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Tolerance analysis of overconstrained and flexible assemblies by polytopes and finite element computations: application to a flange

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Abstract

In industrial contexts, overconstrained assemblies are often used to ensure sufficient stiffness and accuracy of assembly. Such architectures are quite usual, however, analysis and synthesis of the tolerance are not easy to define and quantify. In these cases, the compliance of the assembly is not automatic and deformations may often occur, requiring a particular and difficult analysis of the assembly from scientific and computing points of view.The present work addresses such overconstrained mechanisms through a general and a sequential approach. Based on this, it is possible to determine the final assembly condition (with or without interference) as a function of part defects. First, the assembly procedure is performed based on polytope computations, assuming a rigid part behavior. From this, a stochastic simulation is performed and some non-compliant assemblies (assemblies with interferences) are identified. For these assemblies, the rigid behavior of parts is then overcome by means of finite element simulations and a typical procedure is set up to introduce part defects. We then deduce whether the assembly can be made from the load needed to assemble the parts. This procedure is applied to a flange composed of five pin/hole pairs, as this is a highly overconstrained mechanism.

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Abbreviations

\(\mathbf {t_{M-1,i/2,i}}\) :

Translation vector of surface i of part 1 in relation to surface i of part 2 at point M. If \(i=0\), we are considering the translation of the nominal geometry of part 1 in relation to the nominal geometry of part 2 at point M

\(\mathbf {r_{1,i/2,i}}\) :

Rotation vector of surface i of part 1 in relation to surface i of part 2. If \(i=0\), we are considering the rotation of the nominal geometry of part 1 in relation to the nominal geometry of part 2

\(\mathbf {e_{M-1,i/1,0}}\) :

Location defect vector of surface i of part 1 in relation to its nominal geometry at point M

\(\mathbf {e_{M-2,i/2,0}}\) :

Location defect vector of surface i of part 2 in relation to its nominal geometry at point M

\(D_{n}\), \(D_{1,i}\) and \(D_{2,i}\) :

The diameter of the nominal surface, the diameters of surface i of part 1 and surface i of part 2 respectively

\(\overline{H}_{i,j}^-\) :

Half-space of the contact constraint derived from the jth discretization point between surface i of part 1 and surface i of part 2,

\(P_{i}\) :

Contact polytope of surface i of part 1 in relation to surface i of part 2

\(P_{R}\) :

Resulting contact polytope of part 1 in relation to part 2

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Authors and Affiliations

  1. Univ. Bordeaux, I2M, UMR 5295 CNRS, Esplanade des Arts et Métiers, 33405, Talence, France

    Doriane Gouyou, Yann Ledoux, Denis Teissandier & Vincent Delos

Authors
  1. Doriane Gouyou
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  2. Yann Ledoux
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  3. Denis Teissandier
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  4. Vincent Delos
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Correspondence to Doriane Gouyou.

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Gouyou, D., Ledoux, Y., Teissandier, D. et al. Tolerance analysis of overconstrained and flexible assemblies by polytopes and finite element computations: application to a flange. Res Eng Design 29, 55–66 (2018). https://doi.org/10.1007/s00163-017-0256-5

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