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
1
DECLARATION OF ORIGINALITY
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
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:
………………………………………………………………………………………
I
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
………………
II
DEDICATION
To my loving mother, Mary Okello.
III
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
IV
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
V
5.2 Recommendation ............................................................................................................. 36
References ..................................................................................................................................... 37
VI
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
VII
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
VIII
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
IX
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
𝜗 - Peripheral Velocity
Lb- Length of bar
yss– Stator slot pitch
ysr
X
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 selfsustaining 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
XI
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.
1
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.
2
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.
3
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
4
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.
Fig. 2. 2Diagram showing the operation of a D.C Motor
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
5
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
6
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].
7
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
8
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 shortcircuiting 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
9
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.
10
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
Output
(Examine Result)
Are specified constraints/ condition satisfied?
Are performance specifications satisfied?
Print all the machine design values and expected
performance values
STOP
Fig. 3. 1Design Flow Chart Diagram
11
Change machine
directions and
winding
parameters
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
12
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(𝛑D/p)
3.3
13
Ac= (2TmI)/ (𝛑D)
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
𝑛𝑠
D
KVA =4.44KW ( 2 ) (Bav𝛑𝑃 L) (
𝑎𝑐π𝐷
2
)*10-3
3.7
= (1.11v𝛑2KWBavac*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
𝐾𝑊 = 2.2 𝐾𝑊
𝑉 = 240 𝑉
𝑊 = 3 𝐻𝑃
𝐹 = 50 𝐻𝑧
𝑁𝑠 = 2900 𝑅𝑃𝑀
Take full load efficiency to be 80% and power factor 85%
3.4 Design solution
3.4.1 Main dimension
Watts output = 3 𝐻𝑃
= 3 × 746
14
= 2238 𝑊𝑎𝑡𝑡𝑠
Actual speed = 2900 𝑅𝑃𝑀
Nearest synchronous speed= 3000 𝑟𝑝𝑚
Number of poles P =
120 ×f
3.11
ns
120 × 50
3000
𝑃 =
=2
3000
𝑛𝑠 (𝑟𝑝𝑠) = (
) = 50 𝑟𝑝𝑠
60
𝑊𝑎𝑡𝑡𝑠 − 𝑜𝑢𝑡𝑝𝑢𝑡
2238
=(
)
𝑟. 𝑝. 𝑠
50
= 44.76
From the graph, the value of 𝐶𝑜. 𝜂. 𝐶𝑜𝑠 is given by;
= 27
Therefore the main dimension of the motor is given by;
𝑙.𝑝×0.746
𝐷2 𝐿 = 𝐶𝑜.𝜂.𝐶𝑜𝑠 𝜙.𝜂
=
3.12
𝑠
3 × 0.746
27 × 50
= 0.00165778𝑚3
Since the motor is in high demand;
We take
𝐿
= 1.5
𝑙𝑝
Hence for a 2-pole machine;
𝐿×2
= 1.5 ; 𝐿 = 2.3562
𝜋𝐷
𝐷2 𝐿 = 0.00165778
2.356𝐷3 = 0.00165778𝑚3
3
𝐷=√
0.00165778
2.356
𝐷 = 0.08894 𝑚
𝐷 = 8.894 𝑐𝑚
15
𝐿 = 8.894 × 2.3562
= 20.956 𝑐𝑚
𝐷 = 8.894 𝑐𝑚
𝑜𝑟 3.50157 𝐼𝑛𝑐ℎ𝑒𝑠
From the standard stamping taste
Selecting size 138 M of Guest Keen Williams then the bore diameter
1
𝐷 = 3 " ≅ 8.9 𝑐𝑚
2
Core length, 𝐿 =
𝐷2 𝐿
𝐷2
=
1657.78
(8.9)2
3.13
= 20.929 𝑐𝑚
Pole pitch 𝜏𝑝 =
𝜋×8.9
2
= 13.98 𝑐𝑚
𝜏𝑝 ≅ 14.00𝑐𝑚
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.
𝐿𝑖 = 0.9 𝐿
= 0.9 × 20.929
= 18.836 𝑐𝑚
Check for peripheral velocity 𝜗
𝜗 = 𝜋𝐷𝜂 = 𝜋 × 0.089 × 50
= 13.98𝑚/𝑠𝑒𝑐
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.
