Fractional-slot Permanent Magnet Machines Research Articles

Investigation of Asymmetrical Winding Layouts for Fractional-Slot Permanent Magnet Machine

Investigation of Asymmetrical Winding Layouts for Fractional-Slot Permanent Magnet Machine

Torque Ripple and Radial Force Minimization of Fractional-Slot Permanent Magnet Machines Through Stator Harmonic Elimination

This article proposes a torque ripple minimization strategy based on minimizing interactive space harmonics of fractional-slot permanent magnet (PM) machines using a space-shifted wye–delta stator winding. A radial force analysis has also been carried out, which showed a substantial reduction in the second-order mode for these space-shifted wye–delta wound machines; this will improve the noise and vibration performance. The effectiveness of the proposed method is shown by analyzing the performances of a low-power surface-mounted permanent magnet (SPM) machine for the electric power steering (EPS) applications and a high-power interior permanent magnet (IPM) machines for the hybrid electric vehicle (HEV) applications on the 12-slot/10-pole (12 S/10 P) configuration. The proposed winding doubles the stator slot number of the base model, and as a result, the base 12 S/10 P configuration becomes 24-slot/10-pole (24 S/10 P) combination. Compared with the existing ripple minimization techniques of magnet shaping or rotor skewing, the proposed stator winding-based strategy achieves better torque ripple performance and magnet utilization leading to an improvement in average torque while reducing the amplitude of the low-order radial force. A 10-pole SPM machine has been built and tested for experimental validation of both the concept and the finite element analysis (FEA) simulation results.

Cogging Torque Dynamic Reduction Based on Harmonic Torque Counteract

This article presents a method to reduce cogging torque in permanent magnet (PM) machines from dynamic control based on harmonic torque counteract (HTC). We find the possibility of dynamic cancellation of cogging torque and harmonic torque by studying their generation mechanism and period characteristics, and further study the current harmonic injection scheme for cogging torque reduction. Further, two case studies of an integer slot PM machine and a fractional slot PM machine based on finite element analysis well validate the proposed method. Among them, the cogging torque of a 6-slot/2-pole PM synchronous machine is weakened from 932.0 to 56.2 mN.m, with a weakening ratio of 94.0%, and the cogging torque of the other with 6-slot/4-pole is weakened from 1.23 N.m to 44.21 mN.m, with a weakening ratio of 96.4%. The theory of this article can be extended to PM machines with other different pole/slot combinations and topologies.

Influence of Pole and Slot Combination on Torque Characteristics and Radial Force of Fractional Slot Permanent Magnet Machines

The fractional slot concentrated winding structure effectively solves the difficulty of low‐speed and high‐torque permanent magnet (PM) machines with a large number of poles and slots, but it also brings a wealth of magnetomotive force (MMF) harmonic. The winding function method is used to compare and analyze the stator MMF distribution and harmonic content of the fractional slot PM machines with different pole and slot combinations, and the cogging torque waveform and torque ripple are calculated by the finite element method. The influence of pole and slot combination on radial force and vibration modes of fractional slot PM machines is studied. The main vibration mode can be determined from the lowest order of radial force harmonics. The results show that in a fractional slot PM motor, the radial force is the main cause of noise and vibration, rather than the cogging torque and torque ripple. The dominant radial force is mainly produced by the interaction of rotor field harmonics and armature reaction field harmonics, and the vibration and noise will significantly increase with the decrease of the dominant vibration mode order, which largely depends on the pole and slot combination. This paper provides a certain reference for the selection of pole and slot combination in the electromagnetic design process of low speed high torque fractional slot PM motors. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

EMF Voltage Distortion Mitigation in Fractional-Slot Permanent Magnet Machines by Varying Coil Distribution and Turn Ratio

Electromagnetic force (EMF) voltage distortion, caused by armature reaction, not only deteriorates torque ripple in constant torque region but also reduces the flux weakening operation region, especially for fractional slot permanent magnet (PM) machines. This article mitigates voltage distortion by varying coil distribution and turn ratio with employment of triple layer (TL) and quadruple layer (QL) windings with varied coil turns. Coil turn ratios of TL and QL windings are optimized to minimize voltage distortion ratio. Reduction mechanisms are exhaustively analyzed. It is found that, for the TL winding with optimal turn ratio, the armature leakage flux and PM leakage flux in tooth tips will not reverse polarities simultaneously, resulting in much lower voltage distortion. On the other hand, for the QL winding, voltage distortion reduction is realized by lowering the amplitude of armature tooth tips leakage flux. Compared with conventional double or single layer (SL) winding machines, torque ripple can be reduced and flux weakening capability is greatly enhanced. The 12-slot/10-pole prototypes with both SL and optimum TL windings are fabricated and tested to verify the analysis.

