design and fabrication of single phase...

1

UNIVERSITY OF NAIROBI

FACULTY OF ENGINEERING

DEPARTMENT OF ELECTRICAL AND INFORMATION

ENGINEEERING

DESIGN AND FABRICATION OF SINGLE PHASE INDUCTION MOTOR FOR

NUMERICAL MACHINE COMPLEX

PROJECT INDEX: 107

SUBMITTED BY:

CHRISTOPHER OKEYO OKELLO

F17/1373/2010

SUPERVISOR: DR. C. WEKESA

EXAMINER: DR. W. MWEMA

PROJECT REPORT SUBMITTED IN PARTIAL FULFILLMENT

OF THE REQUIREMENT FOR THE AWARD OFTHE DEGREEOF

BACHELOR OF SCIENCE IN ELECTRICAL AND ELECTRONICENGINEERING

OF THEUNIVERSITY OF NAIROBI 2014

SUBMITTED ON:

24th April, 2015

I

DECLARATION OF ORIGINALITY

1) I understand what plagiarism is and I am aware of the university policy in this regard.

2) I declare that this final year project report is my original work and has not been

submitted elsewhere for examination, award of a degree or publication. Where other

people’s work or my own work has been used, this has properly been acknowledged and

referenced in accordance with the University of Nairobi’s requirements.

3) I have not sought or used the services of any professional agencies to produce this work

4) I have not allowed, and shall not allow anyone to copy my work with the intention of

passing it off as his/her own work.

5) I understand that any false claim in respect of this work shall result in disciplinary

action, in accordance with University anti-plagiarism policy.

Signature:

……………………………………………………………………………………

Date:

………………………………………………………………………………………

NAME OF STUDENT: CHRISTOPHER OKEYO OKELLO

REGISTRATION NUMBER: F17/1373/2010

COLLEGE: Architecture and Engineering

FACULTY/SCHOOL/INSTITUTE: Engineering

DEPARTMENT: Electrical and Information Engineering

COURSE NAME: Bachelor of Science in Electrical and Electronic Engineering

TITLE OF WORK: DESIGN AND FABRICATION OF SINGLE PHASE INDUCTION

MOTOR FOR NUMERICAL MACHINE COMPLEX

II

CERTIFICATION

This report has been submitted to the Department of Electrical and

Information Eng. University of Nairobi with my approval as supervisor:

Dr. C. WEKESA

Date: 24/04/2015

………………

III

DEDICATION

To my loving mother, Mary Okello.

IV

ACKNOWLEDGEMENTS

I would like to thank the Almighty God for his guidance throughout the five years of my

undergraduate studies

I would like to thank my supervisor, Dr. C. Wekesa for his unending motivation;insight and

supervisory role in making this project a success

I would like to express my gratitude towards my parents for their prayers, encouragement and

support throughout this time.

Lastly, I am highly indebted to my classmates, Dennis Lubanga, Bana Clifford , Kimani Mugo,

Billy Ochieng’, Doreen Mutekhele and Atanasio Maugambi for their insight into the project. It

wouldn’t have been possible without your support

V

TABLE OF CONTENTS DECLARATION OF ORIGINALITY ........................................................................................ I

CERTIFICATION ..................................................................................................................... II

DEDICATION .......................................................................................................................... III

ACKNOWLEDGEMENTS...................................................................................................... IV

LIST OF TABLES .................................................................................................................. VII

LIST OF FIGURES ............................................................................................................... VIII

LIST OF ABBREVIATIONS................................................................................................... IX

CHAPTER 1 ...............................................................................................................................1

INTRODUCTION ...................................................................................................................1

1.1 BACKGROUND INFORMATION ................................................................................1

1.2 Problem statement ..........................................................................................................1

1.2.1 Project Organization ....................................................................................................2

CHAPTER 2 ...............................................................................................................................3

LITERATURE REVIEW ........................................................................................................3

2.1 What is Motor? ..............................................................................................................3

2.2 Basic Parts of a motor ....................................................................................................3

2.4 Single Phase Motors .......................................................................................................5

CHAPTER 3 ............................................................................................................................. 11

DESIGN OF SINGLE PHASE INDUCTION MOTOR ......................................................... 11

3.2 The Design Procedure .................................................................................................. 12

3.3 Single Phase Induction Motor Design Specifications Determination ............................. 14

3.3.1 Motor specifications .................................................................................................. 14

3.6 Design of starting winding for resistance split phone .................................................... 30

CHAPTER 4 ............................................................................................................................. 32

RESULTS AND ANALYSIS ................................................................................................ 32

4.1 Results ......................................................................................................................... 32

4.2 Result Analysis ............................................................................................................ 34

CHAPTER 5 ............................................................................................................................. 35

CONCLUSIONS AND RECOMMENDATIONS .................................................................. 35

5.1 Conclusion ................................................................................................................... 35

VI

5.2 Recommendation ......................................................................................................... 36

References ................................................................................................................................ 37

VII

LIST OF TABLES

Table 4. 1 Results ...................................................................................................................... 32

Appendix Table 1 Standard Load Efficiency and Power Factor For Small Single Phase, 50hz

Cage - Motors ........................................................................................................................... 38

Appendix Table 2 The Standard Approximate Values For Co.η.Cos For Different Values Of

Watts/R.P.S. .............................................................................................................................. 39

VIII

LIST OF FIGURES

Fig. 2. 1 Parts of a Motor .............................................................................................................4

Fig. 2. 2 Diagram showing the operation of a D.C Motor ............................................................5

Fig. 3. 1 Design Flow Chart Diagram ....................................................................................... 11

Fig. 3. 2 Arrangement of Stator Coils ........................................................................................ 19

Fig. 3. 3 Rotor Set ..................................................................................................................... 24

IX

LIST OF ABBREVIATIONS

Li – Iron Length

F = Flux per Pole

Kw=Winding Factor

f=Frequency

V=Rated voltage

I=Full load current in the main winding, A

Tm=Number of turns of the main winding

P=Number of poles

D=stator bore diameter, m

L=Stator core length, m

τP=Pole Pitch

ns=Synchronous speed, r.p.s

Bav=Average value of flux density in the air gap, Wb/m2 (Specific magnetic loading)

ac= Ampere-conductor per meter of arm. Periphery, ac/m (specific electric loading)

