abstract: Parts are always manufactured with deviations from their nominal geometry due to many reasons such as inherent inaccuracies in the machine tools and environmental conditions. It is a designer job to devise a proper tolerance scheme to allow reasonable freedom to a manufacturer for imperfections without compromising performance. It takes years of experience and strong practical knowledge of the device function, manufacturing process and GD&T standards for a designer to create a good tolerance scheme. There is almost no theoretical resource to help designers in GD&T synthesis. As a result, designers often create inconsistent and incomplete tolerance schemes that lead to high assembly scrap rates. Auto-Tolerancing project was started in the Design Automation Lab (DAL) to investigate the degree to which tolerance synthesis can be automated. Tolerance synthesis includes tolerance schema generation (sans tolerance values) and tolerance value allocation. This thesis aims to address the tolerance schema generation. To develop an automated tolerance schema synthesis toolset, to-be-toleranced features need to be identified, required tolerance types should be determined, a scheme for computer representation of the GD&T information need to be developed, sequence of control should be identified, and a procedure for creating datum reference frames (DRFs) should be developed. The first three steps define the architecture of the tolerance schema generation module while the last two steps setup a base to create a proper tolerance scheme with the help of GD&T good practice rules obtained from experts. The GD&T scheme recommended by this module is used by the tolerance value allocation/analysis module to complete the process of automated tolerance synthesis. Various test cases are studied to verify the suitability of this module. The results show that software-generated schemas are proper enough to address the assemblability issues (first order tolerancing). Since this novel technology is at its initial stage of development, performing further researches and case studies will definitely help to improve the software for making more comprehensive tolerance schemas that cover design intent (second order tolerancing) and cost optimization (third order tolerancing). / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2016

La cotation fonctionnelle doit garantir la montabilité et le bon fonctionnement d'un mécanisme en imposant les spécifications fonctionnelles à respecter sur les pièces. Ces spécifications sont exprimées avec les normes ISO de cotation et doivent être vérifiées à 20°C. Pour les mécanismes soumis à de fortes températures, il est nécessaire de cumuler l'influence des tolérances et des dilatations aux différents régimes thermiques. Après avoir formulé des hypothèses de comportement dans les liaisons avec contact ou avec jeux affectés par les déformations thermiques et l'influence des incertitudes sur les températures, la méthodologie proposée permet de séparer le calcul thermique et le tolérancement. Le bureau de calcul thermique détermine les champs de température et les déplacements des mailles par la méthode des éléments finis à partir des modèles nominaux des pièces. Le cumul des tolérances et des dilatations est basé sur la méthode des droites d'analyse. Pour chaque exigence, la surface terminale est discrétisée en différents points d'analyse. Dans chaque jonction, les relations de transfert déterminent les points de contact et l'influence des dilatations et des écarts thermiques en ces points sur l'exigence. Une application à un mécanisme industriel démontre l'intérêt d'optimiser les dimensions nominales des modèles afin de maximiser les tolérances tout en respectant l'ensemble des exigences. / Functional dimensioning should guarantee assembly feasibility and proper functioning of a mechanism giving functional specifications on parts to be met. Those specifications are defined with ISO standard and may be considered at 20°C. For high heated mechanisms, impacts of tolerances and thermal expansion for all thermal stages have to be combined. After giving behavior assumption into links with clearance or not while considering thermal expansion and uncertainty of temperature, the proposed method makes it possible to separate thermal calculations and tolerancing. Thermal calculations office determines temperature field and displacements from nominal parts by finite elements method. Integration of tolerancing and thermal expansion is based on analysis direction method. For each requirement, final surface is discretized in various points. In every link, transfer relations determine contact points and impact of thermal expansion on these analysis points on the requirement. A study case shows the interest of nominal dimension optimization in order to maximize tolerances while respecting all mechanism requirements.

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Error equivalence concerns the mechanism whereby different error sources result in identical deviation and variation patterns on part features. This could have dual effects on process variation reduction: it significantly increases the complexity of root cause diagnosis in process control, and provides an opportunity to use one error source as based error to compensate the others. There are fruitful research accomplishments on establishing error equivalence methodology, such as error equivalence modeling, and an error compensating error strategy. However, no work has been done on developing an efficient process design approach by investigating error equivalence. Furthermore, besides the process mean shift, process fault also manifests itself as variation increase. In this regard, studying variation equivalence may help to improve the root cause identification approach. This thesis presents engineering driven approaches for process design and control via embedding error equivalence mechanisms to achieve a better, insightful understanding and control of manufacturing processes. The first issue to be studied is manufacturing process design and optimization based on the error equivalence. Using the error prediction model that transforms different types of errors to the equivalent amount of one base error, the research derives a novel process tolerance stackup model allowing tolerance synthesis to be conducted. Design of computer experiments is introduced to assist the process design optimization. Secondly, diagnosis of multiple variation sources under error equivalence is conducted. This allows for exploration and study of the possible equivalent variation patterns among multiple error sources and the construction of the library of equivalent covariance matrices. Based on the equivalent variation patterns library, this thesis presents an excitation-response path orientation approach to improve the process variation sources identification under variation equivalence. The results show that error equivalence mechanism can significantly reduce design space and release us from considerable symbol computation load, thus improve process design. Moreover, by studying the variation equivalence mechanism, we can improve the process diagnosis and root cause identification.

