Slot Number Combinations Research Articles

Selection of induction motor stator and rotor slot number combination for optimal NVH

With the rise of vehicle electrification, considerable research has been directed towards reducing motor noise, predominantly focusing on Permanent Magnet Synchronous Motors (PMSM). Despite the increasing popularity of the induction motor, driven by its reliability, cost-effectiveness, and lower environmental impact, discussions surrounding the Noise, Vibration, and Harshness (NVH) aspects of induction motors remain limited. This paper addresses the NVH implications associated with stator and rotor slot combinations in conventional squirrel-cage induction motors. Through a design parametric study that examines the impact of varying the number of rotor bars through analytical simulation, the findings not only identify the optimal slot combination for minimizing motor noise but also demonstrate the critical importance of selecting the proper slot configuration, as NVH performance can exhibit significant variations. A physical test was conducted to validate the analytical simulations. This research contributes valuable insights into the induction motor design, especially at the early design stage, emphasizing the necessity of considerations in achieving enhanced NVH performance.

Influence of Slot and Pole Number Combinations on Cogging Torque in PM Machines With Interaction of Tooth Bulge and Rotor Eccentricity

Influence of Slot and Pole Number Combinations on Cogging Torque in PM Machines With Interaction of Tooth Bulge and Rotor Eccentricity

Electro-Mechanical Characteristics of Dual-Winding Motor According to Winding Arrangement for Brake Systems in Highly Automated Driving Vehicles

Manufactures of automotive parts are struggling to secure redundancy in various ways. An alternative is to configure the system via a dual-winding motor and two electronic control units (ECUs). The dual-winding motor contains different winding arrangements according to poles/slots, and when only one of the two circuits is used owing to a failure, the electrical and mechanical characteristics differ depending on the winding arrangement. In this study, the electrical and mechanical characteristics were analyzed and compared according to the winding arrangement when the failure occurs. In particular, the winding arrangement of the motor is divided into line symmetry, point symmetry, and alternating symmetry. For each winding arrangement, the back-electromotive force, torque, and torque ripple were compared and analyzed through simulation and test. Also, vibration caused by electromagnetic force was analyzed. Here, to consider the tooth modulation effect, concentrated force was investigated and tangential force as well as radial force were considered. Additionally, the thermal characteristics were analyzed during fault operation using a lumped parameter thermal network with piecewise stator-housing modules. Lastly, the mechanical design characteristics of the motor hardware size that need to be changed according to the winding arrangement of the brake motor are explained. This study provides guidelines for the winding arrangement selection of a dual-winding motor with a similar magnetic field distribution suitable for the design purpose, by analyzing the electromechanical characteristics and size according to the winding arrangement during fault operation. The characteristics of other motor types or pole and slot number combinations can also be inferred from the results of this study, since the magnetic flux density distribution will be determined with line, point and alternating symmetry.

Design of Limited-Angle Wound Rotor Resolvers for High Accuracy and Easy Manufacturability

The limited-angle resolver is commonly employed instead of an optical encoder as a position sensor in medical, special industrial, custom robotics, transportation and military applications owing to their reliability, low cost, and ability to work steadily in harsh and contaminated environments. In the design and optimization of resolvers, achieving high precision while maintaining a simple manufacturing process for mass production is a big challenge. This study proposes a systematic method for the determination of slot and pole number combinations of limited-angle wound rotor resolvers (LAWRRs) for high accuracy and easy manufacturability. A set of stator and rotor slot numbers ranging from 8–64 for 2 and 4 poles, which are suitable for concentric winding (CW) topology, have been considered. For high accuracy, number of turns distribution waveforms and their total harmonic distortion (THD) percentages are investigated. In addition, for easy manufacturability, low slot number combinations providing high accuracy are determined and the feasibility of employing solid core instead of laminated core is examined. Analytical calculation results of the proposed configurations are validated utilizing a two-dimensional time-stepping finite-element analysis (2D-FEA). Finally, in order to experimentally validate the methodology and analyses, two prototypes with low and high slot numbers are manufactured and tested.

