Max Giordano

Tolerance Analysis and Synthesis by Means of Deviation Domains, Axi-Symmetric Cases

The small displacement torsors are generally used for the represeolation of the geometrical deviations. The standardised tolerances can then be translated by a set of inequalities between the components of a deviation torsor. hi me case of cylindrical possible to reduce the space to three dimensions at the maximum instead of six in the general case. Topological operations like the Minkowski sum to carry OUT the domains presented application relates to metro-logic inspection for a specification with maximum material condition on both the toleranced surface and the datum. The second example makes it possible to determine the deviation between two surfaces belonging to two different parts after mating them by two contact features.

Mathematical representation of Tolerance Zones

The notion of tolerance zone is fundamental for geometric tolerance analysis and synthesis. In this paper, a definition is proposed for the tolerance zones, slightly different from the ISO standard definition, but leading to a non ambiguous model. The tolerance zones are represented by inequations between the real variables that represent relative admissible displacements from the theoretical nominal positions. In the limit case of equality, the equations obtained are those of boundaries that limit a domain in the displacement space.

A new calculation method for the worst case tolerance analysis and synthesis in stack-type assemblies

Productivity and industrial product quality improvements entail a rational tolerancing process to be applied as early as product design. Once functional conditions are defined, an optimal specification for each component in a mechanical system is to be developed. Despite numerous studies in this area, the problem is still far from solved. It may be decomposed into two stages: development of specifications based on standards, or qualitative synthesis, and calculation of tolerances. To the extent that these two sets of problems are related, we propose to address them in parallel. In this paper, we present an original method that enables us to solve these two problems for the case of serial assembly (stacking) without clearances. This method is based on the use of influence coefficients to obtain the relationship between the functional tolerance and the tolerances associated with the geometry of the mechanisms interface surfaces. We will describe a calculation algorithm that helps obtain influence coefficients solely from the assemblys geometric definition. Then, we will show that under our working hypothesis, this relationship is piecewise linear.

Tolerance analysis and synthesis by means of clearance and deviation spaces

A mathematical representation of tolerance zones is used to analyse toleranced mechanisms. This method permits to choose optimal geometric tolerances, in many cases. A mechanism is considered as constituted of solid bodies and joints. The set of displacements allowed by a joint is called clearance space. It takes into account the degrees of freedom of the joint but also the clearance between the two bodies linked by this joint. For each functional and toleranced surface, the set of displacements of the actual surface with regard to its nominal location and according to the tolerance zone, is called deviation space. For a simple closed loop mechanism, topological operations are made on the clearance spaces, and on the deviation spaces. In the case of a mechanism with a complex structure, the analysis is more complex but can be computed thanks to a few topological operations on the clearance and deviation spaces. This method allows to compare different tolerancings for each part. Consequently, it is possible to define optimal geometrical tolerances in many cases.

Comparison of Two Similar Mathematical Models for Tolerance Analysis: T-Map and Deviation Domain

The major part of production cost of a manufacturing product is set during the design stage and especially by the tolerancing choice. Therefore, a lot of work involves trying to simulate the impact of these choices and provide an automatic optimization. For integrating this modeling in computer aided design (cad) software, the tolerancing must be modeled by a mathematical tool. Numerous models have been developed but few of them are really efficient. Two advanced models are “T-map” model developed by Joseph K. Davidson and “deviation domain” developed by Max Giordano. Despite the graphical representation of these two models seems to be similar, they have significant differences in their construction and their resolution method. These similarities and differences highlight the needs of tolerancing modeling tool in each kind of problems, especially in case of assembly with parallel links.

Virtual Gauge Representation for Geometric Tolerances in CAD-CAM Systems

Abstract: The CAD software seeks to represent the syntax of the geometric tolerances, i.e. their writing on the drawings. We propose to represent their semantics, i.e. their meaning with respect to the part. We show that the meaning of the geometric tolerances can be defined thanks to a model of virtual gauges. These gauges concern geometrical entities of the part which are represented on the three-dimensional geometrical model of the part (CAD model). The topology of a gauge is related to that of the part. Recording these attributes is sufficient. The advantages of this representation are its simplicity, the semantic coherence which can be guaranteed, the independence from the standards, their limits and their evolutions, and the extension of the tolerancing possibilities for the designer. Key words: Tolerancing, Virtual gauge, CAD-CAM.1. INTRODUCTIONThe subject of this paper is to present the bases of a data-processing representation of the geometric tolerances. The tolerances which are considered are those which are allowed by the ISO and ASME standards. Nevertheless, we will show that the suggested representation allows to specify functional tolerances which are difficult and even impossible to express with the writing rules of the standards. Indeed it is necessary to distinguish the

