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The purpose of this paper is to describe a semi-analytical modeling technique to predict eddy currents in three-dimensional (3D) conducting structures with finite dimensions. Using the developed method, power losses and parasitic forces that result from eddy current distributions can be computed.

In conducting regions, the Fourier-based solutions are developed to include a spatially dependent conductivity in the expressions of electromagnetic quantities. To validate the method, it is applied to an electromagnetic configuration and the results are compared to finite element results.

The method shows good agreement with the finite element method for a large range of frequencies. The convergence of the presented model is analyzed.

Because of the Fourier series basis of the solution, the results depend on the considered number of harmonics. When conducting structures are small with respect to the spatial period, the number of harmonics has to be relatively large.

Because of the general form of the solutions, the technique can be applied to a wide range of electromagnetic configurations to predict, e.g. eddy current losses in magnets or wireless energy transfer systems. By adaptation of the conductivity function in conducting regions, eddy current distributions in structures containing holes or slit patterns can be obtained.

With the presented technique, eddy currents in conducting structures of finite dimensions can be modeled. The semi-analytical model is for a relatively low number of harmonics computationally faster than 3D finite element methods. The method has been validated and shown to be computationally accurate.

This paper aims to find the optimal winding topology for a 14‐pole permanent magnet synchronous motor (PMSM) to be used as an in‐wheel motor in automotive applications.

Comparison is first performed among lap windings with different combinations of slot numbers and pole numbers. A general method for calculating the winding factors using only these numbers is proposed, thus the preferable slot numbers resulting in relatively large winding factors for this 14‐pole PMSM are found. With these slot numbers, the Joule losses of armature windings are further investigated, where the impacts of different end‐winding lengths are considered. By this means, the optimal slot number that causes the least Joule loss is obtained. On the other hand, as a competitor to lap windings, toroidal windings are also discussed. The thermal performances of these two types of windings are compared by performing a finite element analysis (FEA) on their 2‐D thermal models.

For the 14‐pole in‐wheel PMSM discussed in this paper, the preferable slot numbers leading to relatively large winding factors are 12, 15 and 18. However, with the specified geometry constraints, the optimal choice of slot number is 15, which results in the least Joule loss and thus the highest efficiency. On the other hand, by implementing the toroidal winding topology, the armature windings of this machine can be effectively cooled and thus allow a larger electrical loading than the lap windings do.

This work can be continued with investigating the impacts of different combinations of slot number and pole number on harmonics and cogging torques.

This paper proposes a general method for calculating the winding factor of PMSMs using only the phase number, the slot number, and the pole number. With this method, the calculation procedure can be easily programmed and repeated.

This paper is aimed at investigating the potential advantages of flux‐switching machines (FSM) compared to permanent magnet synchronous machines (PMSM), particularly for the applications of electric vehicle traction.

A 12‐slot 14‐pole PMSM designed for an in‐wheel traction application is chosen for the comparison. With the same volume constraint, three 12/14 FSM structures are created. Both the PMSM and the three FSM structures are modeled using the software Flux. Based on these models, finite element analyses (FEA) are performed, and the results are compared in terms of open‐circuit back electromotive force (EMF), electrical loading capability, and thermal conditions.

Within the same volume constraint, a 12/14 FSMs can achieve the maximum torque higher than the one of 12/14 PMSM. This conclusion is drawn based on the observed facts that at the same rotor speed, a larger open‐circuit back EMF is induced in the FSM, while a larger electrical loading is also allowed in this machine, compared to the PMSM. In addition, the risk of demagnetization during the process of field weakening proves to be lower in FSMs than PMSMs. This advantage suggests a potentially wide constant power speed range (CPSR) of FSMs, which is especially beneficial in automotive applications.

This research can be continued with investigating the field weakening capability and iron losses of FSMs.

This paper proposed two optional structures of FSMs to reduce the amount of permanent magnets. It also highlighted the effectiveness of FSMs in cooling these magnets.

The purpose of this paper is to investigate winding topologies for flux-switching motors (FSMs) with various segment-tooth combinations and different excitation methods.

