Nonlinear design optimization of electric machines by using parametric Fourier coefficients of air gap flux density

2016 ◽  
Author(s):  
Norman Borchardt ◽  
Roland Kasper
Keyword(s):  
Design Optimization ◽  
Flux Density ◽  
Fourier Coefficients ◽  
Electric Machines ◽  
Air Gap ◽  
Nonlinear Design

Parametric model of electric machines based on exponential Fourier approximations of magnetic air gap flux density and inductance

2018 ◽  
Vol 37 (1) ◽  
pp. 520-535 ◽  
Author(s):  
Norman Borchardt ◽  
Roland Kasper
Keyword(s):  
Finite Element ◽  
Magnetic Flux ◽  
Flux Density ◽  
Fourier Coefficients ◽  
Magnetic Circuit ◽  
Parametric Model ◽  
Air Gap ◽  
Magnetic Flux Density ◽  
Electrical Machine ◽  
Content Type

Purpose This study aims to present a parametric model of a novel electrical machine, based on a slotless air gap winding, allowing for fast and precise magnetic circuit calculations. Design/methodology/approach Approximations of Fourier coefficients through an exponential function deliver the required nonlinear air gap flux density and inductance. Accordingly, major machine characteristics, such as back-EMF and torque, can be calculated analytically with high speed and precision. A physical model of the electrical machine with air gap windings is given. It is based on a finite element analysis of the air gap magnetic flux density and inductance. The air gap height and the permanent magnetic height are considered as magnetic circuit parameters. Findings In total, 11 Fourier coefficient matrixes with 65 sampling points each were generated. From each, matrix a two-dimensional surface function was approximated by using exponentials. Optimal parameters were calculated by the least-squares method. Comparison with the finite element model demonstrates a very low error of the analytical approximation for all Fourier coefficients considered. Finally, the dynamics of an electrical machine, modeled using the preceding magnetic flux density approximation, are analyzed in MATLAB Simulink. Required approximations of the phase self-inductance and mutual inductance were given. Accordingly, the effects of the two magnetic circuit parameters on the dynamics of electrical machine current as well as the electrical machine torque are explained. Originality/value The presented model offers high accuracy comparable to FE-models, needing only very limited computational complexity.

A novel analytical calculation of magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping

2020 ◽  
pp. 1-15
Author(s):  
Jianqi Li ◽  
Yu Zhou ◽  
Jianying Li
Keyword(s):  
Magnetic Field ◽  
Conformal Mapping ◽  
Permanent Magnet ◽  
Flux Density ◽  
Analytical Method ◽  
Electromotive Force ◽  
Analytical Calculation ◽  
Air Gap ◽  
Permanent Magnet Machines ◽  
Peak Value

This paper presented a novel analytical method for calculating magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping. Firstly, flux density without slots and complex relative air-gap permeance of slotted air gap are derived from conformal transformation separately. Secondly, they are combined in order to obtain normalized flux density taking account into the slots effect. The finite element (FE) results confirmed the validity of the analytical method for predicting magnetic field and back electromotive force (BEMF) in the slotted air gap of spoke-type permanent-magnet machines. In comparison with FE result, the analytical solution yields higher peak value of cogging torque.

scholarly journals Design of a New 1D Halbach Magnet Array with Good Sinusoidal Magnetic Field by Analyzing the Curved Surface

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2522
Author(s):  
Guangdou Liu ◽  
Shiqin Hou ◽  
Xingping Xu ◽  
Wensheng Xiao
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Permanent Magnet ◽  
Flux Density ◽  
Permanent Magnets ◽  
Air Gap ◽  
Curved Surface ◽  
Magnetic Flux Density ◽  
Sinusoidal Magnetic Field ◽  
The Magnetic Field