A Method for Three Dimensional Tolerance Analysis and Synthesis Applied to Complex and Precise Assemblies

The tolerancing process for precise mechanical systems in a context of short or long run in industrial production requires a rational method from the specification of the functional requirements until the final products are checked. Nowadays the optimization of the tolerances is generally carried out empirically. Compromises must be made between the functional requirements in the design process and the manufacturing step. The limits of accuracy imposed by the process must be taken into account. The need for a rational method is particularly necessary for new products in the field of traditional mechanisms as well as of micromechanics or even of micro-systems. In the design process, in the case of an assembly, the functional requirements must be defined in geometrical terms, in order to satisfy the customer requirements. Then, these geometrical requirements must be translated into specifications on the various parts so that on the one hand the assembly can be carried out under well defined conditions and on the other hand, after assembly, the functional requirements are strictly respected. This transfer of specifications with creations of new specifications of the assembly requires a three-dimensional geometrical analysis taking into account the geometrical deviations- form defects, position and orientation- and size deviations. Clearances in the assemblies also will intervene. They are necessary to ensure the mechanical motions but also to compensate for variations of geometry in the case of hyper constrained assemblies. In the phase of industrialisation, the geometrical and dimensional tolerances will be necessary for the choice of machines, for manufacturing planning process and for the measurement processes during the production but also for the final quality control of the parts and of the system. The methods of assemblies are also strongly conditioned by the functional requirements.

Simultaneous analysis method for tolerancing flexible mechanisms

We propose a simultaneous method to make a tolerancing analysis of a deformable system. This method solves effective configurations on an assembly, deformations of mechanical parts and joints, and internal forces. It can be used in the aim of testing tolerancing and its technological consequences as life cycles or load levels (maximum static equivalent stress, fatigue stress,...). We have to discretize the assembly in elastic parts and joints (a joint can be a couple of surfaces or a component).

Computer Aided Tolerancing - Solver and Post Processor Analysis

The world of the designer is three dimensional, and the language of tolerancing is a set of ISO specifications. We have built a methodology in order to compute geometric specifications on parts and clearances in joints through a mathematical model based on the small displacement torsors. A tolerancing object becomes a 6D object thanks to the developed solver. One objective is to represent 6D polytopes in the 3D world of the designer in order to inform him of the results for his tolerancing choices: assemblability performance, best and worst precision zones, and functional requirements. Therefore, it is necessary to indicate, the results to the designer graphically. This representation will be done in a CAD application by means of zones (3D volumes), which will be associated with functional features of the mechanism. An assembly example is presented to illustrate this method.

A New Method for Integrated Design and Tolerancing

The dimensional and geometrical tolerancing of machine elements is an important step in the design and manufacturing of a product. Unfortunately, tolerancing takes place late in the current design processes. Generally, it is only in the detail drawings of the parts that the tolerances are determined qualitatively and quantitatively. Some design problems appear which could have been detected upstream if the tolerances had been introduced from the very start. In the proposed design process, the mechanism is defined from a minimal kinematics structure to a detailed geometry. The tolerancing method is directly integrated into this design process. There is an inevitable growing complexity of the mechanical structure. Some technical choices are carried out at each level and it would be interesting to evaluate their geometrical influence on the expressed conditions. Therefore, we propose to deal with the problem of tolerance in an integrated manner with the process of design. The recursive top-down design and tolerancing process is general. The different design solutions, and technological choices, directly influence the dimensional and geometrical tolerances. We present a graph tool, which allows definition of the topology of the mechanism, during all phases of its design. The tolerancing graph is translated into ISO standards conforming tolerances. Different views are possible depending on the detail level needed by the designer. During the design process, the graph is simultaneously updated. An example is studied with the different steps to illustrate this integrated method. The influence of different possible design solutions on the tolerances is compared in order to validate these choices.