Dissertations / Theses on the topic 'Linear suspension'

Este trabalho foca o estudo e desenvolvimento de um atuador linear com ímãs permanentes aplicado a sistemas de suspensão ativa, com ênfase em suspensão veicular. Seu desenvolvimento considera aspectos específicos como força, volume, razão força/volume, curso e resposta em frequência. Junto ao estudo teórico desenvolve-se o projeto baseado na simulação paramétrica em elementos finitos que analisa aspectos qualitativos e quantitativos importantes para tomada de decisão do projeto, especificamente na definição de materiais e geometrias. Para servir como ferramenta de análise foi empregada uma modelagem analítica que se mostrou eficiente, pois foi capaz de produzir resultados de forma mais rápida que o método de elementos finitos para avaliar grandezas de interesse como força e densidade de fluxo magnético. Por fim e com base nos aspectos de projeto, foi construído um protótipo que permitiu validar os modelos. Os resultados experimentais e teóricos mostraram boa concordância o que permite concluir que os métodos empregados são eficazes, fornecendo subsídios à aplicação em foco.
This work aims the study and development of a linear actuator with permanent magnets applied to active suspension systems, with emphasis on vehicular suspension. That development takes into account specific features such as force, volume, force per volume ratio, stroke and frequency response. Together with the theoretical study the design of the actuator is carried out based on parametric simulation by means of finite elements which analyses qualitative and quantitative aspects that are important to make the project decision, specifically to define materials and geometry. To suit as an analysis tool it was employed an analytical modelling, which showed to be efficient because it was capable of producing faster results than the finite elements method to evaluate physical quantities of interest such as force and magnetic flux density. Finally and based on project aspects, a prototype was built which allowed to validate all models. Experimental and theoretical results showed a good agreement which led to conclude that the employed methods are efficient, providing subsidies to the studied application.

The scope of the presented research project is to provide a reliable guideline for the preliminary design of cable supported bridges. In order to pursue this objective, a thorough literature research has been conducted in the first phase of the project. This has been of relevant importance for the understanding of the subject and further implementation of the case study: the design of a suspension bridge model in Strand7. The conducted research has shown that there is not a unique book to which engineers may refer in order to conduct the type of analysis presented in this project. Therefore, the proposed guideline has been created on the basis of multiple text books. Further analyses have been conducted in order to evaluate the accuracy of theoretical-based results and software-based results. In particular the Steinman Modified Elastic Treatment has been applied to the case study and its results compared to those obtained on Strand7. The obtained results finally show that Steinman’s Theory represents a quick and reliable method to be adopted for preliminary design purposes as its results are in line with Strand7 results.

This thesis is concerned with the synthesis of linear-optimal heave control of electromagnetic suspension systems. The methods of computer-aided analysis and simulation were employed in this research. The intrinsic properties of electromagnetic suspension system were investigated to facilitate the synthesis and to provide guidelines for the design of electromagnets or linear motors suitable for use in suspension systems. The technique of complementary filtering, which resolves the conflicting requirements of high stiffness to load and high compliance for ride-comfort, was further developed. This led to the ability of directly comparing the merits of systems with different configurations and determining the optimal natural frequency. Together with a novel way of removing steady state gap error during the traversing of transition curves, the filtering technique was applied to the system using fixed-gain and sliding-mode variable-structure control methods. The latter method is well known for its abi1ity in maintaining closed-loop characteristics in the presence of disturbance. However, further development was required before it was applied. The resultant suspension system gave a 20% improvement in ride-quality over the best published result which was carried out under similar test conditions. Even so, theoretical analysis showed that a four-fold improvement may be possible.

This thesis presents the study of a quarter car model which consists of a two-degree-of-freedom (2 DOF) with a linear spring and a nonlinear spring configuration. In this thesis, the use of non-linear vibration attachments is briefly explained, and a survey of the research done in this area is also discussed. The survey will show what have been done by the researches in this new field of nonlinear attachments. Also, it will be shown that this topic was not extensively researched and is a new type of research where no sufficient experimental work has been applied. As an application, a quarter car model was chosen to be investigated. The aim of the Thesis is to validate theoretically and experimentally the use of nonlinear springs in a quarter car model. Design the new type of suspension and insert it in the experimental set up, built from the ground up in the laboratory. A novel criterion for optimal ride comfort is the root mean square of the absolute acceleration specified by British standards ISO 2631-1997. A new way to reduce vibrations is to take advantage of nonlinear components. The mathematical model of the quarter-car is derived, and the dynamics are evaluated in terms of the main mass displacement and acceleration. The simulation of the car dynamics is performed using Matlab® and Simulink®. The realization of vibration reduction through one-way irreversible nonlinear energy localization which requires no pre-tuning in a quarter car model is studied for the first time. Results show that the addition of the nonlinear stiffness decreases the vibration of the sprung mass to meet optimal ride comfort standards. As the passenger is situated above the sprung mass, any reduction in the sprung mass dynamics will directly have the same effect on the passenger of the vehicle. The future is in the use of a nonlinear suspension that could provide improvement in performance over that realized by the passive, semi active and active suspension. The use of a quarter car model is simple compared to a half car model or a full car model, furthermore in the more complex models you can study the heave and the pitch of the vehicle. For the initial study of the nonlinear spring the quarter car model was sufficient enough to study the dynamics of the vehicle. Obtaining an optimum suspension system is of great importance for automotive and vibration engineer involved in the vehicle design process. The suspension affects an automobile’s comfort, performance, and safety. In this thesis, the optimization of suspension parameters which include the spring stiffness and damper coefficient is designed to compromise between the comfort and the road handling. Using Genetic algorithm an automated optimization of suspension parameters was executed to meet performance requirements specified. Results show that by optimizing the parameters the vibration in the system decreases immensely.

The design, fabrication, and testing of a quarter-car facility coupled with various control algorithms are presented in this thesis. An experimental linear tubular motor, capable of producing a 52-N force, provides control actuation to the model. Controllers consisting of two designs were implemented: a classical controller employing lead and lag networks and a state-space feedback design. Each design was extensively simulated to screen for receptiveness to actuation force limitations and robustness regarding the inexact tire modeling. The goal of each controller was to minimize the acceleration of the sprung mass in the presence of simulated road disturbances, modeled by both sinusoidal and step input excitation wheels. Different reference velocity inputs were applied to the control scheme. Responses to a zero reference were juxtaposed to those that resulted from tracking a reference built off a model that incorporated inertial-frame damping attached to the sprung mass. The outcome of this comparison was that low-frequency disturbances were attenuated better when tracking a zero reference, but the reference relaxation introduced by the inertialframe damping model allowed for better-attenuated high frequency signals. Employing an inertial-frame damping value of 250 N-s/m, the rejected frequency component of the system response synchronous with the disturbance input excitation of 40 rad/s bettered by 33% and 28% when feeding control force from the classical controller and state-space controller, respectively. The experimental analysis conducted on the classical and state-space controllers produced sinusoidal disturbance rejection of at worst 50% within their respective bandwidths. At 25 rad/s, the classical controller was able to remove 80% of the base component synchronous with the disturbance excitation frequency, while the state-space controller filtered out nearly 60%. Analysis on the system's ability to reject step disturbances was greatly confounded with the destructive lateral loading transferred during the excitation process. As a result, subjection to excitation could only occur up to 25 rad/s. At the 20 rad/s response synchronous to the disturbance excitation, the classical and state-space controllers removed 85% and 70% of the disturbance, respectively. Sharp spikes in timebased amplitude were present due to the binding that ensued during testing.

L'amélioration permanente de la qualité et des performances des systèmes automatiques constitue un défi majeur dans la théorie du contrôle. La théorieHinf a permis d'améliorer considérablement les performances des correcteurs. Ces derniers reposent sur des modèles mathématiques qui sont potentiellement d'ordre élevé (c.-à-d. comprenant un nombre élevé d'équations différentielles). De plus, l'ajout de poids de pondérations spécifiant les performances à respecter accroit encore plus leur ordre. La complexité algorithmique résultante peut alors rendre leur implantation difficile voire même impossible pour un fonctionnement en temps réel.Les travaux présentés visent à réduire l'ordre de correcteurs Hinf dans le but de faciliter leur intégration tout en respectant les performances imposées d'une part et proposent une majoration de l'erreur introduite par l'étape de réduction d'autre part.Dans la littérature, de nombreuses méthodes pour la réduction d'ordre de modèles et de correcteurs des systèmes LTI ont été développées. Ces techniques ont été étudiées, comparées et testées sur un ensemble de benchmarks. S'appuyant sur ces travaux, nous proposons une extension aux systèmes linéaires à paramètres variants (LPV). Pour valider leurs performances, une application sur une commande d'une suspension semi-active a montré l'efficacité des algorithmes de réduction développés
The work presented in this dissertation is related to the Hinf-LPV-controller orderReduction. This latter consists of the design of a robust reduced-order LPV-controller for LPV-systems. The order reduction issue has been very fairly investigated. However, the case of LPV-control design is slightly discussed. This thesis focuses primarily on two topics: How to obtain an LPV-reduced-order controller even the high order generated by the classical synthesis and how this reduced order controller can deal with a practical engineering problem (semi-active suspension control). In view of this, the order-reduction topic and the Hinf-synthesis theory have been widely studied in this thesis. This study, has allowed the development of a new method forH1-LPV-controller order reduction

To achieve passive vibration control, an adaptive flywheel design is proposed and fabricated from two different materials. The corresponding mathematical models for the adaptive flywheels are developed. A two-terminal hydraulic device and a two-terminal inverse screw device are introduced to analyze the two adaptive flywheels. Experiments are carried out to identify key parameters for both the two-terminal hydraulic system and the inverse screw system. The performance of three different suspension systems are evaluated; these are the traditional suspension system, the suspension system consisting of an ideal two-terminal device with constant flywheel and the suspension system consisting of an ideal two-terminal device with an adaptive flywheel (AFW suspension system). Results show that the AFW suspension system can outperform the other two suspension systems under certain conditions. The performance of a suspension system with the adaptive flywheel under different changing ratio is evaluated, and an optimal changing ratio is identified under certain circumstances. To obtain the steady-state response of the two-terminal device with adaptive flywheel, three different methods have been applied in this thesis. These methods are the single harmonic balance method, the multi-harmonic balance method and the scanning iterative multi-harmonic balance method, respectively. Compared to the single harmonic balance method, the multi-harmonic balance method provides a much more accurate system response. However, the proposed scanning iterative multi-harmonic balance method provides more accurate system response than the single harmonic balance method with much less computational effort.

Este trabalho apresenta uma metodologia de projeto de atuadores eletromagnéticos lineares inovadora para aplicação em sistemas de suspensão semiativa e ativa. A metodologia, apresentada na forma de fluxograma, define critérios para determinar os requisitos de força e curso que um atuador deve desenvolver considerando um sistema mecânico vibratório com um grau de liberdade com excitação harmônica de base quando o método de controle skyhook é aplicado. Um atuador eletromagnético linear de bobina móvel com duplo arranjo de quase-Halbach que apresenta elevada densidade de força, reduzida massa móvel, ausência de força de relutância e baixa ondulação de força é definido como estudo de caso. Um modelo numérico parametrizado em elementos finitos do comportamento eletromagnético de um passo polar do dispositivo é criado e analisado, considerando restrições dimensionais, com os objetivos de projeto definidos como: elevada densidade de força e reduzida ondulação de força com acionamento brushless CA. Com base no modelo de um passo polar do dispositivo, define-se o volume ativo que o mesmo deve apresentar e, a partir deste, todas as dimensões são definidas de forma a atender os requisitos de projeto. Uma vez definidas as dimensões do atuador com base no modelo eletromagnético, realiza-se a modelagem térmica numérica que permite avaliar qual a máxima densidade de corrente elétrica aplicável de forma que a temperatura, estipulada como máxima, nos enrolamentos não seja excedida. Ainda, a distribuição térmica permite determinar a temperatura de operação dos ímãs permanentes que têm curva de operação dependente da temperatura. A partir dos resultados da simulação térmica e do modelo eletromagnético para um passo polar, realizou-se o acoplamento eletromagnético-térmico por meio da correção das propriedades dos ímãs permanentes e aplicando uma densidade de corrente eficaz dependente das dimensões do modelo parametrizado. O modelo acoplado é simulado e analisado, de modo que as dimensões finais do atuador podem ser obtidas atendendo aos mesmos objetivos de projeto previamente mencionados, respeitando os limites de operação térmica. Adicionalmente, são apresentados modelos analíticos do comportamento eletromagnético e térmico do atuador que podem servir de base para implementação da metodologia proposta, se esta for baseada em modelos analíticos, e podem futuramente ser empregados para a aplicação de otimização matemática do dispositivo. Por fim, um protótipo do dispositivo é construído de forma a validar a metodologia proposta. Com este protótipo são realizados ensaios de densidade de fluxo magnético no entreferro, tensão induzida a vazio, força estática e ensaio dinâmicos com o dispositivo instalado em uma bancada de testes de vibrações controladas desenvolvida durante o projeto. Os resultados mostram a eficácia da metodologia proposta, uma vez que os resultados experimentais mostraram boa concordância com os resultados esperados.
This work presents an innovative linear electromagnetic actuator design methodology for application in semi-active and active suspension systems. The methodology, synthesized in a flowchart, sets criteria to determine requirements such as axial force and stroke that an actuator should develop considering a vibration system with one degree of freedom with harmonic base excitation when the skyhook control method is applied. A linear moving-coil electromagnetic actuator with dual quasi-Halbach arrays of permanent magnets that presents high force density, low moving-mass, no reluctance force and low force ripple is defined as a case study. A finite element numerical parameterized model that describes the electromagnetic behavior of one pole pitch of the device is created and analyzed, considering dimensional constraints, with the design objectives defined as: high force density and low ripple of force with brushless AC drive. Based on the model of one pole pitch of the device the active volume and all dimensions are defined in order to meet the design requirements. Once the actuator dimensions are defined, based on the electromagnetic model, a numerical thermal model was constructed, which allows to evaluate the maximum applicable electric current density so that the maximum temperature at the windings is not exceeded. Furthermore, the thermal distribution gives the operating temperature of the permanent magnets, which present performance highly dependent on temperature. With the results of the thermal simulation, the electromagnetic-thermal coupling is performed by correcting permanent magnet properties and by applying a parametric-dependent effective current density. The coupled model is simulated and analyzed so that the final dimensions of the actuator can be obtained with the same design objectives previously mentioned, while respecting thermal operating limits. In addition, the work presents analytical models of the electromagnetic and thermal behavior of the actuator that can be the basis for implementation of the proposed methodology, if it is based on analytical models, and can further be used for the application of mathematical optimization of the device. Finally, a prototype was built to validate the proposed method. Measurements were carried out to assess magnetic flux density in the air gap, open-circuit induced voltage, static force and dynamic tests with the device installed in a test bench that was developed during this work. The results show the effectiveness of the proposed method since experimental results have shown good agreement with the expected results.

