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A survey on algorithmic aspects of modular decomposition
The modular decomposition is a technique that applies but is not restricted
to graphs. The notion of module naturally appears in the proofs of many graph
theoretical theorems. Computing the modular decomposition tree is an important
preprocessing step to solve a large number of combinatorial optimization
problems. Since the first polynomial time algorithm in the early 70's, the
algorithmic of the modular decomposition has known an important development.
This paper survey the ideas and techniques that arose from this line of
research
Topological model for machining of parts with complex shapes
Complex shapes are widely used to design products in several industries such
as aeronautics, automotive and domestic appliances. Several variations of their
curvatures and orientations generate difficulties during their manufacturing or
the machining of dies used in moulding, injection and forging. Analysis of
several parts highlights two levels of difficulties between three types of
shapes: prismatic parts with simple geometrical shapes, aeronautic structure
parts composed of several shallow pockets and forging dies composed of several
deep cavities which often contain protrusions. This paper mainly concerns High
Speed Machining (HSM) of these dies which represent the highest complexity
level because of the shapes' geometry and their topology. Five axes HSM is
generally required for such complex shaped parts but 3 axes machining can be
sufficient for dies. Evolutions in HSM CAM software and machine tools lead to
an important increase in time for machining preparation. Analysis stages of the
CAD model particularly induce this time increase which is required for a wise
choice of cutting tools and machining strategies. Assistance modules for
prismatic parts machining features identification in CAD models are widely
implemented in CAM software. In spite of the last CAM evolutions, these kinds
of CAM modules are undeveloped for aeronautical structure parts and forging
dies. Development of new CAM modules for the extraction of relevant machining
areas as well as the definition of the topological relations between these
areas must make it possible for the machining assistant to reduce the machining
preparation time. In this paper, a model developed for the description of
complex shape parts topology is presented. It is based on machining areas
extracted for the construction of geometrical features starting from CAD models
of the parts. As topology is described in order to assist machining assistant
during machining process generation, the difficulties associated with tasks he
carried out are analyzed at first. The topological model presented after is
based on the basic geometrical features extracted. Topological relations which
represent the framework of the model are defined between the basic geometrical
features which are gathered afterwards in macro-features. Approach used for the
identification of these macro-features is also presented in this paper.
Detailed application on the construction of the topological model of forging
dies is presented in the last part of the paper
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