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This paper attempts to present a quasi-3D finite element method technique for modeling and analyzing tubular linear permanent magnet machines (TLPM) with translator eccentricity. Normal tubular linear machines can be modeled effectively using 2D axisymmetric models, but with the introduction of the eccentricity factor into the geometry the axis symmetry is no longer valid, and hence 3D modeling techniques become the only way for studying the machine. However, sometimes 3D modeling can become time-consuming and requires a huge amount of resources especially for non-linear problems, so the interest in modeling techniques that can represent the problem at hand with less computation time and relatively accurate results is high. A quasi-3D technique was specifically developed to be able to represent the eccentricity in TLPMs. The finite element method (FEM) was used for modeling. Eccentricity analysis has been carried on two different TLPM structures using the proposed quasi-3D, and the results from the quasi-3D model were compared to those obtained using the 3D FEM model. Both the open circuit and the on-load operating conditions were studied with the magnetic saturation taken into account. The behavior and the accuracy of the proposed model varied between the two studied structures and for the different operating conditions, and with very low computation time and cost the results obtained from the quasi-3D model were satisfactory in general except for certain cases.

This paper is an introduction to mesh based generated reluctance network modeling. An overview of scientific works which led to the development of this approach is first presented. Basic concepts of the approach are then presented in the case of electromagnetic devices. A step-by-step procedure for coding the approach in the case of a flat linear permanent magnet machine is presented. Codes developed under MATLAB and Scilab environments are also included.

Purpose This paper aims to develop a new quasi-three dimensional (3D) analytical model devoted to the study of nonlinear transient magneto-thermal coupled problems in permanent magnet (PM) transverse flux induction heating device (TFIHD). Design/methodology/approach The presented work is based on analytical development of strongly coupled problem, including electromagnetic and thermal boundary problems. The electromagnetic problem is first solved by using the separation variables method to evaluate the induced currents in the nonmagnetic plate and the resulting power density loss distribution. The plate temperature profile is then obtained thanks to strong involvement of this magnetic model in a new analytical thermal model combining the separation of variables method and the Green’s functions transient regime analysis method. The coupled model is then used in a simulation procedure of the magneto-thermal process allowing taking into account the workpiece electrothermal nonlinear properties. The developed coupled model is validated by computing the performances of the studied PM TFIHD and comparing them to those obtained by finite element simulations. Finding An efficient transient quasi-3D magneto-thermal analytical model is developed allowing rapid analysis of PM induction heating for core heating of parallelepiped parts. The developed model also allows fast and accurate simulations of nonlinear and transient three dimensional (3D) magneto-thermal phenomena for planar induction heaters. Research limitations implications The developed quasi-3D magneto-thermal analytical model is limited to design induction heating devices of planar structure with PM inductors. Originality/value A new transient quasi-3D magneto-thermal analytical model accounts for non-linearity and edge effect and helps to fast study and fast design of linear permanent magnet induction heating device.

This contribution presents the study of eccentricity in a tubular linear (TL) flux switching (FS) permanent magnet (PM) (TLFSPM) machine using 3D finite element analysis. Regarding the 3D nature of magnetic flux under eccentricity fault, 3D finite element (FE) method is used for that purpose. The developed 3D FE models construction and exploitation are presented in details. The effect of eccentricity is studied under open-circuit and load conditions.

This contribution discusses the integration of bearing function within the tubular linear (TL) flux switching (FS) permanent magnet (PM) machines (TLFSPM machines). The mechanical integration allows reducing the machines volumes and therefore increasing the force density. The goal here is not to present a final design which has proven to be feasible and reliable, but rather to discuss the concept. It is aimed at stimulating new ideas.

