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

Active electromagnetic suspension system for improved vehicle dynamics

This paper offers motivations for an active suspension system which provides for both additional stability and maneuverability by performing active roll and pitch control during cornering and braking as well as eliminating road irregularities, hence increasing both vehicle and passenger safety and drive comfort. Various technologies are compared to the proposed electromagnetic suspension system which uses a tubular permanent magnet (PM) actuator together with a passive spring. Based upon on-road measurements and results from the literature, several specifications for the design of an electromagnetic suspension system are derived. The measured on-road movement of the passive suspension system is reproduced by electromagnetic actuation on a quarter car setup proving the dynamic capabilities of an electromagnetic suspension system

Tubular permanent magnet actuators: cogging forces characterization

Tubular permanent magnet actuators are evermore used in demanding industrial and automotive applications. However, these actuators can suffer from large cogging forces, which have a destabilizing effect on the servo control system and compromise position and speed control accuracy. This paper focuses on the identification of the cogging forces by means of finite element software, where an approach is introduced within the 2D finite element analysis to model the linear tubular permanent magnet actuator compared to conventional axisymmetrical models. This gives that the contribution of the stator teeth and finite length of the ferromagnetic armature core to the total cogging force can be separately analyzed. The cogging force predictions is characterized and the effectiveness of the new method is verified comparing the results of the tubular structure in both the axisymmetrical model and 2D finite element model, normally used for rotary machines

Analytical force, stiffness, and resonance frequency calculations of a magnetic vibration isolator for a micro balance

The accuracy of a micro balance is highly dependent on the level of floor vibrations. One strategy to reduce floor vibrations is a magnetic vibration isolator. Magnetic vibration isolators have the possibility to obtain a zero-stiffness region, which is beneficial for attenuating vibrations. In this paper a 3D analytical magnetic surface charge model is used to calculate the spring characteristics of a cone-shaped magnetic vibration isolator for different angles

On the atomic line profiles in high pressure plasmas

In a previous contribution to this journal [H. P. Stormberg, J. Appl. Phys. 51(4), 1963 (1980)], Stormberg presented an analytical expression for the convolution of Lorentz and Levy line profiles, which models atomic radiative transitions in high pressure plasmas. Unfortunately, the derivations are flawed with errors and the final expression, while correct, is accompanied by misguiding comments about the meaning of the symbols used therein, in particular the "complex error function." In this paper, we discuss the broadening mechanisms that give rise to Stormberg's model and present a correct derivation of his final result. We will also provide an alternative expression, based on the Faddeeva function, which has decisive computational advantages and emphasizes the real-valuedness of the result. The MATLAB/Octave scripts of our implementation have been made available on the publisher's website for future reference

Analytical force and stiffness calculations for magnetic bearings and vibration isolation

Accurate vibration isolation and magnetic levitation are extremely important in the high-precision industry. Nowadays, high-performance vibration isolation and magnetic bearings based on permanent magnets are increasingly considered. This paper proposes the stiffness matrix necessary for the design of such a structure. The analytical force and stiffness expressions are derived for the cases where the conventional analytical expressions are difficult to solve and are compared with results from the Maxwell Stress method. With these adapted expressions it is possible to optimize planar bearing structures without having to correct for non-solving configurations