Skip to main content

Advertisement

SpringerLink
Log in

Evolutionary cost-tolerance optimization for complex assembly mechanisms via simulation and surrogate modeling approaches: application on micro gears

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

Abstract

With the introduction of new technologies, the scope of miniaturization has broadened. The conditions under which complicated products are designed, manufactured, and assembled ultimately influence how well they perform. The intricacy and crucial functionality of products are frequently only fulfilled through the use of high-precision components such as micro gears. In power transmission systems, gears are used in a variety of industries. Micro gears or gears with micro features, with tolerances of less than 5 μm, are pushing manufacturing processes to their technological limits. Monte-Carlo simulation methods enable an accurate forecast of inaccuracies in compliance. The complexity of the micro gear’s design, on the other hand, increases the simulation computation and runtime. An alternative method for simulation is to create a surrogate model to predict the behavior. This paper proposes a statistical surrogate model to predict the conformity of a pair of micro gears. Afterward, the advantage of the surrogate model enables the optimal tolerance assignment while taking gear functionality and production cost into account.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Data availability

The data that support the findings of this study are available in the Recherche Data Gouv, https://doi.org/10.57745/3EELGX.

Code availability

The findings of this study are supported by the codes available on GitHub repository, https://doi.org/10.5281/zenodo.7817677.

References

  1. Wagner R, Kuhnle A, Lanza G (2017) Optimising matching strategies for high precision products by functional models and machine learning algorithms. WGP Annals 7:231–240

    Google Scholar 

  2. Dantan J-Y, Eifler T (2021) Tolerance allocation under behavioural simulation uncertainty of a multiphysical system. CIRP Annals 70:127–130. https://doi.org/10.1016/j.cirp.2021.04.054

    Article  Google Scholar 

  3. Lanza G, Haefner B, Kraemer A (2015) Optimization of selective assembly and adaptive manufacturing by means of cyber-physical system based matching. CIRP Annals 64:399–402. https://doi.org/10.1016/j.cirp.2015.04.123

    Article  Google Scholar 

  4. Queipo NV, Haftka RT, Shyy W, Goel T, Vaidyanathan R, Tucker PK (2005) Surrogate-based analysis and optimization. Progress in aerospace sciences 41:1–28. https://doi.org/10.1016/j.paerosci.2005.02.001

    Article  Google Scholar 

  5. Söderberg R, Wärmefjord K, Carlson JS, Lindkvist L (2017) Toward a digital twin for real-time geometry assurance in individualized production. CIRP annals 66:137–140. https://doi.org/10.1016/j.cirp.2017.04.038

    Article  Google Scholar 

  6. Schleich B, Anwer N, Mathieu L, Wartzack S (2017) Shaping the digital twin for design and production engineering. CIRP annals 66:141–144. https://doi.org/10.1016/j.cirp.2017.04.040

    Article  Google Scholar 

  7. Kontoravdi C, Asprey SP, Pistikopoulos EN, Mantalaris A (2005) Application of global sensitivity analysis to determine goals for design of experiments: an example study on antibody-producing cell cultures. Biotechnology progress 21:1128–1135. https://doi.org/10.1021/bp050028k

    Article  Google Scholar 

  8. Mack Y, Goel T, Shyy W, Haftka R (2007) Surrogate model-based optimization framework: a case study in aerospace design. Journal:323–342

  9. Ziegler P, Wartzack S (2015) Sensitivity analysis of features in tolerancing based on constraint function level sets. Reliability Engineering & System Safety 134:324–333. https://doi.org/10.1016/j.ress.2014.09.017

    Article  Google Scholar 

  10. Dumas A, Dantan J-Y, Gayton N (2015) Impact of a behavior model linearization strategy on the tolerance analysis of over-constrained mechanisms. Computer-Aided Design 62:152–163. https://doi.org/10.1016/j.cad.2014.11.002

    Article  Google Scholar 

  11. Qureshi AJ, Dantan J-Y, Sabri V, Beaucaire P, Gayton N (2012) A statistical tolerance analysis approach for over-constrained mechanism based on optimization and Monte Carlo simulation. Computer-Aided Design 44:132–142. https://doi.org/10.1016/j.cad.2011.10.004

