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The peripheral magnetic field of the motor may cause magnetic field interference to the surrounding sensors, which would reduce the accuracy of sensors and affect the safety and concealment of vessel. This article explored the environmental magnetic field distribution law of a permanent magnet (PM) motor with two-pole parallel magnetization. A no-cogging magnetic field model was obtained by solving Maxwell equations, and the relationship between the air gap flux density and the environment flux density was built considering the motor cogging effect. In addition, a mathematical model of connections between the back electromotive force (EMF) and the environmental flux density was built, and the correctness of the model was verified by COMSOL. It is concluded that the circumferential and radial components of the environmental magnetic field are distributed sinusoidally, and the magnetic flux density modulus remains constant on the equidistant circumferential line, but attenuates squarely with the distance from the motor. It provides ideas for magnetic field analysis in the peripheral environment of other types of motors, sensors, and other anti-motor electromagnetic interference, magnetic field compensation for geomagnetic measurement, and motor fault diagnosis. [ABSTRACT FROM AUTHOR]

A new partitioned stator field modulation machine (PSFMM) with H-shape permanent magnet (HPM) excitation (HPM-PSFMM) is proposed, which is evolved from the conventional flux-switching machine (FSM) and flux-reversal machine (FRM). The proposed HPM-PSFMM combines the merits of high reliability and good heat dissipation characteristic. In addition, it exhibits high torque production with low torque ripple. Based on the theory of electrical machine operation, the FSM and FRM can be transformed into PSFMM with interior permanent magnet (IPM) and surface-mounted PM (SPM) excitation by changing the position of PM excitation, respectively. It benefits to improve space utilization and increase slot area for a large number of armature windings. For reducing the flux leakage and enhancing the flux density in air gaps, the IPM and SPM excitation are combined into HPM excitation. The iron-pole rotor between the inner and outer stators acts the role of modulator to modulate the magnetic field excited by HPM excitation to couple with the armature reaction for converting electromechanical energy. The evolution process, operating principle, and key design parameters of the proposed HPM-PSFMM are presented. Finally, using the finite element analysis (FEA), it can be proven that the proposed HPM-PSFMM has the merits of high torque production, low flux leakage, low total harmonic distortion (THD), and low torque ripple when compared to other stator-PM machines, which is a desirable choice for high stability applications. [ABSTRACT FROM AUTHOR]

This article proposes a new hybrid-excited partitioned stator flux modulated machine with a dual-permanent magnet (HE-PSFMDPMM). The HE-PSFMDPMM employs consequent-pole (CP) permanent magnets (PMs) on the inner stator and Halbach array CP PMs on the rotor, which can yield abundant air-gap flux density working harmonics to increase the torque capability. Meanwhile, the field windings are housed in the inner stator to achieve flux weakening. The topology, working principle, and design optimization of HE-PSFMDPMM are investigated, respectively. The electromagnetic performances of HE-PSFMDPMM are analyzed and compared with that of a contrast model with conventional CP PMs on the rotor. The results indicate that by using dual-PM excitation, HE-PSFMDPMM can provide large flux linkage, high torque production with low torque ripple, and high efficiency. Meanwhile, a good flux weakening capability is obtained with the aid of direct current (dc) excitation. Moreover, compared with the contrast model, the proposed HE-PSFMDPMM with Halbach array CP PMs on the rotor can offer the merits of lower cogging torque and torque ripple, higher power factor, and better flux weakening capability. [ABSTRACT FROM AUTHOR]

This article proposes a novel axial field switched flux memory machine (AF-SFMM) which is analyzed by a combined analytical method. Compared with conventional axial field (AF) permanent magnet (PM) machines having magnets in the rotor side, the AF-SFMM benefits from good heat dissipation, high rotor robustness, and improved power density. Meanwhile, because of the utilization of low coercive force PM materials, the proposed machine can flexibly regulate air-gap flux. This analytical method is characterized by the combination of a quasi-3-D (quasi-3D) finite element method, a magnetomotive force–permeance-based method, and a virtual linear hysteresis model of low coercive force PM. In addition, compared with conventional time-consuming 3-D finite element analysis (FEA), the proposed method can improve the computational efficiency significantly with satisfactory accuracy. This makes the proposed combined analytical method suitable for preliminary sizing determination of AF-SFMM. Meanwhile, the effectiveness of the proposed analytical method is validated by FEA results. [ABSTRACT FROM AUTHOR]