This paper presents a literature review of relevant contributions found in the literature concerning the end effects with a focus mainly on linear permanent magnet synchronous machines. This work presents a classification of the obtained information to classify the end effects and provides essential information for its understanding, categorization, modeling, mitigation, and control. The causes and consequences of the end effects are presented, according to the geometrical structure. Additionally, the main approaches for end effects modeling are discussed. Also, several existing techniques for mitigation of consequences of end effects are presented, considering changes in the machine geometry or in the electromagnetic structure, and electronic compensation using control techniques. The control of linear machines accounting for end effects, and compensation to achieve better performance to mitigate negative impacts on machine characteristics are also addressed.

This contribution presents a comparison study of the translator eccentricity effects on two different tubular linear permanent magnet (TLPM) machines. One structure is a surface mounted PM machine, and the second has its PMs embedded in the translator structure. Both structures have the same type of PM and the same PM volume. The comparison study spans all operating conditions: open-circuit and underload conditions. It has been conducted for different eccentricity values. 3D finite element method is used. The comparison study is also exploited in order to analyze the impact of magnetic saturation on the machine under eccentricity effects. The eccentricity effects on one of the two structures were shown to be remarkably higher than on the other.

This paper presents multi-physic early-stage design optimization of 15 MW Permanent Magnet Synchronous Generators dedicated to wind turbines. In this work, a two-dimensional magneto-thermal model was developed. The magnetic design is based on an Analytical Model, considering the direct solution of Maxwell equations and using separation of variables technique. However, the thermal model is issued from Lumped Parameter Model using mesh-based formulation. Further, multi-objective optimization using the genetic algorithm coupled with magneto-thermal model is applied to minimize the rare-earth permanent magnet mass within the generator, with respect to the required torque and the thermal limitations. The obtained Pareto front is, then, verified using an already validated magneto-thermal reluctance network model. The obtained Pareto fronts are then compared in terms of precision and computation time.

Permanent magnet flux switching machines are gaining more and more interest due to their relatively good characteristics. Indeed, the presence of all magnetic field sources in the stator (armature windings, permanent magnets and/or field windings), which implies a completely passive rotor, makes it suitable for a large variety of applications [1] [2]. Different flux switching machines topologies have been studied in scientific literature. In this contribution, a relatively new modeling approach [3] based on the coupling of mesh based generated reluctance networks (MBGRN) and analytical models (AM), based on the formal solution of Maxwell’s equations, is used for the accurate prediction of cogging force of a linear tubular flux switching machine. This type of machines could be favorably used in oceanic renewable energy conversion. Figure 1(a) illustrates how the two approaches are combined for the case of a tubular linear flux switching structure. In this example the analytical solution is used for modeling the mechanical air-gap, and inner and outer airs, and the RN method is used to model the moving and static armatures. In order to have a more generic approach, the stator and moving armatures are modeled using mesh based generated reluctance network (MBGRN) technique [3]. This technique, as classical RN method, can be used with a minimum number of reluctances for regions where flux tubes are not highly affected by topology changes. As for finite elements analyses (FEA), the studied domain in MBGRN should be finely meshed in some regions (air-gap for example) and coarsely meshed in other regions. However, in contrast to FEA, the mesh relaxation in MBGRN can be done more easily conducting to reduced system matrix dimensions, and consequently reduced computation time. Indeed, while in FEA two adjacent elements should share an edge, it is no more necessary for RN method, as illustrated in Fig. 1(b). This new modeling approach has been used to analyze the performance of different electromagnetics devices (2D and 3D) [3]–[7]. In this contribution, this technique is used for the computation of cogging force of a linear tubular flux switching permanent magnet structure, something which has never been reported yet, to the best of our knowledge, in scientific literature. The goal is to further extend the investigation of this technique for the computation of relatively sensitive quantities, such as the cogging force, in more complex structures. Another goal is to highlight advantages of HAM as compared to other modeling techniques, and more particularly FEA, in order to obtain reduced order equations system [8] [9].