    Article  Google Scholar 

  12. Drake PJ (1999) Dimensioning and tolerancing handbook. McGraw-Hill Education

  13. Ji S, Li X, Ma Y, Cai H (2000) Optimal tolerance allocation based on fuzzy comprehensive evaluation and genetic algorithm. The International Journal of Advanced Manufacturing Technology 16:461–468. https://doi.org/10.1007/s001700070053

    Article  Google Scholar 

  14. Lecompte J, Legoff O, Hascoet J-Y (2010) Technological form defects identification using discrete cosine transform method. The International Journal of Advanced Manufacturing Technology 51:1033–1044. https://doi.org/10.1007/s00170-010-2687-2

    Article  Google Scholar 

  15. Schleich B, Anwer N, Mathieu L, Wartzack S (2014) Skin model shapes: a new paradigm shift for geometric variations modelling in mechanical engineering. Computer-Aided Design 50:1–15. https://doi.org/10.1016/j.cad.2014.01.001

    Article  Google Scholar 

  16. Homri L, Goka E, Levasseur G, Dantan J-Y (2017) Tolerance analysis—form defects modeling and simulation by modal decomposition and optimization. Computer-Aided Design 91:46–59. https://doi.org/10.1016/j.cad.2017.04.007

    Article  Google Scholar 

  17. Lê H-N, Ledoux Y, Ballu A (2014) Experimental and theoretical investigations of mechanical joints with form defects. Journal of Computing and Information Science in Engineering 14. https://doi.org/10.1115/1.4028195

  18. Du Z, Wu J, Yang J (2017) Modified Jacobian-Torsor based error modeling and quantitative sensitivity analysis for single axis assembly of machine tool. Paper presented at the ASME 2017 international design engineering technical conferences and computers and information in engineering conference. https://doi.org/10.1115/DETC2017-67716

  19. Chen H, Jin S, Li Z, Lai X (2015) A modified method of the unified Jacobian-Torsor model for tolerance analysis and allocation. International Journal of Precision Engineering and Manufacturing 16:1789–1800. https://doi.org/10.1007/s12541-015-0234-7

    Article  Google Scholar 

  20. Jaballi K, Bellacicco A, Louati J, Riviere A, Haddar M (2011) Rational method for 3D manufacturing tolerancing synthesis based on the TTRS approach “R3DMTSyn”. Computers in industry 62:541–554. https://doi.org/10.1016/j.compind.2011.02.003

    Article  Google Scholar 

  21. Mansuy M, Giordano M, Hernandez P (2011) A new calculation method for the worst case tolerance analysis and synthesis in stack-type assemblies. Computer-Aided Design 43:1118–1125. https://doi.org/10.1016/j.cad.2011.04.010

    Article  Google Scholar 

  22. Zeng W, Rao Y, Wang P, Yi W (2017) A solution of worst-case tolerance analysis for partial parallel chains based on the unified Jacobian-Torsor model. Precision Engineering 47:276–291. https://doi.org/10.1016/j.precisioneng.2016.09.002

    Article  Google Scholar 

  23. Beaucaire P, Gayton N, Duc E, Dantan J-Y (2013) Statistical tolerance analysis of over-constrained mechanisms with gaps using system reliability methods. Computer-Aided Design 45:1547–1555. https://doi.org/10.1016/j.cad.2013.06.011

    Article  Google Scholar 

  24. Goka E, Beaurepaire P, Homri L, Dantan J-Y (2019) Probabilistic-based approach using kernel density estimation for gap modeling in a statistical tolerance analysis. Mechanism and Machine Theory 139:294–309. https://doi.org/10.1016/j.mechmachtheory.2019.04.020

    Article  Google Scholar 

  25. Umaras E, Barari A, Tsuzuki MSG (2021) Tolerance analysis based on Monte Carlo simulation: A case of an automotive water pump design optimization. Journal of Intelligent Manufacturing 32:1883–1897. https://doi.org/10.1007/s10845-020-01695-7

    Article  Google Scholar 

  26. Etienne A, Dantan J-Y, Qureshi J, Siadat A (2008) Variation management by functional tolerance allocation and manufacturing process selection. International Journal on Interactive Design and Manufacturing (IJIDeM) 2:207–218. https://doi.org/10.1007/s12008-008-0055-3

