Air-gap Induction Research Articles

Model of Five-Phase Permanent Magnet Synchronous Machines Including the Third Harmonic of the Airgap Induction

Model of Five-Phase Permanent Magnet Synchronous Machines Including the Third Harmonic of the Airgap Induction

Torque Assessment of Multiphase AFPM Machines With Experimental Validation for YASA Topology

This work presents a theoretical and experimental study on the electromagnetic torque of multiphase axial-flux permanent-magnet (AFPM) machines. Initially, a torque equation is obtained through four different methods. The first method follows the definition of electromagnetic power, the second uses the magnetic shear stress, the third is based on the concept of co-energy, and the fourth applies the principle of Lorentz force. Although these methods are based on different assumptions, they lead to the same generalized torque equation, which depends on four parameters: i) the fundamental air gap induction; ii) the electrical loading defined for an arbitrary rotor radius; iii) the ratio of inner and outer rotor radius; iv) the cubic power of the outer rotor diameter. The torque equation is then validated using finite element (FE) analyses and experimental results obtained with a 32-pole/30-slot yokeless and segmented armature (YASA) machine. For this machine, the coils can be connected according to different arrangements so that the phase number can be chosen as three, five, or fifteen. The results show that the torque equation derived here provides sufficient accuracy in practical cases and that it can be applied to machines with phase numbers higher than three.

Scaling Effect On Inter-Turn Short-Circuit Fault of PM Machines for Wind Power Application

This paper proposes a general analytical model of surface-mounted permanent magnet (SPM) machines with series-connected coils under inter-turn short circuit (ITSC) fault. One prominent feature of this fault model is that the air-gap and slot-leakage components of inductances under fault are calculated separately, and the influences of pole number and spatial distribution of coils have been considered in the calculations. In the model, the winding function approach (WFA) is used to calculate the air-gap inductance components by considering all space harmonics whilst slot-leakage inductance components are obtained by using slot permeance method. The proposed fault model built in Matlab/Simulink is validated by time stepping FE simulations for a 3 kW 96-slot 32-pole SPM machine. The fault model has acceptable accuracy and is suitable for the fast evaluation of fault performance of SPM machines and its accuracy considering core saturation can be improved using FE-based results. Other power ratings (0.5 MW and 3 MW) have also been investigated to study the scaling effect on machine fault-tolerant capability. A 12-slot 4-pole small scale prototype has been built to validate the developed fault models.

Impact of Aspect Ratios of Solid Rotor, Large Air Gap Induction Motors on Run-Up Time and Energy Input

This article introduces a unique three-phase induction machine with a large air gap and a copper-coated iron cylinder. The motor is built in an X-ray tube for medical applications where key performance indicators are the start-up time, generated rotor, and total energy during the run-up. The common equivalent circuit for induction motors is utilized to systematically analyze the effect of the rotor protrusion length variation on these key performance indicators by means of three-dimensional (3D)-FEA. However, due to the large air gap and dominating winding head standard evaluation tools, such as the no-load and locked-rotor tests do not provide accurate circuit parameters. Thus, a combined no-load and locked-rotor test evaluation is introduced. Furthermore, to avoid the time and computational effort of time-stepping 3D-FEA, time harmonic and static 3D-FEA is introduced. To validate these simplified 3D-FEA simulations, results are compared with the selected time-stepping 3D-FEA results. Experimental results verify the 3D-FEA results. After establishing a routine to identify accurate equivalent circuit parameters by means of 3D-FEA, the parameters for three different stator lengths each combined with six different rotor lengths are identified. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V/f</i> -controlled run-up simulations are then conducted to generate the results. Results quantify the tradeoff between start-up time, generated rotor, and total energy depending on the rotor protrusion, e.g., the start-up time is indirectly proportional to the rotor protrusion and directly proportional to the rotor frequency (the relative frequency between stator field and rotor speed). The effect of the rotor temperature, which can reach up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sim 390^\circ \,$</tex-math></inline-formula> C, on the results is included.

Design of a voltage regulation device based on virtual air gap principle

PurposeThis paper aims to present the principle of virtual air gap inductance and the design of a voltage regulation device based on this principle. The authors provide a comprehensive analysis of this specific application that consists of locally saturating the magnetic circuit of the voltage regulator to modify its global properties. This saturation is created by a direct current flowing in a small auxiliary coil inserted in the specific area of the magnetic circuit to saturate this zone.Design/methodology/approachAnalytical calculation and finite elements simulations are used to optimize the device for a specific application tied to the supply of electrical ovens in metallurgic usage. Experimental results are presented at the end of the paper.FindingsThe experimental results presented in this paper are in concordance with the analytical calculation and with the finite element simulations for different operation points. The difficulty of the study of the virtual air gap comes mainly from the nonlinearity of the phenomena because the principle is based on a local and controllable saturation of the magnetic circuit.Originality/valueThe originality of the paper concerns the introduction of virtual air gap principle in a specific industrial application.

