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A hybrid analytical and lumped-parameter thermal model is proposed in this paper to estimate the transient and steady-state two- and three-dimensional (2/3-D) spatial magnet temperature distributions for an interior permanent magnet synchronous machine (IPMSM). On the basis of a lumped-parameter thermal model (LPTM), the magnet analytical thermal models (ATMs) are synergized to establish the hybrid thermal model. By utilizing the transient or steady-state boundary conditions calculated by the LPTM, the ATMs are obtained by solving the heat conduction equations to estimate the spatial magnet temperature distributions in the 2-D horizontal-vertical and axial-vertical planes, which can also be extended to the 3-D temperature distribution by utilizing the multi-slice method. Meanwhile, the non-uniform magnet eddy current loss is also considered. Finally, both electromagnetic-thermal coupled finite element analysis method and experiments are used for verification based on a totally enclosed IPMSM. [ABSTRACT FROM AUTHOR]

Consequent-pole (CP) permanent magnet (PM) configuration suffers asymmetric electromagnetic characteristics although it saves PM usage. The CP-based stator-PM synchronous machines are investigated in this paper, with particular reference to symmetrical issues. The electromagnetic performances of the CP-based stator-PM synchronous machines are firstly evaluated. Afterwards, the rule of even order harmonics cancellation is presented for different slot/pole number combinations and winding layouts, based on which symmetrical phase flux-linkages can be obtained although the unbalanced magnetic flux naturally occurs. Moreover, based on the three-dimensional finite element analysis, the unipolar end leakage-flux caused by the asymmetric magnetic field is identified, and the risk of the shaft magnetization is revealed. Finally, a pair of prototype machines are fabricated and measured to validate the analyses. [ABSTRACT FROM AUTHOR]

Asymmetric interior permanent magnet (AIPM) rotor topologies can achieve torque enhancement in IPM synchronous machines without the increase of PM usage due to utilizing magnetic-field-shifting (MFS) effect by reducing the current angle difference between maximum PM and reluctance torque components. This paper investigates the influence of armature reaction on MFS effect in AIPM machines. A general model of IPM machines considering MFS effect is analytically developed and the AIPM and IPM machines using the same stator, rotor diameter and total PM amount are comparatively studied. It shows that the armature reaction affects the MFS effect in both AIPM and IPM machines and the influence is more significant in AIPM machine. The relationships between MFS effects in PM flux-linkage and inductance characteristics and current angles for maximum PM and reluctance torque components are revealed. It confirms that the change of current angles of torque components is due to the MFS effect in PM flux-linkage and inductance characteristics in both AIPM and IPM machines. Besides, the developed machine model considering MFS effect is verified by finite element analysis. Finally, a small-scale AIPM machine prototype is fabricated and measured to validate the finite element analysis. [ABSTRACT FROM AUTHOR]

Consequent pole (CP) permanent magnet (PM) machines offer scope for reducing the quantity of PM material and hence cost compared to more conventional PM machine topologies of the same rating. In this type of machine, the rotor pole arc is usually optimized to realize the largest output torque with pole shaping methods used to reduce torque ripple. However, such approaches tend to be limited by constraints imposed on the pole shapes. It is a common practice to adopt similar PM and iron pole shapes, an approach that does not fully account for the different characteristics of PM and iron poles in CPPM machines, often leading to large even order harmonics in the airgap flux density. This article proposes a shaping method with a variable rotor profile and pole arc span being established by means of optimization by Genetic Algorithm. It is demonstrated that for a fixed quantity of PM material, different PM and iron pole shapes in combination with optimal PM and iron pole arc spans are essential for ensuring both maximum output torque and lower torque ripple when the due account is taken of flux leakage. It also demonstrates that since the flux density in the region under a PM pole is governed by the magnetic potential produced by magnets while it is governed by magnetic reluctance under iron pole, different PM pole and iron pole shapes are necessary to reduce the even-order harmonics in a CPPM machine and consequently to reduce torque ripple. The performances of optimized and more conventional CP machines are compared by finite-element method on 12-slot/8-pole prototype motors. [ABSTRACT FROM AUTHOR]

A novel asymmetric interior permanent magnet (AIPM) machine is proposed in this paper for electric vehicle application. It has a skewed V-shape permanent magnet (PM) cavity, two PMs with different dimensions and an additional flux barrier outside the V-shape cavity in each pole. This asymmetric rotor topology can inherently utilize the magnetic-field-shifting (MFS) effect to reduce the current angle difference between the maximum PM and reluctance torque components, thereby enhancing the maximum synthetic torque with the same PM usage. The influences of cavity positions in the proposed AIPM and an existing AIPM with extra flux barrier inside the V-shape cavity are investigated and compared using finite element analysis. It is found that the proposed structure with outside flux barrier has higher average torque than the one with inside flux barrier. Both AIPM topologies are designed with the same stator, rotor diameter, and PM usage as the conventional V-shape IPM benchmark for Prius 2010. Electromagnetic, mechanical and steady-state thermal performance of three machines are compared. The results confirm that the proposed AIPM machine can achieve significant torque enhancement due to utilizing MFS effect, compared with the existing AIPM and the IPM benchmark. Finally, a small prototype of the proposed AIPM machine is designed, manufactured and tested to validate the FE analysis. [ABSTRACT FROM AUTHOR]