η=Full load efficiency

Cos F= Full load power factor

dcs – Depth of Stator Core

dss-Depth of Stator slot

Ss- Stator Slots

Lg – Length of air gap

Dr – Rotor diameter

am- Area of main conductor

X

Lmt - Length of mean turn

Xom- Open circuit reactance

Xk- Auxiliary Winding reactance

Xm- Magnetising reactance

Xo – Overhang reactance

Xlm- Leakage reactance

Kr-Leakage factor

�- Peripheral Velocity

Lb- Length of bar

yss– Stator slot pitch

ysr

XI

ABSTRACT

The energy sector plays a major role in driving Kenya’s economy. The need to conceive,

develop and sustain energy generating sources cannot be underestimated. Being a

growing economy, Kenya therefore needs to redirect her effort in production of self-

sustaining energy generating sources. It is in this line that the government through the

ministry of industrialization, energy and vision 2030 sought to establish the Numerical

Machine Complex, which serves as a hub for fabrication, assembling and servicing small

to medium scale moving machines.

Since its conception NMC has been used majorly for assembling small motors and

generators from the imported machine parts. The economic burden of importing already

fabricated parts in addition to the high assembling costs, is considerably high for a

growing economy which not only strives to self- sustain itself but also seeks to create

employment for a semi-skilled workforce.

It is in this line that the NMC management decided to look into a more economical option

which involves fabrication of the single phase induction motor. Single phase induction

motors have a wide range of application in small loads fromfridges, water pumps, fans,

washing machines etc.

This project seeks to provide solutionsto the required design specifications for 2.2 KW,

240 V SINGLE PHASE INDUCTION MOTOR forNumerical Machine Complex

1

CHAPTER 1

INTRODUCTION

1.1 BACKGROUND INFORMATION

Today, single-phase induction motors are used in a wide range of applications.Single-phase

induction motors are used in small loads from fridges, water pumps, fans, washing machines.

Even though the three-phase induction motor has taken up the larger portion of the market, the

need to cater for all the consumers of different levels of energy demand has ensured that the

single phase induction motors continue to exist within the market.Additionally, most domestic

applications use only one line, this therefore makes single-phase induction motors the most

suitable for these applications.Generally, induction motors are easy to fabricate and more

efficient than other types of motors of the same rating, this makes it easy to readily initiate the

induction motor fabrication projects.

Owing to the existing demand and need to derive the advantages that come with producing local

products, NMC initiated the single-phase induction motor design and fabrication I Kenya.

1.2 Problem statement

1.2.1Project objectives

The objectives of this project is to come with the required desired design specifications for the

single phase induction motor for fabrication by the Numerical Machine Complex.

In wake of the increasing demand to locally fabricate the low rated induction motors, this project

seeks to solve the design problem by presenting an easy to use design specification generating

program to be used in the fabrication process.

2

1.2.1 Project Organization

The project has been organized in to five chapters as follows;

In Chapter 1, the project objectives and scope is introduced.

In Chapter 2, a literature review on motors, motor action, and single phase motor operation is

reviewed. Additionally, methods of starting a single-phase induction motor are introduced.

In Chapter 3, the design procedure of single phase induction motor is introduced and applied.

The pseudo code has been generated for simulating design specification is implemented and a

flow chart is provided.

In Chapter 4, the simulated results are tabulated and in-depth analysis on the results is presented

In Chapter 5, a discussion and a conclusion on the project is presented.

3

CHAPTER 2

LITERATURE REVIEW

2.1 What isMotor?

An electric motor is a machine that converts electric energy into mechanical energy. [1]

2.2 Basic Parts of a motor

2.2.1Stator

The stator is the stationary part of the motor.

2.2.2 Rotor

The rotor is the rotating member of the motor.

2.2.3FIELD SYSTEM

The field system functions to produce a uniform magnetic field within which the armature rotates

2.2.4 Armature winding

Armature winding consists of insulated conductors that are connected in a suitable manner.

2.2.5 Commutator

A commutator which is a mechanical rectifier found in D.C.machines which convert

thealternating voltage supplied to the armature winding into direct voltage across the brushes.

2.2.6 Brushes

The purpose of the brushes is to ensure electrical connections between the stationary commutator

and the rotating armature conductors.

4

Diagram illustrating the parts of a motor

Fig. 2. 1Parts of a Motor

A motor operates on the principle that a current- conductor placed in a magnetic field

experiences a magnetic force whose direction is defined by the Fleming’s Left – hand Rule and

whose magnitude is given by the expression , F=BIl Newton [1,2]

Consider the DC motor shown below; for the DC motor shown, when the field magnets are

excited and the armature conductor is supplied with the current, the conductor experiences a

force whose direction is defined by the Fleming’s left hand rule. This force tends to rotate the

armature conductor [2, 3]

When the armature rotates, the conductors also rotate and hence cut the flux. An e.m.f is induced

in the armature conductors whose direction is opposite to the applied voltage as defined by the

Fleming’s Right hand Rule. This voltage is referred to as the counter e.m.f. or back e.m.f. [2]

The voltage applied at the motor terminals therefore has to force the current against the back

e.m.f. The electric work done in overcoming and causing the current to flow against the back

5

e.m.f. is converted into mechanical energy usually developed in the armature [1]. Therefore, it is

clear that the energy conversion in dc motor is only possible due to the production of back e.m.f.

The presence of back e.m.f. in dc motors regulates the flow of armature current i.e., it

automatically changes the armature current to meet the load requirement.

2.4 Single Phase Motors

Single phase motors are used on single-phase power supplies.

