Air-gap Permeance Research Articles

Analytical Calculation of Synchronous Reactances of Homopolar Inductor Alternator

In this paper, the direct-axis (d-axis) and quadrature-axis (q-axis) synchronous reactances of homopolar inductor alternator (HIA) are calculated. First, an approximate 2-D model of HIA is developed and its relative air-gap permeance function is described. Then, the analytical expressions for the synchronous reactances in the d-axis and q-axis are derived from magnetomotive force-relative air-gap permeance function theory, including armature reaction reactance and armature leakage reactance. Finally, theoretical results are compared with the simulation and experimental results.

Design and Magnetic Noise Reduction of the Surface Permanent Magnet Synchronous Machine Using Complex Air-Gap Permeance

Nowadays, developing electric motorization for land vehicles is essential owing to the crucial need to save energy. This paper presents the development of a tool used in optimal acoustic and electromechanical modeling whose highly accurate calculations and speed of resolution make it stand out from standard analytical and finite element (FE) models. By coupling an analytical model with static FE simulations, our hybrid model calculates a complex global air-gap permeance per area unit, to take into account magnetic wedge permeability, preslot height, and rotor shape. An unparalleled level of precision and speed of resolution is obtained for the computation of air-gap magnetic pressures. Several results of comparisons between acoustic measurements and simulations on a concentrated winding motor for different speeds are presented.

Investigation of Line Current Harmonics in Cascaded Multi-level Inverter Based Induction Motor Drive and an Adaptive On-line Selective Current Harmonic Elimination Algorithm

Multilevel Inverters (MLIs) have drawn increasing attention in numerous applications, especially in drives, distributed energy resources area, utility etc. MLIs have the ability to synthesize a near sinusoidal output voltage wave with minimal Total Harmonic Distortion (THD) in low frequency switching. Even though they offer lower THD, the presence of lower order harmonics is objectionable and harmonics elimination in Multilevel Inverters (MLIs) has been receiving immense attention for the past few decades. Existing Selective Harmonic Elimination (SHE) techniques can eliminate the objectionable lower order voltage harmonics with low switching frequency by solving the Fourier non-linear transcendental equations of the output voltage. The line current harmonics has a direct role to play on the magneto-motive force and results in increase of mismatching of air-gap permeance, vibrations, acoustic noise etc. This study proposes Normalized Least Mean Squares (NLMS) algorithm based scheme to eliminate the selected dominant harmonics in load current using only the knowledge of the frequencies to be eliminated. The algorithm is simulated using MATLAB/SIMULINK tool for a three-phase VSI to eliminate the fifth and seventh harmonics. The informative simulation results verify the validity and effectiveness of the proposed algorithm. The system performance is analyzed based on the simulation results considering Total Harmonic Distortion (THD), magnitude of eliminated harmonics and frequency spectrum.

Calculation improvement of no-load stray losses in induction motors with experimental validation

On the basis of the known fact that all air gap main flux density variations are enclosed by permeance slot harmonics, only one component of stray losses in rotor (stator) iron is considered in the new classification, instead of 2 components: rotor (stator) pulsation iron losses, and rotor (stator) surface iron losses. No-load rotor cage (high-frequency) stray losses are usually calculated. No-load stray losses are caused by the existence of space harmonics: the air-gap slot permeance harmonics and the harmonics produced by no-load MMF harmonics. The second result is the proof that the corresponding components of stray losses can be calculated separately for the mentioned kind of harmonics. Determination of the depth of flux penetration and calculations of high frequency iron losses are improved. On the basis of experimental validation, it is proved that the new classification of no-load stray losses and the proposed method for the calculation of the total value is sufficiently accurate.

A study of cogging torque in permanent magnet synchronous machines with fractional slot windings

Results of an investigation of cogging torque in permanent magnet synchronous machines with fractional slot windings are given, and the nature of their origin is considered. This research is important because of the necessity to assess cogging torque at the stage of design of machines developed for areas of application in which there are rigid requirements for noise and vibration level. To simplify the solution, the design of an electrical machine with radial location of magnets is chosen as am object of research. A formula of cogging torque determined as the result of interaction between magnetic field harmonics and corresponding harmonics of the surface current density is developed. Conditions required for cogging torque are determined. Equations for calculating the number of air gap permeance harmonics and magnetomotive force harmonics contributing to the generation of this cogging torque are presented. This study shows that the cogging torque has two components. The first component is the result of interaction of permeance and magnetic field harmonics having the same number; the second component is caused by interaction between the permeance harmonics and mixed harmonics of the magnetic field induced by the stator slotting. An experimental investigation of cogging torque in a machine with 12 slots and 10 poles has been conducted. Fourier analysis of the experimental data verifies the analytical results of experimental data.

