Leakage Permeance Research Articles

An Enhanced Magnetic Equivalent Circuit Model for a Magnetorheological Clutch Including Nonlinear Permeability, Flux Fringing, and Leakage Effects

Magnetorheological (MR) clutches have significant potential in electromechanical interface and are a promising technology with high commercial value in the automotive industry. A quick and precise magnetic circuit modeling method is demanded to calculate performance or optimize design of the MR clutch. Conventional magnetic circuit models present poor accuracy because they often fail to accurately include nonlinearities such as magnetic saturation, magnetic fringing, and magnetic leakage. In this regard, an enhanced magnetic equivalent circuit (EMEC) model based on lumped parameter method is proposed. This model can not only cope with clutch geometry and material properties (nonlinear permeability) but can also consider flux fringing and leakage effects. Combined with the specific structure, formulae for the calculation of fringing permeances and leakage permeances in the magnetic circuit of the MR clutch are presented. Finite-element analysis (FEA) and experimental results show that the proposed EMEC model can provide better accuracy compared with magnetic equivalent circuit (MEC) model from available literature and provide less computational effort compared with FEA. Moreover, the influence of design parameters corresponding to device geometry and material properties on the output flux density is discussed based on the proposed EMEC model. All taken together, the proposed EMEC model provides a comprehensive knowledge in optimize design and performance prediction of MR device.

Magnetic Design Aspects of Coupled-Inductor Topologies for Transient Suppression

Based on the discovery of the surge absorption capability of supercapacitors, a transient protector named supercapacitor-assisted surge absorber (SCASA) was designed and implemented in a commercial device. Despite its simplicity, the circuit topology consisted of a coupled inductor wound around a specially selected magnetic core. This paper elucidates the design aspects of SCASA coupled-inductor topologies with a special focus on the magnetic action of core windings during transient propagation. The non-ideal operation of the SCASA transformer was studied based on a semi-empirical approach with predictions made by using magnetizing and leakage permeances. The toroidal flux distribution through the transformer was also determined for a 6 kV/3 kA combinational surge, and these findings were validated by using a lightning surge simulator. In predicting the possible effects of magnetic saturation, the hysteresis properties of different powdered-iron and ferrite core types were considered to select the optimal design for surge absorption. The test results presented in this research revealed that X-Flux powdered-iron toroid and air-gapped EER ferrite yielded exceptional performance with ∼10% and ∼20% lower load–voltage clamping compared to that of the existing Kool μu design. These prototypes further demonstrated a remarkable surge endurance, withstanding over 250 consecutive transients. This paper also covers details of three-winding design optimizations of SCASA and LTSpice simulations under the IEC 61000/IEEE C62.45 standard transient conditions.

Multi-objective optimum design of five-phase squirrel cage induction motor by differential evolution algorithm

Compared with the traditional induction motors, five-phase squirrel cage induction motor (FSCIM) have the advantages of lower torque ripple and single-phase power, flexible control strategy, higher power density and fault-tolerant operation, which has been widely applied on electrical vehicles, rail transit, underwater vehicles and so on. This paper presents an analytical design optimization method based on the coupling of electromagnetic equivalent circuit (EEC) and differential evolution algorithm (DEA). Furthermore, the difference between three and five-phase winding on harmonic specific leakage permeance is investigated in detail. The nonlinear and oeolotropic influences of design geometrical parameters (slots openings, main dimension ratio, yoke height, airgap length, etc.) on the performances of the basic FSCIM model are evaluated with analytical model. For more accurate results, the harmonic characteristics of five-phase winding structure, iron core saturation, rotor slot skew width, stator end winding, slot leakage inductance and stator and rotor slot structure are considered. Meanwhile, the efficiency, power factor, maximum torque, slot fill factor and material consumption of FSCIM are calculated as the comprehensive objective function. The transient finite element analysis (TFEA) and experimental test verify the accuracy of the proposed optimum model. In addition, the feasibility of the multi objective optimization design scheme provided by the analytical model is verified by TFEA.

