Magnetic gears are the contactless mechanisms for torque-speed conversion using permanent magnets or electromagnets. They are utilized in several renewable energy applications, increasing the speed of wind energy, ocean energy, and flywheel energy storage in order to match the specification of the electromagnetic generator. Unlike their mechanical counterparts, magnetic gears offer inherent overload protection, have high reliability due to frictionless operation, and require no lubrication. Today, we’ll discuss how to simulate magnetic gears in 2D and 3D with COMSOL Multiphysics.

The Construction and Working Principle of Magnetic Gears
A typical magnetic gear consists of three rotors, each with a different number of magnetic pole pairs separated by a small air gap. The ferromagnetic steel poles (middle rotor) modulate the magnetic fields produced by inner and outer rotors and create space harmonics in the air gaps. The modulated magnetic fields via the steel poles interact with the magnetic field on the other side to transmit the torque.
Illustrated in the figure below is the working principle of a typical magnetic gear. For simplicity, we chose the linear magnetic gear configuration. However, the working principle will also be the same for rotating magnetic gears. In this configuration, the model consists of 11 pole pairs on the outer rotor, 4 pole pairs on the inner rotor, and 15 pole pairs in the middle. They are denoted by , , and , respectively.
The 4 pole pairs on the inner rotor produce the magnetic field with a dominant 4th harmonic. This field is then modulated by 15 steel pole pairs to generate a field with a dominant 11th harmonic. The modulated field interacts with the dominant 11th harmonic field that is produced by the outer rotor to transfer torque. This generates the torque, as the field harmonic component from the outer rotor matches with the harmonic component created by the modulated inner rotor field.
Schematic showing the components of linear magnetic gears.
A schematic depicting the components of linear magnetic gears. Red arrows represent the magnetization direction of the permanent magnets. The magnetic fields produced by the inner and outer rotors are shown in the blue curves. The air gap between the rotors is not included in the scale (exaggerated).
In order to attain the highest torque density, the number of pole pairs on each of the rotors should satisfy the following relation:

The relation between the pole pairs and the angular speed for all three rotors for maximum torque transmission is given by:

where , , and  denote the speed for the inner rotor, outer rotor, and steel poles, respectively. If the middle rotor is kept stationary, the speed and pole pairs relation is given by:

The best combination for , , and  is the one with the minimum of torque ripples. Such ripples can be primarily attributed to the cogging torque that is created from the field interaction between the permanent magnet motors and the steel poles. The parameter that is used to minimize the cogging torque is called a cogging factor. It is given by the following equation:

where LCM is a least common multiple. The minimum cogging torque is obtained with . In all of the examples presented here, this condition is satisfied and the ferromagnetic steel pole is kept stationary.