Hybrid excited machines, with synergies of permanent magnet (PM) and wound field (WF) excitations, exhibit high torque density as well as controllable flux and are perceived as promising candidate for variable speed application. A novel doubly salient hybrid excited (DSHE) machine with non-overlapped field winding is presented in this paper. It inherits simple structure of conventional doubly salient PM (DSPM) machine and facilitates the regulation of magnetic field by field winding. The electromagnetic performances of the proposed machine with different stator and rotor pole number combinations are investigated by finite element method (FEM), confirming these advantages. Furthermore, the effect of iron bridge on the hybridization between PM and WF excitations is analyzed to obtain a trade-off between high torque density and wide flux regulation range with the frozen permeability method (FPM). It is revealed that the proposed DSHE machine possesses higher power and fault tolerance at flux weakening region compared with the DSPM machine, albeit with sacrificed torque density and efficiency with introduction of field winding. Finally, a prototype is fabricated and tested to validate the theoretical analyses. [ABSTRACT FROM AUTHOR]

Hybrid excited (HE) machines have the synergies of high torque density and high efficiency of permanent magnet (PM) machines and excellent flux controllability of wound-field machines. The PMs and field coils (FCs) coexist in HE machines to provide excitations simultaneously, and can be coupled either in series or parallel. The topologies of HE machines are very diverse, which bring challenges in the selection and design of HE machines. Based on the partitioned stator (PS) platform, a pair of series and parallel HE machines having similar structures and PM usage are evaluated and compared to identify their merits and demerits. With the help of finite element analysis, the flux regulation, energy conversion capability, parasitic effects and irreversible demagnetization of the two kinds of the HE machines are comprehensively investigated and the guidance to the machine design is provided. A pair of prototypes are fabricated and tested to validate the analyses. [ABSTRACT FROM AUTHOR]

This paper aims to identify the optimal number of flux modulation pole (FMP) in Vernier permanent magnet synchronous machines (VPMSMs) with concentrated tooth-coil windings. First, the influence of number of FMP on machine performance is revealed based on the unified permanent magnet magnetomotive force permeance analytical model. It is found that for a fixed stator slot number, there always exists an optimal number of FMP to maximize the torque, thanks to the enhanced contribution by the fundamental permeance harmonic. Then, the influence of critical dimensional parameters, including the machine diameter, the permanent magnet thickness, and the width of FMP, on the electromagnetic performance of VPMSMs with different numbers of FMP are parametrically analyzed by both analytical and finite element analyses. Results show that the VPMSMs with the optimal number of FMP always have advantages of a higher torque density together with a reduced PM volume, particularly for those with a relatively large diameter. Finally, two VPMSM prototypes with different numbers of FMP are manufactured and tested to validate the analyses. [ABSTRACT FROM AUTHOR]

This paper presents a novel modular stator hybrid-excited synchronous machine with stator slot permanent magnets (PMs). By regulating the field current, the magnetic field, and consequently the back electromotive force, as well as the average torque can be controlled. The existence of stator slot PMs alleviates the magnetic saturation and improves the flux regulation ratio. The frozen permeability method is employed to investigate the torque contributions by different magnetic sources. Possible stator and rotor pole combinations are illustrated, and the corresponding electromagnetic performances are evaluated with the finite-element method. It is revealed that 12-stator pole machines with 11- and 13-rotor poles exhibit superior average torque and lower torque ripple due to even-order harmonics elimination. Finally, a prototype with modular stator segments is manufactured to validate the analyses and simulations. [ABSTRACT FROM AUTHOR]

This paper aims to comprehensively analyze the influence of number of permanent magnet (PM) pieces on electromagnetic performance of flux reversal permanent magnet (FRPM) machines. First, the unified analytical model of FRPM machines having different numbers of PM pieces is established, from which the optimal number of PM pieces and the corresponding rotor pole number can be identified. It shows that by employing the optimal number of PM pieces instead of the conventional two on each stator tooth, additional back-EMF component can be generated which is beneficial to boost the machine performance. Then, the influence of critical design parameters including stator slot opening ratio, split ratio, and stator slot number is investigated, providing a guidance to the design of FRPM machines aiming at maximum output torque. In addition, both finite element analyses and experimental tests are conducted to verify the analytical analyses. For 6-slot-stator FRPM machines, experimental results show that more than 40% higher output torque can be achieved in the machine with optimal number of PM pieces when compared to the conventional one. [ABSTRACT FROM AUTHOR]