Operation and Design Principles of a PM Vernier Motor

In this paper, the back electromotive force and power equations of a permanent-magnet (PM) vernier motor are accurately derived considering an air-gap permeance function expressed in terms of practical machine dimensions. Using these equations, the nature of a PM vernier motor is analytically surveyed, and substantial information such as main geometric factors affecting torque and the maximally obtainable torque for a given current are provided, leading to a new relation for torque per air-gap volume. In addition, these equations provide a means to determine the slot and pole combinations to realize greater power density. Finally, the effects of an increased reactance are investigated in respect to machine performance with a given voltage.

New Approach to Cogging Torque Simulation Using Numerical Functions

This paper presents a new approach for simulation of the cogging torque in a permanent-magnet (PM) machine. The method exploits the numerical functions for modeling the magnetic circuit of the machine. This paper introduces two improved functions to model the PMs and the air-gap permeance, aiming to compute the cogging torque in the PM machine. The first function states the magnetomotive-force drop on the machine air gap with respect to the angular position. The other function, named permeance function, models the air-gap permeance accurately, taking into account the stator saliency due to the teeth. The described procedure has been tested on a prototype PM machine.

An Improved Analytical Model for Inductance Calculation of Interior Permanent Magnet Machines

This paper proposes an improved analytical model to calculate the inductances of interior permanent magnet (IPM) machines, equipped with either fractional slot concentrated windings or distributed windings. A modified stator magnetic motive force expression is also presented firstly. It has been proven that the normal method for inductance calculation by airgap permeance function and winding function is not accurate enough for IPM machines. The improved analytical model is competent to predict the distribution of the armature-reaction magnetic field and inductances accurately. Several finite element analysis (FEA) models have been built, and a prototype has been designed and tested. Results by the improved analytical model are verified by both FEA and experimental results.

Radial Force Analytic Modeling for a Novel Bearingless Switched Reluctance Motor When Considering Rotor Eccentricity

—Analytic modeling of radial forces is proposed for the novel bearingless switched reluctance motor, where the rotor eccentricity is taken into account. The novel bearingless switched reluctance motor's model is never disclosed, even though there are many advantages, such as fewer suspension windings and simpler control circuit and algorithm, when compared to the conventional bearingless switched reluctance motor. The analytic model of radial forces is very important to achieve this new bearingless switched reluctance motor's suspension control. The rotor eccentricity is a key cause to affect the radial forces. This article calculates the air-gap permeances through considering rotor eccentricity. The self-inductance and mutual-inductance expressions of the motor torque windings and the suspension windings are derived by using the magnetic equivalent circuit method. The derived radial force model discloses the effects of winding currents, rotor position angle, and rotor eccentricity displacement. The finite-element analysis based results verify the built model.

Static Eccentricity Fault Recognition in Three-Phase Line Start Permanent Magnet Synchronous Motor Using Finite Element Method

This paper is dedicated to investigating static eccentricity in a three-phase LSPMSM. The modeling of LSPMSM with static eccentricity between stator and rotor is developed using finite element method (FEM). The analytical expression for the permeance and flux components of nonuniform air-gap due to static eccentricity fault is discussed. Various indexes for static eccentricity detection using stator current signal of IM and permanent magnet synchronous motor (PMSM) are presented. Since LSPMSM is composed of a rotor which is a combination of these two motors, the ability of these features is evaluated for static eccentricity diagnosis in LSPMSM. The simulated stator current signal of LSPMSM in the presence of static eccentricity is analyzed in frequency domain using power spectral density (PSD). It is demonstrated that static eccentricity fault generates a series of low frequency harmonic components in the form of sidebands around the fundamental frequency. Moreover, the amplitudes of these components increase in proportion to the fault severity. According to the mentioned observations, an accurate frequency pattern is specified for static eccentricity detection in three-phase LSPMSM.