Types of single phase motors

Single phase motors are generally built I the fractional-horsepower range and may be classified

into the following for basic categories [1]

1. Single-phase induction motors

i. Split-phase type

ii. Shaded-pole type

Fig. 2. 2Diagram showing the operation of a D.C Motor

6

iii. Capacitor type

2. A.C. series motor

3. Repulsion Motors

i. Repulsion-start induction-run motor

ii. Repulsion-induction motor

4. Synchronous motors

iv. Reluctance motor

v. Hysteresis motor

2.4.1 AC SERIES MOTOR

The a.c. series motor is also known as the universal motor. The a.c. series motor works on the

same principle as the D.C. series motor, however, with little modification on the specific part of

the motor [1]. These modifications include;

i) Completely laminated magnetic circuit in order to reduce the eddy current loss.

ii) Reduced number of turns of the series field winding to reduce the reactance of the

field winding to a minimum. This reduces the voltage drop across the field

winding.

iii) It incorporates a low- reluctance magnetic circuit which ensures a high field flux

within the set-up.

Operation of a.c. series motor

When the motor is connected to the single phase a.c. supply, the same alternating current flows

through the field and armature windings. The field windings produce an alternating flux that

reacts with the current flowing in the armature to produce a torque [1, 2]. The torque developed

always acts in the same direction as both the armature current and the flux reverse

7

simultaneously [1]. The motor, therefore, does not enjoy the influence of a rotating flux. As such

it operates on the same principle as the D.C. motor.

2.4.2 Single phase Repulsion Motor

A single phase repulsion motor is a modified a.c. series motor with short- circuited brushes i.e.

brushes are not connected to the supply. It also has a field structure with non-salient pole

construction [2]. The short- circuited brushes allow the currents to be induced in the armature

conductors by the transformer action.

The starting torque in the motor is developed by adjusting the position of the short-circuited

brushes on the commutator [1].

Principle of operation

A single phase Ac motor with transformer action coupling between the windings of the stator

and rotor. The stator is of non-salient pole design and has two series-connected windings, whose

axes form a 90 degrees angle. The rotor is similar in design to the armature of the DC machine.

The commutator brushes are short circuited, and the brush holder can be turned with respect to

the axis of the motor. If the brush axis is aligned with the axis of one of the stator windings a

current is induced in the rotor winding, as in the secondary winding of the transformer. This

current interacts with the magnetic flux of the secondary stator winding and creates a torque that

causes the rotor to rotate. By shifting the brushes around the commutator, the torque can be

varied from zero to a maximum value [1]. These motors have the advantage that their rotational

speed can be varied within limits without the use of auxiliary apparatus [2]

2.4.3 Single Phase Synchronous Motors

These are very small single-phase motors which run at real synchronous speed [1].

8

These small motors characteristically do not require D.C. excitation of the rotor. As a result they

are also referred to as the unexcited single-phase synchronous motor [1, 3].

They are of two types:

i) Reluctance Motors

ii) Hysteresis motors

2.4.4 Single phase induction motor

Generally, the conversion of electrical power into mechanical power takes place in the rotating

part of an electric motor [2]. In a.c motors the rotor of the machine receives electric power by

induction in a similar manner as the energy is transferred from the primary part to the secondary

part of the transformer [1, 2].

2.4.4.1 Construction of an Induction motor

An induction motor consists essentially of two main parts:

I) Stator

II) Rotor

i) The Stator

The stator of an induction consists of a number of stampings, which are strategically placed to

house the windings. The windings are wound for a definite number of poles which is determined

by the required speed of the motor [1, 2, and 3]. The greater the number of poles, the lower the

speed of the motor [2].When supplied with the current, the stator windings produce a rotating

fluxwhich is of constant magnitude but which rotates at synchronous speed. The revolving flux

induces an e.m.f in the rotor by induction.

ii) Rotor

9

A single phase induction motor has a squirrel- cage rotor. The squirrel-cage

rotor consists of a cylindrical laminated core with parallel slots for carrying the rotor conductors

(heavy bars of copper or aluminum). The rotor bars are electrically welded to two short-

circuiting end-rings thereby forming a squirrel case construction. The rotor bars are not aligned

straight to the rotor bar but are skewed to reduce the locking tendency of the rotor and to reduce

the magnetic hum hence allowing the motor to run quietly [2].

2.4.4.2 Single phase induction motor operation

When the motor is fed from a single-phase supply, the stator winding produces a flux which only

alternates along one space axis only, i.e. the flux produced does not rotate [1, 2 and 3]. A single –

phase induction motor is therefore not self-starting. However, if the rotor is given a push in either

direction, it accelerates to its final speed and continues to rotate in the given direction even after

the force has been removed.

2.4.4.3 Making a single phase induction motor self-starting

Single phase induction motors are not self- starting, therefore to make them self-starting they are

temporarily converted into two phase and then reverted to single phase upon gaining the desired

motion in the desired direction. There are several methods of making a single phase self-starting.

These include:-

1. Split-phase induction motors

In split phase induction motor, the stator has twowindings- main and auxiliary- which are used to

start up the motor. The main winding has low resistance but high reactance whereas the starting

winding has a high resistance but low reactance [1, 2]. At starting the winding current Im lags the

applied voltage by about 70-80 degrees, the auxiliary winding current Ia by about 30-40 degrees.

This result in a non-uniform travelling –wave field and consequently a rotor torque proportional

10

to ImIaSinα where α is the difference between the two angles of lag [5]. A starting torque of

between 2.5-2 times the full load value is generated. After reaching 75% of the rated speed, the

auxiliary winding may be open circuited with the help of centrifugal switch and the motor would

still continue to run.

2. Capacitor split phase motor.

Capacitor split phase motors incorporates capacitors in the auxiliary winding so as to greatly

vary the phase difference between the auxiliary and the main winding [2]. There are two types:

I. Capacitor start motor- In these types of single phase induction motor, the starting

winding along with the capacitor is isolated when the motor has attained the

desired speed.

II. Capacitor-run motor- In these type of single phase induction motors, the starting

winding (winding with the capacitor) remains in the rotor circuit after starting the

motor. The starting winding helps improve the power factor.

11

CHAPTER 3

DESIGN OF SINGLE PHASE INDUCTION MOTOR

START

(Human decisions) Specifications, constraints, output requirements, initial machine dimensions, winding parameters, objective function

Input

Run the equivalent machine program and analyze the

results

Change machine directions and

winding parameters

Output

STOP

Print all the machine design values and expected performance values

(Examine Result) Are specified constraints/ condition satisfied?

Are performance specifications satisfied?