Analytical calculation of leakage permeance of coreless axial flux permanent magnet generator

PurposeThis paper aims to study the relationship between leakage flux coefficient and the coreless axial magnetic field permanent magnet synchronous generator (AFPMSG) size and obtain the expressions of leakage flux coefficient.Design/methodology/approachIn this paper, a magnetic circuit model of coreless AFPMSG is proposed. Four kinds of leakage permeances of permanent magnet (PM) are considered, and the expression of no-load leakage flux coefficient is obtained. Solving the integral region of leakage permeances by generator size, which improves the accuracy of the solution.FindingsFinite element method and magnetic circuit method are used to obtain the no-load leakage flux coefficient and its variation trend charts with the change of pole arc coefficient, air gap length and PM thickness. The average errors of the two methods are 2.835%, 0.84% and 1.347%, respectively. At the same time, the results of single-phase electromotive force obtained by magnetic circuit method, three dimensional finite element method and prototype experiments are 19.36 V, 18.82 V and 19.09 V, respectively. The results show that the magnetic circuit method is correct in calculating the no-load leakage flux coefficient.Originality/valueThe special structure of the coreless AFPMSG is considered in the presented equivalent magnetic circuit and equations, and the equations in this paper can be applied for leakage flux evaluating purposes and initial parameter selection of the coreless AFPMSG.

Improved Method for Distributed Parameter Model of Solenoid Valve Based on Kriging Basis Function Predictive Identification Program

In this paper, a method for the improvement of the calculation accuracy of the distributed parameter model (DPM) of electromagnetic devices is proposed based on the kriging basis function predictive identification program (PIP). Kriging is mainly an optimal interpolation method which uses spatial self-covariance, and takes a polynomial as the basis function. The accuracy of the kriging-based surrogate model can be improved by adjusting the related functions and hyperparameters. Based on the DPM of a solenoid valve, there exist certain errors in the estimation. They can be summarized as follows: Firstly, the estimation error of magnetic flux leakage (MFL) permeance is caused directly by the deviation of the magnetic flux tube due to the segmented magnetic field line. Secondly, the estimation error of soft magnetic resistance because of the nonlinearity of the permeability of soft magnetic material leads to the change of soft magnetic resistance alongside the magnetic flux. In this paper, an improved kriging error correction method is applied to modify the leak permeance and soft magnetic resistance calculation. The kriging basis function is adjusted to adapt to the data curve of the MFL permeance error data. The calculated MFL permeance data are compared with the error variation data to select the appropriate basis function. To improve the computational efficiency, the PIP is proposed to select the appropriate basis function. The modified MFL permeance data and soft magnetic resistance are substituted into the DPM for improving the computational accuracy and efficiency of the solenoid valve.

Magnetic Circuit Modeling of Dual-Armature Flux-Switching Permanent Magnet Machine

Three lumped-parameter magnetic circuit (LMC) models of dual-armature flux-switching permanent magnet (DA-FSPM) machines are proposed and compared in this article. First, the characteristics of the magnetic flux fields produced by the PM, stator armature reaction, and rotor armature reaction flux sources are analyzed, with particular attention paid to the air-gap and slot leakage flux paths. Based on the former analyses, three LMC models are developed, which consider the air-gap and slot leakage permeances in different ways. The electromagnetic performances of the DA-FSPM machines are predicted by the three LMC models and validated by the finite-element method, including the flux linkage, average torque, inductance, and power factor. The model accuracy sensitivity to the geometric parameters, copper loss allocation, electric loading, stator pole/rotor tooth number combinations, power level, and conductor distributions are analyzed. It shows that appropriate consideration of slot leakage permeance is important to improve the model accuracy.

Modeling and analysis of spoke-type permanent magnet vernier machine based on equivalent magnetic network method

In this paper, a new equivalent magnetic network(EMN) model is established for a spoke-type permanent magnet(PM) vernier(PMV) machine. Two different modeling methods are proposed for different parts of the PMV machine, considering that their magnetic field distributions are quite different. Hierarchical modeling method is proposed for the modeling of the rotor as the magnetic intensity of the rotor iron core presents gradient distribution along the radial direction. Mesh based reluctance network method is used for the modeling of flux modulation poles with irregular and unstable magnetic field distributions. Moreover, accurate PM leakage permeance calculation formulae are deduced to improve the simulation precision. The electromagnetic parameters, such as flux linkage, back electromagnetic force, electromagnetic torque and iron loss are predicted by the proposed EMN model. Finally, finite element analysis(FEA) and experimental results are given to verify the effectiveness of the proposed methods.

Permeance Analysis and Calculation of the Double-Radial Rare-Earth Permanent Magnet Voltage-Stabilizing Generation Device

The structure and magnetic circuit of the modern permanent magnet (PM) generator are often very complicated, which makes the traditional finite element analysis of magnetic field highly difficult. This paper establishes an equivalent magnetic circuit model of a new double-radial PM generator using the traditional equivalent circuit method and data analysis, introduces the calculation formulas of permeance and leakage permeance (LP) in magnetic circuits in detail, analyzes the influence factors of the LP, and provides the solutions. These studies will have a certain guiding significance for the design and optimization of generator circuits. To obtain the best matching parameters, the main parameters of the generator are tested and analyzed, such as the thickness of PM steel in the magnetization direction, length of PM steel, number of pole pairs, and the thickness of spacer bush. Finally, a prototype is tested, and the results show that the output characteristics of the designed double-radial PM voltage-stabilizing generation device are very good.

