Rozprawy doktorskie na temat „Static and dynamic transmission error”

The gear noise problem that widely occurs in power transmission systems is typically characterised by one or more high amplitude acoustic signals. The noise originates from the vibration of the gear pair system caused by transmission error excitation that arises from tooth profile errors, misalignment and tooth deflections. This work aims to further research the effect of tooth profile modifications on the transmission error of gear pairs. A spur gear pair was modelled using finite elements, and the gear mesh was simulated and analysed under static conditions. The results obtained were used to study the effect of intentional tooth profile modifications on the transmission error of the gear pair. A detailed parametric study, involving development of an optimisation algorithm to design the tooth modifications, was performed to quantify the changes in the transmission error as a function of tooth profile modification parameters as compared to an unmodified gear pair baseline. The work also investigates the main differences between the static and dynamic transmission error generated during the meshing of a spur gear pair model. A combination of Finite-Element Analysis, hybrid numerical/analytical methodology and optimisation algorithms were used to scrutinise the dynamic behaviour of the gear pairs under various operating conditions.

Due to their large torque-speed ratio and transmission efficiency, planetary gears are widely used in the automotive industry. However, high amplitude vibrations remain their critical weakness, which limits their usage especially when new strict noise legislations come into action. A new approach to handle the instability problems of planetary gears encountered in real industrial context is presented in this work. First, the dynamic response of a planetary gear failing to pass the noise regulations is theoretically investigated through an analytical model. The equations of motion were solved using the Spectral Iterative Method. The observed experimental results correlated well with those from the developed model. In order to limit the resonance phenomena, impacts of different macro and micro-geometry modifications were analytically investigated: quadratic teeth profile, different planets positioning, different number of teeth and number of planets. Optimum modifications were retrieved and are expected to be tested experimentally on a test bench and on the truck. Finally, the analytical model’s limits and sensitivity to different parameters were investigated in order to certify its reliability, and suggestions for improvements were presented.

Noise from heavy trucks is an important environmental issue. Several sources contribute to the total noise level of a vehicle, such as the engine, gearbox, tires, etc. The tonal noise from the gearbox can be very disturbing for the driver, even if the noise level from the gearbox is lower than the total noise level. The human ear has a remarkable way of detecting pure tones of which the noise from loaded gears consists of. To be allowed to sell a heavy truck within the European Union, the so called pass-by noise test must be completed successfully. The maximum noise level permitted is 80dB(A) and undercertain conditions, the gearbox can be an important contributor to the total noise level. Gear noise is therefore an important issue for the automotive industry. In this thesis gear noise and dynamic transmission error is investigated. Traditionally, transmission error (TE) is considered to be the main excitation mechanism of gear noise. The definition of TE is ”the difference between the actual position of the output gearand the position it would occupy if the gear drive were perfect”. Measurements of dynamic transmission error (DTE) and noise have been performed on a gearbox. The measurement object was a commercial truck gearbox powered by an electrical motor. The torque used was in the normal operating range of the gearbox and the correlation between gear noise and DTE, when the torque is changed, is investigated. The result differs for different gear pairs and for the first gear stage, located close to the housing, the correlation is high for most speeds. The measured DTE and noise show a poor correlation with calculated transmission error. A minimisation of TE therefore does not necessarily mean a minimisation of gear noise. A transfer function can be employed to calculate the relationship between DTE and noise. The general trend of the gear noise is an increase of 6dB per doubling of the rotational speed together with fluctuations around the mean due to resonances of the system. The magnitude of the transfer function can be estimated using the amplitudesof the gear mesh orders and harmonics. Two gear pairs with similar macro geometry but different profile modifications are investigated. Although the gear pairs have similar transmission error, the noise level display a significantly different trend, further strengt hening the position that transmission error is not the single most important gear noise excitation mechanism. Further analysis concludes that shuttling forces and friction forces can be more important than what is often suggested. A dynamic model including transmission error and shuttling forces is used to investigate the two gear pairs. The bearing forces show that for some frequency regions shuttling forces can be of the same order of magnitude as the forces caused by transmission error. This work highlights the importance of considering other excitations of gear noise besides transmission error when designing quiet gears. The influence of transmission error can not be determined by investigating the gears only. A deeper knowledge of the gear system is needed in order to minimise gear noise for a specific gear design.
QC 20100719

COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
Tradicionalmente, as avaliações da confiabilidade composta de sistemas de potência têm enfatizado a análise de adequação, avaliando a capacidade dos sistemas de geração e transmissão em suprir todas as cargas considerando apenas os requisitos de desempenho estático. Este trabalho apresenta uma nova metodologia, que estende o conceito e as técnicas de avaliação da confiabilidade composta de modo a incluir os aspectos ligados a segurança. Isto exige a caracterização probabilística do desempenho dinâmico dos sistemas em termos da estabilidade transitória, bem como um melhor entendimento dos efeitos cascata decorrentes do desdobramento de uma seqüência de eventos. A metodologia apresentada baseia-se num processo de simulação seqüencial, que permite representar os possíveis desdobramentos de estados instáveis e especialmente os processos não-Markovianos envolvidos, como os processos de restauração. É calculado um conjunto de índices que mede o nível de segurança do sistema, e ainda permite avaliar o desempenho dos sistemas de proteção, esquemas de emergência e processos de restauração. A metodologia é aplicada ao sistema IEEE-MRTS, Permitindo identificar os fatores que mais influenciam a segurança do sistema, e ainda as relações entre os problemas de adequação e segurança.
Traditionally, bulk power reliability evaluations have concentrated on the analysis of system adequacy, the ability of the generating and the transmission systems to supplhy all loadas within performance requirements. This work presents a new methodology that extends the scope of reliability evaluations to include probabilistic assessment of system security, involving considerations of transient stability and the effects of cascading sequences. The methodology is based on a sequential simulation process which is suitable for representing the effects of system disturbances and non-Markovian processes, like the restoration process. The calculated set of reliability indices may be used to measure the security level, and to evaluate the performance of the protection systems, emergency control schemes and restoration processes. The test system IEEE-MRTS is used to illustrate the application of the proposed methodology, identifying the features that are most influent to system security, and also the relationship between adequacy and security problems.

