For a given rotor diameter, the number of magnetic poles on the rotor directly affects the torque available, the top speed available, and the power needed to hold a load. Higher pole counts lead to higher torque, lower top speed, and a higher motor quality factor, which is defined as

K_{q} = T / √ P (in units of Nm/W)

The effect is as if a hypothetical gearhead had been inserted; this is sometimes called “magnetic gearing” in the literature.

**How it works:** For the same rotor dimensions and gap flux, for a given speed, the rate of change of gap flux varies directly with the number of poles, as the frequency of the variation varies directly with the number of poles. Given the same winding window, for a given drive current rating, the number of turns is almost constant (although some designs do allow for a slightly larger fill factor, thus a few more turns). The result is that the back-EMF drive current increases approximately linearly with the number of poles. As the back-EMF constant in V/Radian/sec equals the torque constant in Nm/A, the continuous torque thus increases with the number of poles. In the above graph, the higher rate of change of flux with angle is apparent for the higher pole count rotor, even though the magnitude of flux for both motors is equal. For a given number of turns on the stator pole, the back-EMF generated is given by

V =* − N x (*∂φ / ∂t)

(number of turns times the rate of change of flux with time)

**Tradeoff:** Although the increase in torque is helpful, the increased back-EMF reduces the speed needed to generate enough voltage to oppose a given power supply level. Thus the higher torque capability must be traded against the maximum speed for a given power supply voltage.

The back-EMF constant of the motor in Volts/radian/sec is numerically equal to the torque constant in Newton*meter/Amp if the motor moving losses are separately accounted. For the same winding configuration, doubling the back-EMF doubles the torque constant, and only requires ½ the current to hold the same load. With the resistive losses being P = I^{2}R doubling the torque constant requires only ¼ of the power to hold a given torque load. Tripling the torque constant brings the power needed to that same load down to 1/9 the power – all else being the same.

Thus, low-speed, high-torque applications can be effectively handled without a gearhead by increasing the pole count of the motor. One size does not fit all: Selecting the appropriate motor for the application can optimize the performance and minimize the price.

Similarly, high-speed, low-torque applications are best handled with lower pole count motors to keep from having excessive back-EMF which would otherwise exceed a given power supply voltage.

*Contributed by Donald Labriola P.E.*

*QuickSilver Controls, Inc.*

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