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This paper aims to present an analytical method, which combines the complex permeance (CP) and the superposition concept, to predict the air-gap magnetic field distribution in surface-mounted permanent-magnet (SMPM) machines with eccentric air-gap.

The superposition concept is used twice; first, to predict the magnetic field distribution in slot-less machine with eccentric air-gap, the machine is divided into a number of sections. Then, for each section, an equivalent air-gap length is determined, and the magnetic field distribution is predicted as a concentric machine model. The air-gap field in the slot-less machine with eccentricity can be combined from these concentric models. Second, the superposition concept is used to find the CP under eccentricity fault. At this end, the original machine is divided into a number of sections which may be different from the one for slot-less magnetic field prediction, and for each section, the CP is obtained by equivalent air-gap length of that section. Finally, the air-gap magnetic field distribution is predicted by multiplying the slot-less magnetic field distribution and the obtained CP.

The radial and tangential components of the air-gap magnetic flux density are obtained using the proposed method analytically. The finite element analysis is used to validate the proposed method results, showing good agreements with the analytical results.

This paper addresses the eccentricity fault impact upon the air-gap magnetic field distribution of SMPM machines. This is done by a combined analysis of the complex permeance (CP) method and the superposition concept. This contrasts to previous studies which have instead focused on the subdomain method.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

The electromagnetic excited audible noise of electrical machines can be mostly attributed to radial forces on stator tooth‐heads. The methodology proposed in this paper uses numerical field simulation to obtain the magnetic air gap field of electrical machines and an analytical‐based post‐processing approach to reveal the relationship between air gap field harmonics and the resulting force wave.

The simulated air gap field is sampled in space and time and a two‐dimensional Fourier transform is performed. The convolution of the Fourier transformed air gap field by itself represents a multiplication in space time domain. During the convolution process, all relevant combinations of field waves are stored and displayed using space vectors.

The effectiveness of the proposed approach is shown on an example machine. Particular examples of individual force waves demonstrate how the approach can be used for practical application in analysis of noise and vibration problems in electrical machines. The proposed method is compared to the result of a Maxwell stress tensor calculation. It shows that the deviation is small enough to justify the approach for analysis purposes.

The combination of analytically understood force waves and the use of numerical simulation by means of air gap field convolution has not been proposed before.

The purpose of this paper is to present an improved conformal mapping (ICM) method that simultaneously considers the influence of relative recoil permeability of PMs, the armature reaction, the stator slotting, and the magnetic saturation on determination of the PM operating point in its different parts.

The ICM method is a time-effective method that considers the magnetic saturation by suitable increments in air-gap length under each tooth and also the width of slot openings. In this paper, the analytical and numerical conformal mappings such as the Schwarz-Christoffel (SC) mapping are used for magnetic field analysis due to the permanent magnets and the armature reaction in one slotted air gap. The field solution in the slotted air gap is obtained through the modulation of field solution in one slotless air-gap using the complex air-gap permeance.

The ICM method can consider the magnetic saturation in different electric loadings, and also the variation of PM operating points in its different parts.

The ICM method is applied to one surface mounted permanent magnet (SMPM) motor and is verified by comparing with the corresponding results obtained through finite element method (FEM), and frozen permeability finite element method (FP-FEM).

This paper presents an ICM method with a new technique for saturation effect modeling, which can be used to separate and calculate the on-load components of air-gap field and torque.

The purpose of this paper is to introduce a reverted way to design electrical machines. The authors present a work flow that systematically yields electrical machine geometries from given air gap fields.

The solution process exploits the inverse Cauchy problem. The desired air gap field is inserted to this as the Cauchy data, and the solution process is stabilized with the aid of linear algebra.

The results are verified by solving backwards the air gap fields in the standard way. They match well with the air gap fields inserted as an input to the system.

The paper reverts the standard design work flow of electrical motor by solving directly for a geometry that yields the desired air gap field. In addition, a stabilization strategy for the underlying Cauchy problem is introduced.

This paper aims to propose an analytical model for the harmonic content no-load magnetic fields and Back electric motive force (EMF) in double-sided TORUS-type non-slotted axial flux permanent magnet (TORUS-NS AFPM) machines with surface-mounted magnets considering the winding distribution and iron saturation effects.

First, a procedure to calculate the winding distribution with a rectangular cross-section is proposed. The magnetic field distribution and magnetic motive force (MMF) drop due to saturation in iron cores are then exactly extracted in a 2-D analytical model. The consequent influence on air-gap magnetic field and Back EMF are also calculated using a new iterative algorithm. The results are compared with those of the conventional analytical model without saturation, 2-D finite element analysis (FEA) and an experiment on a fabricated prototype machine.

Unlike the conventional method, the new method yields the no-load magnetic field distributions in air-gap and iron cores and Back EMF very exactly such that the results well match to those of the FEA and experiment.

Unlike the conventional winding factor, the winding distribution is considered here along the both axial and circumferential directions, which improves the accuracy level of results for non-slotted structures with relatively large air-gaps. The magnetic field distribution and MMF drop-in iron parts are also calculated as the basis for exact recalculation of air-gap magnetic field and Back EMF. Because of small computational burden beside superior accuracy, the proposed model can be treated as an accurate and fast substitute for FEA to be used during the design procedure or for predicting the other performance characteristics of TORUS-NS AFPM machines.