La plupart des environnements naturels et artificiels présentent du rayonnement ionisant (RI) interagissant avec l'électronique. Les effets du RI sont étudies depuis longtemps surtout pour des applications de critiques et de sécurité dans le domaine de l'espace, nucléaire, militaire et médical. L'étude des effets de rayonnement sur les appareils électroniques est complexe et demande la combinaison d'une connaissance pluridisciplinaire allant de la physique nucléaire à l'architecture à haut niveau, l'électronique et la science de matériaux. La réduction de la taille des transistors et l'augmentation simultanée de la complexité des systèmes contribuent à rendre plus critiques les problématiques. En occupant la plus grande surface de systèmes sur puce, les mémoires électroniques représentent la source principale des fautes induits par la radiation. Par conséquent, la compréhension des effets du rayonnement ionisant sur les mémoires et leur atténuation sont essentielles. Ces travaux de thèse introduisent des nouvelles méthodes de test à niveau de simulation et expérimental. En particulier, à niveau de simulation, est proposée une méthodologie pour l'estimation du taux de soft erreurs (SER) des circuits électroniques. Cette méthode prend en compte les variations environnementales et paramétriques des circuits pendant leur exposition au rayonnement ionisant. La méthode est évaluée à travers le cas d'étude représentée par une cellule SRAM de technologie 40nm interagissant avec des neutrons atmosphériques. Au niveau expérimental, des nouvelles méthodes pour le test sous accélérateur de SRAMs sont présentées, tout en mettant l'accent sur les défaillances que le test dynamique peut révéler. Les méthodes proposées s'appuient sur les algorithmes de type March et des séquences d'adressage spécifique des mémoires. Le choix des méthodes des tests dynamiques plutôt que des tests statiques est justifié par leur capacité de sensibiliser les effets électriques et du fait qu'ils sont très représentatifs du comportement réel des mémoires de vrais systèmes électroniques. Dans ces études, sont analyses en détail des évènements de large échelle qui apparaissent pendant les tests en accélérateurs et qui menaient à des MCUs (Multiple Cell Upsets), des effets singuliers permanent SEL (Single Event Latchups) et des effets singuliers de type SEFI (Single Event Functional Interrupt). Les protons à basses menaçant les technologies le plus récentes, donc, ici, leur contribution aux effets singuliers est aussi étudiée toujours en appliquant les nouvelles méthodes des tests proposés. Avec l'expérience acquise pendant les tests accélérés, un capteur des Hadrons à Haute Energie a été proposé et par la suite testé sur le faisceau de la structure H4IRRAD du CERN. La fonction principale de ce moniteur est basée sur l'extraction de la fluence des hadrons en tant qu'une fonction des effets singuliers SEU enregistrés. En outre, sont également présentés les résultats d'un test en temps réel fait à la station Concordia en Antarctique. Dans ce cas, l'instrument de détection était une version modifié du précédent capteur. Les résultats récoltés ont démontré que cet instrument de détection peut être utilisé dans des environnements et des conditions de rayonnement diverses. Enfin, des technologies de mémoire émergeantes ont été évaluées par rapport à leur réponse au rayonnement ionisant
Most of the known natural and artificial environments present ionizing radiation interacting with electronics. The effects of ionizing radiation have been a concern for many years especially for safety and critical applications such as space, nuclear, avionics, military and medical. The study of radiation effects on electronic devices is complex and requires the combination of multidisciplinary knowledge from nuclear physics to high-level system design, electronics and science of materials. The downscaling of the transistor size and the concurrent increase of systems' complexity contributes to worsen this problematic.By occupying the largest area of Systems on Chip, electronic memories represent the biggest source of radiation induced failures. Consequently, the understanding of ionizing radiation effects on memory devices and their mitigation is crucial. This thesis introduces novel test methods for both the simulation and the experimental level. More specifically, at the simulation level a framework is proposed for the estimation of the Soft Error Rate of electronic devices. This framework considers environmental and parametric variations of the device, while subjected to ionizing radiation. The framework is evaluated by considering the case study of a 40nm SRAM cell interacting with atmospheric neutrons. At the experimental level, novel methods for the accelerated testing of SRAM devices are presented, emphasizing to the failures that dynamic mode testing is able to reveal. These proposed methods are based on March algorithms in combination with specific addressing schemes for the memories.The choice to focus on dynamic testing methods is justified by their capability to sensitize electric effects that static mode testing is not able to do, and because they are highly representative of the realistic behavior of memories in actual electronic systems. Large scale events occurring during accelerated testing as a result of Multiple Cell Upsets, Single Event Latchups and Single Event Functional Interrupts are thoroughly analyzed. With low energy protons posing a threat for latest technologies, their contribution to Soft Errors is also studied by applying the proposed testing methods. Using the experience acquired from accelerated testing, a monitor for the sensing of the High Energy Hadrons was proposed and next tested at H4IRRAD beam line (CERN). The main functionality of this monitor is based on the extraction of the hadrons fluence as a function of the recorded Single Event Upsets. Furthermore, the results from a real-time test at the Concordia station in Antarctica are also presented. This time the sensing instrument was a customized version of the previous monitor and the retrieved results proved the usability of the instrument under different radiation environments and conditions. Finally emerging memory technologies are assessed for their response under ionizing radiation

