Slot Number Combinations Research Articles

Optimal Pole Number and Winding Designs for Low Speed–High Torque Synchronous Reluctance Machines

This paper studies the feasibility of using synchronous reluctance machines (SynRM) for low speed–high torque applications. The challenge lies in obtaining low torque ripple values, high power factor, and, especially, high torque density values, comparable to those of permanent magnet synchronous machines (PMSMs), but without resorting to use permanent magnets. A design and calculation procedure based on multistatic finite element analysis is developed and experimentally validated via a 200 Nm, 160 rpm prototype SynRM. After that, machine designs with different rotor pole and stator slot number combinations are studied, together with different winding types: integral-slot distributed-windings (ISDW), fractional-slot distributed-windings (FSDW) and fractional-slot concentrated-windings (FSCW). Some design criteria for low-speed SynRM are drawn from the results of the study. Finally, a performance comparison between a PMSM and a SynRM is performed for the same application and the conclusions of the study are summarized.

Analytical Prediction and Optimization of Cogging Torque in Surface-Mounted Permanent Magnet Machines With Modified Particle Swarm Optimization

An analytical method is proposed to predict and optimize cogging torque accurately. It is derived by the exact subdomain model, equivalent current sheet of magnet, and modified particle swarm optimization (PSO), in surface-mounted permanent magnet machines (SPMs) accounting for the effect of stator slotting and tooth-tips. The analysis works for internal/external rotor motor topologies, radial/parallel magnetization, as well as for any combinations of pole and slot numbers. Then, four important design parameters, viz. magnet thickness, air-gap length, slot-opening to slot pitch ratio, and pole-arc to pole-pitch ratio, are adopted as optimal variables, and the peak of fundamental order of the radial component of the air-gap flux density is constrained to optimize cogging torque by modified PSO based on forgoing model. Finally, the cogging torque of two prototype machines with both radial and parallel magnetizations is optimized notably. The paper validates the results of analytical prediction by finite-element analysis.

Analysis of Back-EMF Waveform of a Novel Outer-Rotor-Permanent-Magnet Flux-Switching Machine

In this paper, a novel outer-rotor-permanent-magnet flux-switching (ORPMFS) machine is proposed and analyzed. First, the geometric topology of the ORPMFS machine is introduced. Then, the PM-excited magneto motive force and open-circuit air-gap flux density are analyzed. Throughout the analysis, the ORPMFS machine is found to have the same air-gap flux density waveform as surface-mounted permanent magnet machine. Furthermore, the analytical equation of the back-electromotive force in the ORPMFS machine is deduced. Then, based on the analytical equation, different combinations of stator slot and rotor pole numbers are evaluated. Finally, the analytical results are verified by 2-D finite element analysis results.

Effect of pole number and slot number on performance of dual rotor permanent magnet wind power generator using ferrite magnets

Dual rotor permanent magnet (DRPM) wind power generator using ferrite magnets has the advantages of low cost, high efficiency, and high torque density. How to further improve the performance and reduce the cost of the machine by proper choice of pole number and slot number is an important problem to be solved when performing preliminarily design a DRPM wind generator. This paper presents a comprehensive performance comparison of a DRPM wind generator using ferrite magnets with different slot and pole number combinations. The main winding factors are calculated by means of the star of slots. Under the same machine volume and ferrite consumption, the flux linkage, back-electromotive force (EMF), cogging torque, output torque, torque pulsation, and losses are investigated and compared using finite element analysis (FEA). The results show that the slot and pole number combinations have an important impact on the generator properties.

Difference in unbalanced magnetic force of fractional-slot PM machines between interna and external rotor topologies

This paper presents a comparative investigation into unbalanced magnetic force (UMF) of asymmetric permanent magnet machines without rotor eccentricities, particularly focusing on the difference between internal- and external-rotor topologies. The asymmetric field distribution results in radial and tangential asymmetric force waves. Although the radial and tangential stresses are in different direction, the UMF components they produce are nearly aligned. The UMF from asymmetric radial force wave can be additive or subtractive to that from asymmetric tangential force wave. Investigation shows that for the same pole slot number combination, if the UMFs due to radial and tangential force waves are additive in internal rotor machine, they are subtractive in the external rotor counterpart, and vice versa. Investigation reveals a general rule determining whether additive or cancelling: for a UMF produced by any two field harmonics, they are additive if the higher order is produced by the outer part outside the airgap, but cancelling if the higher order is produced by the inner part. Therefore, for a machine with pole number 2p=3k+1, they are additive if it is an external-rotor machine, but otherwise subtractive. On the other hand, for a machine with pole number 2p=3k−1, they are subtractive if it is an external-rotor machine, but otherwise additive. For the UMF due to armature reaction only, they are subtractive for external-rotor machines, but otherwise additive. The investigation is carried out by an analytical model and validated by finite element analysis.