Owing to the salient pole structure and stator slots of hydro-generator, the air gap magnetic field in the generator is unevenly distributed. High-frequency harmonic components contained in the inhomogeneous air gap magnetic field will have a negative impact on the generator performance. The purpose of this paper, therefore, is to improve the distribution of air gap magnetic field by using appropriate magnetic slot wedge, thereby improving the generator performance.

Taking a 24 MW, 10.5 kV bulb tubular turbine generator as an example, the 2 D electromagnetic field model of the generator is established by finite element method. The correctness of the model is verified by comparing the finite element calculation data with the experimental data. The influences of the permeability and thickness of the magnetic slot wedge on the generator performance are studied.

It is found that the intensity and harmonic content of the air gap magnetic field will change with the permeability of slot wedge and then the performance parameters of the generator will also change nonlinearly. The relationship between the eddy current loss, torque ripple, output voltage and other parameters of the generator and the permeability of slot wedge is confirmed. In addition, the variation of losses and torque with wedge thickness is also obtained.

The influence mechanism of magnetic slot wedge on the performance of hydro-generator is revealed. The presented results give guidelines to selecting suitable magnetic slot wedge to improve generator performance.

This paper aims to propose a novel mathematical model of bearingless switched reluctance motor (BSRM). This model differs from conventional mathematical models in the calculation of torque and suspension forces. Conventional mathematical models neglect the coupling relationship between the α- and β-axes or ignore the magnetic saturation of the Si-Fe material. This study considers these issues simultaneously. Additionally, considering the air-gap edge effect, the fringing coefficient is used to establish a high-precision mathematical model.

An innovative mathematical model of BSRM based on the Maxwell stress method was established by selecting an appropriate integration path. The fringing coefficient of the air-gap was computed based on the finite element analysis results at the aligned position of the stator and rotor poles. Using the least squares fitting method, the piecewise fitted magnetization curve of the Si-Fe material was utilized to calculate flux density.

The appropriate integration path of the Maxwell stress method was selected, which considered the coupling relationship of the suspension forces in the α- and β-axes and was closer to the actual situation. The fringing coefficient of the air-gap improved the calculation accuracy of air-gap flux density. The magnetomotive force was consumed by the magnetic resistance of the stator and rotor poles considering the magnetic saturation.

A novel mathematical model of BSRM is proposed. Different from conventional mathematical models, the proposed model can effectively solve the coupling relationship of the suspension forces in the α- and β-axes. Additionally, this model is consistent with the actual situation of motor as it includes a reasonable calculation of the air-gap flux density, considering the air-gap edge effect and magnetic saturation.

The purpose of this paper is to present a new optimal design for integral slot permanent magnet synchronous motors (PMSMs) to shape the air-gap magnetic field in sinusoidal and to reduce the cogging torque, simultaneously.

For obtaining this new optimal design, the influence of different magnetizations of permanent magnets (PMs), including radial, parallel and halbach magnetization is investigated on the performance of one typical PMSM by using the conformal mapping (CM) method. To reduce the cogging torque even more, the technique of slot opening shift is also implemented on the stator slots of analyzed PMSM without reduction in the main performance, including the air-gap magnetic field, the average torque and back-electromotive force (back-EMF).

Finally, an optimal configuration including the Hat-type magnet poles with halbach magnetization on the rotor and shifted slot openings on the stator is obtained through the CM method, which shows the main reduction in cogging torque and the harmonic content of air-gap magnetic field.

The obtained optimal design is completely practical and is validated by comparing with the corresponding results obtained through finite element method.

This paper presents a new optimal design for integral slot PMSMs, which can include different design considerations, such as the reduction of cogging torque and the total harmonic distortion of air-gap magnetic field by using the CM method.

The purpose of this paper is to study the effect of curvature on the magnetic field distribution and no-load rotor eddy current losses in electric machines, particularly in high-speed permanent magnet (PM) machines.

The magnetic field distribution is obtained using conformal mapping, and the eddy current losses are obtained using a cylindrical multilayer model. The analytical results are validated using a two-dimensional finite element analysis. The analytical method is based on a proportional-logarithmic conformal transformation that maps the cylindrical geometry of a rotating electric machine into a rectangular configuration without modifying the length scale. In addition, the appropriate transformation of PM cylindrical domains into the rectangular domain is deduced. Based on this conformal transformation, a coefficient to quantify the effect of curvature is proposed.

Neglecting the effect of curvature can produce significant errors in the calculation of no-load rotor losses when the ratio between the air-gap length and the rotor diameter is large.

The appropriate transformation of PM cylindrical domains into the rectangular domain is deduced. The proportional-logarithmic transformation proposed provides an insight into the effect of curvature on the magnetic field distribution in the air-gap and no-load rotor losses. Furthermore, the proposed curvature coefficient gives a notion of the effect of curvature for any particular geometry without the necessity of any complicated calculation. The case study shows that neglecting the effect of curvature underestimates the rotor eddy-current losses significantly in machines with large gap-to-rotor diameter ratios.