SINGLE-PHASE INDUCTION MOTOR

INTRODUCTION     

Single-phase motors are the most familiar of all electric motors because they have used extensively in home appliances, shops, offices and lot of more. it is a fact that single-phase motors are less efficient substitute for 3-phase motors but 3-phase power is normally not available except in large commercial and industrial establishment.

TYPES OF SINGLE-PHASE MOTORS     

Single-phase motors are generally built in the fractional-horsepower range and may be classified into:

1. Single-phase induction motors

• Split-phase type
• Capacitor type
• Shaded-pole type

2. A.C. series motor or universal motor

3. Repulsion motor ( sometimes called Inductive-series motor )

• Repulsion-start induction-run motor
• Repulsion-induction motor

4. Un-excited synchronous motor

• Reluctance motor
• Hysteresis motor 

SINGLE-PHASE INDUCTION MOTORS   

It is very similar to a 3-phase squirrel cage induction motor or we can say that it is less/more similar to a poly-phase induction motor, except that 

(a) Its stator is provided with a single-phase winding

(b) Centrifugal switch is used in some types, in order to cut-out a winding(used only for starting purposes)

(c) It has distributed stator winding and a squirrel-cage rotor,

A single-phase induction motor is not self-starting like a 3-phase induction motor but requires some starting means. The single-phase stator winding produces a magnetic field that pulsates strength in a sinusoidal way. The field polarity reverses after each half cycle but the field does not rotate. Consequently, the alternating flux cannot produce rotation in a stationary squirrel-cage rotor. Even if the rotor of a single-phase motor is rotated in one direction by some mechanical methods, it will continue to run in that direction of rotation, then immediately a torque arises and the motor accelerates to its final speed.

Such strange behaviour of the motor has been explained in two ways:-

(i) by two-field or double-field revolving theory and

(ii) By cross-field theory.

CONSTRUCTION   

• The construction of a single phase induction motor is a similar to that a 3-phase induction motor. The rotor is cylindrical shape and always in squirrel cage while the stator carries only a single phase winding. 
• The stator winding placed in slots around the inner periphery of a laminated ring. In addition the stator also carries an auxiliary winding for providing the starting torque(so that motor becomes self starting).
• The slots of rotor are not made parallel to each other but skewed to prevent magnetic locking of stator and rotor teeth. 
• The squirrel cage rotor are made up of aluminium bars. These aluminium bars are called rotor conductors and are placed in the slots on the periphery of the rotor. 
• The rotor conductors are permanently shorted by the aluminium rings. The absence of the sliprings and brushes make the construction of single phase induction motor very simple and robust. 

It is not possible to add external resistance as the bars are permanently shorted.

WORKING PRINCIPLE   

1. When single phase a.c. supply is given to stator winding of the motor, the alternating current produces an alternating flux called main flux. 
2. This magnetic field is pulsating in nature which means that field builds up in one direction falls to zero and again builds up in another direction. 
3. This pulsating current is lack of producing a rotating torque in stationary rotor. But if the rotor is rotate by some external force in either direction, rotor start to rotate in that direction continuously. 
4. So single phase induction motor is not self starting. In order to obtain a rotating field, that stator is provided with two windings the main winding and a starting winding(Starting winding is also called auxiliary winding). 
5. The phase difference of 90° between two windings is obtained by splitting the phase. 
6. There are two fluxes, one is main flux and another is called rotor flux. These two fluxes produce the desired torque which is require to rotate the motor.  
7. When motor pick up 75% of rated speed, starting winding is generally disconnected from supply and motor continuously run. 

DOUBLE-FIELD REVOLVING THEORY   

Statement: The double field revolving theory states that any alternating quantity can be resolved into two components having magnitude half of the maximum magnitude of the alternating quantity and both these components rotating in opposite direction.

Theory:

In double field revolving theory an alternating sinusoidal flux (ϕ= ϕ𝑚×𝑐𝑜𝑠𝜔𝑡) can be represented by two revolving fluxes, each equal to one-half of the maximum value of 

alternating flux (i.e., ϕ𝑚/2) and each rotating at synchronous speed (𝑁𝑠 = 120𝑓/𝑃, 𝜔 = 2𝜋𝑓) in opposite directions. 