Hybrid permanent-magnet (PM) variable-flux memory (VFM) machines employ both high coercive force PM, i.e., the constant PM (CPM), and low coercive force PM, i.e., the variable PM (VPM). The high energy-product CPM guarantees the benefits of high torque density of the conventional PM machines, while the PM magnetization state of the VPM is flexibly regulated to match various operation requirements. In fact, the two kinds of PMs can be magnetically connected in either parallel or series, with which the machine characteristics are quite different. In this paper, based on the two-dimensional and three-dimensional finite-element analyses, a pair of VFM machines with parallel and series connections, respectively, are investigated with specific reference to identify their difference in end effects. The comparison results show that the series hybrid PM VFM machine suffers more serious end leakage flux. The prototype machines are manufactured and tested to validate the analyses and predictions. [ABSTRACT FROM AUTHOR]

A new type of three-phase stator hybrid excited machine with permanent magnets (PMs) located at the slot openings of field winding slots is presented in this paper. It has the advantage of good flux regulation capability due to the field excitation. The machines with different stator/rotor pole combinations, i.e., 6-stator pole and 7-/8-/10-/11-/13-/14-rotor poles, have been comparatively investigated in terms of the open-circuit and on-load characteristics, as well as the influence of dc current and the unbalanced magnetic forces. The 2-D finite element analysis (FEA) has been employed for analysis and optimization of the machines together with experimental validation. [ABSTRACT FROM AUTHOR]

This paper proposes a double superposition method to quickly and accurately predict the cogging torque and unbalanced magnetic force (UMF) of permanent magnet machines with axial-varying rotor eccentricities. The original axial-varying eccentric machine is cut into several uniform slices along the axial direction and each slice is considered to be axially uniform, i.e., axial even. For each axial-even eccentric machine slice, the circumferential superposition method can be used to predict the cogging torque and UMF of this slice. Finally, the cogging torque and UMF of the original axial-varying eccentric machine can be obtained by using an axial superposition technique which combines the cogging torque and UMF of each slice with different eccentricity magnitudes together. The 3-D finite-element analysis is adopted to validate the efficacy of the proposed method and the merit of high accuracy and computational efficiency is also identified by comparing the results predicted from these two methods. [ABSTRACT FROM AUTHOR]

This paper proposes a novel variable flux memory (VFM) machine, in which the “constant” permanent magnet (CPM) with high coercive force and the “variable” PM (VPM) with low coercive force are alternatively located in the interior-PM rotor. Thus, the VPMs and CPMs are magnetically connected in series, with which the CPMs can assist the VPMs to withstand the unintentional demagnetization caused by armature reaction. Therefore, a high armature current can be applied to the machine. Meanwhile, the reluctance torque is retrieved. Thus, a high torque density can be obtained. Based on two-dimensional finite element analysis, first, the electromagnetic performance of the proposed VFM machine in two extreme magnetization states is evaluated in detail. Then, the demagnetization and remagnetization characteristics are investigated, in which the working points of VPMs are illustrated. Furthermore, the advantages of improved efficiency of the proposed VFM machine are demonstrated. A prototype machine is manufactured and tested to validate the predictions. [ABSTRACT FROM AUTHOR]

A dual-stator hybrid-excited switched-flux (DS-HESF) machine, which is based on the conventional SF permanent magnet machine but employs a secondary stator to accommodate the field windings, is proposed in this paper. The DS-HESF machine inherits the robust rotor and benefits from a better space utilization. The topology and operating principle of the proposed machine are introduced in detail. Based on the 2-D finite-element analysis, the comparison between the DS-HESF machines having different rotor pole numbers is carried out, accompanied with a conventional HESF machine as a baseline. The results reveal that the DS-HESF machines exhibit not only higher torque density but also a better flux regulation capability. The prototype is manufactured and tested to validate the predictions. [ABSTRACT FROM PUBLISHER]

This paper proposes a new partitioned stator flux reversal permanent magnet (PM) (PS-FRPM) machine having integer-slot overlapping windings, i.e., the slot number per pole per phase q is an integer, based on the magnetic gearing effect in stator-PM machines. Compared with the existing PS-FRPM machine with fractional-slot nonoverlapping windings, a more sinusoidal armature reaction magnetomotive force can be achieved in the proposed PS-FRPM machine with integer-slot overlapping windings, resulting in lower iron loss and PM loss. Electromagnetic performance of the PS-FRPM machine, which has q = 1 overlapping windings is analyzed and compared with PS-FRPM machine, which has q = 0.5 nonoverlapping windings by finite element (FE) analysis. FE results show that the proposed 24/10/12-outer-stator/rotor/inner-stator-pole PS-FRPM machine with q = 1 overlapping winding exhibits higher fundamental phase back-electromotive force, higher average electromagnetic torque and lower torque ripple, lower loss and higher efficiency, higher self-inductance but lower mutual inductance, higher d-axis inductance, and potential infinite flux-weakening capability compared with the 12/10/12-outer-stator/rotor/inner-stator-pole PS-FRPM machine with q = 0.5 nonoverlapping windings. Both prototype machines with q = 1 overlapping winding and q = 0.5 nonoverlapping windings are built and tested to verify the FE analyzes. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel rotor contour design for variable reluctance (VR) resolvers by injecting auxiliary air-gap permeance harmonics. Based on the resolver model with nonoverlapping tooth-coil windings, the influence of air-gap length function is first investigated by finite element (FE) method, and the detection accuracy of designs with higher values of fundamental wave factor may deteriorate due to the increasing third order of output voltage harmonics. Further, the origins of the third harmonics are investigated by analytical derivation and FE analyses of output voltages. Furthermore, it is proved that the voltage harmonics and the detection accuracy are significantly improved by injecting auxiliary air-gap permeance harmonics in the design of rotor contour. In addition, the proposed design can also be employed to eliminate voltage tooth harmonics in a conventional VR resolver topology. Finally, VR resolver prototypes with the conventional and the proposed rotors are fabricated and tested respectively to verify the analyses. [ABSTRACT FROM PUBLISHER]