Influence of unequal stator tooth width on the performance of outer-rotor permanent magnet machines

AbstractOuter-rotor permanent magnet machines for low-speed and high-torque applications have been used due to their high moment of inertia and torque density. In this paper, the 12-slot/10-pole outer-rotor fractional-slot permanent magnet machine model is established by finite element analysis, the influence of unequal stator tooth width and tooth tip width is investigated for the PM machine, and five different schemes of stator tooth and tip width are designed and analyzed. Detailed comparisons of the performance characteristics of the machines are presented including important issues such as output torque, magnetic field distribution, and tooth flux density. It is shown that the torque density and cogging torque and efficiency can be effectively improved by choosing reasonable tooth and tip width, which lays a foundation for further optimum design and efficiency improvement of the machine.

Investigation of Unbalanced Magnetic Force in Fractional-Slot Permanent Magnet Machines Having an Odd Number of Stator Slots

Fractional-slot permanent magnet (PM) machines with an odd number of stator slots are attractive candidates for industrial applications due to their high torque density and low torque ripple. However, the unbalanced magnetic force is detrimental to the bearing and yields noise and vibration. This paper determines the existence criterion of UMF on both open-circuit and on-load conditions by analysis of air gap field and magnetic force waves. Only when the machine periodicity is one, will the open-circuit UMF be generated due to the mutual interaction between the modulated PM harmonics and the original PM harmonics. In addition, the existence of on-load UMF in machines with a periodicity of one is confirmed even when the slotting effect is ignored. Furthermore, among the five investigated machines with a given odd slot number of 9 but different pole numbers, the UMF in a machine with two poles is the smallest since the magnitude of the 2nd harmonic in the armature reaction is the smallest compared with other contributing harmonics. Meanwhile, the UMF in a machine with pole number 2p = Ns-1 is the largest due to the relatively larger magnitude of the (p + 1) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> armature reaction harmonic and the additive effect between the first order radial and tangential stresses.

Deadbeat Direct Flux Vector Control of Surface Permanent Magnet Motor Drives

The predictive control algorithms for electrical drives are currently subject to considerable interest and development. In particular, the predictive torque control is a competitive solution that may replace in the future the conventional control schemes based on linear controllers. Therefore, this article proposes a predictive torque control for surface permanent magnet motor drives requiring a wide constant power range. The predictive algorithm uses a deadbeat direct flux vector control approach for the simultaneous control of the stator flux amplitude and torque-producing current component. The proposed control scheme is suitable for applications requiring a wide speed range with current and voltage constraints. The proposed deadbeat torque controller has been tested on a fractional slot permanent magnet machine and the experimental results demonstrate the full drive controllability, including deep flux-weakening operation with limitation of the load-angle.

Novel Modular Fractional Slot Permanent Magnet Machines With Redundant Teeth

In order to ease the manufacture process of very large permanent magnet (PM) machines, such as direct drive wind power generators, modularity technique is usually adopted. Although conventional fractional slot PM machines with all teeth wound windings show good performance, the coils located at the end part of each segment could be easily damaged because of being exposed to the air. In addition, the local winding faults could easily proliferate to the whole machine due to the physical touch of adjacent coils. Thus, a novel modular fractional slot PM machine with redundant teeth is proposed in this paper, while three phases within each set of winding are still balanced. The construction of the proposed modular PM machine having 42-slots/32-poles (42S/32P) combination is described in detail as an example, which can be treated as the integration of six 6S/5P segments and a redundant 6S/2P machine. The reason for using 6S/2P machine is to get rid of the undesirable unbalanced magnetic force (UMF), which usually exists in rotating asymmetric machines, such as 3S/2P PM machine. Since the end part of each segment in the proposed modular PM machine can be covered by half redundant tooth during the production, more protection can be provided for coils located in these regions. Furthermore, the separation of six segments can improve the fault-tolerant capability of the machine. The electromagnetic performance predicted by finite-element analysis (FEA) also demonstrates that the proposed modular machine will perform better if dual three-phase winding is adopted. Finally, the experiments on the prototyped machine validate the analysis in the paper.