Este trabalho apresenta a aplicação da teoria de Controle Robusto H-infinito em modelo não linear de sistema de suspensão ativa com Atuador Tubular de Ímã Permanente (ATIP). Os principais objetivos na aplicação dos sistemas ativos de suspensão são a obtenção de melhores níveis de conforto do usuário e dirigibilidade do veículo em relação aos sistemas de suspensão passivo e semi-ativo, e a manutenção dos limites de deslocamento da suspensão. Inicialmente, são apresentados os modelos de suspensão ativa de um quarto de carro e carro completo, utilizados respectivamente como planta para o projeto dos controladores H-infinito e como modelo para as simulações dos sistemas de suspensão em malha fechada. Em seguida, o conjunto de controladores H-infinito e desenvolvido, baseado em especificações de projeto definidas, para posterior avaliação e comparação dos sistemas projetados. Verificações de robustez dos sistemas de suspensão ativos, utilizando-se da Análise-µ como ferramenta de avaliação, são feitas em conjunto com as análises de desempenho de cada sistema. A avaliação de desempenho dos sistemas é realizada tanto no domínio do tempo (avaliando-se angulações, velocidades, acelerações, defexões e energia do sistema) quanto no domínio da frequência (através da análise de densidade espectral de potência, ou Power Spectral Density (PSD), das acelerações verticais do veículo e do esforço de controle do atuador). A excitação do sistema é realizada por meio de distúrbios impostos às posições das rodas, dos tipos determinístico e estocástico, representativos de condições reais da aplicação de um veículo. O conjunto de controladores desenvolvido neste trabalho apresenta resultados satisfatórios para distúrbios de entrada do tipo determinísticos e estocásticos, com ganhos de desempenho dos sistemas de suspensão ativa em relação ao sistema passivo de referência de até 34; 92% para a métrica de avaliação do conforto do usuário, de 17; 23% para a métrica da manutenção da dirigibilidade, e de 43; 48% e 30; 10% para as métricas das acelerações dos ângulos de arfagem e de rolagem da carroceria, respectivamente.
This work presents the application of the H-infinity robust control theory into a non-linear model of active suspension system with a Tubular Permanent Magnet Actuator (TPMA). The main objectives in the application of the active suspension systems are the achievement of greater levels of comfort to the user and of road holding for the vehicle, when compared to the passive and semi-active suspension systems, besides the maintenance of suspension displacement limits. Initially are presented the active suspension models of a quarter-car and of a full-car, used respectively as a plant for the design of the H-infinity controllers and as a model for the simulations of the closed loop suspension systems. In the sequel, the controllers are developed, based on properly defined specifications, for further evaluation and comparison among the systems designed. Robustness verications of the active suspension systems, using the µ-Analysis as assessment tool, are performed together with the performance analysis of each system. The performance evaluation of the systems is performed both in the time domain (assessing angles, speeds, accelerations, dections and the energy of the system) and in the frequency domain (through the analysis of Power Spectral Density (PSD) of vertical accelerations of the vehicle and the control efort of the actuator). The excitation of the system is carried out by means of disturbances imposed to the vertical wheel\'s positions. Those disturbances are of deterministic and stochastic types, which are representatives of real working conditions of the vehicle. The set of controllers developed in this work presents satisfactory results for both deterministic and stochastic input disturbances, with performance gains of the active suspension systems in relation to the passive system of reference up to 34; 92%, 17; 23%, 43; 48% and 30; 10% respectively to the assessment metrics of user comfort, handling maintenance and acceleration of the pitch and roll angles of the chassis.

Este trabalho aborda a aplicação de uma máquina elétrica síncrona do tipo tubular linear de ímãs permanentes em um sistema de suspensão semiativa. O uso de amortecedores eletromagnéticos lineares em sistemas de suspensão não é uma ideia nova, mas a maioria dos trabalhos publicados sobre este assunto concebem soluções ativas e negligenciam as semiativas, sobretudo com estudos experimentais. Nesta pesquisa é discutido um modelo dinâmico eletromecânico acoplado de um sistema de suspensão semiativa, considerando um amortecedor eletromagnético linear e também apresentando dados experimentais. Leis da mecânica clássica e do eletromagnetismo são aplicadas para descrever o sistema que combina teoria de vibrações e máquinas elétricas. Um modelo virtual com vários subsistemas foi implementado no ambiente MATLABR /Simulink/Simscape para associar equações e simular o desempenho global. Para o caso passivo, os resultados numéricos e experimentais validam os parâmetros e confirmam a funcionalidade do sistema e a metodologia proposta. Simulações e testes experimentais para o caso semiativo são consistentes, mostrando uma melhoria na transmissibilidade de deslocamento, em relação ao modo passivo, e a possibilidade de regeneração de energia.
This work addresses the application of a tubular linear permanent magnet synchronous machine working as a damper for a semi-active suspension system. The use of linear electromagnetic dampers in suspension systems is not a new idea. However, most published papers on this subject outline active solutions and neglect semi-active ones, above all, with experimental studies. Here a dynamic mechanicalelectromagnetic coupled model for a semi-active suspension system is reported. This is in conjunction with a linear electromagnetic damper and also presents experimental data. Classical laws of mechanics and electromagnetics are applied to describe a dynamic model combining vibration and electrical machines theories. A multifaceted MATLABR /Simulink/Simscape model was implemented to incorporate equations and simulate global performance. For the passive case, numerical and experimental results validate the parameters and confirm system function and the proposed methodology. Simulation and practical results for the semi-active case are consistent, showing an improvement in the displacement transmissibility and the possibility of energy regeneration.

Linear-motion compliant mechanisms have generally been developed for small displacement applications. The objective of the thesis is to provide a basis for improved large-displacement linear-motion compliant mechanisms (LLCMs). One of the challenges in developing large-displacement compliant mechanisms is the apparent performance tradeoff between displacement and off-axis stiffness. In order to facilitate the evaluation, comparison, and optimization of the performance of LLCMs, this work formulates and presents a set of metrics that evaluates displacement and off-axis stiffness. The metrics are non-dimensionalized and consist of the relevant characteristics that describe mechanism displacement, off-axis stiffness, actuation force, and size. Displacement is normalized by the footprint of the device. Transverse stiffness is normalized by a new performance characteristic called virtual axial stiffness. Torsional stiffness is normalized by a performance characteristic called the characteristic torque. Because large-displacement compliant mechanisms are often characterized by non-constant axial and off-axis stiffnesses, these normalized stiffness metrics are formulated to account for the variation of both axial and off-axis stiffness over the range of displacement. In pursuit of mechanisms with higher performance, this work also investigates the development of a new compliant mechanism element. It presents a pseudo-rigid-body model (PRBM) for rolling-contact compliant beams (RCC beams), a compliant element used in the RCC suspension. The loading conditions and boundary conditions for RCC beams can be simplified to an equivalent cantilever beam that has the same force-deflection characteristics as the RCC beam. Building on the PRBM for cantilever beams, this paper defines a model for the force-deflection relationship for RCC beams. Included in the definition of the RCC PRBM are the pseudo-rigid-body model parameters that determine the shape of the beam, the length of the corresponding pseudo-rigid-body links and the stiffness of the equivalent torsional spring. The behavior of the RCC beam is parameterized in terms of a single parameter defined as clearance, or the distance between the contact surfaces. The RCC beams exhibit a unique force-displacement curve where the force is inversely proportional to the clearance squared. The RCC suspension is modeled using the newly defined PRBM. The suspension exhibits unique performance, generating no resistance to axial motion while providing significant off-axis stiffness. The mechanism has a large range of travel and operates with frictionless motion due to the rolling-contact beams. In addition to functioning as a stand-alone linear-motion mechanism, the RCC suspension can be configured with other linear mechanisms in superposition to improve the off-axis stiffness of other mechanisms without affecting their axial resistance.

Due to the emergence of new materials and advanced engineering technology, slender footbridges are increasingly becoming popular to satisfy the modern transportation needs and the aesthetical requirements of society. These structures however are always "lively" with low stiffness, low mass, low damping and low natural frequencies. As a consequence, they are prone to vibration induced by human activities and can suffer severe vibration serviceability problems, particularly in the lateral direction. This phenomenon has been evidenced by the excessive lateral vibration of many footbridges worldwide such as the Millennium Bridge in London and the T-Bridge in Japan. Unfortunately, present bridge design codes worldwide do not provide sufficient guidelines and information to address such vibrations problems and to ensure safety and serviceability due to the lack of knowledge on the dynamic performance of such slender vibration sensitive bridge structures. A conceptual study has been carried out to comprehensively investigate the dynamic characteristics of slender suspension footbridges under human-induced dynamic loads and a footbridge model in full size with pre-tensioned reverse profiled cables in the vertical and horizontal planes has been proposed for this purpose. A similar physical suspension bridge model was designed and constructed in the laboratory, and experimental testings have been carried out to calibrate the computer simulations. The synchronous excitation induced by walking has been modelled as crowd walking dynamic loads which consist of dynamic vertical force, dynamic lateral force and static vertical force. The dynamic behaviour under synchronous excitation is simulated by resonant vibration at the pacing rate which coincides with a natural frequency of the footbridge structure. Two structural analysis software packages, Microstran and SAP2000 have been employed in the extensive numerical analysis. Research results show that the structural stiffness and vibration properties of suspension footbridges with pre-tensioned reverse profiled cables can be adjusted by choosing different structural parameters such as cable sag, cable section and pretensions in the reverse profiled cables. Slender suspension footbridges always have four main kinds of vibration modes: lateral, torsional, vertical and longitudinal modes. The lateral and torsional modes are often combined together and become two kinds of coupled modes: coupled lateral-torsional modes and coupled torsionallateral modes. Such kind of slender footbridges also have different dynamic performance in the lateral and vertical directions, and damping has only a small effect on the lateral vibration but significant effect on the vertical one. The fundamental coupled lateral-torsional mode and vertical mode are easily excited when crowd walking dynamic loads are distributed on full bridge deck. When the crowd walking dynamic loads are distributed eccentrically on half width of the deck, the fundamental coupled torsional-lateral mode can be excited and large lateral deflection can be induced. Higher order vertical modes and coupled lateral-torsional modes can also be excited by groups of walking pedestrians under certain conditions. It is found that the coupling coefficient introduced in this thesis to describe the coupling of a coupled mode, is an important factor which has significant effect on the lateral dynamic performance of slender suspension footbridges. The coupling coefficient, however, is influenced by many structural parameters such as cable configuration, cable section, cable sag, bridge span and pre-tensions, etc. In general, a large dynamic amplification factor is expected when the fundamental mode of a footbridge structure is the coupled lateral-torsional mode with a small coupling coefficient. The research findings of this thesis are useful in understanding the complex dynamic behaviour of slender and vibration sensitive suspension footbridges under humaninduced dynamic loads. They are also helpful in developing design guidance and techniques to improve the dynamic performance of such slender vibration sensitive footbridges and similar structures and hence to ensure their safety and serviceability.

Este trabalho apresenta uma proposta para o controle da suspensão veicular utilizando o amortecedor magneto-reológico, sendo o controle proposto composto pela associação de duas estratégias de controle, o controle ótimo e o controle fuzzy. O Controle ótimo é utilizado para determinar a força a ser utilizada pelo amortecedor magneto-reológico, e o controle fuzzy é utilizado para determinar a corrente elétrica, a ser utilizada no amortecedor magento-reológico e é obtido considerando o modelo de Mandani. Para o controle fuzzy, são consideradas duas entradas, a velocidade de deslocamento do pistão do amortecedor e a força prevista pelo controle ótimo, e uma saída, a corrente elétrica [A]. Para demonstrar a eficiência do controle proposto são consideradas simulações computacionais, utilizando um modelo matemático não-linear de um quarto de veículo. A análise do desempenho do controle é realizada, considerando excitações provocadas por irregularidades na pista, as irregularidades são representadas por entradas tipo degrau, impulso e senoidal. As simulações computacionais são realizadas, utilizando o Matlab® e o Simulink. Os resultados das simulações demonstram que o controle proposto aumenta a segurança do veículo e melhora sua dirigibilidade, reduzindo o deslocamento vertical do conjunto eixo e roda e o espaço de trabalho do amortecedor, quando comparado como o sistema passivo. Também contribui com o conforto dos passageiros, reduzindo as oscilações da carroceria, mantendo os níveis de aceleração abaixo dos considerados desconfortáveis pela norma BS 6841, 1987. Para verificar o comportamento do controle proposto, diante de incertezas, são realizadas simulações computacionais, considerando a possibilidade de erros paramétricos. As simulações, considerando os erros paramétricos, demonstram que o controle ótimo, mesmo quando sujeito a incertezas, permanece sendo estável e ótimo.
This work presents a proposal for control of vehicular suspension using the magneto-rheological damper, the proposed control is composed by association of two control strategy, the optimal control and the fuzzy control. The optimal control is used to determine the power to be applied by the magneto-rheological damper, and the fuzzy control is used to determine the electric current to be used in the magneto-rheological damper and is obtained considering the Mandani's model. For the fuzzy control two inputs are considered, the velocity of the piston's damper and the force provided by the optimal control, and one output, the electric current [A]. To demonstrate the efficiency of the proposed control, computational simulations are considered using a nonlinear mathematical model for a quarter-car. The performance of the control is analyzed considering excitements provoked by irregularities in the track, the irregularities are represented by entrances step type, pulse and sinusoidal. The computational simulations are performed using the Matlab® and the Simulink. The results of simulations show that the proposed control increases the vehicle security and improves the drive ability by reducing the vertical wheel displacement and the workspace to be used by the damper when compared to the passive system. It also helps with the comfort of passengers, reducing the bodywork oscillations, maintaining levels of accelerating below considered uncomfortable by standard BS 6841, 1987. To verify the behavior of the proposed control, in the face of uncertainty, computational simulations are carried out, considering the possibility of parametric errors. The simulations, show that the Optimal Control, even when subject to uncertainties, remains stable and optimal.

