Tolerance analysis of mechanical assemblies based on small displacement torsor and deviation propagation theories

Construction of the quality tolerances (Q-T) function is a key step in assembly tolerance analysis process. This paper presents a new feature-based tolerance analysis method for mechanical assemblies with GD&T, location tolerances, and fixture tolerances. In this method, tolerances and deviations are modeled by the small displacement torsor theory, the accumulation and propagation of deviations are expressed by the deviation propagation theory, and the quality requirements are solved by the deviations of specific features. Thus, the Q-T function relies on three sub-functions: tolerance deviation function, feature deviation function, and quality description function. Based on the functions, the paper presents an integrated solution for tolerance analysis. This method is competitive in three aspects: (1) the descriptions of the tolerances are close to reality, nonlinear relationships, and correlated tolerances can be analyzed as well; (2) the analysis process and acquired Q-T function is relatively concise to the other feature-based method; (3) the integrated assembly information is more intact. A case study is provided to illustrate the proposed method.

[1]  James N. Asante,et al.  A constraint-based tolerance analysis in a multi-operation single setup and multi-operation multi-setup part–fixture assembly , 2013 .

[2]  Caux Mickaël,et al.  3D ISO manufacturing specifications with vectorial representation of tolerance zones , 2012 .

[3]  Wenzhen Huang,et al.  Process capability surrogate model-based tolerance synthesis for multi-station manufacturing systems , 2009 .

[4]  Nicolas Gayton,et al.  Statistical tolerance analysis of a mechanism with gaps based on system reliability methods , 2013 .

[5]  Nicolas Gayton,et al.  A statistical tolerance analysis approach for over-constrained mechanism based on optimization and Monte Carlo simulation , 2012, Comput. Aided Des..

[6]  Jaime A. Camelio,et al.  Modeling Variation Propagation of Multi-Station Assembly Systems With Compliant Parts , 2003 .

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

[8]  Saeed Maghsoodloo,et al.  Optimization of mechanical assembly tolerances by incorporating Taguchi's quality loss function , 1995 .

[9]  Jean-Yves Dantan,et al.  Improved algorithm for tolerance allocation based on Monte Carlo simulation and discrete optimization , 2009, Comput. Ind. Eng..

[10]  Daniel E. Whitney,et al.  Modeling and controlling variation propagation in mechanical assemblies using state transition models , 1999, IEEE Trans. Robotics Autom..

[11]  S. Khodaygan,et al.  Tolerance analysis of assemblies with asymmetric tolerances by unified uncertainty–accumulation model based on fuzzy logic , 2011 .

[12]  Ping Yi,et al.  Tolerance synthesis by a new method for system reliability-based optimization , 2005 .

[13]  Jian Liu,et al.  State Space Modeling for 3-D Variation Propagation in Rigid-Body Multistage Assembly Processes , 2010, IEEE Transactions on Automation Science and Engineering.

[14]  M. Shunmugam,et al.  A unified framework for tolerance analysis of planar and spatial mechanisms using screw theory , 2013 .

[15]  Wayne W. Cai,et al.  A new tolerance modeling and analysis methodology through a two-step linearization with applications in automotive body assembly , 2008 .

[16]  F. González Contreras.  An improved tolerance charting technique using an analysis of setup capability , 2012 .

[17]  Nicolas Gayton,et al.  Statistical tolerance analysis of a hyperstatic mechanism, using system reliability methods , 2012, Comput. Ind. Eng..

[18]  Utpal Roy,et al.  Interpreting the semantics of GD&T specifications of a product for tolerance analysis , 2014, Comput. Aided Des..

[19]  Cenk Özler,et al.  Optimum tolerance design using component-amount and mixture-amount experiments , 2013 .

[20]  Nicolas Gayton,et al.  Statistical tolerance analysis of over-constrained mechanisms with gaps using system reliability methods , 2013, Comput. Aided Des..

[21]  J. W. Wittwer,et al.  The direct linearization method applied to position error in kinematic linkages , 2004 .

[22]  D. Ravindran,et al.  Multi-objective optimization for optimum tolerance synthesis with process and machine selection using a genetic algorithm , 2013 .