The above statement can be prove by the following:-

Consider two rotating magnetic fluxes ϕ₁and ϕ₂ each of magnitude ϕ𝑚/2 and rotating in opposite directions with angular velocity 𝜔. The two fluxes start rotating from OX axis at t=0. After time "t" seconds, the angle through which the flux vectors have rotated is 𝜔𝑡. By resolving the flux vectors along-X-axis and Y-axis, 

            

Therefore, an alternating field can be replaced by two relating fields of half its amplitude rotating in opposite directions at synchronous speed. 

Rotor at standstill.  

Consider the rotor is in stationary position and the stator winding is connected with a single-phase supply. The alternating flux produced by the stator winding can be presented as the sum of two rotating fluxes ϕ₁and ϕ₂, each equal to one half of the maximum value of alternating flux and each rotating at synchronous speed 𝑁𝑠 = 120𝑓/𝑃 in opposite directions. Let the flux ϕ₁ rotate in anti-clockwise and flux ϕ₂,  in clockwise direction. 

The flux ϕ₁ will result in the production of torque T₁ in the anti clockwise direction and flux ϕ₂ will result in the production of torque T₂ In the clockwise direction. At standstill, these two torques are equal and opposite. Also, the net torque developed will be zero. Therefore, single-phase induction motor is not self- starting.  

SPLIT-PHASE INDUCTION MOTOR   

The stator of a split-phase induction motor is provided with an auxiliary/starting winding 'S' in addition to the main or running winding 'M'. The starting winding is located 90° electrical from the main winding and operates only during the brief period when the motor starts up.

The windings are designed like that the starting winding 'S' has a high resistance and relatively small reactance while the main winding 'M' has relatively low resistance and large reactance.

Main Parts of Split Phase Induction Motor: 

Following are the main parts of Split Phase Induction Motor-

1. Stator 
2. Stator winding  
3. Rotor  
4. Centrifugal switch  
5. End shield  

1. Stator: Stator consists of steel sheet stampings having slots in its inner periphery. It serves the purpose to carry stator winding and to cover, support and covering to other parts of the machine as well. 

2. Stator winding: Split phase induction motor has two stator windings at a phase displacement of 90°. The running winding is always lower than the starting winding(because the starting winding has more resistance). 

*The split phase motors are usually wound to give 12 to 13 horse power. 

3. Rotor: The rotor of a split phase motor is very similar to the squirrel cage rotor of 3- phase induction motor. The core consists of steel sheet laminations having slots on the rotor periphery. The slots carries a number of copper, aluminium bars. The ends of the conductors in slot are connected and permanently short circuited by means of copper end rings. 

4. Centrifugal switch: Centrifugal is a mechanical device which is used in split phase induction motor to disconnect the winding when starting the motor attains 75-80% of the synchronous speed. When the rotor of the motor pick up speed about 75% of synchronous speed, switch behaves as open circuit of the starting winding. The centrifugal switch also prevents the motor from putting the excessive current from main by starting winding out of the circuit. 

5. End Shield: End shields are the end covers of the motor. It protects the motor from the dust and moisture etc. The entire weight of the rotor comes on the end bearings of the motor. 

Working Principle:

The working principle of split-phase induction motor are-

Performance Characteristics:

(i) The starting torque is 1.5 to 2 times the full-loud torque mid (lie starting current is 6 to 8 times the full-load current).  

(ii) It is cheap, that's why split-phase induction motors are most popular single phase motors in the market. 

(iii) Since the starting winding is made up of fine wires, the current density is high and the winding heats up quickly. If the starting period exceeds 5 seconds, the winding may burn out unless the motor is protected by built-in-thermal relay. Therefore, it is suitable where starting periods are not frequent. 

(iv) These motors are essentially constant-speed motors. The speed variation is 2-5% from no-load to full-load. 

(v) These motors are suitable where a moderate starting torque is required and where starting periods are infrequent to drive. 

