Development of an Optimized tool for Designing DC machines, Induction

Machines and BLDC Machines

A thesis submitted in partial fulfillment of the requirements for the degree of

Master of Electrical Engineering

by

Bijaya Kumar Das

Examination Roll No: M4ELE 14-14 Class Roll No: 001210802016 Reg. No: 120907 of 2012-13

Under the guidance of

Prof. Nirmal Kumar Deb

&

Sri. Nikhil Mondal

Department of Electrical Engineering Faculty of Engineering and Technology

Jadavpur University Kolkata – 700 032

2014

Declaration of Originality and Compliance of Academic Ethics

I hereby declare that this thesis contains literature survey and original research

work by the undersigned candidate, as a part of his Master of Electrical

Engineering studies.

All information in this document have been obtained and presented in accordance

with academic rules and ethical conduct.

I also declare that, as required by these rules and conduct, I have fully cited and

referred all materials and results that are not original to this work.

Name: Bijaya Kumar Das

Exam. Roll No. : M4ELE14-14

Thesis Title: Development of an optimized Tool for designing DC machines,

Induction Machines and BLDC Machines.

Signature with Date:

Department of Electrical Engineering Jadavpur University

This is to certify that the thesis entitled “Development of an optimized Tool for designing DC machines, Induction machines and BLDC machines”. submitted by Bijaya Kumar Das in partial fulfillment of the requirements for the award of Master of Engineering Degree in Electrical Engineering at Jadavpur University, Kolkata is an work carried out by him under my supervision and guidance. To the best of my knowledge, the matter embodied in the thesis has not been submitted to any other University / Institute for the award of any degree or diploma.

CERTIFICATE

_________________________ _________________________

[Nirmal Kumar Deb] [Nikhil Mondal] Professor Associate Professor Dept. of Electrical Engineering Dept. of Electrical Engineering Jadavpur University Jadavpur University Kolkata-700032 Kolkata -700032

Countersigned by

_____________________ _______________________ Head of the Department Dean of the Faculty of Engineering Electrical Engineering Department and Technology, Jadavpur University Jadavpur university Kolkata – 700 032 Kolkata -700 032

Department of Electrical Engineering Jadavpur University

CERTIFICATE OF APPROVAL

*

The foregoing thesis is hereby approved as a creditable study of an engineering

subject carried out and presented in a satisfactory manner to warrant its acceptance as

pre-requisite to the degree for which it has been submitted. It is notified to be

understood that by this approval, the undersigned do not necessarily endorse or

approve any statement made, opinion expressed and conclusion drawn therein but

approve the thesis only for the purpose for which it has been submitted.

Final Examination for the Evaluation of the thesis

Board of Examiners

1. ___________________

2. ___________________

3. ___________________

* Only in case the thesis is approved

i

ACKNOWLEDGEMENTS

I am really indebted to my thesis supervisors Prof. Nirmal Kumar Deb and Sri. Nikhil Mondal

whose motivation, advice and support are the guiding factors behind this work.

I would like to convey my sincere thanks to Shri Dipten Maity, Assistant Professor of this

department for helping me out in working with MATLAB.

I would like to express my sincere thanks to all my classmates for being my comfort zone and

providing me moral support.

And finally my parents, whose financial and moral support over the past two years have been

greatly appreciated.

Bijaya Kumar Das

ii

ABSTRACT

Advances in electrical machinery with high efficiency could significantly reduce the cost of industrial and residential energy systems, thereby reducing the fossil fuel needs and emissions. Electrical machine design is a comprehensive process based on several factors. Basically, a design involves the determination of dimensions of each parts of the machine, material specifications, output parameters and performance of the machine. Design has to be carried out keeping in view the optimizing of the cost, volume and weight and at the same time achieving the desired performance as per specification. Knowledge of latest technological trends to supply a competitive product is a must. Design should conform to stipulations specified by International or National standards.

The work focuses on the development of optimized design tools for dc machines, Induction motor and BLDC motors. Thesis portion covers the design calculations steps for each of the three machines. The design of each machine is done in Computer Program written in "c" language using MATLAB software. For each machine, the design is split into several parts in a proper sequence. Finally all the programs are added together to get the total program by running which we can get the total design.

The process of design as here treated is to assume trial values, taken from rules, tables and curves, for some of the factors, carry through calculations until the probable results may be determined, and then, if necessary, modify the original assumptions to get the final values.

iii

LIST OF CONTENTS

PAGE No.

