Brushless Motor: Minimizing Cogging Torque

Cogging torque is an undesirable effect that prevents the smooth rotation of the rotor and results in noise. In this example, OptiNet is used with MagNet in order to minimize the cogging torque by changing a number of geometric parameters while maintaining a certain running torque.

The rotor and stator use a laminated structure and there are four permanent magnets on the rotor, each magnetized to alternate between north and south.

Results

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Using periodic boundary conditions, modeling only one quarter of the motor is possible. The magnetic field solution is obtained using the 2d magnetostatic solver in MagNet. For the purposes of the cogging torque, it is enough to solve the problem with the rotor over a 15-degree span.

This figure shows the flux plot for two rotor positions (at 0 deg. and 15 deg.). The magnetic field simulation is performed for 16 different positions from 0 deg. to 15 deg. in increments of 1 degree.

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Variables: The geometry of the motor is defined based on the parameters shown in this figure. The parameter MH is the magnet height, AG is the width of the air gap, TFA is the tooth face angle and TH is the tooth height. In OptiNet, a minimum and a maximum value for each variable is specified. OptiNet then searches within this range to find the optimum design.

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Objective function: The maximum cogging torque over a 15 degree span is defined as the objective function and the goal is to minimize this quantity. In OptiNet, it is possible to use any quantity obtained from MagNet -- in this case, the torque -- and use it as an objective function.

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Constraints: There is one constraint in this optimization, and that is, the running torque should be maintained at a certain value.

In MagNet, it is possible to use parameterization for the stator winding current so that the system automatically solves both at zero current and with current as a function of rotor position, all in one run. OptiNet will then obtain the cogging torque and running torque values directly from MagNet.

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Graph of variables: For every iteration of the optimization process, OptiNet updates and displays the changes (in the form of graphs) for the goal, variables, objectives, and constraints -- these graphs are displayed on the Progress page. In this example, each of the four variables' graphs is updated as OptiNet finds a new design.

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Results: OptiNet produces a report for each optimization run. In this report, the designs that satisfy the constraints are shown in the order that they are improved. The user can view each design individually. The report also shows the time that it took to arrive at the improved design. The values of all the variables and the optimization function are displayed in this report for every iteration. The values of each parameter can be examined to determine the sensitivity of the design to that particular parameter.

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Initial design: In the initial design that the user supplied to OptiNet, the cogging torque over a 15 degree span was calculated and is shown in this figure.

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Final design: The final design that OptiNet produced after running for 12850 seconds (about 3.5 hours) on an AMD Athlon XP2800+ (2.08 GHz processor) is shown in this figure. As can be seen, the cogging torque has been reduced significantly. Of course, the user can examine previous improved designs. In this case, the cogging torque had dropped significantly during the first 20 minutes of the optimization process and during the remaining time OptiNet tried to find further improvement.

In OptiNet, it is possible to stop the solution at different points, to examine the design and re-start the optimization process, for further improvements.