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The purpose of this paper is to analyse the accuracy of the thrust force of a linear actuator computed with different finite elements models.

A series of 2D and 3D models corresponding to different levels of approximation of the original problem are considered. A reliable error estimator based on dual magnetostatic formulations is used.

A 3D model does not necessarily ensure more accurate results than a 2D model. Because of limitations on the number of mesh elements, the discretisation error in 3D can be of the same order of magnitude as the error introduced by the 2D approximation.

The results emphasise the need to consider errors arising from different simplifications with respect to one another, in order to avoid improvements of the model increasing the complexity but not improving the accuracy of the results.

A finite element analysis of a permanent magnet transverse flux linear actuator is presented. In this application where we need a small model (for optimisation purposes) as well as a high accuracy on the computed force, we propose to combine several models with different levels of size and complexity, in order to progressively elaborate an accurate, but nevertheless tractable, model of the system.

The purpose of this paper is to present a method of modeling the variable reluctance stepper motor using the time‐stepping finite element technique. The proposed model is used to minimize the step response overshoots considering the stator and rotor tooth geometry.

A strongly coupled field‐circuit model considering magnetic nonlinearity of the stepper motor is presented. As the main contribution, the Nelder‐Mead method of the motor geometry optimization that minimize the step response overshoots and positioning error is proposed.

The proposed method can be applied to obtain the optimal tooth/pole geometry of the stepper motor which is efficient to perform the possibly accurate positioning.

The paper examines the application of the presented optimization method to minimize the positioning error of the four‐phased variable reluctance stepper motor.

This paper aims to give a perspective about the variety of techniques which are available and are being further developed in the area of coupled field formulations, with selective bibliography and practical examples, to help postgraduate students, researchers and designers working in design or analysis of electrical machinery.

This paper reviews the recent trends in coupled field formulations. The use of these formulations for designing and non‐destructive testing of electrical machinery is described, followed by their classifications, solutions and applications. Their advantages and shortcomings are discussed.

The paper gives an overview of research, development and applications of coupled field formulations for electrical machinery based on more than 160 references. All landmark papers are classified. Practical engineering case studies are given which illustrate wide applicability of coupled field formulations.

Problems which continue to pose challenges to researchers are enumerated and the advantages of using the coupled‐field formulation are pointed out.

This paper gives a detailed description of the application of the coupled field formulation method to the analysis of problems that are present in different electrical machines. Examples of analysis of generators and transformers with this formulation are presented. The application examples give guidelines for its use in other analyses.

The coupled‐field formulation is used in the analysis of rotational machines and transformers where reference data are available and comparisons with other methods are performed and the advantages are justified. This paper serves as a guide for the ongoing research on coupled problems in electrical machinery.

The purpose of this paper is to calculate the electromagnetic torque at a radius of an integration contour for which an optimal value is determined.

To analyze electrical machine dynamics, the electromagnetic torque should be precisely determined. This paper presents a method for calculating the torque, where the radius of the integration contour is variable and estimated from the field distribution.

The electromagnetic torque of the three‐phase AC motor model proposed in TEAM Problem No. 30 is estimated using the proposed method. The obtained results are compared to solutions obtained analytically.

This paper examines the application of the presented method to determine the electromagnetic torque in three‐phase AC motors.

The purpose of this paper is to focus on the frequency-dependent non-linear magnetization behaviour of the soft magnetic material, which influences both the energy loss and the performance of the electrical machine. The applied approach is based on measured material characteristics for various frequencies and magnetic flux densities. These are varied during the simulation according to the operational conditions of the rotating electrical machine. Therewith, the fault being committed neglecting the frequency-dependent magnetization behaviour of the magnetic material is examined in detail.

The influence of non-linear frequency-dependent material properties is studied by variation of the frequency-dependent magnetization characteristics. Two different non-oriented electrical steel grades having the same nominal losses at 1.5 T and 50 Hz, but different thickness, classified as M330-35A and M330-50A are studied in detail. Both have slightly different magnetization and loss behaviour.