Purpose This work aims to study a new design of linear permanent magnet transverse flux induction heating devices of nonmagnetic parallelepipedic workpiece. In these topologies, the permanent magnet inductor produces a static magnetic field, and the workpiece to be heated is subjected to a linear movement. To study the magnetothermal process, a new analytical coupling method between the magnetic and thermal phenomena is developed. This analytical model described in this study takes into account the variation of the physical properties of the heated workpiece. The analytical results are compared with good agreement to those issued from finite elements simulations, as well as those issued from measurements on an actual prototype. Design/methodology/approach The research methodology is based on analytical development of coupled problem, including the electromagnetic and thermal boundary problems. A strongly coupled magneto-thermal analytical model is developed; the time dependent magnetic problem is first solved by using the separation of variables method to evaluate the induced currents in the nonmagnetic plate and the resulting power density loss distribution. The plate temperature profile is then obtained, thanks to strong involvement of this magnetic model in a new analytical thermal model based on a synergy of separation of variables method and Green’s function transient regime analysis method. Findings The results show that an efficient transient magneto-thermal analytical model was developed allowing fast analysis of permanent magnet induction heater for deep heating of parallelepipedic workpieces. Developed model allows also fast and precise simulations of nonlinear and transient magneto-thermal phenomena for different types of permanent magnet induction heating devices. Practical implications The developed magneto-thermal analytical model can be used for fast designing of permanent magnet linear induction heating devices for moving parallelepipedic nonmagnetic workpiece. Originality/value A new analytical coupled model, including the electromagnetic and transient thermal boundary problem with additional algebraic equations and taking into account the nonlinearity, has been developed. The developed model accuracy was validated with a permanent magnet linear induction heating device. Developed coupled analytical model allows fast analysis and designing of such permanent magnet linear induction heating devices.

The aim of this paper is to present the design and modeling of a machine that possesses some advantageous characteristics for wind energy conversion applications. The studied machine is a double stator inner rotor axial airgap flux switching permanent magnet machine (AFSPM). The paper will start by presenting this type of machine and its points of interest. Then, it will continue by introducing the constructed prototype and its specifications and structure. This prototype has been designed based on a reference specification used at GREAH to develop different prototypes and compare their performances. The second part will introduce the reluctance network model specifically constructed for this type of machine. The constructed model was validated by comparing its results to the results from the finite element method model. Finally, the experimental results will be presented and compared to the reluctance network (RN) model results where satisfying agreement between both results was obtained.

This contribution describes some developments towards the construction of a generic framework for reluctance networks. This tool is used for the study of a permanent magnet (PM) machine. The focus will be put on the modelling methodology, and software implementation. More precisely, the aspects related to genericity will be discussed. In order to validate the developed tool, results obtained from this framework are compared to corresponding finite element analyses (FEA).

This paper presents a multi-criteria design optimization procedure of a concentrated flux permanent magnet synchronous generator CFPMSG dedicated to ultra-large direct-drive wind turbines using analytical model coupled with genetic algorithm NSGA II, in order to reduce the weight of both the magnets and the machine’s active parts. Simulation results are presented and compared with design model based on reluctance network model.

The aim of this paper is, first, to extend the application of the hybrid analytical modeling (HAM) approach for the analysis of tubular linear machines (TLPM), something that has never been reported yet in the scientific literature. The HAM consists of a strong coupling between the reluctance network and the Fourier series solution of magnetic scalar potential. In order to assess the merits and capabilities of the HAM, it is applied to the study of the cogging force in linear machines and compared with finite element analyses (FEA). The cogging force is a global quantity, which is very sensitive to magnetic field computation accuracy and constitutes, therefore, a good measure of the accuracy of the HAM as compared with FEA. The HAM should require less computation time as compared with FEA, and is then more suitable for predesign stage. Three different structures are analyzed: a flat linear machine, a TLPM with internal mobile armature, and, finally, a TLPM with external mobile armature. The analyses are conducted, considering the effect of magnetic saturation.

