A proposition of 3D inertial tolerancing to consider the statistical combination of the location and orientation deviations

Tolerancing of assembly mechanisms is a major interest in the product life cycle. One can distinguish several models with growing complexity, from 1-dimensional (1D) to 3-dimensional (3D) (including form deviations), and two main tolerancing assumptions, the worst case and the statistical hypothesis. This paper presents an approach to 3D statistical tolerancing using a new acceptance criterion. Our approach is based on the 1D inertial acceptance criterion that is extended to 3D and form acceptance. The modal characterisation is used to describe the form deviation of a geometry as the combination of elementary deviations (location, orientation and form). The proposed 3D statistical tolerancing is applied on a simple mechanism with lever arm. It is also compared to the traditional worst-case tolerancing using a tolerance zone

Inertial tolerancing and capability indices in an assembly production

International audienceTraditional tolerancing considers the conformity of a batch when the batch satisfies the specifications. The characteristic is considered for itself and not according to its incidence in the assembly. Inertial tolerancing proposes another alternative of tolerancing in order to guarantee the final assembly characteristic. The inertia I2 = σ2 + δ2 is not toleranced by a tolerance interval but by a scalar representing the maximum inertia that the characteristic should not exceed. We detail how to calculate the inertial tolerances according to two cases, one aims to guarantee an inertia of the assembly characteristic the other a tolerance interval on the assembly characteristic by a Cpk capability index, in the particular but common case of uniform tolerances or more general with non uniform tolerances. An example will be detailed to show the results of the different tolerancing methods

The pilot dimension method: Reconciling Steering and Conformity in Workshops

International audienceIn machining workshops, workpieces are produced according to dimensions known as manufacturing dimensions. For the same workpiece and the same manufacturing plan, several sets of manufacturing dimensions can be used but none satisfy simultaneously the two main missions workshops need to fulfil: (a) Ensuring conformity of products to their design dimension tolerances (also called blueprint tolerances) and (b) steering machines in order to compensate for tool wear. The set of manufacturing dimensions obtained from the design dimensions using the minimal chain of dimensions method is optimal for a conformity check of workpieces but is practically unusable for steering machines because of the complexity of its relationships toward the tool correctors and tools dimensions. The pilot dimensions method consists in, on the one hand, identifying and representing these tool correctors and these tool/program dimensions on the production drawings (besides the manufacturing dimensions) and, on other the other hand, determining their correction values through a mathematical set of relations after having measured the manufacturing dimensions on a workpiece. Doing so will strongly reduce adjustment time, reduce the number of workpieces used for adjustments and greatly enhance the quality of workpiece batches

Copilot Pro®: A full method for a steering of the machining.

International audienceCopilot Pro® is a method for the initial and regular machine-tools setup, developed by the Symme laboratory of the Savoy University and by the Technical Center of Industries of Screw-machining (Ctdec) in France. Its first step is the organization of the different machining operations, in setup steps, themselves subdivided into measuring steps. The second step consists in determining the manufacturing dimensions to measure at the end of each measuring step. Finally, the third step consists in linking the manufacturing dimensions to both the correctors and the tool-dimensions, in the aim of calculating the corrections that have to be done in function of the deviations measured on the manufacturing dimensions. With this method, the steering of an industrial workpiece is performed with two steering parts instead of ten before

Modeling of 2D and 3D Assemblies Taking Into Account Form Errors of Plane Surfaces

The tolerancing process links the virtual and the real worlds. From the former, tolerances define a variational geometrical language (geometric parameters). From the latter, there are values limiting those parameters. The beginning of a tolerancing process is in this duality. As high precision assemblies cannot be analyzed with the assumption that form errors are negligible, we propose to apply this process to assemblies with form errors through a new way of allowing to parameterize forms and solve their assemblies. The assembly process is calculated through a method of allowing to solve the 3D assemblies of pairs of surfaces having form errors using a static equilibrium. We have built a geometrical model based on the modal shapes of the ideal surface. We compute for the completely deterministic contact points between this pair of shapes according to a given assembly process. The solution gives an accurate evaluation of the assembly performance. Then we compare the results with or without taking into account the form errors. When we analyze a batch of assemblies, the problem is to compute for the nonconformity rate of a pilot production according to the functional requirements. We input probable errors of surfaces (position, orientation, and form) in our calculus and we evaluate the quality of the results compared with the functional requirements. The pilot production then can or cannot be validated

