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.