CST – Computer Simulation Technology

Electromechanically-Coupled Simulation of a Coaxial Magnetic Gear with Multiple Rotational Moving Gaps

Magnetic gears are an attractive alternative to mechanical gears since they are contact-free, silent and more reliable. An application of such gears is to increase the torque density in electrical machines.

This article demonstrates features useful for the simulation of such magnetic gears with CST EM STUDIO®. Transient analysis of the gear, in essence two synchronous machines, eliminates the tedious need to determine the load angle between the moving rotors.

Useful in the simulation is the application of a moving mesh, as opposed to re-meshing at each time-step, and also the ability to calculate the start-up characteristics of the gear by means of solving the motional equations at each time-step.

Figure 1 shows the CST EMS model of a simple magnetic gear which consists of an inner and an outer rotor on which permanent magnets are surface mounted. The ratio of the number of inner and outer permanent magnet poles determines the gear ratio - in this case, 1.5. The magnets are radially outward magnetized with alternating polarity. The rotor and stator materials are both defined as non-linear materials. ...

In CST EMS, a 3D model may be simulated in 2D. The user merely specifies the desired cut-plane for the 2D simulation. 2D is a valid approach here and is much faster and more efficient than 3D simulations.

Figure 1: CST EMS model of the magnetic gear

A magnetic gear can be simulated via a series of magnetostatic simulations but this approach is tedious due to the need to establish the load angle between the two rotors. A much easier method is to apply the LF transient solver even under the assumption that eddy currents cannot arise due to the laminations in the machine.

The LT transient motor solver requires the definition of motional gaps, in this case, rotational. Three possibilities exist depending on the simulation needs but in this case all 3 are required - constant speed, angular position versus time curve, and dynamic equation of motion.

In this model, the 3 types are shown in Figure 2. An acceleration curve has been attributed to the outer rotor. The magnetic coupling bridges, located between both rotors, are stationary i.e. constant speed = 0 RPM. Finally, the inner rotor is allowed to rotate freely and is attributed with an equation gap type for which the equation of motion is solved at each time step. Typical parameters required for this motion type are shown also in Figure 2.

Figure 2: Definition of 3 rotation gaps: angular position versus time, constant speed and dynamic equation

Critical to accuracy and performance in LF Transient motion solver is the moving mesh feature which, as the name suggests, does not require the re-meshing of the rotational gaps at each time-step. This technique reduces numerical noise which adversely affects results such as cogging torque. The moving mesh technique is demonstrated in animated form in Figure 3.

Figure 3: Multiple moving mesh used for the magnetic gear simulation

The previous definitions of the rotating gaps lead to the following behaviour. The outer rotor is accelerated which generates a torque which is transmitted to the internal rotor via the stator bridges. Due to the inertia, drag and other coefficients, the inner rotor will start up and attempt to synchronize itself with the outer rotor. This can be seen in Figure 4 where the normalized torque and speed variation with time in the outer rotor (red curves) and inner rotor (blue curves) is depicted.

Figure 4: Graphs of normalized speed and torque for the outer (red) and inner (blue) rotors during start-up until synchronism is lost

Since the load torque is defined as a linear function of speed, at higher speeds the applied load exceeds the maximum admissible torque. As a consequence, this leads to a loss of synchronism of the machine and the complete stop of the rotor since the driving torque quickly oscillates around zero.

This article demonstrates several aspects of simulation that CST EMS offers that may be useful for the design of magnetic gears, magnetic couplings and similar electromechanical components.

The focus was intentionally on the ability to apply several rotating gaps each with different excitations, such as position-time curves, and mechanical characteritistics. A steady-state solution, whereby the start-up characteristics are of no concern, can also be applied. The designer of such devices may wish to apply simulation and especially the integrated CST EMS Optimizer module for improving the coupling of the device, torque maximization, reduction of torque ripple, permanent magnet volume and type etc.

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