Machine Design

# Optimizing Method Applied

Consider, for example, specifying the lightest possible three-phase dc-brushless motor for use in a miniature aircraft. The stator ID and stack length is set by the design at 0.38 and 0.17 in., respectively. The motor is to be fitted with a gear reducer and an electronic controller. Required power output is 2 W at 5,000 rpm with at least 80% efficiency. Because high-power density is an important factor, use high-energy neodymium magnets with an air gap flux density of 10,500 gauss, and Hyperco stator iron with a flux density of 15,000 gauss. The combination results in a b of 0.7. A four-pole stator seems reasonable given the small motor size. In general, pole count scales with motor size. The peak of the b = 0.7 curve on the four-pole plot gives a CMO = 0.2, and = 0.5.

Next, calculate KO, a factor directly related to the tightness of the stator windings, and therefore to the manufacturing cost. Estimate the following parameters:

KCU
= 0.45 to 0.65 typically; choose 0.5
KW = 0.7 to 1.0 for motors in the power range of 1-1,000 W; choose 1.0

Next, calculate KET = 2.580, and finally KO = 0.402. Substituting these values into the KM expression gives:

Because the required power output at 5,000 rpm is 2 W, the output torque is 0.541 oz-in. Use a 6:1 gear reducer so that the torque at the motor is approximately 0.090 oz-in. From the definition of KM, the losses in the motor windings are 0.21 W, or about 10% of the required output. Motor efficiency is 90%, allowing for a total of 10% for motor friction and transmission losses. 