Variability affects the performance and power of a circuit. Along with static variations, dynamic variations, which occur during chip operation, necessitate a safety margin. The safety margin makes it difficult to meet the target performance within a limited power budget. This research explores methodologies to minimize the safety margin, thereby improving the energy efficiency of a system. The safety margin can be reduced by either minimizing the variation or adapting to the variation. This research explores three different methods to compensate for variations efficiently. First, post-silicon tuning methods for minimizing variations in 3D ICs are presented. Design methodologies to apply adaptive voltage scaling and adaptive body biasing to 3D ICs and the associated circuit techniques are explored. Second, non-design-intrusive circuit techniques are proposed for adaptation to dynamic variations. This work includes adaptive clock modulation and bias-voltage generation techniques. Third, design-intrusive methods to eliminate the safety margin are proposed. The proposed methodologies can prevent timing-errors in advance with a minimized performance penalty. As a result, the methods presented in this thesis minimize static variations and adapt to dynamic variations, thereby, enabling robust low-power operation of digital systems.

Les spectres de bruit mesurés en cabine d’hélicoptère montrent que la boîte de transmission principale (BTP) est un des principaux contributeurs au bruit perçu par les usagers. Elle génère en effet plusieurs raies émergeant fortement du bruit large bande et dont les fréquences se situent dans la plage de sensibilité maximale de l’oreille humaine. Dans un contexte d’amélioration permanente du confort acoustique des usagers, un modèle numérique est développé pour prédire le comportement dynamique des BTP. Les équations du mouvement sont écrites sur la base de fonctions du temps représentatives des excitations générées par l’engrènement (raideur d’engrènement et erreurs de transmission). Plusieurs éléments de validation sont présentés pour confirmer la pertinence de la formulation proposée. Différents résultats numériques et expérimentaux de la littérature sont utilisés à des fins de comparaison, montrant que le modèle s’applique aux systèmes à simple étage de réduction, par engrenage cylindrique ou spiro-conique. La validation est ensuite étendue aux systèmes à deux étages de réduction et les résultats confirment que la formulation basée sur les erreurs de transmission permet de tenir compte des corrections de profil. Finalement, le modèle est utilisé pour diverses applications. Premièrement, l’influence des erreurs de pas sur le comportement dynamique de transmissions par engrenages est discutée, ainsi que l’influence combinée du niveau de chargement appliqué. Dans un second temps, la relation entre l’erreur de transmission dynamique et différents coefficients dynamiques est étudiée. Le contenu spectral de la réponse au niveau des roulements est ensuite analysé pour des systèmes à deux engrènements cylindriques et l’influence de différents paramètres est discutée. Enfin, une application est réalisée sur un système comprenant un engrenage cylindrique et un engrenage spiro-conique. Les phénomènes de couplage entre les étages successifs sont mis en évidence ainsi que la contribution des deux engrènements au contenu spectral de la réponse aux roulements
Noise measurements have shown that helicopters main gearboxes highly contribute to the overall cabin noise. Gear mesh vibrations propagate through the shafts to the rolling element bearings and the casing which becomes a source of radiated noise. The latter is characterized by high-amplitude tones emerging from broadband noise whose frequencies lie in the range of maximum human ear sensitivity. In the context of continuous improvement in the acoustic comfort of helicopter passengers, it is therefore necessary to analyse and optimize gearbox vibrations in order to reduce casing noise radiations. The research work presented in this memoir is focused on the development of a numerical model dedicated to the prediction of gear system dynamic behaviour, comprising several gear stages and different types of gears. This model relies on classic beam and lumped parameter elements along with specific two-node gear elements for both cylindrical (spur, helical) and spiral-bevel gears. The equations of motion are developed based on time-varying functions representative of mesh excitations which comprise: (a) mesh stiffness functions, (b) quasi-static transmission error under load, and (c) kinematic (or no-load) transmission error. A number of comparisons with benchmark numerical and experimental results from the literature are presented which demonstrate that the proposed approach is sound as far as single-stage systems with spur, helical or spiral-bevel gears are considered. Validations are then extended to double-stage gears and, here again, it is confirmed that the proposed transmission error based formulation is accurate and can account for tooth shape modifications. In the second part of the memoir, several examples of application are presented and commented upon. First, the combined influence of tooth pitch errors and load on the dynamic behaviour of gear transmissions is tackled. An extended three-dimensional model and a reduced torsional version are then confronted in order to investigate the dependency between dynamic transmission errors and mesh force / root stress dynamic factors. Further investigations on bearing dynamic response in two-stage spur gear systems are conducted and the particular contributions of profile modifications are analysed. Finally, a system combining a cylindrical gear and a spiral-bevel gear is considered and particular attention is paid to the dynamic couplings between the various meshes and their influence on bearing dynamic responses