ACKNOWLEDGEMENT i

ABSTRACT ii

CONTENTS iii

LIST OF FIGURES v

LIST OF TABLES vi

CHAPTER-1 INTRODUCTION

1.1 Basic design overview 1

1.2 Objectives of design 2

1.3 Thesis Organization 3

CHAPTER-2 MATERIAL SELECTION

2.1 Conducting Materials 4

2.2 Magnetic Materials 5

2.3 Insulating Materials 9

CHAPTER-3 DESIGN DC MACHINES

3.1 Design of main dimensions 11

3.2 Design of armature windings 16

3.3 Design of poles and ampere turns calculation 19

3.4 Design of field windings 24

3.5 Design of commutator and brushes 25

3.6 Design of interpoles 29

3.7 Losses and performace of machine 31

CHAPTER-4 DESIGN OF INDUCTION MOTOR

4.1 Introduction 34

iv

4.2 Design of main dimensions 37

4.3 Design of Stator 41

4.4 Design of Rotor 45

4.5 Magnetic circuit calculation 52

4.6 Performance Evaluation 54

CHAPTER 5 DESIGN OF BLDC MOTOR

5.1 Introduction 56

5.2 Basic design choices 59

5.3 Permanent magnet materials 62

5.4 Basic Electrical design choices 74

5.5 Losses and performance of the machine 78

CHAPTER-6 CONCLUSION AND SCOPE FOR FUTURE WORKS

6.1 Conclusion 80

6.2 Scope for future works 80

REFERENCES 81

ADDITIONAL BIBLIOGHARPHY 82

APPENDICES

A. Design of Dc Machine in MATLAB Programming

B. Design of Induction machine in MATLAB programming

C. Design of BLDC machine in MATLAB programming

v

LIST OF FIGURES

Figure 2.1: Magnetization curve for cast steel and cast iron

Figure 2.2: Magnetization curve of non oriented silicon steel M-27

Figure 2.3: Magnetization curve of non oriented silicon steel M-45

Figure 3.1: Armature resistance drop

Figure 3.2: Carter's coefficient for slots

Figure 4.1: Stator and rotor laminations

Figure 5.1: Hysteresis loop and maximum energy product

Figure 5.2: Slot geometry of radial flux motor topology

vi

LIST OF TABLES

Table 2.1: Properties of copper and aluminum

Table 2.2: Specific core loss of non oriented silicon steel M-27 at 60hz

Table 3.1: DC machine efficiencies

Table 3.2: Approximate values of Bg

Table 3.3: Approximate values of ampere conductor per meter

Table 3.4: Armature mmf per pole

Table 3.5: Shunt field current percentage of full load current

Table 3.6: Leakage co-efficients

Table 3.7: Properties of Brush material

Table 3.8: Windage and bearing friction loss

Table 4.1: Specific magnetic and electric loading

Table 4.2: Efficiencies and poer factor

Table 4.3: Current densities for squirell cage and wound rotor

Table 4.4: Friction and windage loss

Table 4.5: No load current

Table 5.1: Comparision of brushless motors with different phase numbers

Table 5.2: Temperature coefficients and curie temperature of common PM materials

Table 5.3: Magnetic characterestics of different grades of NdFeB magnets

Table 5.4: Thermal characterestics of NdFeB magnets

Table 5.5: Physical and mechanical properties of NdFeB magnets

vii

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2. Materials for Electrical Machines

The main material characteristics of relevance to electrical machines are those associated with

conductors for electric circuit, the insulation system necessary to isolate the circuits, and with the

specialized steels and permanent magnets used for the magnetic circuit.

2.1 Conducting materials

Commonly used conducting materials are copper and aluminum. Some of the desirable

properties a good conductor should possess are listed below.

1. Low value of resistivity or high conductivity

2. Low value of temperature coefficient of resistance

3. High tensile strength

4. High melting point

5. High resistance to corrosion

6. Allow brazing, soldering or welding so that the joints are reliable

7. Highly malleable and ductile

8. Durable and cheap by cost

Some of the properties of copper and aluminum are shown in the Table-2.1.