Expansion of the Feasible Slot/Pole Combinations in the Fractional Slot PM Machines by Applying Three-Slot Pitch Coils

In this paper, existing feasible slot/pole combinations of the fractional slot permanent magnet (FSPM) machines are extended. In comparison with the existing slot/pole combinations, the proposed ones could result in a higher winding factor, lower torque ripple, and lower cogging torque. This diversity in the number of the slot/pole combinations brings the designers more alternative solutions. To reach such slot/pole combinations three-slot pitch coils are applied. The existing slot/pole combinations are limited to the designs with an integer number of slots per phase in one periodicity of the FSPM machine. In the presented work, FSPM machines with fractional numbers of the slots per phase in one periodicity of the machines are introduced. However, the phase back electromotive force signals are balanced. Moreover, to achieve a slot/pole combination with small unbalance magnetic force (UMF) and low THD value of the armature MMF, the multilayer winding technique is applied. In addition, a simple technique is presented to find an arrangement of the multilayer winding with very small UMF. Extensive finite element simulations are used to compare the FSPM machines with the proposed slot/pole combinations with the traditional FSPM machines.

Study on Shaft Voltage in Fractional Slot Permanent Magnet Machine With Different Pole and Slot Number Combinations

A novel shaft voltage, which can also be consider the effect of slot, will be induced by the intrinsic electromagnetic structure in some fractional slot permanent magnet machines (FSPMMs) with certain pole and slot number combinations. By the aid of analytical method and finite-element method (FEM), the relationship of the shaft voltage and pole and slot number combinations is investigated and verified. A qualitative expression of the shaft voltage and the characteristic frequencies of the shaft voltage are predicted by the analytical method. The law of pole and slot number combinations which can yield or avoid the shaft voltage is deduced by the analytical method at the same time. By the FEM, the induced shaft voltages in eight FSPMMs with different slot and pole number combinations are calculated, and the results are well agree with the analytical deductions. As a result, the proposed work provides a theoretical foundation for the novel shaft voltage in FSPMMs and a general method to avoid and reduce the shaft voltage by suitable selection of pole and slot number, which can be a reference for FSPMMs design and fault diagnosis.

Analytical Modeling and Optimization for Electromagnetic Performances of Fractional-Slot PM Brushless Machines

This paper presents a closed-form solution to optimize surface permanent magnet (PM) machines using concentrated windings. An analytical model is developed to predict the electromagnetic performances of fractional-slot PM machines. The model can be used to evaluate open-circuit magnetic field distribution with stator slotting effects, armature reaction field distributions, back-EMF waveform, winding inductance, cogging torque, electromagnetic ripple torque, efficiency, specific power, radial force density, and vibration mode order. Particle swarm optimization technique is applied to the proposed model in order to search for solutions that are a good compromise between conflicting objectives. The performances of the optimized machine are verified using finite element analysis. Finally, the analytical and finite element results have been validated with the experimental data, demonstrating a strong correlation between key machine parameters.

Superposition Method for Cogging Torque Prediction in Permanent Magnet Machines With Rotor Eccentricity

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.

3-D Analytical Model With the End Effect Dedicated to the Prediction of PM Eddy-Current Loss in FSPMMs

The paper deals with a 3-D analytical model by considering the end effect which is dedicated to the prediction of the permanent-magnet (PM) eddy-current loss in fractional-slot permanent-magnet machines. Following the derivation of the proposed model, it is applied to the case of a 12-slot 10-pole machine with unsegmented PMs operating at rated speed. A good agreement is found while comparing the analytical results and those computed by 3-D finite element analysis. In the next step, the proposed model is applied to the investigation of the effect of PM segmentation on the reduction of their eddy-current loss, considering: 1) the radial segmentation and 2) the axial one. The obtained results highlight the better capability exhibited by the radial segmentation over the axial one in reducing the PM eddy-current loss. Finally, the proposed analytical model is applied to the investigation of the coupled-effects of the PM segmentation and geometry on their eddy-current loss reduction.

Iron loss in FSPMM: 2D FEA-based comparative study between single and double-layer topologies

Purpose – The purpose of this paper is to compare the study between two topologies of fractional-slot permanent-magnet machines such that: double-layer topology and single-layer one. The comparison considers the assessment of the iron loss in the laminated cores of the magnetic circuit as well as in the permanent magnets (PMs) for constant torque and flux weakening ranges. Design/methodology/approach – The investigation of the hysteresis and eddy-current loss has been carried out using 2D transient FEA models. Findings – It has been found that the stator iron losses are almost the same for both topologies. Whereas, the single-layer topology is penalized by higher iron loss especially the eddy-current ones taking place in the PMs. This is due to their denser harmonic content of the armature air gap MMF spatial repartition. Originality/value – The analysis of the iron loss maps in different parts of each machine including stator and rotor laminations as well as the PMs, in one hand, and the investigation of their variation with respect to the speed, in the other hand, represent the major contribution of this work.

