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

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.

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Fast analytical calculation of the air-gap flux density in an outer-rotor permanent-magnet brushless motor

MATEC Web of Conferences ◽

10.1051/matecconf/201818906008 ◽

2018 ◽

Vol 189 ◽

pp. 06008

Author(s):

Shuaichen Ye ◽

Xiaoxian Yao

Keyword(s):

Permanent Magnet ◽

Flux Density ◽

Analytical Method ◽

Analytical Calculation ◽

Air Gap ◽

Element Analysis ◽

Design And Optimization ◽

Brushless Motor ◽

Practical Engineering ◽

Analytical Result

The air-gap flux density must be considered in the design and optimization of the structure parameters of permanent-magnet brushless motors (PMBMs). Existing methods for calculating the air-gap flux density are complex and thus cannot be easily applied in practical engineering. This paper presents a fast analytical method for calculating the air-gap flux density that is more efficient and practicable than existing methods. A lumped magnetic circuit model is presented to illustrate the proposed method. Then, the analytical result and finite element analysis (FEA) results obtained for a PMBM prototype are compared. The results indicate that the error between the two methods does not exceed 5%. Therefore, the proposed analytical method is highly efficient and accurate, which may be applied in the motor pro-design process of many engineering instruments.

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An Exact Analytical Solution of Halbach Arrays Permanent-Magnet Motor for Magnetic Field on Load

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.416-417.58 ◽

2013 ◽

Vol 416-417 ◽

pp. 58-65 ◽

Cited By ~ 1

Author(s):

Chen Li ◽

Hang Zhang ◽

Li Bing Jing ◽

Yue Jin Zhang ◽

Jie Bao Li

Keyword(s):

Magnetic Field ◽

Permanent Magnet ◽

Flux Density ◽

Analytical Method ◽

Exact Analytical Solution ◽

Air Gap ◽

Reaction Field ◽

Armature Reaction ◽

Air Gap Magnetic Field ◽

Halbach Arrays

An exact analytical model of Halbach arrays permanent-magnet (PM) motor is established for the calculation of air-gap magnetic field on load in this paper. The exact analytical method is based on the resolution of Laplaces or Poissons equations by applying the boundary conditions on the interface between each sub-domain: air-gap, Halbach arrays and slots. The waveforms of no-load magnetic field flux density, back electromotive force (EMF), armature reaction field flux density, air-gap magnetic field flux density on load and electromagnetic torque, which computed by the analytical method were validated through the finite-element method (FEM).

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

Sensors ◽

10.3390/s21072522 ◽

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.

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