Table 2.1 Properties of copper and aluminum Sl. No

Particulars Copper Aluminium

1 Resistivity at 20°C 0.0172 ohm/m/mm2 0.0269 ohm/m/mm2 2 Conductivity at 20°C 58.14×106 S/m 37.2×106 S/m 3 Density at 20°C 8933 kg/m3 2689.9 m3 4 Temperature

coefficient (0-100°C)

0.393 % per °C 0.4% per °C

5 Coefficient of linear expansion (0-100°C)

16.8×10-6 per °C 23.5×10-6 per °C

6 Tensile strength 25 to 40 kg/mm2 10 to 18 kg/mm2 7 Melting point 1083 °C 660 °C 8 Thermal conductivity

(0-100°C) 599 W/m °C 238 W/m °C

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For the same resistance and length, cross-sectional area of aluminum is 61% larger than that of

the copper conductor and almost 50% lighter than copper.

Though the aluminum reduces the cost of small capacity transformers, it increases the size and

cost of large capacity transformers. Aluminum is being much used now days only because

copper is expensive and not easily available. Aluminum is almost 50% cheaper than Copper and

not much superior to copper.

2.2 Magnetic materials

All magnetic materials possess magnetic properties to a greater or lesser degree. The magnetic

properties of materials are characterized by their relative permeability. In accordance with the

value of relative permeability, materials may be divided into three broad categories.

1. Ferromagnetic materials: These materials have their relative permeabilities only slightly

greater than unity and these permeability values are dependent upon the magnetizing force.

2. Paramagnetic materials: These materials have their permeabilities only slightly greater than

unity. The value of susceptibility is thus positive for these materials.

3. Diamagnetic materials: These materials have their relative permeabilities slightly less than

unity. In both paramagnetic and diamagnetic materials the value of permeability is dependent of

the magnetizing force.

Types of magnetic materials The Ferromagnetic materials can be classified as Hard or Permanent Magnetic materials and Soft

Magnetic materials.

1. Soft magnetic materials: Soft magnetic materials have small size hysteresis loop and a steep

magnetization curve. Soft magnetic materials are used in the manufacture of electrical machines,

transformer and many kinds of apparatus, instruments and devices.

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2. Hard or permanent magnetic materials: have large size hysteresis loop (obviously hysteresis

loss is more) and gradually rising magnetization curve.

Ex: carbon steel, tungsten steal, cobalt steel, alnico, hard ferrite etc.

Soft magnetic materials: Soft magnetic materials employed in commercial practice may be considered under the following

three classifications:

i. Solid core materials

ii. Electrical sheet and strip

iii. Special purpose alloys

Solid core materials: These materials are used in parts of magnetic circuit carrying steady flux

such as cores of dc electromagnets, relays, and field frames of dc machines. The basic

requirement used foe steady magnetic fields is high permeability, particularly at high values of

flux densities. For majority of uses it is also desirable that hysteresis loss be low. The principal

materials used are soft iron, relay steel, cast steel, cast iron and ferrow cobalt.

1. Iron low carbon, and silicon steel: Low carbon electrical steel and iron have a comparatively

low resistivity. Because of their low resistivity these materials have large eddy current loss if

they are operated at high flux density in alternating current fields. This limits their use to fields

carrying steady flux or weak alternating current fields.

2. Cast Iron: It has low relative permeability and is used principally in field frames when cost is

of primary importance and extra weight is not objectionable.

3. Gray cast iron: It is magnetically inferior to wrought iron or steel but is used to a limited

extent because of ease of casting complex shapes.

4. Cast steel: Cast steel is used extensively for those portion of the magnetic circuit which carry

steady flux and need superior mechanical qualities.

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5. Soft steel: Rolled and welded frames of soft steel plates are now widely used in place of cast

steel.

6. Ferro cobalt: It is characterized by very high permeability in the upper part of the normal

induction range. It has saturation flux density 10 percent higher than that of pure iron. Its cost is

relatively high and its use is limited to pole pieces where a high value of induction (flux density)

is desired.

The magnetization curve of cast iron and cast steel is given below in Fig. 1.1(a) and (b)

Fig. 2.1 (a) Magnetization curve of cast iron and (b) Magnetization curve of cast steel

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. 2.3 Electrical Steel Sheets (Non oriented Steel): The electrical sheet steels available vary from those having a low silicon content and therefore

possesses good permeability at high flux densities (high saturation flux density), high ductility

but high losses, to those having a high silicon content and subsequently lower permeability,

lower ductility but also lower losses. These electrical sheet steels may be manufactured by either

hot rolling or cold rolling.

Silicon steels are generally specified and selected on the basis of allowable specific core

losses(W/kg or W/lb). The most universally accepted grading of electrical steels by core losses is

the American Iron and steel industry(AISI) system so called M-grading. The M-number indicates

maximum specific core losses in W/lb at 1.5 T and 50 or 60 hz.