The local magnetic saturation in tooth-tips of surface-mounted permanent magnet (SPM) machines generates on-load terminal voltage distortion, especially when small or closed slot openings are adopted. This paper focuses on investigating the influence of slot and pole number (Ns/2p) combinations on this phenomenon in both fractional slot and integer slot SPM machines. The mechanism of this phenomenon and how it is influenced by current advance angle and tooth-tip geometric parameters are introduced first. Then, voltage distortion pattern is proposed to analyze the occurring time or rotor positions of voltage ripples and their relative amplitudes according to the winding arrangements of different Ns/2 p combinations, with the influence of PM leakage flux considered. By 2-D finite-element analysis, the voltage distortion of various machines is calculated and compared, such as Ns \pm 1 = 2p, Ns \pm 2 = 2p, N s/2p = 3/2 (3/4), and integer slot machines with slot number per pole per phase q = 1 or 2. The analysis results reveal that under the same comparison conditions, the integer slot machines have less voltage distortion than the fractional slot machines, especially when q \geq 2. Meanwhile, for the same slot number, the fractional slot machines with Ns > 2p suffer from on-load voltage distortion less than their counterparts with Ns < 2p. Finally, three prototype machines with 12/10, 12/14, and 12/8 slot/pole numbers are manufactured and tested to validate the analyses. [ABSTRACT FROM AUTHOR]

A novel stator hybrid-excited, parallel flux path, synchronous machine of doubly salient topology is proposed. It has the novel features of: 1) hybrid dc field and permanent magnet (PM) excitation in the stator; 2) magnets placed in the slots between adjacent salient stator poles; and 3) the magnetic poles of PMs arranged, such that the flux premagnetizes the stator, but it is in a direction to oppose the dc excitation flux. The electromagnetic characteristics of the machine are analyzed on open-circuit and load. Since the new machine topology is developed from the variable-flux machine (VFM), a comparison of their electromagnetic torque and machine losses is conducted. The average electromagnetic torque of the hybrid-excited machine can be increased by 18% for fixed copper loss in comparison with the VFM due to the reduction of magnetic saturation in the stator. It is also shown that at high temperatures some risk of PM demagnetization exists when excited with dc and armature currents due to fringing flux that exists between the stator and the rotor poles. However, this affects only a very small area of the PMs. The performance of the hybrid-excited machine is predicted by a 2-D finite-element analysis and experimentally validated. [ABSTRACT FROM AUTHOR]

This paper presents a simple analytical model for two types of three-phase surface-mounted permanent magnet machines: modular and unequal tooth (UNET) width machines with different slot/pole number combinations. It is based on the slotless open-circuit air-gap flux density and the slotted air-gap relative permeance calculations. This model allows calculating the opencircuit air-gap flux density, phase flux linkage, back electromotive force, and average torque of both the modular and UNET machines. Its accuracy has been validated by the 2-D finite-element (FE) method. A flux focusing/defocusing factor has also been introduced to analyze the influence of flux gaps in alternate stator teeth of modular machines on the machine electromagnetic performances. It has been found that by properly choosing the slot/pole number combination and flux gap width, the open-circuit air-gap flux density, the winding factor, and the flux focusing effect can all be improved. As a result, the performance of the modular machine can be significantly boosted. The analytical and FE models have been validated by experiments. [ABSTRACT FROM AUTHOR]

A rotor shaping technique with optimal third harmonic is presented to enhance the average torque of interior permanent-magnet (IPM) machines in this paper. The optimal value of third harmonic injected into the rotor outer surface shape has been derived and further confirmed by both finite-element analyses and experiments. The impact of the optimal third harmonic to the rotor shape on the electromagnetic performance, including harmonics in the back electromotive forces, cogging torque, average torque, and torque ripple, is investigated. It is demonstrated that without any modification of the costly rare earth permanent magnet employed for the inverse-cosine-shaped rotor, the average torque of the machine of an inverse cosine injected with an optimal third-harmonic-shaped rotor can be improved by > 6%. Simultaneously, the torque ripple remains almost unchanged, and the saliency ratio is also improved, further boosting the average torque. Finally, the machines with both conventional and optimal third harmonic rotors are prototyped and tested to validate the analysis. [ABSTRACT FROM PUBLISHER]

