考虑磁齿轮偏心率和倾斜度的三维磁场数学模型

IF 2.1 3区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC
Jiaxin Ding;Yaming Liu;Sijie Huang;Haocheng Su;Ligang Yao
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引用次数: 0

摘要

偏心和倾斜是磁齿轮中常见的故障类型,是摆线磁齿轮(CyMG)和转轴磁齿轮(NMG)稳定传动的先决条件。偏心和倾斜会改变磁齿轮气隙的磁导率,从而在其中产生复杂的谐波磁场。为了阐明偏心率和倾角对气隙磁场的调制效应,并解决目前二维磁场模型无法计算磁齿轮倾角引起的三维磁场分布的局限性。本文提出了一种磁齿轮偏心和倾斜的三维数学模型,称为基于磁导系数的改进子域方法(PC-ISM)。首先,该方法计算同轴磁齿轮的三维磁场。然后,利用磁导系数将其映射到非均匀气隙磁齿轮对的三维磁场上,从而在保持精度的同时,减轻了计算偏心和倾角引起的三维磁场所带来的挑战。磁导系数不仅可作为各种磁齿轮设置的三维磁场映射,还可作为非均匀气隙对磁场调制效应的描述符。本文研究了磁场特性(包括分布、强度和阶次)以及机械特性(如扭矩、扭矩纹波和轴向力),并通过有限元模拟进行了验证。研究发现,CyMG 和 NMG 都能将 $p_{\text {pm}}$ 三阶基波磁场转换为 $p_{\text {pm}}\pm 1$ 三阶谐波磁场。因此,为确保稳定传输,磁极对的数量差必须为 1。当最小气隙恒定时,转角气隙中的平均谐波磁场强度超过摆线气隙中的平均谐波磁场强度,这表明转角增强了谐波磁场强度。在机械特性分析中,NMG 的最大传动扭矩达到 13.82 N $\cdot $ m,计算的体积扭矩密度等于 189.90 kN $\cdot $ m/m3。在不同的输入速度下,磁齿轮 1(MG1)的输出速度很快趋于稳定,稳定后的传动比为-8.71。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
3-D Magnetic Field Mathematical Model Considering the Eccentricity and Inclination of Magnetic Gears
Eccentricity and inclination are common fault types in magnetic gears, serving as prerequisites for the stable transmission of cycloidal magnetic gears (CyMG) and nutation magnetic gears (NMGs). Eccentricity and inclination alter the permeance of the magnetic gear air gap, leading to the generation of complex harmonic magnetic fields within it. To clarify the modulation effects of eccentricity and inclination on the air gap magnetic field, and address the limitation of current 2-D magnetic field models, which fail to calculate the 3-D magnetic field distribution caused by magnetic gear inclination. This article presents a 3-D mathematical model for magnetic gears’ eccentricity and inclination, termed the permeance coefficient-based improved subdomain method (PC-ISM). First, this method computes the 3-D magnetic field of the coaxially facing magnetic gear. Then, by mapping it onto the 3-D magnetic field of the nonuniform air-gap magnetic gear pair using the magnetic permeance coefficient, it mitigates the challenge of calculating the 3-D magnetic field arising from eccentricity and inclination while preserving accuracy. The magnetic permeance coefficient serves not only as a 3-D magnetic field mapping for various magnetic gear setups but also as a descriptor of the modulation effect of nonuniform air gaps on the magnetic field. This article examines the magnetic field characteristics, including distribution, intensity, and order, along with the mechanical characteristics such as torque, torque ripple, and axial force, and verifies these through finite element simulation. The study found that both CyMG and NMG can convert the $p_{\text {pm}}$ th order fundamental magnetic field into the $p_{\text {pm}}\pm 1$ th order harmonic magnetic field. Thus, to ensure stable transmission, the number difference of magnetic pole pairs must be 1. When the minimum air gap is constant, the average harmonic magnetic field intensity in the nutation air gap exceeds that in the cycloid air gap, indicating that the nutation angle enhances the harmonic magnetic field intensity. In the mechanical characteristics analysis, the maximum transmission torque of the NMG reaches 13.82 N $\cdot $ m, and the calculated volume torque density equals 189.90 kN $\cdot $ m/m3. At different input speeds, the output speed of magnetic gear 1 (MG1) quickly stabilizes, with a transmission ratio of −8.71 after stabilization.
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来源期刊
IEEE Transactions on Magnetics
IEEE Transactions on Magnetics 工程技术-工程:电子与电气
CiteScore
4.00
自引率
14.30%
发文量
565
审稿时长
4.1 months
期刊介绍: Science and technology related to the basic physics and engineering of magnetism, magnetic materials, applied magnetics, magnetic devices, and magnetic data storage. The IEEE Transactions on Magnetics publishes scholarly articles of archival value as well as tutorial expositions and critical reviews of classical subjects and topics of current interest.
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