Analytical Calculation of Back EMF Waveform for Linear PM Motors in Slotted and Slotless Structures

This paper presents the analytical calculation of back electromotive force (EMF) waveform for linear permanent magnet motors in either slotted or slotless structures. The predictions are based on the analysis of the 2-D magnetic field distributions and the 3-D end effects. In the slotted structure, the relative permeance function obtained by the Schwarz-Christoffel conformal mapping is used to take into account the effects of slotting and to calculate the air-gap flux density. Subsequently, to evaluate the leakage components resulting from the slot opening, slot opening factor is introduced to reflect the elements which do not follow the intended path to produce the back EMF. In the slotless structure, the effective values of the magnetic field quantities, together with the extended theory of winding factors, are employed to evaluate the back EMF waveform. For the analysis of the axial end effects, the 3-D leakage factor is incorporated into the analytical solutions by adding the end leakage permeance to the entire magnetic circuit models. The validity of the analytical results for each topology is confirmed by 2-D finite element and experimental results.

Analytical Method for the Magnetic Field Line Distribution of a Fan-shaped Permanent Magnet and the Calculation of Leakage Permeance

Leakage permeance of a permanent magnet (PM) is an important factor for improving the accuracy of electromagnetic device calculations based on a magnetic equivalent circuit (MEC). For PM leakage permeance calculations, the traditional simulation method of finite element analysis (FEA) and the lumped parameter analytical method (LPAM) have been considered; it was found that FEA has the disadvantage of a long calculation time and LPAM has low accuracy. The magnetic field lines distribution analytical method (MFLD) is proposed in this paper in order to raise computational efficiency and keep accuracy within a certain range. The electromagnetic features of open circuit fan-shaped PMs are presented by MFLD and finite element analysis (FEA) is adopted to match the MFLD results. In order to verify the validity of the proposed method in a magnetic system, the working points of PMs in an electromagnetic actuator are calculated, and the numerical results compared with the experimental results.

Magnetic Circuit Analysis for a Magnetless Double-Rotor Flux Switching Motor

In this paper, an efficient and effective magnetic circuit model is developed for the analysis of a magnetless double-rotor flux switching motor. First, a magnetic circuit network for the proposed machine is built, and formulas for the calculation of the magnetic components in the circuit, including the permeances of teeth, yokes, slots, leakage permeances, and air-gap permeances, are derived. Then, by applying Kirchhoff’s current law to each node in the network, nodal analysis is used to solve the matrix equation. All the circuit variables, and hence the complete motor magnetic characteristics are being considered. When the rotor rotates, the air-gap permeances are adjusted accordingly, and the above calculations are repeated, so as to find the complete static performance of the motor. Last, the validity and the effectiveness of the proposed method are verified using both the experimental results and the simulation results obtained from the time-stepping finite-element method.

Research on Leakage Permeance Calculation of Bar Permanent Magnet in Open Magnetic Circuit

For electric magnetic system which contains permanent magnet, its calculation results often has a low level accuracy when using equivalent circuit method .The calculation method of permanent magnet leakage permeance is the key point and needs to be improved. The leakage permeance calculation formulas of bar type permanent magnet are deduced. The magnetic field simulation method and analytical method for calculating leakage permeance of bar type permanent magnet in open magnetic circuit are investigated based on the finite element method. An example is given and the results are validated by experiment. The methods and results can be used to found the equivalent magnetic model with high accuracy.

An Analytical Model for Leakage Effect in the Electrical Generator of Rim-Driven Marine Current Power System

This paper presents an equivalent magnetic circuit model to predict the leakage effect, especially the end leakage effect, of surface-mounted permanent magnet synchronous machine (SPMSM) in rim-driven marine current power (RMCP) system. The end leakage effect is usually neglected in most conventional permanent magnet (PM) machines. However, it is significant in the electrical generator of RPCM due to the short axial length. The idealized path and analytical expressions of end leakage permeance are given in this paper. Finite Element Method (FEM) 3D/2D and experimental values are presented to validate the proposed analytical model. With no need for the time-consuming FEM-3D calculation, a correction factor base on the analytical mode is proposed to adjust the results (e.g. back-EMF, torque) of conventional design when end leakage is ignored in the calculation. The calculation results and experimental values show that the proposed analytical model is accurate to analyze the leakage effects of SPMSM in RMCP system.

