Magnetic field analytical model for magnetic harmonic gears using the fractional linear transformation method

Yuejin Zhang,Junda Zhang,Ronghui Liu

doi:10.23919/cjee.2019.000005

Yuejin Zhang, Junda Zhang + Show 1 more

Open Access

https://doi.org/10.23919/cjee.2019.000005

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Abstract

Magnetic harmonic gears with high gear ratios exhibit high torque densities. However, the revolution and rotation of the eccentric rotor makes the magnetic field analysis complex. In this study, an analytical model of magnetic fields for magnetic harmonic gears is developed by using the fractional linear transformation method. The transformation formula is accurate in theory and suitable for the analysis of magnetic fields with large eccentricity. The rotor eccentricity region in the z-plane is mapped onto a uniform region in the w-plane. The magnetic field solutions are obtained by modulating the magnetic field distributions without rotor eccentricity with the relative permeance function derived from the effect of rotor eccentricity. The torque of magnetic harmonic gears is calculated from the radial and tangential components of the air-gap magnetic fields. Results of the finite element method and prototype test confirm the validity of the analytical prediction.

Highlights

Magnetic harmonic gears with high gear ratios exhibit high torque densities
It has been shown that eccentric magnetic harmonic gears with high gear ratios and pole pieces freely exhibit torque densities of as much as 150 kN·m/m3 [2,3]
This study develops an analytical model for magnetic harmonic gears using the fractional linear transformation (FLT) method

Summary

Introduction1

Magnetic gears have the advantages of being lubricant-free and having low noise, reduced maintenance, and inherent overload protection. Concentric magnetic gears with soft magnetic pole pieces that modulate the fields can exhibit torque densities of up to 100 kN·m/m3 [1]. It has been shown that eccentric magnetic harmonic gears with high gear ratios and pole pieces freely exhibit torque densities of as much as 150 kN·m/m3 [2,3]. The analytic method has clear physical concepts, fast calculation, and free rotation without mesh restriction. It is flexible even if the air gap lacks uniformity as a result of eccentric rotation of the rotor. A high gear ratio can be obtained by increasing the number of pole pairs on the low-speed rotor

Analytical model with fractional linear transformation method

Practical implementation

Experimental validation

Findings

Conclusion