Analysis and Reduction of Pole-Frequency Vibration of Surface Mounted Permanent Magnet Synchronous Machines With Fractional Slot Concentrated Winding Considering the Radial and Tangential Forces

The pole-frequency vibration is significant in permanent magnet synchronous machines (PMSMs) with various pole and slot number combinations, and its weakening is difficult. For conventional analysis in literature, only radial force is considered as the excitation source of pole-frequency vibration. In this paper, the causes of the pole-frequency vibration are considered as the collaborative action of radial and tangential forces, and an optimization method of the piecewise stagger unequal poles is proposed for the reduction of the pole-frequency vibration of the surface mounted permanent magnet synchronous machines (SPM) with fractional slot concentrated winding (FSCW). First, taking a 10-poles 12-slots PMSM as an example, the deep cause of the vibration caused by radial and tangential forces are analyzed, respectively. Then, the optimized structure of piecewise stagger unequal poles is shown, and radial force, tangential force, and vibration spectrum between the common and proposed motors are compared with the finite element model (FEM). The results show that the piecewise stagger unequal poles structure can effectively weaken the pole-frequency vibration while ensuring the torque density. Finally, the vibration experiment of the two prototypes is carried out, and the effectiveness of the optimized structure is verified.

Design Method and Performance Evaluation of Modular Multiphase PMSM with Hybrid Single/Double Layer Fractional-Slot Concentrated Winding

This paper proposes a general design method of modular multiphase permanent-magnet synchronous machine with hybrid single/double layer (HL) fractional-slot concentrated winding (FSCW), which indicates that double-layer (DL) FSCW machines satisfying two preconditions can be transformed into HL FSCW machines. HL FSCW machines with different slot and pole number combination are designed to prove the feasibility and universality of the proposed method. Performance of single-layer (SL) FSCW machine, DL FSCW machine, and HL FSCW machine are compared, from aspects of magnetomotive force, back electromotive force, average torque, torque ripple, core loss, eddy current loss in PMs (PM loss), efficiency, cogging torque, and flux density distribution. Besides, phase-to-phase magnetic isolation of HL FSCW machine, indicating by flux lines distributions and phase-to-phase mutual inductances, is also researched. HL FSCW machine has advantages of higher torque, lower PM loss, higher efficiency, better phase-to-phase thermal, physical and magnetic isolation compared with SL FSCW machine and DL FSCW machine.

Investigation of Torque Ripple in an Induction Motor with Respect to Slot Number Combinations

In this study, the harmonic orders of varying magnetic flux density with respect to slot combinations are scrutinized through a spatial and temporal fast Fourier transform. A three-phase four-pole induction motor is selected, and, as its base model, 36 and 28 slots are set up in the stator and rotor, respectively. Eleven models with different numbers of rotor slots were designed to study torque ripples with respect to slot combinations. The correlation between torque ripple and slot harmonics in a stator and rotor is described thoroughly by comparing the tangential and radial magnetic flux densities in the air gap, tangential force density, and harmonic orders in torque. Some models having deteriorated torque ripples have one or more slot harmonic orders in common in the stator and rotor. The other models exhibit the same commonalities, but a small torque ripple occurs because of the high harmonic orders. Models with 24 stator slots are investigated through the same procedure to generalize the relationship between torque ripple and slot harmonics in 36 stator slots.

Influence of Stator Slot and Rotor Pole Number Combination on Field Winding Induced Voltage Ripple in Hybrid Excitation Switched Flux Machine

The induced voltage ripple in DC field windings can cause many problems in hybrid excitation machines (HEMs). It can generate ripple current in field winding, thus causing unsteady magnetic field excitation and hence additional torque ripple and losses. Besides, the torque and power density of hybrid excitation machines may be deteriorated as a result of the influence of the induced voltage ripple on field winding's excitation circuit, particularly under high-speed conditions. Based on a hybrid excitation switched flux machine (HESFM), the influence of stator slot and rotor pole number combination on no-load and on-load field winding induced voltage ripples are studied and compared by the finite element method (FEM). It reveals that the harmonic content and thus the peak-to-peak value of the field winding induced voltage ripple are closely related to the stator slot and rotor pole number combination at both no-load and on-load operating conditions. The FEM calculations are verified by experiments on a prototype HESFM.

