# Minimizing the Cogging Torque in a Brushless DC Motor

Motors & generators with MagNet
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 varying the geometry yet maintaining a required running torque in a brushless dc motor.

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.

This optimization run took an hour to complete and resulted in reducing the cogging torque by about 73 % with respect to the initial design.

### METHODS and RESULTS

## MAGNETIC FLUX from 0 to 15 DEGREES

The video shows the magnetic flux density field at every angle between 0 and 15 degrees. This angular range is equivalent to half a cogging torque cycle, which is sufficient to predict the maximum or peak cogging torque. Note that only a quarter of the model was simulated due to periodicity which significantly reduces the computation time of the problem.

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## Brushless DC DESIGN VARIABLES for OPTIMIZING

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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## DESIGN VARIABLES in OptiNet

When the model is opened, all the user-defined parameters are imported in the variables window of OptiNet. A search range defined by the minimum and maximum values must be defined for the design variables to be optimized, while the rest are set to type constant.

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## OPTIMIZING the GEOMETRY for MINIMAL COGGING TORQUE

Minimizing the cogging torque over a 15 degree span is defined as the goal. This is set by specifying the maximum value permitted for the cogging torque, any design that exceeds this limit will be rejected.

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## DEFINING the RUNNING TORQUE CRITERIA

There is one constraint in this optimization: the running torque should be maintained at or above the specified 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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## ITERATIONS of the OPTIMIZATION

For every iteration of the optimization process, OptiNet updates and displays the changes 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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## OPTIMIZATION RESULTS for MINIMAL COGGING TORQUE

OptiNet produces a final report with all of the improved designs listed (as shown in the image). The report includes the optimized parameter values (design variables), the predicted maximum cogging torque (objective) and the average running torque (constraint).

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## COMPARING INITIAL & OPTIMIZED BRUSHLESS DC Motor

The cogging torque over a 15 degree span for the initial and optimized design are compared on this graph. The cogging torque was reduced approximately 73% from 1.014 Nm to 0.277 Nm.

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## EVOLUTION of the BLDC GEOMETRY

This video shows the successive models evaluated by OptiNet and MagNet.

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