Comprovadamente, o sistema de suspensão veicular passivo é uma proposta confiável e econômica de solução tanto para redução dos níveis de vibração do chassi e da roda, quanto para a redução dos níveis de aceleração do chassi. Embora este sistema seja amplamente empregado nos veículos, ele apresenta a desvantagem que seus parâmetros não podem ser modificados de acordo com as variações geradas pela pista. Com isso surge o emprego da utilização do sistema de suspensão ativa, que possibilita a variação dos parâmetros da suspensão a tempo real, no entanto, o emprego deste tipo de suspensão requer um elevado nível de energia para o funcionamento correto de seus atuadores, acarretando na inviabilidade de algumas aplicações. Para solucionar as desvantagens encontradas para o sistema de suspensão passivo e ativo, surge o sistema de suspensão semiativo, que reúne as vantagens do sistema ativo, porém com um menor consumo de energia, gerando consequentemente uma opção de controle confiável e econômica de solução para os problemas de dirigibilidade e conforto veicular. O presente trabalho pretende realizar duas avaliações, sendo a primeira, a avaliação e comparação de um sistema de suspensão passivo com o desempenho de quatro controladores semiativos (on/off, skyhook, groundhook e híbrido) e a segunda é testar os mesmos controladores, porém considerando a dinâmica de um amortecedor magnético-reológico através do modelo de LuGre. Estes controladores serão aplicados a um modelo não linear de um quarto de carro com dois graus de liberdade, sendo as suas variáveis estimadas, através de um observador de estados não linear. A análise para a comparação dos sistemas será realizada através de simulações numéricas utilizando o software MatLab®. As simulações dos distúrbios gerados pela pista serão realizadas através de uma função degrau e uma função pulso com o objetivo de avaliar o desempenho de cada controlador. Após a implementação dos algoritmos de controle, foi possível verificar que o sistema de suspensão semiativo, frente às excitações propostas, apresentou um desempenho superior em relação ao conforto. Contudo, não tão significativas quanto ao do conforto, o sistema controlável também, comparativamente ao sistema passivo, apresentou melhoras no requisito dirigibilidade.
Proven, the passive vehicle suspension system is a reliable and cost-effective solution solution for both chassis and wheel vibration levels reduction and chassis acceleration levels reduction. Although this system is widely used in vehicles, it has the disadvantage that its parameters can not be modified according to the variations generated by the track. This results in the use of the active suspension system, which allows the variation of the parameters of the suspension in real time, however, the use of this type of suspension requires a high level of energy for the correct operation of its actuators, resulting in the unfeasibility of some applications. To solve the disadvantages found for the passive and active suspension system, the semiactive suspension system arises, which combines the advantages of the active system, but with a lower energy consumption, consequently generating a reliable and economical solution control option to the problems of maneuverability and vehicular comfort. The present work intends to perform two evaluations, the first being the evaluation and comparison of a passive suspension system with the performance of four semi-active controllers (on/off, skyhook, groundhook and hybrid) and the second is to test the same controllers, but considering the dynamics of a magneticrheological damper through the LuGre model. These controllers will be applied to a nonlinear model of a quarter-car with two degrees of freedom, with its variables being estimated through a nonlinear state observer. The analysis for the comparison of the systems will be performed through numerical simulations using MatLab® software. The simulations of the disturbances generated by the track will be performed through a step function and a pulse function in order to evaluate the performance of each controller. After the implementation of the control algorithms, it was possible to verify that the system of semi-active suspension against the proposed excitations presented a superior performance in relation to comfort. However, not as significant as comfort, the controllable system alo compared to the passive system, presented improvements in the steerability requirement.

O tema do conforto na automobilística é bastante extenso e possuidor de muitas interpretações. A ideia central deste trabalho é definir e direcionar alguns métricos para que, durante as fases de conceituação e desenvolvimento de um veículo, seja possível ter um direcional de definição de componentes e atributos veiculares de modo a facilitar o direcionamento dos atributos no programa veicular, e assim atingir suas necessidades. Como exemplo empregado, é empregado um veículo de plataforma tipo B em desenvolvimento por uma montadora, o qual teve as molas de suspensão definidas e rigidezes laterais de eixos com base em material técnico interno equivalente aos estudos apresentados neste trabalho. É adotada uma abordagem inicialmente empírica conforme os primeiros estudos de suspensões independentes realizados neste continente, depois o trabalho é complementado com exigências de normas especificas para vibrações (ISO2361, ISO5008, BS6055) de modo a caracterizar energia vibracional e a interpretação pelo ser humano. Porém como hoje em dia as suspensões automotivas são muito mais complexas, existem componentes específicos para as várias condições de solicitação, deste modo a análise é limitada a situações de ride (conforto) primário e handling (dirigibilidade) em situações de sublimite na faixa linear (cerca de 0,5 g). Como conclusão dos estudos, é possível ter em um veículo atributos de estabilidade sem necessariamente prejudicar o conforto, pois sendo definidos corretamente os componentes elásticos da dinâmica vertical para situações estacionárias e de ride primário, é definido seu equilíbrio estacionário e assim não é necessário comprometimento dos atributos de outros componentes para compensar alguma deficiência existente.
The range of assumptions for ride comfort is considered very wide in the automotive world and they can assume lots of possible interpretations. The central idea in this work is define and manage some metrics that, during the concept and development phases of a vehicular program, be possible to follow a better direction for the attributes development and so reach the program targets. As the example in this work, a B platform typical vehicle is used and it is under development in a carmaker, its suspension springs and axle roll stiffness were setup with technical information similar to the ones presented in this work. The initial approach is empiric as occurred with the first independent suspension system studies in this continent and in the sequence, the work is complemented with standards for vibrational issues (ISO2361, ISO5008, BS6055), after this, finally how the vibrational energy is defined and perceived by human beings. The automotive suspensions of current days are very complex and there are lots of specific components to do a specific work, so the analysis are limited to primary ride and sub limit handling (up to 0,5 g). As conclusion, its possible setup a car that is comfortable and stable in the same time, since the elastic components for the vertical dynamics and steady state conditions are correctly set, so its correct balance is reached and no other components attributes are compromised to compensate any deficiency.

O objetivo deste trabalho é apresentar um novo tipo de sistema de levitação baseado na força de interação magnética entre uma bobina de núcleo não-magnético e um imã permanente, em casos de simetria axial entre os dispositivos, nos moldes do problema 23 proposto no TEAM Workshop. Este tema é bastante atual e vários métodos têm sido estudados e propostos em razão da complexidade na determinação precisa das forças sobre os imãs permanentes imersos em um campo magnético em um circuito magnético aberto. O primeiro grande desafio deste trabalho é obter uma expressão analítica para esta força de interação magnética em casos de simetria axial usando o método de cargas magnéticas ligadas. Para tal, algumas hipóteses simplificadoras foram adotadas como considerar o campo magnético gerado pela bobina aproximadamente uniforme em toda a face do imã permanente e assumir que a magnetização do imã é constante e independente da variação de sua distância para a bobina. Pretende-se aproveitar o sistema implementado neste trabalho como bancada experimental no Laboratório de Controle da Universidade de São Paulo. Foi projetado um controlador PID através de ferramentas gráficas obedecendo a alguns critérios de desempenho, tanto no domínio do tempo como no domínio da freqüência. Uma vez sintonizado, foi utilizado o toolbox Real-Time Windows Target do Simulink e a placa de aquisição PCI 6221 (da National Instruments) para controlar em tempo real a planta de levitação em malha fechada. Os resultados experimentais foram muito satisfatórios de modo que o modelo analítico foi considerado válido. O sistema apresentou boas características como, por exemplo, um bom acompanhamento do sinal de referência, mesmo em grandes excursões, erro de regime nulo, levitação estável em distâncias relativamente grandes e uma boa estabilidade radial. O uso de dois sensores Hall mostrou-se eficiente na determinação da posição do imã permanente.
The objective of this work is to present a new kind of levitation system based on the interaction force between a non-magnetic core coil and a permanent magnet, in the case of axial symmetry between devices, as proposed by TEAM Workshop problem 23. This theme is very current and various methods have been studied and proposed in face of the complexity in determining precisely the force over permanent magnets immersed in a magnetic field in an open magnetic circuit. The first big challenge of this work is to obtain an analytical expression for this interaction magnetic force in the case of axial symmetry using the equivalent magnetic charge method. For this, some simplifying hypothesis have been adopted like considering the magnetic field created by the coil approximately uniform over all the permanent magnets face and assuming that magnets magnetization is constant and independent of the variation of its distance to the coil. The system implemented in this work is intended to be used as an experimental bench for the Laboratory of Control of Sao Paulo University. A PID controller was projected by means of graphical tools according to some criteria for performance, both in the field of time as in the frequency domain. Once tuned, the toolbox Real-Time Windows Target of Simulink and the PCI-6221 acquisition board (of National Instruments) were used to control in real time the levitation plant in closed loop. The experimental results were very satisfactory so that the analytical model was considered valid. The system showed good characteristics as, for instance, a good tracking of reference signal, even in large excursions of it, null stationary error, stable levitation at relatively big gaps and a good radial stability. The use of two Hall-effect sensors proved to be efficient in the determination of permanent magnets position.

Os modelos simplificados de veículos são importantes em fases iniciais do projeto de um veículo, quando muitas características geométricas ainda não estão definidas. No caso de ônibus com sistema de suspensão a ar, os modelos encontrados na literatura não levam em conta efeitos da válvula niveladora de altura. Dois modelos de um ônibus foram desenvolvidos: um modelo não linear de veículo com três graus de liberdade e um modelo em sistema multicorpos com 109 graus de liberdade. Os dois modelos possuem sistema de suspensão a ar com a modelagem termodinâmica do bolsão com a válvula niveladora de altura. As equações do modelo não linear de três graus de liberdade foram construídas utilizando o conceito de derivativos de estabilidade. Para a validação dos modelos, foram realizados ensaios experimentais com o veículo e as seguintes grandezas foram medidas: aceleração lateral, velocidade em guinada, velocidade lateral, ângulo de escorregamento do veículo e ângulo de rolamento. Os resultados obtidos com os modelos foram validados experimentalmente. O comportamento do ângulo de rolamento do veículo devido ao sistema de suspensão a ar foi reproduzido nos dois modelos. Foi desenvolvida uma interface gráfica dentro do ambiente ADAMS para a geração automática de modelos simplificados. Os dados do veículo são inseridos através de uma interface gráfica com caixas de diálogo. Modelos simplificados de veículos são utilizados no controle da dinâmica do veículo. Neste tipo de aplicação, as equações do modelo não linear de três graus de liberdade são resolvidas em tempo real e podem servir como um modelo de referência para sistemas adaptativos de controle.
Simplified vehicle models are very important at the initial stages of vehicle development when all geometric data are not yet available. In the case of a bus with an air suspension system, the models you find in the literature does not taken into account the control leveling valve effects. Two bus models were developed: a nonlinear three degrees of freedom model and a multibody model with 109 degrees of freedom. Both models have thermodynamic air suspension system model with control leveling valve. The three degrees of freedom equations were built using the stability derivative concept. In order to validate the models, experimental tests were carried out and the following variables were measured: lateral acceleration, yaw velocity, sideslip angle and roll angle. The model results were validated against actual data. The roll angle behavior due to air suspension system was reproduced in both models. A graphic user interface for developing simplified vehicle model, based on the nonlinear three degrees of freedom model equations, was built using the ADAMS interface. All the data necessary for the model are introduced via dialog boxes. Simplified vehicle models can be used in vehicle dynamics control. In this kind of application, the three degrees of freedom equations can be solved in real time simulation and can be used as a reference model in adaptive control system, for instance.

