Variation analysis, or tolerance analysis as it is sometimes called, is typically used to predict variation in critical dimensions in assemblies by calculating the stack-up of the contributing component variations. It is routinely used in manufacturing and assembly environments with great success. Design engineers are able to account for the small changes in dimensions that naturally occur in manufacturing processes, in equipment, and due to operators and still ensure that the assemblies will meet the design specifications and required assembly performance parameters. Furthermore, geometric variation not only affects critical fits and clearances in static assemblies, it can also cause variation in the motion of mechanisms, and their dynamic performance. The fact that variation and motion analysis are both dependent upon the geometry of the assembly makes this area of study much more challenging. This research began while investigating a particular application of dynamic assemblies - automobiles. Suspension and steering systems are prime examples dynamic assemblies. They are also critical systems, for which small changes in dimension can cause dramatic changes in the vehicle performance and capabilities. The goals of this research were to develop the tools necessary to apply the principles of static variation analysis to the kinematic motions of mechanisms. Through these tools, suspension and steering systems could be analyzed over a range of positions to determine how small changes in dimensions could affect the performance of those systems. There are two distinct applications for this research, steering systems and suspension systems. They are treated separately, as they have distinct requirements. Steering systems are mechanisms, for which position information is most critical to performance. In suspension systems, however, the higher order kinematic terms of velocity and acceleration often are more important than position parameters.

Three growing power electronics applications have massive requirements for properly operating their medium-voltage and high-voltage systems: electric transportation, renewable energy, and the power grid. Their needs include dense power systems with higher efficiency and higher voltage and current devices. This requires devices with higher switching frequencies to lower the size of the passives in the converter and devices that can withstand higher operating temperatures as components move closer together to improve power densities. Devices that achieve higher switching speeds and lower specific on-state resistances also reduce losses. Wide bandgap devices (WBG) like silicon carbide (SiC) have a higher bandgap, higher electric field strength, higher thermal conductivity, and lower carrier concentration than silicon (Si). This allows for higher temperature operation, faster switching, higher voltage blocking, and lower power losses, directly meeting the requirements of the previously noted applications. However, the current packaging schemes are limiting the ability of SiC to operate in these applications by applying packaging schemes used for Si. Therefore, it is critical to use and refine advanced packaging techniques so that WBG devices can better operate and meet the growing demands of these power electronic applications. Low-inductance, wirebond-less, high-density, scalable modules are possible due to advanced packaging methods. While beneficial to the operation and design, these techniques introduce new challenges to the fabrication process. This requires refinement to improve the yield of sandwich-structure modules with wirebond-less interconnects. For this module, encapsulated, silver-sintered substrates reduce the peak electric field within the package, improving the partial discharge inception voltage to meet insulation requirements. It is essential to have a uniform bondline between the substrates to achieve all bond connections and improve reliability. Silver sintering is also used to attach the molybdenum (Mo) post interconnects. These interconnects allow for sandwich-structure modules with low inductances; however, they have tolerance variation from manufacturing and bondline thicknesses, which become problematic for multi-chip power modules with an increased number of die and posts. The variation results in tilt, causing some posts to disconnect altogether. Additionally, soldering MCPMs involves a large thermal mass that the soldering reflow profile from a datasheet does not account for. Ultimately, these fabrication concerns can result in misalignment or disconnected post interconnects to the top substrate. Post interconnect planarity and alignment are vital for this multi-chip power module to avoid open or shorted connections that can derate switch positions. This thesis aims to refine each packaging step in assembling a wirebond-less, multi-chip power module. The bond uniformity of silver (Ag) sintering is addressed in dried preform and wet paste cases. The soldering methods are explored and improved by creating a modified reflow profile for large thermal masses and introducing pressure to reduce bondline variation and voiding content. The entire sandwich structure module is analyzed in a statistical tolerance analysis to understand which component introduces the most variation and height mismatch, providing insight as to which packaging techniques need further control to improve the yield of multi-chip power modules. / Master of Science / The electrification of many systems worldwide has increased the need for compact, efficient power electronics. Their applications span electric transportation, renewable energy systems, grid applications, and data centers, to name a few medium-voltage applications. Wide bandgap (WBG) semiconductors can outperform silicon in these applications, offering higher temperature robustness, higher efficiency performance, and higher voltage capabilities. The faster switching will reduce the size and weight of the converters containing these devices. However, using typical packaging schemes such as wirebonds will limit the potential of WBG devices in these applications. Advanced packaging techniques have been developed to increase the electric field strength, reduce the power loop inductances, reduce electromagnetic interference from fast-switching transients, and improve the power densities of multi-chip power modules for medium voltage and current applications. However, these packaging techniques are not trivial to implement and have resulted in a low yield of these modules. This thesis aims to refine each packaging step in assembling a wirebond-less, multi-chip power module. The bond uniformity of silver sintering is addressed in cases of dried preform and wet paste. The soldering methods are explored and improved by creating a modified reflow profile for large thermal masses and introducing pressure to reduce bondline variation and voiding content. The entire sandwich structure module is analyzed in a statistical tolerance analysis to understand which component introduces the most variation and height mismatch, providing insight as to which packaging techniques need further control to improve the yield of multi-chip power modules.

