Pole Number Combinations Research Articles

Novel High-Performance Switched Flux Hybrid Magnet Memory Machines With Reduced Rare-Earth Magnets

This paper proposes two high-performance switched flux hybrid magnet memory machines (SF-HMMMs) based on the design concepts of E-core and C-core SF permanent magnet (PM) machine topologies. Since two kinds of PMs (i.e., NdFeB and low coercive force magnets) are employed, the proposed machines can offer the merits of high torque capability, excellent flux adjustability, and high efficiency across a wide speed range. In this paper, the PM arrangement and dimensions, stator/rotor pole number combination, as well as the major design parameters are optimized first. Then, the electromagnetic characteristics of the proposed machines are investigated and compared with their conventional 12-stator pole SF-HMMM. It is found that compared with their conventional 12-stator pole counterpart, the proposed machines offer improved torque density and flux adjustability, even with the reduced PM usage. Finally, two machine prototypes are manufactured and tested to validate the analyses.

Comparative study of biased flux permanent magnet machines with doubly salient permanent magnet machines considering with influence of flux focusing

Different from the doubly salient permanent magnet (PM) machines (DSPMMs), the stator/rotor pole number combination (Ns/Nr) in biased flux PM machines (BFPMMs) is flexible and Nr can be any integer except the phase number and its multiples. When Ns/Nr differ by one, 6-stator pole BFPMM exhibits bipolar phase flux-linkage and symmetrical phase back-electromotive force waveforms. Based on the optimal 6/7 Ns/Nr and the rated copper loss, the torque density of BFPMMs is enhanced by 19%, 18.8% and 40.3% respectively when employing the flux-focusing structures with inner-type, outer-type and combined-type. Meanwhile, the PM utilization efficiency is also enhanced. Moreover, based on the inner-type flux-focusing structure, the optimized 6/7 Ns/Nr BFPMM exhibits about 18% higher average torque and 80% lower torque ripple than the optimized 6/4 Ns/Nr DSPMM. Further, the unbalance between phases which is observed in DSPMMs is overcome in the BFPMMs. The analyses are validated experimentally on a prototype machine.

Influence of Slot and Pole Number Combinations on Voltage Distortion in Surface-Mounted Permanent Magnet Machines With Local Magnetic Saturation

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 ( N s/2 p ) 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 $N_{s} \pm 1 = 2p$ , $N_{s} \pm 2 = 2p$ , N s /2 p = 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 $N_{s} > 2p$ suffer from on-load voltage distortion less than their counterparts with $N_{s} . Finally, three prototype machines with 12/10, 12/14, and 12/8 slot/pole numbers are manufactured and tested to validate the analyses.

Performance of Fractional-Slot Winding PM Machines due to Un-even Coil Turns and Asymmetric Design of Stator Teeth

PM machines in which slot number and pole number combination differs by one have to be configured with asymmetric winding pattern in order to maximize it back-emf performance. However, this asymmetric winding configuration inherently results an unwanted Unabalanced Magnetic Force (UMF). Investigations of electromagnetic performance of fractional-slot asymmetric winding PM machines using 2-D Finite-Element Analysis are presented. The investigations are mainly driven by the effort of minimizing the UMF. By employing techniques such as non-uniform number of coil turns in every tooth and asymmetric design of stator tooth, the UMF are expected can be minimized. The investigations show that the radial component of UMF has greater effect than the tangential component on the UMF itself. In all proposed techniques, a slight reduction of machine torque performance is inevitable.

Novel linear switched-flux PM machine with 9/10 primary/secondary pole number combination

Purpose – Due to linear structure, linear switched flux permanent magnet machines (LSFPMMs) also may have odd pole primary, such as 9, 15, 21, etc., without unbalanced magnetic force in equivalent rotary machines. The paper aims to discuss these issues. Design/methodology/approach – In order to increase the thrust force density, the influence of some major design parameters, including split ratio, PM thickness, primary slot width and secondary pole width, are investigated by finite element analysis. For reducing the thrust force ripple under on-load condition, the end auxiliary teeth are adopted and their positions are also optimized. Findings – This novel 9/10 primary/secondary poles LSFPMM has high average thrust force and low thrust force ripple by optimization. The results demonstrate that the odd pole primary may be a good candidate for long-stroke linear direct drive application. Originality/value – A novel 9/10 primary/secondary poles linear switched flux permanent magnet machine is developed in this paper. The similar conclusions could be obtained for other LSFPMMs with odd pole primary.

