Article

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

(Impact Factor: 0.37). 02/2010; 9(4). DOI: 10.1115/1.3249575
Source: arXiv

ABSTRACT

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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ABSTRACT: The assembly stages enhancement is an important economic challenge for aeronautics industries. After the pre-assembly, gaps exist between components because of compliance and geometrical defects of components. Assembly requirements impose to fill these gaps, without installing internal stresses. A shimming step is currently necessary. It needs gaps measurement, which was identified as a problematic and expensive non-added value stage. Thus the trend is at gap prediction in order to remove gap measurement operations. This paper develops a numerical process allowing predicting gap before assembly step from component measurements. The main issue relates to the integration of measuring data into simulation process. Gap prediction stage is firstly located into the assembly process, in order to define constraints about gap representation. Then gap prediction process principle is detailed, highlighting measuring data integration. This method was subjected to an experimental validation. The entire process was carried out, from component measurement to gap prediction. Several comparisons were achieved to characterize the predicted gap.
12/2015; 27. DOI:10.1016/j.procir.2015.04.050
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• "In addition, it does not allow to simulate different assembly sequences as assembly constraints among mating features are modeled through "linearized equivalent" joints, not allowing to model non-linear constraint conditions (see contact constraints). A contact search algorithm was proposed in [15] to simulate 2D and 3D assembly operations accounting shape errors, modeled by natural mode shapes. In [16] a framework for a constrained optimization method was described to simultaneously solve geometric 2D constraints. "
##### Article: A Sequential Constraint Solver to Simulate Assembling Operations for Tolerance Analysis
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ABSTRACT: In the variational modeling of assemblies it is important to define the location of a part both in absolute terms and with respect to the position/orientation of other assembled parts. The present paper proposes a programming optimization approach to solve this problem. The algorithm, by using the heuristic Nelder-Mead technique - combined with a penalty function - simulates and solves sequential assembly strategies to find the optimal geometric configuration of a rigid part with variational features satisfying all the assembly constraints in the given sequence. The algorithm best aligns mating features avoiding, at the same time, feature-to-feature interferences, and automatically calculating the amount of movement the part being assembled must obey to satisfy assembly constraints, at that state of the assembly process. Thus, different assembly sequences can be simulated also including variational features.
12/2013; 10:169-177. DOI:10.1016/j.procir.2013.08.028
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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. "
##### Article: On the role of form defects in assemblies subject to local deformations and mechanical loads
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ABSTRACT: Tolerancing activity is usually based on the traditional assumptions that surfaces have no form defects and are rigid under external loads. These assumptions tend to simplify the tolerance analysis of mechanical assemblies and hence the allocation of geometrical specifications. The present paper proposes an original procedure to systematically analyze and quantify the assembly of parts with form and position defects and deformable contact surfaces. Based on this procedure, stochastic simulations are performed by modifying the ratio between the position defects and form defects of surfaces. Even if the form defects are limited, they can lead to a non-compliant assembly. Clearly, the engineer's traditional approach, where form defects are assumed to have no influence, is generally not appropriate if we are to ensure that the expected performance is to be achieved on assembly.
International Journal of Advanced Manufacturing Technology 04/2012; 65(9-12):1-10. DOI:10.1007/s00170-012-4298-6 · 1.46 Impact Factor