This paper presents a novel gradient-based topology optimization method for the design of permanent magnet electrodynamic suspensions, using a 3-D hybrid analytical model. It enables the exploration of new magnet configurations, with the aim of improving both the lift-to-weight and lift-to-drag ratios. The results reveal that modifying the magnet arrangement can change the trade-off between these competing objectives. In particular, a configuration with alternating poles in both the longitudinal and the transverse directions offers significantly better performance than the classical single-direction arrangement. The method is further validated on a small-scale experimental setup. Six Pareto optimal topologies are identified, manufactured, and tested. The resulting front is reconstructed experimentally and aligns with simulation predictions.

Self-bearing machines use rotor magnetic levitation to suppress friction and reach high rotation speeds. Recent studies have considered the integration of electrodynamic suspension in permanent magnet self-bearing machines in order to achieve fully passive levitation, improving the compactness and reliability. However, the influence of the d-axis current injected by the power supply on the dynamic behavior has not been addressed so far, as previous models were based on hypotheses that resulted in axial force and torque being independent of this current component. This paper develops an electromechanical model of an electrodynamic thrust self-bearing machine that accounts for the reluctant effects, both axial and angular, and the nonlinear evolution of magnetic flux linkage, revealing an impact of the d-axis current. Based on this model, quasi-static expressions of the suspension currents and the electromagnetic forces are derived and analyzed. A prototype is then tested in various conditions to compare model predictions with measurements. The results demonstrate that d-axis current injection can modulate the suspension force, even at zero speed.

Intensive rehabilitation through challenging and individualized tasks are recommended to enhance upper limb recovery after stroke. Robot-assisted therapy (RAT) and serious games could be used to enhance functional recovery by providing simultaneous motor and cognitive rehabilitation. The aim of this study is to clinically validate the dynamic difficulty adjustment (DDA) mechanism of ROBiGAME, a robot serious game designed for simultaneous rehabilitation of motor impairments and hemispatial neglect. A proof of concept, with 24 participants in subacute and chronic stroke, was conducted using a 5-day protocol (two days were dedicated to assessment and three days to consecutive training sessions). Participants performed three consecutive ROBiGAME sessions during which overall task difficulty was determined through simultaneous DDA of motor and attentional parameters. Relationships between clinical and robotic assessment scores with respective task-difficulty parameters were analyzed using a multivariate regression model and a principal component analysis. Game difficulty rapidly (within approximately thirty minutes) auto-adapted to match individual impairment levels. The relationship between task-difficulty parameters with motor (Fugl Meyer Assessment: r = 0.84 p < 0.05) and with attentional impairments (Bells test total omissions: r = 0.617 p < 0.05) showed that task-difficulty during RAT adapted to each participant’s degree of impairment. Principal component analysis identified two data subsets determining overall task-difficulty, one subset for motor and the other for cognitive functional evaluation scores with respective task-difficulty parameters. This proof of concept clinically validated a DDA mechanism and showed how task-difficulty adequately adapted to match individual degrees of impairment during RAT after stroke. ROBiGAME provided simultaneous motor and attentional exercises with parameters determining task-difficulty strongly related with respective clinical and robotic evaluation scores. Individualized levels of game difficulty and rapid adjustment of the system suggest implementation in clinical practice. Registry number This study was registered at ClinicalTrials.gov (NCT02543424).

Permanent magnet electrodynamic suspensions rely on induced currents for the magnetic levitation of transportation systems. To predict these currents and the forces they generate, a partial element equivalent circuit model is presented in this paper. By discretizing the conductive track into a network of interconnected elements, the model is able to compute complex patterns of eddy currents and consider the skin effect. Suspensions with both bulk and perforated conductors are modeled with an error below 3% compared to precise references and with a significantly reduced computational cost compared to time-dependent finite element simulations. Experimental measurements further validate the predictions of the model. Additionally, the model is also adapted to study the vertical dynamics of the suspension, without using additional finite element identifications, and confirmed its unstable behavior.

This paper proposes a hybrid analytical model for addressing 3-D quasi-static eddy current problems involving a magnetic field source moving with respect to a bulk conductive material. The proposed model is particularly useful in applications that include ferromagnetic components, such as a permanent magnet electrodynamic suspension. The model integrates mesh-based magnetic equivalent circuits using a loop formulation with Fourier-based modeling, thereby enabling it to accurately account for non-linear magnetic materials and eddy currents. In comparison to finite element analyses, the model demonstrates a high accuracy, with an error below 2.5% for a fine mesh. Its computational time can be one to two orders of magnitude less than finite element methods for accuracies above 90%, depending on the mesh refinement. Furthermore, the model scales better with the dimensions by alleviating the numerical issues associated with finite element methods for eddy current calculations in bulk conductive materials.

