Les structures planaires de tailles finies sont de plus en plus utilisées dans les applications des satellites et des radars. Deux grands types de ces structures sont les plus utilisés dans le domaine de la conception RF à savoir Les Surfaces Sélectives en Fréquence (FSS) et les Reflectarrays. Les FSSs sont un élément clé dans la conception de systèmes multifréquences. Elles sont utilisées comme filtre en fréquence, et trouvent des applications telles que les radômes, les réflecteurs pour antenne Cassegrain, etc. Les performances des FSSs sont généralement évaluées en faisant l'hypothèse d'une FSS de dimension infinie et périodique en utilisant les modes de Floquet, le temps de calcul étant alors réduit quasiment à celui de la cellule élémentaire. Plusieurs méthodes permettant la prise en compte de la taille finie des FSSs ont été développées. La méthode de Galerkin basée sur l'approche rigoureuse permet la prise en compte des interactions entre les différents éléments du réseau, mais cette technique ne fonctionne que pour les FSSs de petite taille, typiquement 3x3 éléments. Pour les grands réseaux, cette méthode n'est plus adaptée, car le temps de calcul et l'exigence en mémoire deviennent trop grands. Donc, une autre approche est utilisée, celle basée sur la décomposition spectrale en onde plane. Elle permet de considérer un réseau fini comme un réseau périodique infini, illuminé partiellement par une onde plane. Avec cette approche, des FSSs de grande taille sont simulées, mais elle ne permet pas dans la plupart des cas, de prendre en compte les couplages qui existent entre les différentes cellules du réseau, les effets de bord non plus. La simulation des FSSs par les méthodes numériques classiques basées sur une discrétisation spatiale (méthode des éléments finis, méthode des différences finies, méthode des moments) ou spectrale (méthodes modales) aboutit souvent à des matrices mal conditionnées, des problèmes de convergence numérique et/ou des temps de calcul excessifs. Pour éviter tous ces problèmes, une technique appelée technique par changements d'échelle tente de résoudre ces problèmes. Elle est basée sur le partitionnement de la géométrie du réseau en plusieurs sous-domaines imbriqués, définis à différents niveaux d'échelle du réseau. Le multi-pôle de changement d'échelle, appelé Scale-Changing Networks (SCN), modélise le couplage électromagnétique entre deux échelles successives. La cascade de ces multi-pôles de changement d'échelle, permet le calcul de la matrice d'impédance de surface de la structure complète et donc la modélisation globale du réseau. Ceci conduit à une réduction significative en termes de temps de calcul et d'espace mémoire par rapport aux méthodes numériques classiques. Comme le calcul des multi-pôles de changement d'échelle est mutuellement indépendant, les temps d'exécution peuvent encore être réduits de manière significative en parallélisant le calcul. La SCT permet donc de modéliser des FSSs Finies tout en prenant en compte le couplage entre les éléments adjacents du réseau. / The finite size planar structures are increasingly used in applications of satellite and radar. Two major types of these structures are the most used in the field of RF design ie Frequency Selective Surfaces (FSS) and the Reflectarrays. The FSSs are a key element in the design of multifrequency systems. They are used as frequency filter, and find applications such as radomes, reflector Cassegrain antenna, etc.. The performances of FSSs are generally evaluated by assuming an infinite dimensional FSS using periodic Floquet modes, the computation time is then reduced almost to that of the elementary cell. Several methods have been developed for taking into account the finite dimensions of arrays. For example the Galerkin method uses a rigorous element by element approach. With this method, the exact interactions between the elements are taken into account but this technique works only for small FSS, typically 3x3 elements. For larger surfaces, this method is no more adapted. The computation time and the memory requirement become too large. So another approach is used based on plane wave spectral decomposition. It allows considering the finite problem as a periodic infinite one locally illuminated. With this approach, large FSS are indeed simulated, but the exact interactions between the elements are not taken into account, the edge effects either. The simulation of FSS by conventional numerical methods based on spatial meshing (finite element method, finite difference, method of moments) or spectral (modal methods) often leads in the practice to poorly conditioned matrices, numerical convergence