566 research outputs found

    Automated generation of hybrid automata for multi-rigid-body mechanical systems and its application to the falsification of safety properties

    Get PDF
    © 2017 The Authors. Published by Taylor & Francis. This is an open access article available under a Creative Commons licence. The published version can be accessed at the following link on the publisher’s website: https://doi.org/10.1080/13873954.2017.1369437What if we designed a tool to automatically generate a dynamical transition system for the formal specification of mechanical systems subject to multiple impacts, contacts and discontinuous friction? Such a tool would represent an advance in the description and simulation of these complex systems. This is precisely what this paper offers: Dyverse Rigid Body Toolbox (DyverseRBT). This tool requires a sufficiently expressive computational model that can accurately describe the behaviour of the system as it evolves over time. For this purpose, we propose an alternative abstraction of multi-rigid-body (MRB) mechanical systems with multiple contacts as an extended version of the classical hybrid automaton, which we call MRB hybrid automaton. One of the chief characteristics of the MRB hybrid automaton is the inclusion of computation nodes to encode algorithms to calculate the contact forces. The computation nodes consist of a set of non-dynamical discrete locations, discrete transitions and guards between these locations, and resets on transitions. They can account for the energy transfer not explicitly considered within the rigid-body formalism. The proposed modelling framework is well suited for the automated verification of dynamical properties of realistic mechanical systems. We show this by the falsification of safety properties over the transition system generated by DyverseRBT.This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of the UK: [Grant Number EP/I001689/1] (‘DYVERSE: A New Kind of Control for Hybrid Systems’), and the Research Councils UK (RCUK): [Grant Number EP/E50048/1].Published versio