Computational Modeling of an Axial Airgap Induction Motor With a Solid Rotor

This article presents analytical calculations of an axial airgap or disk induction machine with a solid rotor. A quasi-3-D analytical analysis for the eddy current estimation in the solid disk rotor and 1-D and 2-D analytical analyses for the torque calculation are performed. The third-dimension effect in 1-D and 2-D analytical analyses is estimated by quasi-3-D analytical calculations of the eddy currents in the solid disk rotor. The analytical calculations are compared with the 3-D finite element method (FEM) and experimental results of a solid-rotor axial airgap induction motor. The analytical calculations are also used for the optimization of the axial airgap machine to improve torque characteristics at higher speeds.

Estimation of Parameters of Five-Phase Induction Motors Using Step Voltage At Standstill

This paper proposes a new method to estimate the electrical parameters of five-phase induction motors based on the response to a step voltage applied to the stator with the rotor at standstill. The first part of the method consists of the identification of the parameters of the dynamic model expressed in terms of transfer functions including the fundamental and third-harmonic components of the airgap induction. The second part consists of an open-phase test proposed to estimate the stator leakage inductances of each circuit separately. Further, the impact of iron saturation on the parameters is discussed through Finite Element Analysis of a case study. The accuracy of the proposed method is experimentally assessed through the analysis of the behavior of a 4.5-kW motor running in a closed loop under Rotor Field-Oriented Control. The theoretical and practical results suggest that the method can also be applied to self-commissioned drives, given that the estimation proceeds under null torque and speed. The prominent advantages of the proposed method are (i) the possibility of tracking the saturation effects on the parameters, (ii) the tests are easy to execute, and (iii) few sensors are required.

Magnetic circuit optimization of linear dynamic actuators

&lt;p class="Abstract"&gt;Contactless braking methods (with capability of energy recuperation) are more and more widely used and they replace the traditional abrasive and dissipative braking techniques. In case of rotating motion, the method is trivial and often used nowadays. But when the movement is linear and fast alternating, there are only a few possibilities to break the movement. The basic goal of research project is to develop a linear braking method based on the magnetic principle, which enables the efficient and highly controllable braking of alternating movements. Frequency of the alternating movement can be in wide range, aim of the research to develop contactless braking method for vibrating movement for as higher as possible frequency. The research includes examination and further development of possible magnetic implementations and existing methods, so that an efficient construction suitable for the effective linear movement control can be created. The first problem to be solved is design a well-constructed magnetic circuit with high air gap induction, which provides effective and good dynamic parameters for the braking devices. The present paper summarizes the magnetostatics design of “voice-coil linear actuator” type actuators and the effects of structure-related flux scattering and its compensation.&lt;/p&gt;

Improved Analytical Method to Determine Flux-Linkage Characteristics of a Switched Reluctance Machine

This article proposes an improved analytical method for accurate evaluation of flux-linkage characteristics for a given switched reluctance machine (SRM). Initially, air-gap inductance is calculated using an approximated analytical method, which incorporates the effect of fringing fluxes. Then, precepts of a conventional method are used to compute these characteristics under saturation, with a proposed new analytical model for nonuniform flux distribution in stator and rotor poles. Finally, for error quantification, these characteristics are benchmarked against those from a standard finite element analysis (FEA) based software. Both mean and standard deviation of the estimation errors are presented to quantify estimation accuracy. To establish its general validity, these characteristics are evaluated using the proposed method for six SRMs of different geometries and compared with those obtained from FEA. For further benchmarking, speed-torque characteristics obtained from the proposed method and FEA are presented and compared. Finally, both flux-linkage and torque-speed data are experimentally obtained from a 5 kW, 270 V, 12 000 r/min, 6/4 SRM and presented for validating the accuracy of the proposed method.

Air Gap Inductance Calculation for Transformer Transient Model

Zero sequence characteristic and parameters play a vital role in some transformer transients involving unbalance or saturation conditions such as inrush, ferroresonance, and Geomagnetically Induced Current (GIC). An important parameter of the zero-sequence characteristic is the inductance of the air gap between the core and the tank. Based on a Finite-Element Method (FEM), this letter determines the air gap inductance, considering fringing flux effects. The comparison of the simulation results with an analytical method shows a good agreement for small air gaps but reveals a significant difference for relatively large air gaps. Thus, an inductance enhancement factor (IEF) is introduced to correct the analytical results and facilitate the transformer modeling parameter estimation from the design data. Furthermore, the significance of the accurate calculation of the air-gap inductance is demonstrated in the time-domain simulation of different saturation levels of the transformer core, when the transformer is subjected to GIC.

