A Declarative Information Model for Functional Requirements

Clément, André; Rivière, Alain; Serré, Philippe

doi:10.1007/978-94-009-1529-9_1

Cited by 21 publications

(9 citation statements)

References 1 publication

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“…By discretizing the surface 0 S into n points i N gives n equations (7) with 1 i n   . Using small displacement torsors, equation (8) can be written for every point M of the Euclidean space [19]:…”

Section: Geometric Constraintsmentioning

confidence: 99%

Tolerance analysis by polytopes: Taking into account degrees of freedom with cap half-spaces

Homri

Teissandier

Ballu

2015

Computer-Aided Design

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To determine the relative position of any two surfaces in a system, one approach is to use operations (Minkowski sum and intersection) on sets of constraints. These constraints are made compliant with half-spaces of n  where each set of half-spaces defines an operand polyhedron. These operands are generally unbounded due to the inclusion of degrees of invariance for surfaces and degrees of freedom for joints defining theoretically unlimited displacements. To solve operations on operands, Minkowski sums in particular, "cap" halfspaces are added to each polyhedron to make it compliant with a polytope which is by definition a bounded polyhedron. The difficulty of this method lies in controlling the influence of these additional half-spaces on the topology of polytopes calculated by sum or intersection. This is necessary to validate the geometric tolerances that ensure the compliance of a mechanical system in terms of functional requirements.

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Section: Geometric Constraintsmentioning

confidence: 99%

Tolerance analysis by polytopes: Taking into account degrees of freedom with cap half-spaces

Homri

Teissandier

Ballu

2015

Computer-Aided Design

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“…Only in the very rare case of complex surfaces the obtained sets are bounded. This is a consequence of the degrees of invariance of the toleranced features or the degrees of freedom of the joints which define unbounded displacements [22,23]. For this reason, the algorithms for summing polytopes discussed previously are not directly applicable.…”

Section: Introductionmentioning

confidence: 99%

Model reduction in geometric tolerancing by polytopes

Delos

Arroyave-Tobón

Teissandier

2018

Computer-Aided Design

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There are several models used in mechanical design to study the behavior of mechanical systems involving geometric variations. By simulating defects with sets of constraints it is possible to study simultaneously all the configurations of mechanisms, whether over-constrained or not. Using this method, the accumulation of defects is calculated by summing sets of constraints derived from features (toleranced surfaces and joints) in the tolerance chain. These sets are usually unbounded objects (R 6-polyhedra, 3 parameters for the small rotation, 3 for the small translation), due to the unbounded displacements associated with the degrees of freedom of features. For computational and algorithmic reasons, cap facets are introduced into the operand polyhedra to obtain bounded objects (R 6-polytopes) and facilitate computations. However, the consequence is an increase in the complexity of the models due to the multiplication of caps during the computations. In response to this situation, we formalized and tested a method for controlling the effects of cap facets. Based on the combinatorial properties of polytopes, we propose to trace the operand faces during the different operations. An industrial case is solved and discussed in order to show the significant gain in computational time when applying the new method. This example has been chosen to be as general as possible to illustrate the genericity of the method.

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“…In order to improve the rotary accuracy of the spindle system, it is necessary to study the factors affecting the motion error. Bourdet [1]and Clement [2] proposed a method using Small Displacement Torsor to describe part error; Desrochers [3] studied the error transferred between assembly parts with Jacobi method. Samper [4][5] proposed the theory of convex hull to analyze the bearing accuracy and stiffness.…”

Section: Introductionmentioning

confidence: 99%

Research of the influence of geometrical factors on rotary accuracy of high-precision spindle

Zhu

Zhang

Guo

2013

2013 IEEE International Symposium on Assembly and Manufacturing (ISAM)

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As an important component of machine tools, spindle is the end part directly determining the quality of machined surfaces. It is essential to guarantee the spindle rotary accuracy for improving the machining quality. Spindle rotary accuracy is determined by bearing accuracy and other components' geometric error. Firstly, a 5-DOF bearing model is applied to describe the position and orientation deviations between inner ring and outer ring. It is also used to describe bearings' rotational error. Secondly, the distance of curvature centers of inside and outside raceways is calculated when the position and orientation of inner ring changes, in consideration of the dimensioned and form errors of the inner, outer rings and balls. Small Displacements Torsor (SDT) is used to describe machining error of spindle. Finally, geometric factors such as shaft machining error, bearing's preload and the assembly angle are discussed.

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A Declarative Information Model for Functional Requirements

Cited by 21 publications

References 1 publication

Tolerance analysis by polytopes: Taking into account degrees of freedom with cap half-spaces

Tolerance analysis by polytopes: Taking into account degrees of freedom with cap half-spaces

Model reduction in geometric tolerancing by polytopes

Research of the influence of geometrical factors on rotary accuracy of high-precision spindle

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