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

02/2010; 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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    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.
    Procedia CIRP. 01/2013; 10:169-177.
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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 01/2012; · 1.78 Impact Factor
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    ABSTRACT: In order to improve digital mock-up, a tolerancing phase should be integrated in the geometric models. However, in CAD software, tolerances are represented by annotations, which are neglected as well as the tolerance impact. Thus, the system malfunction is generated. For these reasons, in this paper a tolerancing phase is integrated in the numerical model to form a realistic model, where worst case config-urations of assemblies are determined from the tolerances assigned to the nominal model. The proposed model incorporates tolerances on CAD models in the case of planar face, cylindrical face and planar face with non quadratic loop. In addition, the model ability to respect the maximum material condition (MMC) and the requirement of datum priority order in the CAD models is shown. Finally, functional requirement of a linear guide mechanism is inspected by using the proposed model.
    01/2013; 14:191-206.

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