A Simple Analytical Model of Static Eccentricity for PM Brushless Motors and Validation through FEM Analysis

The paper firstly summarizes a simple analytical model of the air gap flux-density distribution for isotropic permanent magnet (PM) synchronous machines, in the presence of static eccentricity. The model was proposed by the authors in a previous paper and is based on an efficacious analytical expression of the variable length of air gap magnetic field lines which occur in eccentric brushless machines with surface-mounted permanent magnets. The approximate expression of the air gap field makes it possible to achieve a mathematical model with concentrated parameters close to that of a PM machine without eccentricity. The expression of the armature voltages and electromagnetic torque are found, also with reference to steady-state operating conditions at fixed rotor speed and impressed currents. The differences introduced by the considered type of eccentricity are evaluated and highlighted especially with reference to the air gap inductance and to waveforms and frequency spectra of voltages and shaft torque. Numerical results in a case-study of an 8-pole, 110 kW PM motor are compared to those obtained by using finite element analysis.

Influence of Design Parameters on the Airgap Induction of Five-Phase Induction Machines Operating With One Phase Opened

This paper addresses the relation between some constructive parameters of five-phase induction machines and the airgap induction distribution under operation with one phase opened; we focus on the impact of design parameters on the airgap induction and the Joule losses. The influence of design parameters of the rotor and the stator is assessed using three distinct machines as a case study: two with identical stator but different rotors, and one with a distinct stator and also a distinct rotor. The results from the case study show that the characteristics of the stator windings, such as the number of slots per pole and phase and the number of layers, have less impact on the airgap induction under fault than under healthy operation. Besides, the case study shows that a decrease in the number of rotor bars contributes to an increase in the amplitude of the third harmonic component of the airgap induction. Finally, theoretical results are validated through analysis with the finite element method.

Induction distribution of five-phase induction machines under open-phase fault

The main objective of the paper is to determine the induction distribution of five-phase induction machines operating under unbalanced steady state, focusing on the operation with two opened stator phases. Firstly, we present an analytical model based on symmetric components which includes the third harmonic component of the airgap induction. The model is then used to determine the induction distribution in the airgap and also in the main iron parts, i.e. cores and teeth of the stator and rotor parts. The analytical model is thoroughly validated through two-dimensional Finite Element Analysis (FEA) and using extensive experimental data obtained from tests taken on a prototype machine of 5.5 kW; experimental data, as well results from FEA, showed a close agreement with theoretical data, which confirms the accuracy of the proposed model. The results indicate that when two phases are opened and with no control strategy to compensate the fault, the induction distributions can change significantly, predominantly in the stator and rotor teeth, as a result of additional induction harmonic components. These changes in the field distribution of stator and rotor teeth, in turn, can increase the associated magnetic losses as they are no longer evenly distributed among the teeth, thus potentially creating hot spots inside the machine. The model proposed can, therefore, serve as a basis to assess the overall magnetic losses and the load capacity under fault, given that the field distribution, as well as its associated effects, is essential to establish the machine capacity under unbalance.

Coil Inductance Model Based Solenoid on⁻off Valve Spool Displacement Sensing via Laser Calibration.

Direct acting solenoid on–off valves are key fluid power components whose efficiency is dependent upon the state of the spool’s axial motion. By sensing the trajectory of the valve spool, more efficient control schemes can be implemented. Therefore, the goal of this study is to derive an analytical model for spool displacement sensing based on coil inductance. First, a mathematical model of the coil inductance as a function of air gap width and lumped magnetic reluctance is derived. Second, to solve the inductance from coil current, an optimization to obtain an initial value based on physical constraints is proposed. Furthermore, an experiment using a laser triangulation sensor is designed to correlate the magnetic reluctance to the air gap. Lastly, using the obtained empirical reluctance model to eliminate unknowns from the proposed air gap-inductance model, the model in atmosphere or hydraulic oil environments was tested. Initial results showed that the proposed model is capable of calculating the spool displacement based on the coil current, and the estimation errors compared to the laser measurement are within ±7% in air environment.

Analysis and Comparative Study of Flux Weakening Capability in Fractional-Slot Concentrated Windings

This paper presents a detailed investigation of the winding inductance and the flux weakening capability in fractional-slot motors equipped with concentrated windings. An analytical model has been developed for evaluating the winding inductance by merging existent theories. Subsequently, a simple factor called weakening factor, which is proportional to the d -axis inductance and the pole pair, has been introduced to indicate the level of the flux weakening capability for different pole/slot combinations in the case where the air gap or slot leakage inductance is the dominant component. From the comparative study, it is shown that the multiple 4-pole/3-slot, i.e., ${\boldsymbol{S}_{\boldsymbol{pp}}} = 1/4$ , can have the highest flux weakening capability resulting from the highest air gap inductance. The experimental results from several prototype motors, together with finite element analysis, are employed to confirm the validity of key analyses discussed in the paper.