A new type of hybrid magnet dual stator field modulation machine with different split ratios of stators (DSR-HMDSFMM) is proposed in this article, which has the merit of high torque density. The split teeth of stator sever as modulators to modulate air gap flux density based on the magnetic gearing effect for high torque production. The total split tooth number of inner stator is equal to that of outer stator because the pole pair numbers of armature reaction and permanent magnet (PM) excitation on rotor are equal. Furtherly, the inner and outer stators with different split ratios and same split tooth number are employed to increase torque production because armature windings with high winding factor and high turn number can be used. In addition, the employment of hybrid magnet excitation can increase space utilization and enhance the air gap flux density with low harmonic distortion. Therefore, the proposed DSR-HMDSFMM can achieve high torque production with the same volume and PM usage. In order to find the optimal split ratio match of stators, several DSR-HMDSFMMs with different combinations of split ratios are proposed and calculated. The configuration and operating principle are illustrated, together with electromagnetic performances of the proposed machines analyzed using finite element analysis (FEA). The FEA-predicted results show that the proposed HMDSFMM exhibits high air-gap flux density with low harmonic distortion and high torque density, which is promising for the direct-drive applications. [ABSTRACT FROM AUTHOR]

In this article, a process for reducing the electromagnetic vibration and noise by changing the shape of the stator is presented. Although the fundamental wave of the air gap magnetic flux density contributes to the average torque of the motor, other spatial harmonics which were except the fundamental wave of that cause vibration and enfeeble the output of the motor. Therefore, it is important to reduce the spatial harmonics for performance of the motor. Through the proposed process, it is possible to obtain an objective function to reduce the specific harmonics by assigning weights to each spatial harmonic. The reduction in the fundamental wave is minimized and it is possible to reduce the spatial harmonics that have an adverse impact on vibration. After the process, a model can be found that maintains the electromagnetic performance as much as possible while optimally reducing the vibration. To verify the process, the electromagnetic vibrations by a radial force of the proposed and conventional models were compared, and it was confirmed that the electromagnetic vibration of the proposed model was reduced. The validity of the analysis was proved through finite-element analysis. [ABSTRACT FROM AUTHOR]

This article presents two novel double-layer permanent-magnet flux reversal (PMFR) machines to improve the torque capability, namely Machine A and Machine B. Both the Machine A and Machine B are designed as the consequent-pole PMFR machines. The rotors of two machines are identical, which adopt Halbach array permanent-magnet (PM) in the rotor slot to guide the flux into the rotor teeth to reduce the leakage flux. However, the PM relative positions of two PMFR machines on the adjacent stator teeth are different, which result in different pole numbers of air-gap flux density. The operation principles and performances of two machines are introduced and compared in this article. In addition, the air gap fields of two machines by PM magnetomotive force (MMF) are analyzed and the contribution of the dominant air-gap flux density harmonics to torque is revealed. [ABSTRACT FROM AUTHOR]

Determining the stator slot design parameters of the alternator has a great importance to provide the desired magnetic flux distribution for a permanent magnet generator (PMG). The objective of this article was to investigate the optimum design parameters of PMG slot design for small-scale low-speed wind turbine generator by using the design of experiment techniques. The Maxwell simulations have been used for numerical experiments on geometric design variables of stator slots (Bs0, Bs1, Bs2, and Hs2) in order to evaluate the coefficients of second-order models for the responses. Efficiency, stator teeth flux density, stator yoke flux density, and air-gap flux density are determined as the responses that have to be optimized. A gradient search was used for optimization. The solution of this design problem shows how the experimental design method can be combined with the numerical simulation and how this approach is well adapted to the optimization process. As a result, the efficiency of the PMG is improved under the desired magnetic flux conditions. [ABSTRACT FROM AUTHOR]