Torque Speed Characteristics:

❖ Due to high resistance in the starting winding of split phase induction motor, the high starting torque is obtained. Such motors are available in sizes of 30 to 200 watts. They normally gives constant speed. 

Applications:  

❖ As starting torque is not so high so this machine is not used where large starting torque is required. It is used for smaller sizes about 0.25 H.P.  

❖ It is used in fans, washing machines, blowers, oil burners, wood working tools, grinders and various other low starting torque applications. 

The direction of rotation of a 1-ϕ split phase induction motor can be reversed by reversing (inter-changing) the connections of either starting winding or running winding. 

Q1:- A 0.5 h.p., 230V, single-phase induction motor(split-phase) takes a current of 4.2A lagging the voltage by 10° for the starting winding and a current of 6.2A lagging the voltage by 40° for its main winding. Find

(i) total current and power factor at the time of starting

(ii) total current and power factor during running

(iii) phase angle between the main winding current and starting winding current

(iv) power drawn by starting winding

(v) power drawn by main winding

(vi) total power drawn during starting

(vii) total power drawn during running.

Q2:- A single-phase split-phase motor is rated at 220V, 175W, 180 rad/s, 0.5 p.f. and 45% efficiency at rated load. Calculate its rated load

(i) line current

(ii) torque

Q3. A 4-pole, 50 Hz, single-phase induction motor is running with a slip of 3.4%. Calculate the speed of the motor.

Q4. At starting, the windings of a 230V, 50 Hz, split-phase induction motor have the following parameters:

             
Find: (i) current in main winding

         (ii) current in starting winding

        (iii) phase angle between them

        (iv) line current

         (v) power factor of the motor.

CAPACITOR START MOTOR   

Working Principle:

• In these types of motors, the necessary splitting of phase for starting is provided using capacitor.  

• The capacitor generally used of electrolyte type and designed for short duty period. Electrolyte capacitor is connected in series with the starting winding along with centrifugal switch S. 

• This switch disconnects the capacitor as soon as motor reaches 75% of full speed. The motor is not operated on running winding only. It is used where high starting is required. 

Performance Characteristics: 

(i) The starting characteristics of a capacitor-start motor are better than those of a split- phase motor, both machines possess the same running characteristics because the main windings are identical. 

(ii) The phase angle between the two currents is about 80° compared to about 25° in a split-phase motor. Consequently, for the same starting torque, the current in the starting winding is only about half that in a split-phase motor. Therefore, the starting winding of a capacitor start motor heats up less quickly 

(iii) It is well suited to applications involving either frequent or prolonged starting periods. 

(iv) Its full load efficiency is about 65%. 

(v) It is a constant speed motor as there is a very small fall in speed with load.  

Torque-speed Characteristics: 

Capacitor Start Motor is having a high starting torque as compared to an ordinary split phase motor. The power factor is also improved. 

Applications:  

❖ Capacitor-start motors are used where high starting torque is required and where the starting period may be long to drive.  

❖ Hence these motors find their applications in pumps, compressor, conveyer and refrigerators etc. Such motors are available between 0.5 H.P to 1 H.P.

The direction of rotation of such motors can be reversed simple by interchanging the leads of either running or starting winding.

Q1. A 200W, 230 V, 50 Hz capacitor-start motor has the following winding constants 

       

Find the value of starting capacitance that will result in the maximum starting torque.

CAPACITOR RUN MOTOR   

Working Principle:

• In these motors, a paper capacitor is permanently connected in the starting winding. In this case electrolytic capacitor cannot be used since this type of capacitor is designed only for short time rating and hence cannot be permanently connected in the winding.

• Both main as well as starting winding is of equal rating and similar. 

• No centrifugal switch or other such device has been used for disconnecting the starting winding. The rotor is squirrel cage. 

• In this motor the phase difference between two current is 90° .so starting torque is high.

Performance Characteristics:

(i) The capacitor remains in circuit so resultant line current is low. 

(ii) Power factor is improved may be about unity.  

(iii) Its full load efficiency is higher about 75%.    

Torque-speed Characteristics:

Applications:

This motor finds application in fans, room coolers, portable tools and other domestic and commercial appliances. 

