022- Lecture 22 360 Chapter 7 Single Phase Induction Motor

EEE 360

Energy Conversion and Transport George G. Karady & Keith Holbert

Chapter 7 Induction Motors

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360 Chapter 7 Induction Motor

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Lecture 22

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Construction

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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

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7.6 Single Phase Induction Motor

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7.6 Single Phase Induction Motor •

•

•

This “single-phase” motors are truly twophase machines. The motor uses a squirrel cage rotor, which has a laminated iron core with slots.

Stator with laminated iron core

Slots with winding Rotor with laminated iron core

+

Main winding

+

Bars

_ _ Starting winding

Ring to short circuit the bars

Aluminum bars are molded on the slots and short-circuited at both ends with a ring.

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Figure 7.42 Single-phase induction motor. 360 Chapter 7 Induction Motor

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7.6 Single Phase Induction Motor

Figure 7.10 Squirrel cage rotor 10/14/08

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7.6.1 Operating principle

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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

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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 10/14/08

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7.6 Single Phase Induction Motor Main winding flux

•

•

•

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.

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-ωt

+ωt

Main winding

Starting winding

Figure 7.43 Single-phase motor main winding generates two rotating fields, which oppose and counter-balance one another.

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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 s pos = (n sy − nm ) n sy

•

Reverse rotating field generates a larger (1.95%) negative slip s neg = (n sy + nm ) n sy

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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 T m_start ( s ) :=

(

3 ⋅ Irot_t ( s )

)

2

Rrot_t ⋅ s

2 ⋅ π⋅ nsy

•

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.

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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.

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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 singlephase 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

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7.6 Single Phase Induction Motor Ista

Xsta/2

Forward rotating field

Vsta

Reverse rotating field

Rsta/2 Rc/2

Xsta/2

Rsta/2 Rc/2

Xrot/2 Xm/2

Xrot/2 Xm/2

Rrot/2 Ipos

Rrot(1-spos)/(2spos)

Rrot/2 Ineg

Rrot(1-sneg)/(2sneg)

Figure 7.44 Equivalent circuit of a single-phase motor in running condition. 10/14/08

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7.6 Single Phase Induction Motor The results of the calculations are: –

Input power:

S in = Vsta I –

Developed or output power:

Pdev = I pos

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* sta

2

Rrot 1 − s pos + I neg 2 s pos

2

360 Chapter 7 Induction Motor

Rrot 1 − s neg 2 s neg 17

7.6 Single Phase Induction Motor nm := 400rpm , 410rpm .. 1780rpm 500 Pmech( n m)

Pdev_max

400

nmax

Pmech_max

W Pmot_dev( n m) 300 W Pmech( n rated) W

200

Operating Point Stable Operating Region

100 0 400

600

800

1000

1200

1400

1600

1800

nm rpm

Figure 7.47 Single-phase motor mechanical output power and electrically developed power versus speed. 10/14/08

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7.6.2.2 Starting torque

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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° outof-phase can generate the necessary rotating magnetic fields which start the motor.

•

Therefore, single-phase motors are built with two perpendicular windings.

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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.

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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.

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I

V

Centrifugal switch

Main winding

Starting winding

C

Rotor

Figure 7.50 Single-phase motor connection.

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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.

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I

V

Centrifugal switch

Main winding

Starting winding

C

Rotor

Figure 7.50 Single-phase motor connection.

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7.6 Single Phase Induction Motor n m := 0.1rpm, 1rpm.. n sy 12

( )

T sm nm

10

Combined main and starting windings generated torque

N⋅ m

( )

T m nm

8

Starting winding is disconnected

N⋅ m

( )

T nm

6

N⋅ m T nom

Figure 7.51 Torque–speed characteristic of a small singlephase induction motor.

Main winding generated torque

4

N⋅ m 2

Operating Point 0

0

500

1000

1500

nm rpm

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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 shortcircuited 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.

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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.

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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

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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

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Shorted coil Shaded pole Unshaded pole

Squirrel cage rotor

Unshaded pole

Shaded pole Shorted coil

Main winding

Figure 7.52 Concept of singlephase shaded pole motor.

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7.6 Single Phase Induction Motor

Figure 7.53 Shaded pole motor for household fan.

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