Power capability of synchronous machines, when operating in motoring mode, is discussed in this contribution. Maximum power limits and partial loads operations are both examined in the case of variable speed drives applications when the synchronous motors are driven with idealized inverters with limited volt–ampere ratings. This study is based on a per-unit ${d}$ - ${q}$ model normalized according to the base speed operation quantities. Different control strategies are thoroughly analyzed for different motors parameters. The use of per-unit quantities will help to draw some general conclusions regarding the effect of motors parameters on the drives performance. Since wound field (WF) excited and permanent magnet (PM) excited synchronous motors could be considered as particular cases of hybrid excited synchronous motors, the findings of this contribution would be applicable to all synchronous motors with a magnetic excitation source.

In this paper, the translator eccentricity of a tubular linear permanent magnet (TLPM) machine is studied using a 3D finite element analyses. Translator eccentricity in linear machines, as rotor eccentricity in rotating machines, is inevitable. It should then be evaluated and studied during the design stage to avoid performance degradation and life time reduction. Apart from few publications, translator eccentricity in tubular linear machines has been rarely addressed in scientific literature. The aim of this study is to contribute to filling this gap. The effect of static eccentricity of the translator is studied for a surface mounted TLPM motor. While the novelty may seem limited, this study should be regarded as a step toward the development of modeling approaches allowing a good “accuracy/computation time” ratios.

For electromagnetic actuators whose magnetic fields are three-dimensional, the use of the 3D finite element (FE) method is required. On the other hand, 3D FE analysis is expensive in computation time, especially for high power machines involving potentially high numbers of nodes. In this paper, a 3D reluctance network (RN) modeling approach is proposed for the pre-design of permanents magnets synchronous machines (PMSM). The RN model developed is used to model three types of electrical machines (linear machine, radial field rotating machine and axial field rotating machine). Our goal is to establish lightweight models for the pre-design of electrical machines. The performances (local and global quantities) of these machines are evaluated using this 3D RN modeling. The results obtained from this approach are validated by comparison with results issued from the 3D FE analyses.

In highly concurrential markets the time to market is reduced, which implies a need of design tools having relatively high accuracy to computation time ratio. It is to address this problematic that the presented modelling approach has been developed. A general framework for the analysis and design of electromagnetic devices is presented. This framework is based on a new hybrid analytical model (HAM) [1]-[4]. The HAM can be applied to different electric machines types (synchronous and asynchronous) and structures (rotating with radial field or axial field, linear flat or tubular structures, or multi-degree-of-freedom structures). It is based on a direct coupling of analytical solution of Maxwell's equations (AM) with reluctance networks (RN). This new technique allows to combine advantages of both methods and should help reduce computation time as compared to finite elements method [3]. This modeling approach is relatively simple and allows the accurate prediction of performances of electromagnetic devices.

The aim of this study is to explore the possibility of using flux switching linear tubular machines in a free piston energy conversion (FPEC) system. In FPEC systems, acceleration and therefore speed are often relatively high, which impose to have a reduced number of poles, meanwhile the cogging force will be relatively high. In order to reduce the cogging force two techniques are combined. The analysis is done using finite element method.

Fast design procedures of electrical machines require the use of adapted modeling approaches. This is particularly true for axial flux permanent magnet (AFPM) machines, which have an intrinsic 3-D electromagnetic structure. Indeed, accurate modeling of AFPM machines requires the use of 3-D finite-element analysis (3-D FEA), which is highly time consuming, especially at first design stages. This paper presents a new quasi-3-D analytical model (AM) that allows modeling accurately AFPM machines while saving a huge amount of time as compared with 3-D FEA. This new approach combines a multislice AM, which takes into account a part of the 3-D effects, and considers the end-effects by a simple and effective radial dependence modeling of the magnetic field in AFPM machines.

Generally, accurate modelling of electrical machines requires the use of finite-element method. However, FE analysis is too time consuming, especially at firsts design stages, from the point of view of engineers working in R&D departments in the electrical machine industry. To reduce pre-design stages duration, analytical models are often preferred. Two types of analytical models are often used: magnetic equivalent circuits (MEC) and analytical models based on the formal solution of Maxwell's equations in constant permeability regions. However, MEC method is not as generic as the finite element method. In fact, even in the case of a given structure geometry, MEC method has to be adapted if the geometric parameters vary in a large scale. Analytical models based on the formal solution of Maxwell's equations help overcome aforementioned problem. This paper is intended as a tutorial overview based on a review of the state of the art, describing recent developments in the field of analytical modelling of permanent magnet machines.