In this paper, the influence of stator teeth number on permanent magnet (PM) field couplings of co-axial dual-mechanical-port flux-switching permanent magnet (CADMP-FSPM) machines for fuel-based extended-range electric vehicles is investigated. First, the relationships between the inner and outer stator teeth numbers are analytically evaluated. Second, four typical structures, including 5/6–12/22, 10/12–12/22, 5/6–18/42, and 10/12–18/42, of CADMP-FSPM machines are analyzed, and three key stator teeth types, namely, series, parallel, and independent teeth, are defined. Third, the PM field coupling levels of four structures, featured by PM field distributions and air-gap flux densities, are compared with stator teeth matchings. The results indicate that the 10/12–12/22 structure exhibits the lowest PM field coupling and the prior open-circuit performance. Furthermore, the PM field coupling effects on the inner and outer air-gap flux densities are analyzed. Finally, a prototyped 10/12–12/22 CADMP-FSPM machine is designed, optimized, and manufactured, and the experimental results verify that the PM field coupling level of the prototype is negligible, which agrees well with the finite-element predictions and the proposed matching criteria for the selection of the inner and outer stator teeth numbers of CADMP-FSPM machines. [ABSTRACT FROM AUTHOR]

In this paper, a novel switched reluctance motor with two magnetically dependent stator and rotor sets (TMDSRM) is proposed and tested. The novelty of the TMDSRM is that there is an assistant exciting winding (short for exciting winding), which is placed between the two-stator sets and can be energized by controllable dc current to boost the air-gap flux density and to improve the output torque and torque density. What deserves to be mentioned the most is that the air-gap flux density is compensated when armature winding is in commutation because of the exciting winding carrying dc current and being permanently energized, and thus, the torque ripple is reduced. This paper describes the magnetic structure and the principle of the proposed motor in detail. Moreover, finite-element analysis has been carried out to investigate the influence of exciting field on electromagnetic torque of the motor. A prototype TMDSRM is manufactured, and the experimental results are presented. [ABSTRACT FROM AUTHOR]

In this paper, the partitioned stator (PS) structure is extended to variable-flux memory machines, forming two newly emerged PS switched-flux memory machines (PS-SFMMs) with series and parallel hybrid magnet configurations. From the perspective of geometry, both two PS-SFMMs share identical outer stator and rotor segments, while two different types of permanent magnet (PM) arrangements are employed in the inner stationary part. Thus, the developed machines can inherent the geometric separation of the armature winding and PM excitations from the PS design, thus achieving acceptable torque capability, and excellent air-gap flux control. A comparative study between PS-SFMMs with series and parallel structures is established. First, the topologies and operating principle are introduced, respectively. In addition, the design tradeoffs and PM sizing of the two PS machines are revealed and optimized with a simplified magnetic circuit model. Then, the electromagnetic characteristics of PS-SFMMs with different magnetic circuits are investigated and compared with the finite-element (FE) method. The FE results are validated by the experiments on a parallel prototype. [ABSTRACT FROM AUTHOR]

This paper proposes a dual-stator consequent-pole permanent magnet vernier machine comprised of two stators and a sandwiched rotor. The proposed topology has high torque density owing to its special working principle and low cost due to the consequent-pole structure. To verify the superiority of the proposed machine, it is compared with an existing dual-stator vernier machine in terms of important electromagnetic characteristics. The finite-element analysis comparison of the two machines shows that the proposed machine achieves a higher average torque and a higher torque-per-magnet volume in comparison with the existing machine. Moreover, the proposed machine uses less magnet volume; therefore, the cost of the machine is significantly reduced. Furthermore, the proposed machine is more efficient compared with the existing machine. [ABSTRACT FROM AUTHOR]

In this paper, an improved flux-barrier geometry configuration of transversally laminated rotor synchronous reluctance machine (TLR-SynRM) is proposed to suppress the torque ripple. The flux-barrier geometry configuration has two remarkable features. First, its flux barriers are step shaped and their shapes could be described by the parameter X. Second, the widths of multi-flux barriers in the middle regions are changing in a gradient style. The conformal mapping method is introduced to calculate the reluctances of the improved flux-barrier geometry configuration, and the corresponding magnetic equivalent circuit is established to analyze how the parameter X influences air-gap flux density distribution in order to obtain the minimum torque ripple. Based on the above analysis, the results are used to improve the flux-barrier geometry configuration. Last, the effectiveness of the improved flux-barrier geometry configuration is verified by finite-element analysis. [ABSTRACT FROM AUTHOR]

This paper presents the detail analysis of the radial force and bending moment responsible for vibration in the stator permanent magnet synchronous motors (PMSMs). The vibration characteristics, especially vibration mode, of stator PMSM are studied. First, the air-gap flux density distribution and radial force density distribution are derived in detail. Then, two types of vibration modes, called pulsating and bending modes, and their reasons as pulsating force and bending moment are analyzed and elaborated which are not analyzed and verified before. In addition, the relationships between these two vibration shapes and pole width, pole number, and slot number are analyzed. To confirm the analysis and theory, the multi-probe mode-included test method of vibration acceleration is used to obtain the vibration mode information of motors, and the experimental results on a 6-pole/36-slot stator PMSM match well with the simulation results. [ABSTRACT FROM AUTHOR]

