Electromagnetic fields and interactions in 3D cylindrical structures : modeling and application

The demand for more efficient and compact actuation systems results in a search for new electromagnetic actuator configurations. To obtain actuators that meet these challenging specifications, accurate modeling of the electromagnetic fields is often a prerequisite. To date, analytical modeling techniques are widely used to predict electromagnetic fields in classical rotary and linear machines represented in two dimensional coordinate systems. This thesis presents the extension of an analytical modeling technique to predict the 3D field distribution in new cylindrical actuator configurations. One specific technique that is used to analyze and design electromagnetic devices is based on Fourier series to describe sources and the resultingmagnetic fields. In this research, the harmonic modeling technique is extended to describe electromagnetic fields due to presence of permanent magnets in regular and irregular shaped 3D cylindrical structures. The researched modeling technique can be applied to current-free cylindrical problems exhibiting periodicity or a soft-magnetic boundary in the axial direction. The cylindrical structure can posses either circumferential slots, axial slots or rectangular cavities. The assignment and a method to solve the various boundary conditions are discussed in a generic manner to enable model application to a wide range of 3D cylindrical structures. The magnetic field solutions are provided, and the model implementation is presented in matrix form. Model validation is presented by means of a comparison of the magnetic fields in a cylindrical structure with a rectangular cavity calculated using the analytical model and a finite element model. To calculate the magnetic interactions, e.g., attraction and cogging forces due to permanent magnets, the Maxwell stress tensor is analytically evaluated. The harmonic magnetic field solution is used in this evaluation resulting in compact force equations describing the 3D force components between concentric cylinders

Modeling And Analysis Of The Eds Maglev System With The Halbach Magnet Array

The magnetic field analysis based on the wavelet transform is performed. The Halbach array magnetic field analysis has been studied using many methods such as magnetic scalar potential, magnetic vector potential, Fourier analysis and Finite Element Methods. But these analyses cannot identify a transient oscillation at the beginning stage of levitation. The wavelet transform is used for analyzing the transient oscillatory response of an EDS Maglev system. The proposed scheme explains the under-damped dynamics that results from the cradle\u27s dynamic response to the irregular distribution of the magnetic field. It suggests this EDS Maglev system that responds to a vertical repulsive force could be subject to such instability at the beginning stage of a low levitation height. The proposed method is useful in analyzing instabilities at the beginning stage of levitation height. A controller for the EDS maglev system with the Halbach array magnet is designed for the beginning stage of levitation and after reaching the defined levitation height. To design a controller for the EDS system, two different stages are suggested. Before the object reaches a stable position and after it has reached a stable position. A stable position can be referred to as a nominal height. The former is the stage I and the latter is the stage II. At the stage I, to achieve a nominal height the robust controller is investigated. At the stage II, both translational and rotational motions are considered for the control design. To maintain system stability, damping control as well as LQR control are performed. The proposed method is helpful to understand system dynamics and achieve system stability

Extended analytical charge modeling for permanent-magnet based devices : practical application to the interactions in a vibration isolation system

This thesis researches the analytical surface charge modeling technique which provides a fast, mesh-free and accurate description of complex unbound electromagnetic problems. To date, it has scarcely been used to design passive and active permanent-magnet devices, since ready-to-use equations were still limited to a few domain areas. Although publications available in the literature have demonstrated the surface-charge modeling potential, they have only scratched the surface of its application domain. The research that is presented in this thesis proposes ready-to-use novel analytical equations for force, stiffness and torque. The analytical force equations for cuboidal permanent magnets are now applicable to any magnetization vector combination and any relative position. Symbolically derived stiffness equations directly provide the analytical 3 £ 3 stiffness matrix solution. Furthermore, analytical torque equations are introduced that allow for an arbitrary reference point, hence a direct torque calculation on any assembly of cuboidal permanent magnets. Some topics, such as the analytical calculation of the force and torque for rotated magnets and extensions to the field description of unconventionally shaped magnets, are outside the scope of this thesis are recommended for further research. A worldwide first permanent-magnet-based, high-force and low-stiffness vibration isolation system has been researched and developed using this advanced modeling technique. This one-of-a-kind 6-DoF vibration isolation system consumes a minimal amount of energy (Ç 1W) and exploits its electromagnetic nature by maximizing the isolation bandwidth (> 700Hz). The resulting system has its resonance > 1Hz with a -2dB per decade acceleration slope. It behaves near-linear throughout its entire 6-DoF working range, which allows for uncomplicated control structures. Its position accuracy is around 4mum, which is in close proximity to the sensor’s theoretical noise level of 1mum. The extensively researched passive (no energy consumption) permanent-magnet based gravity compensator forms the magnetic heart of this vibration isolation system. It combines a 7.1kN vertical force with <10kN/m stiffness in all six degrees of freedom. These contradictory requirements are extremely challenging and require the extensive research into gravity compensator topologies that is presented in this thesis. The resulting cross-shaped topology with vertical airgaps has been filed as a European patent. Experiments have illustrated the influence of the ambient temperature on the magnetic behavior, 1.7h/K or 12N/K, respectively. The gravity compensator has two integrated voice coil actuators that are designed to exhibit a high force and low power consumption (a steepness of 625N2/W and a force constant of 31N/A) within the given current and voltage constraints. Three of these vibration isolators, each with a passive 6-DoF gravity compensator and integrated 2-DoF actuation, are able to stabilize the six degrees of freedom. The experimental results demonstrate the feasibility of passive magnet-based gravity compensation for an advanced, high-force vibration isolation system. Its modular topology enables an easy force and stiffness scaling. Overall, the research presented in this thesis shows the high potential of this new class of electromagnetic devices for vibration isolation purposes or other applications that are demanding in terms of force, stiffness and energy consumption. As for any new class of devices, there are still some topics that require further study before this design can be implemented in the next generation of vibration isolation systems. Examples of these topics are the tunability of the gravity compensator’s force and a reduction of magnetic flux leakage