16
The width of stator tooth = 0.1425" ≅ 0.362 𝑐𝑚
= 0.1425" = 0.362 𝑐𝑚
Flux density in the stator slot
The stator tooth density 𝐵𝑡𝑠 is within the range of 1.4 to 1.7 𝑊𝑏 /𝑚2
𝐵𝑡𝑠 =
∅
3.14
𝑆
( 𝑠 )×𝐿𝑖 ×𝑊𝑡𝑠
𝑃
𝑆
∅𝑚 = 𝐵𝑡𝑠 {( 𝑃𝑠 ) × 𝐿𝑖 × 𝑊𝑡𝑠 }
3.15
= 1.4 {(28/2) × 0.00362 × 0.188}
= 13.339 × 10−3 𝑊𝑏
The selected stamping has outer diameter
7
𝐷0 = 5 16"=13.81
Depth of stator slots𝑑𝑠𝑠 = 0.573” ≅ 1.455 𝑐𝑚
Depth of stator core, 𝑑𝑐𝑠
1
𝑑𝑐𝑠 = 2 [𝐷0 − (𝐷 + 2𝑑𝑠𝑠 )]
=
3.16
1
[13.81 − (8.9 + 2.91)]
2
= 1 𝑐𝑚
Check for flux density in the stator case
∅𝑚
𝐵𝑐𝑠 = 2𝑑
3.17
𝑐𝑠 ×𝐿𝑖
13.339 × 10−3
=
2 × 1 × 10−2 × 18.836 × 10−2
= 3.5408𝑥𝑥𝑥/𝑚2
3.4.3 Stator winding
Assuming winding factor for mail winding to be 𝐾𝑤𝑚 = 0.8
Stator induced e.m.f 𝐸 ≅ 0.95 𝑉 ≅ 228 𝑣𝑜𝑙𝑡𝑠
Number of turns in the main winding
𝐸
𝑇𝑛 = 4.44 𝐾𝑤𝑚 𝑓∅
=
3.18
𝑚
228
4.44 × 0.8 × 50 × 13.339 × 10−3
= 96.243
17
≅ 96
Turns in series per pole
= 48
3.4.4Winding arrangement
Number of stator slots (total) = 28
28
Number of stator slots per pole = ( 2 )
= 14
Therefore selecting the number of coils for main winding = 7
18
Fig. 3. 2Arrangement of Stator Coils
19
For sinusoidal distribution the number of turns of each coil are calculated as;
2
𝐶𝑜𝑖𝑙 7 − 9; 𝑆𝑖𝑛 𝑜𝑓 ½ 𝑐𝑜𝑖𝑙 𝑠𝑝𝑎𝑛 = 𝑠𝑖𝑛 ( × 900 ) = 0.2225
14
4
𝐶𝑜𝑖𝑙 6 − 10; 𝑆𝑖𝑛 𝑜𝑓 ½ 𝑐𝑜𝑖𝑙 𝑠𝑝𝑎𝑛 = 𝑠𝑖𝑛 ( × 900 ) = 0.4339
14
6
𝐶𝑜𝑖𝑙 (5 − 11); 𝑆𝑖𝑛 𝑜𝑓 ½ 𝑐𝑜𝑖𝑙 𝑠𝑝𝑎𝑛 = 𝑠𝑖𝑛 ( × 900 ) = 0.6235
14
8
𝐶𝑜𝑖𝑙 (4 − 12); 𝑆𝑖𝑛 𝑜𝑓 ½ 𝑐𝑜𝑖𝑙 𝑠𝑝𝑎𝑛 = 𝑠𝑖𝑛 ( × 900 ) = 0.7818
14
10
𝐶𝑜𝑖𝑙 (3 − 13); 𝑆𝑖𝑛 𝑜𝑓 ½ 𝑐𝑜𝑖𝑙 𝑠𝑝𝑎𝑛 = 𝑠𝑖𝑛 ( × 900 ) = 0.9009
14
12
𝐶𝑜𝑖𝑙 (2 − 14); 𝑆𝑖𝑛 𝑜𝑓 ½ 𝑐𝑜𝑖𝑙 𝑠𝑝𝑎𝑛 = 𝑠𝑖𝑛 ( × 900 ) = 0.9749
14
14
𝐶𝑜𝑖𝑙 (1 − 15); 𝑆𝑖𝑛 𝑜𝑓 ½ 𝑐𝑜𝑖𝑙 𝑠𝑝𝑎𝑛 = 𝑠𝑖𝑛 ( × 900 ) = 0.5000
14
= 4.4375
Percentage of turns in coil 7-9
0.2225
(
× 100) = 5.014
4.4375
Percentage of turns in coil 6-10
0.4339
(
× 100) = 9.778
4.4375
Percentage of turns in coil 5-11
(
0.6235
× 100) = 14.051
4.4375
(
0.7818
× 100) = 17.618
4.4375
(
0.9009
× 100) = 20.302
4.4375
Percentage of turns in coil 4-12
Percentage of turns in coil 3-13