La suspension joue un rôle central pour la dynamique verticale d’un véhicule automobile afin d’améliorer le confort des passagers et la tenue de route. Les travaux de recherche de cette thèse sont divisés en deux grandes parties. La première partie considère le problème de commande d’une suspension semi-active dont le défi principal est de prendre en compte les contraintes de dissipativité et de débattement maximum des amortisseurs. Celles-ci sont transformées en des contraintes sur la commande et l’état d‘un système linéaire. Deux approches sont alors proposées pour la synthèse de la commande de la suspension semi-active : la commande Linéaire à Paramètres Variants (LPV) avec prise en compte de la saturation et la Commande Prédictive à base de Modèle (MPC).La deuxième partie est consacrée à l’estimation de défaut actionneur et à la commande Tolérante à ce type de défauts, avec comme application majeure le système de suspension semi-active. On considère ici comme défaut une perte de puissance de l’amortisseur (par exemple une fuite de l’huile), qui est estimée en utilisant plusieurs approches fondées sur des observateurs d’état. Puis, en fonction de l’estimation du défaut, la commande en boucle fermée est reconfigurée afin de conserver des performances pour la dynamique verticale du véhicule
Semi-active suspension system plays a key role in enhancing comfort and road holding of vertical dynamics in automotive vehicles. This PhD thesis research work, focused on that topic, is divided into two main parts. The first one considers the semi-active suspension control problem, the main challenge of which being to handle the dissipativity constraint and suspensions stroke limitation of semi-active dampers. These constraints are recast into input and state constraints in a linear state space representation. Thereby, the semi-active suspension control is designed in the framework of Linear Parameter Varying (LPV) approach with input constraints, and of Model Predictive Control (MPC) approach.The second part is devoted to Fault Estimation and Fault Tolerant Control (FTC) in case of actuator fault, and its application to Semi-Active suspension systems. The fault considered here is the loss of actuator's efficiency (due to an oil leakage of the damper for instance when a ), which is estimated using several observer-based approaches. Then, thanks to the fault information from the estimation step, an LPV/FTC fault scheduling control is designed to limit the vehicle performance deterioration

Der zunehmende Einsatz regenerativer Energiequellen erfordert die Nutzung von Energiezwischenspeichern, die umweltfreundlich, günstig und skalierbar sein sollten. Die Zink-Luft-Flussbatterie (ZLFB) kann perspektivisch diese Anforderungen erfüllen, wobei zur Bereitstellung der gespeicherten Energie eine Suspension aus Zinkpartikeln in einem gelierten Elektrolyt durch eine elektrochemische Zelle gepumpt wird. Um die Strömungsstruktur der ZLFB auszulegen und Fehlfunktionen zu vermeiden, ist ein grundlegendes Verständnis der Rheologie der Zinksuspension notwendig. Außerdem kann über die Einstellung einer geeigneten Strömung die bei der Entladung erreichte elektrische Leistungsdichte gesteigert werden. Bereits die Flüssigphase der Zinksuspension weist eine komplexe nicht-Newtonsche Rheologie auf, welche durch die Zugabe der Partikel komplexer wird. Für das grundlegende Verständnis der Rheologie werden daher Modellexperimente durchgeführt, wobei in dieser Arbeit ein L-förmiger Kanal mit Strömungsaufweitung untersucht wurde, um die komplexen strömungsmechanischen Eigenschaften der Zinksuspension abzubilden. Zur Erfassung des Strömungsfeldes ist eine Ortsauflösung von 1 … 2 mm in einem Messbereich von 20 × 15 mm2 erforderlich. Ultraschall ist prinzipiell geeignet, um das Strömungsfeld in der opaken Suspension zu erfassen, wobei die wesentliche Herausforderung in den starken Wellenfrontverzerrungen besteht, welche durch die Zinkpartikel eingebracht werden. Es konnte gezeigt werden, dass die Ultrasound Imaging Velocimetry (UIV) robuster gegenüber diesen Störungen ist, als die Ultraschall-Doppler-Velozimetrie (UDV). Die UIV wurde daher mittels Geschwindigkeitsnormal an die messtechnischen Randbedingungen der Zinksuspension angepasst und charakterisiert. Bei einer Ortsauflösung von 1,6 mm wurde eine Gesamtmessunsicherheit von 2,5 % axial und 4,1 % lateral zur Schallausbreitungsrichtung erreicht. Das im Modellexperiment gemessene Strömungsfeld weist eine Totzone an der Strömungsumlenkung auf, deren Auftreten durch eine von der Scherhistorie abhängige Viskosität erklärt werden kann. Dieser Effekt wird als Thixotropie bezeichnet. Durch die In-situ-Messung der Strömung in einer aktiven ZLFB kann eine Korrelation von Strömung und elektrischer Leistung erfolgen und die erzielte Leistungsdichte perspektivisch durch eine Anpassung der Strömung gesteigert werden. Bei der Messung im 2,6 mm hohen Anodenspalt muss aufgrund der komplexen Rheologie der Suspension und der daraus resultierenden hohen Geschwindigkeitsgradienten eine Ortsauflösung von unter 100 µm bei gleichzeitig kleiner Ultraschallfrequenz realisiert werden, da der Ultraschall für hohe Frequenzen nicht in die Zinksuspension eindringt. Um dieses Ziel zu erreichen, wurde die Super Resolution Ultrasound Particle Tracking Velocimetry (SRPTV) genutzt, welche Ortsauflösungen unterhalb des Beugungslimits ermöglicht. Einzelne nichtlineare Streupartikel werden mittels Harmonic Imaging isoliert abgebildet und verfolgt, wobei die durch die Zinkpartikel eingebrachten Wellenfrontstörungen durch einen kohärenzgewichteten Strahlformer kompensiert werden. Es wurde eine Ortsauflösung von 67 µm axial und 30 µm lateral zur Schallausbreitungsrichtung bei einer Anregungswellenlänge von 330 µm erreicht. Trotz der stark streuenden Zinksuspension, konnte so eine Messung in der aktiven ZLFB mit einer maximalen Messunsicherheit von 12,5 % durchgeführt werden. Dabei wurde eine Wandgleitgeschwindigkeit von 3 mm s−1 bei einer maximalen Geschwindigkeit von etwa 8 mm s−1 festgestellt. Die SRPTV kann darüber hinaus in anderen technischen Prozessen eingesetzt werden, in denen Suspensionsströmungen in kleinen Geometrien auftreten.:Symbolverzeichnis xiii Abkürzungsverzeichnis xv 1 Einleitung 1 1.1 Motivation und Zielstellung 1 1.2 Stand der Technik 4 1.3 Lösungsansatz und Struktur der Arbeit 8 2 Theoretische Grundlagen 11 2.1 Grundlagen der Schallausbreitung 11 2.1.1 Schallausbreitung in homogenen Medien 11 2.1.2 Schallausbreitung in inhomogenen Medien 13 2.2 Ultraschall Bildgebung 14 2.2.1 Phased-Array-Prinzip 15 2.2.2 Plane wave imaging 16 2.2.3 Grenzen der Schallfeldfokussierung 16 2.3 Messung von Strömungsfeldern 17 2.3.1 Ultraschall-Doppler-Velozimetrie 18 2.3.2 Ultrasound Imaging Velocimetry 19 2.3.3 Ultrasound Particle Tracking Velocimetry 19 2.4 Nichtlineare akustische Effekte 20 2.4.1 Beschreibung von Linearität 20 2.4.2 Interaktion von nichtlinearen Streupartikeln und Schallwelle 20 2.4.3 Harmonic Imaging 21 3 Experimentelle Grundlagen 25 3.1 Charakterisierung der Zinksuspension 25 3.1.1 Zusammensetzung der Zinksuspension 25 3.1.2 Bestimmung von Dämpfung und Schallgeschwindigkeit 26 3.1.3 Bestimmung der spezifischen akustischen Impedanz 29 3.2 Messtechnik 30 3.2.1 Ultraschallforschungsplattform: Phased Array Ultrasound Dopp- ler Velocimeter 30 3.2.2 Ultraschallwandler 32 4 Verfahren zur Strömungsmessung im Modellexperiment 37 4.1 Experimenteller Aufbau 37 4.2 Untersuchung geeigneter Verfahren zur Messung von Strömungsfel- dern in der Zinksuspension 38 4.3 Optimierung der Signalverarbeitung und Charakterisierung der Messei- genschaften 44 4.3.1 Geschwindigkeitsnormal 44 4.3.2 Optimierung der Messsystemparameter 45 4.3.3 Charakterisierung der Messeigenschaften 48 4.3.4 Validierung 49 4.4 Messung der Suspensionsströmung im Modellexperiment 55 4.4.1 Messergebnisse 55 4.4.2 Vergleich von Simulation und Messung 58 4.5 Fazit 61 5 Verfahren zur In-situ-Strömungsmessung in einer Zink-Luft-Flussbatterie 63 5.1 Experimenteller Aufbau 63 5.2 Strömungsmessung unterhalb des Beugungslimits - Super Resolution Ultrasound Particle Tracking Velocimetry (SRPTV) 65 5.2.1 Nutzung nichtlinearer Streupartikel 68 5.2.2 Trennung von linearem und nichtlinearem Signalanteil 72 5.2.3 Strahlformung mit Kompensation der Streuung 76 5.2.4 Particle Tracking 80 5.3 Charakterisierung der Messeigenschaften 81 5.3.1 Vorgehen zur Charakterisierung der Messeigenschaften 82 5.3.2 Untersuchung der Positionsunsicherheit 83 5.3.3 Untersuchung der Geschwindigkeitsunsicherheit 92 5.4 Messung an einer aktiven Zink-Luft-Flussbatterie 95 5.4.1 Aufbau und Durchführung 95 5.4.2 Messergebnisse 97 5.4.3 Vergleich von Simulation und Messung 97 5.5 Fazit 102 6 Zusammenfassung und Ausblick 103 6.1 Erkenntnisse und Fortschritt 103 6.1.1 Ultrasound Imaging Velocimetry 103 6.1.2 Super Resolution Ultrasound Particle Tracking Velocimetry 104 6.1.3 Fazit 106 6.2 Ausblick und weiterführende Arbeiten 106 6.2.1 Messtechnik 106 6.2.2 Anwendung 107 Literaturverzeichnis 109 Publikationsverzeichnis 117 Artikel in Zeitschriften mit peer-review 117 Tagungsbeiträge 117 Patente 119
For the efficient use of renewable energies, energy storage systems are required that are environmentally friendly, low priced and scalable. The zinc-air flow battery (ZAB), which is operated by pumping an opaque suspension of zinc particles in an gelled electrolyte through an electrochemical cell, is a promising candidate as energy storage system for these requirements. To design the fluidic structures and avoid malfunction, a fundamental understanding of the rheology of the zinc suspension is required. Additionally, the electrical performance of the cell can be imporved by optimizing the flow in the electrochemical cell. The liquid phase of the suspension itself has complex non-Newtonian properties, which are even more complex when the particles are considered. For the fundamental understanding of the suspension rheology, model experiments are conducted. In this work an L-shaped channel with a widening is used to represent relevant effects from the complex rheology of the suspension. To measure the flow field, a spatial resolution of 1 … 2 mm and a measurement area of 20 × 15 mm2 are required. Ultrasound can be used to measure the flow in opaque liquids, but wavefront distortions are introduced by the zinc particles. Established measurement methods for homogeneous opaque fluids, the Ultrasound Imaging Velocimetry (UIV) and the Ultrasound Doppler Velocimetry (UDV), were compared for the application at the suspension. The UIV has a 50 % lower random deviation, which makes it more suitable for the flow measurement in the suspension and it was adapted to the measurement conditions in the suspension. At a spatial resolution of 1.66 mm, a velocity uncertainty of 2.5 % axial and 4.1 % lateral to the ultrasound propagation were achieved. The application of the UIV to the suspension flow in the model experiment revealed a thixotropic behavior of the fluid, which resulted in a dead flow zone opposite to the inlet of the channel. The in situ measurement of the flow in an active ZAB, allows to correlate electrical performance and flow and thereby an improvement of the cell performance by adapting the flow. For the measurement in the anodic channel with a width of 2.6 mm, a spatial resolution of 100 µm is required because of the high velocity gradients due to the non-Newtonian rheology of the suspension. The high spatial resolution has to be achieved at low ultrasound frequencies, since the ultrasound does not penetrate into the suspension for high frequencies. To achieve this, the Super Resolution Ultrasound Particle Tracking Velocimetry (SRPTV) was used, which allows a spatial resolution beyond the diffraction limit. Harmonic Imaging is used to image isolated non-linear tracer particles, which are tracked for velocity estimation. The speckle and image distortion due to the induced wavefront distortions are compensated with a coherence weighting beamformer. A spatial resolution of 67 µm axial and 30 µm lateral to the ultrasound propagation were achieved. Despite the strong scattering of the ultrasound at the zinc particles, a maximum velocity uncertainty of 12.5 % referred to the maximum velocity was achieved for the measurement in the active ZAB. A slip velocity of 3 mm at a maximum velocity of 8 mm was observed. The SRPTV can be applied to other technical processes, where suspension flows in small geometries play an important role.:Symbolverzeichnis xiii Abkürzungsverzeichnis xv 1 Einleitung 1 1.1 Motivation und Zielstellung 1 1.2 Stand der Technik 4 1.3 Lösungsansatz und Struktur der Arbeit 8 2 Theoretische Grundlagen 11 2.1 Grundlagen der Schallausbreitung 11 2.1.1 Schallausbreitung in homogenen Medien 11 2.1.2 Schallausbreitung in inhomogenen Medien 13 2.2 Ultraschall Bildgebung 14 2.2.1 Phased-Array-Prinzip 15 2.2.2 Plane wave imaging 16 2.2.3 Grenzen der Schallfeldfokussierung 16 2.3 Messung von Strömungsfeldern 17 2.3.1 Ultraschall-Doppler-Velozimetrie 18 2.3.2 Ultrasound Imaging Velocimetry 19 2.3.3 Ultrasound Particle Tracking Velocimetry 19 2.4 Nichtlineare akustische Effekte 20 2.4.1 Beschreibung von Linearität 20 2.4.2 Interaktion von nichtlinearen Streupartikeln und Schallwelle 20 2.4.3 Harmonic Imaging 21 3 Experimentelle Grundlagen 25 3.1 Charakterisierung der Zinksuspension 25 3.1.1 Zusammensetzung der Zinksuspension 25 3.1.2 Bestimmung von Dämpfung und Schallgeschwindigkeit 26 3.1.3 Bestimmung der spezifischen akustischen Impedanz 29 3.2 Messtechnik 30 3.2.1 Ultraschallforschungsplattform: Phased Array Ultrasound Dopp- ler Velocimeter 30 3.2.2 Ultraschallwandler 32 4 Verfahren zur Strömungsmessung im Modellexperiment 37 4.1 Experimenteller Aufbau 37 4.2 Untersuchung geeigneter Verfahren zur Messung von Strömungsfel- dern in der Zinksuspension 38 4.3 Optimierung der Signalverarbeitung und Charakterisierung der Messei- genschaften 44 4.3.1 Geschwindigkeitsnormal 44 4.3.2 Optimierung der Messsystemparameter 45 4.3.3 Charakterisierung der Messeigenschaften 48 4.3.4 Validierung 49 4.4 Messung der Suspensionsströmung im Modellexperiment 55 4.4.1 Messergebnisse 55 4.4.2 Vergleich von Simulation und Messung 58 4.5 Fazit 61 5 Verfahren zur In-situ-Strömungsmessung in einer Zink-Luft-Flussbatterie 63 5.1 Experimenteller Aufbau 63 5.2 Strömungsmessung unterhalb des Beugungslimits - Super Resolution Ultrasound Particle Tracking Velocimetry (SRPTV) 65 5.2.1 Nutzung nichtlinearer Streupartikel 68 5.2.2 Trennung von linearem und nichtlinearem Signalanteil 72 5.2.3 Strahlformung mit Kompensation der Streuung 76 5.2.4 Particle Tracking 80 5.3 Charakterisierung der Messeigenschaften 81 5.3.1 Vorgehen zur Charakterisierung der Messeigenschaften 82 5.3.2 Untersuchung der Positionsunsicherheit 83 5.3.3 Untersuchung der Geschwindigkeitsunsicherheit 92 5.4 Messung an einer aktiven Zink-Luft-Flussbatterie 95 5.4.1 Aufbau und Durchführung 95 5.4.2 Messergebnisse 97 5.4.3 Vergleich von Simulation und Messung 97 5.5 Fazit 102 6 Zusammenfassung und Ausblick 103 6.1 Erkenntnisse und Fortschritt 103 6.1.1 Ultrasound Imaging Velocimetry 103 6.1.2 Super Resolution Ultrasound Particle Tracking Velocimetry 104 6.1.3 Fazit 106 6.2 Ausblick und weiterführende Arbeiten 106 6.2.1 Messtechnik 106 6.2.2 Anwendung 107 Literaturverzeichnis 109 Publikationsverzeichnis 117 Artikel in Zeitschriften mit peer-review 117 Tagungsbeiträge 117 Patente 119