Torque ripple reduction of synchronous reluctance machines

Purpose – The purpose of this paper is to investigate the influence of stator and rotor pole number combinations together with the flux-barrier layers number on the performance of synchronous reluctance machine with emphasis on output torque capability and torque ripple. Design/methodology/approach – AC synchronous reluctance machine (SynRM) or permanent magnet assisted SynRM presently receives a great deal of interest, since there is less or even no rare-earth permanent magnet in the rotor. Most of SynRM machines employ a stator that is originally designed for a standard squirrel cage induction motor for a similar output rating and application, or the SynRM machine with 24-slot, four-pole are often directly chosen for investigation in most of the available literature. Therefore, it is necessary to investigate the influence of stator and rotor pole number combinations together with the flux-barrier layers number on the performance of SynRM machine with emphasis on output torque capability and torque ripple. Findings – The average torque decreases with the increase of the pole numbers but remain almost constant when employing different stator slot numbers but with the same pole number. In addition, the torque ripple decreases significantly with the increase of the stator slot number. The machine with double-layer flux-barrier in the rotor has the biggest average torque, while the machines with three- and four-layer flux-barrier in the rotor have almost the same average torque but their value is slightly smaller than that of machine with double-layer flux-barrier. However, the machine with three-layer flux-barrier has the lowest torque ripple but the highest torque ripple exists in the machine with double-layer flux-barrier. Research limitations/implications – The purely sinusoidal currents are applied in this analysis and the effects of harmonics in the current on torque ripple are not considered in this application. Originality/value – This paper has analyzed the torque ripple and average torque of SynRMs with considering slot/pole number combinations together with the flux-barrier number.

Stator/Rotor Pole Combinations and Winding Configurations of Variable Flux Reluctance Machines

In this paper, stator/rotor pole combinations, winding configurations, and electromagnetic performance of novel variable flux reluctance machines (VFRMs), which employ a doubly salient structure similar to switched reluctance machines (SRMs) but with stator-located dc field windings, are investigated. VFRMs with 12 stator poles are taken as examples to illustrate the method for determining the winding connections and winding factors. The back-electromotive force (EMF), self- and mutual inductances, cogging torque, static torque, torque ripple, and unbalanced magnetic force (UMF) are investigated by finite-element analyses. It is found that many stator/rotor pole combinations, i.e., 12/8 (which may be derived from the conventional three-phase SRM), 12/10, 12/11, 12/13, and 12/14, are feasible for the 12-stator-pole VFRMs. Among these pole number combinations, the 10- and 14-rotor-pole VFRMs can eliminate the inherent UMF in 6/5 and 6/7 VFRMs and exhibit more sinusoidal back-EMF waveforms and have higher torque density than an 8-rotor-pole VFRM, whereas the 11- and 13-rotor-pole VFRMs exhibit similar torque density as the 10- and 14-rotor-pole VFRMs, but with negligible cogging torque and torque ripple, albeit with UMF. Five prototype VFRMs with 12 stator poles and different rotor poles have been designed, manufactured, and tested to verify the analyses.

Optimization Design and Direct Torque Control of a Flux Concentrating Axial Flux Permanent Magnet Motor for Direct Driving System

Optimization design and direct torque control (DTC) of a flux concentrating axial flux permanent magnet motor (AFPMM) are presented in this paper, which leads the AFPMM to exhibit high torque capability at low-speed and wide speed operation range for direct driving system. Firstly design parameters and manufacturing materials which affect the output performances of the motor are discussed, and then based on finite element analysis (FEA) and response surface methodology (RSM), slot and pole number combinations, and structure dimensions are optimized. Furthermore, a novel DTC based on stator flux linkage tracking is introduced, which combines maximum torque per ampere (MTPA) control and field weakening (FW) control. Independent H-bridge inverter is used to enhance the voltage limit and enlarge the speed operation range. A prototype AFPMM is fabricated on the basis of the optimum model, and experimental measurements are conducted to verify the usefulness of the proposed optimization design and control methods.

Influence of Pole and Slot Number Combinations on Cogging Torque in Permanent-Magnet Machines With Static and Rotating Eccentricities

With the aid of finite-element and analytical methods, this paper investigates the influence of static/rotating eccentricities on the cogging torque of permanent-magnet machines having various pole/slot number combinations (2p/N 8 ), including fractional-slot topologies, such as 2p = N 8 ± 1, 2p = N 8 ± 2, and 2p/N 8 = 8/12, as well as an integer-slot machine 2p/N 8 = 4/12. It is found that the influence of eccentricity reduces significantly with the number of structure cyclic symmetry, which is equal to the greatest common divisor of slot and pole numbers. Hence, the eccentricity shows the largest influence in machines having 2p = N 8 ± 1, small influence in machines having 2p = Ne ± 2, and the smallest influence in the other machines. The static and rotating eccentricities result in cogging torque components multiples of (2p)th and (N 8 )th orders, respectively. Both static and rotating eccentricities produce similar cogging torque magnitude. The experimental results validate the FE and analytical investigation.

