Modeling of 2D and 3D Assemblies Taking Into Account Form Errors of Plane Surfaces

Journal of Computing and Information Science in Engineering (Impact Factor: 0.37). 02/2010; 9(4). DOI: 10.1115/1.3249575
Source: arXiv


The tolerancing process links the virtual and the real worlds. From the former, tolerances define a variational geometrical language (geometric parameters). From the latter, there are values limiting those parameters. The beginning of a tolerancing process is in this duality. As high precision assemblies cannot be analyzed with the assumption that form errors are negligible, we propose to apply this process to assemblies with form errors through a new way of allowing to parameterize forms and solve their assemblies. The assembly process is calculated through a method of allowing to solve the 3D assemblies of pairs of surfaces having form errors using a static equilibrium. We have built a geometrical model based on the modal shapes of the ideal surface. We compute for the completely deterministic contact points between this pair of shapes according to a given assembly process. The solution gives an accurate evaluation of the assembly performance. Then we compare the results with or without taking into account the form errors. When we analyze a batch of assemblies, the problem is to compute for the nonconformity rate of a pilot production according to the functional requirements. We input probable errors of surfaces (position, orientation, and form) in our calculus and we evaluate the quality of the results compared with the functional requirements. The pilot production then can or cannot be validated.

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Available from: Maurice Pillet
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    • "Likewise modal representation used by Samper [8] is a way to represent geometry with defects. This is a discrete representation, based on natural modes of an ideal surface. "
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    • "The main advantages of these models lie in the fact that they are tractable according to the required time to estimate local deformations due to external loads. More recent work dealing with local form defects and tolerance analysis has been addressed by Samper in [11] where an original concept of surface-sum defects is developed and used to simplify the consideration of surfaces with form defects. Finally, in preliminary studies by Le [12] on a simple planar joint, the influence of form defects is determined experimentally both from measurements of surfaces in contact and the relative mobility between one part and another. "
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