In this paper, an analytical method for predicting the rotor overhang (OH) effect is presented using two types of conformal mappings (CMs), which are the ${r}$ – ${\theta }$ and zr plane CMs. First, the no-load air-gap flux density (AFD) of a slotted air gap without OH is determined using the ${r} {\theta }$ plane CM. Second, the complex relative air-gap permeance (CRAP) in the zr plane is obtained by the zr plane CM. This helps in taking the OH effect into account. Finally, the no-load AFD of the slotted and OH air gaps in cylindrical coordinates is derived from the no-load AFD in the ${r} {\theta }$ plane with CRAP along the ${z}$ -axis. The accuracy of the presented method is verified by comparing the results of no-load analysis with those of 3-D finite-element analysis. [ABSTRACT FROM AUTHOR]

In this paper, the torque production mechanisms of flux-reversal permanent magnet (FRPM) machine and Vernier permanent magnet (PM) machine are analyzed and compared based on air-gap field modulation. Working harmonics of PM magnetomotive force (MMF) and air-gap permeance in two machines are analytically identified and compared, indicating that the fundamental PM MMF together with all permeance harmonics contribute to the torque production of Vernier machine whereas all PM MMF harmonics but only fundamental permeance in FRPM machine produces the torque. Thanks to the utilized large dc component of air-gap permeance, the torque density of Vernier machine is revealed to be better. Influence of critical parameters on machine performance, such as PM thickness and slot width ratio of the modulation pole, is also investigated. It shows that FRPM machine is more sensitive to the design parameters. Both finite-element analysis and experimental validation are conducted to verify the conclusion. [ABSTRACT FROM AUTHOR]

This paper presents the simple analytical modeling for switched flux memory machine to provide in-depth insight into its working mechanism. The analytical approach is based on the slotless open-circuit air-gap flux density and the slotted air-gap relative permeance calculations for a doubly salient structure. In addition, due to low coercivity and highly nonlinear hysteresis curve at the second quadrant, the piecewise and virtual-linear hysteresis models of AlNiCo permanent magnet (PM) are presented to determine the PM working point. This combined analytical solution allows rapid calculation of several electromagnetic characteristics, e.g., air-gap flux density and back electromotive force. The effectiveness of the analytical method is validated by both finite-element results and measurements. [ABSTRACT FROM AUTHOR]

A nonlinear equivalent magnetic network (EMN) model is proposed for a linear permanent magnet vernier (LPMV) machine. The meshing method is employed to solve the problem of the modeling of complex flux paths in stator teeth tips. Especially, an end-region model based on the electromagnetic principle is developed to consider the longitudinal end effect of the LPMV machine. The key contribution of this paper is to present a faster and simpler approach to separate the detent force (end force component and cogging force component) than finite-element analysis (FEA). Besides, taking the iron saturation and air-gap flux leakage into account, the proposed model is used to predict the electromagnetic performances of the LPMV machine, such as air-gap flux density, back-electromotive force, cogging force, and thrust force. Finally, through comparisons among the FEA simulations, experimental measurements and EMN analyses, the accuracy and effectiveness of the proposed model are verified. [ABSTRACT FROM PUBLISHER]

In this paper, a study was conducted using a unit equivalent magnetic circuit (EMC) in correlating the relationship between the magnet thickness, the modulating ring pole-piece thickness, and their circumferential pitch. A numerical optimization method is employed in selecting the optimum ratio of the magnet to pole-piece thickness. The study reveals the need to simultaneously consider these parameters during the design of a magnetic gear electric machine because of their strong mutual dependency. A finite element analysis (FEA) was conducted using the optimum ratios. The results correspond to those of the EMC. Also, the performance of the machine is analyzed and found to have a power factor of 0.78. To further verify the results of FEA, a prototype was built using the same configurations of the FEA model. Measurements taken from the prototype are on par with the simulated results. [ABSTRACT FROM AUTHOR]

