Induction Motors General Principal Engineering Essay

As a general regulation, transition of electrical power into mechanical power takes topographic point in the revolving portion of an electric motor. In D.C motors, the electric power is conducted straight to the armature or the revolving portion with the aid of coppices and observer. Hence, in this sense a D.C motor can be called or referred to as a conductivity motor. But in the instance of A.C motors, the rotor receive power ( electric ) by initiation in precisely the same manner as the secondary of a 2-winding transformer receives its power from the primary and non by conductivity. That is why such motors are branded as initiation motors. In some instances an initiation motor is treated as a revolving transformer, since its primary twist is at a standstill but the secondary rotates freely.

The multi-phase initiation motors is widely used in footings of applications of A.C. motors, the chief advantages and disadvantages attributed to it are as follows:

Advantages

It has an highly strong and rough physical construction.

It is comparatively less expensive and really dependable.

It has high efficiency

It does non necessitate major care work

It starts from remainder and does non necessitate a separate starting motor

Disadvantages

Its efficiency is affected with fluctuations in velocity

Its velocity decreases with addition in burden

Its get downing torsion is lower as compared to D.C. shunt motor

Construction

There are two major parts in an Induction motor:

Stator

Rotor

Stator

The stator of an initiation motor is in theory the same as that of a synchronal motor or generator. It is made up of a figure of slots which hold the twists. Different stators carry different twists such as individual stage or three stages depending on the power that it is fed with. The figure of poles upon which it is wound depends on the velocity, more the figure of poles, lesser the velocity and lesser the figure of poles, more the velocity.

1.2.2. Rotor

a. Squirrel-cage rotor, besides known as initiation motors:

Fig. 1.1 Squirrel-cage initiation motor

About 90 % of initiation motors are of this type because this agreement has the strongest and simplest physical construction. It basically consists of a cylindrical laminated nucleus with slots that are parallel transporting music directors made up or Cu and aluminium or metal. These bars or rods are welded to stop rings that are short circuited at either terminal, therefore deducing its name as squirrel coop.

Though the slots are anticipated to be kept in analogue, it is in most occasions intentionally given a little skew, which is utile in the undermentioned ways:

It helps the motor to run softly

It reduces the locking inclination of the rotor, which is the affinity of the rotor dentition to stay under the stator dentitions due to direct magnetic attractive force between the two. In little rotors another method of building is used which consists of puting the full rotor nucleus in a molds and projecting all the bars and stop rings in one piece, this procedure normally uses aluminium.

b. Phase-wound rotor, besides known as slip-ring motors or lesion motors.

This type of rotor is provided with 3-phase distributed twists dwelling of spirals. The rotor is wound for every bit many poles as the figure of stator poles and is ever wound 3-phase even when the stator is wound two-phase. The point of this type of rotor is that the three twist terminuss are brought out and connected to three insulated faux pas rings, this make the accretion of external opposition possible and therefore assists the starting of the motor by increasing the get downing torsion of the motor and for altering its variable features like velocity and torsion.

1.3 Single Phase Induction Motor

Fig. 1.2 Single stage initiation motor

When we look at the physical make-up of the individual stage initiation motor it is quiet similar to the multi-phases initiation motors with the fluctuation that its stator it provided with a individual stage twist and a switch is used in some types of motors in order to cut out a weaving by and large used merely for get downing intents. This type of motor has dispersed stator twist and a squirrel-cage rotor. When it is given an input from a single-phase supply, its stator twist produces a field which is jumping. It is non a synchronously go arounding flux as in the instance of a two or three stage stator weaving acquiring input from two or three stage power supply.

We say that a individual stage motor is non self-starting because the jumping flux moving on the squirrel coop rotor which is at a deadlock can non do it revolve.

However, as seen in the lab, if the rotor of such a machine is given an initial start by manus, so a torsion arises and the motor accelerates to its concluding velocity.

This behaviour of the motor can be explained by different theories like the 1s called two-field or double-field revolving theory and the cross field theory among others.

Chapter 2: Equivalent Circuit of Single Phase Induction Motor ( Without Core Loss )

Fig.2.1 Equivalent Circuit of Single Phase Induction Motor

A single-phase motor may be treated as a digest of two motors, holding the same stator weaving but with the several rotors go arounding in opposite waies. The figure shown supra is the tantamount circuit of such a motor. The individual stage motor has been imagined to be made up of one stator twist and two fanciful rotors.

