03 Nov 2014 |
article de recherche |
Technologies de l'information et des communications
Modélisation d’un assemblage réaliste pour les tolérances CAD
Dans les modèles de CAO (CAD), les tolérances sont représentés comme des annotations. Dans les faits, le modèle numérique est utilisée dans la configuration nominale. Les valeurs des tolérances dimensionnelles et géométriques n’ont pas d’impact sur les modèles de CAO ou les résultats de simulation numérique. Les recherches démontrent que l’accumulation des tolérances a un impact sur les résultats d’analyse des éléments finis (EF)  et le processus d’assemblage , comme cela est aussi le cas avec l’assemblage de tôles . Ainsi, une modélisation réaliste de l’ensemble, qui tient compte des tolérances géométriques et dimensionnelles sur des modèles de CAO, est un réel besoin industriel. Dans cet article, une méthode de modélisation réaliste d’assemblage (assemblage variationnel) est présentée. Cette nouvelle méthode permet l’analyse de la tolérance tout en tenant compte de planification du processus d’assemblage, les types de contact et le mouvement de l’assemblage.
Dans nos travaux précédents, une méthode tenant compte des tolérances sur les modèles CAO a été établie . Ce modèle est basé sur l’hypothèse que nous obtiendront les cas d’assemblage les plus défavorables en utilisant des composants dans des cas de configurations les plus défavorables. Les configurations des pires cas de composants sont calculées en utilisant le pire cas de tolérancement. Le caractère aléatoire d’obtention des pièces mécaniques et la complexité des assemblages jettent un doute sur cette hypothèse. Ainsi, dans ce travail, l’hypothèse d’obtenir les pires cas d’assemblage avec des composants aléatoires est adoptée. De nouveaux algorithmes pour calculer les possibles configurations de composants et redéfinir l’ensemble des contraintes de contact seront établis.
La suite de ce RPI sera présentée dans sa langue originale de rédaction.
In this paper, the components with dimensional and geometrical tolerances are modeled in CAD models by using two algorithms to respect the principle of independence (ISO 8015):
- The first one leads to obtaining a component with dimensional defects. This algorithm is founded on a numerical perturbation method which determines the relationships between dimensions. The tolerance interval is discretized to define the realistic configuration of components;
- The second algorithm allows the determination of components with geometrical tolerances. The tolerance zone is discretized according to the parameters specified by Small Displacement Torsors (SDT) . The face displacements are performed to obtain components with geometrical defects.
In nominal assembly, the ideal components are linked by mating constraints. The replacement of those components by the realistic ones requires the updating of mating constraints. A tolerance analysis is performed by using the proposed method and showed through the crankshaft system (fig. 1). The proposed analysis method takes into account not only part deviations but also assembly process planning and contact types between parts. In addition, the impact of the tolerance stack-up on the functional requirement in a dynamic environment can be determined.
Literature review synthesis
The literature review relates two aspects. The first aspect consists of tolerance analysis and synthesis [5, 7 -24]. The second aspect consists of the variational geometry and the redefinition of assembly mating constraints [30, 33-38].
In most of the references cited, the tolerance analysis and syntheses are based on the spatial math representations (polyhedral and Technical Manual Application System (T-Maps)) or mathematical model. The solutions for the tolerance analysis and syntheses, which are presented in mathematical form (equations), are modeled in a geometrical solution. The spatial math models (polyhedral and T-Maps) are difficult tools to use in industry as this model does not predict the impact of dimensional and geometrical deviation, permitted by tolerances, on assembly deformations. The proposed model in this paper is considered a tool for visualization and tolerance impact analysis (interference detection) in assembly simulation cases. The second aspect addressed in the literature appears to be closest to this work [30, 33-38]. Indeed, we can learn a great deal from the methods used in this second aspect. The later can be applied to solve some issues of the problem as contemplated: The parametric variational features is used to generate realistic assembly.
The approach presented in this paper is an extension of these works. The realistic modeling of components allows us to take into account the tolerances in CAD models. The redefinition of mating constraints leads us to consider the relationships between realistic components and the assembly process planning. The realistic assembly modeling in a CAD environment allows for direct use of computation applications which already exist in CAD software as assembly motion simulations.
Modeling of a realistic component with dimensional defects
In CAD model, obtaining realistic configurations allowed by dimensional tolerances requires modifications of the component dimensions. CAD software defines two dimension types. The driving dimensions are used to build the CAD model. The driven dimensions are controlled by driving ones. In fact, the driven dimension values are deduced from driving dimension ones. The toleranced dimension can correspond to a driving dimension: the driven dimension is controlled by one driving dimension in Fig. 2(a). Therefore, the modification of the driving dimension value ( 40 mm ) allows us to directly change the driven dimension’s value. In the other case, obtaining a target value of the driven dimension requires the determination and the modification of the corresponding values for each driving dimensions (25 mm,35 mm and 100 mm in Fig. 2 (b)).
