Impact of a behavior model linearization strategy on the tolerance analysis of over-constrained mechanisms

All manufactured products have geometrical variations which may impact their functional behavior. Tolerance analysis aims at analyzing the influence of these variations on product behavior, the goal being to evaluate the quality level of the product during its design stage. Analysis methods must verify whether specified tolerances enable the assembly and functional requirements. This paper first focuses on a literature overview of tolerance analysis methods which need to deal with a linearized model of the mechanical behavior. Secondly, the paper shows that the linearization impacts the computed quality level and thus may mislead the conclusion about the analysis. Different linearization strategies are considered, it is shown on an over-constrained mechanism in 3D that the strategy must be carefully chosen in order to not over-estimate the quality level. Finally, combining several strategies allows to define a confidence interval containing the true quality level. A tolerance analysis approaches overview is proposed.A linearization procedure of the behavior model is required for both approaches.Some linearization strategies provide conservative probability of failure results.A confidence interval is obtained using two different linearization strategies.The order of magnitude of the probability has an effect on the convergence speed.

[1]  Joseph K. Davidson,et al.  Effects of Size, Orientation, and Form Tolerances on the Frequency Distributions of Clearance Between Two Planar Faces , 2011, J. Comput. Inf. Sci. Eng..

[2]  Max Giordano,et al.  A Generic Method for the Worst Case and Statistical Tridimensional Tolerancing Analysis , 2013 .

[3]  Spencer P. Magleby,et al.  Tolerance Analysis of 2-D and 3-D Mechanical Assemblies with Small Kinematic Adjustments , 1997 .

[4]  Edward P. Morse.  Statistical Analysis of Assemblies Having Dependent Fitting Conditions , 2004 .

[5]  Alex Ballu,et al.  Geometrical reliability of overconstrained mechanisms with gaps , 2008 .

[6]  A. Desrochers.  Geometrical Variations Management in a Multi-Disciplinary Environment with the Jacobian-Torsor Model , 2007 .

[7]  J. Shah,et al.  Tolerance-Maps Applied to the Straightness and Orientation of an Axis , 2007 .

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

[9]  Serge Samper,et al.  Tolerance Analysis and Synthesis by Means of Deviation Domains, Axi-Symmetric Cases , 2007 .

[10]  Shiyu Zhou,et al.  Kinematic Analysis of Dimensional Variation Propagation for Multistage Machining Processes With General Fixture Layouts , 2007, IEEE Transactions on Automation Science and Engineering.

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

[12]  Jean-Yves Dantan,et al.  Worst-case and statistical tolerance analysis based on quantified constraint satisfaction problems and Monte Carlo simulation , 2009, Comput. Aided Des..

[13]  Spencer P. Magleby,et al.  Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments , 1998 .

[14]  Zhihua Zou,et al.  Applications of the GapSpace Model for Multidimensional Mechanical Assemblies , 2003, J. Comput. Inf. Sci. Eng..

[15]  Max Giordano,et al.  A new calculation method for the worst case tolerance analysis and synthesis in stack-type assemblies , 2011, Comput. Aided Des..

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

[17]  Olivier Legoff,et al.  Manufacturing errors modelling: Two three-dimensional approaches , 2004 .

[18]  Joseph K. Davidson.  Models for Computer Aided Tolerancing in Design and Manufacturing , 2006 .

[19]  Joshua U. Turner,et al.  Review of statistical approaches to tolerance analysis , 1995, Comput. Aided Des..

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

[21]  Nicolas Gayton,et al.  Mathematical issues in mechanical tolerance analysis , 2012 .

[22]  Joseph K. Davidson,et al.  Modeling of Geometric Variations for Line-Profiles , 2012, J. Comput. Inf. Sci. Eng..

[23]  Gaurav Ameta,et al.  Comparison of Spatial Math Models for Tolerance Analysis: Tolerance-Maps, Deviation Domain, and TTRS , 2011, J. Comput. Inf. Sci. Eng..

[24]  Pierre-Antoine Adragna,et al.  Rigid and Elastic Precision Domains of Ball Bearings , 2012, J. Comput. Inf. Sci. Eng..