Experimental Testing and Analytical Solution by Means of Lambert W-Function of Inductor Air Gap Length

In this paper the exact analytical closed form solutions for inductor air gap length have been presented. To be specific, in a mathematical sense, the dependence between the air gap length, inductance and other constructional parameters of inductor is nonlinear, i.e. transcendental. In this paper that nonlinear equation is solved in two manners – by using the Lagrange inversion theorem of the Lambert W function or by using its asymptotic formula and by using Special Trans Functions Theory. The numerical results obtained by using these methods, are mutually compared in terms of the calculation error. In order to prove the validity of the mathematical dependence between the inductance, air gap length, and the other constructional parameters, two inductors have been created. The measured results of inductance and air gap length are compared with the corresponding results obtained by the calculations. Very good agreement is shown between the measured and the calculated value of both the air gap length and the inductance value.

Multiobjective Optimization of Five-Phase Induction Machines Based on NSGA-II

The paper proposes a multiobjective optimization procedure for five-phase induction machines based on the NSGA-II (nondominated sorting genetic algorithm). In the optimization procedure, two objective functions are used (efficiency and cost of conductor material) along with 14 design variables, producing a large number of viable solutions. The design variables describe geometrical constraints, electrical and magnetic loading, and the waveshape of the airgap induction. The underlying analytical model of the machine includes the saturation of the iron parts and magnetic losses produced by higher space harmonic waves present in the airgap induction. The most relevant solutions regarding the objectives are validated through the finite element method, showing that the method proposed here is able to find practical solutions which represent a high efficiency, a reduced volume, or even a compromise between these objectives.

Design, analysis, and implementation of extra low air-gap single-phase axial-flux induction motors for low-cost applications

Summary In this paper, design and prototyping of two-speed capacitor-run single-phase axial-flux induction motor (AFIM) for direct-drive applications is presented. The proposed structure has single stator-single rotor configuration with high magnetic pull between the stator and rotor, which may compel rotor to lock. Although the most efficient method to overcome this problem is using a second rotor or stator in the mirror with the first one, it is not applicable in low-cost applications. So, in this paper, two new and fast construction techniques are proposed to fabricate an AFIM with extra low air-gap length and minimum cost. Beside design and optimization process, a thermal equivalent circuit considering radial and lateral heat transfers is proposed. Then different losses and thermal resistances are exactly calculated to estimate the temperature rise of different motor parts and the maximum specific magnetic and electric loadings. Then, motor performance is evaluated using three-dimensional time-stepping finite-element analysis. Finally, a comprehensive fabrication algorithm for AFIMs is presented, and a prototype of the studied motor is fabricated and tested. The experimental results validate the design, optimization, thermal model, and finite element simulations. Copyright © 2016 John Wiley & Sons, Ltd.

A Model for Analyzing a Five-Phase Fractional-Slot Permanent Magnet Tubular Linear Motor with Modified Winding Function Approach

This paper presents a model for analyzing a five-phase fractional-slot permanent magnet tubular linear motor (FSPMTLM) with the modified winding function approach (MWFA). MWFA is a fast modeling method and it gives deep insight into the calculations of the following parameters: air-gap magnetic field, inductances, flux linkages, and detent force, which are essential in modeling the motor. First, using a magnetic circuit model, the air-gap magnetic density is computed from stator magnetomotive force (MMF), flux barrier, and mover geometry. Second, the inductances, flux linkages, and detent force are analytically calculated using modified winding function and the air-gap magnetic density. Finally, a model has been established with the five-phase Park transformation and simulated. The calculations of detent force reveal that the end-effect force is the main component of the detent force. This is also proven by finite element analysis on the motor. The accuracy of the model is validated by comparing with the results obtained using semianalytical method (SAM) and measurements to analyze the motor’s transient characteristics. In addition, the proposed method requires less computation time.

A Method for Optimization of Five-Phase Induction Machines Based on Genetic Algorithms

The optimization of five-phase induction machines is addressed using a new procedure based on genetic algorithms. A constrained optimization model is introduced which considers the main machine dimensions as free variables. Number of stator and rotor slots, winding pitch, and rotor bar inclination angle are among the free design variables. In addition, the relationship between fundamental and third harmonic component of the airgap induction is also considered as a free variable. This relationship is used to shape the airgap induction making it near to a trapezoid, thus potentially increasing the output torque. The underlying machine model used in the optimization process is detailed in previous works and includes the effect of losses and saturation on the steady state performance. Thus, a mixed-integer optimization problem is defined, in which the continuous variables are codified as integer variables making the optimization problem easier to solve. Three objective functions are defined and tested: efficiency, cost of conductor material, and a weighted combination of efficiency and material costs; other objective functions can be defined, too. The proposed method was applied to the optimization of a 5.5-kW prototype machine, and the results are presented and discussed.