The magnetization curve of of non oriented electrical steel M-27 is shown in Fig 1.2. Core loss

curves of non oriented electrical steels measured at 60 hz. Core losses at 50 hz are approximately

0.79 times the core loss at 60 hz.

Fig. 2.2 Magnetization curve of fully processed Armco DI-MAX nonoriented electrical steels M-27

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Table 1.2 Specific core losses of Armco DI-MAX nonoriented electrical steels M-27 at 60 hz

Typical magnetization curve and core loss curve foe non-oriented steel of grade M-45 is at 50 hz shown in the tabular form Table 1.2 Specific core loss and magnetic field strength of non oriented steel of grade M-45 at 50 hz

Magnetic flux density T

Specific core losses W/kg

Magnetic field strength A/cm

0.4 0.5 7 0.6 1.2 8.8 0.8 1.5 12 1.0 2.4 15 1.2 3.2 17.5 1.4 4.4 30 1.6 5.6 90 1.7 6.2 100.5

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2.4 Insulating materials To avoid any electrical activity between parts at different potentials, insulation is used. An ideal

insulating material should possess the following properties.

(i) High dielectric strength, sustained at elevated temperature

(ii) High resistivity or specific resistance

(iii) Low dielectric hysteresis

(iv) Good thermal conductivity

(v) High degree of thermal stability i.e it should not detoriate at high temperature

In addition to the above the material should have good mechanical properties such as ease of

working and application should be able to with stand moisture, it should be non-hygroscopic

vibration, abrasion and bending. Also it should be able to withstand chemical attach, heat and

other adverse conditions of service.

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3. DESIGN OF DIRECT CURRENT MACHINES

3.1 design of main dimensions

The size of the DC machine depends on the main or leading dimensions of the machine viz., diameter of the armature D and armature core length L. As the output increases, the main dimensions of the machine D and L also increases.

Output Equation Output equation relates the output and main dimensions of the machine. Actually it relates the power developed in the armature and main dimensions.

Power developed in the armature in KW = EIa×10-3

= PφNZ60a

× Ia × 10−3

= Pφ×Ia Z

a×

N×10−3

60 (3.1)

The term PΦ represents the total flux and is called the magnetic loading. Magnetic loading/unit area of the armature surface is called the specific magnetic loading or average value of the flux density in the air gap Bav. That is,

Bav = Pφ/πDL Wb/m2 or tesla denoted by T

Therefore PΦ = Bav

The term (Ia Z/a) represents the total ampere-conductors on the armature and is called the electric loading. Electric loading/unit length of armature periphery is called the specific electric

πDL (3.2)

loading q. That is,

q = IaZ/aπD ampere-conductors/m

Therefore IaZ/a = qπD (3.3)

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Substitution of equations 2.2 and 2.3 in 2.1 leads to

KW = Bav

= 1.64×10

πDL× qπD× N×10−3

60

-4BavqD2

= Co D

LN

2

Where Co is called the output coefficient of the DC machine and is equal to 1.64× 10-4 Bav q

LN (3.4)

Therefore D2

L = KW1.64×10−4Bav qN

m3

The above equation is called the output equation. The D2

machine or volume of iron used. In order that the maximum output is obtained/kg of iron used,

L product represents the size of the

D2L product must be as less as possible. For this, the values of q and Bav

Power developed by the armature Pa, is different from rated power output P, of the machine. The

relationships between the two are

must be high.

Pa = P/η for generator and Pa = P for motors

Where η = efficiency of the motor

The approximate value of efficiency can be selected from the Table 3.1 given below

Table 3.1 Machine Efficiencies

Horse Power or Kilowatts

Efficiency percent

Horsepower or kilowatts

Efficiency percent

0.25 50 to 60 25 88 to 90 1 76 to 82 50 89 to 91 3 81 to 85 100 90 to 91.5

10 86 to 88 300 an up 91 to 93

3.1.1 Choice of average air gap flux density (Specific magnetic loading, Bav)

(i) As Bav

(ii) As B

increases, core loss increases, efficiency reduces.

av increases, degree of saturation increases, mmf required for the magnetic circuit

increases. This calls for additional copper and increases the cost of the machine.

