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Tolerance analysis of mechanical assemblies based on modal interval and small degrees of freedom (MI-SDOF) concepts

Abstract

Tolerance analysis is a key analytical tool for estimation of accumulating effects of the individual part tolerances on the design specifications of a mechanical assembly. This paper presents a new feature-based approach to tolerance analysis for mechanical assemblies with geometrical and dimensional tolerances. In this approach, geometrical and dimensional tolerances are expressed by small degrees of freedom (SDOF) of geometric entities (faces, feature axes, edges, and features of size) that are described by tolerance zones. The uncertainty of dimensions and geometrical form of features due to tolerances is mathematically described using modal interval arithmetic. The two concepts of modal interval analysis and SDOF are combined to describe the tolerance specifications. The algorithm is presented which explains the steps and the procedure of tolerance analysis. The proposed method is compatible with the current GD&T standards and can incorporate GD&T concepts such as various material modifiers (maximum material condition, least material condition, and regardless of feature size), envelope requirement, and bonus tolerances. This method can take into account multidimensional effects due to geometrical tolerances in tolerance analysis. The application of the proposed method is illustrated through presenting an example problem and comparing results with tolerance charting method.

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References

  1. 1.

    Pasupathy TMK, Morse EP, Wilhelm RG (2003) A survey of mathematical methods for the construction of geometric tolerance zones. Trans ASME J Comput Inf Sci Eng 3(2):64–75

    Article  Google Scholar 

  2. 2.

    Turner JU, Wozny MJ (1987) Tolerances in computer-aided geometric design. Visual Comput 3:214–226

    Article  Google Scholar 

  3. 3.

    Movahedy MR, Khodaygan S (2007) Tolerance analysis of mechanical assemblies with asymmetric tolerances. Trans SAE J Materials Manuf 116:44–52

    Google Scholar 

  4. 4.

    Creveling CM (1997) Tolerance design: a handbook for developing optimal specifications. Addison-Wesley, Boston

    Google Scholar 

  5. 5.

    Ranyak PS, Fridshal R (1988) Features for tolerancing a solid model. Proc ASME Comput Eng 1:262–274

    Google Scholar 

  6. 6.

    Roy U, Liu CR (1988) Feature-based representational scheme of a solid modeler for providing dimensioning and tolerancing information. Robot Com-Int Manuf 4(3–4):335–345

    Article  Google Scholar 

  7. 7.

    Maeda T, Tokuoka N (1995) Toleranced feature modeling by constraint of degree of freedom for assignment of tolerance. In: Proceedings of 4th CIRP Design Seminar, Tokyo, Japan, 5–6 April, pp 89–103

  8. 8.

    Requicha AAG (1983) Toward a theory of geometric tolerancing. Int J Robot Res 2(4):45–59

    Article  Google Scholar 

  9. 9.

    Jayaraman R, Srinivasan V (1989) Geometric tolerancing: I. Virtual boundary requirements. IBM J Res Developm 33(2):90–104

    MATH  Article  MathSciNet  Google Scholar 

  10. 10.

    Turner JU, Subramaniam S, Gupta S (1992) Constraint representation and reduction in assembly modeling and analysis. IEEE T Robot Automt 8(6):741–750

    Article  Google Scholar 

  11. 11.

    Davidson JK, Mujezinović A, Shah JJ (2002) A new mathematical model for geometric tolerances as applied to round faces. ASME J Mech Des 124:609–621

    Article  Google Scholar 

  12. 12.

    Chase KW, Gao J, Magleby SP (1995) General 2-D tolerance analysis of mechanical assemblies with small kinematic adjustments. J Des Manuf 5(4):263–274

    Article  Google Scholar 

  13. 13.

    Chase KW, Magleby SP, Gao J, Sorensen CD (1996) Including geometric feature variations in tolerance analysis of mechanical assemblies. IIE Trans 28(10):795–807

    Google Scholar 

  14. 14.

    Gao J, Chase KW, Magleby SP (1998) General 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments. IIE Transactions 30(4):367–377

    Google Scholar 

  15. 15.