Analysis of a fractional slot permanent magnet machine for a series hybrid truck

Purpose – The purpose of this paper is to discuss the performance of a proposed machine design for an in‐wheel motor with the required torque‐speed characteristic.Design/methodology/approach – Calculation of the winding factor of the machine with the star of slots theory is performed first. The field weakening capability of the machine is investigated and the operating speed range is determined. The tooth contour modeling method for calculating the performance of the machine with a limited number of elements is introduced. The method is used to construct two models of different complexity and the results obtained with the models are compared with the results obtained by finite element models.Findings – The 14 pole 12 slot in‐wheel PMSM discussed in this paper is able to meet the stringent performance requirements. The results obtained with the tooth contour models show good agreement with the results obtained with finite element models despite the limited number of elements. Increasing the number of eleme...

Faulty Operations of a PM Fractional-Slot Machine With a Dual Three-Phase Winding

The permanent-magnet (PM) machine with dual three-phase windings is proposed for applications requiring continuous operating even under a partial fault. The two windings are supplied by two separate inverters. Thus, in the event of a fault of one winding, this is disconnected, and the machine continues to be operated by means of the healthy winding. This paper investigates the PM machine with dual three-phase windings and its capabilities during faulty operating conditions. A fractional-slot interior PM machine with 12 slots and 10 poles is taken into account. Its performance is investigated according to different winding configurations. The torque behavior, overload capability, and thermal limits are evaluated under open-circuit and short-circuit faults. A finite-element analysis as well as experimental tests is carried out on a prototype of such a machine.

Analytical Modeling and Finite-Element Computation of Radial Vibration Force in Fractional-Slot Permanent-Magnet Brushless Machines

An analytical model has been developed for analyzing the radial vibration force in fractional-slot permanent-magnet machines. It is compared extensively by finite-element analyses and used to investigate the influence of the following: 1) stator slotting; 2) tangential field component; 3) radius in the air gap for computation; 4) load condition, etc. The major findings include the following: 1) even on an open circuit, the low harmonic component (e.g., the second for a 10-pole/12-slot machine) of the radial force exists due to the slotting effect, although the amplitude is relatively low, while the slotless analytical model cannot predict this phenomenon; 2) on a load, the slotless analytical model is accurate enough for the radial force analysis since the low-order harmonic component of the radial force is mainly due to the interaction between the magnet field and the armature-reaction field and is largely determined by the combination of the pole and slot numbers; 3) it is much more reliable to calculate the radial force in the middle of the air gap rather than close to the stator bore; and 4) the simple formula accounting only for the radial field component in the middle of the air gap is accurate enough for the radial force calculation.

Winding Configurations and Optimal Stator and Rotor Pole Combination of Flux-Switching PM Brushless AC Machines

A simple analytical method is developed to compare the combinations of stator and rotor pole numbers in flux-switching permanent magnet (PM) machines in terms of back electromotive force (EMF) and electromagnetic torque. The winding connections and winding factors of machines having all poles and alternate poles wound, and different numbers of phases, from two to six, are determined by the coil-EMF vectors. Their differences from analyzing the conventional fractional-slot PM machines with concentrated nonoverlapping windings are highlighted. The general conditions are established for balanced symmetrical back-EMF waveform. It shows that the optimized rotor pole number should be close to the number of stator poles, whereas larger torque can be obtained by the machine with relatively higher rotor pole number. The analysis is validated by finite-element analyses and experiment.

Impact of MMF Space Harmonic on Rotor Losses in Fractional-Slot Permanent-Magnet Machines

The fractional-slot permanent-magnet (PM) machines are used in many applications due to their high torque density, low torque ripple, and high efficiency. However, the fractional-slot machines are characterized by high contents of space harmonics in the air-gap MMF distribution. Such harmonics cause flux variation in the air gap, and the main consequence is the induced losses in the rotor. Depending on the combination of slots and poles of the machine, there are different harmonic contents and then rotor losses. By means of a simple model of the rotor losses, this paper investigates the link between the rotor losses and the combination of the slots and the poles of the fractional-slot PM machines.