Pole Pairs Research Articles

Performance Evaluation and Optimization of Flux-Regulated Axial-Radial Eddy Current Coupling

Abstract This paper proposes a novel axial-radial permanent magnet eddy-current coupling equipped with a mechanical magnetic adjuster. The innovative design integrates mechanical flux weakening technology with an enhanced magnetic method rooted in axial-radial hybrid flux topology. Concise analytical models for air-gap field and torque are developed, leveraging the magnetic equivalent circuit method and Faraday’s law. These models are subsequently validated using the 3D finite-element method. The results indicate that this device boasts an exceptionally broad torque adjustment range, reaching approximately 93% at a given slip. Furthermore, it exhibits a substantial optimal working area, spanning from 20% to 80% of the mechanical magnetic adjuster's movable distance. To comprehensively analyze the impact of structural parameters on overall performance, three novel metrics are defined. The analysis reveals that the pole pairs of the radial magnetic circuit (RMC) have the most significant influence on the device's comprehensive performance. In the end, a multi-objective optimization method to maximize the global torque regulation capabilities, local torque regulation abilities, and maximum torque potential is developed to enhance the overall performance of this innovative magnetic coupling design.

Study on Winding Inductances in Stator Surface-Mounted Permanent Magnet Machines

Winding inductance always plays a key role in the electromagnetic performances of stator surface-mounted permanent magnet (SSPM) machines, including their flux-weakening capability, prospective fault current, power factor, current ripple, etc. Generally speaking, winding inductance mainly comprises three components: an air-gap component, a slot-leakage component, and an end-leakage component. In this paper, firstly, the winding pole pairs of SSPM machines are investigated based on the magneto-motive force-permeance model, through which the winding configurations can also be determined. Then, according to the winding configurations, three analytical expressions for each inductance component are derived to evaluate the winding inductance per phase. In addition, finite element analysis (FEA) is employed to verify the effectiveness of the derived analytical expressions. Meanwhile, three prototyped SSPM machines are manufactured, and their winding inductances are measured to further verify the analytical expressions. The measured results agree with both the analytical and FEA results very well.

ОБЕРТАЛЬНИЙ МОМЕНТ БЕЗПАЗОВОГО МОМЕНТНОГО ДВИГУНА З ПОСТІЙНИМИ МАГНІТАМИ ТА МАСИВНИМ МАГНІТОПРОВОДОМ СТАТОРА

The properties of the solid magnetic core of the stator of a slotless torque motor with permanent magnets are considered. It is noted that the solid stator under the conditions of low rotation speed has some advantages over the traditional laminated magnetic circuit. These advantages consist in the cost reduction of the design, its compactness and the low time of production preparation. The mathematical model's assumptions and the input data's limitations are formulated. A model of a static magnetic field with a moving electrically conductive medium is chosen. The two-dimensional model is implemented in the "Magnetic fields" interface of the "COMSOL Multiphysics" software. The maximum torque values were obtained and the optimal number of pole pairs was found. The method of calculating the torque based on eddy current losses in the magnetic medium is used. The decrease in torque with increasing rotor speed is calculated. The correction coefficients of the maximum moment were obtained to correct the results of two-dimensional modelling using a three-dimensional model. References 5, figures 6, tables 1.

Extreme Superposition: High-Order Fundamental Rogue Waves in the Far-Field Regime