Fig. 3. 1Design Flow Chart Diagram

12

3.2 The Design Procedure

The purpose of design is to obtain the dimensions and electrical particulars of a given machine to

satisfy a given set of specifications covering the starting characteristics to output ratings.

The main specifications for a single phase induction motor for design purposes are:-

1. Rated output in W or K.W.

2. Rated Voltage V

3. Rated current A

4. Rated speed r.p.m.

5. Frequency HZ

6. Poles, P

7. Pull out torque Nm

8. Starting torque Nm

9. Efficiency %

10. Power-factor %

11. Motor – type : split phase

a) Resistance start induction run (low starting torque)

b) Capacitor start induction run (medium starting torque)

c) Capacitor start capacitor run (High starting torque)

I. One capacitor

II. Two capacitor

Optimum characteristics, starting as well as running

13

3.2.1 Output Equation

The output equation relates the desired output characteristics of the induction motor to the

machine’ main determining specifications to which the motor should be designed based on.

The following standard nomenclature will be adopted in the derivation of the output equation;

F = Flux per Pole

Kw=Winding Factor

f=Frequency

V=Rated voltage

I=Full load current in the main winding, A

Tm=Number of turns of the main winding

P=Number of poles

D=stator bore diameter, m

L=Stator core length, m

τP=Pole Pitch

ns=Synchronous speed, r.p.s

Bav=Average value of flux density in the air gap, Wb/m2 (Specific magnetic loading)

ac= Ampere-conductor per meter of arm. Periphery, ac/m (specific electric loading)

η=Full load efficiency

Cos F= Full load power factor

The KVA rating of a single phase induction motor is given by;

KVA= VI*10-3 3.1

V=4.44KWfϕTm 3.2

ϕ=BavL(�D/p) 3.3

14

Ac= (2TmI)/ (�D) 3.4

f= nsP/2 3.5

Substituting for the value of V in equation (1); then

KVA= 4.44Kwf FTm I*10-3 3.6

Substituting for the values of f, F, and Tm

KVA =4.44KW (��

) (Bav��

L) (��

)*10-3 3.7

= (1.11v�2KWBavac*10-3) D2Lns 3.8

Again this can be expressed as;

KVA=COD2Lns 3.9

Where;

Co=1.11vπ2KWBavac*10-3 3.10

3.3 Single Phase Induction Motor Design Specifications Determination

3.3.1 Motor specifications

�� = 2.2��

� = 240�

� = 3��

� = 50��

�� = 2900��

Take full load efficiency to be 80% and power factor 85%

3.4 Design solution

3.4.1 Main dimension

Watts output = 3��

= 3 × 746

15

= 2238� ��

Actual speed = 2900��

Nearest synchronous speed= 3000��

Number of poles P = ��× ��

3.11

� = 120 × 50

3000

= 2

��= �3000

60 �= 50��

� ��− ��. �. � = �

223850 �

= 44.76

From the graph, the value of��. �. �� is given by;

= 27

Therefore the main dimension of the motor is given by;

�� = �.�× �.��.�.�� .��

3.12

=3 × 0.74627 × 50

= 0.00165778� �

Since the motor is in high demand;

We take

�� = 1.5

Hence for a 2-pole machine;

� × 2�� = 1.5; � = 2.3562

�� = 0.00165778

2.356�� = 0.00165778� �

� = � 0.001657782.356

�

� = 0.08894�

� = 8.894��

16

� = 8.894 × 2.3562

= 20.956��

� = 8.894��

��3.50157��ℎ��

From the standard stamping taste

Selecting size 138 M of Guest Keen Williams then the bore diameter

� = 312 " ≅ 8.9��

Core length, � = �� = ��.��

��.�� 3.13

= 20.929��

Pole pitch �� = �× �.��

= 13.98��

�� ≅ 14.00��

3.4.2 Net iron length Li;

Choosing a stacking factor of 0.9 then;

The stacking factor is the ratio of electrical steel along the axial length of the iron core. It is

important to account for the stacking factor when designing an electrical machine, since a

stacking factor of less than 1.0 reduces the flux carrying capacity of the iron core accordingly.

The stacking factor is low for very thin iron laminations and is approaching unity as the

lamination thickness increases. The stacking factor is sometimes also called lamination factor or

space factor.

�� = 0.9�

= 0.9 × 20.929

= 18.836��

Check for peripheral velocity �

� = �� = � × 0.089 × 50

= 13.98� /��

The maximum permissible peripheral velocity for normal construction is 30m/sec. therefore the

chosen D is within the permissible limit

The selected stamping has 28 stator slots with parallel sided teeth and tapered slots.

17

The width of stator tooth = 0.1425" ≅ 0.362��

= 0.1425" = 0.362��

Flux density in the stator slot

The stator tooth density �� is within the range of 1.4 to 1.7 � �/� �

�� = ∅

�� × ��× � ��

3.14

∅� = ��

�× ��× � �� 3.15

= 1.4��28/2�× 0.00362 × 0.188�

= 13.339 × 10��

The selected stamping has outer diameter

�� = 5 ��

"=13.81

Depth of stator slots�� = 0.573” ≅ 1.455��

Depth of stator core, ��

�� = ��

�� − (� + 2��)� 3.16

=12

�13.81 − �8.9 + 2.91��

= 1��

Check for flux density in the stator case

�� = ∅��× ��

3.17

=13.339 × 10��

2 × 1 × 10�� × 18.836 × 10��

= 3.5408��/� �

3.4.3 Stator winding

Assuming winding factor for mail winding to be �� = 0.8

Stator induced e.m.f � ≅ 0.95� ≅ 228��

Number of turns in the main winding

�� = ��.�� ∅�

3.18

=228

4.44 × 0.8 × 50 × 13.339 × 10��

= 96.243

18

≅ 96

Turns in series per pole

= 48

3.4.4Winding arrangement

Number of stator slots (total) = 28

Number of stator slots per pole = ��

�

= 14

Therefore selecting the number of coils for main winding = 7

19

Fig. 3. 2Arrangement of Stator Coils

20

For sinusoidal distribution the number of turns of each coil are calculated as;