Percentage of turns in coil 2-14
(
0.9749
× 100) = 21.9696
4.4375
20
Percentage of turns in coil 1-15
0.500
(
× 100) = 11.2676
4.4375
The turns in each coil will be
𝐶𝑜𝑖𝑙 7 − 9 = (0.05014 × 48)
= 2.406
≈2
𝐶𝑜𝑖𝑙 6 − 10 = (0.09778 × 48)
= 4.693
≈5
𝐶𝑜𝑖𝑙 5 − 11 = (0.1405 × 48)
= 6.744
≈7
𝐶𝑜𝑖𝑙4 − 12 = (0.17618 × 48)
= 8.456
≈8
𝐶𝑜𝑖𝑙 3 − 13 = (0.20302 × 48)
= 9.745
≈ 10
𝐶𝑜𝑖𝑙 2 − 14 = (0.219696 × 48)
= 10.545
≈ 11
𝐶𝑜𝑖𝑙 1 − 15 = (0.112676 × 48)
= 5.40
Total
≈5
48
Amended value of 𝜏𝑚 = 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
𝐼=
𝐻.𝑝×746
3.19
𝑣.𝜂.𝐶𝑜𝑠
21
=
3 × 746
240 × 0.85 × 0.80
𝐼 = 13.713𝐴
Assuming a current density of 5 𝐴/𝑚𝑚2
Area of main winding conductor𝑎𝑚 is given by
𝑎𝑚 =
13.713𝐴
5𝐴/(𝑚𝑚^2 )
= 2.7426/𝑚𝑚2
Diameter of bare conductor
√2.7426 ×
4
𝜋
= 1.868 𝑚𝑚
From the conductor sizes available. The nearest size available has a bare conductor diameter
1.900 mm
Therefore
Area of main winding conductor 𝑎𝑚 ;
𝜋
𝑎𝑚 = × 2. 902
4
= 2.835𝑚𝑚2
And diameter of insulated conductor = 2.4268𝑚𝑚
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;
𝜋
11 × × 2. 42682
4
= 50.88 𝑚𝑚 2
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;
𝐿𝑚𝑡 =
8.4 (𝐷+𝑑𝑠𝑠 )
𝑆𝑠
× 𝑠𝑙𝑜𝑡𝑠 𝑠𝑝𝑎𝑛𝑛𝑒𝑑 + 2𝐿
3.20
Where 𝑑𝑠𝑠 = 𝑑𝑒𝑝𝑡ℎ 𝑜𝑓 𝑠𝑡𝑎𝑡𝑜𝑟 𝑠𝑙𝑜𝑡 = 1.46 𝑐𝑚
22
𝐷 = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑠𝑡𝑎𝑡𝑜𝑟 = 8.9
𝑆𝑠 = 𝑁𝑜. 𝑜𝑓 𝑠𝑡𝑎𝑡𝑜𝑟 𝑠𝑙𝑜𝑡𝑠 = 28
𝐿 = 20.956 𝑐𝑚
8.4(8.9 + 1.46)
× 14 + 2 × 20.656 = 85.424 𝑐𝑚
28
8.4(8.9 + 1.46)
𝐿𝑚𝑡 𝑓𝑜𝑟 𝑐𝑜𝑖𝑙 2 − 14 =
× 12 + 2 × 20.656 = 79.208 𝑐𝑚
28
8.4(8.9 + 1.46)
𝐿𝑚𝑡 𝑓𝑜𝑟 𝑐𝑜𝑖𝑙 3 − 13 =
× 10 + 2 × 20.656 = 72.992 𝑐𝑚
28
8.4(8.9 + 1.46)
𝐿𝑚𝑡 𝑓𝑜𝑟 𝑐𝑜𝑖𝑙 4 − 12 =
× 8 + 2 × 20.656 = 66.776 𝑐𝑚
28
8.4(8.9 + 1.46)
𝐿𝑚𝑡 𝑓𝑜𝑟 𝑐𝑜𝑖𝑙 5 − 11 =
× 6 + 2 × 20.656 = 60.56 𝑐𝑚
28
8.4(8.9 + 1.46)
𝐿𝑚𝑡 𝑓𝑜𝑟 𝑐𝑜𝑖𝑙 6 − 10 =
× 4 + 2 × 20.656 = 54.344 𝑐𝑚
28
8.4(8.9 + 1.46)
𝐿𝑚𝑡 𝑓𝑜𝑟 𝑐𝑜𝑖𝑙 7 − 9 =
× 2 + 2 × 20.656 = 48.128 𝑐𝑚
28
𝐿𝑚𝑡 𝑓𝑜𝑟 𝑐𝑜𝑖𝑙 1 − 15 =
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)
𝐿𝑚𝑡 𝑚 =
48
{
= 69.884 𝑐𝑚
Resistance of main winding;
𝐴𝑡 750 𝐶
0.021
96 × 0.69884