This paper presents the simplified analytical optimization and comparison between electrically excited (EE) and permanent-magnet (PM) machines in terms of torque per volume T/V and torque per weight T/G for low-speed applications when their copper loss and overall size are the same. Analytical torque models for both machines are individually developed and optimized to obtain the optimal flux density ratio, split ratio, and maximum torque densities. Furthermore, the variation of optima with the number of poles and machine size is also investigated. The analytical analyses are validated by both finite-element analyses and experiments. It is concluded that torque densities of PM machines can be more than \sqrt2 times higher than those of EE machines. For EE machines, there is an optimal pole number to maximize torque densities, and large volume applications are preferred. In actual applications, EE machines are more likely to compromise the torque density to meet the thermal constraints. It also shows that the optimal T/G designs have significantly higher split ratio and are more cost- and weight-effective than the optimal T/V designs. [ABSTRACT FROM PUBLISHER]

This paper presents a simplified analytical model based on one slot per pole for predicting the open-circuit AC winding loss of surface-mounted permanent-magnet machines accounting for the influence of tooth-tips but neglecting the redistribution effect of eddy currents. The comparison between the analytical models and finite-element results shows that the simplified analytical model has similar accuracy as the analytical model accounting for all slots together. The influence of various design parameters, such as conductor layout, slot width, slot opening width, tooth-tip height, magnet pole-arc to pole-pitch ratio, and gap between tooth-tips and conductors, on the open-circuit AC winding loss is investigated. It shows that the open-circuit AC winding loss gradually decreases with the number of radial conductor layers if the number of circumferential layers is larger than 1, although the radial segmentation is ineffective when there is no circumferential segmentation. The loss decreases greatly when the number of circumferential layers changes from 1 to 2, but reduces slowly when the conductors are further circumferentially segmented. [ABSTRACT FROM PUBLISHER]

In order to simplify manufacture processes and improve fault-tolerant capabilities, modular electrical machines, especially the ones with segmented stators, are increasingly employed. However, flux gaps between segments are often inevitable. In this paper, to take advantage of these flux gaps to enhance the machine performance, novel modular permanent magnet machines with different slot/pole combinations have been proposed. The influence of these flux gaps on the electromagnetic performance of modular PM machines, such as winding factor, open-circuit air-gap flux densities, back-EMFs, cogging torque, on-load torque, inductances, magnetic saturation and copper losses, are comprehensively investigated and general rules have been established. It is found that for modular machines having slot number higher than pole number, the flux gaps between stator segments degrade the electromagnetic performance due to the lower winding factor and the flux defocusing effect. However, for modular machines having slot number lower than pole number, the electromagnetic performances can be significantly improved using proper flux gap width due to the higher winding factor and the flux focusing effect. The finite element results are validated by experiments using two prototype modular machines. [ABSTRACT FROM PUBLISHER]

This work presents a permanent magnet (PM) shaping technique with optimal third harmonic to improve the output torque without deteriorating the torque ripple in surface-mounted PM (SPM) machines. The optimal value of third harmonic injected into the sinusoidal PM shape for maximum torque improvement is analytically derived and confirmed by finite-element analysis. Further, the influence of magnet edge thickness on the airgap field distribution is investigated and utilized to compensate the inter-pole flux leakage and curvature effect. It is found that the optimal third harmonic is 1/6 of the fundamental one. For the SPM machines having rotors without shaping, Sine shaping, Sine shaping with third harmonic injected, the electromagnetic performance, including the back-EMF waveforms, cogging torque, average torque, and torque ripple are compared. It is demonstrated that the average torque in the machine of a Sine shaping with an optimal third harmonic injected can be improved by >9\%, while the torque ripple remains similar to that of the one with Sine shaping. Finally, the machines with both conventional (without shaping) and optimal third harmonic PM rotors are prototyped and measured to validate the analyses. [ABSTRACT FROM PUBLISHER]

In order to improve the electromagnetic performance and ease the manufacture process, particularly stator winding, it is often preferable to employ a modular stator, e.g., individual stator tooth/back-iron segments, or separate stator tooth segments and back-iron segments. However, due to manufacture limits, there always exhibit additional air gaps between the stator teeth and back-iron segments. In practice, such gaps are likely to be nonuniform due to manufacture tolerances. This paper investigates the influence of uniform and nonuniform additional gaps on the cogging torque of permanent-magnet machines having either unskewed or step-skewed rotors. It is found that the presence of these gaps increases the cogging torque magnitude due to increased flux leakage through the tooth tips, while the uneven gaps can cause a significant increase in both the peak and periodicity of cogging torque waveform, which causes the skew method ineffective, as confirmed by both finite-element analyses and experiments. [ABSTRACT FROM PUBLISHER]