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It is clear that there is no advantage gained by selecting higher values of Bav. If the values

selected are less, then D2

Lesser values are used in low capacity, low speed and high voltage machines. In general B

L will be large or the size of the machine will unnecessarily be high.

av lies

between 0.45 and 0.75 T. Table 3.2 should be consulted for values of B

g.

Table 3.2 Approximate values of Bg

Output KW

Bg Wb/m2

Output KW

Bg Wb/m2

5 0.58 500 0.92 10 0.65 1000 0.96 50 0.78 2000 0.98

100 0.82 5000 1.05 200 0.87 10000 1.15

3.1.2 Choice of ampere conductors per meter (Specific electric loading, q)

(i) As q increases, number of conductors increases, resistance increases, I2

(ii) As q increases, number of conductors increases, conductors/slot increases, quantity of

insulation in the slot increases, heat dissipation reduces, temperature increases, losses increases

and efficiency of the machine reduces.

R loss increases and therefore the temperature of the machine increases. Temperature is a limiting factor of any equipment or machine.

(iii) As q increases, number of conductors increases, armature ampere-turns per pole ATa / pole

= (Ia Z / 2 a P) increases, flux produced by the armature increases, and therefore the effect of

armature reaction increases. In order to overcome the effect of armature reaction, field mmf has

to be increased. This calls for additional copper and increases the cost and size of the machine.

(iv) As q increases, number of conductors and turns increases reactance voltage proportional to (turns) 2

increases. This leads to sparking commutation.

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In general q lies between 15000 and 50000 ampere-conductors/m. Typical values of q used for machines having class A insulation are given in Table 3.3

Table 3.3 Approximate values of q ac/m (Ampere conductors per meter)

Output

KW q ac/m Output

KW q ac/m

5 15000 500 35000 10 17500 1000 40000 50 25000 2000 43000

100 27500 5000 49500 200 31000 10000 51000

3.1.3 Selection of number of poles

The following may be taken as guiding factors for the choice of number of poles:

(i) The frequency of flux reversals in the armature core generally lies between 25 to 50 hz.

Lower values of frequency are used for large machines.

(ii) The value of current per parallel path is limited to about 200 A. Thus the current per brush

arm should not be more than 400 A.

(iii) The armature mmf should not be excessively large. Table 3.4 gives the normal values of

armature mmf per pole. These values should not be exceeded under average conditions.

Table 3.4 Armature mmf per pole

3.1.4 Separation of D2

Knowing the value of KW and N and assuming the values of q and Bav, a value for

L product

Output KW

Armature mmf per pole A

Upto 100 5,000 or less 100 to 500 5,000 to 7,500

500 to 1500 7,500 to 10,000 Over 1500 Upto 12,500

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D2

Since the above expression has two unknowns namely D and L, another expression relating D

and L must be known to find out the values of D and L.

L = KW1.64×10−4Bav qN

can be calculated.

Usually a value for the ratio armature core length L to pole pitch is assumed to separate D2

Considering a suitable value of L/τ the value of armature diameter and armature core length can be calculated. The D

L

product. The pole pitch τ refers to the circumferential distance corresponding one pole at

diameter D. In practice L/τ lies between 0.55 and 1.1

2

L product can be separated by considering the peripheral velocity of the armature.

3.1.4.1 Limitations of D and L As the diameter of the armature increases, the peripheral velocity of the armature

v = πDN / 60 m/s , centrifugal force and its effects increases. Therefore the machine must be

mechanically made robust to withstand the effect of centrifugal force. This increases the cost of

the machine. In general for normal construction, peripheral velocity should not be greater than

30 m/s as for as possible.

To prevent arcing between commutator segments, voltage between the commutator segments

should not be greater than about 20V on open circuit. If a single turn coil is used then the

voltage/conductor e = Bav

L v should not be more than 10V.

Therefore, armature core length L =

eBav V

should not be greater than 10 / (0.75 × 30) = 0.44m for normal design.

3.1.5 Length of air gap (Lg) The length of air gap can be fixed by considering armature reaction, circulating currents, pole

face losses, noise, cooling and mechanical consideration.

Mmf required for air gap of salient pole machines is ATg=800,000BgKgLg ( 3.5)

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And armature mmf per pole ATa= ac×τ

2

The value of air gap mmf lies between 0.5 to 0.7 of armature mmf i.e

ATg=(0.5 to o.7)ATa

Equating equations 2.4 and 2.5 the air gap length Lg can be calculated. The gap contraction

coefficient, Kg can assumed as 1.15

(3.6)

Usually the value of air gap length lies between 0.01 to 0.015 of pole pitch.