2.835
𝑒 = 0.021
0.49664Ω
𝐴𝑡 200 𝐶
0.017
96 × 0.69884
2.835
𝑒 = 0.017
0.402Ω
3.4.6 Rotor design
Length of the air gap, 𝐿𝑔 𝑖𝑠 𝑔𝑖𝑣𝑒𝑛 𝑏𝑦
𝐿𝑔 = 0.2 + 2√𝐷𝐿 𝑚𝑚
3.21(a)
Or
23
𝐿𝑔 = 0.2 + 𝐷 𝑚𝑚
3.21(b)
= 0.2 + 0.08894
= 0.289 𝑚𝑚
A length of air gap = 0.3 mm approximately can be taken
1
The selected stamping (pg. 598(138 m)) has rotor outer diameter 3 2 " ≅ 8.9 𝑐𝑚 and slots
number 20
It has to be machined to create an air gap of 0.3 mm
Thus making rotor diameter 𝐷𝑟 = 8.9 − 2(0.3) = 8.84 𝑐𝑚
3
Rotor inner diameter = 4 " = 1.9 𝑐𝑚
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);
0.145”
1”/16R
0.
3
0
0
0.145”
Fig. 3. 3Rotor Set
Area of the rotor slot is
”
= 0.3 × 0.145
= 0.0435 𝑠𝑞. 𝑖𝑛𝑐ℎ𝑒𝑠
= 0.280 𝑐𝑚2
24
Allowing for rounding of corners and clearances, the area of the rotor bar can be taken as;
𝑎𝑏 = 24𝑚𝑚2
Total rotor copper section 𝐴𝑟 = 𝑆𝑟 . 𝑎𝑏
3.22
20 × 24
= 480𝑚𝑚2
And the total stator cooper section for main winding;
𝐴𝑚 = 2𝑇𝑚 𝑎𝑚
= 2 × 96 × 2.7426
= 526.5792mm2
≅ 527𝑚𝑚2
3.5.8 End Ring design
𝐴 𝛿𝑏 )
Area of each end = 𝛿𝑒 = 𝜋 𝑟
𝑝
3.23
𝛿𝑒
480
𝛿𝑒 = 𝜋×2 (Taking𝛿𝑏 = 𝛿𝑒 )
𝛿𝑏 – 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑖𝑛 𝑒𝑛𝑑 𝑟𝑖𝑛𝑔 3.24
𝛿𝑒 − 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑖𝑛 𝑟𝑜𝑡𝑜𝑟 𝑏𝑎𝑟
≈ 76.394𝑚𝑚2
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 𝑊𝑜𝑠 = 0.065−11 = 1.65 𝑚𝑚
Ratio
𝑠𝑙𝑜𝑡 𝑜𝑝𝑒𝑛𝑖𝑛𝑔
𝑔𝑎𝑝 𝑙𝑒𝑛𝑔𝑡ℎ
=
Stator slot pitch 𝑦𝑠𝑠
1.65
0.3
= 5.5 𝑐𝑚
𝐾×8.9
28
3.25
= 0.9985 𝑐𝑚
Carter’s coefficient for semi-enclosed slots correspond to a ratio 5.5 from the standard taste [5] is
0.64
Therefore;
𝐾𝑔𝑠 = 𝑦
𝑦𝑠𝑠
𝑠𝑠 −𝐾𝑐𝑠 .𝑊𝑜𝑠
0.9985
= 0.9985−0.64×0.165
3.26
25
= 1.118
𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟𝑖𝑛𝑔 𝑡ℎ𝑒 𝑟𝑜𝑡𝑜𝑟 𝑠𝑙𝑜𝑡 𝑡𝑜 ℎ𝑎𝑣𝑒 𝑎𝑛 𝑜𝑝𝑒𝑛𝑖𝑛𝑔 1.0𝑚𝑚
𝑊𝑜𝑟 = 1.0 𝑚𝑚
𝑅𝑎𝑡𝑖𝑜
𝑠𝑙𝑜𝑡 𝑜𝑝𝑒𝑛𝑖𝑛𝑔 1.0
=
= 3.33
𝑔𝑎𝑝 𝑙𝑒𝑛𝑔𝑡ℎ
0.3
For which 𝐾𝑐𝑠 = 0.48
𝜋 × 8.84
= 1.3885
20
1.3885
=
1.3885 × 0.48 × 0.1
𝑦𝑠𝑟 =
𝐾𝑔𝑠𝑟
= 1.036
Therefore gap extension 𝐾𝑔 = 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;
𝐿𝑏 = √(20.956)2 (1.3885)2
= 21.00 𝑐𝑚