Investigation of Voltage Distortion in Fractional Slot Interior Permanent Magnet Machines Having Different Slot and Pole Number Combinations

This paper investigates the terminal voltage distortion in the interior permanent magnet machines with fractional slot concentrated windings, with particular emphasis on the influence of stator slot Ns and rotor pole 2 p combinations. The 12-slot/10-pole machine is first employed to show the voltage distortion phenomenon. Using the frozen permeability method, the mechanism is then investigated, which reveals that the variation of armature flux paths due to rotor saliency is the origin of such phenomenon, especially when the current advancing angle $\beta $ approaches 90°. Further, the terminal voltage distortion of the six machines are compared, i.e., ${N_s} \pm 1 = 2p$ (9-slot/8-pole, 9-slot/10-pole), ${N_s} \pm 2 = 2p$ (12-slot/10-pole, 12-slot/14-pole), ${N_s}/2p = 3/2$ (12-slot/8-pole), 3/4 (12-slot/16-pole), which shows that the machines with ${N_s} suffer more severe voltage distortion than their counterparts with ${N_s} > 2p$ . In addition, considering the inevitable machine saturation, a design trade-off is proposed by selecting proper ${N_s}/2p$ combinations to minimize the influence. Finally, prototypes are fabricated and tested to validate the analyses.

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.

A Comprehensive Analytical Subdomain Model and Its Field Solutions for Surface-Mounted Permanent Magnet Machines

This paper presents a comprehensive analytical subdomain model together with its field solutions for predicting the magnetic field distributions in surface-mounted permanent magnet (PM) machines. The tooth tips and slotting effects during open-circuit, armature reaction, and on-load conditions are considered when deriving the model and developing its solutions. The model derivations and field solutions are extended from a previous model, and can be applied to PM machines with any combinations of slot and pole numbers and any magnetization patterns in the magnets. This model is initially formulated according to Laplace's and Poisson's equations in 2-D polar coordinates by the separation of variables technique in four subdomains, such as magnet, airgap, winding slots, and slot-openings. The field solution of each subdomain is obtained applying the appropriate boundary conditions and interface conditions between every two subdomains, respectively, which can precisely account for the mutual influence between slots. Finite element analysis (FEA) is later deployed to validate the analytical results in a surface-mounted PM machine that has nonoverlapping winding arrangement. For validation purposes, PM machines having 3-slot/2-pole with parallel magnetization and 12-slot/10-pole with either parallel or radial magnetizations are used for comparisons. Computation of global quantities for the motor which include the phase back-EMF and cogging torque is also included. The results indicate that the proposed analytical model can accurately predict the magnetic field distributions in each subdomain and the motor's global quantities, which are in good agreement with those obtained from the FEA.

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.

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.

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.

Investigation of winding topologies for permanent magnet in‐wheel motors

Purpose – This paper aims to find the optimal winding topology for a 14‐pole permanent magnet synchronous motor (PMSM) to be used as an in‐wheel motor in automotive applications.Design/methodology/approach – Comparison is first performed among lap windings with different combinations of slot numbers and pole numbers. A general method for calculating the winding factors using only these numbers is proposed, thus the preferable slot numbers resulting in relatively large winding factors for this 14‐pole PMSM are found. With these slot numbers, the Joule losses of armature windings are further investigated, where the impacts of different end‐winding lengths are considered. By this means, the optimal slot number that causes the least Joule loss is obtained. On the other hand, as a competitor to lap windings, toroidal windings are also discussed. The thermal performances of these two types of windings are compared by performing a finite element analysis (FEA) on their 2‐D thermal models.Findings – For the 14‐po...