Google Scholar 

  16. Y. Shi, X. Zhao, H. Zhang, Y. Nie and D. Zhang, A new top-down design method for the stiffness of precision machine tools, Int. J. Adv. Manuf. Technol., 83(9–12) (2016) 1887–1904.

    Article  Google Scholar 

  17. X. Tao, Research on hobbing error and compensation technology, Doctoral Thesis, Hefei University of Technology, China (2006).

    Google Scholar 

  18. Q. Guo, Research on real time compensation technology for geometric error and thermal error of CNC gear hobbing machine, Doctoral Thesis, Shanghai Jiaotong University, China (2008).

    Google Scholar 

  19. J. Zhao, Research on precision of precision transmission system of CNC gear hobbing machine, Master’s Thesis, Chongqing University, China (2017).

    Google Scholar 

  20. S. Sun, Research on multi source error modeling and compensation method of CNC hobbing, Doctoral Thesis, Chongqing University, China (2018).

    Google Scholar 

  21. L. Ren, Research on geometric error mapping and compensation of large size CNC hobbing machine, Doctoral Thesis, Chongqing University, China (2019).

    Google Scholar 

  22. H. Sheng and W. Yang, Development direction and key of precision distribution theory of modern mechanism, Optical Technology, 5 (1990) 33–36.

    Google Scholar 

  23. Q. Cheng, Z. Zhang, G. Zhang, P. Gu and L. Cai, Geometric precision allocation for multi-axis CNC machine tools based on sensitivity analysis and reliability theory, Proc. Inst. Mech. Eng. C. J. Mech. Eng. Sci., 229(6) (2015) 1134–1149.

    Article  Google Scholar 

  24. H. Sheng and W. Yang, Value analysis method of mechanism precision distribution, Optical Technology, 5 (1991) 3–6.

    Google Scholar 

  25. Z. Dong, W. Hu and D. Xue, New production cost-tolerance models for tolerance synthesis, ASME. J. Eng. Industry, 116(2) (1994) 199–206.

    Article  Google Scholar 

  26. C. Feng and A. Kusiak, Robust tolerance design with the integer programming approach, Journal of Manufacturing Science and Engineering, 119(4) (1997) 603–610.

    Article  Google Scholar 

  27. A. Ashiagbor, H. Liu and B. O. Nnaji, Tolerance control and propagation for the product assembly modeler, International Journal of Production Research, 36(1) (1998) 75–94.

    Article  MATH  Google Scholar 

  28. S. Rao and W. Wu, Optimum tolerance allocation in mechanical assemblies using an interval method, Engineering Optimization, 37(3) (2005) 237–257.

    Article  MathSciNet  Google Scholar 

  29. X. Huang, W. Ding and R. Hong, Research on precision design for remanufactured machine tool, Proc. of International Technology and Innovation Conference, Hangzhou (2006).

  30. F. Kang and J. Fan, Optimal allocation method for manufacturing precision of CNC machine tools, Mechanical Science And Technology, 27(5) (2008) 588–591.

    Google Scholar 

  31. Sarina, S. Zhang and J. Xu, Transmission system precision optimum allocation for multiaxis machine tools’ scheme design, Proc. of Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 227(12) (2013) 2762–2779.

    Google Scholar 

  32. X. Xu, Research on precision allocation design and optimization method and application of high grade CNC machine tools, Master’s Thesis, Zhejiang University, China (2013).

    Google Scholar 

  33. Z. Yu et al., Geometric error modeling and precision allocation based on reliability theory for large CNC gantry guide rail grinde, Journal of Mechanical Engineering, 49(17) (2013) 142–151.

    Article  Google Scholar 

  34. Y. Xing et al., Precision inverse design method for CNC machine tools based on multi-body theory, Journal of Agricultural Machinery, 45(3) (2014) 282–287.

    Google Scholar 

  35. J. Guo et al., Optimal tolerance allocation for precision machine tools in consideration of measurement and adjustment processes in assembly, The International Journal of Advanced Manufacturing Technology, 80(9–12) (2015) 1625–1640.

    Article  Google Scholar 

  36. Y. Guo, Transmission precision analysis and design of c-axis indexing device for heavy machine tool table, Master’s Thesis, Harbin Institute of Technology, China (2015).

    Google Scholar 

  37. P. Liu et al., Research on machine tool tolerance allocation using adaptive genetic algorithm, Journal of Xi’an Jiaotong University, 50(1) (2016) 115–123.

    Google Scholar 

  38. Z. Ma, Research on geometric precision analysis and error compensation of boring and milling machining center, Master’s Thesis, Xi’an University of Technology, China (2016).

    Google Scholar 

  39. B. Cheng et al., Optimal allocation of assembly tolerance based on actual working conditions, Mechanical Design and Research, 32(2) (2016) 123–126.

    Google Scholar 

  40. Z. Zhang et al., An approach of comprehensive error modeling and accuracy allocation for the improvement of reliability and optimization of cost of a multi-axis NC machine tool, The International Journal of Advanced Manufacturing Technology, 89(1–4) (2017) 561–579.

    Article  Google Scholar 

  41. X. Liu, Research on optimal allocation method of geometric precision of precision horizontal machining center, Master’s Thesis, Tianjin University, China (2018).

    Google Scholar 

  42. J. Wu, Research on optimal allocation method of geometric precision for precision horizontal machining center, Master’s Thesis, Shanghai Jiaotong University, China (2018).

    Google Scholar 

  43. Z. Zhang et al., An accuracy design approach for a multi-axis NC machine tool based on reliability theory, International Journal of Advanced Manufacturing Technology, 91 (2017) 1547–1566.