The stator electric resistance is:

The electric resistance of each rotor is: ( ) ; where, and represent half the existent rotor values in stator footings, that is, stands for half the standstill reactance of the rotor, as referred to stator.

Each rotor has been assigned half the magnetising reactance or represents half the existent reactance.

The electric resistance of ‘forward running ‘ rotor is: ( taking into history all the halved values )

And it runs with a faux pas of ‘ ‘ .

The electric resistance of the ‘backward running ‘ rotor is: ( taking into history all the halved values )

It runs with a faux pas of ( 2-s ) . Under standstill conditions, , but in running status, is about 95 % of the applied electromotive force.

The entire torsion is besides found to be:

Chapter 3: Analysis of the Equivalent Circuit

To continue with the analysis of the tantamount circuit, the values of the chief parametric quantities as assumed to be as follows:

Resistance of the stator chief twist

Reactance of the stator chief twist

Magnetizing reactance of the stator chief twists

Rotor opposition at deadlock

Rotor reactance of deadlock

Faux pas

Voltage v=110 Vs

Step-A

i??

Fig. 3.1 Equivalent Circuit with regard to

We know,

Upon replacing the values that have been taken into consideration,

== ?

Assume ;

Hence we get in Eqn ( 3.1 ) ,

a== 3.56/2= 1.78

b== 2.56/2= 1.28

c== 53.5/2= 26.75

Substituting the values in eqn. 2,

1.6146 + J ( 1.2166 )

Step-B

i??

Fig.3.2 Equivalent Circuit with regard to

We know,

Upon replacing the values that have been taken into consideration,

Assume ;

Hence we get in eqn. 3

= 3.56/2 ( 2-0.04 ) = 0.908

= 2.56/2= 1.28

= 53.5/2= 26.75

Substituting the values in eqn. 4,

= 0.8260 + J ( 1.248 )

Step-C

Fig. 3.3 Equivalent Circuit with regard to

Upon replacing the values that have been taken into consideration,

=

Step-D

We know ; and is 110volts

Hence,

Step-E

Unifying Step-D and Step-A

Fig. 3.4 Equivalent Circuit with regard to and

Substituting the values,

=-0.02070-j0.0104

=2.015+j2.0217

Step-F

Step-G

Step-H

Step-I

Step-J

Where,

Since ;

Chapter 4: Application of MATLAB Software

4.1 Introduction to MATLAB

MATLAB which is the short signifier for “ MATrix LABoratory ” , a numerical computer science linguistic communication. Developed by The MathWorks, MATLAB allows matrix uses, plotting of maps and informations, execution of algorithms, creative activity of user interfaces, and interfacing with plans written in other linguistic communications, including C, C++ , and Fortran.

Fig 4.1 Screen shooting of the MATLAB desktop

4.1.1 Application of the Windows on the MATLAB package desktop [ 5 ] A­

*Command History View a log of or hunt for the statements you entered in the Command Window, copy them, put to death them, and more.

*Command Window Run MATLAB linguistic communication statements.

* Current Directory Browser View files, perform file operations such as unfastened, happen files

and file content, and manage and tune your files.

*Editor Create, edit, debug, and analyze M-files ( files incorporating MATLAB linguistic communication statements ) .

*Figures Create, modify, position, and print figures generated with MATLAB.

*File and Directory Comparisons View line-by-line differences between two files.

*Help Browser View and search the certification and demos for all your MathWorks merchandises.

*Profiler Improve the public presentation of your M-files.

*Start Button Run tools and entree certification for all your MathWorks merchandises.

*Variable Editor View array contents in a table format and redact the values.

*Web Browser View HTML and related files produced by MATLAB.

*Workspace Browser View and do alterations to the contents of the workspace.