    Predictive Modelling of Tribological Systems using Movable Cellular Automata

    Get PDF
    In the science of tribology, where there is an enormous degree of uncertainty, mathematical models that convey state-of-the-art scientific knowledge are invaluable tools for unveiling the underlying phenomena. A well-structured modelling framework that guarantees a connection between mathematical representations and experimental observations, can help in the systematic identification of the most realistic hypotheses among a pool of possibilities. This thesis is concerned with identifying the most appropriate computational model for the prediction of friction and wear in tribological applications, and the development of a predictive model and simulation tool based on the identified method. Accordingly, a thorough review of the literature has been conducted to find the most appropriate approach for predicting friction and wear using computer simulations, with the multi-scale approach in mind. It was concluded that the Movable Cellular Automata (MCA) method is the most suitable method for multi-scale modelling of tribological systems. It has been established from the state-of-the-art review in Chapter 2 of this thesis, that it is essential to be able to model continuous as well as discontinuous behaviour of materials on a range of scales from atomistic to micro scales to be able to simulate the first-bodies and third body simultaneously (also known as a multi-body) in a tribological system. This can only be done using a multi-scale particle-based method because continuum methods such as FEM are none-predictive and are not capable of describing the discontinuous nature of materials on the micro scale. The most important and well-known particle-based methods are molecular dynamics (MD) and the discrete element methods (DEM). Although MD has been widely used to simulate elastic and plastic deformation of materials, it is limited to the atomistic and nanoscales and cannot be used to simulate materials on the macro-scale. On the other hand, DEM is capable of simulating materials on the meso/micro scales and has been expanded since the algorithm was first proposed by Cundall and Strack, in 1979 and adopted by a number of scientific and engineering disciplines. However, it is limited to the simulation of granular materials and elastic brittle solid materials due to its contact configurations and laws. Even with the use of bond models to simulate cohesive and plastic materials, it shows major limitations with parametric estimations and validation against experimental results because its contact laws use parameters that cannot be directly obtained from the material properties or from experiments. The MCA method solves these problems using a hybrid technique, combining advantages of the classical cellular automata method and molecular dynamics and forming a model for simulating elasticity, plasticity and fracture in ductile consolidated materials. It covers both the meso and micro scales, and can even “theoretically” be used on the nano scale if the simulation tool is computationally powerful enough. A distinguishing feature of the MCA method is the description of interaction of forces between automata in terms of stress tensor components. This way a direct relationship between the MCA model parameters of particle interactions and tensor parameters of material constitutive law is established. This makes it possible to directly simulate materials and to implement different models and criteria of elasticity, plasticity and fracture, and describe elastic-plastic deformation using the theory of plastic flow. Hence, in MCA there is no need for parametric fitting because all model parameters can be directly obtained from the material mechanical properties. To model surfaces in contact and friction behaviour using MCA, the particle size can be chosen large enough to consider the contacting surface as a rough plane, which is the approach used in all MCA studies of contacting surfaces so far. The other approach is to specify a very small particle size so that it can directly simulate a real surface, which allows for the direct investigation of material behaviour and processes on all three scale levels (atomic, meso and macro) in an explicit form. This has still been proven difficult to do because it is too computationally extensive and only a small area of the contact can be simulated due to the high numbers of particles required to simulate a real solid. Furthermore, until now, no commercial software is available for MCA simulations, only a 2D MCA demo-version which was developed by the Laboratory of CAD of Materials at the Institute of Strength Physics and Materials Science in Tomsk, Russia, in 2005. The developers of the MCA method use their own in-house codes. This thesis presents the successful development of a 3D MCA open-source software for the scientific and tribology communities to use. This was done by implementing the MCA method within the framework of the open-source code LIGGGHTS. It follows the formulations of the 3D elastic-plastic model developed by the authors including Sergey G. Psakhie, Valentin L. Popov, Evgeny V. Shilko, and the external supervisor on this thesis Alexey Yu. Smolin, which has been successfully implemented in the open-source code LIGGGHTS. Details of the mathematical formulations can be found in [1]–[3], and section 3.5 of this thesis. The MCA model has been successfully implemented to simulate ductile consolidated materials. Specifically, new interaction laws were implemented, as well as features related to particle packing, particle interaction forces, bonding of particles, and others. The model has also been successfully verified, validated, and used in simulating indentation. The validation against experimental results showed that using the developed model, correct material mechanical response can be simulated using direct macroscopic mechanical material properties. The implemented code still shows limitations in terms of computational capacity because the parallelization of the code has not been completely implemented yet. Nevertheless, this thesis extends the capabilities of LIGGGHTS software to provide an open-source tool for using the MCA method to simulate solid material deformation behaviour. It also significantly increases the potential of using MCA in an HPC environment, producing results otherwise difficult to obtain

    Enclosing the behavior of a hybrid automaton up to and beyond a Zeno point

    Get PDF
    Even simple hybrid automata like the classic bouncing ball can exhibit Zeno behavior. The existence of this type of behavior has so far forced a large class of simulators to either ignore some events or risk looping indefinitely. This in turn forces modelers to either insert ad-hoc restrictions to circumvent Zeno behavior or to abandon hybrid automata. To address this problem, we take a fresh look at event detection and localization. A key insight that emerges from this investigation is that an enclosure for a given time interval can be valid independent of the occurrence of a given event. Such an event can then even occur an unbounded number of times. This insight makes it possible to handle some types of Zeno behavior. If the post-Zeno state is defined explicitly in the given model of the hybrid automaton, the computed enclosure covers the corresponding trajectory that starts from the Zeno point through a restarted evolution