O principal intento deste trabalho é demonstrar como a combinação de resultados de modelos radiométricos e de análises do limite de resolução de imagens produzem impactos positivos não apenas no projeto óptico de retinógrafos de alta resolução, mas que também geram ferramentas que auxiliam na definição da arquitetura de todo o equipamento, considerando, inclusive, os limites impostos por normas internacionais para a segurança do paciente em relação a radiação emitida na realização dos exames. Particularmente ao projeto óptico, foram desenvolvidos os sistemas de iluminação e imageamento da retina, onde se destacam duas propostas de metodologias: a primeira para a implementação da técnica de eliminação das bem conhecidas retro-reflexões geradas no conjunto óptico que é comum à iluminação e ao imageamento da retina, e a segunda para a obtenção de soluções efetivas em sistemas imageadores, que prima pela diminuição da sensibilidade dos componentes aos erros que são introduzidos pelos processos de fabricação e montagem. Analisando os resultados obtidos com o protótipo, foram validados os sistemas e modelos propostos, que se tornaram parte integrante de um produto oftalmológico aprovado para a comercialização, o retinógrafo Kiron. / The fundamental objective of this work is to demonstrate how radiometric models and analysis of the limit of resolution can provide not only positive impacts to the optical project of high resolution fundus cameras, but also creates tools to perform an optimization of all the equipment, considering the limits imposed by international standards to ensure security to the patient regarding the equipment radiation emission. In the optical project in particular, the imaging and illuminating systems of the retina were developed, in which stands out two proposed methodologies: first, to eliminate the well known retro-reflections in the common optical assembly of the imaging and illuminating systems, and a second one that helps the optical designer to find effective solutions in imaging systems, focused in the reduction of the component sensitivity to the fabrication and assembly processes errors. Analyzing the results from the prototypes the systems and the models proposed were validated, becoming integrant part of an ophthalmic product approved for commercialization, the Kiron fundus camera.

En analyse de tolérances géométriques, une approche consiste à manipuler des polyèdres de R' issus d’ensembles de contraintes linéaires. La position relative entre deux surfaces quelconques d'un mécanisme est déterminée par des opérations (somme de Minkowski et intersection) sur ces polyèdres. Ces polyèdres ne sont pas bornés selon les déplacements illimités dus aux degrés d’invariance des surfaces et aux degrés de liberté des liaisons.Dans une première partie sont introduits des demi-espaces "bouchons" destinés à limiter ces déplacements afin de transformer les polyèdres en polytopes. Cette méthode implique de maîtriser l’influence des demi-espaces bouchons sur la topologie des polytopes résultants. Ceci est primordial pour garantir la traçabilité de ces demi-espaces dans le processus d’analyse de tolérances.Une seconde partie dresse un inventaire des problématiques de mise en oeuvre numérique des polytopes. L’une d’entre elles repose sur le choix d’une configuration de calcul (point et base d’expression, coefficients d’homogénéisation) pour définir un polytope. Après avoir montré que le changement de configuration de calcul est une transformation affine, plusieurs stratégies de simulations sont déclinées afin d’appréhender les problèmes de précision numérique et de temps de calculs. / In geometric tolerancing analysis area, a classical approach consists in handling polyhedrons coming from sets of linear constraints. The relative position between any two surfaces of a mechanism is determined by operations (Minkowski sum and intersection) on these polyhedrons. The polyhedrons are generally unbounded due to the inclusion of degrees of invariance for surfaces and degrees of freedom for joints defining theoretically unlimited displacements.In a first part are introduced the cap half-spaces to limit these displacements in order to transform the polyhedron into polytopes. This method requires controlling the influence of these additional half-spaces on the topology of calculated polytopes. This is necessary to ensure the traceability of these half-spaces through the tolerancing analysis process.A second part provides an inventory of the issues related to the numerical implementation of polytopes. One of them depends on the choice of a computation configuration (expression point and base, homogenization coefficients) to define a polytope. After proving that the modification of a computation configuration is an affine transformation, several simulation strategies are listed in order to understand the problems of numerical precision and computation time.

