A single phase induction motor is constructed of a stator, which contains the stationary main winding, and a rotor, which is a conductive cage which rotates. The stationary main winding is a two pole coil.
The rotor is not a permanent magnet, and it is not connected to the AC supply voltage: it is a brushless motor. However, due to the AC current in the main winding of the stator, an oscillating magnetic field is created, which induces an EMF in the rotor bars, driving a current through the rotor. By Lorentz Force law, a force and thus torque is exerted on the rotor.
I am now attempting to compute the torque in terms of angular speed of the motor.
For low angular speeds this formula is at least qualitatively correct, it is expected that torque is linearly proportional to the angular speed of the rotor, but at the full load torque, the torque no longer varies linearly, but looks like the black line in the image (ignore the red and blue lines for now):
The cause of the torque no longer being linearly proportional to the speed is probably due to losses, and in the literature the rotor is modelled as a secondary winding of a transformer circuit, with the mechanical load on the shaft as resistance, and additional rotor reactance to model flux losses.
My analysis seems to miss out the zero torque near synchronous speed criterion. What phenomenon is responsible for this which I have not included?
My question is: within the context of Maxwell's Equations (physically), how can I calculate these losses using the geometry of the motor?