Sinusoidal back-EMF Waveform Research Articles

Principle of Flux-Switching Permanent Magnet Machine by Magnetic Field Modulation Theory Part I: Back-Electromotive-Force Generation

The flux-switching permanent magnet (FSPM) machine has aroused wide interest recently due to high-power density, favorable PM cooling capability, and essentially sinusoidal electromotive-force (EMF) waveform per phase. Previously, the phase back-EMF generation mechanism of FSPM machines is exposed from a flux-switching perspective, however, which is rethought from the viewpoint of air-gap modulation magnetic field in Part I as in this article, and electromagnetic torque generation mechanism of FSPM machines will be reported in Part II as another sister paper. With the aid of magnetic field modulation theory, the air-gap PM magnetic field and back-EMF of the FSPM machine are modeled based on modulation and winding functions. Their characteristics are analyzed in detail and consequently, principles concerning FSPM machines on arbitrary stator-slot/ rotor-pole combinations can be obtained, including the basic feature of FSPM machines, the principle and necessary conditions for the back-EMF generation, the fundamental reason of sinusoidal back-EMF waveform, and the contributions of modulation harmonics to phase back-EMF. Finally, experimental verification on a 12s/10p prototyped machine is conducted.

A Novel Variable Flux Reluctance Generator for Vehicles

The general vehicle generators are claw-pole synchronous generators, which have the problems such as complicated processing technology of claw poles, low reliability of brushes and low operating efficiency. In this paper, a novel variable flux reluctance generator (VFRG) for vehicles is introduced and it is different from common reluctance machines. It has field coils on each stator pole and forms sinusoidal flux-linkage at each phase’s winding. Compared with general vehicle generators, it has the advantages of simple structure, strong robustness and high efficiency. The structure and operating principle are illustrated at first. Then a VFRG vehicle generator of 28V output voltage for 24V power systems is designed and optimized, which has low cogging torque as well as sinusoidal back-EMF waveforms. In addition, the characteristics and voltage ripple are obtained by simulation. And the technical specifications meet the requirements for a vehicle generator to work in a wide speed range. The results validate the applicability and superiority of VFRG to be a novel generator for vehicles.

Design of Doubly Complementary Stator-PM Machine With High Magnet Utilization Factor for Low-Cost Applications

Aiming to improve permanent magnet (PM) utilization factor, suppress cogging torque, and reduce back-EMF harmonics in stator-PM machines, a new type of stator-PM doubly complementary machines (DCMs) are proposed in this paper. These machines employ two complementarities in the structure, as one exists in double rotors and the other exists in the units belonging to same phases. The first complementary characteristic supplies a consecutive switching path for PM exciting flux, so that shorted or open magnetic path could be avoided to reduce cogging torque and improve PM utilization. The second one is designed to reduce back electromotive force (EMF) harmonics and improve the torque density. The topology, operation principle, characteristics, and design methodology for DCMs are presented. Simulation and experiments are conducted for a 12/11(stator teeth/rotor teeth) DCM to evaluate its performance and verify this design methodology. It is revealed that this machine could obtain good sinusoidal back-EMF waveform, small torque ripple, and high PM utilization factor due to the doubly complementary characteristic.

The Influence of Dummy Slots on Stator Surface-Mounted Permanent Magnet Machines

In this paper, the concept of harmonic permanent-magnet (PM) torque is defined and deduced first. Then, a conventional stator surface-mounted PM (SSPM) machine, namely, the 6/8 SSPM machine, is investigated. The finite element (FE) predicted and measured results reveal that the back electro-motive force (back EMF) of the 6/8 SSPM machine is asymmetrical, leading to large harmonic PM torques, cogging torque, and torque ripple. Hence, a 6/7 SSPM machine exhibiting coil complementarity is proposed afterward, which exhibits improved electromagnetic performances, such as lower cogging, more sinusoidal back EMF waveforms, and smaller harmonic PM torques, resulting in less torque ripple. After that, the influence of the dummy slots located in the center of two magnets on the same stator pole for the SSPM machines is investigated. The FE-predicted results indicate that the electromagnetic performances including cogging torque and torque ripple can be improved for the machines exhibiting coil complementarity, whereas for the machines having no coil complementarity, the performances will degrade further.

Back-EMF waveform optimization of flux-reversal permanent magnet machines

Due to the special doubly-salient structure, flux-reversal permanent magnet (FRPM) machines typically suffer from relatively large torque and speed ripples, as well as acoustic noise and vibration, especially at low speeds. As one of the main sources of torque ripples, harmonics in phase back electro-motive-force (EMF) should be suppressed as much as possible in order to produce a smooth torque. In this paper, an improved configuration of FRPM machine is proposed by introducing a small space-gap between the two adjacent magnets belonging to the same stator tooth to improve the symmetry of phase back-EMF waveform. The influence of the small space-gap on phase back-EMF waveform is evaluated by employing 2D finite element analysis (FEA), and consequently, an optimal value of space-gap for a more sinusoidal back-EMF waveform is obtained.