    Article  Google Scholar 

  27. Andolfatto L, Thiébaut F, Lartigue C, Douilly M (2014) Quality-and cost-driven assembly technique selection and geometrical tolerance allocation for mechanical structure assembly. Journal of Manufacturing Systems 33:103–115. https://doi.org/10.1016/j.jmsy.2013.03.003

    Article  Google Scholar 

  28. Chase KW, Greenwood WH, Loosli BG, Hauglund LF (1990) Least cost tolerance allocation for mechanical assemblies with automated process selection. Manufacturing review 3:49–59

    Google Scholar 

  29. Dantan J-Y, Bruyere J, Vincent J-P, Bigot R (2008) Vectorial tolerance allocation of bevel gear by discrete optimization. Mechanism and Machine Theory 43:1478–1494. https://doi.org/10.1016/j.mechmachtheory.2007.11.002

    Article  MATH  Google Scholar 

  30. Etienne A, Dantan J-Y, Siadat A, Martin P (2009) Activity-based tolerance allocation (ABTA)–driving tolerance synthesis by evaluating its global cost. International journal of production research 47:4971–4989. https://doi.org/10.1080/00207540701819225

    Article  Google Scholar 

  31. Walter M, Spruegel T, Wartzack S (2015) Least cost tolerance allocation for systems with time-variant deviations. Procedia Cirp 27:1–9. https://doi.org/10.1016/j.procir.2015.04.035

    Article  Google Scholar 

  32. Sutherland G, Roth B (1975) Mechanism design: accounting for manufacturing tolerances and costs in function generating problems. ASME. J Eng Ind 97(1):283–286

    Article  Google Scholar 

  33. Dong Z, Hu W, Xue D (1994) New production cost-tolerance models for tolerance synthesis. ASME. J Eng Ind 116(2):199–206. https://doi.org/10.1115/1.2901931

  34. Hallmann M, Schleich B, Wartzack S (2020) From tolerance allocation to tolerance-cost optimization: A comprehensive literature review. The International Journal of Advanced Manufacturing Technology 107:4859–4912. https://doi.org/10.1007/s00170-020-05254-5

    Article  Google Scholar 

  35. 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. AI EDAM 34:430–443. https://doi.org/10.1017/S0890060420000219

    Article  Google Scholar 

  36. Wu H, Li X, Sun F, Zheng H, Zhao Y (2021) Optimization design method of machine tool static geometric accuracy using tolerance modeling. The International Journal of Advanced Manufacturing Technology 118:1793–1809. https://doi.org/10.1007/s00170-021-07992-6

    Article  Google Scholar 

  37. Hallmann M, Schleich B, Wartzack S (2021) Process and machine selection in sampling-based tolerance-cost optimisation for dimensional tolerancing. International Journal of Production Research 60:5201–5216. https://doi.org/10.1080/00207543.2021.1951867

    Article  Google Scholar 

  38. Tsutsumi D, Gyulai D, Kovács A, Tipary B, Ueno Y, Nonaka Y, Fujita K (2020) Joint optimization of product tolerance design, process plan, and production plan in high-precision multi-product assembly. Journal of Manufacturing Systems 54:336–347. https://doi.org/10.1016/j.jmsy.2020.01.004

    Article  Google Scholar 

  39. Wang K, Yin Y, Du S, Xi L (2021) Variation management of key control characteristics in multistage machining processes considering quality-cost equilibrium. Journal of Manufacturing Systems 59:441–452. https://doi.org/10.1016/j.jmsy.2021.03.013

    Article  Google Scholar 

  40. Han Y, Tu Y, Ouyang L, Wang J, Ma Y (2022) Economic quality design under model uncertainty in micro-drilling manufacturing process. International Journal of Production Research 60:1086–1104. https://doi.org/10.1080/00207543.2020.1851792

    Article  Google Scholar 

  41. Dantan J-Y, Etienne A, Mohammadi M, Khezri A, Homri L, Tavakkoli-Moghaddam R, Siadat A (2022) Modular cost model for tolerance allocation, process selection and inspection planning. Procedia CIRP 114:1–6. https://doi.org/10.1016/j.procir.2022.10.001