problems or/and excessive computation time. To avoid these problems, a new technique called Scale Changing Technique attempts to solve these problems. The SCT is based on the partition of discontinuity planes in multiple planar sub-domains of various scale levels. In each sub- omain the higher-order modes are used for the accurate representation of the electromagnetic field local variations while low-order modes are used for coupling the various scale levels. The electromagnetic coupling between scales is modelled by a Scale Changing Network (SCN). As the calculation of SCN is mutually independent, the execution time can still be significantly reduced by parallelizing the computation. With the SCT, we can simulate large finite FSS, taking into account the exact interactions between elements, while addressing the problem of excessive computation time and memory

Les systèmes d’ancrages adhésifs sont utilisés dans plusieurs applications en génie civil, notamment en réhabilitation et réparation des ouvrages d’infrastructure tels que des dalles de ponts, chaussées, tunnels, barrages, murs, poteaux, ainsi que dans certains travaux d’exploration géologique et minière. Un système d’ancrage adhésif comprend trois composants : l’élément d’ancrage : une barre d’armature ou une tige filetée ; le matériau adhésif : polymérique, cimentaire ou hybride ; et le substrat : en béton ou en maçonnerie. Les charges imposées sur les barres d’ancrage sont transmises au substrat par adhérence chimique (réactions) et liaison mécanique (interlock) entre les composants mentionnés. Le modèle de design d’adhérence uniforme établit que la performance structurale d’un système d’ancrage adhésif est déterminée par la contrainte de l’adhérence (τ), développée sur toute la surface de contact, entre les composants à l’intérieur du trou d’ancrage. Ce projet, en partenariat avec l’entreprise AMBEX, étudie et évalue la performance des systèmes d’ancrage avec adhésifs en matériau cimentaire, par rapport au comportement sous chargement continu. Pour ce faire, on a ancré des barres d’armature dans un substrat en béton conventionnel. Les deux adhésifs étudiés sont les cartouches d’ancrage AAC et ARC. On a tenu compte des paramètres géométriques et d’installation en assurant la rupture de l’adhérence lors des essais d’arrachement. On a évalué deux conditions en service: température ambiante (21ºC) et élevée (43ºC). On a effectué des essais statiques de traction et des essais sous chargement soutenu. Les résultats sont présentés dans des graphiques « chargedéplacement-temps », afin d’établir des prédictions futures de comportement. Le projet montre les avantages des ancrages adhésifs en matériau cimentaire, tels que le taux de fluage très faible sous chargement soutenu, et quelques limitations aussi, comme la variabilité des résultats à l’arrachement pour les ancrages avec la cartouche AAC. / Abstract : Adhesive anchoring systems are used in many civil engineering applications, including rehabilitation and repair of infrastructure such as bridge decks, roadways, tunnels, dams, walls, columns, and in some geological explorations and mining. An adhesive anchoring system consists of three components: the anchor: a reinforcing bar or a threaded rod; the adhesive material: polymeric, cementitious or hybrid; and a substrate of concrete or masonry. The loads applied on the anchor rods are transmitted by a chemical adhesion to the substrate (reactions) and mechanical interlock between the components mentioned. The design pattern of uniform adhesion establishes that the structural performance of an adhesive anchoring system is determined by the bond strength (τ) developed across the contact surface, between the components within the anchor hole. This project, in partnership with AMBEX, investigates and assesses the performance of an anchoring system, with an adhesive of cementitious material, related to the creep behaviour. To achieve this, steel rebars were anchored in a conventional concrete substrate. Two adhesives were evaluated: AAC and ARC cartridges. Geometrical and installation parameters were taken into account, to ensure bond failure during pullout tests. Two service conditions were studied: room temperature (21ºC) and high temperature (43ºC). Static tensile tests and creep tests were performed. The results are presented in graphs “load-displacement-time”, in order to make predictions of future behavior. The project shows the advantages of adhesive anchors made of cementitious material, as a feeble creep rate at sustained load, and also some limitations, as the variability of tension test results for anchors tested with AAC cartridge.