This Memoir concerns fundamental rogue-wave solutions of the focusing nonlinear Schrödinger equation in the limit that the order of the rogue wave is large and the independent variables ( x , t ) (x,t) are proportional to the order (the far-field limit). We first formulate a Riemann-Hilbert representation of these solutions that allows the order to vary continuously rather than by integer increments. The intermediate solutions in this continuous family include also soliton solutions for zero boundary conditions spectrally encoded by a single complex-conjugate pair of poles of arbitrary order, as well as other solutions having nonzero boundary conditions matching those of the rogue waves albeit with far slower decay as x → ± ∞ x\to \pm \infty . The large-order far-field asymptotic behavior of the solution depends on which of three disjoint regions C \mathcal {C} (the “channels”), S \mathcal {S} (the “shelves”), and E \mathcal {E} (the “exterior domain”) contains the rescaled variables. On the region C \mathcal {C} , the amplitude is small and the solution is highly oscillatory, while on the region S \mathcal {S} , the solution is approximated by a modulated plane wave with a highly oscillatory correction term. The asymptotic behavior on these two domains is the same for all continuous orders. Assuming that the order belongs to the discrete sequence characteristic of rogue-wave solutions, the asymptotic behavior of the solution on the region E \mathcal {E} resembles that on S \mathcal {S} but without the oscillatory correction term. Solutions of other continuous orders behave quite differently on E \mathcal {E} .

Riemann–Hilbert method to the Ablowitz–Ladik equation: Higher‐order cases

AbstractWe focus on the Ablowitz–Ladik equation on the zero background, specifically considering the scenario of pairs of multiple poles. Our first goal was to establish a mapping between the initial data and the scattering data, which allowed us to introduce a direct problem by analyzing the discrete spectrum associated with pairs of higher‐order zeros. Next, we constructed another mapping from the scattering data to a matrix Riemann–Hilbert (RH) problem equipped with several residue conditions set at pairs of multiple poles. By characterizing the inverse problem on the basis of this RH problem, we are able to derive higher‐order soliton solutions in the reflectionless case.

A High Torque Density Dual-Stator Flux-Reversal-Machine with Multiple Poles Halbach Excitation on Outer Stator

This paper proposes a high torque density dual-stator flux-reversal-machine with multiple poles Halbach excitation (MPHE-DSFRM), which uses two pole pairs’ numbers (PPNs) of PM excitation on one outer stator tooth, and one PPN of PM excitation on one inner stator tooth. The introduction of different PPNs of PM excitation on the outer and the inner stators can optimize magnetic circuit and airgap flux density. A Halbach array is formed by inserting three pieces of circumferentially magnetized PMs into four pieces of radially magnetized permanent magnets (PMs) on the outer stator, which aims to further enhance torque density, and reduce torque ripple. Based on the flux modulation effect, the analytical modeling of the proposed MPHE-DSFRM is established, together with the evolution process, and the working principle is presented. Then, the key design parameters of MPHE-DSFRM are optimized to achieve high torque density and low torque ripple for high torque quality. Three representative DSFRMs and a conventional FRM are designed and analyzed, and they share the same design key parameters, including PM usage, outer radius of the outer stator, and active airgap length. The electromagnetic performances, including airgap flux density, back electromotive force (back-EMF), and torque characteristics, are analyzed and compared by finite element analysis (FEA). The calculated results show that the proposed MPHE-DSFRM can provide high torque density and high PM utilization.

Analysis of the Behavior of the Electromagnetic Frequency Regulator (EFR) Used in Hybrid Wind-Solar Photovoltaic Generation Systems

Within the context of integrating renewable energy sources, the Electromagnetic Frequency Regulator (EFR) presents a promising technology, particularly in hybrid distributed generation systems. This paper conducts a comprehensive analysis of pole pair configurations for both the EFR and the induction generator within such systems to enhance overall performance. An algorithm developed in Scilab is utilized for steady-state analyses considering various configurations. The methodology involves repetitive computations to evaluate the angular velocity of both the EFR and the generator, as well as the transformation ratios of the speed multiplier for different pole pairs. Scenarios with varying combinations of pole numbers are explored, demonstrating the impact on EFR velocity and the drive frequency of the EFR. Results showcase the efficacy of the proposed algorithm, providing insights into the selection of the most appropriate pole pairs to improve system performance.