Research on Characteristics of Cogging Torque of Permanent Magnet Synchronous Motor Based on Finite Element Method

This paper presents a method of reducing cogging torque of Permanent Magnet Synchronous Motor (PMSM) based on Finite Element Method (FEM). Cogging torque can be reduced by pole and slot number combination and the length of air gap reasonably. An investigation into the cogging torque in 4 pole, 48 slot and 6 pole, 54 slot interior-magnet machines with overlapping winding is described. The calculation results show that cogging torque can be reduced by nearly 50% by pole and slot number combination reasonably. Then influence of different length of air gap on cogging torque is also researched. Cogging torque can be weaken by increasing the length of air gap effectively, the smoothness of the motor running can be improved.

Influence of Slot and Pole Number Combinations on Unbalanced Magnetic Force in PM Machines With Diametrically Asymmetric Windings

Unbalanced magnetic forces (UMFs) exist in permanent magnet machines with diametrically asymmetric windings, e.g., machines having pole and slot numbers differed by one and two, even when there is no rotor eccentricity. In machines having pole and slot numbers differed by two, the on-load UMF results only when the single-layer winding is employed and the number of coils is odd. This paper investigates the influence of slot and pole number combinations on the UMF by using an analytical method based on the finite-element predicted airgap flux densities. A UMF may be divided into two components due to the radial and circumferential traveling stresses. It is found that they are additive for machines having pole number 2p = 3k - 1, e.g., 8-pole/9-slot and 8-pole/6-slot, but partially canceling for machines having 2p = 3k + 1, e.g., 16-pole/15-slot and 16-pole/18-slot. Furthermore, due to the additive and canceling effects, for the same slot number, the machine having a smaller pole number exhibits a larger UMF when the slot/pole numbers differ by one, whereas the machine having a larger pole number exhibits a larger UMF when the slot/pole numbers differ by two and the slot number is higher than 6. For the same pole number, machines having slot/pole numbers differed by two exhibit a smaller UMF than machines having slot/pole numbers differed by one. It is also found that, if 2p = 3k + 1, the UMF gradually diminishes to 0 with the increase in pole number. On the other hand, when 2p = 3k - 1 , it reduces to a certain value with the increase in pole number. The experimental results are provided to verify the analysis.

Performance evaluation of a five-phase modular external rotor PM machine with different rotor poles

The performance of fault-tolerant modular permanent magnet (PM) machines depends on the proper selection of the pole and slot numbers which result in negligible coupling between phases. The preferred slot and pole number combinations eliminate the effect of low order harmonics in the stator magneto motive force and thereby the vibration and stray loss are reduced. In this paper, three external rotor machines with identical machine dimensions are designed with different slots per phase per pole (SPP) ratios. A simulation study is carried out using finite element analysis to compare the performance of the three machines in terms of machine torque density, ripple torque, core loss, and machine efficiency. A mathematical model based on the conventional phase model approach is also used for the comparative study. The simulation study is extended to depict machine performance under fault conditions.

Design and Analysis of a Novel Hybrid Excited Linear Flux Switching Permanent Magnet Motor

A hybrid excited linear flux switching permanent magnet motor (HLFSPMM) is a possible solution for developing a rare-earth-magnet-free electric motor with high force density. We designed an HLFSPMM that uses a ferrite magnet in place of a rare earth magnet. A suitable mover slot and stator pole number combination was selected in the initial design stage to achieve the desired performance capability. Structural refinements using design sensitivity analysis (DSA) based on the finite element method (FEM) were performed to enhance the machine performance. Simulation results have been validated by experimental measurements.

Radial Forces in External Rotor Permanent Magnet Synchronous Motors With Non-Overlapping Windings

In external rotor permanent magnet synchronous motors with non-overlapping windings, the higher frequency harmonics of the radial forces generate considerable resonant vibrations and acoustic noise. Therefore, diversity of spatial and specifically frequency harmonic ordinal numbers of representative slot and pole number combinations are derived analytically with open circuit and under load. Amplitudes of radial force waves are calculated by means of the finite element method and 2-D Fourier analysis. The obtained results confirm the analytical investigation. Determining factors on amplitudes are studied on machines having different slot and pole numbers and double-layer windings. Higher frequency harmonics significantly depend on the pole and tooth shape as well as the current profile. With open circuit, the calculations are validated by experiments. The findings are applied to reduce the noise of a centrifugal fan.