Ce travail contribue à développer des méthodes de résolution associées à la méthode de simulation MMP (Model of Manufactured Part) développée par F.Vignat et F.Villeneuve. Le MMP est un modèle générique 3D des défauts géométriques engendrés sur les pièces fabriquées par un processus de fabrication donné. Ce modèle permet de générer un ensemble de pièces virtuellement fabriquées incluant les incertitudes de fabrication et permet par conséquent de mener l'analyse de tolérances fonctionnelles. Les méthodes de résolution développées autour du MMP permettent aux ingénieurs de fabrication d'évaluer une gamme de fabrication candidate du point de vue géométrique. Le développement des méthodes de résolution s'est effectué selon 2 axes. Le premier axe consiste à développer des méthodes pour la recherche du pire des cas (WCTA). La première approche de cet axe utilise des méthodes d'optimisation (SQP pour Sequential Quadratic Programming et GA pour les algorithmes génétiques) basées sur la recherche du pire des cas. La recherche du pire des cas consiste en un algorithme d'optimisation multicouche comportant deux boucles principales. La deuxième approche de cet axe consiste à faire une adaptation de la méthode du torseur des petits déplacements avec intervalle (modèle Jacobien Torseur développé au Canada) à la méthode MMP. Le deuxième axe concerne les méthodes stochastiques permettant une simulation de production d'un ensemble de pièces et l'analyse des résultats d'un point de vue statistique. La méthode stochastique est basée sur une méthode de tirage aléatoire sous contraintes. Les différentes approches sont finalement comparées entre elles.

L’analyse de tolérances par des ensembles de contraintes repose sur la détermination de l’accumulation de variations géométriques par des sommes et intersections d’ensembles opérandes 6d. Les degrés de liberté des liaisons et les degrés d’invariance des surfaces génèrent des opérandes non-bornés (polyèdres), posant des problèmes de simulation. En 2014, L. Homria proposé une méthode pour résoudre ce problème, consistant à ajouter des limites artificielles(contraintes bouchon) sur les déplacements non-bornés. Même si cette méthode permet la manipulation d’objets bornés (polytopes), les contraintes bouchon augmentent la complexité des simulations. En réponse à cette difficulté, une méthode dérivée est proposée dans cette thèse.Cette méthode consiste à tracer et simplifier les contraintes bouchon au travers des opérations.Puis une seconde stratégie basée sur la décomposition d’un polyèdre en une somme d’un polytope et de lignes droites (associées aux déplacements non-bornés). Cette stratégie consiste à simuler d’une part les sommes de droites, et d’autre part, à déterminer la somme de polytopes dans un sous-espace de dimension inférieur à 6. Ces trois stratégies sont comparées au travers d’une application industrielle. Cela montre que la traçabilité des contraintes bouchons est un aspect fondamental pour contrôler leur propagation et pour réduire le temps de calcul des simulations. Toutefois, cette méthode exige encore de déterminer les limites des déplacements non-bornés. La deuxième méthode, adaptant systématiquement la dimension de l’espace de calcul, elle permet de diminuer davantage le temps de calcul. Ce travail permet d’envisager la mise en oeuvre de cette méthode selon des formulations statistiques avec la prise en compte des défauts de forme des surfaces. / The cumulative stack-up of geometric variations in mechanical systems can be modelled summing and intersecting sets of constraints. These constraints derive from tolerance zones or from contact restrictions between parts. The degrees of freedom (DOF) of jointsgenerate unbounded sets (i.e. polyhedra) which are difficult to deal with. L. Homri presented in 2014 a solution based on the setting of fictitious limits (called cap constraints) to each DOFto obtain bounded 6D sets (i.e. polytopes). These additional constraints, however, increase the complexity of the models, and therefore, of the computations. In response to this situation,we defined a derived strategy to control the effects of the propagation of the fictitious limits by tracing and simplifying the generated, new cap constraints. We proposed a second strategy based on the decomposition of polyhedra into the sum of a polytope and a set of straight lines.The strategy consists in isolating the straight lines (associated to the DOF) and summing the polytopes in the smallest sub-space. After solving an industrial case, we concluded that tracing caps constraints during the operations allows reducing the models complexity and,consequently, the computational time; however, it still involves working in 6d even in caseswhere this is not necessary. In contrast, the strategy based on the operands decompositionis more efficient due to the dimension reduction. This study allowed us to conclude that the management of mechanisms’ mobility is a crucial aspect in tolerance simulations. The gain on efficiency resulting from the developed strategies opens up the possibility for doing statistical treatment of tolerances and tolerance synthesis.