For the ac winding of FSM, two winding topologies, namely the concentrated winding and the distributed winding, are compared in terms of the winding factor and efficiency. For the field winding of dc-excited FSM (DCEFSM), another two winding topologies, namely the lap winding and the toroidal winding, are compared in terms of effective coil area, end-winding length, and thermal conditions. Analytical derivation is used for the general winding factor calculation. The calculation results are validated using finite element analysis.

Winding factors can be used as an indication of winding efficiency for FSMs in the same manner as done for synchronous motors. For FSMs with concentrated windings, the winding factor increases when the rotor tooth number approaches a multiple of the stator segment number. For FSMs with certain segment-tooth combinations, e.g. 6/8, the theoretical maximum winding factor can be achieved by implementing distributed windings. Furthermore, the toroidal winding can be an efficient winding topology for DCEFSMs with large stator diameter and small stack length.

This work can be continued with investigating the variation of reluctance torque with respect to different segment-tooth combinations of FSM.

This paper proposes a general method to calculate the winding factor of FSMs using only the phase number, the stator segment number, the rotor tooth number, and the skew angle. Using this method, a table of winding factors of FSMs with different segment-tooth combinations is provided. Principle of design of FSMs with high-winding factors are hence concluded. This paper also proposed the implementation of distributed windings for FSM with certain segment-tooth combinations, e.g. 6/8, by which means a theoretical maximum winding factor is achieved. In addition, different winding topologies for the field winding of DCEFSM are also investigated.

Transient torque calculations of the parallel flux switching machines, both cogging and electromagnetic, require a long simulation time for transient analyses. This paper seeks to present an optimization method for the accurate but time consuming transient models.

A superposition principle is used to optimize the simulation time of the machine model. Finite element method (FEM) is chosen as the example machine model, since it is widely used among researchers for its accuracy. The machine geometry is simplified by reducing the number of rotor teeth, because these parts are re‐meshed with each transient step. Torque results are compared to the full machine model to find the best representation.

Among compared simplified machine geometries, the two teeth model gives the most accurate results.

The superposition method requires a modelling method such as FEM. The method offers a geometrical simplification of the machine, not a complete model.

Parallel flux switching machines should be considered as promising candidates for hybrid and electrical truck applications due to their high power density. For these kind of applications, a fast torque estimation tool helps greatly in investigating noise related mechanical problems, which have a direct effect in passenger comfort.

Whereas researchers in this area mainly focus on accurate but time‐consuming modeling of this nonlinear machine, this research shows an optimization of these methods to speed‐up them. The proposed optimization method can be integrated with any analytical or numerical machine model.

The purpose of this paper is to present novel analytical expressions which describe the 3D magnetic field of arbitrarily magnetized triangular‐shaped charged surfaces. These versatile expressions model that the field of triangular‐shaped permanent magnets (PMs) are very suitable to model skewed slotless machines.

The analytical 3D surface charge method is normally used to provide field expressions for PMs in free space. In this paper, the analytical surface charge integrals are analytically solved for charged right‐triangular surfaces. The resulting field is compared with that obtained by finite element modeling (FEM) and subsequently applied in two examples.

The comparison with FEM shows that the 3D analytical expressions are very accurate and exhibit very low‐numerical noise. These fast‐solving versatile expressions are therefore considered suitable to model triangular‐shaped or polyhedral‐shaped PMs.

The surface charge method assumes that the relative permeability is equal to 1 and therefore soft‐magnetic materials need to be modeled using the method of images. The PMs are assumed to be ideal in terms of homogeneity, magnetization vector, permeability, demagnetization, and geometrical tolerances.

Many applications, such as the subclass of slotless synchronous linear actuators with a skewed PM structure and planar magnetic bearings, are very suitable to incorporate this modeling technique, since it enables the analysis of a variety of performance data.

As an addition to the common 3D analytical field expressions for cuboidal or cylindrical PMs, this paper presents novel expressions for magnets having triangular surfaces.

The space‐mapping (SM) optimization technique, with its input, implicit or output mapping‐based implementations, provides a basis for computationally efficient engineering optimization. Various algorithms and design optimization problems, related to microwave devices, antennas and electronic circuits, are presented in numerous publications. However, a new application area for SM optimization is currently expanding, i.e. the design of electromechanical actuators. The purpose of this paper is to present an overview of the recent developments.