Generic Slot and Pole Number Combinations for Novel Modular Permanent Magnet Dual 3-Phase Machines With Redundant Teeth

In order to provide the general guidance in constructing the novel modular machines with redundant teeth, the available slot and pole number combinations based on the balanced conditions are summarized in this article. After the brief review of the machine structure, the general slot and pole number combinations are listed: Firstly, the conventional modular machines used to construct the proposed modular machines need to possess integer times of 3 repetitive machine units. Each machine unit should construct as a 3-phase type. Then, a redundant machine unit providing the redundant teeth for modularity is necessary. This redundant machine only has one pole pair to make sure the space waste is minimal. The slot number of this redundant machine is determined by the greatest common divisor of the slot and pole pair numbers of the conventional modular machine. Finally, the combination of the conventional modular machine and the redundant one generates the proposed modular machine. In order to clearly illustrate the influence of slot and pole number combinations on machine performance, four combinations are chosen as examples to be compared. A 42-slot/32-pole machine is prototyped and tested to validate the analyses.

Electromagnetic Vibration Analysis of High-Speed Permanent Magnet Synchronous Machines With Amorphous Metal Stator Cores Considering Current Harmonics

This article investigates the electromagnetic vibration characteristics of high-speed (HS) permanent magnet synchronous machines (PMSMs) with amorphous metal stator cores (AMSCs) considering current harmonics. First, an analytical model of radial forces in PMSMs considering current harmonics due to both nonsinusoidal back electromotive force and pulsewidth modulation effects is developed. The cross influences of the two types of current harmonics on vibrations of HS PMSMs in different frequency bands are discussed. Second, the equivalent elasticity modulus parameters of laminated AMSCs are identified by utilizing modal experiment. Third, the influences of slot and pole number combinations on magnetic field harmonic contents and radial force orders for HS PMSMs are investigated by the analytical model. Then, the radial forces of a 15-kW HS PMSM fed by ideal sinusoidal current and experimental current are calculated under different rotational speeds by finite-element method. Finally, the vibrations of the prototype under rated torque and different rotational speeds are tested to verify the theoretical analysis.

Comparative Study of Modular Dual 3-Phase Permanent Magnet Machines With Overlapping/Non-overlapping Windings

For modular permanent magnet (PM) machines with overlapping (OLP) windings widely employed in wind power generation, the large torque ripple and long end winding are major issues. In order to solve these problems, PM machines with non-overlapping (NOLP) windings and redundant teeth for easy modularity are proposed in this paper. The comparative study between modular machines with these two kinds of windings is necessary and is the major focus of this paper. For the sake of clarity, two modular dual 3-phase machines with 42-slots/32-poles (42S/32P) and 192S/32P combinations are chosen as examples to show the differences in terms of machine performance. The proposed 42S/32P modular machine adopts NOLP winding, while the conventional 192S/32P one uses the OLP type. Based on the results, it is found that the modular machine with NOLP winding has comparable average torque and efficiency. In the meantime, much lower torque ripple exists for the proposed modular machine regardless of the current value. The shorter and simpler end windings are beneficial to manufacturability. Moreover, the proposed modular machine with NOLP winding will be more fault tolerant due to smaller mutual inductances between phases and larger d -axis inductance. Finally, the proposed 42S/32P modular machine is prototyped and the experiments validate the correctness of the analyses in this paper. Despite two specific examples being used, the conclusion should be generic and can be employed to modular machines with other slot and pole number combinations.

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.