4.2 Stairss for Implementation of the formulated job in MATLAB

4.2.1 Measure A: Low-level formatting of Variables

As in most computing linguistic communications, the know values of the invariables are initialized at the start, in MATLAB, the format for low-level formatting of the values is

( Alphanumeric name of variable ) = ( Value the user wants to delegate ) ;

As per the above sentence structure, the known changeless values from Chapter 3 ( pg 8 ) are initialized as:

v=230.0 ; //The electromotive force have assumed for the application in the equation

poles=4 ; //The figure of poles in the Induction machine

f=50 ; //The frequence ( in Hz )

r1=1.86 ; //The opposition of the stator chief twist

r2=3.56 ; //The rotor opposition at deadlock

x1=2.56 ; //The reactance of the stator chief twist

x2=2.56 ; //The rotor reactance at deadlock

xm=53.5 ; //The magnetising reactance of the stator chief twists

j=sqrt ( -1 ) ; //Initialization of fanciful portion

4.2.2 Measure B: Low-level formatting of Arraies

In MATLAB, the format for low-level formatting of an array is give by:

( Alphanumeric name of array ) = ( Get downing point value ) : ( Interval between the array ) : ( Ending point value )

As per the above sentence structure, the value of Slip is initialized as:

s=2: -0.01: .01 ;

that is:

s =

Columns 1 through 16

2.0000 1.9900 1.9800 1.9700 1.9600 1.9500 1.9400 1.9300 1.9200 1.9100 1.9000 1.8900 1.8800 1.8700 1.8600 1.8500

Columns 17 through 32

1.8400 1.8300 1.8200 1.8100 1.8000 1.7900 1.7800 1.7700 1.7600 1.7500 1.7400 1.7300 1.7200 1.7100 1.7000 1.6900

Columns 33 through 48

1.6800 1.6700 1.6600 1.6500 1.6400 1.6300 1.6200 1.6100 1.6000 1.5900 1.5800 1.5700 1.5600 1.5500 1.5400 1.5300

Columns 49 through 64

1.5200 1.5100 1.5000 1.4900 1.4800 1.4700 1.4600 1.4500 1.4400 1.4300 1.4200 1.4100 1.4000 1.3900 1.3800 1.3700

Columns 65 through 80

1.3600 1.3500 1.3400 1.3300 1.3200 1.3100 1.3000 1.2900 1.2800 1.2700 1.2600 1.2500 1.2400 1.2300 1.2200 1.2100

Columns 81 through 96

1.2000 1.1900 1.1800 1.1700 1.1600 1.1500 1.1400 1.1300 1.1200 1.1100 1.1000 1.0900 1.0800 1.0700 1.0600 1.0500

Columns 97 through 112

1.0400 1.0300 1.0200 1.0100 1.0000 0.9900 0.9800 0.9700 0.9600 0.9500 0.9400 0.9300 0.9200 0.9100 0.9000 0.8900

Columns 113 through 128

0.8800 0.8700 0.8600 0.8500 0.8400 0.8300 0.8200 0.8100 0.8000 0.7900 0.7800 0.7700 0.7600 0.7500 0.7400 0.7300

Columns 129 through 144

0.7200 0.7100 0.7000 0.6900 0.6800 0.6700 0.6600 0.6500 0.6400 0.6300 0.6200 0.6100 0.6000 0.5900 0.5800 0.5700

Columns 145 through 160

0.5600 0.5500 0.5400 0.5300 0.5200 0.5100 0.5000 0.4900 0.4800 0.4700 0.4600 0.4500 0.4400 0.4300 0.4200 0.4100

Columns 161 through 176

0.4000 0.3900 0.3800 0.3700 0.3600 0.3500 0.3400 0.3300 0.3200 0.3100 0.3000 0.2900 0.2800 0.2700 0.2600 0.2500

Columns 177 through 192

0.2400 0.2300 0.2200 0.2100 0.2000 0.1900 0.1800 0.1700 0.1600 0.1500 0.1400 0.1300 0.1200 0.1100 0.1000 0.0900

Columns 193 through 200

0.0800 0.0700 0.0600 0.0500 0.0400 0.0300 0.0200 0.0100

4.2.3 Step C: Low-level formatting of Equations

In MATLAB, it is possible to initialise equations to alphanumeric variables for simpleness:

ws=4*pi*f/poles ;

b=x2/2 ;

c=xm/2 ;