    Modeling and Control of Reluctance Actuators

    Get PDF
    Los actuadores de reluctancia son dispositivos que se caracterizan por una elevada densidad de fuerza, buena eficiencia, gran tolerancia frente a fallos y un coste reducido. Estas características hacen que estén siendo considerados como una alternativa muy prometedora frente a otro tipo de actuadores electromagnéticos en ciertas aplicaciones que requieren gran velocidad y precisión. Por otro lado, los actuadores de reluctancia también son la solución ideal para algunos dispositivos electromecánicos que requieren unas prestaciones modestas, lo cual es debido principalmente a que son compactos, tienen un bajo coste y consumen relativamente poco. En concreto, los relés electromecánicos y las válvulas de solenoide son dispositivos cuya operación está basada en la fuerza creada por un pequeño actuador de reluctancia.A pesar de sus ventajas, los actuadores de reluctancia son sistemas complejos cuya dinámica es no lineal. Una de sus características más distintivas es que la fuerza magnética que provoca el movimiento es siempre de atracción y, además, depende fuertemente de la posición de la armadura. Básicamente, el comportamiento de esta fuerza es lo que explica que dispositivos como los relés y las electroválvulas sufran fuertes impactos y desgaste cada vez que son activados. Adicionalmente, algunos fenómenos electromagnéticos como la histéresis magnética o las corrientes inducidas hacen que el modelado dinámico de los actuadores de reluctancia sea bastante complejo. El trabajo realizado en esta tesis doctoral está enfocado en estudiar las posibilidades que ofrecen estos actuadores y, en concreto, en analizar el comportamiento dinámico y proponer algoritmos de estimación y control para relés electromecánicos y válvulas de solenoide.El primer objetivo de la investigación es el desarrollo de modelos dinámicos para actuadores de reluctancia, es decir, modelos de orden reducido que puedan ser utilizados para realizar simulaciones transitorias lo más precisas posibles con un bajo coste computacional. Para ello, lo primero que se ha estudiado es el comportamiento electromagnético de estos sistemas. El método de modelado más usado en la tesis es el de los circuitos magnéticos equivalentes (MEC, por sus siglas en inglés). No obstante, también se han realizado algunas simulaciones con modelos de elementos _nitos, en concreto para validar las aproximaciones del método MEC o para calcular la reluctancia del entrehierro. Se han estudiado los principales fenómenos electromagnéticos que aparecen en los actuadores de reluctancia, lo que ha llevado a la obtención de expresiones analíticas para modelar la dispersión de flujo, las corrientes inducidas y la saturación e histéresis magnéticas. Por otra parte, la expresión de la fuerza magnética que produce el movimiento se ha obtenido mediante un balance energético del sistema.El movimiento de la armadura también se ha estudiado en la tesis. Dado que los actuadores de reluctancia tienen generalmente un recorrido físicamente acotado, se han propuesto dos técnicas diferentes que permiten modelar los límites del movimiento y los rebotes de la armadura. Una vez estudiado el movimiento, el modelo mecánico se ha combinado con las ecuaciones electromagnéticas para poder analizar el comportamiento dinámico del actuador en su conjunto. Se han desarrollado cinco modelos dinámicos distintos, desde el más sencillo posible hasta uno que incluye todos los fenómenos electromagnéticos citados con anterioridad, y posteriormente se han comparado teniendo en cuenta su precisión y coste computacional.Las medidas experimentales son fundamentales a la hora de analizar y caracterizar cualquier sistema dinámico. Por ello, otro de los objetivos de la tesis ha sido la evaluación de distintas técnicas de medida que pudieran ayudar a mejorar la comprensión sobre el comportamiento dinámico de los actuadores de reluctancia y, en caso de que fuera posible, formar parte de un bucle de control realimentado. En este sentido, se ha intentado grabar el movimiento de uno de los dispositivos estudiados mediante tres instrumentos ópticos distintos. Los resultados indican que, a pesar de que en ciertas situaciones sí sería posible medir la trayectoria del dispositivo durante su movimiento, ninguno de los instrumentos podría aplicarse en la práctica por su baja flexibilidad y alto coste. Por este motivo, también se ha explorado el uso de otras variables que puedan ser medidas mucho más fácilmente.Otra parte importante de la investigación ha estado centrada en técnicas de estimación. Se han desarrollado dos algoritmos que son capaces de estimar, en tiempo real, el flujo magnético, la resistencia y la inductancia de un actuador dado. Los algoritmos utilizan únicamente medidas de tensión y corriente, lo cual representa una clara ventaja ya que no se necesita utilizar sensores o equipamiento añadido. Las prestaciones de ambos estimadores han sido analizadas mediante simulación y experimentos reales. El problema de estimar la posición de la armadura también se ha abordado en la tesis. En concreto, se ha prestado especial atención en resaltar los efectos que la histéresis magnética produce en la estimación, algo que no había sido