As per my understanding to produce torque from a machine, we need an angle between stator and rotor flux. In an induction machine rotor flux is created in response to stator flux, why is there an angle between rotor and stator flux?
If there is no angle between the two fields, the only force would be in the radial direction, pulling the stator and rotor together rather than turning the rotor. To have torque, there must be a force that is tangental to the rotor. That requires an angle between the stator and rotor fields. That is called the torque angle.
Here is a detailed conceptual explanation. For all of the mathematics and underlying principles, you will need to consult a text book.
The stator and rotor magnetic fields will tend to align themselves with each other. If torque is applied to the rotor that torque is matched by torque developed between the two fields. That torque represents a force that is tangential to the rotor and proportional to the sine of the angle between the fields. The angle between the fields is measured in “electrical” degrees where 180 degrees is the rotational distance from one stator pole to the next. For a 2-pole motor, that is rotation half way around the motor or 180 mechanical degrees. For a 4-pole motor, 180 electrical degrees is 90 mechanical degrees etc.
The torque developed between the rotor and stator fields is matched by throe developed between the fields and the structures that produce them, the stator and rotor conductors.
Thus the stator field rotation is caused by the progression of the changing currents from phase to phase and from poe to pole.
In an induction motor, the rotating stator field sweeping through the rotor conductors generates alternating current in the rotor conductors. If the rotor is standing still, the frequency of the rotor current is equal to the frequency of the stator current. As a result, the rotor field rotates synchronously with the stator field. The movement of the rotor field is resisted by the rotor conductors, so the conductors develop torque to turn the rotor that torque is resisted by the friction and inertial torques of the motor parts and the external coupled load. The rotor field then starts to pull out of alignment with the stator field that increases the angle between the stator and rotor fields increasing the torque between the two fields to the maximum torque that the motor can supply. The stator field develops torque agains the stator windings and the motor frame.
As the rotor accelerates, the frequency of the rotor current decreases, but the mechanical speed of the rotor plus the rotational speed of the rotor field equals the rotational speed of the stator field keeping the fields rotating synchronously with each other.
The angle between the two fields is whatever is necessary for the motor to develop the torque necessary to turn the load. If the motor is adequate to drive the load, it will accelerate to a stable operating point where the load’s torque vs. speed demand curve intersects the motor’s torque vs. speed supply curve.
A very perceptive question!
The rotor of an induction motor is a very peculiar piece of electromagnetic mechanism. It has a set of rivet-like rods parallel to the axis, and end-caps where those rods terminate in good electrical contact. So, the entire rotor is equipped with a low-impedance winding, and it is subject to the usual time constant (L/R) of such a wound core. It is the magnetization delay due to that winding (and to a lesser extent, due to the eddy currents in the magnetic material) that causes the rotor magnetization to lag the stator field.
The motor, in most schematics, is shown as a box, which hides the fact of this bit of electric circuitry from sight. Out of sight, out of mind.