Define RMF; torque-speed characteristics

Rotating magnetic field (RMF)

A rotating magnetic field is a magnetic field of constant magnitude ($1.5\phi_m$ for a three-phase winding) whose axis rotates in space at synchronous speed $N_s = \frac{120f}{P}$ rpm. It is produced by feeding balanced three-phase currents to three windings displaced $120^\circ$ in space.

Torque-speed (T-N) characteristics

The torque developed is

$$T = \frac{3}{\omega_s}\cdot\frac{s E_2^2 R_2}{R_2^2 + (sX_2)^2}$$

 T
 |            Tmax
 |          _.-*-._
 |   Tst  /         \
 |    *--'            \
 |   /                  \
 |  /                     \
 +--+------+----------------+--> N
  N=0   N(Tmax)             Ns

Main points of the curve:

1. Starting (N = 0, s = 1): the torque is the starting torque $T_{st}$. For a squirrel-cage motor it is about 1.5 to 2 times full-load torque.
2. Between standstill and pull-out: the torque rises with speed, because the rotor reactance $sX_2$ falls and the power factor improves, until it reaches the maximum (breakdown) torque at $s_m = \frac{R_2}{X_2}$, where $T_{max} = \frac{3E_2^2}{2\omega_s X_2}$.
3. Stable region ($s < s_m$): from $T_{max}$ down to $N_s$ the torque falls almost linearly with speed. The motor works here at rated load with slip of 2 to 5 %.
4. At $N = N_s$ ($s=0$): the torque is zero.
5. Unstable region ($s > s_m$): if the load torque exceeds $T_{max}$, the speed falls and the torque falls too, so the motor stalls.

Increasing the rotor resistance moves $s_m$ toward standstill (the same $T_{max}$), and with $R_2 = X_2$ the maximum torque occurs at starting. A fall of supply voltage reduces torque in proportion to $V^2$.