Skip to main content
Log in

A new computer-aided tolerance analysis and optimization framework for assembling processes using DP-SDT theory

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

Abstract

Tolerance analysis is frequently used in predicting the product quality and balancing the design tolerances in mechanical assemblies. Generally, the tolerance analysis procedure is rather complex and cumbersome, and the existing computer-aided tolerance analysis methods are insufficient in dealing with some assembly information and user-defined quality requirements. This paper presents a new comprehensive tolerance analysis and optimization framework using deviation propagation and small displacement torsor (DP-SDT) theory. In this framework, four modules are designed to model the tolerances, analyze the assembly processes, predict the product quality, and optimize the tolerances respectively. Comparing with the existing methods, this framework can better support the complex assembly information like 3D dimensional tolerances, geometric dimensioning and tolerancing (GD&Ts), different tolerance zones, geometric information, assembly sequence, and various kinds of locating modes. And more practical quality requirements besides the distance precisions can be analyzed. The framework is a helpful supplement in tolerance analysis field. An application prototype using the framework has been developed for SolidWorks, and a tolerance optimization example of lathe saddle is provided to verify the performance of the framework.

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. Robles N, Roy U (2004) Optimal tolerance allocation and process-sequence selection incorporating manufacturing capacities and quality issues. J Manuf Syst 23(2):127–133

    Article  Google Scholar 

  2. Khodaygan S, Movahhedy MR, Fomani MS (2010) Tolerance analysis of mechanical assemblies based on modal interval and small degrees of freedom (MI-SDOF) concepts. Int J Adv Manuf Technol 50(9–12):1041–1061

    Article  Google Scholar 

  3. Zhang Y, Li Z, Gao J, Hong J (2011) New reasoning algorithm for assembly tolerance specifications and corresponding tolerance zone types. Comput Aided Des 43(12):1606–1628

    Article  Google Scholar 

  4. Zhu Z, Qiao L (2015) Analysis and control of assembly precision in different assembly sequences. Procedia CIRP 27:117–123

    Article  Google Scholar 

  5. Camelio J, Ceglarek D, Hu SJ (2004) Modeling variation propagation of multi-station assembly systems with compliant parts. J Mech Des 125(4):673–681

    Article  Google Scholar 

  6. Shi J, Jin J (1999) State space modeling of sheet metal assembly for dimensional control. J Manuf Sci Eng 121(4):756–762

    Article  Google Scholar 

  7. Armillotta A (2013) A method for computer-aided specification of geometric tolerances. Comput Aided Des 45(12):1604–1616

    Article  Google Scholar 

  8. Germer C, Hansen U, Franke H, Büttgenbach S (2004) Computer aided tolerance analysis and synthesis in micro systems (μ-ToAST). Analog Integr Circ Sig Process 40(2):131–140

    Article  Google Scholar 

  9. Cho N, Tu JF (2002) Quantitative circularity tolerance analysis and design for 2D precision assemblies. Int J Mach Tools Manuf 42(13):1391–1401

    Article  Google Scholar 

  10. Liu J, Shi J, Hu SJ (2009) Quality-assured setup planning based on the stream-of-variation model for multi-stage machining processes. IIE Trans 41(4):323–334

    Article  Google Scholar 

  11. Li H, Zhu H, Li P, He F (2014) Tolerance analysis of mechanical assemblies based on small displacement torsor and deviation propagation theories. Int J Adv Manuf Technol 72(1–4):89–99

    Article  Google Scholar 

  12. Franciosa P, Gerbino S, Lanzotti A, Patalano S (2013) Automatic evaluation of variational parameters for tolerance analysis of rigid parts based on graphs. Int J Interact Des Manuf 7(4):239–248

    Article  Google Scholar 

  13. Dantan JY, Gayton N, Qureshi AJ, Lemaire M, Etienne A (2013) Tolerance analysis approach based on the classification of uncertainty (aleatory/epistemic). Procedia CIRP 10:287–293

    Article  Google Scholar 

  14. Chen H, Jin S, Li Z, Lai X (2015) A modified method of the unified Jacobian-Torsor model for tolerance analysis and allocation. Int J Precis Eng Manuf 16(8):1789–1800

    Article  Google Scholar 

  15. Schleich B, Wartzack S (2015) Evaluation of geometric tolerances and generation of variational part representatives for tolerance analysis. Int J Adv Manuf Technol 79(5–8):959–983

