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04/11/23 360 Chapter 7 Induction Motor 1
EEE 360
Energy Conversion and Transport
George G. Karady & Keith Holbert
Chapter 7Induction Motors
04/11/23 360 Chapter 7 Induction Motor 2
Lecture 22
04/11/23 360 Chapter 7 Induction Motor 3
Construction
04/11/23 360 Chapter 7 Induction Motor 4
7.6 Single Phase Induction Motor
The single-phase induction machine is the most frequently used motor for refrigerators, washing machines, clocks, drills, compressors, pumps, and so forth.
The single-phase motor stator has a laminated iron
core with two windings arranged perpendicularly. One is the main and The other is the auxiliary winding or starting
winding
04/11/23 360 Chapter 7 Induction Motor 5
7.6 Single Phase Induction Motor
04/11/23 360 Chapter 7 Induction Motor 6
7.6 Single Phase Induction Motor
• This “single-phase” motors are truly two-phase machines.
• The motor uses a squirrel cage rotor, which has a laminated iron core with slots.
• Aluminum bars are molded on the slots and short-circuited at both
ends with a ring.
Stator with laminatediron core Slots with winding
Bars
Ring to shortcircuit the barsStarting winding
+
_
Main winding
Rotor withlaminatediron core+
_
Figure 7.42 Single-phase induction motor.
04/11/23 360 Chapter 7 Induction Motor 7
7.6 Single Phase Induction Motor
Figure 7.10 Squirrel cage rotor
04/11/23 360 Chapter 7 Induction Motor 8
7.6.1 Operating principle
04/11/23 360 Chapter 7 Induction Motor 9
7.6 Single Phase Induction Motor
• The single-phase induction motor operation can be described by two methods:
– Double revolving field theory; and
– Cross-field theory.
• Double revolving theory is perhaps the easier of the two explanations to understand
• Learn the double revolving theory only
04/11/23 360 Chapter 7 Induction Motor 10
7.6 Single Phase Induction Motor
7.6.1 Double revolving field theory
• A single-phase ac current supplies the main winding that produces a pulsating magnetic field.
• Mathematically, the pulsating field could be divided into two fields, which are rotating in opposite directions.
• The interaction between the fields and the current induced in the rotor bars generates opposing torque
04/11/23 360 Chapter 7 Induction Motor 11
7.6 Single Phase Induction Motor
• The interaction between the fields and the current induced in the rotor bars generates opposing torque.
• Under these conditions, with only the main field energized the motor will not start
• However, if an external torque moves the motor in any direction, the motor will begin to rotate.
Starting winding
Main winding
+t-t
Main winding flux
Figure 7.43 Single-phase motor main winding generates two rotating fields, which oppose and counter-balance one another.
04/11/23 360 Chapter 7 Induction Motor 12
7.6 Single Phase Induction Motor
7.6.1 Double revolving field theory
• The pulsating filed is divided a forward and reverse rotating field
• Motor is started in the direction of forward rotating field this generates small (5%) positive slip
• Reverse rotating field generates a larger (1.95%) negative slip
symsypos nnns )(
symsyneg nnns )(
04/11/23 360 Chapter 7 Induction Motor 13
7.6 Single Phase Induction Motor
7.6.1 Double revolving field theory• The three-phase induction motor starting torque inversely
depends on the slip
• This implies that a small positive slip (0.01–0.03) generates larger torque than a larger negative slip (1.95–1.99)
• This torque difference drives the motor continues to rotate in a
forward direction without any external torque.
Tm_start s( )
3 Irot_t s( ) 2Rrot_t
s
2 nsy
04/11/23 360 Chapter 7 Induction Motor 14
7.6 Single Phase Induction Motor
7.6.1 Double revolving field theory
• Each of the rotating fields induces a voltage in the rotor, which drives current and produces torque.
• An equivalent circuit, similar to the equivalent circuit of a three phase motor, can represent each field
• The parameters of the two circuits are the same with the exception of the slip.
04/11/23 360 Chapter 7 Induction Motor 15
7.6 Single Phase Induction Motor
7.6.1 Double revolving field theory
• The two equivalent circuits are connected in series.
• Figure 7.44 shows the equivalent circuit of a single-phase motor in running condition.
• The current, power and torque can be calculated from the combined equivalent circuit using the Ohm Law
• The calculations are demonstrated on a numerical example
04/11/23 360 Chapter 7 Induction Motor 16
7.6 Single Phase Induction Motor
Forwardrotating field
Xsta/2
Vsta
Ista
Rrot(1-spos)/(2spos)
Rsta/2
Rc/2 Xm/2
Xrot/2 Rrot/2
Reverserotating field
Xsta/2
Rrot(1-sneg)/(2sneg)
Rsta/2
Rc/2 Xm/2
Xrot/2 Rrot/2
Ipos
Ineg
Figure 7.44 Equivalent circuit of a single-phase motor in running condition.