DECREASING TORQUE RIPPLE OF A SLOTLESS PERMANENT MAGNET TORQUE MOTOR USING A DOUBLE-LAYER WINDING

The torque of a magnetoelectric torque motor with surface-mounted permanent magnets on the rotor was studied. The sinusoidal current supply mode is considered. The torque was calculated according to the static model of the magnetic field. It was determined that the sixth harmonic makes a significant contribution to the torque ripple. To reduce the sixth harmonic it is proposed to use a winding with a shortened pitch, for which it is necessary to make this winding in two layers. The optimal values of the number of pole pairs, the angular width of the magnets of the magnetic field exci-tation system, and the shortening of the winding pitch were determined. It was found that shortening of the winding pitch decreases the torque ripple by 2 ... 2.5 times. References 7, figures 6, tables 3.

Design and optimization of high torque density flux modulated multi-winding permanent magnet machines for electric vehicles

In order to achieve high-quality energy conversion operation in electric vehicles, the optimization design of drive motors has been considered as one of the most crucial research areas. For enhancing torque density without deteriorating power factor, a spoke-type flux modulated multi-winding permanent magnet machine is proposed and optimized, where the highly efficient utilization of harmonic flux is realized according to the contribution of windings with various pole pairs. Firstly, the operating principles and the initial design of topology are investigated. Then, the improved non-dominated sorting genetic algorithm is adopted for multi-objective optimization. To enhance the efficiency and accuracy of the optimization, the weight coefficients of the multi-objectives are established through a gray correlation strategy, while the design parameters are stratified based on a comprehensive sensitivity degree analysis. In addition, the comparative analysis of machines before and after optimization are carried out. Finally, the correctness of the theoretical analysis and the effectiveness of the proposed optimization are verified by a prototype machine. It shows that high torque density without deteriorating power factor is achieved on the proposed machines.

Selecting the Best Permanent Magnet Synchronous Machine Design for Use in a Small Wind Turbine

The article describes the selection of a permanent magnet synchronous machine design that could be implemented in a small wind turbine designed by the GUST student organization together with researchers working at the Technical University of Lodz. Based on measurements of the characteristics of available machines, eight initial designs of machines with different rotor designs were proposed. The size of the stator, the number of pairs of poles, and the dimensions of the magnets were used as initial parameters of the designed machines. The analysis was carried out about the K-index, the so-called index of benefits. The idea was to make the selected design as efficient as possible while keeping production costs and manufacturing time low. This paper describes how to select the best design of a permanent magnet synchronous generator intended to work with a small wind turbine. All generator parameters were selected keeping in mind the competition requirements, as the designed generator will be used in the author’s wind turbine. Based on the determined characteristics of the generator variants and the value of the K-index, a generator with a latent magnet rotor was selected as the best solution. The aforementioned K-index is a proprietary concept developed for the selection of the most suitable generator design. This paper did not use optimization methods; the analysis was only supported by the K-index.

Revisiting O(N) σ model at unphysical pion masses and high temperatures

Roy-equation analysis on lattice data of ππ scattering phase shifts at mπ=391 MeV reveals that the lowest f0 meson becomes a bound state under this condition. In addition, there is a pair of complex poles below threshold generated by crossing symmetry [X.-H. Cao , ]. We use the N/D method to partially recover crossing symmetry of the O(N) σ model amplitude at leading order of 1/N expansion, and qualitatively reproduce the pole structure and pole trajectories with varying pion masses as revealed by Roy-equation analyses. The σ pole trajectory with varying temperature is also discussed and found to be similar to its properties when varying mπ. As the temperature increases, the complex σ poles firstly move from the second Riemann sheet to the real axis becoming two virtual state poles, and then one virtual state pole moves to the first sheet turning into a bound state pole and finally tends to the pion pole position at high temperature which is as expected from the chiral symmetry restoration. Our results provide further evidence that the lowest f0 state extracted from experiments and lattice data plays the role of the σ meson in the spontaneous breaking of chiral symmetry. Finally, we also briefly discuss the problems of the effective potential in the situation when mπ and the temperature become large. Published by the American Physical Society 2024

Analysis of pole pair number impact on single-sided linear induction machine performances

This paper presents a parametric study of linear induction motor for design purpose. The chosen mathematical model uses a 2D formulation with magnetic vector potential A. The implementation of the model is carried out with the finite element method on the free platform Gmsh-GetDP. Circuit model is coupled to FE model so that constant voltage supply mode can be considered. This work aims to highlight the effect of the pole pair number on the characteristics and the performances of the linear induction machine through two numerical models associated to an analytical one. Furthermore, the study shows the effect of the pole pair number on the phase imbalance and the spatial harmonic spectrum of the machine. Reducing this imbalance and higher order harmonics presence will increase machine performances.