    Article  Google Scholar 

  42. Khezri A, Homri L, Etienne A, Dantan J-Y, Lanza G (2022) A Framework for integration of resource allocation and reworking concept into design optimisation problem. IFAC-PapersOnLine 55:1037–1042

    Article  Google Scholar 

  43. Khezri A, Homri L, Etienne A, Dantan J-Y (2022) An integrated resource allocation and tolerance allocation optimization: a statistical-based dimensional tolerancing. Procedia CIRP 114:88–93

    Article  Google Scholar 

  44. Khezri A, Homri L, Etienne A, Dantan J-Y (2023) Hybrid cost-tolerance allocation and production strategy selection for complex mechanisms: simulation and surrogate built-in optimization models. ASME. J Comput Inf Sci Eng 23(5):051003. https://doi.org/10.1115/1.4056687

  45. VDI2608:2001 (2001) Tangential composite and radial composite inspection of cylindrical gears, bevel gears, worms and worm wheels. VDI/VDE-Gesellschaft Mess- und Automatisierungstechnik

  46. Bruyere J, Dantan J-Y, Bigot R, Martin P (2007) Statistical tolerance analysis of bevel gear by tooth contact analysis and Monte Carlo simulation. Mechanism and Machine Theory 42:1326–1351. https://doi.org/10.1016/j.mechmachtheory.2006.11.003

    Article  MATH  Google Scholar 

  47. Gurumani R, Shanmugam S (2011) Modeling and contact analysis of crowned spur gear teeth. Engineering Mechanics 18:65–78

    Google Scholar 

  48. Li G, Wang Z, Zhu W, Kubo A (2017) A function-oriented active form-grinding method for cylindrical gears based on error sensitivity. The International Journal of Advanced Manufacturing Technology 92:3019–3031. https://doi.org/10.1007/s00170-017-0363-5

    Article  Google Scholar 

  49. Wu D, Yan P, Guo Y, Zhou H, Chen J (2022) A gear machining error prediction method based on adaptive Gaussian mixture regression considering stochastic disturbance. Journal of Intelligent Manufacturing 33:2321–2339. https://doi.org/10.1007/s10845-021-01791-2

    Article  Google Scholar 

  50. Litvin F, Chen J-S, Sep T, Wang J-C (1995) Computerized simulation of transmission errors and shift of bearing contact for face-milled hypoid gear drive. Journal of Mechanical Design 117:262–268. https://doi.org/10.1115/1.2826133

    Article  Google Scholar 

  51. Lee C-K (2009) Manufacturing process for a cylindrical crown gear drive with a controllable fourth order polynomial function of transmission error. Journal of Materials Processing Technology 209:3–13. https://doi.org/10.1016/j.jmatprotec.2008.03.065

    Article  Google Scholar 

  52. Head T, Kumar M, Nahrstaedt H, Louppe G, Shcherbatyi I (2020) Scikit-optimize/scikit-optimize (version 0.8.1). Zenodo

  53. Fernández A, Garcia S, Herrera F, Chawla NV (2018) SMOTE for learning from imbalanced data: progress and challenges, marking the 15-year anniversary. Journal of artificial intelligence research 61:863–905. https://doi.org/10.1613/jair.1.11192

    Article  MathSciNet  MATH  Google Scholar 

  54. Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V (2011) Scikit-learn: machine learning in Python. the Journal of machine Learning research 12:2825–2830. https://doi.org/10.48550/arXiv.1201.0490

    Article  MathSciNet  MATH  Google Scholar 

  55. Chollet F (2015) Keras

  56. Platt J (1999) Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods. Advances in Large Margin Classifiers 10:61–74

    Google Scholar 

  57. Ho TK (1998) The random subspace method for constructing decision forests. IEEE transactions on pattern analysis and machine intelligence 20:832–844. https://doi.org/10.1109/34.709601

    Article  Google Scholar 

  58. Hinton GE (1990) Connectionist learning procedures. Journal:555–610

  59. Goldberger J, Hinton GE, Roweis S, Salakhutdinov RR (2004) Neighbourhood components analysis. Advances in neural information processing systems 17