In the linear and planar motors, the 1D Halbach magnet array is extensively used. The sinusoidal property of the magnetic field deteriorates by analyzing the magnetic field at a small air gap. Therefore, a new 1D Halbach magnet array is proposed, in which the permanent magnet with a curved surface is applied. Based on the superposition of principle and Fourier series, the magnetic flux density distribution is derived. The optimized curved surface is obtained and fitted by a polynomial. The sinusoidal magnetic field is verified by comparing it with the magnetic flux density of the finite element model. Through the analysis of different dimensions of the permanent magnet array, the optimization result has good applicability. The force ripple can be significantly reduced by the new magnet array. The effect on the mass and air gap is investigated compared with a conventional magnet array with rectangular permanent magnets. In conclusion, the new magnet array design has the scalability to be extended to various sizes of motor and is especially suitable for small air gap applications.

scholarly journals DESIGN OF A SINGLE-PHASE RADIAL FLUX PERMANENT MAGNET GENERATOR WITH VARIATION OF THE STATOR DIAMETER

2019 ◽  
Vol 81 (4) ◽  
Author(s):  
Hari Prasetijo ◽  
Winasis Winasis ◽  
Priswanto Priswanto ◽  
Dadan Hermawan
Keyword(s):  
Magnetic Flux ◽  
Permanent Magnet ◽  
Flux Density ◽  
Single Phase ◽  
Air Gap ◽  
Wire Diameter ◽  
Terminal Phase ◽  
Magnetic Flux Density ◽  
Phase Voltage ◽  
Radial Flux

This study aims to observe the influence of the changing stator dimension on the air gap magnetic flux density (Bg) in the design of a single-phase radial flux permanent magnet generator (RFPMG). The changes in stator dimension were carried out by using three different wire diameters as stator wire, namely, AWG 14 (d = 1.63 mm), AWG 15 (d = 1.45 mm) and AWG 16 (d = 1.29 mm). The dimension of the width of the stator teeth (Wts) was fixed such that a larger stator wire diameter will require a larger stator outside diameter (Dso). By fixing the dimensions of the rotor, permanent magnet, air gap (lg) and stator inner diameter, the magnitude of the magnetic flux density in the air gap (Bg) can be determined. This flux density was used to calculate the phase back electromotive force (Eph). The terminal phase voltage (V∅) was determined after calculating the stator wire impedance (Z) with a constant current of 3.63 A. The study method was conducted by determining the design parameters, calculating the design variables, designing the generator dimensions using AutoCad and determining the magnetic flux density using FEMM simulation.  The results show that the magnetic flux density in the air gap and the phase back emf Eph slightly decrease with increasing stator dimension because of increasing reluctance. However, the voltage drop is more dominant when the stator coil wire diameter is smaller. Thus, a larger diameter of the stator wire would allow terminal phase voltage (V∅) to become slightly larger. With a stator wire diameter of 1.29, 1.45 and 1.63 mm, the impedance values of the stator wire (Z) were 9.52746, 9.23581 and 9.06421 Ω and the terminal phase voltages (V∅) were 220.73, 221.57 and 222.80 V, respectively. Increasing the power capacity (S) in the RFPMG design by increasing the diameter (d) of the stator wire will cause a significant increase in the percentage of the stator maximum current carrying capacity wire but the decrease in stator wire impedance is not significant. Thus, it will reduce the phase terminal voltage (V∅) from its nominal value.

Effect of Stator Insulation Failure on the Motor Drive System Performance

2021 ◽  
Vol 35 (11) ◽  
pp. 1370-1371
Author(s):  
Hassan Eldeeb ◽  
Haisen Zhao ◽  
Osama Mohammed
Keyword(s):  
Flux Density ◽  
System Performance ◽  
Induction Machines ◽  
Air Gap ◽  
Drive System ◽  
Self Control ◽  
Motor Drive ◽  
Iron Core ◽  
Insulation Failure ◽  
Motor Drive System

This study investigates the influence of the stator’s turn-to-turn failures (TTFs) on the electromagnetic (EM) fields, such as air gap flux density, flux density in the stator, and rotor iron core inside of direct self-control (DSC) driven induction machines (IMs). The purpose of the investigation is to capture the fault signatures in the air gap EM flux for detecting the stator’s fault at its embryonic stage.

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