The aim of this paper is to present an electromagnetic model dedicated to the predesign of Radial Switching Flux Permanent Magnet (RSFPM) machines. This model is based on two independent reluctance networks (RN) for the stator and rotor modeling coupled using interpolation functions in the sliding surface located in the air-gap. The validation of the developed model is followed by a parametric study of a 12 slots / 10 poles RSFPM generator in order to maximize the average electromagnetic torque and to reduce its ripples. This operation is established by finding the suitable rotor tooth opening and skewing angle. The used modeling approach takes into consideration the 3D skewing effect. The main results are compared to those obtained by finite elements (FE) simulation with commercial software.

With the advent of more electric aircraft, the use of electrical actuators instead of hydraulic and pneumatic ones becomes necessary. Those actuators must be fault tolerant in order to ensure the continuity of service even in a faulty operating. In this paper, we will proceed to a constrained design of a Double Star Permanent Magnet Synchronous Machine tolerant to certain faults in healthy and faulty operating. First, we present the sizing of this machine and the strategy adopted in the case of an IGBT short-circuit. Then, modeling of a such machine is detailed. Finally, the performances of this fault-tolerant machine in healthy and faulty conditions are discussed. The analysis of results allows to assess the relevance of the adopted strategy and its limits.

The aim of this contribution is to assess the capabilities of a quasi-3D hybrid analytical model for the estimation of iron loss in axial flux permanent magnets machines. The hybrid analytical modelling (HAM) approach is based on a direct coupling of analytical solution of Maxwell's equations with reluctance networks (RN). The quasi-3D hybrid analytical modelling approach consists of dividing the axial field machines in a certain number of concentric slices, each of which can be modelled using a 2D hybrid analytical model. The results obtained from the proposed approach are compared to corresponding results obtained from a quasi-3D finite element method (Quasi-3D FEM) and a 3D finite element method (3D FEM).

The aim of this paper is to compare two approaches for modelling the vibro-acoustic behaviour of a three-phase discoidal switching flux permanent-magnet machine (DSFPM) due to electromagnetic origins. The first approach is based on a full transient vibro-acoustic analysis of the DSFPM emitted acoustic noise. The second modelling approach is based on a modal superposition analysis of the DSFPM vibro-acoustic behaviour. This multi-physic study is based on a weak coupling between two 3D Finite-Element (FE) models: an electromagnetic model computing the magnetic pressure and a vibroacoustic model to quantify the vibration/noise performances. Results comparison between the two modelling approaches shows the effectiveness of the modal superposition model in terms of precision and computation time.

This paper presents a hybrid thermal model which can be used for the predesign of permanent magnet synchronous machines. This hybrid model consists of a direct coupling between two lumped parameter thermal networks (stator and rotor) and an analytical solution in the air-gap region. A flat linear permanent magnet machine and a radial field one are investigated in this study. All results will be compared to those obtained with finite elements method.

This paper describes an analytical technique for prediction of open circuit eddy-current loss in armature windings and permanent magnets (PM) of series double excitation synchronous machines. First, a 2-D exact analytical solution of open circuit magnetic field distribution in idealized geometry of series double excitation synchronous machine is established. It involves solving Maxwell's equations in stator slots, air gap, PM region, and rotor slots. Then, magnetic vector potential solutions in the stator slots and PM regions are respectively used for prediction of resistance limited eddy currents in armature windings and permanent magnets. This analytical model is then used to estimate eddy-current loss in armature windings and permanent magnets. The validity of the developed model, which is also applicable to conventional designs of permanent-magnet machine, is verified by time-stepped transient finite-element analysis (FEA). The developed model is then used to quantify the effectiveness of segmenting the magnets and armature windings in reducing the eddy-current loss.