Permanent-magnet vernier machines are becoming more and more attractive due to their high torque density and low-speed operating capabilities. This paper investigates the effects of the magnet thickness, magnet pole arc ratio, and slot open ratio on the torque capacity. An analytical model is first presented. It is validated by comparing the results with the finite-element analysis (FEA) under the same hypothesis. A mono-objective optimization is then conducted on the basis of the analytical model coupled to genetic algorithm to reach the optimal values yielding the highest value of the torque. Finally, the influence of nonlinear magnetic material behavior on the optimal design is investigated through nonlinear FEA. The results are presented and discussed. [ABSTRACT FROM AUTHOR]

The results of the 3-D finite-element method electromagnetic analysis of the constant speed variable output permanent magnet synchronous motor including the rotor retaining plate structure confirmed that the eddy current flow was induced in the rotor part. Eddy current flows from the permanent magnet to the rotor retaining plate, and it was found that there is induced voltage that generates eddy currents in the retaining plate from the aspect of eddy-current distribution. The eddy current flow from the permanent magnet to the retaining plate is related to the change in magnetic resistance during rotation and is also related to the effect of slot harmonics on the air-gap magnetic flux density. In this paper, the characteristics of the eddy current flow in the rotor assembly were investigated when the retaining plate is included for various slot combinations. The eddy-current generation according to the slot combination is analyzed and the cause of such tendency was investigated. Furthermore, from the pattern of eddy-current formation, it was noted that the aperiodic pole–slot combination models may have a larger eddy-current loss increase when combined with the retaining plate. [ABSTRACT FROM AUTHOR]

The flux of the embedded magnets in the rotor of an interior permanent magnet (IPM) synchronous machine causes a non-homogeneously saturated rotor iron. This alters the reluctance of the stator flux path due to the nonlinear $B$ – $H$ curve of the rotor iron and should be considered in the analytical field calculations; however, it is often neglected in the prior-art methods leading to inaccurate results. Moreover, the effect of a fractional-slot concentrated-wound (FSCW) stator on the analytical field calculations is not addressed in the existing literature. The magnetic field characteristics of IPM synchronous machines are commonly formulated using an equivalent air-gap function. In order to account for the aforementioned shortcomings in the existing methods for the analytical field calculations, an equivalent air-gap function is proposed in this paper that considers the particular properties of an IPM rotor and an FSCW stator. To this aim, based on the rotor geometry and the nonlinear $B$ – $H$ curve of the iron core, a method is first proposed to model the saturation level and the relative permeability at different regions of the rotor iron. This model is then used in the proposed equivalent air-gap function to compute the armature reaction air-gap flux density. The proposed theory is validated through finite element analysis and experimental results on a prototype FSCW IPM machine in the laboratory. [ABSTRACT FROM AUTHOR]

In this paper, a novel magnetic equivalent circuit (MEC) is proposed to calculate magnetic flux of saturated electrical machines. The machine features double salient poles with high saturation. Emphases are made on modeling of air-gap permeance and magnetic saturation using a fitting method. The analyses are applied based on a 4-phase 8/6 switched reluctance machine (SRM) with high power density, which was designed for traction application. The air-gap reluctance in MEC that connects a tooth pair is studied, followed by distribution of magnetic saturation on teeth. The magnetic reluctance of circuit loop can be fitted as well as saturation quantity if the electrical steel is known. The proposed network offers a fast and accurate way of estimating flux characteristics of especially highly saturated machines with double slotting effect. [ABSTRACT FROM AUTHOR]

This paper is aimed at an analytical approach to predict the no-load operation features of tubular-linear permanent magnet synchronous machines (T-LPMSMs). These are currently considered as viable candidates for wave energy conversion. The developed approach is based on the derivation of the air-gap flux density, considering both the first- and second-type modified Bessel functions of appropriate orders. Following its formulation, the air-gap flux density is applied for the prediction of the no-load operation features, with a focus on the cogging force, the phase flux linkages, and the back electromotive forces. A case study is treated considering three axial arrangements of a T-LPMSM, such as the case of an infinite length machine, the case of a finite length machine, and the case of a finite length machine enabling a quasi-cancellation of the end effect. A comparison between the analytically predicted features and those numerically computed by a 2-D finite-element analysis has led to good agreement. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel tubular double-stator vernier permanent-magnet (TDS-VPM) motor for artificial hearts. The key of the proposed motor is double-stator and vernier structures. Due to its vernier structure, more PMs can be adopted in the proposed TDS-VPM motor and the useful harmonics of the air-gap flux density are increased, thus improving thrust density. Furthermore, double stator, namely inner stator and outer stator, has an appropriate 90° (electrical degree) angle difference. Since the inner stator is located inside the mover, the motor space is fully used. Hence, the thrust density is enhanced and the axial direction length is reduced. Meanwhile, the angle difference between the inner and the outer stator can reduce the cogging force of this TDS-VPM motor. The electromagnetic characteristics of the proposed motor are analyzed using the time-stepping finite-element method, confirming the validity of the theoretical analysis. [ABSTRACT FROM PUBLISHER]

