UNIT 6
Principle of operation of Single-Phase induction motors
A Single-Phase Induction Motor consists of a single phase winding which is mounted on the stator of the motor and a cage winding placed on the rotor. A pulsating magnetic field is produced, when the stator winding of the single-phase induction motor shown below is energized by a single phase supply.
The word Pulsating means that the field builds up in one direction falls to zero and then builds up in the opposite direction. Under these conditions, the rotor of an induction motor does not rotate. Hence, a single-phase induction motor is not self-starting. It requires some special starting means.
If the 1 phase stator winding is excited and the rotor of the motor is rotated by an auxiliary means and the starting device is then removed, the motor continues to rotate in the direction in which it is started.
The performance of the single-phase induction motor is analysed by the two theories. One is known as the Double Revolving Field Theory, and the other is Cross Field Theory. Both the theories are similar and explain the reason to produce torque when the rotor is rotating.
Double Revolving Field Theory of Single- Phase Induction Motor
The double revolving field theory of a single- phase induction motor states that a pulsating magnetic field is resolved into two rotating magnetic fields. They are equal in magnitude but opposite in directions. The induction motor responds to each of the magnetic fields separately. The net torque in the motor is equal to the sum of the torque due to each of the two magnetic fields.
The equation for an alternating magnetic field is given as
b(α) = β max sin w t cos α -----------------------(1)
Where βmax is the maximum value of the sinusoidally distributed air gap flux density produced by a properly distributed stator winding carrying an alternating current of the frequency ω, and α is the space displacement angle measured from the axis of the stator winding.
SinA cosB = ½ sin(A-B) + ½ sin(A+B)
So, the equation (1) becomes
b(α) =1/2 β max sin (w t- α) + ½ β max sin (w t+ α) ------------(2)
The first term of the right-hand side of the equation (2) represents the revolving field moving in the positive α direction. It is known as a Forward Rotating field. Similarly, the second term shows the revolving field moving in the negative α direction and is known as the Backward Rotating field.
The direction in which the single -phase motor is started initially is known as the positive direction. Both the revolving field rotates at the synchronous speed. ωs = 2πf in the opposite direction. Thus, the pulsating magnetic field is resolved into two rotating magnetic fields. Both are equal in magnitude and opposite in direction but at the same frequency.
At the standstill condition, the induced voltages are equal and opposite as a result; the two torques are also equal and opposite. Thus, the net torque is zero and, therefore, a single- phase induction motor has no starting torque.
Construction:
The VR stepper motor characterized by the fact there is no permanent magnet either on the rotor or the stator. The construction of a 3-phase VR stepper motor with 6 poles on the stator and 4-pole on the rotor as shown.
The Stator is made up of silicon steel stampings with inward projected even or odd number of poles or teeth. Each and every stator poles carries a field coil an exciting coil. In case of even number of poles, the exciting coils of opposite poles are connected in series. The two coils are connected such that their MMF gets added the combination of two coils is known as phase winding.
The rotor is also made up of silicon steel stampings with outward projected poles and it does not have any electrical windings. The number of rotor poles should be different from that of stators to have self-starting capability and bi- direction. The width of rotor teeth should be same as stator teeth. Solid silicon steel rotors are extensively employed. Both the stator and rotor materials must have lowering a high magnetic flux to pass through them even if a low magneto motive force is applied.
Electrical connection of VR stepper as shown fig. Coil A and A‘ are connected in series to form a phase winding. This phase winding is connected to a DC source with the help of semiconductor switch S1.Similary B and B‘ and C and C‘ are connected to the same source through semiconductor switches S2 and S3 respectively. The motor has 3 –phases a, b and c.
v a phase consist of A and A‘ Coils
v b phase consist of B and B‘ Coils
v c phase consist of C and C‘ Coils
It works on the principle of variable reluctance. The principle of operation of VR stepper motor explained by referring fig.
(a)Mode 1: One phase ON or full step operation
In this mode of operation of stepper motor only one phase is energized at any time. If current is applied to the coils of phase ‗a‘ (or) phase ‗a‘ is excited, the reluctance torque causes the rotor to run until aligns with the axis of phase a. The axis of rotor poles 1 and 3 are in alignment with the axis of stator poles ‗A‘ and ‗A‘‘. Then angle θ = 0° the magnetic reluctance is minimized and this state provides a rest or equilibrium position to the rotor and rotor cannot move until phase ‗a‘ is energized.
Next phase b is energized by turning on the semiconductor switch S2 and phase ‗a‘ is de –energized by turning off S1.Then the rotor poles 1 and 3 and 2 and 4 experience torques in opposite direction. When the rotor and stator teeth are out of alignment in the excited phase the magnetic reluctance is large. The torque experienced by 1 and 3 are in clockwise direction and that of 2 and 4 is in counter clockwise direction. The latter is more than the former. As a result the rotor makes an angular displacement of 30° in counterclockwise direction so that B and B‘ and 2 and 4 in alignment. The phases are excited in sequence a, b and c the rotor turns with a step of 30° in counter- clockwise direction. The direction of rotation can be reversed by reversing the switching sequence in which are energized and is independent of the direction of currents through the phase winding.
The truth table for mode I operation in counter and clockwise directions are given in the table.
(b).Mode II: Two Phase on Mode
In this mode two stator phases are excited simultaneously. When phases a and b are energized together, the rotor experiences torque from both phases and comes to rest in a point mid-way between the two adjacent full step position. If the phases b and c are excited, the rotor occupies a position such that angle between AA‘ axis of stator and 1-3 axis of rotor is equal to 45°.To reverse the direction of rotation switching sequence is changed a and b,a and c etc. The main advantage of this type of operation is that torque developed by the stepper motor is more than that due to single phase ON mode of operation.
The truth table for mode II operation in counter clockwise and clockwise directions is given in a Table.
Mode III: Half step Mode
In this type of mode of operation on phase is ON for some duration and two phases are ON during some other duration. The step angle can be reduced from 30° to 15° by exciting phase sequence a, a+b, b,b+c, c etc. The technique of shifting excitation from one phase to another from a to b with an intermediate step of a+b is known as half step and is used to realize smaller steps continuous half stepping produces smoother shaft rotation.
The truth table for mode III operation in counter and clockwise directions are given in the table.