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

A première vue, les obligations de l’Etat déterminent les comportements de ce dernier, et l’on ne perçoit pas en quoi le droit interne pourrait leur porter atteinte. Pourtant, la production de certains actes juridiques, entendus par le droit international comme réalisant immédiatement des situations individuelles, pourra être considérée comme une violation de ces obligations. Avant même leur exécution, un fait internationalement illicite pourra être consacré. Certaines règles juridiques, en revanche, apparaîtront plus abstraites au regard du droit international, et ne pourront donner lieu, de leur simple fait, qu’à un risque de violation des obligations de l’Etat. Il faudra alors envisager une autre catégorie d’obligations qui, cette fois, se porteront sur l’état du droit interne général. L’existence de règles dont l’état n’est pas celui requis par ces obligations pourra alors donner lieu à un fait internationalement illicite. Se pose toutefois, dans un second temps, la question de la responsabilité qui peut naître de tels faits, dont les conséquences préjudiciables semblent bien limitées. Plus le droit interne à l’origine de l’illicéité sera abstrait, plus la responsabilité de l’Etat s’éloignera d’une quelconque dimension réparatoire, pour se tourner vers une garantie de la légalité future. Vient alors la problématique de la mise en oeuvre de cette responsabilité. Les conditions classiques de recevabilité des demandes devant les juridictions internationales peuvent en effet s’opposer à ce que puisse être prise en compte une violation du fait du droit interne in abstracto. Alors que ces obstacles pourront aisément être levés dans le cas des actes juridiques individuels, les règles internes en conflit avec les obligations de l’Etat seront, à des degrés divers, plus difficiles à mettre en cause dans un cadre contentieux. Toutefois, certaines juridictions ou quasi-juridictions internationales s’affranchissent aujourd’hui de ce cadre, incitant ainsi fortement les Etats à adapter leur droit interne, selon les nouvelles exigences du droit international. / At first sight, international obligations define real actions of States. Domestic law seems, from certain points of view, unable to affect them. However, the mere enactment of national legal acts, understood by international law as immediate realizations of individual situations, may be amount to a breach of these international obligations. Without any enforcement, an international wrongful act will be exposed. Nevertheless, some domestic norms will still be very abstract from an international point of view. Their creation and maintenance in force can’t be seen an international failure rather a risk. Thus, our task will be to find some other kind of State’s obligations, that relates specifically to a given state of general domestic law. An international wrongful act will be then constituted by the very existence of a national norm, if its state is not the one required by international law. Still, the question of State responsibility for such actions, which don’t cause any concrete injury, has to be answered. The more abstract domestic law is, the furthest responsibility will be from a restorative dimension. Responsibility will only be aimed at protecting the international rule of law for the future. Finally, this leads us to the question of the implementation of this responsibility, since classic international litigation law can prevent a claim against domestic law as a wrongful act. This challenge is easily overcome as long as an individual legal act is at stake. On the contrary, a claim against the fact of a general norm is, on different levels, far more difficult to present before international courts. Today however, some international tribunals go beyond this frame, urging States to adapt their domestic law, following the new exigencies of international law.

À partir des observations Z(n) = {(Xi, Yi), i = 1, ..., n} satisfaisant Yi = f(Xi) + ζi, nous voulons reconstruire la fonction f. Nous évaluons la qualité d'estimation par deux critères : le risque Ls et le risque uniforme. Dans ces deux cas, les hypothèses imposées sur la distribution du bruit ζi serons de moment borné et de type sous-gaussien respectivement. En proposant une collection des estimateurs à noyau, nous construisons une procédure, qui est initié par Goldenshluger et Lepski, pour choisir l'estimateur dans cette collection, sans aucune condition sur f. Nous prouvons ensuite que cet estimateur satisfait une inégalité d'oracle, qui nous permet d'obtenir les estimations minimax et minimax adaptatives sur les classes de Hölder anisotropes. / From the observation Z(n) = {(Xi, Yi), i = 1, ..., n} satisfying Yi = f(Xi) + ζi, we would like to approximate the function f. This problem will be considered in two cases of loss function, Ls-risk and uniform risk, where the condition imposed on the distribution of the noise ζi is of bounded moment and of type sub-gaussian, respectively. From a proposed family of kernel estimators, we construct a procedure, which is initialized by Goldenshluger and Lepski, to choose in this family a final estimator, with no any assumption imposed on f. Then, we show that this estimator satisfies an oracle inequality which implies the minimax and minimax adaptive estimation over the anisotropic Hölder classes.