Design and Analysis of Novel Hybrid-Excited Axial Field Flux-Switching Permanent Magnet Machines

The axial field flux-switching permanent magnet machine (AFFSPMM) is a novel brushless AC machine. The magnets and concentrated windings are both in the stator instead of the rotor. The short axial length is beneficial to save the place of electric vehicles (EVs). Furthermore, the AFFSPMM exhibits the advantages of high power density and torque density. However, it is difficult to regulate the air-gap field since the field is produced by magnets alone. The fault-tolerant capability needs to be enhanced in the application of a direct-drive EV. Hence, a novel hybrid-excited AFFSPMM is proposed, in which the air-gap field can be easily regulated and the mutual inductance is largely reduced. In this paper, the design parameters of the novel machine, such as the split ratio, the rotor pole numbers, the rotor pole width, etc., are optimized in order to attain a sinusoidal back-EMF waveform and low cogging torque. Moreover, the static performance including each phase flux-linkage, inductance, and torque is analyzed on the basis of the 3-D finite-element method (FEM).

Design of Ultrahigh Speed Axial-Flux Permanent Magnet Machine With Sinusoidal Back EMF for Energy Storage Application

This paper focuses on the design and the analysis of an ultrahigh speed axial-flux permanent magnet (AFPM) machine for an aerospace flywheel energy storage system. The superiority of the proposed AFPM machine is the material-efficient PM shape, which contributes to obtain a sinusoidal back electromotive force (back EMF) and, hence, reduces the torque pulsations of the machine such as torque ripple. The harmonics present in back EMF have a large influence on iron loss and torque pulsations, which are always unacceptable in the applications involving the speed as high as 1 000 000 r/min. Analytical modeling is first performed to determine the PM shape for the proposed models. Then, the advantages of the proposed models are verified by comparing with the basic model with the conventional ring-shaped PMs using the 3-D finite-element method. The results show that the proposed models have a nearly ideal sinusoidal back-EMF waveform that significantly reduces the torque ripples compared with the basic model.

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.

Magnet asymmetry in reduction of cogging torque for integer slot axial flux permanent magnet motors

Cogging torque component is one of the key issues in the design of radial and axial gap permanent magnet motors and the geometry and the position of the magnets plays a critical role in this process. This study presents the influence of magnet asymmetry in minimisation of the cogging torque for axial flux permanent magnet (AFPM) disc motors. Cogging torque minimisation techniques, such as magnet skewing and magnet shifting or groping are examined in detail by using three-dimensional finite element analysis with various types of magnet skewing alternatives since the shaping and the positioning magnets are low cost approaches to minimise or eliminate the cogging component. A prototype AFPM disc motor is built with shifted magnets based on the models which are the results validated with the experimental results for the minimum cogging component and the sinusoidal back-EMF waveform. It is shown in this study that the cogging component in AFPM motors can be practically eliminated by using magnet asymmetry and perfectly sinusoidal back-EMF can also be obtained even for integer slot/pole/phase motors.

Sinusoidal Back-EMF of Vernier Permanent Magnet Machines

Sinusoidal back-EMF waveform of vernier Permanent Magnet (PM) machines is analyzed in this paper. An analytical expression of Electromotive Force (EMF) of electric machines including vernier machines is developed to analyze EMF harmonics, and the effect of vernier PM machine pole ratio, the ratio of number of rotor poles to stator poles, on the EMF waveform. Moreover, this paper represents several Finite Element Analysis (FEA) models to verify the analysis based on the proposed expression, and the effect of tooth width ratio, which is the ratio of tooth width to tooth pitch, on back-EMF of vernier PM machines, and optimal tooth width ratio is obtained and verified by FEA. Finally, this paper makes comparisons between EMF waveform of vernier PM machines and that of traditional PM machines from the point of view of analytical EMF expression.

A Novel Two-Phase Permanent Magnet Synchronous Motor Modeling for Torque Ripple Minimization

This paper proposes a novel two-phase, two-pole, permanent magnet synchronous motor (PMSM) with dual U-core stator structure for torque ripple minimization. The proposed motor is modeled based on the conventional single-phase U-core PMSM with approximate output power and core dimension. Torque ripple in the novel motor can be reduced significantly due to 90 $^{\circ}$ electrical angle phase shift in two sets of magnet pairs and 90 $^{\circ}$ shift in two-phase excitation currents. Characteristics of both PMSMs such as back-EMF, cogging torque and electromagnetic torque are analyzed and compared by using the 3-D finite element analysis (FEA). As shown in the result, the cogging torque and torque ripple in the novel two-phase PMSM are efficiently reduced with sinusoidal back-EMF waveform and reasonable current density value. The validity of both PMSM models is also verified by the comparison between simulated and experimental measured results.