    Article  Google Scholar 

  16. Wang MY, Liu T, Pelinescu DM (2003) Fixture kinematic analysis based on the full contact model of rigid bodies. J Manuf Sci Eng 125(2):316–324

    Article  Google Scholar 

  17. Wittwer JW, Chase KW, Howell LL (2004) The direct linearization method applied to position error in kinematic linkages. Mech Mach Theory 39(7):681–693

    Article  MathSciNet  MATH  Google Scholar 

  18. Barbero BR, Azcona JP, Pérez JG (2015) A tolerance analysis and optimization methodology. The combined use of 3D CAT, a dimensional hierarchization matrix and an optimization algorithm. Int J Adv Manuf Technol 81(1):371–385

    Article  Google Scholar 

  19. Cai W (2008) A new tolerance modeling and analysis methodology through a two-step linearization with applications in automotive body assembly. J Manuf Syst 27(1):26–35

    Article  Google Scholar 

  20. Dumas A, Gayton N, Dantan JY, Sudret B (2015) A new system formulation for the tolerance analysis of overconstrained mechanisms. Probab Eng Mech 40:66–74

    Article  Google Scholar 

  21. Beaucaire P, Gayton N, Duc E, Dantan J (2013) Statistical tolerance analysis of over-constrained mechanisms with gaps using system reliability methods. Comput Aided Des 45(12):1547–1555

    Article  Google Scholar 

  22. Liu J, Jin J, Shi J (2010) State space modeling for 3-D variation propagation in rigid-body multistage assembly processes. IEEE Trans Autom Sci Eng 7(2):274–290

    Article  Google Scholar 

  23. Asante JN (2013) A constraint-based tolerance analysis in a multi-operation single setup and multi-operation multi-setup part–fixture assembly. Int J Adv Manuf Technol 68(5–8):1001–1014

    Article  Google Scholar 

  24. Mansuy M, Giordano M, Hernandez P (2011) A new calculation method for the worst case tolerance analysis and synthesis in stack-type assemblies. Comput Aided Des 43(9):1118–1125

    Article  Google Scholar 

  25. Khodaygan S, Movahhedy MR (2011) Tolerance analysis of assemblies with asymmetric tolerances by unified uncertainty–accumulation model based on fuzzy logic. Int J Adv Manuf Technol 53(5–8):777–788

    Article  Google Scholar 

  26. Liu S, Jin Q, Wang P, Xie R (2014) Closed-form solutions for multi-objective tolerance optimization. Int J Adv Manuf Technol 70(9–12):1859–1866

    Article  Google Scholar 

  27. Beaucaire P, Gayton N, Duc E, Lemaire M, Dantan J (2012) Statistical tolerance analysis of a hyperstatic mechanism, using system reliability methods. Comput Ind Eng 63(4):1118–1127

    Article  Google Scholar 

  28. Lee SH, Kwak BM (2006) Response surface augmented moment method for efficient reliability analysis. Struct Saf 28(3):261–272

    Article  Google Scholar 

  29. Qureshi AJ, Dantan J, Sabri V, Beaucaire P, Gayton N (2012) A statistical tolerance analysis approach for over-constrained mechanism based on optimization and Monte Carlo simulation. Comput Aided Des 44(2):132–142

    Article  Google Scholar 

  30. Wu F, Dantan J, Etienne A, Siadat A, Martin P (2009) Improved algorithm for tolerance allocation based on Monte Carlo simulation and discrete optimization. Comput Ind Eng 56(4):1402–1413

    Article  Google Scholar 

  31. Piepel G, Özler C, Şehirlioğlu A (2013) Optimum tolerance design using component-amount and mixture-amount experiments. Int J Adv Manuf Technol 68(9–12):2359–2369

    Article  Google Scholar 

  32. Chiang J, Tsai T, Lio YL, Lu W, Shi D (2015) An integrated approach for the optimization of tolerance design and quality cost. Comput Ind Eng 87:186–192

    Article  Google Scholar 

  33. Laifa M, Sai W, Hbaieb M (2014) Evaluation of machining process by integrating 3D manufacturing dispersions, functional constraints, and the concept of small displacement torsors. Int J Adv Manuf Technol 71(5–8):1327–1336

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Haiping Zhu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, H., Zhu, H., Zhou, X. et al. A new computer-aided tolerance analysis and optimization framework for assembling processes using DP-SDT theory. Int J Adv Manuf Technol 86, 1299–1310 (2016). https://doi.org/10.1007/s00170-015-8266-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-015-8266-9

Keywords

Navigation