back-EMF Waveform Research Articles

A Linear Doubly Salient Permanent-Magnet Motor With Modular and Complementary Structure

A linear doubly salient permanent magnet (LDSPM) motor is particularly suitable for long stator applications due to its simple and low cost stator, which consists of only iron. This paper proposes a new LDSPM motor design with complementary and modular structure. The key of this structure is that the primary mover is composed of two modules whose positions are mutually four and one half of the stator pole pitch apart and there is a flux barrier between them. Hence, the back electromotive force (EMF) waveform and cogging force of the two modules have 180 electrical degree differences. This design results in the total cogging force being significantly reduced and the back-EMF of each phase becoming symmetrical because the even harmonics are canceled. For fair comparison, an existing linear LDSPM motor is designed based on the same electromagnetic parameters and compared by the means of finite element analysis (FEA). The results reveal that the proposed LDSPM motor can offer symmetrical back-EMF waveforms, smaller cogging force, lower force ripple, and higher magnet utilization factor than the existing one.

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.

Rotor Position Phase Correction for Sensorless Brushless DC Motor Based on Line Back EMF

This paper proposes a novel rotor position estimation method based on line back EMF for brushless DC motor (BLDCM). The relationship between position phase error and the symmetric line back EMF is analyzed. It is noted that line back EMF error can exactly reflect rotor position phase error. If the amplitude of line back EMF at the beginning of commutation is equal to the amplitude of line back EMF at the end of commutation, the waveform of line back EMF should be symmetric. Based on the above analysis, a closed loop control method to correct rotor position phase is presented. Line back EMF error is employed to keep the waveform of line back EMF symmetrical by PI controller. This paper also develops a sensorless BLDCM driver to implement the proposed method based on DSP and the experimental results prove the validity of the proposed method.

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.

Design and Comparison of Vernier Permanent Magnet Machines

Vernier permanent magnet (VPM) machines can be utilized for direct drive applications by virtue of their high torque density and high efficiency. The purpose of this paper is to develop a general design guideline for split-slot low-speed VPM machines, generalize the operation principle, and illustrate the relationship among the numbers of the stator slots, coil poles, permanent magnet (PM) pole pairs, thereby laying a solid foundation for the design of various kinds of VPM machines. Depending on the PM locations, three newly designed VPM machines are reported in this paper and they are referred to as 1) rotor-PM Vernier machine, 2) stator-tooth-PM Vernier machine, and 3) stator-yoke-PM Vernier machine. The back-electromotive force (back-EMF) waveforms, static torque, and air-gap field distribution are predicted using time-stepping finite element method (TS-FEM). The performances of the proposed VPM machines are compared and reported.

A New Fault-Tolerant Permanent-Magnet Machine for Electric Vehicle Applications

This paper proposes a new fault-tolerant permanent-magnet (PM) brushless machine for four-wheel independently driven electric vehicles (EVs). The key of the proposed machine is to make tooth widths unequal of inner stator, hence, offering more trapezoidal back-EMF waveform. Due to the fact that the radial PMs are embedded in the outer rotor, the proposed machine incorporates the merits of high torque-to-weight ratio, mechanical robustness, and high air-gap flux density. In addition, multiphase and single-layer fractional slot concentrated windings are employed to improve the reliability. The electromagnetic characteristics of the proposed machine are analyzed by using the time-stepping finite-element method (FEM) and field-circuit cosimulation method, such as magnetic field distribution, flux destiny, flux linkage, and torque, verifying the effectiveness of the theoretical analysis.

End-effect of the permanent-magnet spherical motor and its influence on back-EMF characteristics

The permanent-magnet (PM) spherical motor has special configuration and complicated distribution of electromagnetic field. The spatial distribution of the effective flux density produced by permanent magnets is obtained, and the end-effect of the permanent magnets is analyzed. In the 3-dimensional (3-D) finite element (FE) analysis, the calculation of Back-EMF characteristics of the PM spherical motor needs to be conducted by steps, which leads to large computational burden. A novel analyzing method to quantize the end-effect of the PM spherical motor is proposed, that is, the end-effect coefficient of the PM spherical motor is calculated to revise the back-EMF waveform obtained from the 2-D FE model. Under different outer radii of the stator coil and different pole arc coefficients of the PM spherical motor, the revised 2-D results are validated by the results obtained from the 3-D FE model and the experimental results. With this method, the special structural feature of the PM spherical motor is fully considered; the pure 3-D calculation of electromagnetic field is conducted only once; higher precision and less computational burden can be achieved. The method provides a new approach to investigating the back-EMF characteristic of the PM spherical motor.