Mathematical modeling of a novel bearingless switched reluctance motor

Purpose – The novel bearingless switched reluctance motor (BSRM) is proposed recently, which is different from the conventional BSRM in the stator structure and suspension winding arrangement. The reduced number of suspension windings makes the novel BSRM much simpler, so that the control circuit and algorithm are greatly simplified when compared to those of the conventional BSRM. This paper for the first time proposes the novel BSRM's analytic model, including the mathematical relationships among the winding currents, rotor angle, radial forces, and motor torque, to further achieve the suspending forces and torque control. The paper aims to discuss these issues. Design/methodology/approach – The magnetic equivalent circuit method is employed to obtain the self-inductances and mutual-inductances of the motor torque windings (main windings) and suspension windings (control windings). The straight flux paths are combined with the elliptical fringing flux paths to calculate the air-gap permeances, and the stored magnetic energy. Then, the mathematical expressions of radial forces and torque are derived. A novel BSRM prototype is analyzed through using the proposed analytical model and the finite element model. The results of both methods are compared to verify the proposed mathematical model. Findings – The proposed mathematical model of the novel BSRM considering unsaturated magnetic circuits is verified by finite-element analysis results. Research limitations/implications – The mathematical model represents the situation of magnetic circuit unsaturated and is not suitable for the magnetic circuit saturation. It cannot be used to control the motor which is working in the deep magnetic circuit saturation region. Practical implications – Building mathematical model is a necessary step for the motor's suspension and rotating control. The built model provides the fundamental for the preliminary control algorithm and experimental study of this novel BSRM. Originality/value – For the first time, the novel BSRM's mathematical model is proposed. It provides necessary fundamental for the motor's further analysis, design, and suspending and rotating controls.

Stator-Current Spectrum Signature of Healthy Cage Rotor Induction Machines

Before applying current-signature-analysis-based monitoring methods, it is necessary to thoroughly analyze the existence of the various harmonics on healthy machines. As such an analysis is only done in very few papers, the objective of this paper is to make a clear and rigorous characterization and classification of the harmonics present in a healthy cage rotor induction motor spectrum as a starting point for diagnosis. Magnetomotive force space harmonics, slot permeance harmonics, and saturation of main magnetic flux path through the virtual air-gap permeance variation are taken into analytical consideration. General rules are introduced giving a connection between the number of stator slots, rotor bars, and pole pairs and the existence of rotor slot harmonics as well as saturation-related harmonics in the current spectrum. For certain combinations of stator and rotor slots, saturation-related harmonics are shown to be most prominent in motors with a pole pair number of two or more. A comparison of predicted and measured current harmonics is given for several motors with different numbers of pole pairs, stator slots, and rotor bars.

A Fast Inductance Computation Devoted to the Modeling of Healthy, Eccentric, and Saturated Induction Motors

This work deals with a detailed method for the calculation of induction motor inductances based on the convolution theorem. The integral form leading to the inductance expressions is derived from the 2D modified winding function approach, which takes into account the space harmonics, slot skewing, and radial and axial air-gap eccentricities. As first applications, a model is presented that allows teeth saturation to be taken into account by the corresponding air-gap permeance variation. Next, the idea is adapted to the rotor eccentricity modeling. It is shown that appropriate arrangements make it possible to use the convolution theorem for fast calculation of the inductances. The proposed method proves to be competitive compared to the conventional techniques of integration and even those employing equivalent analytical expressions. To demonstrate the effectiveness of the new proposed methodology, simulation tests based on the multiple coupled circuit model, experimental spectra, as well as time processing verification on a personal computer, are provided.

Electromagnetic Performance Analysis of Claw-Pole Alternator with Changing Permeance

A changing air gap permeance model of the alternator and its influence were discussed in this paper. When the alternator was under high-speed operation, taking it into consideration that the claws getting deformation for rotating centrifugal force and electromagnetic exciting force, the alternator’s changing air gap permeance model was established. And the alternator’s Maxwell3D calculation model was built. The field magnetic distribution under the rated speed was obtained as well, also before the claws’ deformation was obtained. The harmonics of the air-gap flux were analyzed and compared. The changing air gap permeance model was proved to be reasonable. It would lead to air-gap magnetic field distortion of the generator, which affected the generator’s electromagnetic properties. Instruction was provided for more precise of air gap magnetic field analysis or vibration noise analysis of alternator.

Detent Force Analysis in Permanent Magnet Linear Synchronous Motor Considering Longitudinal End Effects

This paper presents a uniform analytical model by energy method and Fourier series expansion to analyze detent force in uneven magnetic field for permanent magnet linear synchronous motor (PMLSM). The model reveals that detent force in long-primary type is mainly influenced by non-ideal distribution of permanent magnet magnetic motive force, while nounified air-gap permeance makes a great impact on detent force of short-primary type. Hence, magnetic field similarity of motor design techniques referring rotary counterpart are adopted. For long-primary type novel method of splitting edge magnets is proposed to reduce end effects force, and optimal widths of edge tooth in short-primary type also verify the effectiveness of magnetic field similarity. The experimental results validate finite element analysis results.