04/11/23 360 Chapter 7 Induction Motor 17
7.6 Single Phase Induction Motor
The results of the calculations are:– Input power:
– Developed or output power:
*stastain IVS
neg
negrot
pos
posrotdev s
sR
s
sRP
1
2
1
2
22
negpos II
04/11/23 360 Chapter 7 Induction Motor 18
7.6 Single Phase Induction Motornm 400rpm 410rpm 1780rpm
400 600 800 1000 1200 1400 1600 18000
100
200
300
400
500
Pmech nm W
Pmot_dev nm W
Pmech nrated W
nm
rpm
Pdev_max
nmax
Operating Point
Pmech_max
StableOperating
Region
Figure 7.47 Single-phase motor mechanical output power and electrically developed power versus speed.
04/11/23 360 Chapter 7 Induction Motor 19
7.6.2.2 Starting torque
04/11/23 360 Chapter 7 Induction Motor 20
7.6 Single Phase Induction Motor
• The single-phase motor starting torque is zero because of the pulsating single-phase magnetic flux.
• The starting of the motor requires the generation of a rotating magnetic flux similar to the rotating flux in a three-phase motor.
• Two perpendicular coils that have currents 90° out-of-phase can generate the necessary rotating magnetic fields which start the motor.
• Therefore, single-phase motors are built with two perpendicular windings.
04/11/23 360 Chapter 7 Induction Motor 21
7.6 Single Phase Induction Motor
• The phase shift is achieved by connecting
– a resistance,
– an inductance, or – a capacitance
in series with the starting winding. • Most frequently used is a capacitor to
generate the starting torque.
04/11/23 360 Chapter 7 Induction Motor 22
7.6 Single Phase Induction Motor
• Figure 7.50 shows the connection diagram of a motor using a capacitor to generate the starting torque.
• When the motor reaches the operating speed, a centrifugal switch turns off the starting winding.
I
C
Mainwinding
Rotor
Centrifugal switch
V Startingwinding
Figure 7.50 Single-phase motor connection.
04/11/23 360 Chapter 7 Induction Motor 23
7.6 Single Phase Induction Motor
• The centrifugal switch is necessary because most motors use a cheap electrolytic capacitor that can only carry ac current for a short period.
• A properly selected capacitor produces around 90° phase shift and large starting torque.
I
C
Mainwinding
Rotor
Centrifugal switch
V Startingwinding
Figure 7.50 Single-phase motor connection.
04/11/23 360 Chapter 7 Induction Motor 24
7.6 Single Phase Induction Motor
Operating Point
nm 0.1rpm 1rpm nsy
0 500 1000 15000
2
4
6
8
10
12
Tsm nm N m
Tm nm N m
T nm N m
Tnom
N m
nm
rpm
Starting windingis disconnected
Main windinggenerated torque
Combined main andstarting windingsgenerated torque Figure 7.51
Torque–speed characteristic of a small single-phase induction motor.
04/11/23 360 Chapter 7 Induction Motor 25
7.6 Single Phase Induction Motor
• A less effective but more economical method using shaded pole motors
• The motor has two salient poles excited by ac current.
• Each pole includes a small portion that has a short-circuited winding. This part of the pole is called the shaded pole.
• The main winding produces a pulsating flux that links with the squirrel cage rotor.
• This flux induces a voltage in the shorted winding.
04/11/23 360 Chapter 7 Induction Motor 26
7.6 Single Phase Induction Motor
• The induced voltage produces a current in the shorted winding.
• This current generates a flux that opposes the main flux in the shaded pole (the part of the pole that carries the shorted winding).
• The result is that the flux in the unshaded and shaded parts of the pole will be unequal.
• Both the amplitude and the phase angle will be different.
04/11/23 360 Chapter 7 Induction Motor 27
7.6 Single Phase Induction Motor
• These two fluxes generate an unbalanced rotating field. The field amplitude changes as it rotates.
• Nevertheless this rotating field produces a torque, which starts the motor in the direction of the shaded pole.
• The starting torque is small but sufficient for fans and other household equipment requiring small starting torque.
• The motor efficiency is poor but it is cheap
04/11/23 360 Chapter 7 Induction Motor 28
7.6 Single Phase Induction Motor
• The motor has two salient poles excited by ac current.
• Each pole includes a small portion that has a short-circuited winding.
• This part of the pole is called the shaded pole
Main winding
Shortedcoil
Unshadedpole
Unshadedpole
Shadedpole
Shadedpole
Shortedcoil
Squirrel cagerotor
Figure 7.52 Concept of single-phase shaded pole motor.
04/11/23 360 Chapter 7 Induction Motor 29
7.6 Single Phase Induction Motor
Figure 7.53 Shaded pole motor for household fan.