��7 − 9; ��½�� = ��2

14 × 90�� = 0.2225

��6 − 10; ��½�� = ��4

14 × 90�� = 0.4339

��(5 − 11); ��½�� = ��6

14 × 90��= 0.6235

��(4 − 12); ��½�� = ��8

14 × 90��= 0.7818

��(3 − 13); ��½�� = ��1014 × 90��= 0.9009

��(2 − 14); ��½�� = ��1214 × 90��= 0.9749

��(1 − 15); ��½�� = ��1414 × 90��= 0.5000

= 4.4375

Percentage of turns in coil 7-9

�0.22254.4375 × 100�= 5.014


�0.43394.4375 × 100�= 9.778


�0.62354.4375 × 100�= 14.051


�0.78184.4375 × 100�= 17.618


�0.90094.4375 × 100�= 20.302


�0.97494.4375 × 100�= 21.9696

21


�0.500

4.4375 × 100�= 11.2676

The turns in each coil will be

��7 − 9 = �0.05014 × 48�

= 2.406 ≈ 2

��6 − 10 = �0.09778 × 48�

= 4.693 ≈ 5

��5 − 11 = �0.1405 × 48�

= 6.744 ≈ 7

��4 − 12 = �0.17618 × 48�

= 8.456 ≈ 8

��3 − 13 = �0.20302 × 48�

= 9.745 ≈ 10

��2 − 14 = �0.219696 × 48�

= 10.545 ≈ 11

��1 − 15 = �0.112676 × 48�

= 5.40 ≈ 5

Total 48

Amended value of �� = 2 × 48 = 96

The winding factor is calculated as;

��2 × 0.2225�+ �5 × 0.4339�+ �7 × 0.6235�+ �8 × 0.7818�+ �10 × 0.9009�+ �11 × 0.9749�+ �5 × 0.500� �

96

= 0.3695 ≈ 0.4

3.4.5Conductor size

Main winding full current is given by

�= � .�× ��.�.��

3.19

22

=3 × 746

240 × 0.85 × 0.80

�= 13.713�

Assuming a current density of 5�/� � �

Area of main winding conductor�� is given by

�� =13.713�

5�/(� � ^2)

= 2.7426/� � �

Diameter of bare conductor

�2.7426 ×4�

= 1.868� �

From the conductor sizes available. The nearest size available has a bare conductor diameter

1.900 mm

Therefore

Area of main winding conductor �� ;

�� =�4 × 2. 90�

= 2.835� � �

And diameter of insulated conductor = 2.4268� �

The largest number of turns per coil is 11 and therefore the largest number of main winding

conductor in a slot is 11.

Therefore the space occupied by 11 conductors is;

11 ×�4 × 2. 4268�

= 50.88� � �

The average area of slot used

3.4.6 Length of mean turn

The length of each of the coils per pole of a concentric winding is given by;

�� = �.��

× �� + 2� 3.20

Where �� = ��ℎ��= 1.46��

23

� = �� = 8.9

�� = ��. ��= 28

� = 20.956��

�� 1 − 15 = 8.4�8.9 + 1.46�

28 × 14 + 2 × 20.656 = 85.424��

�� 2 − 14 = 8.4�8.9 + 1.46�

28 × 12 + 2 × 20.656 = 79.208��

�� 3 − 13 = 8.4�8.9 + 1.46�

28 × 10 + 2 × 20.656 = 72.992��

�� 4 − 12 = 8.4�8.9 + 1.46�

28 × 8 + 2 × 20.656 = 66.776��

�� 5 − 11 = 8.4�8.9 + 1.46�

28 × 6 + 2 × 20.656 = 60.56��

�� 6 − 10 = 8.4�8.9 + 1.46�

28 × 4 + 2 × 20.656 = 54.344��

�� 7 − 9 = 8.4�8.9 + 1.46�

28 × 2 + 2 × 20.656 = 48.128��

Length of mean turns of main winding

�� =��5 × 85.424�+ �11 × 79.208�+ �10 × 72.992�+ �8 × 66.776�

�7 × 60.56�+ �5 × 54.344�+ �2 × 48.128� �

48

= 69.884��

Resistance of main winding;

��75��0.02196 × 0.69884

2.835 � = 0.021

0.49664Ω

��20��0.01796 × 0.69884

2.835 � = 0.017

0.402Ω

3.4.6 Rotor design

Length of the air gap, ��

�� = 0.2 + 2√�� 3.21(a)

Or

24

�� = 0.2 + �� 3.21(b)

= 0.2 + 0.08894

= 0.289� �

A length of air gap = 0.3 mm approximately can be taken

The selected stamping (pg. 598(138 m)) has rotor outer diameter 3 ��

" ≅ 8.9�� and slots

number 20

It has to be machined to create an air gap of 0.3 mm

Thus making rotor diameter �� = 8.9 − 2�0.3�= 8.84��

Rotor inner diameter = ��

" = 1.9��

3.5.7 Rotor slots

The selected stamping has 20 slots in the rotor punching

From the standard rotor sets; R-5 by Darydal Stainless steel is chosen (pg. 603);

Area of the rotor slot is = 0.3 × 0.145

= 0.0435��. ��ℎ��

= 0.280��

0.

3

0.145”

0.145”

1”/16R

Fig. 3. 3Rotor Set

25

Allowing for rounding of corners and clearances, the area of the rotor bar can be taken as;

�� = 24� � �

Total rotor copper section �� = ��. �� 3.22

20 × 24

= 480� � �

And the total stator cooper section for main winding;

�� = 2��

= 2 × 96 × 2.7426

= 526.5792mm2

≅ 527� � �

3.5.8 End Ring design

Area of each end = �� = ��

��)��

3.23

�� = ��× �

(Taking�� = ��) ��– �� 3.24

�� − ��

≈ 76.394� � �

Let end ring depth = 10 mm and emf thickness 5 mm

Taking outer diameter of End ring Dero = 9.00 cm

Inner diameter of endring Derl = 8.00 cm

Mean diameter end ring De = 8.5cm

3.5.9 Gap extension coefficient

Width of stator slot opening �� = 0.065�� = 1.65� �

Ratio ��

= �.��.�

= 5.5�� 3.25

Stator slot pitch ��× �.�

��= 0.9985��

Carter’s coefficient for semi-enclosed slots correspond to a ratio 5.5 from the standard taste [5] is