98/02149 Aspects of design optimization for multiple tooth per stator pole switched reluctance motors

A design package has been developed for a multiple tooth switched reluctance motor, which can be run interactively. The rectilinear 2D permeance data, corrected for slot depth and taper, are input of the package. An approximate end effect, estimated on the basis of the assumed flux path method, is used to further correct the 2D unaligned permeance. The leakage permeances, required in the iterative processes of the design, are also calculated by the assumed flux path method. The predicted performance of the motor has a reasonable accuracy in comparison with the measured values and finite element computation.

Design computations and performance characteristics prediction for multiple tooth switched reluctance motor

A design package has been developed for a multiple tooth switched reluctance motor, which can be run interactively. The rectilinear 2D permeance data, corrected for slot depth and taper, are input of the package. An approximate end effect, estimated on the basis of the assumed flux path method, is used to further correct the 2D unaligned permeance. The leakage permeances, required in the iterative processes of the design, are also calculated by the assumed flux path method. The predicted performance of the motor has a reasonable accuracy in comparison with the measured values and finite element computation.

CALCULATION OF ADDITIONAL SLOT LEAKAGE PERMEANCE IN ELECTRICAL MACHINES DUE TO RADIAL VENTILATION DUCTS

The 3D magnetic field in the region with ventilation duct of electrical machine has been analyzed. The method of reduced scalar magnetic potential in connection with the FE method has been used to solve the problem. On the basis of field distribution, the slot leakage permeance has been calculated. The problem has also been solved analytically. It has been assumed that the radial component of magnetic field density in ventilation ducts is equal to zero. The comparison of results leads to the conclusion that, in practice, the analytical calculations are satisfactory accurate.

An improved design procedure for hybrid stepper motors

A design methodology for hybrid stepper motors is presented. It takes into account the saturation throughout the motor, allows for variations in magnet working point, and enables the designer to optimize the balance of coil and magnet MMFS (magnetomotive forces) to achieve a specified holding torque. The procedure is based on the use of the finite-element technique to generate permeance curves for the complex tooth/airgap region of the motor, accounting for localized saturation effects in the teeth. The curves are then used in a nonlinear lumped parameter network of the entire motor. The network models the motor's 3-D nature and may include other saturating elements as well as leakage permeances. By applying the virtual-work technique, the lumped parameter network is used to calculate torque/displacement characteristics as well as the winding inductance and back-EMF (electromotive force) constants. The technique has been used in the design and analysis of several industrial stepper motors utilizing high-energy rare-earth magnets. >

Optimum magnetic circuit design for small DC servometers based on numerical analyses

AbstractFor the purpose of miniaturization of DC servomotors with slotted armatures of the side‐leg type, a numerical analysis is made, taking into account magnetic circuit configurations and materials i;the magnetization characteristics of each section are obtained and the optimum circuit design conditions are specified.For a side‐leg type structure using the rare‐earth magnet, the numerical analysis is made using the difference method and the circuit is divided into main and leakage portions. The design approach is to deal first with the main circuit, in which magnetic saturation is considered, and then to consider the leakage circuit, with the operating points of the magnet made equal. The structure as related to leakage permeance is specified quantitatively. For the armature tooth section constituting the main circuit is analyzed, considering saturation, and the flux density distribution together with the magnetic potential drops as the air‐gap flux increases, are obtained for each section. Based upon these analytical results, the optimum circuit design conditions to yield the maximum power rate‐to‐weight ratio are demonstrated and the relation between material and performance limitations are given.

Recording head design calculations

Factors affecting the design and performance of digital recording heads are discussed with reference to multitrack write/read heads for use with thin high-coercivity disc media. Account is taken of the flux leakage paths round each ferrite core to calculate the core efficiency and crosstalk from an adjacent core. The efficiency for a core with permeability = 1000 is about 20% less than obtained by neglecting leakage. Formulae are given to find the minimum recording gap, leakage permeances, peak output, and write current. Values are plotted versus gap length and depth, pole-tip angle, back gap, core pitch, and permeability.

Determination of Leakage Permeance for Permanentic Generators Used in Control Applications

In the design of permanentic machines for control applications the calculation of leakage permeance can be determined by considering the contribution from the various leakage paths. The method of determining leakage permeance is described in some detail and its use in the optimum design of permanent magnet machines is indicated.