This paper presents an analytical model, based on separation of variables solution of Maxwell's equations in low permeabiliy regions (slots, airgap and permanent magnets), allowing the prediction of open circuit and on load magnetic field distributions for flat linear machines with surface mounted permanent magnets. Developed analytical model is validated via comparison to corresponding finite element analyses.

This paper presents an exact 2-D analytical model for predicting the armature reaction magnetic field in idealized structures of permanent-magnet tubular linear machines with surface-inset mounted magnets. The armature reaction magnetic field distributions is analytically derived and compared to finite-element analyses. The analytical solution allows the prediction of the machine inductance and reluctance force in closed forms, and facilitates the evaluation of any possible partial irreversible demagnetization of the magnets. It can also be used to estimate resistance limited eddy-current losses in armature windings and permanent magnets. The developed analytical model can be advantageously used for the analysis and design of a class of linear tubular machines.

We present an exact 2-D analytical model for predicting the magnetic field in idealized structures of surface mounted permanent-magnet tubular linear machines that account for the stator slotting effect. The open-circuit and armature reaction magnetic field distributions are analytically derived and compared to finite-element analyses. The on-load magnetic field calculation is based on the superposition of the component fields due to permanent magnets and armature field reaction. Our model can be advantageously used for the analysis and design of a class of linear tubular machines.

We describe an exact 2-D analytical model for predicting the open circuit magnetic field in idealized structures of wound field and series hybrid excitation permanent-magnet synchronous machines. This technique can be used for either internal or external rotor radial-field machine topologies. It involves analytical solution of Maxwell's equations in stator and rotor slots and annular air-gap/magnet regions. We compare results from this analytical model to corresponding finite-element analyses. We then use it to estimate the cogging torque, induced back-electromotive force, and to study the effects of rotor skewing.

This paper presents an analytical model for prediction of eddy current loss in armature windings of permanent magnet brushless AC machines. The developed model can either be used in the case of internal or external rotor radial-field machines topologies. First, a 2-D exact analytical solution of magnetic field distribution in an actual geometry of slotted surface mounted PM radial flux synchronous machines is established. It involves solution of Maxwell's equations in slots, airgap and PM's region. Then, magnetic vector potential solution in the slots is used for prediction of resistance limited eddy current in armature windings. Finally, results from this analytical model are compared to corresponding finite element analyses.

This paper presents an analytical solution for prediction of the armature reaction magnetic field in slotted surface mounted permanent magnet radial flux synchronous machines. This technique is used in the case of internal and external rotor radial-field machines. The magnetic field expressions are developed in both slots regions and magnetic airgap region leading to an exact calculation of the effects of slotting on the airgap magnetic quantities. Results from this analytical model are compared to corresponding finite element analyses. This analytical model is then used to estimate the self and mutual inductances.

This paper presents the analysis of open circuit performance of a permanent magnet linear machine using a new hybrid analytical model (HAM). The goal is to show the capabilities offered by this new modeling approach. The new HAM is based on a strong coupling of magnetic equivalent circuits method and analytical models. The analytical model, based on the formal solution of Maxwell’s equations, is established because of the separation of variables method. The open circuit performance are: 1) cogging force; 2) electromotive force; and 3) open circuit iron loss, obtained from the HAM are compared with corresponding results obtained from a finite-element analysis. A very good agreement has been obtained.

The aim of this paper is to present the analysis and prototyping of an axial flux permanent magnet synchronous machine dedicated to a small wind turbine. The analysis of the generator was made with a quasi-3D analytical model based on a multi-slice 2D analytical solution of Maxwell equations coupled sequentially to a thermal model and a mechanical model. The designed generator is a 10 kW, 375 rpm, stator-rotor-stator structure with 20 poles, 24 slots, and modular windings. Results issued from measurements are satisfactory compared to those issued from analytical model.