0.64

Therefore;

�� = ��.� ��

= �.��.��.��× �.��

3.26

26

= 1.118

��ℎ��ℎ��1.0� �

�� = 1.0� �

��ℎ =

1.00.3 = 3.33

For which �� = 0.48

�� =� × 8.84

20 = 1.3885

�� =1.3885

1.3885 × 0.48 × 0.1

= 1.036

Therefore gap extension �� = 1.118 × 1.036 = 1.158

3.5.10 Rotor resistance

The rotor bars are assumed to be skewed through one slot pitch i.e. through 1.3885 cm

Length of each bar;

�� = ��20.956��1.3885��

= 21.00��

Resistance of the rotor refereed to the main winding

��" = 8��

��

��+ �

��

�� 3.27

= 8�96��0.8��0.04��21.00

20 × 24 × 10� +2�

8.5 × 10��

2� × 76.89�

= 0.608Ω��75��

And ��” = �.��

�.��× 0.336Ω

= 0.0492Ωat20��

3.5.11 Reactances

Slot leakage reactance

27

The specific performance for a slot is given by

�� = ��

��

��

� 3.28

For the given case

��.��"��.��”� = 0.533”�= 0� = 0.04"� = 0.065"��/�� = 0.684

From standard table [pf 390]

For ��

= 0.684∅ = 0.47

Therefore

�� = �0.470.5330.38 +

0.040.065�

= 1.27

For rotor slot

�� = ��

+ ��

� 3.29

Now; �� = 0.3" , �� = 0.042", �� = 0.146", � � = 1� � = � ��.�

�"

�� = �0.3

3 × 0.146 +0.042

��.�

�= 1.752

�� = ��

��

�� × ��

� × ��

3.30

For �� = 30�� = 54, �� = 68�� = 0.8�� = 28�� = 2

Then

�� =30�+ 54� + 68�

�152�� ×1

0.8� ×28

4 × 2 ≅ 2.0

28

The slot leakage reactance in terms of the main winding;

�� = 16��

�� + ��

�� 3.31

= 16 × � × 50 × 4� × 10��96 × 0.8�� ×20.956 × 10��

28 × �1.27 +2820 × 1.752�2.0

≈ 1.038Ω

3.5.11.1 Zigzag leakage reactance��;

16��

�� 3.32

�� = � ��

� ��

� 3.33

Where � �� = 0.998 − 0.165 = 0.8329��

� �� = 1.3885 − 0.1 = 1.2885�

�� = 0.998��

�� = 1.3885

�� = 0.3� �

�� =0.8329 × 1.2885�0.8829� + 1.2885��

12 × 0.03 × �0.998�� × �1.3885�

= 5.07

�� = 16 × � × 50 × 4� × 10��96 × 0.8�� ×20.956 × 10��

28

= 0.15

29

3.511.2 Over hang reactance

�� = 16�� .��

�� + ��× ��. �� 3.34

= 16 × � × 50 × 4� × 10��96 × 0.8�� ×1

604 × 28 × 2 × ��0.0894 + 0.0146�× 8�

= 0.136Ω

3.5.11.3 Magnetizing reactance

�� = 16��

�� 3.35

Assuming saturation factor �� = 1.25

�� = 16 × � × 50 × 4� × 10��96 × 0.8�� ×20.956 × 10�� × 14.0 × 10��

10 × 0.03 × 10�� × 1.158 × 2 × 1.25

= 62.927Ω

3.5.11.4 Skew Leakage Reactance

The bars are skewed through one slot pitch

Angle of skew, �� = ��

× 1 × ��

= 0.314��

Skew leakage reactance

�� = ��

�

�� 3.36

�� = 0.95��

62.92 ×0.1314�

12 × 0.95

30

= 0.0895

Now the total leakage reactance

�� = ��+ ��+ �� + �� 3.37

= 1.308 + 0.0895 + 0.15 + 0.136

= 1.06835Ω

�� =��

�

��=

0.4921.6835 = 0.2922

3.5.11.5 Open circuit reactance

�� = �� + ��

= 62.927 + �.��

= 63.7687Ω 3.38

Leakage factor

= ��

3.39

=62.927 − 1.6835

62.927

�� = 0.973

�� = �� = 0.986

3.6 Design of starting winding for resistance split phase

The starting winding is designed for maximum torque per ampere of starting current. Therefore

for purpose of calculating torque and current the rotor resistance is increased by 17.5% to take

into account the skin effect

The total resistance in terms of main winding

31

�� = �� + 1.75�� 20�� 3.40

= 0.402 + 1.75 × 0.492��20��

= 1.263Ω

Total independence in terms of main winding at 200C

�� = �� + ��

� = √1. 263� + 1. 6835� 3.41

= 2.105Ω

Main winding locked Rotor current, ��

�� = ��

= ��.��

= 114 3.42

The starting current is not to exceed about 6 turns the full current i.e.

6 × 13.713 = 82.278

The starter current is hence taken as;

5 × 13.713 = 68.5654

�� = 68.5654

��

��=

68.565114 = 0.601

Auxiliary winding Reactance��

= ��

� ��

��

�� 3.43

=1.6835

0.601� − 1

32

CHAPTER 4

RESULTS AND ANALYSIS

4.1 Results

Table 4.1 Results

DESIGN PARAMETER DESIGN VALUE Rated Power Output, W 2238 Rated Voltage, V 240 Rated Frequency, f 50 Nearest Synchronous Speed, Ns 3000 Poles, P 2 Speed in r.p.s , ns 50 Wattsperrps 44.7600 W/r.p.s ConCosPhi 27 Main Diameter, D 8.894 cm Length , L 20.956cm Standard Diameter, Ds 8.9 cm Standard Length,Ls 20.929 cm Standard Pole Pitch, Tps 14.0 cm Length of Iron, Li 18.836 cm Peripheral Velocity,V1 13.9857 Width of Stator Slot, Wts 0.362 cm Stator Tooth Density, Bts 1.400 Number of Stator Slots, Ss 28 Stator Flux Linkage, FM 0.0135Wb Stator Stamping Outer Diameter, Do 13.8100 cm Depth of Stator Core, dcs 1.4550 cm Depth of Stator Slots, dss 1 cm Flux Density in the Stator Core, Bcs 0.0355 Winding Factor, Kwm 0.800 Number of Turns in the Main Winding, Tm 96 Turns in Series Per Pole, Tmp 48 Power Factor, n 0.8500 Full Load Efficiency, ef 0.800 Main Winding Current, I 13.7132 A Current Density, Id 5 A/mm2 Area of Main Winding Conductor, Am 2.7426 mm2