Atualmente, devido à globalização das empresas e de seus produtos, tem havido uma competição acirrada no mercado mundial entre as organizações. Estas empresas se veêm obrigadas a contemplar as expectativas do mercado quanto à alta tecnologia, a qualidade do produto, os baixos custos e a redução dos tempos de desenvolvimento do produto. Todo este mecanismo gera uma busca contínua de desenvolvimento da tecnologia dentro das empresas na área de fabricação, as quais estão intimamente relacionadas ao surgimento de novos materiais de difícil usinagem, assim como de novos revestimentos para ferramentas e de máquinas-ferramentas cada vez mais rápidas e eficientes. A utilização da tecnologia de usinagem com altas velocidades de corte – HSM (High Speed Machining) tem demonstrado grande eficiência para a fabricação de moldes e matrizes com formas complexas, propiciando uma vantagem competitiva para as organizações. Entretanto, o fresamento de formas complexas ainda apresenta vários gargalos na linha produção. Após as operações de desbaste, além do sobremetal deixado para as operações de acabamento, um volume excedente de material indesejado permanece na geometria. Este volume está relacionado à estratégia de desbaste em 2 1/2 eixos, ao grau de curvatura da superfície e à geometria da ferramenta de desbaste. Por não ser uniforme esta quantidade excedente de material acaba prejudicando o processo, especialmente quando uma das exigências é uma extrema precisão dimensional. Este trabalho procura identificar as características mais relevantes para preservar a qualidade superficial em função da flexão da ferramenta, devido a esse excedente de sobremetal. Desta forma, as variáveis de influência consideradas foram o balanço e o diâmetro da ferramenta, sua trajetória e o volume não-uniforme de material a ser removido. Os piores valores de rugosidade ocorreram com o máximo balanço independentemente de sua inclinação. Também foi possível constatar que a estratégia de usinagem ascendente gerou uma melhor rugosidade comparada com a descendente. Contudo em superfícies com pouca inclinação horizontal e com variações bruscas de sobremetal a usinagem descendente obteve melhores resultados do que a ascendente. / Nowadays the companies and their products have become global and, consequently, are facing an intense competition in the world market. These companies are forced to match the expectations of the market regarding technology, product quality, low costs and reduction of product development time. This entire mechanism generates continue search for the development of manufacturing technology, which are intimately linked to the arise of new and difficult to cut materials, as well as of new coatings for tools, fast and more efficient machine-tools. The use of high speed milling has demonstrate to be of great efficiency for the production of moulds and dies with complex forms, leading to a competitive advantage for companies. However, milling complex form still presents several bottle necks in the production line. After the roughing operations, besides the stock removal left for the finishing operations, an extra volume of unwanted material remains on the workpiece. This material is related to the roughing strategy in 2 1/2 axes, to the degree of curvature of the surface and the geometry of the cutting tool. Since the distribution of that material is not uniform, it affects the product quality, especially when one of the requirements is a high dimensional precision. The present work aims at identifying the most important characteristics necessaries to obtain a good high superficial quality despite of the tool flexion during cutting. The tool length and its diameter are considered as well as the cutting strategy to remove the stock and its excess. The highest roughness values occurred with the largest in-balance length, independently on the surface inclination. It was also verified that for some cases upward cutting has produced smaller roughness being compared to the downward strategy. However, on surfaces with little horizontal inclination and with abrupt variations of stock removal the downward cutting can produce better result than upward cutting.