This paper analyzes Maxwell tensor tangential and radial magnetic forces in permanent magnet synchronous machines in the no-load case. Using matrix notation in the complex domain, a simple expression of the Fourier harmonics of both radial and tangential forces is derived, including all space and time harmonics. These expressions prove that both the frequency content of cogging torque and zeroth-order radial forces are linked to the least common multiple between the stator slot number and the rotor poles number, and that the optimal pole arc to pole pitch ratio to reduce cogging torque is also optimal for the reduction of average radial magnetic forces. It is also shown that both the smallest non-zero spatial order of tangential and radial force harmonics are given by the greatest common divider of the number of slots and the number of poles. These results can be used during the design stage when choosing the pole and slot numbers combination. These analytical results are then compared with calculations using MANATEE vibroacoustic and electromagnetic simulation software. Finally, some variable speed acoustic noise simulations are carried out on three different designs to analyze the efficiency of different vibroacoustic design rules on the slot and pole numbers combination. An attempt to formulate a new vibroacoustic design rule choice is detailed. It is concluded that no simple analytical design rule can be used to evaluate noise and vibrations induced by magnetic forces, and that numerical simulation is necessary. [ABSTRACT FROM AUTHOR]

An analytical model for prediction of air gap flux density and cogging torque in slotted surface-mounted permanent magnet (SPM) machines is presented in this paper. The proposed method is based on superposition theorem, the concept of equivalent magnetization currents (EMCs), and analytically solving of Poisson’s equation. To solve Poisson’s equation easily, the air gap flux density of the slotted SPM machine is stated as superposition of the air gap flux density functions of two slotless machines. The first slotless machine is excited by PMs, while the second one is excited by surface EMCs. Therefore, the concept of EMC is used in an iterative algorithm which converges quickly with a negligible computation time. Using the obtained analytical model and Maxwell’s stress tensor, cogging torque of the slotted SPM machine is predicted. This analytical model provides a quick tool to study the effect of leading design parameters on the machine cogging torque. Finally, the validity of the proposed model and the obtained results are verified with finite element analysis. [ABSTRACT FROM AUTHOR]

This paper presents four types of three-phase permanent magnet (PM) machines, that is, modular and unequal teeth (UNET) machines either with or without tooth tips. Two-dimensional finite element (FE) modeling has been carried out to analyze the influences of flux gaps (in alternate stator teeth) and UNET widths. These influences are mainly on winding factors, air-gap flux density due to PMs, flux linkage, back-electromotive force, and electromagnetic torques. For UNET machines without tooth tips, it has been found that the UNET widths affect both winding factor and air-gap flux density due to PMs. However, for UNET machines with tooth tips, the UNET widths have no effect on machines’ electromagnetic performance. Nevertheless, for modular machines, the flux gaps influence three parameters: winding factor, air-gap flux density due to PMs, and flux focusing/defocusing. Meanwhile, for different slot/pole number combinations, the influences of flux gap and UNET widths are different. Several general rules concerning these influences have been established. These general rules can be extended to other single or dual three-phase modular or UNET machines with different slot/pole number combinations. Prototypes of modular machines have been built, and the predictions and conclusions have been validated. [ABSTRACT FROM PUBLISHER]

In this paper, an analytical method for the computation of the electromagnetic field in the airgap of an inset permanent magnet synchronous machine is proposed. The originality lies in the fact that both the stator and rotor saliencies have been taken into account in the analytical procedure. The purpose in to compute both quickly and accurately the magnetic fluxes and instantaneous torque of the machine, in order to minimize torque ripples in an optimal predesign process. It is shown that the instantaneous torque is in good agreement with finite element results, for a shorter computation time. The model presented here can be used when the 2-D approximation of the machine is valid, which is the case for most of machines' topologies. [ABSTRACT FROM AUTHOR]