CAPACITOR START, CAPACITOR RUN MOTOR     

Working Principle:

• In this case, two capacitors are used one for starting purpose and other for running purpose.  

• The capacitors used for starting purpose 𝐶𝑠 is of electrolytic type and is disconnected from the supply when the motors attain 75% of synchronous speed with the help of centrifugal switch S.  

• Whereas, the other capacitor 𝐶ᵣ which remains in the circuit of starting winding during operation is a paper capacitor. Starting capacitor 𝐶𝑠 which is of higher value than the value of running capacitor 𝐶ᵣ.

Performance Characteristics:

(i) The starting winding and the capacitor can be designed for perfect 2-phase operation at any load. The motor then produces a constant torque and not a pulsating torque as in other single-phase motors. 

(ii) It improves the overload capacity of the motor. 

(iii) It increases the efficiency of the motor. 

(iv) It improves the power factor. 

(v) It reduces the noise of the motor. 

(vi) This type of motor gives best running and starting operation.

 

Torque-speed Characteristics:

Such motors operate as two phase motors giving best performance and noiseless operation. Starting torque is high, starting current is low and gives better efficiency and higher power factor. 

Applications:

Because of constant torque, the motor is vibration free and can be used in 

(a) hospitals 

(b) studios and 

(c) other places where silence is important. 

SHADED POLE TYPE MOTOR    

A shaded-pole motor may be defined as a single phase induction motor provided with short circuited auxiliary winding displaced in magnetic position from the main winding. The shaded pole motor has small output not exceeding 30 watts. Starting torque of shaded pole is very small. It is suitable in low power domestic appliances. 

Working Principle:

(i) When single phase ac. supply is given to the stator of shaded pole induction motor an alternating flux is produced. 

(ii) This changing flux induces emf in the shaded coil. Since this shaded portion is short circuited, the current is produced in shaded portion in such a direction to oppose the main flux.  

(iii) The flux in shaded pole lags behind the flux in the un-shaded pole. The phase difference between these two fluxes produces resultant rotating flux.  

(iv) Thus due to this resultant rotating field emf is induced in the rotor, the rotor starts rotating due to single phase induction motor action additional torque is produced and rotor rotates continuously with the speed less than synchronous speed.  

(v) The direction of rotating field(flux) is from un-shaded to shaded portion of the pole. 

Performance Characteristics:

Torque-speed Characteristics:

The starting torque is small typically only 30 to 50 percent of the rated torque.

   

Applications:

As starting torque is very low, these motors are mainly used in record players, tape recorders, slide projectors, photo copying machine, starting of electric clocks, hair dryers, toys, gramophones.

EQUIVALENT CIRCUIT OF SINGLE-PHASE INDUCTION MOTOR    

It was earlier stated that when the stator of a single-phase induction motor is connected to single-phase supply, the stator current produces a pulsating flux that is equivalent to two-constant-amplitude fluxes revolving in opposite directions at the synchronous speed (double-field revolving theory). Each of these fluxes induces currents in the rotor circuit and produces induction motor action similar to that in a 3-phase induction motor.

         Let,

             

(i) At standstill.  Normally at this condition, the motor is simply a transformer with its secondary short-circuited. The equivalent circuit of single-phase motor at standstill will be as shown in the figure. The double-field revolving theory suggests that characteristics associated with each revolving field will be just one-half of the characteristics associated with the actual total flux. Therefore, each rotor has resistance and reactance equal to R'₂/2 and X'₂/2 respectively. Each rotor is associated with half the total magnetizing reactance.

In the equivalent circuit, the core loss has been neglected.

(ii) Rotor running.
  

Q1. A 2-pole, 240 V, 50 Hz, single-phase induction motor has the following constants referred to the stator:

Find the stator current and input power when the motor is operating at a full-load speed of 2820 rpm.

Q2. In the above question(Q1), if the iron and friction losses amount to 50W, find-

(i) Total mechanical power developed 

(ii) Useful shaft power

(iii) Shaft torque and 

(iv) Efficiency.

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