    Article  Google Scholar 

  44. M. Tlija, M. Ghali and N. Aifaoui, Integrated CAD tolerancing model based on difficulty coefficient evaluation and Lagrange multiplier, The International Journal of Advanced Manufacturing Technology, 101 (2019) 2519–2532.

    Article  Google Scholar 

  45. H. Wang, T. Li and X. Ding, Tolerance analysis of the volumetric error of heavy-duty machine tool based on interval uncertainty, The International Journal of Advanced Manufacturing Technology, 114 (2021) 2185–2199.

    Article  Google Scholar 

  46. C. He et al., Statistical tolerance allocation design considering form errors based on rigid assembly simulation and deep Q-network, The International Journal of Advanced Manufacturing Technology, 111(11–12) (2020) 1–17.

    Google Scholar 

  47. J. Fan et al., Optimal tolerance allocation for five-axis machine tools in consideration of deformation caused by gravity, The International Journal of Advanced Manufacturing Technology, 111(1–2) (2020) 1–12.

    Google Scholar 

  48. B. Cheng et al., Study on mathematical model of tolerance optimization based on service life, Modular Machine Tool and Automatic Processing Technology, 7 (2015) 23–25.

    Google Scholar 

  49. C. Wu and G. Tang, Tolerance design for products with asymmetric quality losses, International Journal of Production Research, 36(9) (1998) 2529–2541.

    Article  MATH  Google Scholar 

  50. A. Jeang and E. Leu, Robust tolerance design by computer experiment, International Journal of Production Research, 37(9) (1999) 1949–1961.

    Article  MATH  Google Scholar 

  51. S. Maghsoodloo and M. C. Li, Optimal asymmetric tolerance design, IIE Transactions, 32 (2000) 1127–1137.

    Article  Google Scholar 

  52. Y. Cao et al., A robust tolerance design method based on fuzzy quality loss, Front. Mech. Eng. China, 1(1) (2006) 101–105.

    Article  Google Scholar 

  53. C. Qiang et al., Robust geometric precision allocation of machine tools to minimize manufacturing costs and quality loss, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 230(15) (2015) 2728–2744.

    Google Scholar 

  54. S. Liu et al., A closed-form method for statistical tolerance allocation considering quality loss and different kinds of manufacturing cost functions, International Journal of Advanced Manufacturing Technology, 93 (2017) 2801–2811.

    Article  Google Scholar 

  55. Q. Ji et al., Structural design optimization of moving component in CNC machine tool for energy saving, Journal of Cleaner Production, 246(10) (2020) 118976.1–15.

    Google Scholar 

  56. A. J. Santhosh et al., Optimization of CNC turning parameters using face centred CCD approach in RSM and ANN-genetic algorithm for AISI 4340 alloy steel, Results in Engineering, 11(9) (2021) 100251.1–9.

    Google Scholar 

  57. F. Abbassi et al., Design of T-shaped tube hydroforming using finite element and artificial neural network modeling, J. Mech. Sci. Technol., 34 (2020) 1129–1138.

    Article  Google Scholar 

  58. Z. Huang et al., Thermal error analysis, modeling and compensation of five-axis machine tools, J. Mech. Sci. Technol., 34 (2020) 4295–4305.

    Article  Google Scholar 

  59. Y. S. Chuo et al., Artificial intelligence enabled smart machining and machine tools, J. Mech. Sci. Technol., 36 (2022) 1–23.

    Article  Google Scholar 

  60. P. V. Badiger et al., Cutting forces, surface roughness and tool wear quality assessment using ANN and PSO approach during machining of MDN431 with TiN/AlN-coated cutting tool, Arabian Journal for Science and Engineering, 44(9) (2019) 7465–7477.

    Article  Google Scholar 

  61. M. Hallmann, B. Schleich and S. Wartzack, From tolerance allocation to tolerance-cost optimization: a comprehensive literature review, The International Journal of Advanced Manufacturing Technology, 107 (2020) 4859–4912.

    Article  Google Scholar 

  62. Y. Zhao, D. Liu and Z. Wen, Optimal tolerance design of product based on service quality loss, International Journal of Advanced Manufacturing Technology, 82(9–12) (2016) 1715–1724.

    Article  Google Scholar 

  63. S. Mirjalili, S. M. Mirjalili and A. Lewis, Grey wolf optimizer, Advances in Engineering Software, 69 (2014) 46–61.

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by Research on Precision Evolution and Control Mechanism of Large-sized Numerical Control Gear Cutting Machine Tool supported by the Key Program of National Natural Foundation of China (51635003), China.

Author information

Authors and Affiliations

  1. The State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, 400044, China

    Zongyan Hu, Shilong Wang & Chi Ma

Authors
  1. Zongyan Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shilong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chi Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shilong Wang.

Additional information

Zongyan Hu is a doctoral candidate of the College of Mechanical Engineering, Chongqing University, Chongqing, China. His research interests include modeling, prediction, traceability and compensation of comprehensive error of gear hobbing machine.

Shilong Wang is a Professor of the College of Mechanical Engineering, Chongqing University, Chongqing, China. His research interests include precision control of gear machine tools, advanced manufacturing technology and structure design.

Chi Ma is an Associate Professor of the College of Mechanical Engineering, Chongqing University, Chongqing, China. His research interests include the precision and the thermal deformation of gear machine tools.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, Z., Wang, S. & Ma, C. Precision allocation optimization modeling of large-scale CNC hobbing machine based on precision reliability. J Mech Sci Technol 37, 901–917 (2023). https://doi.org/10.1007/s12206-023-0131-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-023-0131-4

Keywords

Search

Navigation