This paper presents a 2D and 3D Magnetic Equivalent Circuit (MEC) of the flux focusing permanent magnet synchronous machine. The proposed model is based on reluctance mesh of the structure in order to have a high precision model and to take into account all leakage flux. The saturation effects and rotor motion are taking into account in the proposed model. The extension from 2D to 3D is detailed. The obtained results of 2D and 3D models are compared to finites elements model and validated by experimental measurements.

Flux Switching Permanent Magnet machines have attracted considerable attention due to their simple and robust structure, easy heat dissipation, high torque densities and suitability for high-speed operations. To enhance these proprieties, we present in this paper an analytical model for prediction of the magnetic field for a 3 phase, 12 stator slots and 10 rotor tooth (12/10) flux switching permanent magnet machine. The proposed model is based on an two dimensional analytical solution of Maxwell equations in low permeability regions using the variable separation method. The global quantities can be derived from the local magnetic field expression. The computation provides exact results in relatively short resolution times. Finally, the accuracy of the model is validated by comparing the analytical results with those obtained with a finite element analysis.

Cogging torque is a source of vibration and noise in PM machines. Its reduction is always sought by electrical machine designers. While its study, in radial-flux PM machines, can often be done using 2-D finite element analysis (FEA), 3-D FEA is always required when it comes to its study in axial-flux PM machines (AFPM). AFPM machines have an inherent 3-D electromagnetic structure. There is a rich literature concerning the study of cogging torque in AFPM machines. Indeed, most of the authors use 3-D FEA for its study. However, 3-D FEA is time consuming and always requires expertise to be done correctly. The goal of this paper is to show that alternative techniques, to study cogging torque in AFPM machines, do exist. It is shown that the analytical approach, used in this paper, can be as efficient as the 3-D FEA while saving a huge amount of time and necessitating less initial expertise.

This paper deals with the computation of vibrations and noise of electromagnetic origin for 'U'-shaped stator core flux switching permanent magnet (FSPM) machines. The investigation concerns a family of FSPM stator/rotor configurations with 12 slots and 10, 11, 13, and 14 rotor poles. More precisely, the study focuses on the influence of different number of rotor poles on the sound power level of U-core FSPM machines. Electromagnetic forces acting on the stator frame inner surface are calculated with the Maxwell stress tensor thanks to 2-D finite element (FE) simulations. The local magnetic force density serves then as a boundary condition to the 3-D finite element vibrational simulations of the whole stator frame with housing. Finally, obtained displacements help the authors to conduct the acoustic computations using a dedicated 3-D FE analysis model. The obtained vibro-acoustic spectra help electric machines designers to make appropriate choice of stator/rotor pole combination with respect to specifications at early stages of the design process.

In this paper an analytical model for prediction of the no-load magnetic field in axial field flux switching permanent magnet machines (FSPM) is presented. The proposed method is based on an exact 2D analytical solution of Maxwell's equations in low permeability regions (stator/rotor slots, air gap, permanent magnets (PMs) and surrounding air regions), using the separation of variables technique. For each region, the magnetic vector potential solution is expressed as a sum of Fourier series. Combining obtained solutions in each region and boundary conditions leads to a set of linear equations which allows calculation of the coefficients of the Fourier series in the different regions. The developed model is validated by comparing magnetic field components for a machine modeled with this analytical model and the finite element method (FEM).

This paper presents an analytical solution for prediction of the magnetic field in slotted permanent magnet axial flux synchronous machines in the case of inter-turn short-circuit stator fault. The technique is based on 2-D solution of the Maxwell's equations using the separation of variables method. The magnetic field expressions are developed in slots regions, magnetic airgap region, slot opening region and permanent magnet region leading to an exact calculation of the slot effects on the airgap magnetic quantities. Inter-turn short-circuit fault is then taken into account in the stator phases electrical equations. Simulation results illustrating the impact of the stator winding faults are presented and their comparison with those issued from coupled magnetic circuit based model proof the pertinence of the proposed approach.