New algorithm variants and their application to design problems in electromechanics and related fields are briefly summarized.

The paper finds that SM optimization offers a significant speed‐up of the optimization procedures for the design of electromechanical actuators. Its true potential in the area of magnetic systems and actuator design is still rather unexplored.

This overview is complementary to the previous published reviews and shows that the application of SM optimization has also extended to the design of electromechanical devices.

The purpose of this paper is to present a semi‐analytical modeling technique to describe magnetic fields due to PMs in 3D cylindrical structures. The model is based on 2D Fourier series and is applied to model the magnetic field of checkerboard magnetization patterns for rotary‐linear actuators.

The modeling technique based on Fourier series provides a direct solution of the Poisson and Laplace equation by means of separation of variables and is widely used to describe magnetic fields in electromagnetic devices in 2D coordinate systems. In this paper the magnetic scalar potential is used in the Poisson and Laplace equations.

The magnetic field calculated by the semi‐analytical model is compared with that obtained by Finite Element Modeling and shows excellent agreement. The calculation time of the semi‐analytical model is approximately 60 times shorter than that of finite element analysis.

The method as presented in the paper assumes linear material properties, e.g. the non‐linear B‐H characteristics of iron cannot be taken into account. Furthermore, the structure is assumed to be slotless, that is, stator slots or end‐effects cannot be taken into account.

The semi‐analytical modeling technique is applied to checkerboard magnetization patterns for 2‐DoF actuators in this paper. However, it can be applied to a wide range of slotless cylindrical electromagnetic devices.

As an addition to the common 2D modeling by means of Fourier series, this paper extends the applicability to 3D cylindrical structures. Furthermore, a new checkerboard magnetization is presented which can be used in 2‐DoF rotary linear actuators.

The purpose of this paper is to present comparative analysis of several configurations of the switched reluctance motor (SRM) for an in-wheel drive for a heavy-duty automotive series hybrid system. The SRM motor is regarded as one of the primary candidates for possible replacement of the permanent magnet (PM) motor.

Three SRMs of 10/8, 12/10 and 12/8 configurations have been analysed, where the last two motors had the stator lamination profile taken from the existing PM motor. The analysis is performed using magnetostatic FEM and transient modelling techniques.

The maximum developed electromagnetic torque of the two analysed motors of 12/10 and 12/8 SRM configurations with the stator lamination profile taken from the existing PM motor is limited due to saturation of the stator yoke. Both motor configurations are capable to provide the specified power within the same outer dimensions due to extended speed in the field-weakening region and position independent starting torque. A redesigned stator results in substantial increase in torque developed by the machine and, consequently, ability to provide similar torque-speed performance as the existing PM motor, at cost of increased copper loss at the low-speed regime.

The paper proposes several structures of SRMs for the in-wheel drive for a heavy-duty automotive series hybrid system converted from the present expensive PM machine, having the same power density. The “bottleneck” of the direct conversion of the PM machine into the SRM is highlighted.

The purpose of this paper is to discuss the performance of a proposed machine design for an in‐wheel motor with the required torque‐speed characteristic.

Calculation of the winding factor of the machine with the star of slots theory is performed first. The field weakening capability of the machine is investigated and the operating speed range is determined. The tooth contour modeling method for calculating the performance of the machine with a limited number of elements is introduced. The method is used to construct two models of different complexity and the results obtained with the models are compared with the results obtained by finite element models.

The 14 pole 12 slot in‐wheel PMSM discussed in this paper is able to meet the stringent performance requirements. The results obtained with the tooth contour models show good agreement with the results obtained with finite element models despite the limited number of elements. Increasing the number of elements in the model allows for modeling of armature reaction and increases the accuracy of the model.

This work can be continued with investigating the possibilities to model the armature reaction more accurately.

This paper proposes a modeling method which accurately describes the performance of a PMSM with limited number of elements. With this method, the calculation procedure can be easily used for optimization of the machine design.