Thesis (M.S.)--Ohio State University, 1995.
Advisor: Donald R. Houser, Dept. of Mechanical Engineering. Includes bibliographical references (leaves 99-100). Available online via OhioLINK's ETD Center

Based on conventional static line rating method, the actual current carrying capability of overheadconductors cannot be judged. Due to continuous increment in electricity demand and the difficultiesassociated with new line constructions, the overhead lines are therefore required to be rated based on amethod that should establish their real-time capability in terms of electricity transmission. The methodused to determine the real-time ampacity of overhead conductors not only can enhance their transmissioncapacity but can also help in allowing excessive renewable generation in the electricity network. In thisdiploma work, the issues related to analyzing an impact of wind power on periodical loading of overheadline as well as finding its static and dynamic ampacities with line current are investigated in detail.Initially, in this project, the investigation related to finding a suitable location for the construction of a 60MW wind farm is taken on board. Thereafter, the wind park is integrated with a regional grid, owned byFortum Distribution AB. In addition to that, the electricity generated from the wind park is also calculatedin this project. Later on, the work is devoted to finding the static and dynamic line ratings for‘VL3’overhead conductor by using IEEE-738-2006 standard.Furthermore, the project also deals with finding the line current and making its comparison withmaximum capacity of overhead conductor (VL3) for loading it in such a way that no any violation of safeground clearance requirements is observed at all. Besides, the line current, knowing the conductortemperature when it transmits the required electricity in the presence of wind power generation is also animportant factor to be taken into consideration. Therefore, based on real-time ambient conditions withactual line loading and with the help of IEEE-738-2006 standard, the conductor temperature is alsocalculated in this project.At the end, an economic analysis is performed to evaluate the financial advantages related to applying thedynamic line ratings approach in place of traditional static line ratings technique across an overheadconductor (VL3) and to know how much beneficial it is to temporarily postpone the rebuilding and/orconstruction of a new transmission line. Furthermore, an economic analysis related to wind power systemis taken into consideration as well to get familiar with the costs related to building and connecting a 60MW wind farm with the regional grid.

This master’s thesis is deal with the area of determining the static transmission error in spur gears. Nowadays, around vibration and noise formation, the issue of transmission error is being discussed quite often. In the first part of this master’s thesis, there is a description of the theoretical requirements concerning the above stated issue. These theoretical requirements are further applied in parametric planning of the spur gears as well as in measuring the transmission error itself. In this master’s thesis, both the detailed description of planning the parametric model of spur gears and the strain-stress analysis may be found. These requirements are needed for calculating the transmission error. In conclusion of this master’s thesis, specific results of the static transmission error in spur gears achieved at diversifying load torque, center distance modifications as well as tip relief modifications of spur gears are being presented. The issue was solved by computation approach with the help of CAD software called Creo Parametric and FEM software called Ansys Workbench and Ansys Mechanical APDL.

La boîte de transmission principale (BTP) est une des principales sources dubruit perçu dans les cabines d’hélicoptères et pénalise fortement le confort acoustique deséquipages et passagers. Afin de réduire l’impact de cette source, les phénomènes acoustiqueset vibratoires mis en jeu par les boîtes de transmission à engrenages doivent être compris etsimulés durant les phases de développement. De cette façon, le comportementvibroacoustique des BTP pourra être amélioré dès la conception, réduisant ainsi le coût, lamasse et les difficultés d’intégration des solutions d’insonorisation. Ce travail présente lesBTP d’hélicoptères ainsi que le bruit qu’elles génèrent. Il présente également nosdéveloppements concernant la modélisation du comportement dynamique des BTP afin d’encalculer le bruit. Nous avons développé un code éléments finis permettant d’effectuer desétudes paramétriques afin d’ajuster le design des boîtes de transmission lors des phases dedéveloppement. Notre modèle est capable de calculer les efforts dynamiques aux paliers detransmissions composées de plusieurs engrenages cylindriques et spiro-coniques. Enfin, nousanalysons des mesures acoustiques et vibratoires effectuées autour de deux BTP pourplusieurs conditions de couple et vitesse. Ces mesures nous permettent de mieux comprendrele comportement vibroacoustique des BTP et de confirmer certaines tendances observées avecnotre modèle
Main gearbox (MGB) is one of the main noise sources in helicopter cabinsand it strongly penalizes acoustic comfort of crews and passengers. In order to reduce theimpact of this source, acoustic and vibration mechanisms of gearboxes have to be understoodand simulated during the development phases. By this way, MGB vibroacoustic behaviourcould be improved by design, thus reducing cost, additional weight and integration difficultiesof sound-proofing solutions. This work presents helicopters MGB and the noise they generate.It also presents our developments regarding the modelling of MGB dynamic behaviour fornoise computation. We have developed a finite elements code allowing to conduct parametricstudies to tune the gearboxes design in early development phases. Our model is able tocompute dynamic loads on bearings of any transmission composed of several cylindrical andspiral bevel gears. At last, we analyse acoustic and vibration measurements done around twoMGB for several conditions of torque and speed. These measurements allow to betterunderstand MGB vibroacoustic behaviour and to confirm some trends observed with ourmodel

