How to Synchronous Motor Speed

An AC motor's synchronous speed, ${\displaystyle n_{s}}$, is the rotation rate of the stator's magnetic field,

${\displaystyle n_{s}={2f \over {p}}}$,

where ${\displaystyle f}$ is the motor supply's frequency, where ${\displaystyle p}$ is the number of magnetic poles and where ${\displaystyle n_{s}}$ and ${\displaystyle f}$ have identical units. For ${\displaystyle f}$ in unit Hertz and ${\displaystyle n_{s}}$ in RPM, the formula becomes

${\displaystyle n_{s}={2f \over {p}}\cdot \left({\frac {60\ \mathrm {s} }{\mathrm {min} }}\right)={120f \over {p}}\cdot \left({\frac {\mathrm {s} }{\mathrm {min} }}\right)}$.

For example, for a four-pole three-phase motor, ${\displaystyle p}$ = 4 and ${\displaystyle n_{s}={120f \over {4}}}$ = 1,500  and 1,800 , RPM synchronous speed, respectively, for 50 Hz and 60 Hz supply systems.

The two figures at right and left above each illustrate a 2-pole 3-phase machine consisting of three pole-pairs with each pole set 60 degrees apart.

Slip

Typical torque curve as a function of slip, represented as 'g' here.

Slip, ${\displaystyle s}$, is defined as the difference between synchronous speed and operating speed, at the same frequency, expressed in rpm or in percent or ratio of synchronous speed. Thus

${\displaystyle s={\frac {n_{s}-n_{r}}{n_{s}}}\,}$

where ${\displaystyle n_{s}}$ is stator electrical speed, ${\displaystyle n_{r}}$ is rotor mechanical speed. Slip, which varies from zero at synchronous speed and 1 when the rotor is at rest, determines the motor's torque. Since the short-circuited rotor wingdings have small resistance, a small slip induces a large current in the rotor and produces large torque.^[31] At full rated load, slip varies from more than 5% for small or special purpose motors to less than 1% for large motors. These speed variations can cause load-sharing problems when differently sized motors are mechanically connected.Various methods are available to reduce slip, VFDs often offering the best solution.