Design, Analysis, and Prototyping of an Axial-Flux Permanent Magnet Motor Based on Genetic Algorithm and Finite-Element Analysis

This paper presents an axial-flux permanent magnet motor optimized by the genetic algorithm (GA)-based sizing equation and the finite-element analysis (FEA). The designed slotted TORUS motor produces sinusoidal back-EMF waveform, maximum power density, and reduced cogging torque. The GA obtained the dimensions of motors with different numbers of slots and the highest possible power density. Electromagnetic field analysis of the candidate motors obtained from GA with various dimensions is subjected through FEA to obtain the motors' characteristics. Based on the GA and FEA results, a candidate motor design is introduced and subjected to FEA for reoptimization and finalization of the motor design. Techniques like modifying winding configuration and permanent magnet skewing are investigated to attain the most sinusoidal back-EMF waveform and reduced cogging torque. FEA and GA simulation results are compared and agreed well to the flux density in various areas of the designed motor at no-load condition. The final designed motor (1 kW, 50 Hz, four poles) is fabricated and tested. Experimental results agree with those of the simulation, both satisfying the desired technical specifications.

DESIGN OPTIMIZATION AND ANALYSIS OF AFPM SYNCHRONOUS MACHINE INCORPORATING POWER DENSITY, THERMAL ANALYSIS, AND BACK-EMF THD

This paper presents the design and analysis of an inside-out axial-∞ux permanent-magnet (AFPM) synchronous machine optimized by genetic algorithm (GA) based sizing equation, flnite element analysis (FEA) and flnite volume analysis (FVA). The preliminary design is a 2-pole-pair slotted TORUS AFPM machine. The designed motor comprises sinusoidal back-EMF waveforms, maximum power density and the best heat removal. The GA is used to optimize the dimensions of the machine in order to achieve the highest power density. Electromagnetic fleld analysis of the candidate machines from GA with various dimensions is then put through FEA in order to obtain various motor characteristics. Based on the results from GA and FEA, new candidates are introduced and then put through FVA for thermal behavior evaluation of the designed motors. Techniques like modifying the winding conflguration and skewing the permanent magnets are also investigated to attain the most sinusoidal back-EMF waveform and reduced cogging torque. The performance of the designed 1kW, 3-phase, 50Hz, 4-pole AFPM synchronous machine is tested in simulation using FEA software. It is found that the simulation results fully agree with the designed technical speciflcations. It is also found from FVA results that the motor temperature reaches

Efficiency Comparison between Brushless DC Motor and Brushless AC Motor Considering Driving Method and Machine Design

This paper describes an approach to establish high efficient drive such a Brushless AC (BLAC) drive by a Brushless DC (BLDC) drive. BLDC drive which is excited rectangular voltage for 120 electrical degrees per cycle is commonly used for the low cost applications of Permanent Magnet Synchronous Motors (PMSMs). This drive method contains low-order harmonics in the current waveform. These harmonics cause a mechanical vibration and the electrical losses. Therefore, BLDC drive is not applicable to the sinusoidal back-EMF machines. However, considering about a high frequency loss by the PWM carrier and also about the switching loss, BLDC drive has a potential to have higher efficiency than the BLAC drive. This paper compares the overall efficiency which includes PWM carrier frequency loss by using the coupling analysis between Finite Element Analysis (FEA) and a circuit simulator. The tested machines are two of Surface type PMSMs (SPMSM). One has a sinusoidal back-EMF waveform (BLAC machine) and the other has a trapezoidal back-EMF waveform (BLDC machine). The both driving methods of BLDC drive and BLAC drive are adapted to each machine, their efficiencies are compared by both simulation and experiments. The results show that the BLDC machine with BLDC drive has higher efficiency than BLAC machine with BLAC drive.

A dual-channel flux-switching permanent magnet motor for hybrid electric vehicles

The flux-switching permanent magnet (FSPM) motor is a relatively novel brushless machine having both magnets and concentrated windings in the stator, which exhibits inherently sinusoidal PM flux-linkage, back-EMF waveforms, and high torque capability. However, in the application of hybrid electric vehicles, it is essential to prevent magnets and armature windings moving in radial direction due to the possible vibration during operation, and to ensure fault-tolerant capability. Hence, in this paper based on an original FSPM motor, a dual-channel FSPM (DC-FSPM) motor with modified structure to fix both armature windings and magnets and improved reliability is proposed for a practical 10 kW integral starter/generator (ISG) in hybrid electric vehicles. The influences of different solutions and the end-effect on the static characteristics, are evaluated based on the 2D and 3D finite element analysis, respectively. Finally, both the predicted and experimental results, compared with a prototype DC-FSPM motor and an interior PM motor used in Honda Civic, confirm that the more sinusoidal back-EMF waveform and lower torque ripple can be achieved in the DC-FSPM motor, whereas the torque is smaller under the same coil current.