Magnetically Geared Pseudo Direct Drive for Safety Critical Applications

This paper presents an investigation into the electromagnetic design and performance of a fault-tolerant (FT) magnetically geared pseudo-direct-drive (PDD) electrical machine for primary flight control surface electromechanical actuation. It is shown that a large number of combinations of high-speed rotor pole pairs, pole-piece numbers, and stator slot numbers exist, for which a duplex three-phase FT configuration can be realized. Furthermore, in addition to facilitating a lower mass solution, it is also shown that a PDD presents a significantly lower inertia referred to the screw when compared to direct-drive or mechanically geared motor solutions. The findings are validated on a prototype PDD, which has been designed and built to meet the requirements of a primary control surface electromechanical actuator.

Space Harmonics Elimination for Fractional-Slot Windings With Two-Slot Coil Pitch

Recently, fractional-slot windings with two-slot coil pitch are receiving more and more attention due to their lower space harmonic contents in stator magnetomotive force (MMF) compared with the widely-used fractional-slot nonoverlapping counterparts. To further reduce the detrimental space harmonics for this type of winding, various solutions featured by varied coil turn ratios are investigated in this paper. Firstly, all the feasible slot and pole number combinations for fractional-slot windings with two-slot coil pitch are discussed. Secondly, two types of Slot Harmonic Only Windings (SHOW), i.e., SHOW I and SHOW II, are illustrated on the 18-slot/10-pole (18S10P) and 24S10P windings, through which only the main harmonic and its slot harmonics will be present in stator MMF harmonics. Then, to overcome the drawback of reduced main harmonic magnitude owing to both the decreased winding factor and poor slot area utilization associated with the SHOW, two solutions, i.e., 6-0 solution and 5-1 solution for 18S10P and four alternatives, i.e., 7-1 solution, 6-2 solution, 5-3 solution and 4-4 solution for 24S10P, are proposed based on the SHOW I or SHOW II. It is found that the 5-1 solution for 18S10P and 5-3 solution for 24S10P winding are the most desirable ones considering the tradeoff between larger main harmonic magnitude and lower harmonic contents. Furthermore, electromagnetic performance comparisons are carried out between 24S10P permanent magnet (PM) machines with 5-3 solution and 12S10 two layer and 24S10P two layer machines. Although the average torque of the 24S10P machine with 5-3 solution has a slight decrease, its torque ripple and radial magnetic force density rotor eddy-current losses are greatly suppressed compared with the two layer counterparts.

The Method for Reducing Intrinsic Shaft Voltage by Suitable Selection of Pole-Arc Coefficient in Fractional-Slot Permanent-Magnet Synchronous Machines

This paper presents a method to quickly and accurately deduce the optimal pole-arc coefficient for achieving the maximum suppression of intrinsic shaft voltage in fractional-slot permanent-magnet synchronous machines (FSPMSMs). First, with the aid of the analytical method, not only the pole and slot number combinations which can yield the intrinsic shaft voltage in FSPMSMs but the analytical expression of the intrinsic shaft voltage are derived. Then, the effect of pole-arc coefficient on the intrinsic shaft voltage is investigated, and an optimal pole-arc coefficient which can minimize the intrinsic shaft voltage is calculated. Furthermore, the analytical results are validated by finite element method (FEM) well in 6-pole/9-slot, 8-pole/9-slot, and 8-pole/12-slot FSPMSMs, which indicates that the differences obtained between the optimal pole-arc coefficients by two methods are all less than 10%. In conclusion, considering the rapidity of the analytical method and the precision of the FEM, the analytical method should be used first to deduce an initial value to compress the interval of optimization, then run the calculation iteratively by the FEM to get the exact optimal pole-arc coefficient.