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.

Optimum Design of Slotted Axial Flux Internal Stator Motor Using Genetic Algorithm for Electric Vehicle

Axial flux permanent magnet motors having a dual air-gap configuration have been designed and constructed to achieve high power density and used in industries interestingly and specially in the system of driving electrical vehicles. In this paper, the equation related to the design and dimensions of double-sided slotted axial flux synchronous motor with internal stator (TORUS) will be investigated. Then, an optimum design based on genetic algorithm with the purpose of increasing power density is presented. Twodimensional finite-element analysis (FEM) is used to demonstrate these optimization and its results will be presented. Finally, it presents the resultant back emf waveform and current for a 1.0 kW, 48 V, 50 Hz, 4poles/15-slots TORUS slotted axial motor prototype, based on our optimization techniques .

Transients of electrical and mechanical quantities of a brushless DC motor - computations, measurements

Transients of electrical and mechanical quantities of a brushless DC motor - computations, measurements The paper presents a method of computing electrical and mechanical variables of BLDC motors. It takes into account electrical, magnetic and mechanical phenomena in the power supply-converter-BLDC motor-load machine system. The solution to the problem is the so-called circuit-field method. The results determined with the use of time stepping finite element method were used as the parameters of equations of the developed mathematical model. Losses in the motor, losses in transistors and diodes of the converter as well as the actual back EMF waveforms, variable moment of inertia and variable load torque are accounted for. The designed laboratory stand and the test results are presented in the paper. The experimental verification shows the correctness of the developed method, algorithm and program. The developed computational method is universal with respect to different electromechanical systems with cylindrical BLDC motors. It can be applied to electromechanical systems with BLDC motors operating at constant but also variable load torque and moment of inertia.

Torque Ripple Suppression of Brushless DC Motors with Non-Ideal Back EMF for EPS Applications

The torque ripple of brushless dc (BLDC) motors at low rotation speeds is prominent, while in the majority of working time of the automotive electric power steering (EPS) system, the steering rate is low and the assistant motor runs at low rotation speeds. Therefore, to develop a high-performance EPS system with a BLDC motor, the problem of torque ripple at low rotation speeds must be solved. Otherwise, the steering feel will not be smooth. This paper proposed an algorithm based on BLDC motors’ essential torque formula combined with the back-EMF (Electromotive Force) waveform coefficient to modify the target current to suppress the torque pulsation effectively. Meanwhile, the commutation process of this type motor is very short. Therefore, the torque coefficient can be regarded as constant during the commutation intervals. A direct pulse-width modulation (PWM) control method considering phase resistances is analyzed with a unipolar PWM scheme to reduce the commutation torque ripple further. Finally, simulations and experiments are conducted to verify the effectiveness of this method.

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.

Design and Operation of Interior Permanent-Magnet Motors With Two Axial Segments and High Rotor Saliency

Skewing the magnets in a brushless interior permanent-magnet motor can be difficult. One method to overcome this problem is to use axial segments that are rotated (“twisted”) with respect to each other. Compared to other methods of rotor skewing, this method may reduce manufacturing cost and the complexity of the rotor. This paper addresses the use of two axial segments and the associated effects on the back-electromotive force (EMF) waveform and motor performance. The back-EMF waveforms of an interior permanent-magnet motor are deeply influenced by the tooth-slot and winding harmonics. They should be sinusoidal to reduce torque ripple for ac motor servo drives and other applications where smooth operation is required. In the paper, we present the two-segment rotor structure together with a simple technique for reducing high-order back-EMF harmonics, and we derive the optimal twisted angle of the proposed two-segment rotor. This minimizes the total harmonic distortion of the back-EMF waveform due to tooth-slot effects. We examine cogging torque and the reduction in cogging torque. We apply the twisted angle rotor to two different compressor motors. In addition to the back-EMF, we address the torque ripple under load and the effect of twist on back-EMF constant. We examine the results using finite-element analysis and validate them by experimental measurement.

Comparison of All- and Alternate-Poles-Wound Flux-Switching PM Machines Having Different Stator and Rotor Pole Numbers

The influence of stator and rotor pole numbers, viz. 6/5, 6/7, 12/10, 12/11, 12/13, and 12/14 stator/rotor poles, etc., on the electromagnetic performance of three-phase flux-switching permanent-magnet (FSPM) machines with all and alternate poles wound is investigated in this paper. It shows that the back-EMF waveform, winding inductance, unbalanced magnetic force, and torque density in an FSPM machine are all significantly affected by the stator and rotor pole numbers and winding configurations, as confirmed by both finite-element analyses and measurements.