De récents résultats sur l’étude des systèmes de Lur’e (commutés) à temps discret mettent en avant une fonction de Lyapunov de type Lur’e avancée, dont les lignes de niveau peuvent être non convexes et non connexes. Celles-ci soulèvent de larges questions pour les systèmes de Lur’e à temps discret obtenus par la discrétisation d’un système continu. Les contributions de cette thèse sont d’apporter des éléments de réponse à ces questions. Tout d’abord, le verrou des lignes de niveau non-connexes est levé en construisant à partir de celles-ci une suite décroissante d’ensembles connexes et bornés qui converge vers l’origine et qui contient le futur de la trajectoire à temps continu. Dans un second temps, le problème de la stabilisation conjointe d’un système de Lur’e à données échantillonnées avec un échantillonnage non-uniforme est traité. Quand la période d’échantillonnage est à choisir parmi un nombre fini de valeurs, il est montré que ce problème se traduit comme la stabilisation conjointe d’un système commuté de Lur’e avec des incertitudes bornées en norme. En associant de plus à chaque mode un critère quadratique, une stratégie de type min-switching permet de résoudre cette question à l’aide d’un problème d’optimisation sous contraintes LMI. Enfin, les propriétés de la stratégie de min-switching pour les systèmes de Lur’e commutés à temps discret sont étudiées. Une extension de la notion de consistance permet de prouver que cette stratégie est consistante vis-à-vis de majorants quadratiques modaux du critère de performance et ainsi de garantir l’intérêt de la stratégie d’échantillonnage non-uniforme développée / Recent studies dealing with discrete-time (switched) Lur’e systems involve an adapted Lur’e type function exhibiting possibly non-convex and disconnected level sets. These properties raise fundamental issues in the case of discrete-time Lur’e system obtained by the sampling of a continuous time one. This PhD thesis aims at answering these questions. The first contribution is to avoid the discrete-time disconnected level sets by a decreasing sequence of bounded and connected sets that converges to the origin and that contain the future of the continuous-time trajectory. The second contribution deals with the joint stabilization of a sampled-data Lur’e system with non-uniform sampling. When the sampling period belongs to a finite set of values, this problem is reformulated as the joint stabilization of a discrete-time Lur’e switched system with norm-bounded uncertain parameters. Futhermore, if a quadratic criterion is associated with each mode, a min-switching strategy combined with LMI constraints allow to provide a solution to this problem. Finally the property of consistency for discrete-time switched Lur’e systems is investigated. It is shown that the min-switching strategy is consistent with respect to quadratic upper bounds of the performances. This result is applied on the stabilization of Lur’e systems with non-uniform sampling.

Made available in DSpace on 2016-04-26T20:22:34Z (GMT). No. of bitstreams: 1 Claudia Aparecida Cimardi.pdf: 1385322 bytes, checksum: a491bfd495839b832e44a24d24a264e0 (MD5) Previous issue date: 2014-02-18 / This thesis aims to analyze the current role of jurisprudence in the face of Brazilian legal system. First, the historical aspects that led to the evolution of the concept of legal system were presented. From these considerations, the following approaches were conducted: (i) historical delineation of the development of law enforcement, especially in the Civil Law legal system, showing how mass society demanded that the Brazilian legislator implanted new trial procedural techniques; (ii) presentation of the concepts of jurisprudence and judicial precedents to the Brazilian legal system; (iii) demonstration of need for the jurisprudence to be dedicated to standardization, function to be exercised by superior courts (Supreme Justice Court and Supreme Federal Court; (iv) demonstration that the performance of this function results a paradigm for future trials and, therefore, comply with the ideals of stability and predictability of the legal system; (v) exposure that uniform jurisprudence of higher courts can and must undergo changes, being inadmissible sudden and unjustified changes; (vi) demonstration of the importance of judicial precedents in the Brazilian legal system, as conductors of uniform jurisprudence; (vii) exposure of standardization techniques of jurisprudence governed by civil process, and (viii) new discipline of the subject, presented in the Draft ot Civil Process Law. As a result of the research, it was found that uniform jurisprudence of higher courts integrates the meaning of rules, reason why it is the structuring element of the legal system, hence it should be observed in future trials, throughout society and the Administration. We sought, therefore, to develop a methodical study, based on extensive local and foreign literature, which intended to establish a current legal framework of the uniform jurisprudence of higher courts and techniques for jurisprudence standardization / Esta tese tem como objetivo principal analisar o atual papel da jurisprudência em face do sistema jurídico brasileiro. Primeiramente, foram apresentados os aspectos