A Novel 12/10 Electrical Excitation Flux-Switching Machine

A three phase, electrical excitation flux-switching (EEFS) brushless ac machine is proposed, its electromagnetic performance, viz., the phase flux-linkage and back-EMF waveforms, the torque density, the electromagnetic torque, and the torque-current characteristic, are evaluated based on finite element analysis. An EEFS machine exhibits sinusoidal flux-linkage and back-EMF waveforms. Compared with a hybrid excitation flux-switching (HEFS) machine, when de-excitation at fault is needed, the torque density of EEFS machine is ~20% larger than that of a HEFS machine with the same armature and field current copper loss.

Analysis of the Oversaturated Effect in Hybrid Excited Flux-Switching Machines

Flux-switching permanent magnet (FSPM) machine is a relatively novel brushless machine, which exhibits inherently sinusoidal PM flux-linkage, back-EMF waveforms and high torque capability. However, the air-gap field density is difficult to be regulated since it is produced by the stator magnets alone. Hence, hybrid-excited flux-switching (HEFS) machine is proposed by introducing a set of field windings into an original FSPM machine. However, in HEFS machines the flux linkages of armature windings vary in inverse proportion to the air-gap flux density when significantly saturated, which is different from the conventional machines. So in this paper, the oversaturated phenomenon in HEFS machines is explained and the effect of saturation, especially due to magnet material, on the relationship between air-gap flux density and armature flux linkage is investigated based on 2-D finite element analysis. Also, an effective stator-tooth-width coefficient (kstw) is defined to evaluate the oversaturated effect quantitatively.

Permanent-Magnet Shape Optimization Effects on Synchronous Motor Performance

The magnet shape in permanent-magnet (PM) synchronous motors substantially affects the back-electromotive-force (EMF) waveform and the stator iron losses, which are of particular importance in traction applications, where the energy available in the battery box is limited. This paper presents a methodology based on geometry optimization, providing sinusoidal back-EMF waveform. The method has been applied in a surface PM motor case for electric vehicle, and its validity has been checked by measurements on two prototypes, the first one with constant magnet width and the second one with optimized magnet shape.

GENETIC ALGORITHM AND FINITE ELEMENT ANALYSIS FOR OPTIMUM DESIGN OF SLOTTED TORUS AXIAL-FLUX PERMANENT-MAGNET BRUSHLESS DC MOTOR

This paper presents an inside-out axial-∞ux permanent- magnet brushless DC motor optimized by Finite Element Analysis (FEA) and Genetic Algorithm (GA) that uses sizing equation. The double-sided slotted-stator designed TORUS motor has sinusoidal back EMF waveform and maximum power density. The GA obtained the dimensions that gave the motor its highest power density. Field analysis of the dimensions was then put through FEA, to obtain and re-optimize the motor's characteristics. Possible design parameters were investigated via use of Commercial Vector Field Opera 14.0 software used in three-dimensional FEA simulation and of MATLAB 2010a in GA programming. Techniques such as modifying winding conflguration and skewing the permanent magnets were explored to achieve the most-sinusoidal back-EMF waveform and minimized cogging torque. The desired technical speciflcations were matched by simulation results of the 3D FEA and the GA. The FEA and the GA simulation results comparison of the ∞ux density in difierent parts of the designed motor at no-load condition agreed well.

Torque Ripple Suppression in Flux-Switching PM Motor by Harmonic Current Injection Based on Voltage Space-Vector Modulation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The flux-switching permanent-magnet (FSPM) machine is a relatively novel brushless machine having magnets and concentrated windings in the stator instead of rotor, which exhibits inherently sinusoidal back-EMF waveform and high torque capability. However, due to the high airgap flux density produced by magnets and the salient poles in both stator and rotor, the resultant torque ripple is relatively large, which is unfavorable for high performance drive system. In this paper, instead of conventional optimization on the machine itself, a new torque ripple suppression approach is proposed in which a series of specific harmonic currents are added into <formula formulatype="inline"> <tex Notation="TeX">$q$</tex></formula>-axis reference current, resulting in additional torque components to counteract the fundamental and second-order harmonic components of cogging torque. Both the simulation and experimental results confirm that the proposed approach can effectively suppress the torque ripple. It should be emphasized that this method is applicable to all PM machines having relatively large cogging torque. </para>