A Robust High-Accuracy Wound Rotor Resolver Proposal With One and Two Pole Pairs

A Robust High-Accuracy Wound Rotor Resolver Proposal With One and Two Pole Pairs

Analysis of torsional vibration characteristics for wind turbine drivetrain under external excitation

This work studies the torsional vibration characteristics analysis of the wind turbine drivetrain with the variation of internal parameter and external excitation. The electromechanically coupled torsional vibration model for wind turbine drivetrain is first established by taking into account the torsional vibration angle of the PMSG. Then, frequency response analysis of main parametric resonance is illustrated by multiple scale method, and the influences of the system parameters involving power factor angle, number of pole pairs, torsional stiffness, and wind speed excitation on the torsional vibration characteristics of wind turbine drivetrain are investigated. Moreover, the critical condition for homoclinic chaos in terms of the system parameters is derived by means of Melnikov’s method. The function relationship and the boundary curve of chaos threshold are obtained. Meanwhile, the effects of excitation amplitude and damping factor on the system transition to chaos are studied in detail. The analytical predictions including phase portrait, bifurcation diagram and Lyapunov exponent are investigated. The research results can offer a theoretical basis for further the parameter design and control of wind turbine drivetrain.

Analysis of longitudinal-vertical coupling vibration of four hub motors driven electric vehicle under unsteady condition

The influence of hub motor unbalanced magnetic force (UMF) on the vibration of electric vehicle under steady state conditions has been known, but under unsteady conditions, the hub motor UMF will change with the vehicle operation condition, and there would exist complex coupling vibration for the hub motors driven electric vehicle. Here, the longitudinal-vertical coupling dynamics of the four hub motors driven electric vehicle under unsteady condition is studied. Integrating the motor electromagnetic excitation and electric vehicle dynamics, a longitudinal-vertical coupling dynamics model of the four hub motors driven electric vehicle is established. Based on the variable switching frequency field-oriented control model, analytical model of the UMFs acting on the motor stator and rotor parts under unsteady condition are developed. For model validation, a four hub motors driven electric vehicle has been tested, the accuracy of the longitudinal-vertical coupling dynamics model established in this paper was verified. Then, longitudinal-vertical coupling vibration characteristics of the four hub motors driven electric vehicle under road excitation and coupling excitation are analyzed. The results show that the longitudinal and vertical movement of the four hub motors driven electric vehicle is coupled by hub motor. In addition, under unsteady condition, the motor UMFs will cause vertical vibration of the electric vehicle body and hub motor stator, the vibration shows order characteristics including low order harmonic hfc and inverter switching frequency sideband harmonic k1 fs±k2 fc ( fc = pn/60, fs is inverter switching frequency, k1 and k2 are positive integers, p is the number of pole pairs and n is motor speed.). The motor electromagnetic torque will cause longitudinal vibration of the electric vehicle body, the vibration shows order characteristics including harmonics fs±3 fc and 2 fs. The main harmonic of vehicle body pitch angle acceleration is 2 fs.

Finite Element Analysis of a Three Speed Induction Machine

This paper deals with the Finite Element (FE) analysis of a special Three Speed Squirrel Cage Induction Machine (TSSCIM) with pole changing stator windings. Compared to classical multi-speed induction machines, the studied TSSCIM is designed so as to change in the same time the number of pole pairs (p) and the number of stator phases (m) so as to keep constant the product p x m. The numerical model of the machine used in this study is based on a 2D plane-parallel finite element approach and aims at finding some of the main steady state operation characteristics of the machine working both as motor and generator for three different running speeds. A comparison of the proposed TSSCIM with a classical inverter fed squirrel cage induction machine is also presented in order to underline some advantages and disadvantages of each solution.

