Brushless DC Cogging Torque with a Skewed Stator

This is an example of the calculation of cogging torque in a Brushless DC Motor. Two different stator geometries are compared: a straight stator and a skewed stator, both shown on the left.

Cogging torque is undesirable because it introduces vibration and noise, and also makes precise positioning of the rotor impossible because the rotor tends to lock onto a position where it is aligned with the stator poles. By skewing the stator, the cogging torque can be significantly reduced.

MagNet makes it easy to set up multiple problems for solution at different rotor angles. And MagNet's Static 3D solver reports the magnetic forces and torques experienced by each body in the model, so it is easy to create a torque-angle curve.


Results

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On the right is the graph of the torque exerted on the rotor as a function of rotor angle with a straight stator. A best-fit Fourier series is also shown in the graph; only the sine terms are included since the geometry has odd symmetry. The Fourier coefficients for the first six terms are: -15.996, -7.228, -0.688, 0.079, -0.033, -0.128 mT.

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This graph once again displays torque as a function of rotor angle, but in this case the stator is skewed. Note that the peak torque in the skewed stator case is approximately 50 times smaller than that of straight stator. Since the torque is so small, the discretization error due to the finite element mesh is evident. For this reason a large number of rotor positions were used so the error could be averaged out. This graph also includes the best fit Fourier series, with components -0.119, 0.261, 0.030, -0.003, 0.004, 0.002.

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By using the above torque data as input for the motion solver, it is possible to determine how the speed of the rotor is affected by the cogging torque. The graph on the right shows the speed of each rotor (with straight and skewed stator) as a function of time. A coefficient of viscous friction is added to the model so that the rotor speed decreases from its initial speed.

The videos were created by modeling the dynamics with Infolytica's 2D motion solver, using the torque-angle curve from the 3D model with dummy 2D components, since in this case there are no induced currents and so torque depends only on position. A simple script (10 lines) then generated the video by looping over the time instants and for each one it queried the position of the rotor, updated the model to that position, then added a frame to the video.

If you are a maintained user of MagNet or if you are an evaluator of the software you can download the skewed model by clicking here and the straight motor can be found here.