In the general case, the designer defines the component model by using driving dimensions. In the following steps, he assigns tolerances to the driven dimensions. The determination of the components with dimensional defects requires the identification of the relationships between thedriving and driven dimensions.
The components with dimensional defects are obtained through a numerical perturbation method. In fact, the influence coefficients between driven and driving dimensions are identified. Therefore the values of the new driving dimensions are computed according to those coefficients and tolerance values. After the allocation of those new dimensions to the CAD model, the components with dimensional defects were deduced.
Modeling of a realistic component with geometrical defects
An algorithm to determine all components with geometrical defects is developed. Those realistic configurations are obtained by modeling the geometrical tolerances by the displacements of the corresponding faces. This approach depends on the shape of the tolerance zone, the toleranced feature type and the tolerance type. The overview table in Tab. 1 comprises the sub-algorithms used to model components with geometrical defects.
Tab. 1. Sub-algorithms used to model components with geometrical defects
The deviation between the nominal and the realistic feature is determined by the Small Displacement Torsors (SDT) tool. Then, the assumption of neglecting the form defects relative to the position and orientation defects is used. The deviation torsor, which is based on a SDT tool, defines the Degrees of Freedom (DoFs) of the toleranced feature. In the proposed model, the deviation parameters between the nominal and realistic features are determined by an analogy to the parameters defined by the SDT. Sub-algorithms are developed to obtain realistic configurations of a planar face or a cylindrical axis subjected to a positional and/or orientation tolerance, as the case of planar face subjected to a positional tolerance (Fig. 3). In a CAD model, the realistic part configurations are generated with face displacements: Rotation and/or translation using the parameters deduced from the discretization. In the proposed methodology, the original shape of the feature is conserved as the planar faces remain planar. The algorithm starts by identifying toleranced features, tolerance types and datum references, which are specified by ISO standards.
Redefinition of the assembly mating constraints
In the realistic assembly, these mating constraints must be redefined. These realistic mating constraints are obtained by modifications of the relations between Minimum Geometrical Reference Elements (MGREs). This method depends on the Objective Function of the Assembly (OFA) specified by the designer. In CAD software, the OFA is automatically deduced from the nominal model:
- The mating constraint order, specified in the feature manager design tree of the software, defines the mounting order of the assembly and the joint order priority. Thus, the planning of the assembly process is identified;
- The kinematic state of the nominal assembly defines the DoFs which are to be conserved in the realistic model. The DoFs are identified by a method based on the graphs of primitive kinematic joints: Each assembly or sub-assembly is defined by a graph. In this graph, a node represents a part and an edge represents a primitive joint;
- The contact between the features is conserved;
- The joint type between each couple of components is respected.
In the context of this article, three primitive mating constraints are considered: A coincident between two planar faces, a coaxiality between two axes and a distance between two planar faces.
In this paper, a model for the integration of dimensional and geometrical tolerances in CAD models is presented: the components with defects are automatically obtained according to the tolerances and a new method to redefine mating constraints according to the OFA is established.
The developed model is a tool for tolerance analysis while considering the assembly process planning and the various types of contact between parts. The tolerance integration allows us to use the DMU in a realistic configuration. The tolerance impacts on the results of the F.E. calculation or the dynamic computation can be performed.
Future research will focus on the consideration of form defects on CAD model through another type of tolerancing approach. In addition, a modeling of the realistic assemblies according to statistical tolerancing can be obtained.
For a more comprehensive discussion about “An algorithm for CAD Tolerancing Integration: Generation of assembly configurations according to dimensional and geometrical tolerances”, we invite you to read the following Research Paper:
Borhen Louhichi, Mehdi Tlija, Abdelmajid Benamara, Antoine Tahan. An algorithm for CAD Tolerancing Integration: Generation of assembly configurations according to dimensional and geometrical tolerances. The International Journal of Advanced Manufacturing Technology, July 2014, DOI: 10.1016/j.cad.2014.07.002.
Mehdi Tlija est assistant à l’ISSAT. Il est actuellement candidat au doctorat à l’ENIM. Ses principaux intérêts de recherche sont la conception assistée par ordinateur et le tolérancement.
Antoine Tahan est professeur de génie mécanique de l’ÉTS.
Programme : Génie mécanique
Laboratoires de recherche : LIPPS – Laboratoire d'ingénierie des produits, procédés et systèmes