Analytical Modeling and Analysis of Open-Circuit Magnet Loss in Surface-Mounted Permanent-Magnet Machines

The paper presents an analytical model for predicting the open-circuit magnet eddy-current loss due to slotting in surface-mounted permanent-magnet machines based on the exact subdomain field model. The spatial and temporal characteristics of field harmonics due to slotting and corresponding eddy-current harmonics in the magnet are analyzed in both stator and rotor reference frames. The contribution of interaction between eddy-current harmonics having the same frequency but different spatial order to magnet loss is revealed for the first time by an analytical model. The magnet loss can be under- or overestimated if the interaction is neglected. The developed model is capable of providing both high accuracy and insights of loss generation. The influence of the slot and pole number combination, slot-opening to slot-pitch ratio, pole-arc to pole-pitch ratio, circumferential segmentation, and rotational symmetry order on the open-circuit magnet is investigated using the developed model. The finite-element results validate high accuracy of the developed analytical model.

Design and analysis of new fault-tolerant permanent magnet motors for four-wheel-driving electric vehicles

In this paper, a novel in-wheel permanent-magnet (PM) motor for four-wheel-driving electrical vehicles is proposed. It adopts an outer-rotor topology, which can help generate a large drive torque, in order to achieve prominent dynamic performance of the vehicle. Moreover, by adopting single-layer concentrated-windings, fault-tolerant teeth, and the optimal combination of slot and pole numbers, the proposed motor inherently offers negligible electromagnetic coupling between different phase windings, hence, it possesses a fault-tolerant characteristic. Meanwhile, the phase back electromotive force waveforms can be designed to be sinusoidal by employing PMs with a trapezoidal shape, eccentric armature teeth, and unequal tooth widths. The electromagnetic performance is comprehensively investigated and the optimal design is conducted by using the finite-element method.

Influence of the Slot and Pole Number Combination on the Eddy Current Loss of Permanent Magnet Machines

In this study, the influence of the combination of slot number and pole number of permanent magnet machines on the iron loss is mathematically investigated in order to obtain guidelines that can help reduce iron loss; such reduction can facilitate miniaturization and improve the efficiency. By simplifying the machine electromagnetic model, the iron loss can be evaluated for any combination of slot number and pole number. The distribution of the magnetomotive force on the stator teeth and its complex Fourier series expansion are obtained so that coordinate transform can be easily done and the rotor iron loss can thereby be calculated. A core factor is defined on the basis of the calculated iron losses, and a core factor map of slot and pole number combinations is prepared.

Five-Phase Modular External Rotor PM Machines with Different Rotor Poles: A Comparative Simulation Study

The performance of fault-tolerant modular permanent magnet machines depends on the proper selection of the pole and slot numbers which result in negligible coupling between phases. The preferred slot and pole number combinations eliminate the effect of low-order harmonics in the stator magnetomotive force and thereby the vibration and stray loss are reduced. In this paper, three external rotor machines with identical machine dimensions are designed with different slots per phase per pole ratios. A simulation study is carried out using finite element analysis to compare the performance of the three machines in terms of machine torque density, ripple torque, core loss, and machine efficiency. A mathematical model based on the conventional-phase-model approach is also used for the comparative study. The simulation study is extended to depict machine performance under fault conditions.

A Novel Hybrid-Excited Switched-Flux Brushless AC Machine for EV/HEV Applications

A novel E-core hybrid-excited switched-flux permanent-magnet (SFPM) brushless machine is proposed based on an E-core SFPM machine, which has significantly less magnet and higher torque density than those of a conventional SFPM machine. The proposed machine has a simple structure. The main flux path of dc excitation does not affect the magnet excitation because it is not through magnets. The combination of stator and rotor pole numbers of the proposed machine is optimized, and the flux-enhancing and flux-weakening capabilities are investigated by 2-D finite-element analyses and experimentally validated.

A Novel E-Core Switched-Flux PM Brushless AC Machine

A novel E-core switched-flux permanent-magnet (SFPM) brushless machine is proposed, and its electromagnetic performance is compared with that of the conventional SFPM brushless machine. The operation principle of the E-core SFPM machine will be first described, and the influence of stator and rotor pole number combinations is investigated, while the electromagnetic performance of the optimized E-core SFPM machine is predicted by finite-element analyses and validated by experiment. It is shown that the number and volume of magnets in the E-core SFPM machine is significantly reduced, only half of that in the conventional machine, while the phase back electromotive force and torque of the E-core machine are ~15% larger than those of the conventional machine.