L'objet de ce travail est d'élargir les applications de l'optimisation structurale au cas des systèmes composés de corps déformables articulés, en vue de l'amélioration du comportement cinématique et dynamique de ces systèmes multi corps. Nous travaillons sur la formulation discrétisée du problème. Puis l'on résout le problème d'optimisation en combinant les concepts d'approximation et les méthodes de programmation mathématique. Une première analyse des méthodes d'optimisation structurale nous conduit à adopter l'algorithme de programmation récursive quadratique développé par Powell (1977). Nous montrons alors la nécessité d'utiliser une méthode directe d'analyse de sensibilité qui permet de résoudre simultanément les problèmes dynamique et de sensibilité. Par rapport à une méthode classique d'approximation par différences finies, il ne se pose pas de problème de differentiabilité, les résultats sont plus fiables et le cout de calcul est nettement réduit. Ces résultats sont rendus possibles par l'avancement des méthodes d'analyse dynamique du type mécano. Elles se basent sur une formulation de type dynamique non linéaire des structures, avec prise en compte des grandes rotations dans la matrice d'itération à l'aide du vecteur rotation. Les problèmes de conception traites introduisent des variables de conception géométriques (coordonnées de nœuds) et une dépendance temporelle des fonctions de contrainte et/ou objectif. Nous avons donc dégagé l'ensemble des précautions à prendre pour formuler le bon problème d'optimisation. L'ensemble de ces méthodes sont illustrées par l'application à l'optimisation de l'épure cinématique du train arrière de la Peugeot 406, ce qui contribue à l'amélioration du comportement routier du véhicule.

The objective of this master´s thesis is a design of suspension footbridge across the Elbe river. The footbridge is suspended construction by three spans. The brick deck is supported on the outer edges and it is kept in a parabolic arc. The suspension cables are kept at two inclined levels. The model is implemented in the program ANSYS. The solution is non-linear. The designe is according to the europien standart.

The objective of this master's thesis is a design of suspension footbridge. The footbridge is suspended construction of stress ribbon by one span. The brick deck is supported on the edges and it is kept in a parabolic arc. The suspension cables are kept at two inclined levels. The model lengthways is implemented in the program ANSYS, by non-linear solution. The model crosswise is implemented in the program SCIA ENGINEER 2011. The design is according to relevant current standart.

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Este trabalho tem como objetivo apresentar uma proposta para o controle de um sistema de suspensão veicular semiativo utilizando um amortecedor magneto-reológico e um controlador baseado na técnica de controle preditivo baseado em modelo (MPC – Model-Predictive Control). O princípio de funcionamento dos amortecedores magnetoreológicos é evidenciado e o modelo de Bouc-Wen modificado é utilizado no trabalho. O controlador MPC é projetado para produzir a força ideal a ser utilizada pelo amortecedor, assegurando que a magnitude das forças calculadas pela lei de controle satisfaça às restrições físicas de passividade do amortecedor. A tensão requerida para o amortecedor MR produzir a força de controle estimada pelo controlador MPC é calculada por um algoritmo de controle clipped-optimal. Um modelo matemático não linear de um quarto de veículo com 2 graus de liberdade é utilizado e o desempenho do controle MPC proposto para o sistema de suspensão semiativa é investigado através de simulações numéricas e comparado com o desempenho do controlador LQR. Realiza-se a análise do desempenho dos controladores considerando excitações de estrada com perfil rampa, lombada, buraco e senoidal. Os resultados das simulações demonstram que o controle MPC proposto com malha de controle interna reduz as oscilações na carroceria, mantendo os níveis de aceleração abaixo dos considerados desconfortáveis pela norma BS 6841 (1987), contribuindo para o conforto dos passageiros. Também contribui com o aumento da segurança do veículo e melhora sua dirigibilidade, reduzindo o deslocamento vertical do conjunto eixo e roda e o espaço de trabalho do amortecedor. Além disso, o MPC mostra-se mais eficiente, reduzindo o consumo de energia pelo amortecedor.

A general theory for the analysis of the non-linear behaviour of suspension cables structures by the finite element method is presented. The formulation takes into account the material and geometric nonlinearities. The theory is developed applying a Lagrangian formulation where the corotacional technique is used to obtain the tangent stiffness matrix of the space cable element. The formulation intends to be as general as possible, allowing for the nodes to undergo large displacements and the elements to undertake large strains. Besides, elasto-plastic material can be used. A static incremental analysis will be perfomed, applying an incremental, monotonic and increasing load, proportional or not, until partial or global failure of the cable structure occurs. The solution of the problem requires an incremental-iterative procedure, such as the Newton-Raphson Method, to insure the convergence. An easy-to-use computer program was developed which allows for analyses of suspension cables takingencompassing large displacements effects and the inelastic behaviour of the cables. The computational coding of the element was performed using the PASCAL programming language obeying the DELPHI 4.0 standards. The examples presented were compared with theoretical results and with results produced by some commercial programs, showing the correctness and accuracy of the developed program.
Com o objetivo de avaliar o comportamento não-linear das estruturas de cabos suspensos, é apresentada uma teoria geral para a análise pelo método dos elementos finitos. Essa formulação considera os comportamentos não-lineares físico (NLF) e geométrico (NLG) das estruturas. O desenvolvimento teórico é feito dentro de uma formulação Lagrangiana, que utiliza a técnica corrotacional para a dedução consistente da matriz de rigidez tangente do elemento de cabo. Aformulação apresentada é bastante geral, permitindo que os nós sofram grandes deslocamentos e os elementos sofram grandes alongamentos e, além disso, esses elementos podem ser constituídos de material elasto-plástico. Será feita a análise estática da estrutura através de carregamento incremental, monótono e estritamente crescente, proporcional ou não, até o colapso global da estrutura. A solução do problema exige um procedimento incremental-iterativo, do tipo Newton-Raphson, para se alcançar a convergência da solução. Dessa forma, foi desenvolvido um programa de computador consistente e de fácil utilização que permite a análise de cabos suspensos, levando-se em consideração os efeitos dos grandes deslocamentos envolvidos e o comportamento inelástico dos cabos. A implementação computacional do elemento é feita através da linguagem de programação PASCAL dentro das padronizações do DELPHI. Os exemplos apresentados são comparados com resultados teóricos ou de outros programas decomputador amplamente testados, demonstrando a consistência e precisão do programa desenvolvido.

L'étude porte sur l'analyse et la prédiction du comportement dynamique des structures montées sur suspensions passives non linéaires. Dans un premier temps, une méthode expérimentale est développée pour identifier le comportement de suspension non linéaire de deux types de plots: un en élastomère et un à coussin métallique. Elle est mise en œuvre sur un banc d'essais spécifique. De nombreuses expérimentations ont mis en évidence la complexité du comportement des suspensions. Sachant que l'effet de la déflexion est prépondérant, un modèle théorique qui tient compte de la non-linéarité en raideur, est proposé. L'approche repose sur l'hypothèse de la superposition de déformations statique et dynamique non linéaires. Ensuite, pour prédire le comportement dynamique du système structure-suspension, un code de calcul élément finis et des algorithmes spécifiques ont été mis au point. Afin de rendre acceptable les temps de calcul, particulièrement dans le cas de réponse temporelle, il est indispensable de procéder à une réduction du nombre de degrés de liberté ( d. D. L. ). La méthode de Craigh et Bampton est bien adoptée à ce système: il est nécessaire de conserver les caractéristiques dynamiques de la structure et de disposer à tout instant les d. D. L. Relatifs aux suspension. La fiabilité du modèle de calcul a été éprouvée par des tests de validation analytiques et expérimentaux portant sur diverses structures rigides montées sur suspension non linéaire. Enfin, la prédiction du comportement de structures flexibles, s'est avérée très satisfaisante par rapport aux expérimentations réalisées sur des structures de type poutre montées sur suspension non linéaire et soumises à des chocs, ou des sollicitations harmoniques. Le travail développé permet la modélisation de structures industrielles, tels les supports d'équipements embarqués, et d'en prévoir le comportement
This research is concerned with the analysis and prediction of the dynamic behaviour of structures mounted on non-linear passive suspension. Experimental investigations using a specific experimental set-up have been performed as to identify the role of non linearities in the dynamic behaviour of visco-elastic mounts and of elasto-plastic mounts with dry friction. Experiments show the complex behaviour of the tested mounts and highlight the predominant effect of bath deflection and temperature. These effects are taken into account in the modelling of the mounts which involves the theory of the superposition of non-linear static and dynamic deflection. The specific Finite Element computer program permits the prediction of the dynamic behaviour of the structure/suspension assembly. The Craigh and Bampton method is well adapted to the problem: it permits an acceptable computation time of the time response. The reliability of the computation model has been analytically and experimentally tested on different kinds of rigid structure on non-linear mounts. The response of flexible structures including a beam clamped at one end and retained at the other end by a non-linear mount has been investigated under sine wave excitations and shocks. The experimental results show that the response of the structure is well predicted. The present study allows the modelling of industrial structures, such as shipping equipments, and the prediction of their non-linear behaviour

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Este trabalho explora os diferentes tipos de comportamento dinâmicos, encontrados em sistemas eletromecânicos linear e não-linear análogos, sendo o sistema eletromecânico não-linear constituído de rigidez tipo Duffing. A modelagem matemática dos sistemas físicos hipotéticos é realizada através de técnicas Langrangeanas, inclusive para a modelagem que aborda componentes eletromagnéticos de um circuito RLC. O transdutor utilizado no acoplamento dos subsistemas é o de bobina móvel e magnetismo permanente e tem suas equações conhecidas na literatura. Os modelos são baseados em absorvedores utilizados no automobilismo, no entanto são abordados de forma simplificada, comparando-se com o modelo completo de uma suspensão de automóvel. No trabalho é investigada a influência dos parâmetros do circuito RLC, que podem ser responsáveis pelo aumento do amortecimento mecânico. É feita a correlação do amortecimento mecânico com os parâmetros de resistência e capacitância elétrica para o modelo linear. É realizada também a análise dos autovalores do modelo linear e lugar natural das raízes. Para o modelo não-linear é realizada a análise do comportamento dinâmico, levando-se em consideração a variação da capacitância para quatro valores de frequência da força externa ao sistema. Essa análise mostra a diversidade de comportamento dinâmicos encontrados para esse modelo. As variedades de comportamento dinâmicos resultantes do modelo não-linear variam entre dinâmicas caóticas, periódicas, quasi-periódicas e multiperiódica. Indica a possibilidade de utilização do parâmetro da capacitância como parâmetro de controle do sistema e mostra que a resistência elétrica dissipa a energia oirunda do domínio mecânico, fato esse que abre a discussão para as possibilidades de geração de energia
This work investigates the different types of dynamic behaviour, found in linear and nonlinear electromechanical system, which are analogue, being the nonlinear electromechanical system constituted of rigidity type Duffing. The mathematical modelling of the hypothetical physical system is realized with Langrangian techniques, including for the modeling of the system is a moving coil and permanent magnet tranducer, which it have their equations deducted in other studies. The models are based in absorbers utilized in automobiles, however in this investigation it is discussed in a simplified way, if it is compared with a complete model of and automobile supension. This work investigates the influence of the RLC circuit parameters, which it may be responsible by the increasing of the mechanical damping. It is realized the correlation of the mechanical damping with resistance and capacitance, for the linear model. It is realized the anlysis of the eigenvalues it is found de root locus of the linear model. For the nonlinear model it is realized the analysis of the dynamic behaviour, considering the variation of the capacitance, for each one of the four values of frequency of the external force. This analysis shows the diversity of dynamic behaviours found for the nonlinear model. The variations of dynamic behaviours resulted of the nonlinear model varies around some types of dynamics, which can be, chaotic, periodic, quasi periodic, quasi periodic and multi periodic. That's indicate the possibility of utilization of the capacitance as control parameter of the system and shows the dissipation of energy by the resistance, this energy is from the mechanical domain, this fact open the discussion for the energy generation possibilities