  60. John GH, Langley P (1995) Estimating continuous distributions in Bayesian classifiers. Journal:338–345. https://doi.org/10.48550/arXiv.1302.4964

  61. Breiman L (2017) Classification and regression trees. Routledge, New York. https://doi.org/10.1201/9781315139470

  62. Hinton GE, Osindero S, Teh Y-W (2006) A fast learning algorithm for deep belief nets. Neural computation 18:1527–1554. https://doi.org/10.1162/neco.2006.18.7.1527

    Article  MathSciNet  MATH  Google Scholar 

  63. Freund Y, Schapire RE (1997) A decision-theoretic generalization of on-line learning and an application to boosting. Journal of computer and system sciences 55:119–139. https://doi.org/10.1006/jcss.1997.1504

    Article  MathSciNet  MATH  Google Scholar 

  64. VanderPlas J (2016) Python data science handbook. O'Reilly Media, Inc

  65. Deng W, Yang X, Zou L, Wang M, Liu Y, Li Y (2013) An improved self-adaptive differential evolution algorithm and its application. Chemometrics and intelligent laboratory systems 128:66–76. https://doi.org/10.1016/j.chemolab.2013.07.004

    Article  Google Scholar 

  66. Brest J, Bošković B, Greiner S, Žumer V, Maučec MS (2007) Performance comparison of self-adaptive and adaptive differential evolution algorithms. Soft Computing 11:617–629. https://doi.org/10.1007/s00500-006-0124-0

    Article  MATH  Google Scholar 

Download references

Acknowledgements

Authors extend their thanks to Robert Schmitt, Jochen Wacker, and Christoph Rettig (Sirona Dental Systems GmbH) for their valuable contribution to empirical expert observation and validation of this paper. Also, the authors acknowledge the use of the Cassiopee Arts et Métiers Institute of Technology HPC Center made available for achieving the results reported in this paper.

Funding

The authors would like to acknowledge the Agence Nationale de la Recherche (ANR) and the Deutsche Forschungsgemeinschaft (DFG) for the financial support of the AdeQuaT Project (ANR-19-CE10-0013) and the Université franco-allemande/Deutsch-Französischen Hochschule for the financial support of the French-German Doctoral College (CDFA 03-19).

Author information

Authors and Affiliations

  1. LCFC, Arts et Métiers–ParisTech, Université de Lorraine, F-57000, Metz, France

    Amirhossein Khezri, Lazhar Homri, Alain Etienne & Jean-Yves Dantan

  2. WBK Institute of Production Science, Karlsruhe Institute of Technology (KIT), Kaiserstr. 12, 76131, Karlsruhe, Germany

    Vivian Schiller, Florian Stamer & Gisela Lanza

  3. ArcelorMittal Maizières Research SA, Voie Romaine, 57280, Maizières-lès-, Metz, France

    Edoh Goka

Authors
  1. Amirhossein Khezri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vivian Schiller
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Edoh Goka
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lazhar Homri
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Alain Etienne
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Florian Stamer
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Jean-Yves Dantan
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Gisela Lanza
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

A. Khezri contributed to conceptualization, modelization, analyzing, coding, writing original draft, and editing. V. Schiller contributed to empirical data collection, reviewing, and editing. E. Goka contributed to empirical data collection and reviewing. L. Homri contributed to conceptualization, advising, and reviewing. A. Etienne contributed to conceptualization, methodology, advising, and reviewing. F. Stamer contributed to reviewing, and editing. J-Y. Dantan contributed to conceptualization, reviewing and editing, supervision, project administration, and funding acquisition. G. Lanza contributed to reviewing, supervision, project administration, and funding acquisition.

Corresponding author

Correspondence to Amirhossein Khezri.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khezri, A., Schiller, V., Goka, E. et al. Evolutionary cost-tolerance optimization for complex assembly mechanisms via simulation and surrogate modeling approaches: application on micro gears. Int J Adv Manuf Technol 126, 4101–4117 (2023). https://doi.org/10.1007/s00170-023-11360-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-023-11360-x

Keywords

Search

Navigation