This work describes the use of Multi-Body Simulation (MBS) to create a virtual prototype of a geared drive called Power transfer unit (PTU). PTU is a subsystem of the all-wheel drive driveline responsible for transfer of power between front and rear axles in an Automobile. The objective of the developing the prototype is to simulate the dynamic behavior of the PTU. Focus is on predicting the gear transmission error(TE) and gearbox housing vibration level. A Hypoid gear set, bearings, tubular shaft and housing are the major components in the PTU. This work is carried out at GKN Automotive which specializes in development of Automotive All wheel drive systems. When developing such geared systems one important characteristic analyzed is the noise and vibration it generates. And for companies like GKN it is desirable to predict these characteristics as early as possible for two reasons, to avoid late design changes and to speed up the product development cycle. To achieve this, a validated virtual model which is computationally efficient is desired. The methodology followed contains of two facets, development of the MBS model and validation of the developed model with physical testing. An integrated MBS-FEM approach is used, an FE modal reduction technique is used to create flexible components with which a virtual prototype is built and simulated in an MBS tool MSC ADAMS c . Gear contact and bearings are defined using an analytical approach which considers the nonlinear stiffness and damping. A dynamic analysis and system level modal analysis is performed to predict the TE, housing vibrations and PTU modal parameters. Experimental modal analysis and physical testing on test rig are performed to measure the actual values of the above predicted outputs. Parameters like damping, contact stiffness of the model are then tuned to achieve correlation. When comparing test and prediction, close correlation is seen in the TE and for housing vibration a similar trend is observed with some deviations. Predicted TE is heavily dependent on gear contact parameters. On the modal parameter comparison, a correlation of five modes and mode shapes below 2500Hz is seen which shows the validity of the MBS model. Parameter studies are performed to study the effect of bearing damping and preload on housing vibrations and TE. It is observed that an optimum value of preload and damping is essential to avoid unnecessary vibrations. In conclusion, the model with some fine tuning of damping parameters can be used for virtual noise and vibration analysis of the PTU.
Detta arbete beskriver anv¨andningen av beräkningsmetoden Multi-Body Simulation (MBS) för att skapa en virtuell prototyp av en vinkelväxel (Power Transfer Unit, PTU ). PTU är ett delsystem för fyrhjulsdrift som har funktionen att överföra kraft mellan fram- och bakaxlar i en bil. Målet med att utveckla modellen är att simulera PTUns dynamiska beteende. Fokus ligger på att beräkna vinkelväxelns transmissionsfel och vibrationsnivåer på växellådans hus. De vikitgaste komponenterna i PTUn är hypoidväxeln med kronhjul och pinjong, röraxel, lager och hus. Detta arbete har utförts på GKN Automotive som är specialiserade på utveckling av drivsystem för fyhjulsdrivna bilar. Ljud och vibrationer är viktiga egenskaper att ta hänsyn till under utvecklingen. För företag som GKN är det önskvärt att kunna beräkna dessa egenskaper så tidigt i projektet av två skäl: dels för att undvika sena konstruktionsförändringar och dels att påskynda produktutvecklingscykeln. För att uppnå detta behövs en validerad virtuell modell som är beräkningseffektiv. Den metod som använts innehåller två delar: utveckling av MBS-modellen och validering av den utvecklade modellen med fysisk testning. En integrerad MBS-FEM -mettod har använts. Det innebär att en FE-modal reduktionsteknik andvänds för att skapa flexibla komponenter med vilka en virtuell prototyp byggs och simuleras i ett MBS-verktyg (MSC ADAMS (c) ). Lager och kuggkontakt i växeln definieras med hjälp av en analytisk metod som beaktar den olinjära styvheten och dämpningen. En dynamisk analys och modalanalys på systemnivå har utförts för att beräkna TE, husvibrationer och PTUns modala parametrar. Experimentell modalanalys och testning i rigg gjorts för att mäta motsvarande värden som har beräknats. Parametrar som dämpning och kontaktstyvhet har sedan justerats för att uppnå korrelation. Vid jämförelse av test och förutsägelse ses en god korrelation i TE och för husvibrationer observeras en liknande trend, med vissa avvikelser. Beräknat TE är starkt beroende på parametrar för kuggkontakten i växeln. Vid jämförelse av modala parametrar ses en god korrelation under 2500 Hz mellan fem moder i mätning och beräkning vad gäller frekvens och modform, vilket visar MBS-modellens giltighet. Parameterstudier har utförts för att studera effekten av lagerdämpning och förbelastning på TE och husvibrationer. Ett optimalt värde på förbelastning och dämpning är viktigt för att undvika onödiga vibrationer. Sammanfattningsvis kan modellen med viss finjustering av dämpningsparametrar användas i virtuell ljud- och vibrationsanalys av PTU.