3.2 Armature Design 3.2.1 Choice of armature winding Modern dc machines employ two general types of windings:

(a) Lap winding (b) Wave windings

These two types of windings differ from each other in two general ways: The number of circuits

between positive and negative brushes and the manner in which the coils ends are connected to

the commutator segments.

Simplex windings are invariably used in preference to multiplex windings owing to the

limitations imposed by the equalizer connections upon the later. The choice usually lies between

simplex lap and wave windings.

3.2.1.1 Number of armature conductors Generated emf in the armature E = V + Ia Ra for generator = V − Ia Ra

The armature current may be calculated from for motor

Ia = IL + If for a generator = IL + If for a motor

Where IL = Line current and If = shunt field current The value of If can be taken from the Table 3.5

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Table 3.5 Shunt field current field current percent of full load current Kilowatt capacity

Shunt field current Kilowatt capacity Shunt Field current

0.25 9 100 2.05 1.0 6.4 200 2.0 5.0 4.5 600 1.48

10.0 3.75 1000 1.3 20.0 3 20000 1.15 40 2.4

IaRa is the internal voltage drop . The IaRa drop can be calculated from the Fig. 3.2

Fig.2.1 Armature resistance drop

The number of armature conductors can be calculated from the expression E = PφNZ/60a

3.2.1.2 Number of armature coils

Whenever possible, a single turn coils are used for lap winding, as a simplex wave winding is

preferred to a lap winding with multi turn coils. For small currents, wave winding with multi turn

coils is used. The number of turns per coil and the number coils are so chosen that the voltage

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between adjacent commutator segments is limited to a value where there is no possibility of flash

over. Normally, the maximum voltage between adjacent segments at load should not exceed 30.

Minimum number of coils required C = EP/15

EP/C is the voltage between each commutator segments at no load. The average voltage between

adjacent commutator segments at no load should not go beyond 15 V in order to limit the

maximum voltage at load between adjacent segments to about 30 V.

3.2.2 Number of armature slots

The following factors should be considered while selecting the number of slots

1. Slot pitch: The value of slot-pitch lies between 20 to 40 mm as extreme limits. The usual

limits is between 25 to 35 mm expect in the case of very small machines, where it may be 20 mm

and even less.

2. Slot loading: The slot loading i.e number of ampere conductors per slot should not exceed

about 1500 A.

3. Flux pulsations: The number of slots per pole pair should be an odd integer in order to

minimize pulsation losses.

4. Commutation: The slots per pole should be at least 9 in order to prevent sparking. The

number of slots per pole usually lies between 9 and 16. In very small machines the number may

go down to 8, as the internal resistance is high in their case.

5. Suitability for windings: When selecting the number of slots, we must confirm that the the

number of selected suits the armature winding as regards the total number of coils and the coil

sides per slot.

3.2.3 Cross section of armature conductor

The current density in armature conductors should be taken as high as efficiency and temperature

rise conditions permit. This is because a large value of current density reduces the size of

conductors and therefore there is saving in the cost of copper. Also the slot area required

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becomes small and therefore shallow slots can be employed and use of shallow slots is beneficial

for commutation conditions.

The following values of current densities may be used:

(i) Large strap wound armatures with very good normal ventilation – 4.5 A/mm2

(ii) Small wire wound armatures with very good normal ventilation – 5 A/mm2

(iii) High speed fan ventilated machines – 6 to 7 A/mm2

3.2.4 Armature voltage drop The length of mean turn can be estimated from the following relationship:

Length of mean turn of armature winding Lmt = 2L + 2.3 τ + 4d

For ‘a’ paths connected in parallel r

s

a

The value of resistivity of copper under cold conditions and for a temperature rise of 500 is respectively 0.017 and 0.021 Ω/m and mm

= Z2

× ρLmt

a2AZ

2

3.2.5 Depth of armature core Flux in the armature core Φc = 1/2Φ

The flux density Bc in the armature core can be taken between 1.0 to 1.5 Wb/m2

Area of armature core Ac = φcBc

= Li × dc

Depth of armature core dc = φcBc

3.3 Design of poles and ampere turns calculation

3.3.1 Pole Design The design of poles involves the determination of area of cross section of the poles, their height

and the design of field windings.

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3.3.1.1 Area of Poles Flux in the pole body Φp = leakage coefficient × useful flux per pole

= Cl ×Φ

Thus the determination of flux in the field poles involves the knowledge of leakage coefficient.