Resistance of the rotor refereed to the main winding
"
𝑟𝑟𝑚
= 8𝑇𝑚2 𝐾 2𝑛𝑚 [𝑠
𝐿𝑏
𝑟 𝑎𝑏
= 8(96)
2 𝐷𝑒
+ 𝜋 𝑃2 𝑎 ]
2 (0.8)2 (0.04)
3.27
𝑒
21.00
2 8.5 × 10−2
[
+
]
20 × 24 × 102 𝜋 22 × 76.89
= 0.608Ω 𝑎𝑡 75 𝑜 𝐶
And 𝑟𝑚” =
0.017
0.021
× 0.336Ω
= 0.0492 Ω at 20 0 𝐶
3.5.11 Reactances
Slot leakage reactance
26
The specific performance for a slot is given by
𝑏 𝑑 2𝑐
𝜆𝑠𝑠 = [𝑎
2
𝑒 𝑒+𝑎1
]
3.28
For the given case
𝑎1=0.26" 𝑎2=0.38” 𝑏 = 0.533” 𝑐 = 0 𝑑 = 0.04" 𝑒 = 0.065" 𝑎1 /𝑎2 = 0.684
From standard table [pf 390]
𝑎
For 𝑎1 = 0.684
2
∅ = 0.47
Therefore
𝜆𝑠𝑠 = [0.47
0.533 0.04
+
]
0.38 0.065
= 1.27
For rotor slot
𝐿
𝐿
𝜆𝑠𝑟 = [3𝑊1 + 𝑊4 ]
𝑠
3.29
0
1
"
Now; 𝐿1 = 0.3" , 𝐿4 = 0.042", 𝑊𝑠 = 0.146", 𝑊0 = 1 𝑚𝑚 = (25.4)
𝜆𝑠𝑟 = [
0.3
0.042
+ 1 ] = 1.752
3 × 0.146
25.4
(𝑍 2 +𝑍 2 +𝑍 2 )
1
𝑆
𝐶𝑥 = (𝑍 1+𝑍 2+𝑍 3)2 × 𝐾2 × 4𝑝𝑠
1
2
3
3.30
𝑤𝑚
For 𝑍1 = 30 𝑍2 = 54 , 𝑍3 = 68 𝐾𝑤𝑚 = 0.8 𝑆𝑠 = 28 𝑎𝑛𝑑 𝑝 = 2
Then
𝐶𝑥 =
302 +542 + 682
1
28
×
×
≅ 2.0
(152)2
0.82 4 × 2
27
The slot leakage reactance in terms of the main winding;
𝐿
𝑆
𝐶𝑥 = 16𝜋𝑓𝑀𝑜 (𝑇𝑚 𝐾𝑤𝑚 )2 𝑆 (𝜆𝑠𝑠 + 𝑆𝑠 𝜆𝑠𝑟 ) 𝐶𝑥
𝑠𝑠
3.31
𝑟
= 16 × 𝜋 × 50 × 4𝜋 × 10−7 (96 × 0.8)2 ×
20.956 × 10−2
28
× (1.27 +
× 1.752) 2.0
28
20
≈ 1.038Ω
3.5.11.1 Zigzag leakage reactance𝑿𝒁 ;
𝐿
16𝜋𝑓𝑀𝑜 (𝑇𝑚 𝐾𝑤𝑚 )2 𝑆 𝜆𝑍
3.32
𝑠𝑠
𝑋𝑍 =
2 +𝑊 2 )
𝑊𝑡𝑟 (𝑊𝑡𝑟
𝑡𝑟
3.33
2
12𝐼𝑔 𝑦𝑠𝑠
Where 𝑊𝑡𝑠 = 0.998 − 0.165 = 0.8329 𝑐𝑚
𝑊𝑡𝑟 = 1.3885 − 0.1 = 1.2885𝑚
𝑦𝑠𝑠 = 0.998𝑐𝑚
𝑦𝑠𝑟 = 1.3885
𝐼𝑔 = 0.3𝑚𝑚
𝜆𝑍 =
0.8329 × 1.2885(0.88292 + 1.28852 )
12 × 0.03 × (0.998)2 × (1.3885)
= 5.07
𝑋𝑍 = 16 × 𝜋 × 50 × 4𝜋 × 10−7 (96 × 0.8)2 ×
20.956 × 10−2
28
= 0.15
28
3.511.2 Over hang reactance
1
𝑋0 = 16𝜋𝑓𝑀𝑜 (𝑇𝑚 𝐾𝑤𝑚 )2 6.4𝑆 𝑃 [𝜋(𝐷 + 𝑑𝑠𝑠 ) × 𝑎𝑉. 𝑐𝑜𝑖𝑙 𝑠𝑝𝑎𝑛𝑖𝑛 𝑠𝑙𝑜𝑡𝑠]
𝑠
= 16 × 𝜋 × 50 × 4𝜋 × 10−7 (96 × 0.8)2 ×
3.34
1
× [𝜋(0.0894 + 0.0146) × 8]
604 × 28 × 2
= 0.136 Ω
3.5.11.3 Magnetizing reactance
𝑋𝑚 = 16𝜋𝑓𝑀𝑜 (𝑇𝑚 𝐾𝑤𝑚 )2 10𝑙
𝐿𝐶𝑝
3.35
𝑔 𝐾𝑔 𝑃𝐹𝑠
Assuming saturation factor 𝐹𝑠 = 1.25
𝑋𝑚 = 16 × 𝜋 × 50 × 4𝜋 × 10−7 (96 × 0.8)2 ×
20.956 × 10−2 × 14.0 × 10−2
10 × 0.03 × 10−2 × 1.158 × 2 × 1.25
= 62.927 Ω
3.5.11.4 Skew Leakage Reactance