    Gaunet D (1993) Vectorial tolerancing model. 3rd CIRP international seminar on computer aided tolerancing, 27–28 April, pp 25–50

  16. 16.

    Bernstein N, Preiss K (1989) Representation of tolerance information in solid models. Proceeding of 15th ASME design technical conference, Montreal, Canada, 17–21 September, pp 37–48

  17. 17.

    Hunt KH (1978) Kinematic geometry of mechanisms. Claredan, Oxford

    MATH  Google Scholar 

  18. 18.

    Desrochers A, Clement A (1994) Dimensioning and tolerancing assistance model for CAD/CAM systems. Int J Adv Manufact Technol 9:352–361

    Article  Google Scholar 

  19. 19.

    Laperriére L, Lafond P (1998) Identification of dispersions affecting pre-defined functional requirements of mechanical assemblies. Proceedings of 2nd IDMME conference, France, 27–29 May, pp 721–728

  20. 20.

    Desrochers A (1999) Modeling three dimensional tolerance zones using screw parameters. CD-ROM Proceedings of ASME DETC: 25 the design automation conference, Las-Vegas, paper #DETC99/DAC-8587, 12–15 September, pp 1–9

  21. 21.

    Teissandier D, Couétard Y, Gérard A (1999) A computer aided tolerancing model: proportioned assembly clearance volume. Comput-Aided Des 3:805–817

    Article  Google Scholar 

  22. 22.

    Bourdet P, Clément A (1976) Controlling a complex surface with a 3 axis measuring machine. Ann CIRP 25:359–364

    Google Scholar 

  23. 23.

    Desrochers A, Ghie W, Laperriére L (2003) Application of a unified Jacobian—torsor model for tolerance analysis. ASME J Comput Inf Sci Eng 3(1):2–14

    Article  Google Scholar 

  24. 24.

    Wang Y (2006) Semantic tolerance modeling. ASME international design engineering technical conferences & the computer and information in engineering conference, Philadelphia, Pennsylvania, paper no. DETC2006-99609, 10–13 September, pp 1–13

  25. 25.

    ElMaraghy W, Bourdet P, ElMaraghy H (2005) Small displacement torsor theory and various compensation schemes for complex form realization. 4th international conference in integrated design and production, Casablanca, Morocco, 9–11 November, pp 1–17

  26. 26.

    Moore RE (1966) Interval analysis. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  27. 27.

    Moore RE, Kearfott RB, Cloud MJ (2009) Introduction to interval analysis. Siam, Philadelphia

    MATH  Google Scholar 

  28. 28.

    Gardenes E, Sainz MA, Jorba L, Calm R, Estela R, Mielgo H, Trepat A (2001) Modal intervals. Reliab Comput 7(2):77–111

    MATH  Article  MathSciNet  Google Scholar 

  29. 29.

    Popova ED (2001) Multiplication distributivity of proper and improper intervals. Reliab Comput 7(2):129–140

    MATH  Article  MathSciNet  Google Scholar 

  30. 30.

    Wang Y (2008) Semantic tolerance modeling based on modal interval analysis. Proceeding of the international workshop on reliable engineering computing REC’08, Savannah, Georgia, 20–22 February, pp 46–59

  31. 31.

    Gross J, Yellen J (2004) Handbook of graph theory. Discrete mathematics and its applications. CRC, New York

    Google Scholar 

  32. 32.

    Standard ASME (2009) Dimensioning and tolerancing. Revision of ASME Y14.5M-1994. ASME, USA

  33. 33.

    Henzold G (2006) Geometrical dimensioning and tolerancing for design, manufacturing and inspection: a handbook for geometrical product specification using ISO and ASME standards, 2nd edn. Elsevier, UK

    Google Scholar 

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Correspondence to M. R. Movahhedy.

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Khodaygan, S., Movahhedy, M.R. & Saadat Fomani, M. Tolerance analysis of mechanical assemblies based on modal interval and small degrees of freedom (MI-SDOF) concepts. Int J Adv Manuf Technol 50, 1041–1061 (2010). https://doi.org/10.1007/s00170-010-2568-8

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Keywords

  • Tolerance analysis
  • Tolerance zone
  • Modal interval arithmetic
  • Small degrees of freedom