4.2.4 Step D: Low-level formatting of Loops

Similar to other calculating linguistic communications, it is possible to initialise cringles to avoid repeat of the same sentence structure once more and once more, therefore salvaging clip and memory infinite,

Here we make usage of the ‘for ‘ cringle to accomplish this mark. The sentence structure of the same is same is given by:

//

for ( Name assigned to the counter ) = ( Get downing point value ) : ( Ending point value )

organic structure of the cringle

terminal

//

As per the above sentence structure, the ‘for ‘ cringle is initialized as:

for count=1: length ( s ) -1 // name of the counter: count

// get downing point value:1

// stoping point value: length of the cringle s – 1

//start of the organic structure in the cringle

a ( count ) =r2/ ( 2* ( s ( count ) ) ) ;

cubic decimeter ( count ) = ( ( c^2 ) * ( a ( count ) ) ) / ( ( ( a ( count ) ) ^2 ) + ( ( b+c ) ^2 ) ) ;

m ( count ) = ( ( ( a ( count ) ) ^2 ) *c ) + ( ( b^2 ) *c ) + ( b* ( c^2 ) ) ;

N ( count ) = ( ( ( a ( count ) ) ^2 ) +b+c ) ^2 ;

z1f ( count ) = ( cubic decimeter ( count ) ) + ( j* ( ( m ( count ) ) / ( n ( count ) ) ) ) ;

releasing factor ( count ) =l ( count ) ; // existent portion of z1f

xf ( count ) = ( m ( count ) ) / ( n ( count ) ) ; // fanciful portion of z1f

vitamin D ( count ) =r2/ ( 2* ( 2-s ( count ) ) ) ;

l1 ( count ) = ( ( c^2 ) * ( vitamin D ( count ) ) ) / ( ( ( vitamin D ( count ) ) ^2 ) + ( ( b+c ) ^2 ) ) ;

M1 ( count ) = ( ( ( vitamin D ( count ) ) ^2 ) *c ) + ( ( b^2 ) *c ) + ( b* ( c^2 ) ) ;

n1 ( count ) = ( ( ( vitamin D ( count ) ) ^2 ) +b+c ) ^2 ;

z1b ( count ) = ( l1 ( count ) ) + ( j* ( ( M1 ( count ) ) / ( n1 ( count ) ) ) ) ;

rubidium ( count ) =l1 ( count ) ; // existent portion of z1b

xb ( count ) = ( M1 ( count ) ) / ( n1 ( count ) ) ; //imaginary portion of z1b

U ( count ) =v/ ( ( r1+ ( j*x1 ) ) + ( z1f ( count ) ) + ( z1b ( count ) ) ) ; // Current

chek ( count ) =sqrt ( ( existent ( ( U ( count ) ) ) ^2 ) + ( imag ( ( U ( count ) ) ) ^2 ) ) ;

pgf ( count ) = ( ( chek ( count ) ) ^2 ) * ( releasing factor ( count ) ) ;

pgb ( count ) = ( ( chek ( count ) ) ^2 ) * ( rubidium ( count ) ) ;

Te ( count ) = ( ( pgf ( count ) ) – ( pgb ( count ) ) ) /ws ;

// terminal of the organic structure in the cringle

end //end of the cringle

4.2.5 Step E: Low-level formatting of Plots

Syntax for the plotting of graphs

First we have to specify both the variables to 0 so that they will hold the same array size.

Let us specify the first variable as: ten

Let us specify the 2nd variable as: Y

ten ( length ( y ) ) =0 ; //To do the array length the same for both the variables.

secret plan ( x, y ) ; //Command to plot the graph.

4.3 Source Code of Program created as pas per the formulated job in MATLAB

% specify the tantamount circuit parametric quantities

v=230.0 ;

poles=4 ;

f=50 ;

r1=1.86 ;

r2=3.56 ;

x1=2.56 ;

x2=2.56 ;

xm=53.5 ;

j=sqrt ( -1 ) ;

s=2: -0.01: .01 ;

ws=4*pi*f/poles ;

% bomber parametric quantities for simplified computation

b=x2/2 ;

c=xm/2 ;

for count=1: length ( s ) -1

a ( count ) =r2/ ( 2* ( s ( count ) ) ) ;

cubic decimeter ( count ) = ( ( c^2 ) * ( a ( count ) ) ) / ( ( ( a ( count ) ) ^2 ) + ( ( b+c ) ^2 ) ) ;

m ( count ) = ( ( ( a ( count ) ) ^2 ) *c ) + ( ( b^2 ) *c ) + ( b* ( c^2 ) ) ;