The bars are skewed through one slot pitch
Angle of skew, 𝜃𝑠 =
𝜋
28
2
28
× 1 × 20
= 0.314𝑟𝑎𝑑𝑖𝑎𝑛𝑠
Skew leakage reactance
𝜽𝟐
𝑿𝒔𝒌 = 𝑿𝒎 𝟏𝟐𝒔 𝑲𝒍
3.36
𝐾𝑙 = 0.95 𝑋𝑙𝑚
62.92 ×
0.13142
× 0.95
12
29
= 0.0895
Now the total leakage reactance
𝑋𝑙𝑚 = 𝑋𝑠 +𝑋𝑧 +𝑋𝑜 + 𝑋𝑠𝑘
3.37
= 1.308 + 0.0895 + 0.15 + 0.136
= 1.06835 Ω
𝑅𝑎𝑡𝑖𝑜 =
1
𝑟𝑟𝑚
0.492
=
= 0.2922
𝑋𝑙𝑚 1.6835
3.5.11.5 Open circuit reactance
𝑋0𝑚 = 𝑋𝑚 +
𝑋𝑙𝑚
2
= 62.927 +
1.6835
2
= 63.7687 Ω
3.38
Leakage factor
=
=
𝑋0𝑚− 𝑋𝑙𝑚
3.39
𝑋0𝑚
62.927 − 1.6835
62.927
𝐾𝑟 = 0.973
𝐾𝑙 = √𝐾𝑟 = 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
30
1
𝑅𝑚 = 𝑟𝑠𝑚 + 1.75𝑟𝑟𝑚
𝑎𝑡 20𝑜 𝐶
= 0.402 + 1.75 × 0.492
3.40
𝑎𝑡 20𝑜 𝐶
= 1.263 Ω
Total independence in terms of main winding at 200C
2 + 𝑋 2 = √1. 2632 + 1. 68352
𝑍𝑚 = √𝑅𝑚
𝑙𝑚
3.41
= 2.105 Ω
Main winding locked Rotor current, 𝐼𝑠𝑚
𝑉
240
𝐼𝑠𝑚 = 𝑍 = 2.105 = 114
3.42
𝑚
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
𝐼𝑠 = 68.5654
𝑎𝑛𝑑
𝐼𝑠
68.565
=
= 0.601
𝐼𝑠𝑚
114
Auxiliary winding Reactance𝑋𝑘
=
𝑋𝑙𝑚
3.43
2
𝐼
( 𝑠 ) −1
𝐼𝑠𝑚
=
1.6835
0.6012 − 1
31
CHAPTER 4
RESULTS AND ANALYSIS
4.1 Results
Table 4.1 Results
DESIGN PARAMETER
Rated Power Output, W
Rated Voltage, V
Rated Frequency, f
Nearest Synchronous Speed, Ns
Poles, P
Speed in r.p.s , ns
Wattsperrps
ConCosPhi
Main Diameter, D
Length , L
Standard Diameter, Ds
Standard Length,Ls
Standard Pole Pitch, Tps
Length of Iron, Li
Peripheral Velocity,V1
Width of Stator Slot, Wts
Stator Tooth Density, Bts
Number of Stator Slots, Ss
Stator Flux Linkage, FM
Stator Stamping Outer Diameter, Do
Depth of Stator Core, dcs
Depth of Stator Slots, dss
Flux Density in the Stator Core, Bcs
Winding Factor, Kwm
Number of Turns in the Main Winding, Tm
Turns in Series Per Pole, Tmp
Power Factor, n
Full Load Efficiency, ef
Main Winding Current, I
Current Density, Id
Area of Main Winding Conductor, Am
DESIGN VALUE
2238
240
50
3000
2
50
44.7600 W/r.p.s
27
8.894 cm
20.956cm
8.9 cm
20.929 cm
14.0 cm
18.836 cm
13.9857
0.362 cm
1.400
28
0.0135Wb
13.8100 cm
1.4550 cm
1 cm
0.0355
0.800
96