históricos que resultaram na evolução do conceito de sistema jurídico. A partir de tais considerações, foram realizadas as seguintes abordagens: (i) delineamento histórico do desenvolvimento da aplicação do direito em concreto, especialmente no sistema jurídico do civil Law, evidenciando como a sociedade de massa exigiu que o legislador brasileiro implantasse novas técnicas processuais de julgamento; (ii) exposição dos conceitos de jurisprudência e precedentes judiciais para o sistema jurídico brasileiro; (iii) demonstração da necessidade de a jurisprudência ser vocacionada à uniformização, função a ser desempenhada pelos tribunais superiores (Superior Tribunal de Justiça e Supremo Tribunal Federal; (iv) demonstração de que a jurisprudência uniforme resulta em paradigma de julgamentos futuros e, por essa razão, cumprir com os ideais da previsibilidade e estabilidade do sistema jurídico; (v) exposição de que a jurisprudência uniforme dos tribunais superiores podem e devem sofrer mudanças, sendo inadmissíveis as transformações bruscas e injustificadas; (vi) demonstração da importância dos precedentes judiciais no sistema jurídico brasileiro, como condutores da jurisprudência uniforme; (vii) exposição das técnicas de uniformização de jurisprudência disciplinadas pelo processo civil; e (viii) nova disciplina do tema, apresentada no Projeto de Código de Processo Civil. Como resultado da pesquisa, constatou-se que a jurisprudência uniforme dos tribunais superiores integra o sentido das normas, razão pela qual é elemento estruturante do sistema jurídico e, por isso, deve ser observada em julgamentos futuros, por toda a sociedade e pela Administração. Buscou-se, assim, elaborar um trabalho metódico, baseado em ampla bibliografia nacional e estrangeira, que pretendeu estabelecer o enquadramento jurídico atual da jurisprudência uniforme dos tribunais superiores e das técnicas de uniformização de jurisprudência

En réponse au nombre toujours élevé de décès provoqués par les accidents routiers, l'industrie automobile a fait de la sécurité un sujet majeur de son activité global. Les radars automobiles qui étaient de simples capteurs pour véhicule de confort, sont devenus des éléments essentiels de la norme de sécurité routière. Le domaine de l’automobile est un domaine très exigent en terme de sécurité et les radars automobiles doivent avoir des performances de détection très élevées et doivent répondre à des nombreuses contraintes telles que la facilité de production et/ou le faible coût. Cette thèse concerne le développement d’algorithmes pour la détection et la localisation de piétons et de cyclistes pour des radars automobiles de nouvelle génération. Nous avons proposé une architecture de réseau d'antennes non uniforme optimale et des méthodes d'estimation spectrale à haute résolution permettant d’estimer avec précision la position angulaire des objets à partir de la direction d'arrivée (DoA) de leur réponse. Ces techniques sont adaptées à l'architecture du réseau d'antennes proposé et les performances sont évaluées à l'aide de données radar automobiles simulées et réelles acquises dans le cadre de scénarios spécifiques. Nous avons également proposé un détecteur de cible de collision, basé sur la décomposition en sous-espaces Doppler, dont l'objectif principal est d'identifier des cibles latérales dont les caractéristiques de trajectoire représentent potentiellement un danger de collision. Une méthode de calcul d'attribut de cible est également développée et un algorithme de classification est proposé pour discriminer les piétons, cyclistes et véhicules. Les différents algorithmes sont évalués et validés à l'aide de données radar automobiles réelles sur plusieurs scenarios. / In response to the persistently high number of deaths provoked by road crashes, the automotive industry has promoted safety as a major topic in their global activity. Automotive radars have been transformed from being simple sensors for comfort vehicle, to becoming essential elements of safety standard. The design of new generations automotive radars has to face various constraints and generally proposes a compromise between reliability, robustness, manufacturability, high-performance and low cost. The main objective of this PhD thesis is to design algorithms for the detection and localization of pedestrians and cyclists using new generation automotive radars. We propose an optimal non-uniform antenna array architecture and some high resolution spectral estimation methods to accurately estimate the position of objects from the direction of arrival (DOA) of their responses to the radar. These techniques are adapted to the proposed antenna array architecture and the performance is evaluated using both simulated and real automotive radar data, acquired in the frame of specific scenarios. We propose a collision target detector, based on the orthogonality of angle-Doppler subspaces, whose main goal is to identify lateral targets, whose trajectory features represent potentially a danger of collision. A target attribute calculation method is also developed and classification algorithm is proposed to classify pedestrian, cyclists and vehicles. This classification algorithm is evaluated and validated using real automotive radar data with several scenarios.