N ( count ) = ( ( ( a ( count ) ) ^2 ) +b+c ) ^2 ;

z1f ( count ) = ( cubic decimeter ( count ) ) + ( j* ( ( m ( count ) ) / ( n ( count ) ) ) ) ;

releasing factor ( count ) =l ( count ) ; % existent portion of z1f

xf ( count ) = ( m ( count ) ) / ( n ( count ) ) ; % fanciful portion of z1f

vitamin D ( count ) =r2/ ( 2* ( 2-s ( count ) ) ) ;

l1 ( count ) = ( ( c^2 ) * ( vitamin D ( count ) ) ) / ( ( ( vitamin D ( count ) ) ^2 ) + ( ( b+c ) ^2 ) ) ;

M1 ( count ) = ( ( ( vitamin D ( count ) ) ^2 ) *c ) + ( ( b^2 ) *c ) + ( b* ( c^2 ) ) ;

n1 ( count ) = ( ( ( vitamin D ( count ) ) ^2 ) +b+c ) ^2 ;

z1b ( count ) = ( l1 ( count ) ) + ( j* ( ( M1 ( count ) ) / ( n1 ( count ) ) ) ) ;

rubidium ( count ) =l1 ( count ) ; % existent portion of z1b

xb ( count ) = ( M1 ( count ) ) / ( n1 ( count ) ) ; % fanciful portion of z1b

U ( count ) =v/ ( ( r1+ ( j*x1 ) ) + ( z1f ( count ) ) + ( z1b ( count ) ) ) ; % current

chek ( count ) =sqrt ( ( existent ( ( U ( count ) ) ) ^2 ) + ( imag ( ( U ( count ) ) ) ^2 ) ) ;

pgf ( count ) = ( ( chek ( count ) ) ^2 ) * ( releasing factor ( count ) ) ;

pgb ( count ) = ( ( chek ( count ) ) ^2 ) * ( rubidium ( count ) ) ;

Te ( count ) = ( ( pgf ( count ) ) – ( pgb ( count ) ) ) /ws ;

terminal

pgb ( length ( s ) ) =0 ; // Vary as per the graph required

secret plan ( s, pgb ) ;

4.4 Graphic representation of consequences in MATLAB:

4.4.1 Torque Vs. Slip Characteristic

Fig 4.2 Torque vs. Slip Characteristics

Physical Significance:

a. This graph above helps us cipher electromagnetic torsion at different values of faux pas

B. It facilitates the theory that the end product power of the thrusts is lower than the end product power at burden.

c. It besides assists us to find at what slip the machine will run.

d. The above graph is an of import tool used by research workers to find the breakage part and the interrupting current of the machine.

4.4.2 Torque Vs. Current Characteristic

Fig 4.3 Torque vs. Current Characteristics

Physical Significance:

With aid from the above graph the burden of the machine can be decided since it is know that the merchandise of torsion and angular speed gives the power of the machine

4.4.3 Pgf Vs. Slip Characteristic

Fig 4.4 Pgf vs. Slip Characteristics

4.4.4 Pgb Vs. Slip Characteristic

Fig 4.5 Pgb vs. Slip Characteristics

Based on the Fig 4.4 and Fig 4.5, the interior decorator can foretell the comparative strength of the component field developed in the burden.

Chapter 4: Decision

A individual stage initiation motor is an asynchronous A.C motor, the rotor does non have electric power by conductivity but by initiation in precisely the same manner as the secondary of a 2-winding transformer receives its power from the primary. Its primary twist is stationary but the secondary rotates freely. Induction motors are among the strongest and simplest in footings of physical construction in motors

This undertaking is continuing frontward in analysis of its tantamount circuit. In this study we have derived the first stage of the analysis and have used conjectural values to compare the expression

The analysis of the circuit will go on into the following stage and will finally be synchronized with MATLAB in the concluding stage of the undertaking to obtain a graphical end product and design, enabling us to change the different parametric quantities.