48
0.8500
0.800
13.7132 A
5 A/mm2
2.7426 mm2
32
Diameter of Bare Conductor, Dbc
Length of Air Gap, Lg
Rotor Outer Diameter, Dro
Number of Rotor Slots,Nrs
Rotor Inner Diameter, Dri
Length of Chosen Rotor Stamping, Lrs
Width of Chosen Rotor Stamping, Wrs
Area of Rotor Slot, As
Area with Allowance and Clearance
Incorporated, Ar
Total Copper Section for Main Winding, AM
Current Density in End Ring, db
Current Density in Rotor Bar, de
Area of Each End Ring, Ae
Length of bar, Lb
Resistance of the Rotor Referred to the Main
Winding, rrm
Width of Stator Slot, Wos
Slot Leakage Reactance, Xsr
Stator Slot Pitch, Yss
Zig Zag Leakage Reactance, Xz
Magnetizing Reactance, Xm
Skew leakage Reactance, Xsk
Total Leakage Reactance, XTlm
Open Circuit Reactance, Xom
Gap Extension Coefficient, Kg
1.8683mm
0.3000 mm
8.9 cm
20
1.9 cm
0.3”
0.145”
24cm2
480 mm2
527 mm2
20
20
76.3636 mm2
21 cm
154.0094
0.362 cm
1.0814
0.9985cm
0.0031
62.927
0.0895
1.6835
63.7687
1.158
33
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.
34
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
35
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.
36
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.
37
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
38
Appendix Table 2: The Standard Approximate Values for Co.η.Cos for Different Values of
Watts/R.P.S.
Watts/r.p.s
𝐶𝑜. 𝜂. 𝐶𝑜𝑠
3.6
7.2
12
18
9.5
12
15.5
18
39
%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
1.7 wb/m^2
tooth flux density should be withtin
the range odf 1.4 to
% 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
40
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
Kwm;
E=228
Tm=E/(4.44*Kwm*f*FM)
Tmp=Tm/P
%Define the desirable winding factor for main winding
%Stator Induced Voltage
%Number of turns in the main winding
%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
41
%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;
42
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)
43