Atualmente, devido à globalização das empresas e de seus produtos, tem havido uma competição acirrada no mercado mundial entre as organizações. Estas empresas se veêm obrigadas a contemplar as expectativas do mercado quanto à alta tecnologia, a qualidade do produto, os baixos custos e a redução dos tempos de desenvolvimento do produto. Todo este mecanismo gera uma busca contínua de desenvolvimento da tecnologia dentro das empresas na área de fabricação, as quais estão intimamente relacionadas ao surgimento de novos materiais de difícil usinagem, assim como de novos revestimentos para ferramentas e de máquinas-ferramentas cada vez mais rápidas e eficientes. A utilização da tecnologia de usinagem com altas velocidades de corte – HSM (High Speed Machining) tem demonstrado grande eficiência para a fabricação de moldes e matrizes com formas complexas, propiciando uma vantagem competitiva para as organizações. Entretanto, o fresamento de formas complexas ainda apresenta vários gargalos na linha produção. Após as operações de desbaste, além do sobremetal deixado para as operações de acabamento, um volume excedente de material indesejado permanece na geometria. Este volume está relacionado à estratégia de desbaste em 2 1/2 eixos, ao grau de curvatura da superfície e à geometria da ferramenta de desbaste. Por não ser uniforme esta quantidade excedente de material acaba prejudicando o processo, especialmente quando uma das exigências é uma extrema precisão dimensional. Este trabalho procura identificar as características mais relevantes para preservar a qualidade superficial em função da flexão da ferramenta, devido a esse excedente de sobremetal. Desta forma, as variáveis de influência consideradas foram o balanço e o diâmetro da ferramenta, sua trajetória e o volume não-uniforme de material a ser removido. Os piores valores de rugosidade ocorreram com o máximo balanço independentemente de sua inclinação. Também foi possível constatar que a estratégia de usinagem ascendente gerou uma melhor rugosidade comparada com a descendente. Contudo em superfícies com pouca inclinação horizontal e com variações bruscas de sobremetal a usinagem descendente obteve melhores resultados do que a ascendente. / Nowadays the companies and their products have become global and, consequently, are facing an intense competition in the world market. These companies are forced to match the expectations of the market regarding technology, product quality, low costs and reduction of product development time. This entire mechanism generates continue search for the development of manufacturing technology, which are intimately linked to the arise of new and difficult to cut materials, as well as of new coatings for tools, fast and more efficient machine-tools. The use of high speed milling has demonstrate to be of great efficiency for the production of moulds and dies with complex forms, leading to a competitive advantage for companies. However, milling complex form still presents several bottle necks in the production line. After the roughing operations, besides the stock removal left for the finishing operations, an extra volume of unwanted material remains on the workpiece. This material is related to the roughing strategy in 2 1/2 axes, to the degree of curvature of the surface and the geometry of the cutting tool. Since the distribution of that material is not uniform, it affects the product quality, especially when one of the requirements is a high dimensional precision. The present work aims at identifying the most important characteristics necessaries to obtain a good high superficial quality despite of the tool flexion during cutting. The tool length and its diameter are considered as well as the cutting strategy to remove the stock and its excess. The highest roughness values occurred with the largest in-balance length, independently on the surface inclination. It was also verified that for some cases upward cutting has produced smaller roughness being compared to the downward strategy. However, on surfaces with little horizontal inclination and with abrupt variations of stock removal the downward cutting can produce better result than upward cutting.