Respecting the loss-cost of a non-symmetrical functional requirement with a statistical tolerancing approach

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Tolérancement des Systèmes Assemblés, une approche par le Tolérancement Inertiel et Modal

L'objectif du tolérancement des systèmes assemblés est de définir les tolérances des composants permettant la satisfaction du client : l'assemblage et le bon fonctionnement des systèmes. On peut identifier des cas limites du tolérancement pour lesquelles ces objectifs sont mal respectés. Différents modèles de complexité croissante sont identifiés : 1D, 3D et 3D avec prise en compte des défauts de forme. On peut aussi distinguer différentes hypothèses de comportement des composants du système : rigide non déformable, flexible élastique et élasto-plastique. Ce projet de recherche se propose de traiter les problématiques de tolérancement sous l'hypothèse de comportement rigide des composants, pour les différentes complexités de modélisation existante : 1D, 3D et 3D avec défauts de forme. Notre approche se fonde sur le critère inertie I de quantification des écarts d'une caractéristique par rapport à sa cible. Ce critère, basé sur la fonction de perte de Taguchi, est proposé par Pillet dans une méthode de tolérancement 1D. Pour étendre cette approche de tolérancement à la qualification de plusieurs caractéristiques, dans le cas des surfaces, nous choisissons d'utiliser la méthode modale de description des défauts de forme de toutes géométries proposée par Samper. Ces deux approches, de quantification (inertiel) et de qualification (modal), évoluent pour enfin être fusionnées et proposer une méthode d'acceptation multi-caractéristique, le tolérancement modal inertiel. La modélisation 1D du tolérancement est bien cernée. Le graphe (d,s2) permet l'analyse des tolérances des composants en vue de vérifier la conformité de la résultante pour toutes les configurations. On met ainsi à disposition un outil permettant de vérifier un tolérancement quelle que soit l'expression de la tolérance, intervalle de tolérance ou inertie, quels que soient les indices de capabilité et sous l'hypothèse statistique d'indépendance des variables ou non (non illustrée ici)

How Form Errors Impact on 2D Precision Assembly with Clearance?

International audienceMost models of assembling simulations consider that form errors are negligible, but how can this assumption be assessed? When clearances are high, form deviations can be neglected, but on the case of very precise mechanisms with small clearances, this assumption can lead to non-accurate models. This paper is the continuation of our previous works presented at IPAS 2008 dealing with the assembly of two parts regarding their form deviation. The proposed method considers the positioning of the pair of surface with a given external force to identify contact points. The parts relative positioning is expressed by a small displacement torsor that can be transferred to any referee and compared to the functional requirement. The objective of this paper is to identify the clearance domain of a mechanical linkage regarding the form deviation of parts. Several parameters are identified as influent such as the clearance value, the straightness of the form deviation and the localization of the ideal least squared associated shape

Caractérisation des défauts d'une surface sphérique par décomposition modale

The [ISO 1101] standard specifies the form errors with geometrical tolerances using the zone concept.To complete this concept, we present a generic method which adapts to any geometry and allows to describe any kind of errors. Thus,we can dissociate the part errors according to reference categories: position, orientation,form, waviness and roughnesses. Starting from a cloud of poinds representing the error measurement, the "modal" method decompose, like Fourier series,this error in a sum of sorted errors according to the ircomplexity degree (a number of "wavinesses"). In addition, we propose to show, on a simple example, that according to error complexity to be characterized, an interpolation by the modal method allows to optimize the measuring strategy