Orientador: Bento Rodrigues de Pontes Junior
Co-orientador: Marcos Silveira
Banca: Marcio Antonio Bazani
Banca: Paulo José Paupitz Gonçalves
Resumo: Este trabalho explora os diferentes tipos de comportamento dinâmicos, encontrados em sistemas eletromecânicos linear e não-linear análogos, sendo o sistema eletromecânico não-linear constituído de rigidez tipo Duffing. A modelagem matemática dos sistemas físicos hipotéticos é realizada através de técnicas Langrangeanas, inclusive para a modelagem que aborda componentes eletromagnéticos de um circuito RLC. O transdutor utilizado no acoplamento dos subsistemas é o de bobina móvel e magnetismo permanente e tem suas equações conhecidas na literatura. Os modelos são baseados em absorvedores utilizados no automobilismo, no entanto são abordados de forma simplificada, comparando-se com o modelo completo de uma suspensão de automóvel. No trabalho é investigada a influência dos parâmetros do circuito RLC, que podem ser responsáveis pelo aumento do amortecimento mecânico. É feita a correlação do amortecimento mecânico com os parâmetros de resistência e capacitância elétrica para o modelo linear. É realizada também a análise dos autovalores do modelo linear e lugar natural das raízes. Para o modelo não-linear é realizada a análise do comportamento dinâmico, levando-se em consideração a variação da capacitância para quatro valores de frequência da força externa ao sistema. Essa análise mostra a diversidade de comportamento dinâmicos encontrados para esse modelo. As variedades de comportamento dinâmicos resultantes do modelo não-linear variam entre dinâmicas caóticas, periódicas, quasi-periódicas e multiperiódica. Indica a possibilidade de utilização do parâmetro da capacitância como parâmetro de controle do sistema e mostra que a resistência elétrica dissipa a energia oirunda do domínio mecânico, fato esse que abre a discussão para as possibilidades de geração de energia
Abstract: This work investigates the different types of dynamic behaviour, found in linear and nonlinear electromechanical system, which are analogue, being the nonlinear electromechanical system constituted of rigidity type Duffing. The mathematical modelling of the hypothetical physical system is realized with Langrangian techniques, including for the modeling of the system is a moving coil and permanent magnet tranducer, which it have their equations deducted in other studies. The models are based in absorbers utilized in automobiles, however in this investigation it is discussed in a simplified way, if it is compared with a complete model of and automobile supension. This work investigates the influence of the RLC circuit parameters, which it may be responsible by the increasing of the mechanical damping. It is realized the correlation of the mechanical damping with resistance and capacitance, for the linear model. It is realized the anlysis of the eigenvalues it is found de root locus of the linear model. For the nonlinear model it is realized the analysis of the dynamic behaviour, considering the variation of the capacitance, for each one of the four values of frequency of the external force. This analysis shows the diversity of dynamic behaviours found for the nonlinear model. The variations of dynamic behaviours resulted of the nonlinear model varies around some types of dynamics, which can be, chaotic, periodic, quasi periodic, quasi periodic and multi periodic. That's indicate the possibility of utilization of the capacitance as control parameter of the system and shows the dissipation of energy by the resistance, this energy is from the mechanical domain, this fact open the discussion for the energy generation possibilities
Mestre

This work investigates the effects of long range hydrodynamic fibre-fibre interactions on the orientation state of a semi-dilute, rigid fibre suspension flowing through a linear contracting channel under laminar flow conditions. The effects of fibre-fibre interactions are modeled mathematically, the governing equations solved numerically and the predicted results compared with experimental observations. The theoretical model is based on the assumption that the orientation state of the suspension can be completely described by a probability distribution function and that fibre-fibre interactions are random in nature, thus giving rise to a diffusion-type process. The orientation distribution evolves spatially according to a Fokker-Plank type equation using closure equations for the rotary diffusion coefficient advanced by either (i) Folgar and Tucker (J. Reinforced Plast. Comp. 3 98–119 1984) or (ii) Koch (Phys. Fluids 7(8) 2086–2088 1995). Each of these two closure models for the rotary diffusion coefficient contains an unknown empirical constant that must be determined from experiments. These were fit to experimental data along the central streamline of the contraction as a function of fibre concentration. The diffusion coefficient was found to first increase with increasing suspension concentration up to a maximum, and then decrease with concentration above this point. This non-monotonic behavior was attributed to fibre flocculation, a mechanism not considered in the relationships for the rotary diffusion coefficient. The theoretical model is then extended to predict fibre orientation over the entire plane of the contraction and the two-way momentum coupling between the fluid and fibre phases were investigated numerically. The results show that the structure of the flow field within the contraction is significantly altered when the fibre phase is considered, demonstrating the non-negligible effect of the momentum exchange between the two phases. Comparison is made between the predicted orientation state of the suspension with experimental observations over the contraction plane. Good agreement was found between the model predictions and the experimental observations except in a small region near the solid boundaries. These near wall discrepancies were attributed to an inability to correctly handle the wall boundary conditions in the fibre orientation model.

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O projeto de pesquisa visou o melhor entendimento sobre a dinâmica de dois sistemas de um grau de liberdade: o primeiro é composto por uma estrutura de rigidez negativa, identificado no texto como NSS, o segundo é composto por uma estrutura de rigidez negativa amortecida, identificado no texto como DNSS. Neste trabalho os sistemas foram aplicados para absorver a vibração de um assento veicular buscando melhorar o conforto do condutor. Apresentou-se as equações usadas nas análises teóricas. Gerou-se resultados de análises estáticas, gráficos de força por deslocamento e energia potencial elástica por deslocamento, e de análises dinâmicas, curvas de resposta em frequência, plano de fase e histórico do deslocamento, para entender como os parâmetros influenciam nas respostas dos sistemas. Para as análises dinâmicas aplicou-se uma excitação de base do tipo senoidal e utilizou-se o método de Runge-Kutta de quarta e quinta ordem para a integração numérica das equações de movimento dos sistemas. Comparou-se as respostas, em regime permanente, dos sistemas com NSS e com DNSS com o sistema massa mola amortecedor, muito conhecido na literatura. Nas frequências naturais de cada sistema, chegou-se a reduzir o valor RMS do deslocamento da massa em 60,7 % com NSS e 70,5 % com DNSS quando comparados com o sistema massa mola amortecedor.
The research project aimed at the understanding of the dynamics of two single-degree-of-freedom systems: the first is made of a negative stiffness structure, NSS, the second is made of a damped negative stiffness, DNSS. In this work the systems were applied to absorb the vehicle seat vibration seeking to improve the driver's comfort. It was presented the equations used in the theoretical analysis. Results of static analysis, force by displacement and elastic potential energy by displacement, and of dynamics analysis, frequency response curves, phase portrait and displacement history, were generated to understand how the parameters influence the systems responses. For the dynamics analysis, a sinusoidal base excitation was applied and the fourth and fifth order Runge-Kutta method was used for the system motion equations numerical integration. The responses were compared, in stationary state, of the NSS and DNSS systems with the mass damping spring system, well known in the literature. In the natural frequencies of each system, it was possible to reduce the RMS value of the mass displacement by 60.7% with NSS and 70.5% with DNSS when compared to the mass damping spring system.

The main motivation of this study is the design of a control strategy for semi-active vehicle suspension systems to improve ride comfort for road vehicles. In order to achieve this objective, firstly the damping characteristics of Magnetorheological dampers will be reviewed. Then an appropriate semi-active control strategy manipulating the inputs of the dampers to create suitable damping forces will be designed. Linear Quadratic Regulator (LQR) control strategy is the primary focus area on semi-active control throughout this study. Further, skyhook controllers are examined and compared with optimal LQR controllers. The semi-active controller is tuned using a linearized full (4 wheel) vehicle ride model with seven degrees of freedom. Some selected simulations are carried out by using a nonlinear model to tune LQR controller in an effort to optimize bounce, pitch, and roll motion of the vehicle. Time domain simulations and frequency response analysis are used to justify the effectiveness of the proposed LQR control strategy.

Orientador: Douglas Eduardo Zampieri
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
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Resumo: Este trabalho analisa e compara sistemas semi-ativos de controle de suspensões veiculares com um sistema passivo não-linear. O modelo matemático do sistema de suspensão, detalhado nesta dissertação, tem sete graus de liberdade, de modo a representar um veículo completo com suas quatro rodas. As duas leis de controle semi-ativas utilizadas foram baseadas na teoria do skyhook, sendo que em uma destas leis, o coeficiente de amortecimento varia continuamente (semi-ativa CVD) e, na outra, este coeficiente pode assumir um valor máximo ou um valor mínimo (semi-ativa ON-OFF). Para a análise dos sistemas foi desenvolvido um programa usando a ferramenta computacional SIMULINK, programa que permite a avaliação de diversas situações de sistemas veiculares. Os resultados evidenciam uma alternância de melhor desempenho entre os sistemas passivo não linear, semi-ativo ON-OFF e semi-ativo CVD, sendo que para uma avaliação mais detalhada do desempenho dos sistemas semi-ativos se faz necessária uma otimização dos parâmetros utilizados nas leis de controle. Neste trabalho fica bastante evidente a importância de se considerar o comportamento não linear do conjunto amortecedor e mola no sistema passivo
Abstract: This work describes the analysis and comparison of a vehicle suspension semi-active controlled to a non linear passive system. The mathematic model of a suspension system, detailed in this work, has seven degrees of freedom in order to represent a full vehicle system. The two semi-active control laws used in this work are based on the skyhook theory. In the first one the damping coefficient is continuously variable (semi-active CVD) and, in the second one the damping coefficient can assume a maximum or a minimum value (semi-active ON-OFF). To analyze the systems, it was developed a program using the SIMULINK computational tool. This program can evaluate different situations of vehicle suspension systems. The results show that the non linear passive system, semi-active ON-OFF and semi-active CVD alternate the better performance. To have a better understanding of semi-active performance, an optimization of the parameters used in the control laws is needed. This work also explains the importance of considering the non linear behavior of passive systems elements
Mestrado
Mecanica dos Sólidos e Projeto Mecanico
Mestre em Engenharia Mecânica

Orientador: Bento Rodrigues de Pontes Junior
Banca: Marcio Antonio Bazani
Banca: João Eduardo Guarnetti dos Santos
Resumo: O projeto de pesquisa visou o melhor entendimento sobre a dinâmica de dois sistemas de um grau de liberdade: o primeiro é composto por uma estrutura de rigidez negativa, identificado no texto como NSS, o segundo é composto por uma estrutura de rigidez negativa amortecida, identificado no texto como DNSS. Neste trabalho os sistemas foram aplicados para absorver a vibração de um assento veicular buscando melhorar o conforto do condutor. Apresentou-se as equações usadas nas análises teóricas. Gerou-se resultados de análises estáticas, gráficos de força por deslocamento e energia potencial elástica por deslocamento, e de análises dinâmicas, curvas de resposta em frequência, plano de fase e histórico do deslocamento, para entender como os parâmetros influenciam nas respostas dos sistemas. Para as análises dinâmicas aplicou-se uma excitação de base do tipo senoidal e utilizou-se o método de Runge-Kutta de quarta e quinta ordem para a integração numérica das equações de movimento dos sistemas. Comparou-se as respostas, em regime permanente, dos sistemas com NSS e com DNSS com o sistema massa mola amortecedor, muito conhecido na literatura. Nas frequências naturais de cada sistema, chegou-se a reduzir o valor RMS do deslocamento da massa em 60,7 % com NSS e 70,5 % com DNSS quando comparados com o sistema massa mola amortecedor.
Abstract: The research project aimed at the understanding of the dynamics of two single-degree-of-freedom systems: the first is made of a negative stiffness structure, NSS, the second is made of a damped negative stiffness, DNSS. In this work the systems were applied to absorb the vehicle seat vibration seeking to improve the driver's comfort. It was presented the equations used in the theoretical analysis. Results of static analysis, force by displacement and elastic potential energy by displacement, and of dynamics analysis, frequency response curves, phase portrait and displacement history, were generated to understand how the parameters influence the systems responses. For the dynamics analysis, a sinusoidal base excitation was applied and the fourth and fifth order Runge-Kutta method was used for the system motion equations numerical integration. The responses were compared, in stationary state, of the NSS and DNSS systems with the mass damping spring system, well known in the literature. In the natural frequencies of each system, it was possible to reduce the RMS value of the mass displacement by 60.7% with NSS and 70.5% with DNSS when compared to the mass damping spring system.
Mestre

Parmi les differents mecanismes physiques permettant de premunir un detecteur d'une sur-illumination laser de duree nanoseconde dans le domaine visible, la diffusion non lineaire de la lumiere par des particules de carbone en suspension dans un solvant semble tres prometteuse, comme l'attestent de recentes etudes. Cependant, l'origine physique de la limitation optique observee n'est toujours pas clairement determinee ; ce memoire propose d'en ameliorer la connaissance au moyen d'excitations laser de duree nanoseconde et picoseconde permettant la mise en oeuvre d'experiences resolues temporellement et angulairement. Bien qu'efficaces pour la limitation optique d'excitations nanoseconde, les particules de carbone se revelent ainsi inefficaces pour limiter la transmission d'excitations picoseconde. Des experiences pompe-sonde montrent clairement que le phenomene de limitation, independant du solvant pendant les premieres nanosecondes, est associe a l'existence d'un processus de diffusion lie aux particules, l'influence du solvant devenant significative aux temps longs devant la duree de l'impulsion a travers un processus de relaxation thermique. Des considerations thermodynamiques valident ces observations et montrent que la vaporisation d'une particule de carbone peut etre envisagee comme un phenomene efficace de diffusion de la lumiere a faible flux lumineux et que son ionisation joue un role a plus fort flux. Des mesures de diffusion resolues angulairement soulignent l'importance croissante de la diffusion multiple lorsque l'energie incidente croit et des mesures de diffusion resolues temporellement font apparaitre aux temps courts (< 3 ns) une repartition conique de l'energie lumineuse. Cette observation nous amene a considerer, autour de l'entite diffusante, un profil d'indice particulier resultant d'une onde de choc creee par l'impulsion picoseconde excitatrice, profil qui serait a l'origine du piegeage d'une partie de l'onde incidente.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
O objetivo deste trabalho é estudar o comportamento dinâmico de sistemas de suspensão veicular que empregam amortecimento viscoso assimétrico, com foco na melhoria do conforto para os passageiros, considerando não linearidade geométricas presentes no sistema. Estudos anteriores comprovam que o uso de amortecedores assimétricos nestes tipos de sistema pode ser vantajoso com relação ao conforto dos passageiros. Porém, nota-se que há uma deficiência no entendimento do comportamento dinâmico deste tipo de sistema. Portanto, análises mais aprofundadas deste problema devem ser realizadas. A modelagem e o comportamento de duas configurações de suspensões, uma com amortecimento viscoso simétrico e outra com amortecimento viscoso assimétrico são apresentados e comparados. As simulações são feitas usando um modelo de quarto de carro para analisar a dinâmica vertical. A configuração geométrica de um sistema de suspensão é levada em consideração na modelagem da força de amortecimento e da força da mola, de forma a incluir não linearidade geométricas no modelo. O perfil de pavimento é introduzido no sistema através de uma excitação harmônica. Diversos valores de frequência de excitação são utilizados para descrever as diferentes irregularidades de diferentes tipos de pavimento. Os modelos matemáticos referentes aos sistemas de suspensão descritos são analisados através de simulação numérica. Através da análise computacional e métodos usuais em dinâmica não linear, incluindo históricos de deslocamento, plano de fase e resposta em frequencia é possível identificar regiões nas quais fenômenos indesejados ocorrem. Para esta análise, foram variados os valores do coeficiente de amortecimento tanto para a compressão quanto para a extensão do amortecedor e estabelecida uma razão de assimetria. Através da modelagem e simulações computacionais deste estudo é possível verificar que a escolha da...
The objective of this work is to study the dynamical behaviour of vehicle supension system employing asynmetrical viscous damping, with a focus on improving passenger comfort, considering geometric nonlinearities which are present in the system. Previous studies have shown that the use of asymmetrical dampers in these types of systems can be advantageous with regard to the comfort of the passengers. However, there is a deficiency in understanding the dynamic behaviour of such systems. Therefore, further analysis of this problem should be conducted. The modeling and the behaviour of suspensions of two configurations, one with symmetrical viscous damping and another with asymmetrical viscous damping are presented and compared. The simulations are performed using a quarter-car model to analyze the vertical dynamics. The geometric configuration of a suspension system is taken into account in modeling the damping force and spring force, to include geometrical nonlinearities in the model. The road profile is introduced into the system through a harmonic excitation. Several values of excitation frequency are used to describe the various irregularities of different types of road. Mathematical models of the described suspension systems are analyzed by numerical simulation. Through computational analysis and usual methods in nonlinear dynamics, including time history, phase plane and frequency response, it is possible to identify regions where unwanted phenomena occur. For this analysis, the values of the damping coefficient for the compression and extension of the damper were varied, establishing an asymmetry ratio. Through modeling and computer simulations in this study, the choice of the asymmetry ratio diminishes the effects that the unever road causes on the displacement and acceleration of the sprung mass. This decrease can also improve the comfort for the passengers