Suppression of Even-Order Harmonics and Torque Ripple in Outer Rotor Consequent-Pole PM Machine by Multilayer Winding

The fractional slot concentrated winding consequent pole (CP) permanent magnet (PM) synchronous machines can improve the PM utilization ratio. However, the even-order harmonics exist in phase back electromotive forces (EMFs) for specific slot and pole number combinations, resulting in high torque ripple. Therefore, the multilayer winding is employed in this paper to reduce the torque ripple by suppressing the even-order harmonic back EMFs. The principles of both even-order harmonic back EMFs and torque ripple suppression by the four-layer windings are illustrated. The electromagnetic characteristics of the CP PM machine with four-layer windings are compared with that of PM machines with the traditional and CP rotors by finite-element analysis. It is demonstrated that the four-layer winding can suppress the even-order harmonic back EMFs and torque ripple in the machine with CP rotor. The prototypes of both the traditional rotor and CP rotors with four-layer wingdings are manufactured and tested to verify the theoretical analysis.

Analytical Performance Calculation of Vernier Hybrid Machine with Subdomain Method

The analytical subdomain models of vernier hybrid machines with two kinds of permanent magnet (PM) arrangements are developed, and the magnetic vector potentials are considered unknown variables to obtain the no-load and on-load magnetic field in this article. According to the electromagnetic properties and machine structure, the entire solving region is divided into five subdomains, namely the stator slot, slot opening, PM, air gap, and rotor slot. Using the general solutions of magnetic vector potentials and boundary conditions, the magnetic field distributions of all subdomains are obtained. Then the air gap flux density, flux linkage, back-EMF, cogging torque, electromagnetic torque, unbalanced magnetic pulls, and PM loss are calculated and compared for the two models. With the analytical model, the PM demagnetization withstand capacity, effects of main parameters on the torque ripple and average torque, and combinations of PM and rotor slot numbers are also studied. The 2D finite element method and experimental results of two prototype machines validate the accuracy of the analytical models.

The Examination of Slot and Pole Number Combinations of Consequent-Pole-Type Ferrite PM Axial Gap Motor with DC Field Windings

The Examination of Slot and Pole Number Combinations of Consequent-Pole-Type Ferrite PM Axial Gap Motor with DC Field Windings

Analytical Electromagnetic Performance Calculation of Vernier Hybrid Permanent Magnet Machine

The analytical model of vernier hybrid permanent magnet machines (VHPMMs) with two different permanent magnet (PM) arrays is proposed in this paper. The working principles of VHPMM are discussed based on the magnetic field modulation theory, and the main rotating harmonics of air-gap flux density are determined. The subdomain method is adopted to obtain the no-load and on-load air-gap flux densities of the slotless model, and the relative permeance model is used to consider the effect of the slot opening. Using fast Fourier transformation, the amplitudes and phase angles of the rotating harmonics are obtained, and the flux linkage, back electromotive force, and electromagnetic torque are calculated. With the working principles and performance calculation model, the determination method of the rotor slot number is proposed, and feasible combinations of PM and rotor slot numbers are studied. The analytical model is verified via the finite-element method and prototype machine experiments.

Modeling and Investigation on Electromagnetic Noise in PM Motors With Single- and Double-Layer Concentrated Winding for EV and HEV Application

The radial force and the torque pulsation are identified as two main causes of electromagnetic noise and vibration in permanent magnet (PM) motors for electric vehicle (EV) and hybrid EVs systems. The aim of this paper is to systematically investigate the influence of pole and slot number combinations on noise and vibration characteristics of fractional-slot PM motors with either single- or double-layer concentrated windings. Preferentially, the explicit magnetic field equations are developed for analyzing the radial vibration force and the torque pulsation by the aid of Schwarz-Christoffel conformal mapping. Subsequently, an in-depth investigation of pole ( $2p$ ) and slot ( $Q_{s}$ ) number combinations is carried out to provide a detailed finding of noise behaviors due to the electromagnetic origins. The investigation on the electromagnetic noise is performed depending on the several major $S_{\mathrm{ pp}}$ families. Finally, the relationship between the vibration mode order and the torque variation is established to provide the comprehensive characteristics of the electromagnetic noise.