This paper presents a comparative study of torque–speed characteristics and cogging torque of the fractional-slot interior permanent magnet brushless ac machines having different slot openings, viz. open slot, closed slot, and hybrid slot (sandwiched open and closed slots), and unskewed and step skewed rotors. The influence of such alternate slot openings on the magnetic cross-coupling and cogging torque is particularly emphasized. Furthermore, the repercussion of the manufacturing limitations and tolerances on the cogging torque of machines having these alternate slot openings is also investigated. The magnetic cross-coupling level and the sensitivity of cogging torque to manufacturing limitations and tolerances strongly depend on the slot opening materials. The finite-element analyses are experimentally validated. [ABSTRACT FROM PUBLISHER]

Cogging torque, as a very important design consideration in permanent-magnet (PM) machines, has been widely investigated for decades. In this paper, the study will be focused on the cogging torque behavior in surface-mounted PM (SPM) machines with two types of cost-effective PM designs. The results show that in a SPM machine with either type of cost-effective PM design, low cogging torque performance can be achieved, as confirmed by both finite-element analyses and experiments. [ABSTRACT FROM PUBLISHER]

A subdomain model considering the influence of tooth-tips is developed for predicting the armature reaction field in surface-mounted permanent-magnet machines having either non-overlapping or overlapping windings. In the developed model, the field domain is divided into three types of subdomains, viz. air gap including magnet, slot openings, and slots. The expression of the vector potential distribution in each subdomain is obtained by the variable separation method, and the field solution is obtained by applying the boundary and interface conditions. Compared with the conventional subdomain model, the subdomain model considering the tooth-tips predicts similar flux density in the air gap and magnets, but exhibits much higher accuracy for the flux density in the slot openings and slots. The finite-element results validate the analytical prediction. [ABSTRACT FROM PUBLISHER]

The split ratio, i.e., the ratio of stator bore radius to stator outer radius, is an important design parameter for permanent-magnet (PM) linear machines, as it significantly influences the thrust force capability and efficiency. The optimal split ratio for maximum thrust force is investigated analytically for both surface-mounted PM (SPM) and interior PM (IPM) E-core linear oscillating actuators. It utilizes simple lumped magnetic circuit models and accounts for the magnetic saturation, the curvature effect, the fringing effect, and the armature reaction effect which may greatly affect the accuracy of the analytical model for the optimal split ratio. The optimal split ratio for both SPM and IPM prototype actuators is found to be around 0.55. The developed analytical models are validated by both finite-element analyses and measurements. [ABSTRACT FROM AUTHOR]

We present an analytical model of unbalanced magnetic force (UMF) in fractional-slot surface-mounted permanent magnet (PM) machines having diametrically asymmetrical winding distribution but no static/dynamic rotor eccentricities. It is based on a 2-D analytical field model and accounts for the influence of both the radial and tangential force waves under any load condition. It is capable of providing insight into the generation, harmonic contents, and characteristics of the UMF and accurately predicting the magnitudes, rotation directions, phase angles of its harmonics and various components, such as the UMFs due to armature reaction only, mutual interaction between both PM and armature reaction fields, and radial and tangential force waves. The cancellation and additive effects between the UMF components resulting from the radial and tangential force waves are revealed for the first time by the analytical model. We show that such effects strongly depend on the UMF harmonic order, slot/pole number combinations, and the internal/external rotor machine topologies. We have validated the analytical model by finite-element analyses and partially by experimental results. [ABSTRACT FROM AUTHOR]

The split ratio has been optimized for the maximum torque density when the air-gap flux density is fixed in existing papers. However, the air-gap flux density can vary with the split ratio significantly in interior permanent-magnet (IPM) machines due to flux focusing. Therefore, an optimal air-gap flux density may exist, together with the optimal split ratio, for the maximum torque in IPM machines. This paper analytically optimizes the air-gap flux density and split ratio individually, as well as the global optimum in terms of the torque density in the fractional-slot IPM machines with non-overlapping windings. In addition, the influence of pole-slot combination and tooth-tips on the optimal split ratio and air-gap flux density is discussed. The analytical result is verified by the finite element analysis. It shows that the optimal split ratio reduces with the increase of the air-gap flux density, and the preferred air-gap flux density is around 0.5-0.7 times of maximum flux density in the stator teeth when the rare earth permanent magnets are employed. [ABSTRACT FROM AUTHOR]