Analytical Calculation of No-load Magnetic Field Distribution in the Slotted Airgap of a Permanent Magnet Synchronous Motor

An analytical method for calculation of no-load magnetic field distribution in the slotted airgap of a surface permanent magnet synchronous motor has been presented. The method involves the solution of the governing field equations in polar coordinates in the annular airgap region of a slotless motor in which the magnets are assumed to have uniform radial magnetization and constant relative recoil permeability. Then it introduces the notion of complex relative airgap permeance calculated from the conformal transformation to account the effect of slotting. As a result, an accurate solution of both radial and tangential components of the flux density can be obtained.

Analytical Armature Reaction Field Prediction in Field-Excited Flux-Switching Machines Using an Exact Relative Permeance Function

In this paper, an analytical approach for the prediction of the armature reaction field of field-excited flux-switching (FE-FS) machines is presented. The analytical method is based on the magnetomotive force (MMF)-permeance theory. The doubly-salient air-gap permeance, developed here, is derived from an exact solution of the slot permeance. Indeed, the relative slot permeance is obtained by solving Maxwell's equations in a subdomain model and applying boundary and continuity conditions. In addition, during a no-load study, we found that, regarding the stator-rotor teeth combination, phase distributions were modified. Hence, in this paper, phase MMF distributions, for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> phases, several stator-rotor combinations and also phase winding distribution (single- or double-layers) are proposed. We compare extensively magnetic field distributions calculated by the analytical model with those obtained from finite-element analyses. Futhermore, the model is used to predict the machine inductances. Once again, FE results validate the analytical prediction, showing that the developed model can be advantageously used as a design tool of FE-FS machine.

A Numerical Method of the Electromagnetic Force for the Electromagnetic Track Brake

The object is to propose an accurate and succinct numerical method to compute the electromagnetic force between the electromagnetic track brake and track. The model of the magnetic circuit with variable air-gap permeance is established and the electromagnetic force is obtained by using a method of magnetic flux tubes. The electromagnetic force is compared with that from the finite element method using Ansoft software. The comparison results show that the numerical method is capable of achieving precise and reliable electromagnetic force quickly.

Spatial Discretization Methods for Air Gap Permeance Calculations in Double Salient Traction Motors

Weight limitations in electric/hybrid cars demand the highest possible power-to-weight ratio from the traction motor, as in double salient permanent magnet (PM) machines. Their high flux densities in the air gap result in nonlinear analytical models, which need to be time optimized. The incorporated reluctance networks are sensitive to the correctness of air gap permeances. Conventionally, in these networks, air gap permeances are calculated by approximating flux paths; however, it is time inefficient. For an improved simulation time, spatial discretization techniques are presented to calculate air gap permeances in double salient PM machines. The spatial techniques discussed here cover the tooth contour method and Schwarz-Christoffel (SC) mapping as semidiscrete methods, which are used to discretize only the air gap region. Their results are verified by the spatial discrete method and finite element method, which discretizes the whole machine geometry. For consistency in this paper, all methods are explained on a three-phase 12/10 flux-switching PM motor. Obtained air gap permeances show a very good agreement with only 0.8% difference. Further on, machine characteristics such as phase flux linkage and cogging torque are also compared to show the impact of the modeling techniques. The total machine simulation time is improved by 20% using the SC method. Although methods are explained particularly for double salient PM machines, formulas are generalizable for other machine types as well.

Assessment of Core Losses in a Flux-Modulating Synchronous Machine

In this paper, the core losses that occur in a 4-kVA flux-modulating synchronous machine (SM) (FMSM) are investigated using 2-D finite-element analysis, and the results are supported by experiments. A method for reducing the core losses is also presented. The FMSM is a new type of multipole SM in which the stator field magnetomotive force is modulated by the air-gap permeance to generate the rotating field. A 2pa-pole three-phase armature winding and a 2pf-pole field winding are centrally wound around individual stator teeth, and a reluctance rotor with 2pr (= pa + pf) saliencies is used to provide a magnetic coupling between these windings. As a result of the investigation, it was found that, although the core losses occur in the rotor as well as in the stator, the rotor core loss can be effectively reduced by decreasing the height of the rotor poles.