This paper presents the optimization of a LongTerm Flywheel Energy Storage System (LT-FESS) whose electromechanical converter is a Flux-Switching Machine (FSM). Three topologies of FSM that differ with their excitation source are investigated: the Permanent Magnet FSM (PM-FSM), Wound-Field FSM (WF-FSM) and the Hybrid-Excited FSM (HEFSM). The design parameters of the machines, as well as those of the power electronics and of the rotor of a $10 k W$ and $10 k W h$ LTFESS, are optimized according to energy and economic metrics. The maximization of the energy efficiency of storage cycles of increasing storage durations shows that the HE-FSM is the bestsuited topology for intermediate storage durations with energy efficiencies above 70 % for storage cycles shorter than 7 hours. Beyond, the WF-FSM becomes more efficient thanks to its lower idling losses. The PM-FSM is never observed as the best-suited topology regardless of the storage duration.

ElectroDynamic Thrust Self-Bearing Machine (EDTSBM) provide, in addition to the drive function, the passive levitation of the rotor in the axial direction. Such machine can therefore be combined with permanent magnet centering bearings to achieve fully passive levitation, cumulating the benefits of a bearingless machine, with the compactness, reliability and low cost of passive levitation. However, EDTSBM requires damping to counteract the inherent instability of electrodynamic suspensions at high speed. Recent research has shown the possibility of introducing this damping by controlling the d-axis current of EDTSBM incorporating a magnetic circuit in the rotor. Nevertheless, this method requires an additional position sensor which reduces the compactness and reliability of the system. In this context, this paper introduces a sensorless control method of the EDTSBM based exclusively on current measurements. The simulation results presented in the paper demonstrate the robustness of the active stabilization strategy based on this estimation of the axial states of the EDTSBM in the levitation direction.

Passively levitated self-bearing machines provide the rotor drive and guidance within a single structure without requiring controllers, power electronics and sensors dedicated to the magnetic suspension, leading to compact, reliable and cost-effective systems. Electromechanical models describing their rotor dynamics have recently been derived and experimentally validated. However, these models do not account for non-idealities that could arise from manufacturing imperfections. In this context, this paper investigates the impact of an angular misalignment between the upper and lower windings of passively levitated self-bearing machines on the force and torque production. The existing electromechanical model is extended, highlighting that this misalignment slightly degrades the driving torque and the conventional passive restoring force, on the one hand, and creates additional force and torque components, on the other hand. Among the latter, those arising from the suspension currents are independent from the rotor axial displacement and are thus produced even in centred position, thereby potentially acting as disturbances. Finally, an experimental study is carried out, allowing to validate the suspension force produced by the machine in quasi-static conditions and to confirm the interest of accounting for this winding non-ideality in the model.

Self-bearing machines have gained increasing interest by bringing the benefits of magnetic suspension to high torque density systems. Among them, passively levitated machines have recently been investigated both at the theoretical and experimental levels, but being limited to three-phase machines. For a wide range of applications, e.g. small fans, a single-phase solution would be appropriate, particularly to reduce the cost and space requirements of power and control electronics. This paper introduces a passively levitated self-bearing machine operating on a single-phase power supply. An electromechanical model describing the axial and spin dynamics of the machine is proposed, highlighting additional force and torque terms. A case study-based optimisation is then conducted to compare the performance of the single-phase solution with that of the three-phase solution, revealing that the single-phase configuration provides superior stiffness for equivalent losses, with a subsequent quasi-static analysis explaining the underlying reasons.

This paper presents a novel gradient-based topology optimization method for the design of permanent magnet electrodynamic suspensions, using a 3-D hybrid analytical model. It enables the exploration of new magnet configurations, with the aim of improving both the lift-to-weight and lift-to-drag ratio. It reveals that a configuration with alternating poles in both the longitudinal and the transverse directions offers significantly better performance than the classical single-direction arrangement.

This paper proposes a methodology to quantify the performance of a 12/10 outer rotor Hybrid-Excited Flux-Switching Machine (HE- FSM) over its operating cycle with a view to optimizing its design parameters for a long-term Flywheel Energy Storage System (FESS) application. A low-computational-cost metamodel of the machine is built from the data provided by the Finite Element Model (FEM), to estimate the iron losses and the output torque at the operating points consituting an operating cycle, with a rms error of 1.92% and 1.21 %, respectively. A preliminary design of a HE-FSM is simulated in a fictional 2kWh FESS and exhibits a maximal energy efficiency of 78.73% for a duration of storage of 2 hours. The minimization of the total losses thanks to negative $d$ axis and field winding current densities allows for a reduction of up to 43 % of the no load losses.

Passive thrust self-bearing motor have been the subject of extensive research over the last few years, showing the possibility to reach the fully passive suspension of the rotor. However, this kind of machine becomes axially unstable above a certain rotation speed, requiring the introduction of an axial damping to be used on the full speed range. Recent researches have shown that when reluctant effects are present in such machines, it is possible to create an axial force through the D-axis current component. This open the way to introduce the required damping directly from the machine and not from an external system. This paper investigates this possibility by imposing, via vector control, a D-axis current component proportional to the axial velocity. It demonstrates the effectiveness of this approach through quasi-static analyses and dynamic simulations.