Flux-switching permanent-magnet (FSPM) brushless machines have emerged as an attractive machine type by virtue of their high torque densities, simple and robust rotor structure, and the fact that permanent magnets and coils are both located on the stator. Both 2-D and 3-D finite element analyses are employed to compare the performance of a conventional all poles wound (double-layer winding) topology with that of three modular alternate poles wound (single-layer winding) topologies, in terms of output torque, flux-linkage, back EMF, and inductances. It is shown that the FSPM machine can be designed in this way without incurring a significant performance penalty, but that some degree of rotor skewing or a variation in stator and rotor pole combination may be required in order to maintain a sinusoidal back-EMF waveform and reduce the torque ripple. Experimental validation is reported for both conventional all poles wound and alternate poles wound FSPM machine topologies. [ABSTRACT FROM AUTHOR]

High speed flux-switching permanent magnet (FSPM) machines have been identified as key technologies for aerospace and hybrid electric vehicle applications. The open slot geometry, high stator flux densities and high operating frequencies result in high variable cross slot leakage and proximity losses within the armature windings. The aim of this study is to reduce AC losses in the armature of a high speed FSPM machine by stranding the conductors. The influence of rotor movement across the slot opening is investigated using 2-D finite element analysis. A simple 1-D analytical model is developed and validated by the finite element analysis to accurately estimate the level of proximity losses and then used to determine the optimal number and diameter of conductors. [ABSTRACT FROM AUTHOR]

A simple analytical method is developed for determining the optimal combination of stator pole and rotor pole numbers for a multi-tooth flux-switching permanent magnet (FSPM) machine, and the optimal design of the stator teeth for maximum torque. In addition, the rotor pole width and the split ratio are optimized by finite element analysis. The optimized multi-tooth FSPM machine exhibits a significantly higher torque capability and requires a significantly lower volume of magnet material than a conventional FSPM machine. The performance of the proposed multi-tooth FSPM machine is validated experimentally. [ABSTRACT FROM AUTHOR]

We evaluate the superposition method for calculating the cogging torque in permanent-magnet brushless machines, the resultant torque being synthesized from cogging torque components associated with a pair of magnets. Although finite-element analyses and measurements show that the resultant cogging torque cannot be synthesized directly from the torque components due to a single magnet, we use the concept of a fictitious single magnet to analytically establish the relationship between the cogging torque and key design parameters. The method is particularly useful in assessing the influence of the slot number and pole number combination. [ABSTRACT FROM AUTHOR]

A nonlinear adaptive lumped parameter magnetic circuit model is developed to predict the electromagnetic performance of a flux- switching permanent-magnet machine. It enables the air-gap field distribution, the back-electromotive force (back-EMF) waveform, the winding inductances, and the electromagnetic torque to be calculated. Results from the model are compared with finite-element predictions and validated experimentally. The influence of end effects is also investigated, and optimal design parameters, such as the rotor pole width, the stator tooth width, and the ratio of the inner to outer diameter of the stator, are discussed. [ABSTRACT FROM AUTHOR]

In this paper, a method for predicting the electromagnetic vibration of permanent magnet (PM) brushless motors is presented. It calculates the electromagnetic force on individual stator teeth by the Maxwell stress method, based on two-dimensional finite-element analysis of the electromagnetic field. The resulting radial force contour is then used in an analytical shell model to predict the stator vibration. The method is validated experimentally, and is used to investigate the vibration in various PM brushless motors with different fractional slotlpole number combinations. The relationship between the slot/pole number combination and the dominant vibration frequency and mode order is also established. [ABSTRACT FROM AUTHOR]

Variable flux memory machines (VFMMs) with series hybrid magnets using both low coercive force (LCF) and high coercive force (HCF) permanent magnets (PMs) have been recognized as a viable candidate for wide-speed-range industrial applications due to the advantages of high torque density and wide speed range. Nevertheless, the adverse effects of LCF PM on the HCF PM in series-type VFMM under different magnetization states (MSs) are still unreported. In this paper, the flux barrier effect (FBE) of the LCF PM existing in series hybrid magnet VFMM is first revealed, and its causes are discussed as well as analyzed in depth on the basis of the equivalent magnetic circuit method and finite-element (FE) analyses. A topology of VFMM with dual-layer PMs is further developed to alleviate the FBE induced from LCF PMs. It can be found that the FBE can be effectively suppressed by employing the dual-layer (DL) PM arrangement and additional leakage flux paths. A prototype of the proposed design is built, and the theoretical and FE results are experimentally verified. [ABSTRACT FROM AUTHOR]

Design rules of multiple multiphase winding configurations are investigated from the perspective of phase shift between adjacent winding sets in flux-switching permanent magnet (FSPM) machines. The relations between torque/rectified voltage and phase shift for any multiple multiphase winding topology are theoretically derived, directly showing the influence of phase shift on torque/rectified voltage harmonic components. It can be learned that the optimal phase shift for the lowest torque ripple and dc voltage oscillation depends on the winding types. Symmetrical winding is not always appropriate for any occasion. To verify the analytical results, the static characteristics of the dual three-phase, four three-phase, triplex three-phase, dual six-phase, and triplex four-phase FSPM machines with specific stator/rotor-pole combinations are studied by finite-element (FE) analysis. The FE-predicted dominant torque ripple and rectified voltage pulsation components for symmetrical and asymmetric phase shifts are in good agreement with the theoretical derivation. Prototypes are built and tested to verify the analytical and FE results. [ABSTRACT FROM AUTHOR]

