An automatic generation method of the coordinate system for automatic assembly tolerance analysis

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.

[1]  Yuguang Wu,et al.  The Composition Principle of the Datum Reference Frame , 2016 .

[2]  Pasquale Franciosa,et al.  3D tolerance specification: an approach for the analysis of the global consistency based on graphs , 2010 .

[3]  M. J. Cardew-Hall,et al.  A method of representing dimensions and tolerances on solid based freeform surfaces , 1993 .

[4]  Paolo Chiabert,et al.  Benefits of Geometric Dimensioning and Tolerancing , 1998 .

[5]  Philippe Serré,et al.  Global Consistency of Dimensioning and Tolerancing , 1999 .

[6]  W. Ghie,et al.  A Unified Jacobian-Torsor Model for Analysis in Computer Aided Tolerancing , 2003 .

[7]  Yuguang Wu.  Tolerance Mathematical Model Based on the Variation of Control Points of Geometric Element , 2013 .

[8]  Pasquale Franciosa,et al.  Variational modeling and assembly constraints in tolerance analysis of rigid part assemblies: planar and cylindrical features , 2010 .

[9]  Yuguang Wu.  Assembly Tolerance Analysis Method Based on the Real Machine Model with Three Datum Planes Location , 2015 .

[10]  Zexiang Li,et al.  A geometric method for computation of datum reference frames , 2000, IEEE Trans. Robotics Autom..

[11]  S. Khodaygan,et al.  Tolerance analysis of mechanical assemblies based on modal interval and small degrees of freedom (MI-SDOF) concepts , 2010 .

[12]  Peigen Li,et al.  Tolerance analysis of mechanical assemblies based on small displacement torsor and deviation propagation theories , 2014 .

[13]  Daniel E. Whitney,et al.  Representation of geometric variations using matrix transforms for statistical tolerance analysis in assemblies , 1994 .

[14]  Yusheng Liu.  MATHEMATICAL MODEL OF SIZE TOLERANCE FOR PLANE BASED ON MATHEMATICAL DEFINITION , 2001 .

[15]  O. W. Salomons,et al.  A computer aided tolerancing tool II: tolerance analysis , 1996 .

[16]  Joseph K. Davidson,et al.  A mechanism for validating dimensioning and tolerancing schemes in CAD systems , 2001, Comput. Aided Des..

[17]  B. Anselmetti,et al.  Functional tolerancing of complex mechanisms: Identification and specification of key parts , 2005, Comput. Ind. Eng..

[18]  Min Cai.  MATHEMATICAL MODEL OF FORM TOLERANCE FOR CYLINDRICAL FEATURE BASED ON MATHEMATICAL DEFINITION , 2003 .

[19]  Y. S. Hong,et al.  A comprehensive review of tolerancing research , 2002 .

[20]  Alain Riviere,et al.  A matrix approach to the representation of tolerance zones and clearances , 1997 .

[21]  Joseph K. Davidson,et al.  A New Mathematical Model for Geometric Tolerances as Applied to Round Faces , 2002 .

[22]  Hoda A. ElMaraghy,et al.  Tolerance Analysis and Synthesis Using Jacobian Transforms , 2000 .

[23]  Daniel E. Whitney.  Mechanical Assemblies: Their Design, Manufacture, and Role in Product Development [Book Review] , 2005, IEEE Robotics & Automation Magazine.

[24]  Umberto Prisco,et al.  Overview of current CAT systems , 2002, Integr. Comput. Aided Eng..

[25]  Zhengshu Shen.  Tolerance Analysis with EDS/VisVSA , 2003, J. Comput. Inf. Sci. Eng..

[26]  Yuguang Wu,et al.  An Establishing Method of the Datum Feature Simulator Based on CPVM Model , 2016 .

[27]  Sandro Wartzack,et al.  A Quantitative Comparison of Tolerance Analysis Approaches for Rigid Mechanical Assemblies , 2016 .

[28]  Daniel E. Whitney,et al.  The Datum Flow Chain: A systematic approach to assembly design and modeling , 1998 .

[29]  Zijian Liu.  SURVEY OF RESEARCH ON AIRBAG FOR OCCUPANT INJURY PREVENTION FROM VEHICLE IMPACTS , 2001 .

[30]  Abdelmajid Benamara,et al.  An algorithm for CAD tolerancing integration: Generation of assembly configurations according to dimensional and geometrical tolerances , 2015, Comput. Aided Des..