Ces travaux de thèse sont le résultat de la collaboration entre la société REDEX et le Laboratoire de Mécanique des Contacts et des Structures de l’INSA de Lyon. Ces travaux s’intéressent aux éléments de transmission de puissance du système de guidage d’une machine-outil, dont la conception va naturellement chercher à minimiser les erreurs de fabrication que la machine-outil pourrait générer. Dans le cadre de cette étude, un modèle dynamique de transmission pour machine-outil a été développé, comprenant un couple d’engrenages spiroconiques et un train épicycloïdal, incorporant de nombreuses erreurs d’assemblages et de forme des différents engrenages du système. Ce modèle mathématique à paramètres concentrés exploite des éléments d’engrenages cylindriques, d’engrenages coniques, d’arbres et de paliers. Les arbres sont modélisés par des poutres de Timoshenko, et les éléments de paliers se basent sur une linéarisation des relations effort-déplacement de Palmgren. Les surfaces de contact entre engrenages sont discrétisées en cellules élémentaires, auxquelles sont attribués une raideur élémentaire et un écart normal initial. Les écarts normaux initiaux des éléments d’engrenages sont mis à jour à chaque pas de temps pour prendre en compte les nouvelles positions angulaires relatives des composants et les potentielles erreurs de forme et d’assemblage. Les équations du mouvement sont résolues pas à pas dans le temps à l’aide d’un schéma de Newmark, couplé à un algorithme de gestion des contacts venant s’assurer de la bonne détermination des efforts de contact et des raideurs élémentaires des éléments d’engrenages. Les raideurs élémentaires des engrenages cylindriques sont déterminées suivant la méthode de Weber et Banaschek afin de prendre en compte la contribution des déformations de contact, de la flexion des dentures et de la fondation. Les raideurs élémentaires des engrenages spiroconiques sont déterminées à l’aide d’un élément de coque afin de rendre compte de la flexion de la dent, ainsi qu’à l’aide des théories de Boussinesq pour obtenir la contribution des déformations de contact. Un algorithme de calcul de distance de séparation tridimensionnel de type point sur plan est implémenté afin d’obtenir les écarts normaux initiaux des engrenages spiroconiques. Différents éléments de validation du modèle sont ensuite présentés afin de juger de l’exactitude du modèle et de ses limitations sur certains aspects de modélisation. Enfin, une étude du comportement dynamique du train épicycloïdal seul, du couple d’engrenages spiroconiques et du système complet est proposée, s’intéressant aux couplages existants entre ces deux éléments de la transmission, ainsi qu’à l’impact de différentes erreurs d’assemblages individuelles sur les erreurs de transmission et le coefficient de surcharge dynamique. Pour une même amplitude d’erreur, différents niveaux de criticité sont ainsi mis en valeur selon la nature de l’erreur et le mobile impacté
This research work has been conducted at the Contact and Structural Mechanics Laboratory (LaMCoS) of LaMCoS - INSA Lyon, in collaboration with REDEX. The very nature of machine-tools is to answer a need for automation and reliability of the manufacturing process of mechanical parts. The design stage of a machine-tool will therefore seek to minimise the manufacturing errors that the machine-tool could generate, in particular through the power transmission elements of the system guiding the relative displacements of the tool and the machined part. This work focuses on such power transmission elements. The present work introduces a dynamic model for geared machine-tool transmissions, comprising a pair of spiral bevel gears and an epicyclic gear train, and incorporating numerous shape and assembly errors of the various gears and rotating bodies of the system. This mathematical model adopts a lumped parameters approach, and employs specific elements of cylindrical gears and bevel gears, as well as shafts and bearings elements. The shafts are modelled using Timoshenko beams, and the bearing elements are based on a linearization of Palmgren force-displacement relations. The contact areas between gears are discretised into elemental cells, which are all attributed a local time-varying mesh stiffness element and an initial equivalent normal separation accounting for tooth flank faults and modifications. The initial equivalent normal separations of the gear elements are updated at each time step to account for the new relative angular positions of the components. The equations of motion are solved step-by-step over time using a Newmark integration scheme coupled with a normal contact algorithm to ensure that the contact efforts and the elemental mesh stiffness functions of the various gear elements are consistent. The elemental mesh stiffness functions of cylindrical gears are determined using the Weber and Banaschek approach account for the contribution of contact deformation, tooth bending and foundation displacements. The elemental mesh stiffness function of spiral bevel gears is determined using a shell element to account for tooth bending, and Boussinesq contact theory to account for the contribution of contact deformation. Various experimental and theoretical results are then presented and confronted with the model results to assess the accuracy and limitations of certain aspects of the model. Finally, a study of the dynamic behaviour of the epicyclic gear train, of the spiral bevel gear pair and of the complete system is proposed, focusing on the couplings between these two elements of the transmission, as well as on the impact of different individual assembly errors on the transmission errors and the dynamic overload coefficients. Different levels of criticality are thus highlighted depending on the nature of the error and the rotating body carrying the error

Cette thèse se compose de trois articles empiriques appliquant à divers sujets des techniques d'économétrie sur données de panel. L'article principal étudie l'évolution de la transmission des prix des trois principales céréales (blé, maïs, riz) des marchés internationaux vers les producteurs domestiques pour 52 pays sur la période 1970-2013, et cherche à identifier les principaux facteurs expliquant l'hétérogénéité des pass-through. Le second article mesure l'élasticité du trafic aérien au produit intérieur brut dans le monde et met en évidence la grande stabilité de la relation tant dans le temps que d'une région à l'autre. Enfin, le troisième article modélise le mécanisme de fixation du taux de rendement servi par les assureurs français à leurs clients sur les produits d'assurance-vie
This dissertation is composed of three empirical articles resorting to econometric methods in panel data analysis to address various research questions. The main article investigates the evolution of the level of price transmission for the three major cereals (wheat, maize and rice) from the international commodity markets down to the local producers for 52 countries between 1970 and 2013 while attempting to identify the main drivers of the heterogeneity in pass-through. The second article measures the elasticity of air-traffic to GDP around the world and demonstrates that the relationship is very stable across régions and through time. Eventually, the third article models the mechanisms through which French life-insurers set the rate of return they pay annually to their policyholders

