Andre Clement

A dimensioning and tolerancing assistance model for CAD/CAM systems

A model called TTRS for technologically and topologically related surfaces, has been developed and its application to dimensioning and tolerancing is presented here. According to this model, any part can be represented as a succession of binary surfaces associations forming a tree. Additionally, each surfaces association, termed as a TTRS object, is represented by a set of minimum geometric datum elements (MGDE). Once established, each TTRS can be given appropriate geometric dimensioning and tolerancing (GD & T) symbols through a general procedure making use of GD & T tables and combination rules. Application examples are also presented.

The TTRSs : 13 Constraints for Dimensioning and Tolerancing

The dimensioning and the tolerancing model presented in this paper allows the functional tolerancing declaration of a class of mechanical parts independently from the geometric instantiation. That model is based on the use of the TTRS concept and on relative positioning constraints. Moreover, that model is compatible with the exchange standard ISO/CD 10303-47.

A Declarative Information Model for Functional Requirements

The tolerancing synthesis consists in proposing a part tolerancing diagram directly obtained from the mechanism good-working conditions. However, tools that can be used to describe the functional requirements are a few and often very specific. The objective of this paper is then to propose a mean to define, from a univocal and sufficiently adaptable point of view, all the functional requirement types a design engineer is brought to specify.

Global Consistency of Dimensioning and Tolerancing

The general objective of this paper is to define the problem areas linked to the specification and overall consistency of a dimensioning diagram and to propose a solution principle to solve this problem.

Analysis of functional geometrical specification

“Good” functional tolerancing can only be obtained once the geometrical specification of the mechanism being studied has been analysed from a technological and geometrical standpoint. A geometrical analysis based on a vector approach has been developed. It enables existing tolerancing relations to be written between the design parameters relative to each part and the relative position parameters between two parts of the mechanism in question.

A new variational association process for the verification of geometrical specifications

When this new association process of a datum is performed to verify a geometrical specification, measured points are considered as perturbations which generate modifications of the nominal geometry by variation of its location, orientation, and intrinsic dimensional characteristics, without requiring rotation and translation variables as the traditional methods usually do (Bourdet, et al., 1996, Advanced Mathematical Tools in Metrology II, World Scientific) with torsors or matrices. This new association process (Choley, 2005, Ph.D. thesis, Ecole Central, Paris; Choley, et al., 2006, Advanced Mathematical and Computational Tools in Metrology, VII, World Scientific) is based on both a reduced modeling of the geometry, taken out of the computer aided design system database, and a variational distance function. The whole measured points set influence is taken into account as an optimization criterion is applied (Bourdet and Clement, 1988, Ann. CIRP 37(1), p. 503; Srinivasan, DIMACS Workshop on Computer Aided Design and Manufacturing, Rutgers University, NJ, October 7-9). Thus, the least squares optimization is achieved using the pseudo-inverse matrix, whereas the minimax optimization is treated with an algorithm developed by the Physikalisch-Technische Bundesanstalt and adapted for this purpose. In this paper, it is explained how this association process may be applied to planes and cylinders, used as single datum, datum systems, or common datum, with the least squares and minimax criteria.

Modelling-Simulation-Testing of Compliant Assemblies

Current statistical tolerance analysis of assemblies rely heavily on Monte Carlo simulation. The available software tools using this technique model the assembly of rigid parts, by only considering the kinematic laws. [Sellem et al., 1998] proposed a linear mechanical approach taking deformation into account in the computation of tolerances for welded, riveted, bolted or glued assemblies of compliant parts, avoiding in this way the expensive Monte Carlo simulation. This paper presents some improvements in the modelling of the assembly process, and describes a sensitivity analysis approach to identify the key characteristics of the assembly. The accuracy of this method is evaluated by a comparison with measurements performed on an actual assembly of four complex parts.

Coordinate Free Approach for the Calculation of Geometrical Requirement Variations

This chapter proposes to investigate the use of a coordinate free approach for the mapping of geometrical requirement along a product life cycle. The geometry of the studied assembly is represented using a Gram matrix that is issued from a parametric model constituted of points and vectors. This parametric model is instanced for all relevant phase of the product life cycle. The calculation of instanced parameters is based on part deformation due to changing operating conditions. This calculation is carried out thanks to existing theoretical techniques. The application presented in this paper is constituted of a simple 3D case composed of 3 articulated bars disposed as a tetrahedron and subjected to some thermal expansion.

A Declarative Approach for Geometry and Topology: A New Paradigm for CAD-CAM Systems

The geometric models currently used in CAD-CAM modellers are chiefly based on a procedural approach. Over the past few years, the appearance of parametric and, above all, variational modellers, has opened up the way to a more declarative approach. It is true to say that parametric design is efficient, but it requires knowledge of a design chronology whose flexibility is thus diminished. On the other hand, variational design is very general and flexible but does need the use of solvers to simultaneously solve a large number of non-linear equations.

ANALYSIS OF THE DEPENDENCE BETWEEN MANUFACTURING AND DESIGN SPECIFICATION

The general objective of this paper is to analyse the dependency relations that may exist between manufacturing and design specifications of a geometric object. This object will be modelled on the basis of the TTRS concept and vector modelling synthesised by the metric tensor of a set of vectors. The first problem that we propose to solve therefore is the formal expression of these relations. After that, the dependency will be analysed and illustrated considering a 3D object.