33

Diameter of Bare Conductor, Dbc 1.8683mm Length of Air Gap, Lg 0.3000 mm Rotor Outer Diameter, Dro 8.9 cm Number of Rotor Slots,Nrs 20 Rotor Inner Diameter, Dri 1.9 cm Length of Chosen Rotor Stamping, Lrs 0.3” Width of Chosen Rotor Stamping, Wrs 0.145” Area of Rotor Slot, As 24cm2 Area with Allowance and Clearance Incorporated, Ar

480 mm2

Total Copper Section for Main Winding, AM 527 mm2 Current Density in End Ring, db 20 Current Density in Rotor Bar, de 20 Area of Each End Ring, Ae 76.3636 mm2 Length of bar, Lb 21 cm Resistance of the Rotor Referred to the Main Winding, rrm

154.0094

Width of Stator Slot, Wos 0.362 cm Slot Leakage Reactance, Xsr 1.0814 Stator Slot Pitch, Yss 0.9985cm Zig Zag Leakage Reactance, Xz 0.0031 Magnetizing Reactance, Xm 62.927 Skew leakage Reactance, Xsk 0.0895 Total Leakage Reactance, XTlm 1.6835 Open Circuit Reactance, Xom 63.7687 Gap Extension Coefficient, Kg 1.158

34

4.2 Result Analysis

The design values obtained for the 2.2kw, 240V, 2900rpm, and 50Hz motor are within the

desired values for the specified induction motor.

The specified values for various motor parts ensure flow of the acceptable value of current

within the rotor and stator windings.

35

CHAPTER 5

CONCLUSIONS AND RECOMMENDATIONS

5.1 Conclusion

This project applied the standard motor design procedures to determine the required design

specifications for single phase induction motor for Numerical machine Complex. The objectives

of the experiment were to come up with the proper design specifications for consideration of

local fabrication of the small size single phase induction motor in Kenya.

For the purpose of design, it was established that there exists standard dimensions for different

motor parts especially as regard the stator and the rotor. Companies and governments seeking to

set up fabrication industries will therefore have to consider the process of acquiring these

standard existing parts for the purpose of fabricating the induction machine.

In addition, the project presents a program that automatically generates the numerical

approximations of the design specifications by accepting the input which are the desired machine

output specifications and numerically generating the expected design values of the machine parts

as output for the process of fabrication.

The values generated from the program present an easier way of reducing the tedious numerical

calculations and the chances of occurrence of the errors arising from numerical calculations. As

captured in the workings, this project only provides solutions to the design phase of the Motor

fabrication process. There exists a lot more to be done especially as entails assembling machines,

acquisition of well -trained human labor and procurement of the required materials for

fabrication of motor casing, coils, rotor and the stator. It is, however, a greater step in the right

direction as it provides a basis of reference for the fabrication process. Whatever good or bad

36

that results thereof this stage of the fabrication process determines whether or not the final

product is within the market expectation or demand.

5.2 Recommendation

Industrialization remains a challenge to many developing countries. Lack of adequate finances,

technical know-how and lack of government initiatives are but a few of challenges to the

industrialization process. However, the greater good that comes with initiating the process is

immense.

From job creation, increase in revenue, to self-sustainability, industrialization is an investment

worth making.

Through this project, it is recommended that;

1. The Numerical Machine Complex initiates the process of designing and fabricating local

made single phase induction motors

2. That the company invests in assembling the necessary machines for the fabrication

process

3. The company should equally invest in training her personnel for the purpose of

cementing a better understanding of the fabrication process, and to ensure high quality

products.

37

REFERENCES

[1] M. V.K, Principles of Electrical Machines, India: S. Chand, 2002.

[2] T. a. Chand, A Text Book of Electrical Technology, India : S. Chand , 2005.

[3] F. A. S. U. Charles K., Electric Machinery, New York: Mc Graw Hill, 2003.

[4] J. B., Electrical and Electronic Principles and Technology, New York: Oxford , 2003.

[5] A. R.K., Principles of Electrical Machine Design, India: S.K. karataria &Son, 2007.

38

APPENDIX

Appendix Table 1 Standard Load Efficiency and Power Factor for Small Single Phase, 50 Hz Cage - Motors

RATING (W) FULL LOAD EFFICIENCY POWER FACTOR P.U

40 0.38 0.45

100 0.50 0.55

200 0.60 0.60

400 0.68 0.65

750 0.72 0.67

1000 0.75 0.70

1500 0.77 0.76

2000 0.79 0.81

2500 O.82 O.87

39

Appendix Table 2: The Standard Approximate Values for Co.η.Cos for Different Values of Watts/R.P.S.

