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One of the main obstacles to applying the robust optimization for the permanent magnet motors is the high computational burden, which is mainly caused by the robustness evaluation considering the manufacturing uncertainties. In this article, efforts are made to speed up the process of robust optimization, from the aspects of reducing the computational cost, and avoiding the computing resources being wasted. Firstly, several widely used methods, aiming to identify the worst-case performance under uncertainties, are examined, and compared. And the efficient worst-uncertain-combination-analysis (WUCA) method is consequently adopted to significantly reduce the computational cost of robustness evaluation. From another aspect, the parameter rounding (PR) operation is inevitable due to the constraint of manufacturing accuracy, but its adverse effects on the optimization are often ignored. It is found that parts of the computing resources might be wasted during the optimization. A new PR during the calculation (PRDC) method is proposed, and incorporated into the process of robust optimization. Compared with the conventional one, similar results can be achieved with the computational time reduced by approximately $\text{11}\%$ in the PRDC modified robust optimization. [ABSTRACT FROM AUTHOR]

This paper deals with the design and evaluation of a short-circuit rotor-ring for enhanced self-sensing capability in a two-pole slotless permanent-magnet motor. High-frequency rotor anisotropy is enabled by adding a short-circuited rotor-ring. Optimal ring-dimensions are determined by parametric numerical studies. An effective high-frequency saliency of up to 1.8 is demonstrated. The steady-state estimation error is within $\pm$ 2 $^\circ$ , practically unaffected by current level (in contrast to slotted self-sensing electrical machinery) due to the large effective air-gap. The proposed observer performs properly also during dynamic load changes. Fall-times from 3000 to 0 r/min in less than 50 ms with negligible overshoot are demonstrated. Also parasitic effects, such as power losses, heating, and torque ripple are analyzed. [ABSTRACT FROM AUTHOR]

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A parametric analysis is carried out to investigate the dependence of the rotor iron losses on the stator and rotor geometry of several synchronous reluctance machines. Six four-pole rotors have been designed with different flux barriers per pole through a multiobjective differential evolution algorithm coupled to a finite-element analysis (FEA). Two different stators with 24 and 36 slots are considered. During the optimizations, a rapid finite-element evaluation has been used to predict the performance of the motors. After that, an accurate time stepping FEA is used for computation of the rotor iron losses. Finally, the interaction between the rotor iron losses and several rotor and stator geometrical parameters is highlighted. The effect of the current time harmonics have also been taken into account, weighting its impact on the rotor losses. [ABSTRACT FROM AUTHOR]

Recently, magnetic gears have drawn wide attention due to their inherent merits, such as noncontact operation, high torque density, and intrinsic overload protection. In this paper, an analytical calculation based on magnet magnetomotive force permeance theory is adopted to analyze the modulation effect in a magnetic gear. After that, the effects of some key parameters on magnetic gear performance are investigated, including the air-slot-opening-to-pole-pitch ratio $c_0$ , the magnet-arc-to-permanent-magnet-pole-pitch ratio $\alpha$ , and the permanent magnet thickness $h_m$. In particular, three types of steel pole pieces are considered: radial slots, parallel teeth, and parallel slots. A global optimization design is then carried out by using the differential evolution algorithm, and some useful suggestions are derived from the optimal Pareto range. Finally, the determination of outer rotor yoke thickness is discussed considering the iron saturation, and the iron loss distribution is investigated. This paper will be helpful for the design and optimization of a coaxial magnetic gear. [ABSTRACT FROM AUTHOR]

A criteria to design the rotor of multi flux-barrier synchronous reluctance (REL) machines is proposed. In particular, the focus will be on the proper design of flux-barriers geometry. An analytical model is adopted to compute the impact of the rotor flux-barriers on the torque, focusing on the torque ripple. Thanks to proper assumptions, the analytical model is simplified so as to highlight the main causes of torque ripple. Such an analytical model allows to derive the angles of the flux-barrier ends corresponding to the minimum torque ripple in a closed form. This result has never been presented in the past literature and it represents a useful tool as far as the motor design is concerned. Rotors with one, two, and three flux-barriers per rotor pole are taken into account. However, the advantageous analytical model can be extended to any number of flux-barriers per pole. Some examples referring to four-pole synchronous REL machines with different numbers of stator slots are investigated and illustrated. The results are compared with a full-featured analytical model and validated through finite element simulations. [ABSTRACT FROM AUTHOR]