En conception de systèmes mécaniques, la phase de cotation fonctionnelle consiste à affecter des cotes, constituées d’une valeur nominale et d’un intervalle de tolérance, à des dimensions de pièces. En particulier, l’analyse des tolérances consiste à vérifier que les intervalles de tolérance choisis permettent le respect de la fonctionnalité du mécanisme. A l’inverse, la synthèse des tolérances vise à déterminer ces intervalles de tolérance, si possible de manière optimale, permettant le respect des exigences fonctionnelles. Les approches statistiques traditionnelles, bien que très utiles en phase de préconception, ne sont pas capables d’estimer avec précision le risque de non qualité. Cette thèse aborde ces problèmes selon un angle de vue différent, non plus pour garantir le respect d’exigences fonctionnelles, mais pour garantir le Taux de Non-Conformité (TNC) du mécanisme. Il s’agit de la probabilité que l’exigence fonctionnelle ne soit pas respectée. Les méthodes fiabilistes, s’appuyant sur la théorie des probabilités, permettent un calcul précis et efficace de cet indicateur. L’objectif de cette thèse est d’explorer le domaine de l’analyse et de la synthèse des tolérances afin d’identifier et d’exposer les apports des méthodes fiabilistes sur ces problématiques. Dans ces travaux de thèse, différents outils fiabilistes sont mis à disposition permettant l’analyse des tolérances de tous types de mécanismes avec ou sans jeu. La théorie probabiliste permet une modélisation très complète des dimensions des pièces. En particulier, l’approche APTA (Advanced Probability-based Tolerance Analysis of products) est développée afin de prendre en compte l’évolution aléatoire de certains paramètres de modélisation, notamment les décalages de moyenne, responsables de fortes variations du TNC. L’analyse des tolérances étant plus complexe pour les mécanismes avec jeux, une méthodologie spécifique a été développée basée sur une décomposition en situations de points de contacts et l’utilisation d’une méthode fiabiliste système. Différents indices de sensibilité sont aussi proposés afin d’aider à identifier les cotes ayant le plus d’influence sur le TNC d’un mécanisme. Enfin, l’optimisation du coût de production, sous contrainte de TNC, permet une synthèse des tolérances optimale. Les gains potentiels en termes de coût dépassent 50% par rapport aux conceptions initiales tout en maitrisant le niveau de qualité du produit. Les sociétés RADIALL SA et VALEO Système d’Essuyages, concepteurs et fabricants de produits pour l’automobile et l’aéronautique, ont proposé des cas d’études sur lesquels est démontrée la pertinence des travaux effectués. Sur la base de ces travaux, Phimeca Engineering, spécialisée dans l’ingénierie des incertitudes, développe et commercialise un outil informatique professionnel. / To design mechanical systems, functional dimensioning and tolerancing consists in allocating a target value and a tolerance to part dimensions. More precisely, tolerance analysis consists in checking that chosen tolerances allow the mechanism to be functional. In the opposite, the tolerance synthesis goal is to determine those tolerances, optimaly if possible, such as functional requirements are respected. Traditional statistical approaches are very useful in pre-design phases, but are incapable of estimating precisely non-quality risks. This PhD thesis adresses this problem from a different point of view. The objective is no longer to respect functional requirements but to guarantee the Non-Conformity Rate (NCR) of the mechanism. It is the probability that the functional requirement is not respected. Reliability methods, based on probabilistic theory, allow a precise and efficient calculation of the NCR. The main goal of this thesis is to explore tolerance analysis and synthesis domains in order to identify potential contributions of reliability methods to these issues. In this work, different reliability tools are provided enabling tolerance analysis of all kind of mechanisms with or without gaps. The probability theory allows a detailed modeling of parts dimensions. In particular, the APTA (Advanced Probability-based Tolerance Analysis of products) approach is designed to take into account random variations of some parameters such as mean shifts which influence highly the NCR. As tolerance analysis is more complex for mechanisms with gaps, a specific method is designed based on a decomposition of contact points situations and the use of a reliability system method. Several sensitivity indexes are also proposed to identify the leading dimensions on the NCR. The optimization of the production cost, under a NCR constraint, enables an optimal tolerance synthesis. The potential benefits in terms of costs exceed 50% compared to initial designs while keeping under control quality levels of products. Companies RADIALL SA and VALEO Wiping Systems, designers and manufacturers of products for the automotive and aeronautic industries, have provided case studies on which is demonstrated the relevance of the presented work. Based on this work, the company Phimeca Engineering, specialized in uncertainties, is developing and commercializing a professional computer tool.