O principal intento deste trabalho é demonstrar como a combinação de resultados de modelos radiométricos e de análises do limite de resolução de imagens produzem impactos positivos não apenas no projeto óptico de retinógrafos de alta resolução, mas que também geram ferramentas que auxiliam na definição da arquitetura de todo o equipamento, considerando, inclusive, os limites impostos por normas internacionais para a segurança do paciente em relação a radiação emitida na realização dos exames. Particularmente ao projeto óptico, foram desenvolvidos os sistemas de iluminação e imageamento da retina, onde se destacam duas propostas de metodologias: a primeira para a implementação da técnica de eliminação das bem conhecidas retro-reflexões geradas no conjunto óptico que é comum à iluminação e ao imageamento da retina, e a segunda para a obtenção de soluções efetivas em sistemas imageadores, que prima pela diminuição da sensibilidade dos componentes aos erros que são introduzidos pelos processos de fabricação e montagem. Analisando os resultados obtidos com o protótipo, foram validados os sistemas e modelos propostos, que se tornaram parte integrante de um produto oftalmológico aprovado para a comercialização, o retinógrafo Kiron. / The fundamental objective of this work is to demonstrate how radiometric models and analysis of the limit of resolution can provide not only positive impacts to the optical project of high resolution fundus cameras, but also creates tools to perform an optimization of all the equipment, considering the limits imposed by international standards to ensure security to the patient regarding the equipment radiation emission. In the optical project in particular, the imaging and illuminating systems of the retina were developed, in which stands out two proposed methodologies: first, to eliminate the well known retro-reflections in the common optical assembly of the imaging and illuminating systems, and a second one that helps the optical designer to find effective solutions in imaging systems, focused in the reduction of the component sensitivity to the fabrication and assembly processes errors. Analyzing the results from the prototypes the systems and the models proposed were validated, becoming integrant part of an ophthalmic product approved for commercialization, the Kiron fundus camera.

Diplomová práce se zabývá návrhem metodiky výpočtu závislého šíření trhlin ve více konstrukčních částech s využitím programu AFGROW. Prezentována metodika, která také zahrnuje stanovení zbytkové pevnosti, byla aplikována v damage tolerance analýzách vybraných míst na konstrukci křídla L 410 NG.

L’analyse des tolérances a pour but de vérifier lors de la phase de conception, l’impact des tolérances individuelles sur l’assemblage et la fonctionnalité d’un système mécanique. Les produits fabriqués possèdent différents types de contacts et sont sujets à des imperfections de fabrication qui sont sources de défaillances d’assemblage et fonctionnelle. Les méthodes généralement proposées pour l’analyse des tolérances ne considèrent pas les défauts de forme. L’objectif des travaux de thèse est de proposer une nouvelle procédure d’analyse des tolérances permettant de prendre en compte les défauts de forme et le comportement géométriques des différents types de contacts. Ainsi, dans un premier temps, une méthode de modélisation des défauts de forme est proposée afin de rendre les simulations plus réalistes. Dans un second temps, ces défauts de forme sont intégrés dans la modélisation du comportement géométrique d’un système mécanique hyperstatique, en considérant les différents types de contacts. En effet, le comportement géométrique des différents types de contacts est différent dès que les défauts de forme sont considérés. La simulation de Monte Carlo associée à une technique d’optimisation est la méthode choisie afin de réaliser l’analyse des tolérances. Cependant, cette méthode est très couteuse en temps de calcul. Pour pallier ce problème, une approche utilisant des modèles probabilistes obtenus grâce à l’estimation par noyaux, est proposée. Cette nouvelle approche permet de réduire les temps de calcul de manière significative. / Tolerance analysis aims toward the verification of the impact of individual tolerances on the assembly and functional requirements of a mechanical system. The manufactured products have several types of contacts and their geometry is imperfect, which may lead to non-functioning and non-assembly. Traditional methods for tolerance analysis do not consider the form defects. This thesis aims to propose a new procedure for tolerance analysis which considers the form defects and the different types of contact in its geometrical behavior modeling. A method is firstly proposed to model the form defects to make realistic analysis. Thereafter, form defects are integrated in the geometrical behavior modeling of a mechanical system and by considering also the different types of contacts. Indeed, these different contacts behave differently once the imperfections are considered. The Monte Carlo simulation coupled with an optimization technique is chosen as the method to perform the tolerance analysis. Nonetheless, this method is subject to excessive numerical efforts. To overcome this problem, probabilistic models using the Kernel Density Estimation method are proposed.

While variation analysis methods for compliant assemblies are not new, little has been done to include the effects of multi-step, fixtured assembly processes. This thesis introduces a new method to statistically analyze compliant part assembly processes using fixtures. This method, consistent with the FASTA method developed at BYU, yields both a mean and a variant solution. The method, called Piecewise-Linear Elastic Analysis, or PLEA, is developed for predicting the residual stress, deformation and springback variation in compliant assemblies. A comprehensive, step-by-step analysis map is provided. PLEA is validated on a simple, laboratory assembly and a more complex, production assembly. Significant modeling findings are reported as well as the comparison of the analytical to physical results.