This analysis corroborates that it is important to consider the frequency-dependency and saturation behaviour of the ferromagnetic material as well as its magnetic utilization when simulating electrical machines, i.e., its performance. The necessity to change the magnetization curve according to the applied frequency for the calculation of operating points depends on the applied material and the frequency range. Using materials, whose magnetization behaviour is marginally affected by frequency, causes a deviation in the flux-linkage and the electromagnetic torque in a small frequency range. However, analysing larger frequency ranges, the frequency behaviour of the material cannot be neglected. For instance, a poorer magnetizability requires a higher quadrature current to keep the same torque leading to increased copper losses. In addition, the applied iron-loss model plays a central role, since changes in magnetization behaviour with frequency lead to changes in the iron losses. In order to study the impact, the iron-loss model has to be capable to incorporate the harmonic content, because particularly the field harmonics are influenced by the shape of the magnetization curve.

This paper gives a close insight on the way the frequency-dependent non-linear magnetization behaviour affects the energy loss and the performance of electrical machines. Therewith measures to tackle this could be derived.

The purpose of this paper is to focus on the mechanical bearing load caused by the unbalanced magnetic pull (UMP), which is studied in detail. The applied approach is based on an analysis of static and dynamic eccentricities at different positions and different amplitudes. The influence of the operating points is calculated to show the effective bearing load for machines operating at different speeds. The decreasing lifetime of the applied bearings is examined and evaluated in detail.

To evaluate the proposed methodology a permanent magnet synchronous machine (PMSM) with buried magnets is used. To consider effects of slotting and saturation, a finite element (FE) model is employed. The Monte Carlo method is used to determine the most likely amplitudes of the eccentricities. Calculating the UMP for all possible operating points using a control strategy for the machine and coupling this results with a drive cycle, determines the effective force acting on the bearing.

It has been shown that the position of the eccentricity has a not significant influence on the behavior of the UMP and may therefore be neglected. The amplitude of the eccentricity vector influences the amplitude of the UMP including all harmonic force components. For technical relevant eccentricities, the influence is approximately linear for the average and the dominant harmonics of the UMP. In most cases, it is sufficient to displace the rotor at an arbitrary position and amplitude. It is sufficient to simulate one type of eccentricity (static or dynamic) with an arbitrary value of displacement (rotor or stator) to evaluate all possible airgap unbalances. Using stochastic simulations of the eccentricity amplitudes enables an a priori design and lifetime estimation of bearings.

This paper gives a close insight on the effect of mechanical bearing load caused by rotor eccentricities. The effect of the position of the eccentricity vector, the operational range and a drive cycle are considered. A stochastic simulation and an empirical lifetime model of one bearing gives an example of using this methodological approach.

The purpose of this paper is to clarify the status of Maxwell's tensor with respect to the virtual power principle (VPP).

Mathematical analysis is employed.

The VPP, logically stronger, is more fundamental. Maxwell's tensor derives from it, under further restrictive assumptions, and hence, its range of applicability is limited. In particular, it fails to deal with some aspects of magnetostriction.

The paper shows that when magnetic constitutive laws depend, locally, on strain, the body force is not, as a rule, the divergence of the Maxwell tensor. People who intend to compute forces this way should be wary of that.

The purpose of this paper is to present an analysis of the force ripples of an open slot permanent magnet linear synchronous motor (PMLSM). A calculation procedure using 2D finite elements method (2D‐FEM) is then evaluated with experimentations.

First, the studied PMLSM and its main features are introduced. Then, the 2D‐FEM model used to study the motor is presented. The methods used to calculate the force and the meshing procedures are also highlighted. The calculated no‐load force is compared to measurements. Lastly, the validated model is used to study the influence of the current magnitude on the force ripples at load.

In addition to the no‐load case, the influence of the current magnitude on these forces is presented.

The paper is orientated with a sound industrial background. For that reason, the impact of the current saturation on the thrust generation is presented via the evolution of the thrust coefficient, which is the force to the RMS currents ratio.

The purpose of this paper is to present a method of modeling the variable reluctance stepper motor using the time‐stepping finite element technique. The proposed model is used to obtain the optimal control law for the input circuit solving the linear‐quadratic problem.

A strongly coupled field‐circuit model of the stepper motor is presented. Also, the method of the optimal control that minimizes the power loss in the motor windings is proposed.

The proposed optimal control method can be applied to the electrical machines connected to the electronic converters. Calculated control signals may be used to obtain the optimal waveforms of the input voltages at each phase of the analyzed machine.

The paper examines the application of the presented control method to minimize the power loss in the stator windings of the four‐phased variable reluctance stepper motor.