This paper proposes an analytical method that combines the superposition concept and the subdomain method to predict the cogging torque of permanent magnet (PM) machines with a rotor eccentricity. The original eccentric machine is first divided into several sections along the air-gap circumferential direction. Then, the equivalent air-gap lengths of all sections will be determined and individually used to build up a series of concentric models representing each section. By the superposition method, the air-gap flux density of the original eccentric machine can be synthesized from that of every concentric model predicted through the subdomain method. Consequently, the cogging torque can be predicted by the integral of Maxwell stress tensor based on the synthesized air-gap flux density. To prove the efficacy of the proposed method, two fractional-slot PM machines with different slot/pole number combinations are taken as examples, together with the validation of a finite-element analysis. [ABSTRACT FROM AUTHOR]

The finite-element method incorporating with a hysteresis model has been used to analyze the variation characteristics of flux density of permanent magnets (PM) in the variable flux memory motor (VFMM). It accounts for the local hysteresis curves of PMs under different remagnetizing magnetomotive forces. Excellent agreement between the FEA predicted and measured phase back EMFs and air gap flux per pole has been achieved. It shows that the analysis method is suitable for evaluating the PM remagnetizing state in VFMM machines, and the remagnetization of PM is more difficult than the demagnetization, several times the full demagnetizing MMF is required in order to achieve the full remagnetization of PM. [ABSTRACT FROM AUTHOR]

We present a simple lumped magnetic circuit model for interior permanent-magnet (IPM) machines with multisegment and multilayer permanent magnets. We derived analytically the open-circuit air-gap field distribution, average air-gap flux density, and leakage fluxes. To verify the developed models and analytical method, we adopted finite-element analysis (FEA). We show that for prototype machines, the errors between the FEA and analytically predicted results are <1% for multisegment IPM machines and <2% for multilayer IPM machines. By utilizing the developed lumped magnetic circuit models, the IPM machines can be optimized for maximum fundamental and minimum total harmonic distortion of the air-gap flux density distribution. [ABSTRACT FROM AUTHOR]

In this paper, novel dual-stator switched-flux hybrid magnet machines (DS-SF-HMMMs) are proposed. Two sets of armature winding are employed so as to improve the space utilization and torque density. Meanwhile, two kinds of permanent magnets (PMs), i.e., neodymium–iron–boron and low-coercive-force magnets, are placed on either a common stator or separate stators. The proposed machines can provide the merits of high torque density in DS machines, and excellent flux adjusting capability in memory machines. The topologies and operating principle of the DS-SF-HMMMs having different PM arrangements are introduced and highlighted, respectively. In order to overcome the drawbacks of the original “U”-shaped PM type, two alternate designs are presented to increase the copper area in the inner stator and facilitate the manufacturability. In addition, the equivalent magnetic circuits for various machine models are formulated to reveal the field regulation principle. Then, the electromagnetic characteristics of various available DS-SF-HMMMs are evaluated and compared by the finite-element (FE) method. The stator/rotor pole combinations of the selected machine are analytically optimized in order to maximize the torque density. Finally, two prototypes are manufactured and tested to verify the FE analyses. [ABSTRACT FROM PUBLISHER]

This paper investigates the interaction of the zero sequence component into both permanent magnet (PM) shape and phase current to improve the output torque in dual three-phase surface-mounted PM (SPM) machines. The optimal zero sequence components are analytically derived and validated by finite element (FE) analyses. It is found that the optimal zero sequence components into both PM shape and current waveform are dependent on the fundamental and zero sequence harmonic winding factors. For the dual three-phase SPM machines having rotors without shaping, Sine shape, Sine shape with the zero sequence components, the electromagnetic performances including the back electromotive force (EMF) waveform, cogging torque, average torque, and torque ripple are compared. It is demonstrated that the average torque with the optimal zero sequence component in PM shaping and current waveform can be improved by >30% while the torque ripple remains similar to that of the one with Sine shaping. Finally, the experiments are given to verify both the analytical and FE analysis. [ABSTRACT FROM AUTHOR]

This paper develops a 2-D field analytical model for predicting the magnetic field distribution and the corresponding electromagnetic performance in air- and iron-cored permanent magnet (PM) brushless machines having radially or parallel magnetized two-segment Halbach array. A simple equation is derived to directly predict the optimal magnet ratio for maximum electromagnetic torque, while the influence of pole-pair number and magnet thickness on the optimal magnet ratio is investigated for both air- and iron-cored machines. The analytical model is validated by finite-element analyses and also measurements on a prototype 12-slot/10-pole PM brushless machine. [ABSTRACT FROM AUTHOR]