Une approche de bout en bout du tolérancement statistique sous contraintes industrielles : contribution au jumeau virtuel industriel

In the manufacturing process of a product, various assembly steps are necessary. Several types of requirements have to be met at each level and involve considerations about dimensional uncertainties on the parts to be assembled. Tolerancing is the activity in charge of the management of these uncertainties and takes place both in the product development phase and in the series production phase. In the context of the aeronautics industry, in particular with regards to tolerancing on aerostructures, specificities have to be taken into account in the development of adequate methods and tools. Prior to production, one of the main issues of tolerancing amounts to allocate tolerance limits suited to a given acceptable scrap rate. The aim is to allow the actors concerned with tolerance intervals to agree on a consistent and robust tolerance value. A statistical methodology based on a Chernov bound approach applied to a sum of uniform distributions is proposed. In the production phase, the availability of measurement data allows to refine the statistical tolerancing approach. The linear model often considered can be corrected to serve new approaches. A methodology to manage acceptance criteria on tolerance values is proposed, basing the decision support on risk concepts pertinently defined for industrial actors. Within the framework of the revision of tolerance sharing in an assembly, an optimization problem is formulated with appropriate industrial costs in order to propose the optimal tolerance re-sharing in a stack chain. Finally, the proposed methodologies are implemented in tools allowing industrial processing and end-to-end management of tolerances from elementary parts to final product assembly, thus contributing to the elaboration of the product virtual twin.Dans le processus de fabrication d'un produit, diverses étapes d'assemblage sont nécessaires. Plusieurs types d'exigences sont à respecter à chaque niveau et ils impliquent de considérer les incertitudes de dimensions sur les pièces à assembler. Le tolérancement est l'activité en charge de la gestion de ces incertitudes et intervient à la fois en phase de développement du produit et en phase série. Dans le contexte de l'industrie aéronautique, en particulier en ce qui concerne le tolérancement sur les aérostructures, des spécificités sont à prendre en compte pour l'élaboration de méthodes et outils adéquats. Avant la mise en production, une des problématiques principales du tolérancement est l'allocation de limites de tolérance adaptées à un certain taux acceptable de rebut. Le but est de permettre aux acteurs concernés par les intervalles de tolérance de s'accorder sur une valeur de tolérance cohérente et robuste. Une méthodologie statistique basée sur une approche type borne de Chernov appliquée à une somme de distributions uniformes est proposée. En phase de production, la disponibilité de données de mesure permet de raffiner la démarche du tolérancement statistique. Le modèle linéaire considéré peut être corrigé à la faveur de nouvelles approches. Une méthodologie de gestion des critères d'acceptation sur les valeurs de tolérance est également proposée, en basant l'outil d'aide à la décision sur des notions de risques définies en adéquation avec les acteurs industriels. Dans le cadre de la révision du partage de tolérances dans un assemblage, un problème d'optimisation est formulé avec des coûts industriels appropriés afin de proposer le re-partage optimal de tolérances dans une chaîne de côte. Enfin, les méthodologies proposées sont implémentées dans les outils permettant le traitement industriel et la gestion de bout en bout des tolérances depuis les pièces élémentaires jusqu'à l'assemblage final du produit, contribuant ainsi à l'élaboration du jumeau virtuel du produit

A Chernov bound for robust tolerance design and application

International audienceWithin an industrial manufacturing process, tolerancing is a key player. The dimensions uncertainties management starts during the design phase, with an assessment on variability of parts not yet produced. For one assembly step, we can gain knowledge from the tolerance range required for the parts involved. In order to assess output uncertainty of this assembly in a reliable way, this paper presents an approach based on the deviation of the sum of uniform distributions. As traditional approaches based on Hoeffding inequalities do not give accurate results when the deviation considered is small, we propose an improved upper bound. We then discuss how the stack chain geometry impacts the bound definition. Finally, we show an application of the proposed approach in tolerance design of an aircraft sub-assembly. The main interest of the technique compared to existing methodologies is the management of the confidence level and the emphasis of the explicit role of the balance within the stack chain

A statistical approach for robust tolerance design

Within an industrial manufacturing process, tolerancing is a key player. The dimensions uncertainties management starts during the design phase, with an assessment on variability of parts not yet produced. For one assembly step, we can gain knowledge from the tolerance range required for the parts involved. In order to assess output uncertainty of this assembly in a reliable way, this paper presents an approach based on the deviation of the sum of uniform distributions. As traditional approaches based on Hoeffding inequalities do not give accurate results when the deviation considered is small, we propose an improved upper bound. We then discuss how the stack chain geometry impacts the bound definition. Finally, we show an application of the proposed approach in tolerance design of an aircraft sub-assembly. The main interest of the technique compared to existing methodologies is the management of the confidence level and the emphasis of the explicit role of the balance within the stack chain

A statistical approach for tolerancing from design stage to measurements analysis

International audienceStarting from the development phase, tolerance design must be accurate enough to not only hedge against various uncertainties in order to ensure assembly feasibility but also minimize production cost and avoid expensive over-quality. Once tolerances are agreed, the production allows tolerance features observations and we propose a verification and correction on initial model based on the knowledge of measurement data. The feedback consideration also enables risk evaluation of each tolerance and a more accurate limit definition knowing measures of other assembly contributors is proposed. In addition, we propose an algorithm to optimize the tolerance sharing within a stack chain based on various relevant cost criteria. Finally, an example of tolerancing industrial applications on aerostructures use-cases is detailed to illustrate the methodology from tolerance design to feedback measurement analysis

Gibberellins negatively regulate the development of Medicago truncatula root system

Abstract The root system displays a remarkable plasticity that enables plants to adapt to changing environmental conditions. This plasticity is tightly linked to the activity of root apical meristems (RAMs) and to the formation of lateral roots, both controlled by related hormonal crosstalks. In Arabidopsis thaliana, gibberellins (GAs) were shown to positively control RAM growth and the formation of lateral roots. However, we showed in Medicago truncatula that GAs negatively regulate root growth and RAM size as well as the number of lateral roots depending at least on the MtDELLA1 protein. By using confocal microscopy and molecular analyses, we showed that GAs primarily regulate RAM size by affecting cortical cell expansion and additionally negatively regulate a subset of cytokinin-induced root expansin encoding genes. Moreover, GAs reduce the number of cortical cell layers, resulting in the formation of both shorter and thinner roots. These results suggest contrasting effects of GA regulations on the root system architecture depending on plant species