This paper presents a multi-slice analytical model for prediction of the open-circuit magnetic field in slotted semi-closed permanent-magnet axial flux synchronous machines. The technique is based on 2-D exact solution of the Maxwell's equations using the separation of variables method. The magnetic field expressions are developed in slots regions, slot opening regions, magnetic air gap regions, and permanent magnet regions leading to an exact calculation of the slot effects on the air gap magnetic field. The model is established considering that ferromagnetic parts are infinitely permeable, and end effects at inner and outer radii are neglected. The open circuit machine's global quantities (electromotive force and cogging torque) are then deduced from the local magnetic field expressions. Finally, the accuracy of the presented analytical model is validated by comparing its results to corresponding finite-element analyses for two different axial flux machines.

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Double excitation synchronous machines combine permanent-magnet (PM) excitation with wound field excitation. The goal behind the principle of double excitation is to combine the advantages of PM-excited machines and wound field synchronous machines. These machines can constitute an energy-efficient solution for vehicle propulsion. This paper presents a comparison of the open circuit flux control capability of two structures of double excitation synchronous machines. First, a review of the state of the art of double excitation machines is presented. Then, the structures of these two machines are presented: one is a series double excitation synchronous machine and the other is a parallel double excitation synchronous machine. Finally, the open circuit flux control capabilities of both structures are compared.

This paper presents a comparison of open circuit flux control capability of two structures of double excitation synchronous machines. First, the structures of these two machines are presented: one is a series double excitation machine and the other one is a parallel double excitation machine. The flux control capability of the parallel double excitation machine is evaluated experimentally using a build prototype. For the study of flux control capability of the series double excitation machine, a 2D exact analytical solution of open circuit magnetic field distribution in a idealized geometry of a series double excitation synchronous machine is established. It involves solution of Maxwell's equations in stator slots, airgap, PM's region and rotor slots. The validity of developed model is demonstrated via comparison to finite element analyses. Then, developed model is used to study the open circuit flux control of a series double excitation machine having same overall dimensions as the parallel double excitation machine prototype. Finally, open circuit flux control capabilities of both structures are compared.

This paper presents an analytical solution for prediction of the no-load magnetic field in slotted semi-closed permanent magnet axial flux synchronous machines. The technique is based on 2-D solution of the Maxwell's equations using the separation of variables method, this technique is validated for two different machines. The magnetic field expressions are developed in slots regions, magnetic airgap region, slot opening region and permanent magnet region leading to an exact calculation of the slot effects on the airgap magnetic quantities. Results from this analytical model are compared to corresponding finite element analyses (FEA).

This paper attempts to provide analytical tools to facilitate the analysis and design of flat permanent magnet linear machines. First, a 2D exact analytical solution of magnetic field distribution in a actual geometry of a flat type permanent magnet linear machine is established. The developed model is then used to estimate resistance limited eddy current in armature windings and permanent magnets and corresponding loss.

This paper presents an exact 2D analytical model for predicting the armature reaction magnetic field in idealized structures of permanent magnet tubular linear machines with surface-inset mounted magnets. The armature reaction magnetic field distributions is analytically derived and compared to finite elements analyses. The analytical solution allows the prediction of the machine inductance and reluctance force in closed forms, and facilitates the evaluation of any possible partial irreversible demagnetization of the magnets. It can also be used to estimate resistance limited eddy current losses in armature windings and permanent magnets. The developed analytical model can be advantageously used for the analysis and design of a class of linear tubular machines.

Accurate modeling of axial flux permanent magnet (AFPM) machines requires the use of three dimensional finite-element method (3D FEA). However, 3D FEA is high time consuming especially at first design stages. This paper discusses the validity domain of a multislice analytical model (quasi-3D model) of AFPM machines with trapezoidal magnets. This analytical model (AM) considers the machine as composed of several annular machines, each one being modeled using a two dimensional model. A detailed parametric study investigates the influence of certain design features on the validity domain of proposed approach. The goal is to have a fast pre-design tool with a fairly good accuracy as compared to 3D FEA.