Orientador: Marcos Silveira
Banca: Paulo José Paupitz Gonçalves
Banca: Samuel da Silva
Resumo: O objetivo deste trabalho é estudar o comportamento dinâmico de sistemas de suspensão veicular que empregam amortecimento viscoso assimétrico, com foco na melhoria do conforto para os passageiros, considerando não linearidade geométricas presentes no sistema. Estudos anteriores comprovam que o uso de amortecedores assimétricos nestes tipos de sistema pode ser vantajoso com relação ao conforto dos passageiros. Porém, nota-se que há uma deficiência no entendimento do comportamento dinâmico deste tipo de sistema. Portanto, análises mais aprofundadas deste problema devem ser realizadas. A modelagem e o comportamento de duas configurações de suspensões, uma com amortecimento viscoso simétrico e outra com amortecimento viscoso assimétrico são apresentados e comparados. As simulações são feitas usando um modelo de quarto de carro para analisar a dinâmica vertical. A configuração geométrica de um sistema de suspensão é levada em consideração na modelagem da força de amortecimento e da força da mola, de forma a incluir não linearidade geométricas no modelo. O perfil de pavimento é introduzido no sistema através de uma excitação harmônica. Diversos valores de frequência de excitação são utilizados para descrever as diferentes irregularidades de diferentes tipos de pavimento. Os modelos matemáticos referentes aos sistemas de suspensão descritos são analisados através de simulação numérica. Através da análise computacional e métodos usuais em dinâmica não linear, incluindo históricos de deslocamento, plano de fase e resposta em frequencia é possível identificar regiões nas quais fenômenos indesejados ocorrem. Para esta análise, foram variados os valores do coeficiente de amortecimento tanto para a compressão quanto para a extensão do amortecedor e estabelecida uma razão de assimetria. Através da modelagem e simulações computacionais deste estudo é possível verificar que a escolha da...
Abstract: The objective of this work is to study the dynamical behaviour of vehicle supension system employing asynmetrical viscous damping, with a focus on improving passenger comfort, considering geometric nonlinearities which are present in the system. Previous studies have shown that the use of asymmetrical dampers in these types of systems can be advantageous with regard to the comfort of the passengers. However, there is a deficiency in understanding the dynamic behaviour of such systems. Therefore, further analysis of this problem should be conducted. The modeling and the behaviour of suspensions of two configurations, one with symmetrical viscous damping and another with asymmetrical viscous damping are presented and compared. The simulations are performed using a quarter-car model to analyze the vertical dynamics. The geometric configuration of a suspension system is taken into account in modeling the damping force and spring force, to include geometrical nonlinearities in the model. The road profile is introduced into the system through a harmonic excitation. Several values of excitation frequency are used to describe the various irregularities of different types of road. Mathematical models of the described suspension systems are analyzed by numerical simulation. Through computational analysis and usual methods in nonlinear dynamics, including time history, phase plane and frequency response, it is possible to identify regions where unwanted phenomena occur. For this analysis, the values of the damping coefficient for the compression and extension of the damper were varied, establishing an asymmetry ratio. Through modeling and computer simulations in this study, the choice of the asymmetry ratio diminishes the effects that the unever road causes on the displacement and acceleration of the sprung mass. This decrease can also improve the comfort for the passengers
Mestre

O presente trabalho implementa a otimização dos ganhos de um controle ativo com regulador linear quadrático (LQR), em um modelo veicular completo sujeito a um perfil de estrada proposto pela ISO 8608, para atenuação das acelerações RMS transmitidas para a carroceria e o assento do motorista. Dado que o ganho do controle LQR é formulado a partir das matrizes Q e R, o procedimento determina as matrizes ótimas do controle para a minimização das acelerações RMS transmitidas. O modelo é analisado no domínio do tempo por meio da formulação de espaço-estado, e o procedimento de otimização é avaliado pelo método dos algoritmos genéticos. Os parâmetros Q e R, que fornecem o melhor ganho para minimização do problema de otimização, reduzem em até 1000 vezes as acelerações RMS quando comparadas à situação sem atuação do controle. Após otimizar Q e R, são analisadas a influência nos demais graus de liberdade e as forças necessárias para os resultados obtidos.
This work aims to optimize the gains of an active control with linear quadratic regulator (LQR), applied in a full vehicle model subject to a random road surface profile proposed by ISO 8608, for reduction of RMS accelerations transmitted to the driver’s seat and the vehicle body. Since the gain of LQR control is formulated from the matrices Q and R, the procedure determines the optimal control matrices that minimize the RMS accelerations transmitted. The model is analyzed in the time domain through state-space formulation, and the optimization process evaluated by the method of genetic algorithms. The parameters Q and R, which provide the best gain for minimizing the optimization problem, reduce by up to 1000 times the RMS accelerations when compared to the situation without active control. Finally, after optimizing Q e R, are analyzed the influence to the other degrees of freedom and the forces necessary for the results obtained.

Orientador : Douglas Eduardo Zampieri
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
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Resumo: Neste trabalho, é feito um estudo sobre a aplicação de redes neurais artificiais na identificação e no controle de suspensões ativas não lineares. Considerando um modelo de um quarto de veículo, a modelagem matemática de sistemas passivos e ativos é detalhada. Noções básicas da aplicação das redes neurais, arquitetura, tipos de aprendizado, algoritmos de treinamento, etc., é apresentado, assim como, sua aplicação atual na identificação e controle de sistemas dinâmicos não lineares. O neuro-controlador proposto é do tipo "baseado em um modelo de referência", e seus pesos são ajustados utilizando um novo conceito de mapeamento inverso através do emprego de um neuro-modelo (neuro-veículo) para a retropropagação do sinal de erro (diferença entre a saída de referência desejada e a saída da rede neural). Simulações computacionais são realizadas com a finalidade de testar o modelo proposto, através da análise do espaço de trabalho da suspensão, da aceleração da massa suspensa e da força de contato do pneu com o solo, principais parâmetros utilizados no projeto de suspensões automotivas. Os resultados demonstram o poder das redes neurais na identificação e no controle de sistemas dinâmicos com características não lineares
Abstract: This work presents a study about applications of artificial neural networks in the identification and control of nonlinear active suspensions. Considering an one-quarter vehic1e model, the mathematical modeling of passive and active systems is detailed. Basic concepts of neural networks application, architecture, type of learning, training algorithms, etc., are presented as well as the application in identification and control of nonlinear dynamic systems which is used in this work. The proposed neuro-contoller is of type "model reference neuro-controller", and their weights are set using a new concept of inverse mapping trough the use of a neuro-model (neuro-vehicle) to a backpropagation of the error signal (difference between the output of the desired reference and the output ofthe neural network). Computational simulations are performed in order to test the proposed model, trough the analysis of the suspensions work space, acceleration of the sprung mass and contact force of the tire with the ground, which are the main arameters used in the design of automotive suspensions. The results show the suitability of neural network in the identification and control of dynamic systems with nonlinear characteristics
Mestrado
Mecanica dos Sólidos e Projeto Mecanico
Mestre em Engenharia Mecânica

Diese Arbeit stützt sich auf die theoretische und experimentelle Untersuchung der Thermodiffusion im Magnetfeld. Bei magnetischen Flüssigkeiten als kolloidalen Suspensionen versteht man unter der Thermodiffusion einen durch einen Temperaturgradienten angestoßenen unidirektionalen Partikeltransport, der zur Separation des Fluids führt. Beschrieben wird die Thermodiffusion theoretisch über das Konzentrationsprofil der Partikel in Abhängigkeit von Zeit und Ort in einer Fluidschicht. Die Experimente detektieren die Separation des Fluids über die Konzentrationsdifferenz zwischen zwei Fluidkammern. Die Bestimmung des Soret-Koeffizienten erfolgt über einen Datenfit zwischen experimentellen und theoretischen Daten. Für das kerosinbasierte Ferrofluid EMG905 wurden zwei Effekte festgestellt. Bei kleinen Magnetfeldstärken wandern die Partikel zum kalten Rand der Schicht (ST>0), bei steigenden Feldstärken kehrt sich diese Richtung um (ST<0). Die Ergebnisse der Untersuchungen zur Thermodiffusion gehen dann in eine lineare Stabilitätsanalyse einer Ferrofluidschicht bei anliegendem Temperaturgradienten und Magnetfeld ein. Dabei wird festgestellt, dass die kritische Rayleigh-Zahl als charakteristische Größe zum Einsetzen von Konvektion von dem Soret-Koeffizienten abhängt. Ist letzterer positiv, wird das Einsetzen von Konvektion begünstigt, ist er wiederum negativ, so kann Konvektion vollständig unterdrückt werden.

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Essa dissertação trata da dinâmica de um sistema com não-linearidade na rigidez devido à geometria do mecanismo articulado de duas barras, identificado como NLGS ao longo do texto. Na Introdução do trabalho são mostrados exemplos de sistema com rigidez não-linear devido á geometria, destacando a aplicação desse tipo de sistema como isolador de vibração e também discute-se sobre a exposição humana à vibração como motivação e justificativa para o trabalho, ressaltando-se as frequências de ressonância das diversas partes do corpo humano. Na sequência faz-se a revisão bibliográfica sobre o assunto de vibrações para auxiliar na compreensão do trabalho. Após esses capítulos introdutórios é feita a apresentação e a modelagem matemática dos sistemas dinâmicos estudados: sistema NLGS ideal, sistema com rigidez não-linear e sistema não ideal. As equações de movimento são deduzidas pelo método de Lagrange. Após a dedução das equações de movimento faz-se a integração numérica utilizando o método de Runge-Kutta de quarta e quinta ordem e obtém-se a resposta dos sistemas (deslocamento, velocidade e aceleração). Como resultado da integração numérica são construídas algumas curvas, tais como: histórico de deslocamento, histórico de frequência, plano de fase, FFT, resposta em frequência e diagrama de bifurcação para ajudar na compreensão do comportamento dinâmico dos sistemas. Com base nos resultados obtidos percebe-se que os sistemas NLGS não ideal, NLGS ideal e com rigidez não linear apresentam um comportamento complexo devido à rigidez não-linear. Nesses três sistemas tem-se indicação de regime de movimento caótico inclusive. No sistema não ideal observa-se o efeito Sommerfeld, o qual deixa evidente a captura da rotação do motor pela frequência natural do sistema e o salto na curva da amplitude de deslocamento em função da frequência do motor. Fazendo um comparativo entre o...
This dissertation concerns with the dynamics of a system with nonlinearity in the stiffness due to geometry of a pivot mechanism of two bars, called NLGS in the text. In the Introduction are shown examples of system with nonlinear stiffness due to geometry, emphasizing the application of this kind of system as vibration isolator and is also discussed about the human exposure to vibration as motivation and justification in the research, emphaizing the different resonance frequencies of the human body. In the sequence is carried out the literature review about vibrations to help on understanding the research. After these introductory chapters is done the presentation and mathematical modeling of the studied dynamic systems: non-ideal NLGS system, ideal NLGS system, nonlinear stiffness system and non-ideal system. The equations of motion are deduced by Langrange's method. After the deduction of the equations of motion is carried out the numerical integration using the fourth and fifth order Runger-Kutta's method and it is gotten the response of the systems (displacement, velocity and acceleration). As result of the numerical integration some curves are plotted, such as: displacement history, frequency history, phase portrait, FFT, frequency response and bifurcation diagram to help on understanding the dynamic behavior of the systems. Based on the results is noticed that the following systems have a complex behavior due to nonlinear stiffness: non-ideal NLGS, ideal NLGS and nonlinear stiffness system. In these three systems there are indications of chaotic motion. In the non-ideal system the Sommerfeld effect is observed, evidencing the capture of the frequency of motor by the natural frequency of the system and the jump in the curve of frequency response. Comparing the non-ideal NLGS system and the non-ideal system conludes that the Sommerfeld effect is eliminated and the maximum amplitude of displacement is reduced by 27% in the non-ideal...