This study presents two design methodologies for high-speed synchronous reluctance (REL) machines. The interest for high-speed drives comes from the request for compactness and high efficiency. The synchronous REL motors have been widely studied for several applications, but a coherent design procedure for high speed has not been proposed in the literature. The study proposes some analytical procedures to get an initial design. Then the rotor geometry optimisation through a differential evolution algorithm is described. Finally, a design example is given and thoroughly analysed using these two approaches. [ABSTRACT FROM AUTHOR]

Synchronous reluctance machine has high flux density fluctuations in the iron due to the high harmonics results from the rotor anisotropy. Thus, an accurate computation of the iron losses is of paramount importance, especially during the design stage. In this paper, a nonlinear analytical model considering the magnetic iron saturation and the slotting effect is proposed. The model estimates accurately the iron losses at a wide range of operating speed. In addition, the accuracy of the nonlinear model when the machine is highly saturated, i.e., when it works along the maximum torque per ampere (MTPA) trajectory, is presented and verified. The model presented is general and can be applied to other configurations. A 36-slot four-pole machine, with three flux-barriers per pole is considered as a case study. Finite element analysis is used to validate the results achieved by means of the nonlinear analytical model. Furthermore, an experimental setup is built to validate the simulation results. [ABSTRACT FROM AUTHOR]

The synchronous reluctance motor works under heavy saturation. This paper presents a nonlinear analytical model of the reluctance machine, which is used to derive both average and torque harmonics as a function of the rotor geometry. Maps showing the torque harmonics as a function of the rotor barrier angles are derived. These maps are useful tools for the machine designer to get a proper rotor geometry. The torque maps are compared with those obtained from both linear analytical and finite element models. The maps computed analytically show good agreement with those derived by means of finite element analysis, and they are obtained in a much smaller computing time. [ABSTRACT FROM AUTHOR]

The synchronous reluctance machines with transversally laminated rotor and multi flux barriers per pole reach a high torque density, so that they are proposed as a valid alternative to permanent magnet machines. Such machines have been analyzed for different applications, mainly home appliance, industrial tool, traction, up to low-speed high-power generators. On the contrary, the use of synchronous reluctance machines for high-speed applications remains almost unexplored yet. The aim of this paper is to investigate the potential of a high-speed synchronous reluctance machine. An optimization is carried out so as to maximize the machine performance (high power, proper power factor, low vibration) at a given speed. The machine size is fixed and the focus is on the rotor geometry, with the purpose of maximizing the electromagnetic torque, according to the necessary thickness of the ribs. It is shown that, even if the ribs are thick, it is possible to reach a proper torque density. It is shown that different solutions exist, which allow to reach high torque and minimum torque ripple. However, the optimal solutions are quite sensitive to the geometrical variations, so that a particular care is required in the manufacturing of the machine. Finally, the power limit of the synchronous reluctance motor with barrier rotor is found. [ABSTRACT FROM AUTHOR]

This paper deals with an analytical model of reluctance synchronous motor, able to consider both stator slotting effect and magnetic saturation in the stator and rotor iron paths. It joints the field distribution at the air gap to a lumped-parameter magnetic network. Local saturation factors are defined so as to adjust the flux-density distribution. The analytical approach exhibits great potentiality, since it is a formulation based on an harmonic study, and it is easily adaptable to any motor geometries. As an example, 36-slot 4-pole machine is analyzed, considering three flux barriers per pole. Finite element analysis confirms the results achieved by means of the analytical model. [ABSTRACT FROM PUBLISHER]

This paper deals with a detailed geometry analysis of the rotor structure for both synchronous reluctance and permanent magnet (PM)-assisted reluctance motor in order to suggest an automatic procedure to design the rotor structure. The shape of flux barriers is selected to achieve both high $d$ -axis inductance and low $q$ -axis inductance to obtain high output torque and high power factor. Methods to properly design the geometry of the ends of each barrier and PMs are adopted. In order to draw a rotor with proper shape, different modifications are discussed. All details are described to allow any reader to adopt the same procedures. After that, such a procedure is used to rapidly analyze the impact of some geometry changes on the machine performance to give a design guideline. The analyzing process starts from a reluctance motor considering the number of barriers, insulation ratio, split ratio, and slots per pole per phase. Then, the PMs are inset into flux barriers and the effect of PM width on torque, power factor, and flux weakening capability is investigated. At last, the demagnetization limit under overload operations is analyzed. [ABSTRACT FROM AUTHOR]