Dynamic suspension modeling of an eddy-current device : an application to Maglev

When a magnetic source is simultaneously oscillated and translationally moved above a linear conductive passive guideway such as aluminum, eddy-currents are induced that give rise to a time-varying opposing field in the air-gap. This time-varying opposing field interacts with the source field, creating simultaneously suspension, propulsion or braking and lateral forces that are required for a Maglev system. The 2-D analytic based transient eddy-current force and power loss equations are derived for the case when an arbitrary magnetic source is moving and oscillating above a conductive guideway. These general equations for force and power loss are derived using a spatial Fourier transform and temporal Laplace transform technique. The derived equations are capable of accounting for step changes in the input parameters, in addition to arbitrary continuous changes in the input conditions. The equations have been validated for both step changes as well as continuous changes in the input conditions using a 2-D transient finite-element model. The dynamics of an EDW Maglev is investigated by using both steady-state and transient eddy-current models. The analytic equations for the self as well as mutual damping and stiffness coefficients of an EDW Maglev are derived using the 2-D analytic steady-state eddy-current force equations. It is shown that the steady-state eddy-current model in which the heave velocity is included in the formulation can accurately predict the dynamic behavior of a 2-degree of freedom EDW Maglev vehicle. The 2-D EDW Maglev vehicle has been built using Matlab/SimMechanics™. A 1-degree of freedom pendulum setup of an EDW Maglev has been built in order to investigate the dynamics of an EDW Maglev. The dynamic model of an EDW Maglev has been validated using this pendulum setup. A multi-degree of freedom Maglev vehicle prototype has been constructed using four EDWs. The dynamics of the prototype Maglev has been investigated using the Matlab simulations. This prototype setup will be used to investigate the dynamic behavior of EDW Maglev in the future

Generalized harmonic modeling technique for 2D electromagnetic problems : applied to the design of a direct-drive active suspension system

The introduction of permanent magnets has significantly improved the performance and efficiency of advanced actuation systems. The demand for these systems in the industry is increasing and the specifications are becoming more challenging. Accurate and fast modeling of the electromagnetic phenomena is therefore required during the design stage to allow for multi-objective optimization of various topologies. This thesis presents a generalized technique to design and analyze 2D electromagnetic problems based on harmonic modeling. Therefore, the prior art is extended and unified to create a methodology which can be applied to almost any problem in the Cartesian, polar and axisymmetric coordinate system. This generalization allows for the automatic solving of complicated boundary value problems within a very short computation time. This method can be applied to a broad class of classical machines, however, more advanced and complex electromagnetic actuation systems can be designed or analyzed as well. The newly developed framework, based on the generalized harmonic modeling technique, is extensively demonstrated on slotted tubular permanent magnet actuators. As such, numerous tubular topologies, magnetization and winding configurations are analyzed. Additionally, force profiles, emf waveforms and synchronous inductances are accurately predicted. The results are within approximately 5 % of the non-linear finite element analysis including the slotted stator effects. A unique passive damping solution is integrated within the tubular permanent magnet actuator using eddy current damping. This is achieved by inserting conductive rings in the stator slot openings to provide a passive damping force without compromising the tubular actuator’s performance. This novel idea of integrating conductive rings is secured in a patent. A method to calculate the damping ratio due to these conductive rings is presented where the position, velocity and temperature dependencies are shown. The developed framework is applied to the design and optimization of a directdrive electromagnetic active suspension system for passenger cars. This innovative solution is an alternative for currently applied active hydraulic or pneumatic suspension systems for improvement of the comfort and handling of a vehicle. The electromagnetic system provides an improved bandwidth which is typically 20 times higher together with a power consumption which is approximately five times lower. As such, the proposed system eliminates two of the major drawbacks that prevented the widespread commercial breakthrough of active suspension systems. The direct-drive electromagnetic suspension system is composed of a coil spring in parallel with a tubular permanent magnet actuator with integrated eddy current damping. The coil spring supports the sprung mass while the tubular actuator either consumes, by applying direct-drive vertical forces, or regenerates energy. The applied tubular actuator is designed using a non-linear constrained optimization algorithm in combination with the developed analytical framework. This ensured the design with the highest force density together with low power consumption. In case of a power breakdown, the integrated eddy current damping in the slot openings of this tubular actuator, together with the passive coil spring, creates a passive suspension system to guarantee fail-safe operation. To validate the performance of the novel proof-of-concept electromagnetic suspension system, a prototype is constructed and a full-scale quarter car test setup is developed which mimics the vehicle corner of a BMW 530i. Consequently, controllers are designed for the active suspension strut for improvement of either comfort or handling. Finally, the suspension system is installed as a front suspension in a BMW 530i test vehicle. Both the extensive experimental laboratory and on-road tests prove the capability of the novel direct-drive electromagnetic active suspension system. Furthermore, it demonstrates the applicability of the developed modeling technique for design and optimization of electromagnetic actuators and devices