Orientador: Bento Rodrigues de Pontes Junior
Banca: Marcio Antonio Bazani
Banca: Marcos Silveira
Resumo: Essa dissertação trata da dinâmica de um sistema com não-linearidade na rigidez devido à geometria do mecanismo articulado de duas barras, identificado como NLGS ao longo do texto. Na Introdução do trabalho são mostrados exemplos de sistema com rigidez não-linear devido á geometria, destacando a aplicação desse tipo de sistema como isolador de vibração e também discute-se sobre a exposição humana à vibração como motivação e justificativa para o trabalho, ressaltando-se as frequências de ressonância das diversas partes do corpo humano. Na sequência faz-se a revisão bibliográfica sobre o assunto de vibrações para auxiliar na compreensão do trabalho. Após esses capítulos introdutórios é feita a apresentação e a modelagem matemática dos sistemas dinâmicos estudados: sistema NLGS ideal, sistema com rigidez não-linear e sistema não ideal. As equações de movimento são deduzidas pelo método de Lagrange. Após a dedução das equações de movimento faz-se a integração numérica utilizando o método de Runge-Kutta de quarta e quinta ordem e obtém-se a resposta dos sistemas (deslocamento, velocidade e aceleração). Como resultado da integração numérica são construídas algumas curvas, tais como: histórico de deslocamento, histórico de frequência, plano de fase, FFT, resposta em frequência e diagrama de bifurcação para ajudar na compreensão do comportamento dinâmico dos sistemas. Com base nos resultados obtidos percebe-se que os sistemas NLGS não ideal, NLGS ideal e com rigidez não linear apresentam um comportamento complexo devido à rigidez não-linear. Nesses três sistemas tem-se indicação de regime de movimento caótico inclusive. No sistema não ideal observa-se o efeito Sommerfeld, o qual deixa evidente a captura da rotação do motor pela frequência natural do sistema e o salto na curva da amplitude de deslocamento em função da frequência do motor. Fazendo um comparativo entre o...
Abstract: This dissertation concerns with the dynamics of a system with nonlinearity in the stiffness due to geometry of a pivot mechanism of two bars, called NLGS in the text. In the Introduction are shown examples of system with nonlinear stiffness due to geometry, emphasizing the application of this kind of system as vibration isolator and is also discussed about the human exposure to vibration as motivation and justification in the research, emphaizing the different resonance frequencies of the human body. In the sequence is carried out the literature review about vibrations to help on understanding the research. After these introductory chapters is done the presentation and mathematical modeling of the studied dynamic systems: non-ideal NLGS system, ideal NLGS system, nonlinear stiffness system and non-ideal system. The equations of motion are deduced by Langrange's method. After the deduction of the equations of motion is carried out the numerical integration using the fourth and fifth order Runger-Kutta's method and it is gotten the response of the systems (displacement, velocity and acceleration). As result of the numerical integration some curves are plotted, such as: displacement history, frequency history, phase portrait, FFT, frequency response and bifurcation diagram to help on understanding the dynamic behavior of the systems. Based on the results is noticed that the following systems have a complex behavior due to nonlinear stiffness: non-ideal NLGS, ideal NLGS and nonlinear stiffness system. In these three systems there are indications of chaotic motion. In the non-ideal system the Sommerfeld effect is observed, evidencing the capture of the frequency of motor by the natural frequency of the system and the jump in the curve of frequency response. Comparing the non-ideal NLGS system and the non-ideal system conludes that the Sommerfeld effect is eliminated and the maximum amplitude of displacement is reduced by 27% in the non-ideal...
Mestre

博士
國立清華大學
動力機械工程學系
89
A single-stage magnetic suspended positioning stage directly driven by an inverter-fed linear ac motor with precision positioning capability is developed in this dissertation. The magnetic suspension positioning system is established with all constituted parts being properly matched and constructed. In the propulsion system, the double-sided linear permanent magnet synchronous motor (LPMSM) is adopted. The LPMSM is powered by a hysteresis current-controlled PWM inverter with commutation according to the moving member position information. The dynamic model is indispensable for controller design, but it is not easy to obtain accurately from physical derivation. Hence, the estimation approach is employed as an alternative to obtain the estimated one from measurements. As generally recognized, the driving performance of an inverter-fed electromechanical system is significantly affected by the current switching control performance of its current-controlled PWM scheme, which forms the innermost loop of the multi-loop control system. Owing to its simplicity and robustness, the hysteresis PWM scheme has been widely employed in motor speed driving control. However, it is rarely used for position servo drive, since it possesses varying output harmonic spectrum, and the fixed current error bound becomes comparatively larger as the motor current becomes smaller. In this dissertation, the studies about the promotion of hysteresis PWM inverter for servo application are made. In the proposed control approaches, the error band of hysteresis PWM inverter is tuned to yield the desired constant and random harmonic spectrum distribution characteristics. Effectiveness of the developed control approaches is first tested in a single-phase electrodynamic shaker system. Then the designed three-phase inverter is used to power the magnetic suspension positioning system. Simulated and measured results show that better performances in current tracking control, harmonic spectrum distribution characteristics and position control can be achieved by the proposed varying-band hysteresis current-controlled PWM schemes. As to the positioning control, in order to obtain the desired robust command tracking and load regulation control requirements simultaneously, a two-degrees-of-freedom (2DOF) control scheme combining the H_inf feedback control, the command feedforward control and the model following control is developed. The loop shaping H_inf design procedure is employed to find the feedback controller, which is emphasized in obtaining the desired disturbance and uncertainty rejection control requirements and the guarantee of closed-loop stability. Then, the H_inf feedback controller is augmented with a command feedforward controller to form the 2DOF control structure. Through properly shaping the command by the feedforward controller, the prescribed command tracking control performance can then be independently satisfied. As the operating condition and parameter changes occurred, a model following tracking error driven control is further employed to improve the control performance degradation. It follows that the prescribed control requirements at nominal case still can be preserved for the disturbed cases.

碩士
國立臺北科技大學
車輛工程系所
96
The Bose company applies Linear Motor with the suspension system which named by “Bose suspension system”. The system applies coil motor instead of absorber and spring . The response time of the system is better than hydraulic type. The system depends on the road state to improve ride comfort and to increase the handling stability for vehicle in driving. Because the force constant of the coil motor is smaller, so the system need bigger space to install and consume more electric energy. The paper designs linear synchronous motor which is installed with spring. The motor can be produced over 5000 N under the limit current. Because the force constant of the linear synchronous motor is bigger, so the system don’t need bigger space to install. The control strategy is based on LQR .The system uses PWM and switch transistor to satisfy the controller require. The system uses high sensitive position sensor in order to give accurate phase current of the motor and get better control effect. Finally, frequency response is analyzed to investigate advantage and disadvantage between the traditional suspension system and the active suspension system.

碩士
國立臺北科技大學
車輛工程系
106
Currently, analysis and control of ride quality are mostly conducted using traditional suspension mathematical models. The traditional model’s advantage is that it can simply describe of the relationship between sprung mass and unsprung mass and can save times in calculating lengthy and difficult math. However, the suspension system of a vehicle is not installed directly above the tires nor is not transmitted just a single bounce motion between vehicle’s body and tires. Therefore, the analysis and control results obtain by this mathematical model often have a certain difference with the experimental results of the actual response. In order to better understand the vehicle dynamic behavior which influence by suspension, this study establish a nonlinear model incorporating geometric parameters related to double-wishbone suspension in quarter-vehicle and half-vehicle on two-dimensional space. Static balance and kinematics analyses were conducted to estimate the initial balanced positions of suspension components subjected to various loads. In addition, the proposed nonlinear model was linearized to develop optimal control strategies for semi-active suspension systems. By using vehicle dynamic simulation software ‘’ADAMS’’ to compare of the non-linear model and traditional model, the results show that the non-linear model can enable comprehensively describing how the relative positions, velocity, and force transmission of suspension components affect the motions of the vehicle body and tires. The control results of the non-linear semi-active suspension model are also better than that of the simple semi-active suspension model.

Recently, active suspension has been applied to many commercial automobiles. To develop the control algorithm for active suspension, a quarter-car test bed was built by using a direct-drive tubular linear brushless permanent-magnet motor (LBPMM) as a force-generating component. Two accelerometers and a linear variable differential transformer (LVDT) are used in this quarter-car test bed. Three pulse-width-modulation (PWM) amplifiers supply the currents in three phases. Simulated road disturbance is generated by a rotating cam. Modified lead-lag control, linear-quadratic (LQ) servo control with a Kalman filter, and the fuzzy control methodologies were implemented for active-suspension control. In the case of fuzzy control, asymmetric membership functions were introduced. This controller could attenuate road disturbance by up to 78%. Additionally, a sliding-mode controller (SMC) is developed with a different approach from the other three control methodologies. While SMC is developed for the position control, the other three controllers are developed for the velocity control. SMC showed inferior performance due to the drawback of the implemented chattering-proof method. Both simulation and experimental results are presented to demonstrate the effectiveness of these four control methodologies.

碩士
國立臺北科技大學
車輛工程系所
105
The main purpose of this study is to obtain better vehicle ride responses by using a nonlinear ride model considering the effect of Macpherson suspension geometry. Currently, analysis and control of ride quality are mostly conducted using traditional suspension mathematical models. In practice, the suspension system of a vehicle is not installed directly above the tires or positioned perpendicular to the horizontal plane of the vehicle, nor do the vehicle body and tires exhibit a straight up-and-down motion; hence, analyses conducted using simplified models usually yield results differing from those of experiments with real vehicles. Consequently, control strategies formulated through such analyses are not effective in practice. To accurately determine the effect of suspension on vehicle dynamic behavior and propose practical control strategies, this study established a nonlinear model incorporating geometric parameters related to vehicle suspension. Static balance and kinematics analyses were conducted to estimate the initial balanced positions of suspension components subjected to various loads. This enabled comprehensively describing how the relative positions, velocity, and force transmission of suspension components affect the motions of the vehicle body and tires. In addition, the proposed nonlinear model was linearized to develop control strategies for semi-active suspension systems.

碩士
國立臺北科技大學
車輛工程系所
95
This research aims on the design of a linear motor as an adjustable damper for semi-active suspension systems to improve ride comfort and to increase the handling stability for vehicle in driving. The adjustable damper can be classified as hydraulic type and electric type. The drawback of the hydraulic type is that system time constant is longer. The drawback of the electric type is that extra power is needed. This paper uses the principle to transform magnetic field into electricity to design an adjustable damper which needs no extra power. The power of the linear motor as an adjustable damper is provided by back-electromotive force which is produced by vehicle vibration in driving. The adjust strategy of damper constant in suspension system is based on Linear Quadratic Regulator. PWM control is used to make motor current achieve controller request. Finally, frequency response is analyzed to investigate advantage and disadvantage between the traditional suspension system and the semi-active suspension system.

碩士
國立成功大學
航空太空工程學系
89
Design, Analysis and Realization of Magnetic Suspension Transport System Using Linear Motor Structure Student: Yi Lung Wu Adviser: Chin E. Lin Abstract To design a magnetic suspension transport track, a linear motor model is applied. With repulsive force of drive, the direction of magnetic force in horizontal, X-axis and Y-axis, is a major concern. The repulsive force is controlled to balance both sides of the vehicle, and to maintain its driving direction along the centerline of the track in X-direction. There are many factors in this system to affect the vehicle being driven smoothly, such as applied voltage, enable delay time and disable delay time, and etc. Which one has more contribution rate to the overall performance? Among those factors, any combination of factors may be chosen for different payload implementation. Based on this consideration, the Taguchi Method is applied in system analysis and experiment to find the main and minor factors. Then the system is integrated and carried out running tests with satisfactory results. 中文摘要 英文摘要 誌謝 圖目錄………………………………………………Ⅰ 表目錄………………………………………………Ⅲ 符號說明……………………………………………Ⅳ 目錄…………………………………………………Ⅵ 第一章 緒 論…………………………………………1 1.1 前言……………………………………………………1 1.2 研究動機………………………………………………3 1.3 本文大綱………………………………………………4 第二章 磁浮軌道運輸系統架構…………………5 2.1 研究步驟………………………………………………5 2.2 決定軌道各部形式、規格與尺寸……………………7 2.2.1 軌道…………………………………………………7 2.2.2 車體…………………………………………………8 2.2.3電磁極組……………………………………………9 2.2.4感測系統……………………………………………10 2.2.5驅動系統……………………………………………11 2.2.6線性馬達架構………………………………………12 2.3電磁極組擺放位置與方式……………………………14 2.4車載磁極擺設角度……………………………………15 2.5測試軌道二側電磁極磁力是否相等…………………18 第三章 控制電路之設計、分析及程式之撰寫……20 3.1 控制電路之設計基礎…………………………………20 3.2 感測器…………………………………………………20 3.3控制電路板……………………………………………24 3.4 LED顯示卡及轉換電路………………………………27 3.5微處理機界面卡及擴充槽……………………………29 3.6 486PC電腦及程式之撰寫……………………………31 3.7結論……………………………………………………33 第四章 動態模式之建立及測試……………………34 4.1 動態模式之分析與建立………………………………34 4.2空氣阻力之探討………………………………………35 4.3摩擦力之探討…………………………………………37 4.4實際拉力的量測………………………………………38 4.5磁力之探討……………………………………………39 4.6簡易延遲時間與最適電壓與電流之測試……………41 4.7 結論……………………………………………………42 第五章 田口式品質設計方法………………………43 5.1 何謂田口式品質設計方法……………………………43 5.2 目的、方法與流程圖…………………………………43 5.2.1 目的…………………………………………………43 5.2.2 方法…………………………………………………44 5.2.3流程圖………………………………………………44 5.3 望大特性………………………………………………46 5.4 因素水準配置及魚骨圖之製作………………………46 5.5 直交表…………………………………………………48 5.5.1 數據配置權重………………………………………48 5.5.2 直交表之選定………………………………………49 5.6第一次（L36）實驗與SN比分析……………………50 5.7 第二次實驗（加入動態特性）………………………59 5.8 內部各組之排列組合配對之探討……………………65 5.9 結論……………………………………………………66 第六章 結論………………………………………67 6.1 結果討論………………………………………………67 6.2 未來發展方向…………………………………………69 參考文獻……………………………………………71 自述…………………………………………………72 著作權聲明…………………………………………73