Abstract
The automation of tolerance analysis is the ambitious goal of the researcher. In order to achieve this aim, the homogeneous coordinate transformation is a usual method for the position calculation of geometric features and parts in the assembly tolerance analysis method. The hierarchy definition and the automatic creation of the coordinate system are the key work for the automation of tolerance analysis. In this paper, the position calculation equations of the geometric feature in assembly model are described firstly, then the error propagation relation graph for geometric features in the part model is analyzed based on the datum–target mechanism of geometric tolerance. The assembly errors propagation graph of the part in the machine model is described based on the assembly relation and assembly precedence. The controlling points variation model (CPVM) of a geometric feature is used to generate and represent the position of the substitute geometry of the geometric feature, and the position parameters of substitute geometry are generated using Monte Carlo simulations. Based on the CPVM model and datum–target mechanism, the hierarchy of the coordinate system for a geometric feature is defined on the part level. Based on the assembly relations and the real part model, the assembly coordinate system between the locating part and the assembling part is established. According to these two errors propagation graphs, the homogeneous coordinate transformation matrix between the related coordinate systems is generated automatically. Finally, a case study is provided to illustrate the proposed method.
Similar content being viewed by others
References
Standard ASME (2009) Dimensioning and tolerancing—engineering drawing and related documentation practices, ASME Y14.5M-2009. ASME, USA
Chiabert P, Lombardi F, Orlando M (1998) Benefits of geometric dimensioning and tolerancing. J Mater Process Technol 78(1):29–35
Kandikjan T, Shah JJ, Davidson JK (2001) A mechanism for validating dimensioning and tolerancing schemes in CAD systems. Comput Aided Des 33(10):721–737
Gou JB, Chu YX, Xiong ZH, Li ZX (2000) A geometric method for computation of datum reference frames. IEEE Trans Robot Autom 16(6):797–806
Wu Y, Gu Q (2016) The composition principle of the datum reference frame. Procedia CIRP 43:226–231
Wu Y, Gu Q (2016) An establishing method of the datum feature simulator based on CPVM model, proceedings of ASME IDETC/CIE 2016, Charlotte, North Carolina, USA, paper # IDETC2016-59432, August 21-24, 2016
Hong YS, Chang TC (2002) A comprehensive review of tolerancing research. Int J Prod Res 40(11):2425–2459
Desrochers A, Rivière A (1997) A matrix approach to the representation of tolerance zones and clearances. Int J Adv Manuf Technol 13(9):630–636
Salomons OW, Haalboom FJ, Poerink HJJ, Van Slooten F, Van Houten FJAM, Kals HJJ (1996) A computer aided tolerancing tool II: tolerance analysis. Comput Ind 31(2):175–186
Whitney DE, Gilbert OL, Jastrzebski M (1994) Representation of geometric variations using matrix transforms for statistical tolerance analysis in assemblies. Res Eng Des 6(4):191–210
Cardew-Hall MJ, Labans T, West G, Dench P (1993) A method of representing dimensions and tolerances on solid based freeform surfaces. Robot Comput Integr Manuf 10(3):223–234
Laperrière L, Elmaraghy HA (2000) Tolerance analysis and synthesis using Jacobian transforms. CIRP Ann Manuf Technol 49(1):359–362
Ghie W, Laperrière L, Desrochers A (2003) A unified Jacobian-torsor model for analysis in computer aided tolerancing. Recent advances in integrated design and manufacturing in mechanical engineering. Springer, Netherlands, pp 63–72
Franciosa P, Gerbino S, Patalano S (2010) Variational modeling and assembly constraints in tolerance analysis of rigid part assemblies: planar and cylindrical features. Int J Adv Manuf Technol 49(1):239–251
Louhichi B, Tlija M, Benamara A, Tahan A (2015) An algorithm for CAD tolerancing integration: generation of assembly configurations according to dimensional and geometrical tolerances. Comput Aided Des 62:259–274
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):1041–1061
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
Liu Y, Wu Z, Yang J (2001) Mathematical model of size tolerance for plane based on mathematical definition. Chin J Mech Eng 37(9):12–17 (in Chinese)
Cai M, Yang J, Wu Z (2003) Mathematical model of form tolerance for cylindrical feature based on mathematical definition. Chin J Mech Eng 39(12):86–90 (in Chinese)
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):89–99
Davidson JK, Mujezinovi A, Shah JJ (2002) A new mathematical model for geometric tolerances as applied to round faces. J Mech Des 124(4):609–622
Wu Y, Zhang G (2013) Tolerance mathematical model based on the variation of control points of geometric element. Chin J Mech Eng 49(5):138–145 (in Chinese)
Mejbri H, Anselmetti B, Mawussi K (2005) Functional tolerancing of complex mechanisms: identification and specification of key parts. Comput Ind Eng 49:241–265
Franciosa P, Patalano S, Riviere A (2010) 3d tolerance specification: an approach for the analysis of the global consistency based on graphs. Int J Interact Des Manuf 4(1):1–10
Clément A, Rivière A, Serré P, Valade C (1998) The TTRSs: 13 constraints for dimensioning and tolerancing. Geometric design tolerancing: theories, standards and applications. Springer, USA
Giordano M, Pairel E, Hernandez P (2007) Complex mechanical structure tolerancing by means of hyper-graphs. Models for computer aided tolerancing in design and manufacturing. Springer, Netherlands
Mantripragada R, Whitney DE (1998) The datum flow chain: a systematic approach to assembly design and modeling. Res Eng Des 10(3):150–165
Whitney DE (2004) Mechanical assemblies: their design, manufacture, and role in product development. Oxford University Press, Oxford
Whitney DE, Mantripragada R, Adams JD, Rhee SJ (1999) Designing assemblies. Res Eng Des 11(4):229–253
Clément A, Riviére A, Serré P (1999) Global consistency of dimensioning and tolerancing. Global Consistency Tolerances, pp 1–26
Prisco U, Giorleo G (2002) Overview of current cat systems. Integrated computer aided. Engineering 9(4):373–387
Shen Z (2003) Tolerance analysis with EDS/VisVSA. J Comput Inform Sci Eng 3(1):95–99
Schleich B, Wartzack S (2016) A quantitative comparison of tolerance analysis approaches for rigid mechanical assemblies. Procedia CIRP 43:172–177
Wu Y (2015) Assembly tolerance analysis method based on the real machine model with three datum planes location. Procedia CIRP 27:47–52
Acknowledgements
The authors gratefully acknowledge the supports of the National Natural Science Foundation of China under grants no. 51675147 and 51175132.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wu, Y., Chen, C. An automatic generation method of the coordinate system for automatic assembly tolerance analysis. Int J Adv Manuf Technol 95, 889–903 (2018). https://doi.org/10.1007/s00170-017-1241-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-017-1241-x