The doctoral thesis deals with design of coding for frequency hopping stations in band with intensive jamming. In digital modulations erroneous determination of the modulation state occurs due to jam at the receiver side. The result is erroneously transferred symbols of the message. Errors created during the transmission can be eliminated by using error control systems. It is also possible to prevent these errors by using algorithms (techniques) of frequency hopping which select the appropriate channel. Appropriate communication channel is a channel with a lower probability of erroneous symbol in the message. The main contribution of this thesis is to design a new frequency hopping technique with collision avoidance (FH/CA). The station with FH/CA technique measures signal levels in the considered several channels before every jump. Based on the measurements the most appropriate channel with the lowest value of measured signal level is selected. Therefore, it is more probable that a jump to an unoccupied channel with a transmission will occur. Using a mathematical model, the performance of the newly proposed FH/CA technique is compared with the currently used techniques FH and AFH. Comparison criteria are the probability of a collision between an FH/CA communication system and a static (device transmitting continuously at a fixed frequency) or dynamic jammer (i.e. other FH or AFH systems). By comparing the values of the probability of jammed transmission, indisputable theoretical advantages of the new FH/CA technique were found, compared to the currently used FH and AFH techniques. The FH/CA technique always has better or equal results compared with the FH technique in the case of interference by static and dynamic jammers. The FH/CA technique in a band with static and dynamic jammers usually has better results than the AFH technique. A significant contribution of the FH/CA technique can be seen in the case of dynamic jammers. On the other hand, in the case of static jammers the FH/CA technique is in certain situations worse than the AFH technique. The accuracy of the mathematical models were successfully verified on a simulation model that was created as a part of this thesis in the MATLAB environment. Based on the obtained data from the model there was designed coding for frequency hopping stations with the new technique of frequency hopping FH/CA which is designed for small-volume data transfer in a band with intensive jamming.

The thesis aims to examine the impact of climate change on line rating and to investigate the possibility of a potential increase of capacity of an overhead line. The line rating of an overhead line determines how much current can be transmitted in the line. The weather parameters which affect the line rating are ambient temperature, solar radiation, wind speed, and wind direction. If the line rating is adapted to weather conditions, it is important to be able to predict how the weather will change in the future. Therefore, the impact of climate change on weather parameters is investigated. The ambient temperature and solar radiation are expected to change between different scenarios. However, it is unclear how wind speed and wind direction will be affected. Climate scenarios are designed that take these findings into account. The results show that wind speed has, by a large margin from other weather parameters, the largest impact on the dynamic line rating. This is followed by the wind's angle of attack to the conductor, ambient temperature, and finally solar radiation. For the designed climate scenarios, the dynamic line rating is almost the same in each case, which means that the calculated change in ambient temperature and solar radiation has no significant effect on the line rating. To further increase the capacity of the overhead line, the line could be upgraded with a conductor with a larger cross-sectional area.

This diploma thesis primarily deals with the transmission error issue which is one of the dominant sources of vibration in gear pairs and transmission systems. The vibrations subsequently generate noise which is often subjected to increasingly stricter demands across the industry, including the automotive one. It turns out that reducing the peak-to-peak value of the transmission error has a beneficial effect on the vibro-acoustic properties of gears and gear pairs. This thesis aims to determine the transmission error under static conditions, since a gear pair with a low static transmission error is a good assumption for a low transmission error even under dynamic effects. The resulting values of the transmission error can be influenced already during the design of the gear macro-geometry. It is also suitable to apply micro-geometric adjustments – modifications to the gear teeth. For this reason, the search part of the thesis is dedicated to theoretical knowledge, especially concerning the geometry of gears, modifications of teeth and the overall transmission error and its determination. The transmission error can be determined in several ways, including a technical experiment. However, due to time and financial reasons, this is not always possible, and therefore, the possibility of using numerical simulations is offered. In this thesis, the approach using stress-strain quasi-static contact analysis using the finite element method in Ansys Workbench software is used. The advantage is, among other things, a good comparability of results. The input to the FEM analysis is 3D CAD geometry – in this case, it is specifically a helical gear pair with parallel axes. The model/assembly of this gear pair is created in PTC Creo software fully parametrically, so it is possible to generate arbitrary gear pair configurations by changing the input parameters, which significantly saves time. At the end of this diploma thesis, the stress-strain analysis of various gear configurations is evaluated, with respect to the equivalent stress and contact pressure. Furthermore, the static transmission error – its graphs and peak-to-peak values – is determined from FEM analyses for different gear geometry, including tooth modifications, and for various loading torques. Last but not least, the effects of contact/overlap ratio and centre distance are evaluated.