estudiado con anterioridad.Finalmente, se han propuesto distintas técnicas de control para actuadores de reluctancia. En concreto, el objetivo principal es lograr que estos sigan un movimiento con aterrizaje suave, es decir, un movimiento que no dé lugar a impactos o rebotes. Como un primer paso, se han estudiado las propiedades básicas de los sistemas de control, es decir, la estabilidad, controlabilidad y observabilidad. Después se ha explorado la técnica de linealización por realimentación como un posible método para diseñar un bucle de control realimentado para la trayectoria de la armadura. Los resultados obtenidos demuestran que el control por realimentación es capaz de controlar el movimiento con gran precisión, siempre y cuando haya disponibles medidas o estimaciones precisas de la posición en tiempo real. Como esta situación es difícil que se dé en la práctica, se ha estudiado el uso de técnicas de control óptimo en bucle abierto para aquellos casos en los que la posición de la armadura no se pueda obtener. En particular, se han obtenido distintas soluciones tiempo óptimo y de energía óptima para un actuador nominal y, posteriormente, se ha analizado su robustez utilizando un método de Montecarlo.Como alternativa a los métodos clásicos, se ha estudiado la aplicabilidad de los métodos Run-to-Run (R2R) en actuadores de relutancia. Estas técnicas están diseñadas específicamente para sistemas que realizan un proceso repetitivo y, por lo tanto, son idóneas para dispositivos como los relés y las válvulas. En concreto, los métodos R2R implícitos se basan en la idea de construir una función que evalúe el desempeño del sistema al final de cada repetición. De esta forma, es posible mejorar el comportamiento dinámico del actuador a lo largo de las repeticiones utilizando un algoritmo de búsqueda.Las posibilidades para diseñar un controlador R2R son prácticamente infinitas, así que en la tesis se dan consejos prácticos sobre cómo elegir y parametrizar la señal de entrada, cómo usar las medidas disponibles para evaluar el comportamiento del sistema o cómo comparar distintos algoritmos de búsqueda. Los experimentos realizados demuestran que el algoritmo R2R diseñado es capaz de mejorar enormemente el comportamiento de un relé electromecánico y que, después de unos pocos ciclos, ,los resultados son incluso mejores que con cualquier estrategia presente en la literatura.Reluctance actuators are characterized by having a high force density, good efficiency, high fault tolerance and reduced cost. These features make them a promising alternative to other electromagnetic actuators for high-speed and high-precision applications. In addition, reluctance actuators are also ideal for small switch-type devices that require a modest performance because of their compactness, low cost, reduced mass and low energy dissipation. In particular, electromechanical switches and solenoid valves are devices whose operation is based on the force created by a small reluctance actuator. Despite their advantages, reluctance actuators are systems with highly nonlinear dynamics. One of their most distinctive features is that the magnetic force that produces the motion is always attractive and varies greatly with the position of the armature. In essence, the nature of this force explains why switch-type devices like relays and valves are subject to strong impacts and wear each time they are operated. In addition to that, electromagnetic phenomena such as magnetic hysteresis and eddy currents make the dynamic modeling of reluctance actuators even more difficult. The work of this thesis aims to investigate the capabilities of reluctance actuators and, in particular, to analyze the dynamic behavior and propose estimation and control algorithms for electromechanical switches and solenoid valves. The first objective of the investigation is the development of control-oriented dynamical models for reluctance actuators, i.e., low-order models that can be used to perform accurate transient simulations with low computational requirements. For that, the electromagnetic behavior of these systems is firstly studied. The magnetic equivalent circuit (MEC) methodology is selected as the primary modeling technique. Simulations from finite element models are also used for some specific purposes, e.g., to verify the assumptions of the MEC approach or to calculate the reluctance of the air gap. Then, the main electromagnetic phenomena that occur in reluctance actuators are studied. Analytic expressions are derived to model magnetic saturation, hysteresis, flux fringing and eddy currents, and an energy balance is used to obtain the expression for the magnetic force that produces the motion. After that, the motion of the armature is incorporated to the analysis. Given that reluctance actuators usually have a limited range of motion, two different techniques are proposed to model the limits of the armature stroke and the bouncing phenomenon. Then, the electromagnetic equations and the mechanical models are combined to describe the overall dynamic behavior of the actuator. Five different dynamical models are presented, ranging from a computationally inexpensive structure to a comprehensive model that includes saturation, hysteresis, eddy