In poly-phase induction motors, the motor torque (Tm) can be expressed in terms of various parameters associated with the motor's operation. The torque developed by an induction motor depends on factors such as the stator current, rotor resistance, slip, and the magnetic field created by the stator windings.
The motor torque (Tm) can be roughly expressed using the following formula:
Tm = (3 * V^2 * R2) / (ωs * ((R1 + R2^2) + (X1 + X2)^2) / s)
Where:
Tm is the motor torque.
V is the line-to-line voltage applied to the motor.
R1 and X1 are the stator resistance and reactance, respectively.
R2 and X2 are the rotor resistance and reactance, respectively.
ωs is the synchronous angular frequency.
s is the slip of the motor (s = (Ns - N) / Ns, where Ns is the synchronous speed and N is the actual rotor speed).
Please note that this formula provides a simplified representation of motor torque and may not take into account various complexities like magnetic saturation, core losses, and other factors that can influence motor performance.
For a more accurate analysis, motor torque is often determined through detailed simulations or experiments that consider the specific characteristics of the motor design and operating conditions.