Understanding DC motors through experiments

We present here a set of simple experiments through which various characteristics of a DC motor can be investigated. The experiments also provide insights on how to control a DC motor. We first study the back-emf versus angular speed and the torque versus current characteristics. We then extract the moment of inertia of the rotor and the speedtorque curve for the load from the start-stop dynamics of the motor. Finally, we study an alternate way of obtaining the angular speed from the back-emf waveform.

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

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

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>

A Vector Control Method of LPMBDCM Considering Effects of PM Flux Linkage Harmonic and Cogging Force

This paper presents a general vector control principle of surface-mounted permanent magnet (SPM) motors with arbitrary back-electromotive-force (back-EMF) waveform, then applies it to minimize the force pulsation of three-phase linear permanent magnet brushless dc motors (LPMBDCMs). The principle is derived from the force equation in the dot product form of the current vector and the permanent magnet (PM) flux linkage derivative vector. It indicates that the mutual force is proportional to the amplitude of current vector, and the ohmic loss is at the minimum when the current vector is aligned with the PM flux linkage derivative vector. Based on a d'q' asynchronously rotating reference frame considering the effects of PM flux linkage harmonic, a new id' = 0 vector control method with the cogging force compensation is proposed according to the principle. From the results of simulation with an accurate finite element (FE) based phase variable model, the validity of the proposed control method is verified compared with the conventional PWM current control for a LPMBDCM.

Alternate Poles Wound Flux-Switching Permanent-Magnet Brushless AC Machines

Flux-switching permanent-magnet (FSPM) brushless machines have emerged as an attractive machine type by virtue of their high torque densities, simple and robust rotor structure, and the fact that permanent magnets and coils are both located on the stator. Both 2-D and 3-D finite element analyses are employed to compare the performance of a conventional all poles wound (double-layer winding) topology with that of three modular alternate poles wound (single-layer winding) topologies, in terms of output torque, flux-linkage, back EMF, and inductances. It is shown that the FSPM machine can be designed in this way without incurring a significant performance penalty, but that some degree of rotor skewing or a variation in stator and rotor pole combination may be required in order to maintain a sinusoidal back-EMF waveform and reduce the torque ripple. Experimental validation is reported for both conventional all poles wound and alternate poles wound FSPM machine topologies.

Iron Pole Shape Optimization of IPM Motors Using an Integrated Method

Abstract —An iron pole shape optimi zation method to reduce cogging torque in Interior Permanent Magnet (IPM) motors is developed by using the reduced basis technique coupled by finite element and design of experiments methods. Objective function is defined as the minimum cogging torque. The experimental design of Taguchi method is used to build the approximation model and to perform optimization. This method is demonstrated on the rotor pole sh ape optimization of a 4-poles/24-slots IPM motor. Index Terms—IPM motor, Cogging torque reduction, iron pole shape optimization, reduced basis technique, FEA, Design of Experiments (DOE) I. I NTRODUCTION Brushless permanent motors have been widely used in industrial applications because of their efficiency and power density. In particular, the spoke-type motor, which can concentrate flux from permanent magnets, has a high torque density per unit volume resulting from its high reluctance torque and structure for concentrating flux from permanent magnet. However, cogging torque and torque ripple can be increased due to a distortion of air gap flux density distribution in the IPM motors. This drawback is due to its asymmetric magnetic reluctance on the edge of the permanent magnet. There have been some developments for rotor pole shape optimization. Table I summarizes the literature by showing the type of optimization approach. Cogging torque reduction in IPM motors was performed using a rotor with flux barriers [1]–[3]. Eccentric pole design was proposed to compensate the armature reaction for reducing torque ripple [4]. To obtain better performance, the rotor pole shape was varied and divided into three parts. These consist of two end parts of eccentric surfaces and one uniform surface. Response surface methodology (RSM) was used during the design process [5]. The continuum shape design sensitivity formula and the finite element method are employed to calculate the sensitivity of flux linkage to the design variables, which determine the shape of iron pole piece [6]. They used B-Spline parameterization to optimize the design variables in order to provide the back-EMF waveform as close as possible to a sinusoidal form. The main challenge of current optimization methods, especially for complex one, is the number of design variables required for rotor pole shape optimization and the generality of the procedure. The first method has poor performance due to the loss in flux barriers. The second method is only suitable for motor rotation in one direction. Also, the later method is not a general approach to achieve the optimum rotor pole shape profile.