currents and flux fringing. The models are compared in terms of accuracy and computational requirements. Measurements play an important role in the analysis and characterization of dynamical systems. Thus, another objective of this thesis is the evaluation of different measurement methodologies that may improve the understanding of the dynamic behavior of reluctance actuators and, if possible, be used as part of a feedback controller. In this regard, three optical instruments are explored in order to record the motion of switch-type actuators. The results show that, even though in some cases it is possible to measure the position of several components of the device, none of the instruments could be applied in a practical situation due to their low flexibility and high cost. For that reason, other variables that are much more easily obtainable are also explored. Another significant part of the research is devoted to estimation in reluctance actuators. Two different algorithms are proposed to estimate the magnetic flux, the resistance and the inductance of the device, both of which can be implemented in real time. The algorithms rely only on measurements of the coil voltage and current, which represents a clear advantage because no additional hardware is required. Simulation and experiments are presented to show the performance of the estimators. Furthermore, the estimation of the armature position is also investigated in this work. In particular, special focus is put on highlighting the effects of magnetic hysteresis on the performance of different estimation approaches. Control strategies are then proposed to achieve soft landing in reluctance actuators, i.e., a controlled motion without impacts or bounces. As a first step, the basic properties of control systems theory---stability, controllability and stability---are investigated for a nominal actuator. Then, feedback linearization is explored as a method to design a trajectory tracking controller for the armature position. The obtained results show that soft landing can be accomplished by means of feedback control provided that accurate measurements or estimates of the position are available. Since this situation is rare in practice, open-loop optimal control is proposed as an alternative technique when the position is not accessible. Different time-optimal and energy-optimal solutions are derived for a nominal actuator and then compared in terms of robustness using a Monte Carlo analysis. Finally, Run-to-Run (R2R) control is explored as another method that may be used to improve the performance of reluctance actuators. These techniques are specifically designed for systems that perform a repetitive operation and, hence, they are very well suited to being applied to switch-type devices. In particular, implicit R2R methods are based on the idea of building a function that evaluates the performance of the system at the end of each repetition. In this way, the dynamic behavior of the actuator can be gradually improved along the repetitions by conducting a black-box search. Considering that the possibilities to design a R2R controller are almost endless, practical advice is given on how to select and parameterize the input profile, how to use measurements to evaluate the system performance and how to compare different search algorithms. The performed experiments show that the designed R2R controller is able to improve greatly the behavior of a switch-type device and that, after a few cycles, it outperforms other methodologies in the literature.<br /

    Multiphysics Modeling and Numerical Simulation in Computer-Aided Manufacturing Processes

    Get PDF
    The concept of Industry 4.0 is defined as a common term for technology and the concept of new digital tools to optimize the manufacturing process. Within this framework of modular smart factories, cyber-physical systems monitor physical processes creating a virtual copy of the physical world and making decentralized decisions. This article presents a review of the literature on virtual methods of computer-aided manufacturing processes. Numerical modeling is used to predict stress and temperature distribution, springback, material flow, and prediction of phase transformations, as well as for determining forming forces and the locations of potential wrinkling and cracking. The scope of the review has been limited to the last ten years, with an emphasis on the current state of knowledge. Intelligent production driven by the concept of Industry 4.0 and the demand for high-quality equipment in the aerospace and automotive industries forces the development of manufacturing techniques to progress towards intelligent manufacturing and ecological production. Multi-scale approaches that tend to move from macro- to micro- parameters become very important in numerical optimization programs. The software requirements for optimizing a fully coupled thermo-mechanical microstructure then increase rapidly. The highly advanced simulation programs based on our knowledge of physical and mechanical phenomena occurring in non-homogeneous materials allow a significant acceleration of the introduction of new products and the optimization of existing processes.publishedVersio
    corecore