Watts/r.p.s 3.6 7.2 12 18

��. �. �� 9.5 12 15.5 18

40

%SINGLE PAHSE INDUCTION MOTOR DESIGN SPECIFACTION DETERMINATION PROGRAM Es=2.2e3 % Motor output rating V=240 % Motor Rated voltage HP=3 % Rated Output in horse power W=HP*746 % Motor output in Watts f=50 % Frequency Ns=3000 % speed in revolution per minute P=((120*f)/Ns) % Motor Poles ns=(Ns/60) % speed in revolution per second Wattsperrps=W/ns %Using the value of Watts/r.p.s read the value of the ConCosPhi from the %Watts/r.p.s versus ConCosPhi graph ConCosPhi=46 %Input the value of ConCosPhi from the graph %MAIN DIMENSIONS d2l=((HP*0.746)/(ConCosPhi)) %Determination of the length and Width of the motor %L/TP=1.5;%Input the desirable value depending on the demand of the motor %being designed %(L*2/PiD)=1.5; LTP=1.5 LPD=1.5 %Zout=LPD pi=22/7 %Zout=((L*P)/(pi*D)) D=8.9 %D=((LPD*pi)/(L*P)) %LPD=((L*P)/(pi*D))%Get the value of D and L from line 19 and 22 %From the values of the D & L obtained, choose the appropraiate stamping %from the standard stamping table %Taking the appropriate main dimensions values of the Chosen stamping as Ds %and Ls, then L=(d2l/(D*D)) %Length of the Motor Ds= 0.089 %Diameter of the chosen stamping Ls=((D*D*L)/(D*D)) %corelength of the desired stamping Tps= (((22/7)*D)/P) %Pole pitch %Net Iron Length Li=0.9*Ls%0.9 is the desirable stacking factor %CHECK FOR PEERIPHERAL VELOCITY Vl=(22/7)*Ds*ns %The permissible value of the peripheral velocity should be less than 30m/s Wts= 0.00362 %Enter the value of the Stator teeth from the selected Stamping Bts=1.4 %Stator tooth flux density should be withtin the range odf 1.4 to 1.7 wb/m^2 % Let (Phi)m=Bts((Ss/p)*Li*Wts) flux linkage in the motor be equivalent to FM Ss=28 %Stator slots FM=Bts*(Ss/P)*Li*Wts Do=13.81 %Enter the value of the outer diameter for the selected stamping dss=1.455 %Enter the value of the depth of the stator slots %for the selected stamping

41

dcs=0.5*(Do-(D+(2*dss))) %Depth of the stator core %CHECK FOR FLUX DENSITY IN THE STATOR CORE Bcs Bcs=FM/(2*dcs*Li) %STATOR WINDING Kwm=0.8 %Define the desirable winding factor for main winding Kwm; E=228 %Stator Induced Voltage Tm=E/(4.44*Kwm*f*FM) %Number of turns in the main winding Tmp=Tm/P %Turns in series per per pole %CONDUCTOR SIZE %MAIN WINDING FULL CURRENT I n=0.85 %Full load eficiency ef=0.80 %Power factor I=((3*746)/(V*n* ef)) %Main Winding Full current Id=5 %Enter the value of current density in the line Id %Area of the main winding conductor Am=I/Id %Diameter of bare conductor Dbc= ((Am*4*7)/22)^0.5 %ROTOR DESIGN Lg=0.3 %Desirable Length of the air gap' L %Enter the diamter and the number of slots of the chosen rotor stamping %the slectd stamping has the following maesurements Dro=0.00084 %rotor outer diamter Nrs= 20 %Nrs- Number of Rotor slots %Rotor inner diameter Dri= 0.019 %ROTOR SLOTS %Area of the rotor slot %From the standard rotor sets. Choose sppropriate stamping Lrs=0.003 %Length of the chosen rotor stamping Wrs=0.00145 %Width of the chosen rotor stamping As=Lrs*Wrs%Product of the length of the rotor slot and the width of the rotor slot %Area with clarence and allowance for end corners incorporated Ab=24 Ar=Nrs*Ab %TOTAL STATOR COPPER SECTION FOR MAIN WINDING AM=2*Tm*Am

42

%END RING DESIGN %Area of each end ring ,Ae db=20 de=20 Ae=(Ar*7*db)/(22*P*de) %GAP EXTENSION COEFFICIENT Wos=0.000165; %Enter the value of the width of the stator slot opening %lg=O.OOO3;%Gap Length GP= Wos/Lg;%Gap ratio- this is the ratio of the %Slot openiningWo at the gap surface and the air gap length % This Ratio is used to determine the Carter's coefficient from the % standard tables yss=(pi*8.9)/Ss; %Stator Slot pitch, yss Kcs=0.64; %Carters' coefficient for semi-closed slots %Gap Extension factor Kg is given by Kgs=((yss)/(yss-(Kcs*Wos))); %ROTOR RESISTANCE Lb=21.00 %Length of the rotor bar rho=0.021 %Density of the material Rrm=8*Tm*Kwm*Kwm*rho*((Lb)/(Nrs*Ab))+((2*de)/(pi*P*P*Ae)) %Resistance of %the rotor as reffered to the main winding %REACTANCES a1=0.26 a2=0.38 b=0.0533 c=0 d=0.04 e=0.065 Ra1a2=a1/12 % Form the ratio of a1/a2 determined we estmate %the value of Phi used in determining the value of the %slot leakage reactance from the standard tables provided phi=0.47 Xss=((phi*(a2/b))+(d/e)+((2*c)/(e+a1)))%The specific Perfomance for %a slot L1=0.3 Ws=0.146 h4=0.042 Wo=1/25.4 Xsr=((L1/3*Ws)+(h4/Wo)) ysr=1.3885 Wtr=ysr-0.1 mhu=4*pi*10e-3 %ZIG ZAG REACTANCE LEAKAGE REACTANCE Xz=(Wts*Wtr*(Wtr*Wtr+Wtr*Wtr))/(12*Lg*yss*yss*ysr) Xzl=16*pi*f*mhu*(Tm*Kwm*Tm*Kwm)*(L/Ss)*Xz %OVERHANG REACTANCE cp=8 %Avrage coil span %Ss=28;

43

Xo=16*pi*f*mhu*(Tm*Kwm*Tm*Kwm)*((1/6.4)*Ss*P)*(pi*(D+dss)*cp) %MAGNETISING REACTANCE tao=14e-2 Fs=1.25 %saturation factor Kg=2*1.158 Xm=16*pi*f*mhu*(Tm*Kwm*Tm*Kwm)*((L*tao)/(10*Lg*Kg*P*Fs)) %SKEW LEAKAGE REACTANCE PhiS=0.134 %Rotor bar Skew Anglein radians k1=0.95 Xsk=Xm*((PhiS*PhiS)/12)*k1 %TOTAL LEAKAGE REACTANCE XTlm=Xm+Xo+Xzl+Xsr %OPEN CIRCUIT REACTANCE REFFERED TO MAIN WINDING Xom=Xm+(XTlm/2)

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