A new method of adaptive impulse control is developed to precisely and quickly control the position of machine components subject to friction. Friction dominates the forces affecting fine positioning dynamics. Friction can depend on payload, velocity, step size, path, initial position, temperature, and other variables. Control problems such as steady-state error and limit cycles often arise when applying conventional control techniques to the position control problem. Studies in the last few decades have shown that impulsive control can produce repeatable displacements as small as ten nanometers without limit cycles or steady-state error in machines subject to dry sliding friction. These displacements are achieved through the application of short duration, high intensity pulses. The relationship between pulse duration and displacement is seldom a simple function. The most dependable practical methods for control are self-tuning; they learn from online experience by adapting an internal control parameter until precise position control is achieved. To date, the best known adaptive pulse control methods adapt a single control parameter. While effective, the single parameter methods suffer from sub-optimal settling times and poor parameter convergence. To improve performance while maintaining the capacity for ultimate precision, a new control method referred to as Adaptive Impulse Control (AIC) has been developed. To better fit the nonlinear relationship between pulses and displacements, AIC adaptively tunes a set of parameters. Each parameter affects a different range of displacements. Online updates depend on the residual control error following each pulse, an estimate of pulse sensitivity, and a learning gain. After an update is calculated, it is distributed among the parameters that were used to calculate the most recent pulse. As the stored relationship converges to the actual relationship of the machine, pulses become more accurate and fewer pulses are needed to reach each desired destination. When fewer pulses are needed, settling time improves and efficiency increases. AIC is experimentally compared to conventional PID control and other adaptive pulse control methods on a rotary system with a position measurement resolution of 16000 encoder counts per revolution of the load wheel. The friction in the test system is nonlinear and irregular with a position dependent break-away torque that varies by a factor of more than 1.8 to 1. AIC is shown to improve settling times by as much as a factor of two when compared to other adaptive pulse control methods while maintaining precise control tolerances.

A rotating gear pair experiences high vibration and noise mainly due to tooth profile error, mounting error, tooth wear, friction backlash and periodic change of meshing stiffness. The combined effect of the manufacturing error, mounting error and elastic tooth deformation is considered as the static transmission error that introduces internal displacement excitation within the gear pair. Such internal excitation generates torsional vibration through the driving and driven shafts even in absence of external excitations. Thus the vibration problem of a geared system involves homogeneous equations of motion with time dependent boundary conditions. The present research is to investigate the torsional vibrations of a geared system by developing a continuous model that converts the homogeneous equations with non-homogeneous boundary conditions into non-homogeneous equations with homogeneous boundary conditions. The influence of friction, tooth wear, backlash and other nonlinear variables have been ignored in the formulation. The free vibration results of the proposed model are validated by developing the classical Rayleigh-Ritz model with Bhat's boundary characteristic orthogonal polynomial functions. The results are also validated by performing experiments in the laboratory for a simple geared system. Torsional vibration responses are determined in both time and frequency domains. In addition to the proposed continuous model the discrete model is simulated to determine torsional vibrations and dynamic torque generated due to static tooth error. The experimental investigations are carried out by measuring free torsional vibrations with strain gauge and frequency analysis by a spectrum analyzer

碩士
國立臺灣科技大學
電子工程系
94
Multimedia communications over wireless channels have become a popular topic in recent mobile communication. It is necessary that we apply data compression and channel coding techniques in image transmission when we transmit images in wireless fading channel, which typically suffer serious signal degradation and have only limited bandwidths. However, different degrees of importance bits in a codeword are expectable. Therefore, we should design dynamic channel coding that takes this into account so that the decoded image at the receiver has the best quality. Image quality is not only influenced by the number of incorrectly decoded data bits but also their positions in quantized pixels. We adopt the bit plane division to transmit after using scalar quantization and use different error correcting codes based on different degrees of importance bits. This method is called unequal error protection coding. According to unequal error protection applied on different bits, we can calculate the BER corresponding to each bit and estimate the quality of received image. Energy allocation is part of unequal error protection, where more energy is assigned to more important bits. We make the important bit not only receive more energy to make its ability to resist channel noise but also get lower code rate in its error correcting coding. To simulate the practical situation in image transmission by cellular phones, we also consider the constraints of allowed maximum delay time and the maximum achievable launch energy of a data bit in cell-phone transmission. Simulation results show that dynamic channel coding has the SNR of image very close to exhaustive searching when the signal-to-noise ratio in channel is medium and high. Dynamic channel coding has slightly lower the SNR of image than exhaustive searching when the signal-to-noise ratio in channel is low.

碩士
國立臺灣大學
電信工程學研究所
107
Reliability, latency, and the number of connected users form the golden triangle of Internet of Things. In this thesis, the fundamental trade-off among them are investigated in the multi-user system with quasi-static MIMO channel. By a cross-layer system model, the overall latency including transmission time at the physical layer as well as queuing delay at the network layer is considered. We study two different scenarios of this problem. First, we focus on the static transmission policy and delay-bound metric. Our goal is to find the optimal policy that can minimize the delay-bound, given that the system error probability is below a prescribed threshold. By taking the problem to the high SNR asymptotic regime, it can be formulated into a convex optimization problem. Hence Karush-Kuhn-Tucker (KKT) conditions can be used to find the optimal solution. The result shows that the parameters of arrival distribution, the prescribed threshold of the error probability, and the number of users determine the choice of the optimal policy. In addition, the overall latency grows super-linearly with the number of users. Then we turn to the dynamic policy and average delay metric. We solve this problem based on Markov decision process. By convexity and symmetry of the value function, we can find the optimal policy. In addition, two algorithms for finding the optimal policy are proposed.