Self-bearing machines are designed to be the centerpiece of highly integrated magnetically suspended systems by combining the rotor guidance and drive within a single structure. Their compactness and reliability have been taken a step further with the development of self-bearing machines that do not require sensors, controllers and power electronics to guide the rotor. In these passively levitated machines, the suspension of the axial degree of freedom relies on circulating currents that are induced in the armature windings thanks to the permanent magnet motion. The rotor can therefore not be axially stabilised at zero rotational speed. Hybrid actuation approaches, based on the active control of the rotor position until passive operation can be achieved, have been investigated. However, the requirement for a position sensor compromises the advantages of passive levitation. In this context, this paper proposes a self-sensing technique relying on the injection of a high frequency signal to estimate the winding impedance and extract the rotor axial position. Simulations of the rotor dynamics are performed on the basis of an electromechanical model of the machine to validate the operation principle, assess the tracking capabilities and investigate the robustness of this self-sensing technique.

This article reviews permanent magnet electrodynamic suspensions (PM-EDSs) used in ground transportation systems, such as Magnetic Levitation (MAGLEV) trains. The different suspension topologies are first presented, considering separately their two main components, namely the track and the magnetic field source. Beyond that, a phenomenological explanation of the evolution with the speed of the drag and levitation forces is provided, depending on the track topology. The models aimed at predicting the behavior and performance of the suspension are then detailed, classifying them according to whether they are global or local. Finally, the main experimental setups developed to validate PM-EDSs are described.

Among active magnetic bearings (AMB), homopolar hybrid AMB (HH-AMB) generate a homopolar bias magnetic field using permanent magnets (PM) to reduce Joule and iron losses. The iron losses are further reduced by the slotless topology of the HH-AMB (SHH-AMB). Analytical models of the topology have been implemented using magnetic equivalent circuit (MEC) and Fourier-based (FB) methods. This paper proposes a FB model of a variant of the SHH-AMB topology that has additional saliencies on the rotor to provide an axial stabilization. The validity of the results is assessed with a finite element analysis (FEA) and experimentally, with measurements performed on a prototype of the bearing under study.

High-speed MAGLEV can rely on electrodynamic suspensions for their levitation. The track, the conductive part of the suspension where eddy currents take place, has a great influence on the forces generated in the system. Different track topologies, either discrete or continuous, have been explored so far, but not globally compared. The paper aims therefore to compare objectively continuous and discrete track topologies based on performance criteria such as the lift-to-drag and lift-to-weight ratios.

This paper presents the topology optimization of an alternate permanent magnet electrodynamic suspension in a plane parallel to the track, using therefore a semi-analytical 3-D model. This model is based on the superposition of single permanent magnets to compute the magnetic field of more complex structures. The optimization, divided in three steps, showed that new permanent magnet arrangements can significantly increase the lift-to-drag ratio of the suspension at the expense of a low reduction of the lift-to-weight ratio.

Optimal design of synchronous reluctance machines usually involves a large number of parameters and several objectives or constraints, making the optimization problem hard to solve. This study proposes a method to deal with optimization problems prone to local minima by partitioning it into a sequence of smaller optimization problems. The partitioning is performed by interpreting the results of a global variance-based sensitivity analysis, conducted prior the optimizations. The interest of the approach is demonstrated on the rotor optimization of a 4 poles synchronous reluctance machine, to maximize the mean torque while both limiting the torque ripple and the local Von Mises stresses. The parametrization, finite-element models and results of the sensitivity analysis are presented, from which a coherent partitioning of the optimization problem is proposed. Results show that this approach is computationally time efficient, with a total optimization time that is a fraction of the one necessary to perform a single optimization on all the parameters. The torque ripple is substantially lowered below 5% of the mean torque. Independent runs of the design approach show a good reproducibility in the results.

Homopolar hybrid active magnetic bearings (HHAMB) generate very low power losses. Those losses can be further reduced using slotless toplogies because the slots create local fluctuations of the magnetic flux density, which generate iron losses in the rotor. Such slotless HH-AMB has been studied based on a MEC model that neglects the leakage flux between the PM and the rotor and therefore does not predict correctly the airgap magnetic flux density and the depending quantities such as the current stiffness and the position stiffness. This paper presents an open-circuit model based on Fourier analysis, as well as two methods to consider the eccentricity. One of the methods, which is based on a modulation function, allows to estimate the current stiffness and the position stiffness with an error below 1 %.

This paper presents a novel lumped-parameter model of the equivalent thermal conductivity of PCB windings referred to as the improved parallel circuit model (IPCM). This model can easily be used during the design phase of the machine thanks to its low computational complexity. When compared to other existing analytical models, with as reference a finite-element model, it is shown IPCM has the highest accuracy, i.e. a relative error of less than 5% on the whole range of typical parameters of PCB windings. An experimental characterization is also performed such as to validate the quality of the model against a custom-made PCB winding.