Maximum Torque per Ampere Operation of Brushless Doubly Fed Induction Machines

In this paper, an analytical method for increasing the steady state torque per ampere capability for BDFMs, using equivalent circuit is presented. In this approach, uni-current proposition proposed to define a unique current value for optimization, and find the current angel corresponding to maximum torque. The accuracy of the proposition is verified by simulation. The effect of pole pair number selection of power and control windings on maximum torque is explained by dividing torque expression into synchronous and asynchronous terms. Finally, the optimal current values and optimal torque are achieved. Based on the optimal value of torque, or MTPA index, analytical optimization of machine design is suggested, which can be performed by manipulation of components of the MTPA index

Design of simple nonovershooting controllers for linear high order systems with or without time delay

In this paper, we mainly considered the problem of nonovershooting control of high order systems with or without time delay by simple controllers. As basic principles for nonovershooting control systems, three propositions are offered and proved. Under direction of these principles, a nonovershooting dominant pole control structure having three dominant poles, i.e., one real pole and a pair of complex conjugate poles on its left, is proposed. While its zeroes and nondominant poles are on the left side of these three dominant poles with sufficient distance. The controllers adopted are composed by first order filter and PD-PID controller. Dominance of the three dominant poles can be checked and ensured through the computational method we offered. Two illustrating examples are given to show the effectiveness of our method.

Brushless Doubly-Fed Asynchronous Generator Model for Variable Speed Wind Generation Systems.

Because of the raising percentage of the wind energy in the total electrical energy, quality control and regulation of the provided energy will be needed for the electrical grid correct functioning. It is only possible using Variable Speed Wind Generation Systems (VSWGS). In this paper a new electrical generator, Brushless Doubly-Fed Asynchronous Generator (BDFAG) is proposed as a solution for a variable speed wind generation system. The stator of this machine is composed of two balanced three-phase windings with different pole pair number. The rotor is as robust as a conventional squirrel cage, but it has a special design. A steady state model of a BDFAG. is analyzed. Using this model the power balance in the stator windings and the rotor cage is evaluated. The evaluation results will be experimentally verified with a prototype of BDFAG.

Elucidation of the trapping characteristics of magnetic disk-like particles in a Hagen-Poiseuille flow via Brownian dynamics simulations (usage of multi-magnetic poles)

In the present study, we elucidate the behaviour of a suspension composed of magnetic disk-like particles that flow in a Hagen-Poiseuille flow in a gradient magnetic field and the trapping characteristics of the magnetic particles. To this end, we utilise multiple pairs of magnetic poles located outside the cylindrical system. Brownian dynamics simulations were performed in order to clarify the dependence of these characteristics on a variety of factors. It is seen that an increase in the magnetic field strength improves the trapping characteristics of disk-like particles if the influence of an applied magnetic field is sufficiently more dominant than that of a flow field and that of the magnetic particle-particle interaction. In the case of a strong magnetic particle-particle interaction, thin chain-like clusters are formed from an anchored particle trapped around a magnetic pole. If the two poles are sufficiently close to each other, an arch-type cluster is formed between them. We expect that this arch-type cluster may give rise to good trapping performance even in the presence of a strong flow field if the formation arises at a sufficiently large separation distance between the pair of magnetic poles. Highlights We have performed Brownian dynamics simulations for a magnetic disk-like particle suspension in a Hagen-Poiseuille flow. If the magnetic particle-particle interaction is sufficiently more dominant than the flow field, thin chain-like clusters are formed from an anchored particle. As the pole separation distance decreases, an arch-type configuration tends to be formed along the surface of the wall. This arch-type cluster that is formed between the pair of magnetic poles may be expected to improve the trapping characteristics depending on the pole separation distance.