The leakage flux can be determined from the relationship involving the knowledge of total flux

and the useful flux which can be determined if the dimensions of the main poles are known. But

at this stage the dimensions are not known. Thus, in order to proceed, we have to assume suitable

value of leakage coefficient. Table 3.6 gives the approximate values of leakage coefficient.

Table 3.6 Leakage coefficient

Output

KW Leakage coefficient

Cl 50 1.12 to 1.25 100 1.11 to 1.22 200 1.10 to 1.20 500 1.09 to 1.18

1000 1.08 to 1.16

The flux density in the pole body is assumed to lie between 1.2 to 1.7 Wb/m2 for laminated poles

it is assumed as 1.5 Wb/m2

Area of pole body Ap = φp

Bp

Length of pole is taken less than that of armature in order to permit end play and avoid magnetic centring. The difference in length is about 10 to 15 mm.

Length of pole Lp

Width of pole shank (body) bp = Ap × Lp

= L – (0.001 to 0.015)

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3.3.2 Height of pole

The height of pole is decided by the mmf to be provided on the pole at full load.

In order to proceed with the design we assume the value of field mmf at full load.

3.3.2.1 Full load field mmf In order to prevent the effects of armature reaction becoming too excessive, the field system is

so designed that the mmf developed by the field coils is sufficiently powerful in comparision

with the mmf developed by the armature at full load.

In case of all logically designed machines, there is thus a certain minimum value for the ratio of

the field mmf at full load, ATfl to armature mmf at full load ATa, that is regarded as a safe limit.

Depending upon the duty which the machine has to perform, we decide upon the value of this

ratio. The normal designs are based upon a ratio,

AT fl

AT a = field mmf at full loadarmature mmf at full load= 1.3 to 1.4

The height of field winding hf can be calculated after assuming suitable values of df,Sf and qf

Height of field winding hf = AT fl ×10−4

�qf Sf df

Total height of pole, hpl = hf + he+height taken by insulation and height wasted due to

curvature of yoke.

The height of pole shoe, he

The height of insulation and the space wasted because of curvature may be taken as about 0.1τ to

0.15τ depending upon the size of machine.

is assumed to be 0.1 to 0.2 of height of pole

Yoke: The dimensions of yoke are determined by the value of flux Φy carried by the yoke. The

leakage coefficient for yoke is a little higher than that of the poles. The yoke carries half of the

total flux.

Flux in the yoke Φy = leakage coefficient × 1/2 useful flux per pole = 1/2Cl φ

22 | P a g e

The flux density in cast steel yokes is normally equal to 1.2 Wb/m2 while in laminated yokes it

is about 1.5 Wb/m2

Area of yoke Ay = Φy/By

and the depth of yoke dy = Φ

y/ByL

i

3.3.3 Magnetic circuit calculation 3.3.3.1 Calculation of Total mmf The calculation of total mmf required to establish the requisite flux in a magnetic circuit

involves the knowledge of dimensions and configuration of the magnetic circuit. The magnetic

circuit is split up to convenient parts which may be connected in series or parallel. The flux

density is calculated in every part and the mmf per unit length, ‘at’ is found by consulting ‘B-at’

curves. The summation of mmfs gives the total mmf.

Mmf of air gap: Mmf required for air gap ATg=800,000BgKgL

Where Kg is the carter’s gap coefficient which depends upon the ratio of slot width/gap length.

The value of Carter’s coefficient can be taken from Fig. 3.3. The gap contraction factor for slots

is given by Kgs = ysys −Kcs ws

g

Fig. 3.3 Carter’s coefficient for slots

23 | P a g e

Mmf for pole: Flux density in the pole Bp = φ×ClAp

Let atp be the ampere turns per meter, obtained from the magnetization curve corresponding to

the pole material, at Bp

Mean length of the flux path in the pole = pole height hpl

Total ampere turns for pole ATp = atp×h

p

Mmf for Teeth: Flux density in the armature tooth ( in case of parallel sided slot and tapered tooth) at 1/3 height from the root of tooth

Bt1/3 =φ

bt1/3 × Li × SP�

Where bt1/3 = width of tooth at 1/3 height from the root

=π(D − 4

3� × ht

S − ws

Li = Net iron length of the armature core = Ki

×L

Taking att be the ampere turns per meter, obtained from the magnetization curve corresponding

to the armature core material, at Bt1/3

Mean length of flux path in tooth = height of tooth ℎ𝑡𝑡

Mmf of armature core:

Flux density in armature core Bc = φ/2Ac

T Taking atc be the ampere turns per meter, obtained from the magnetization curve corresponding

to the armature core material, at B

Mmf required for armature core ATc = atc×Lc c

Where Lc = Length of flux path in core = π(D−2ds −dc )2

Mmf of Yoke:

Flux density in the yoke By = φy

Ay

Taking aty be the ampere turns per meter, obtained from the magnetization curve corresponding

to the yoke material, at By

24 | P a g e

Mmf required for yoke ATy = aty×L

L

y

y

Total mmf per pole at no load and normal voltage

= Length of flux path in yoke = π(D+2Lg +2hpl +dy

2P

ATfo = ATg+ATt+ATP+ATy+AT

c

3.4 Design of field windings

3.4.1 Design of shunt field winding

In shunt machines, the entire winding space along the height of pole is taken to be the winding

while in compound machines, 80% of the winding space is taken up by shunt field and the rest

20% by the series field.

Voltage across the shunt field winding = (o.8 to 0.85) V and voltage across shunt field coil is:

Ef

=

(0.8−0.85)VP

As ther are many shunt field coils as the number of poles and they are all connected in series.

Area of shunt field conductor af = AT f ρLmt

Ef

Number of turns provided Tf = hf ×df

Sf

Sf

Resistance of each field coil Rf = Tf ρLmtaf

= space factor for the winding

Field current If = EfRf

And the field mmf is given by ATf = If × Tf

The I2

The cooling surface of each field coil S = 2Lmt (hf + df)

R loss in each field coil is given by Qf = If2Rf

The cooling coefficient is c = 0.14 to 0.161+0.1Va

The temperature rise θm = Qf×cS

25 | P a g e

The value of temperature rise should be within the limits specified. If the temperature rise

exceeds the specified limits, a greater depth for winding is assumed.

3.4.2 Design of series field

The series field conductors are wound with rectangular conductors. The conductors may be flat

wound or wound n edge. The insulation between the turns of series field depends mainly upon

whether the coil is flat wound or wound on the edge.

The mmf provided on series field at full load usually lies between 15 to 25 percent of armature

mmf and for normal machines it may be taken as 20 percent.

Mmf of series field winding ATs=(0.15-0.25)AT

Number of series field turns Ts = AT sIs

a

Area of series field conductor is given by Ase = Isδs

The current density used for series field is somewhat higher value than for the shunt field owing

to better cooling conditions.

3.5 DESIGN OF COMMUTATOR AND BRUSHES The Commutator is an assembly of Commutator segments or bars tapered in section. The

segments made of hard drawn copper are insulated from each other by mica or micanite, the

usual thickness of which is about 0.8 mm. The number of commutator segments is equal to the

number of active armature coils.

The minimum number of segments is that which gives a voltage of 15 V between segments at no load Minimum number of segments = EP/15

2.5.1 Commutator diameter The diameter of commutator generally lies between 0.6 to 0.8 of armature diameter. It varies

from 62% of armature diameter for 350/700 V machines, 68% for 200/250 V machines and 75%

26 | P a g e

for 100/125 V machines .The larger diameter being necessary on heavy current (low voltage)

machines because of higher mechanical stresses and heating. The diameter must be chosen with

regard to the peripheral speed and the thickness of commutator segment.

Peripheral speed: The commutator peripheral speed is generally kept below 15 m/s. Higher

peripheral speeds upto 30 m/s are used but should be avoided where ever possible. The higher

commutator peripheral speeds generally lead to commutation difficulties.

Commutator segment pitch: The thickness of the commutator surface should not be less than 3

mm. If the thickness of mica is about 0.8 mm, then the minimum segment pitch is approximately

4 mm.

Pitch of segment βc = πDc

/C should not be less than 4 mm.

Length of commutator: The length of commutator depends upon the space required by the

brushes and upon the surface required to dissipate the heat generated by the commutator losses.

3.5.2 Dimensions of brushes The thickness of brushes has profound influence on the commutation conditions. The thickness

of brush tc and the commutator segment pitch βc are the factors which determine the width of the

commutating zone and the number of coils under going commutation at a time. The thickness of

brush should be so selected that it covers 2 or 3 commutator segments.

Current carried by each brush spindle is 2Ia

Total brush contact area per spindle A

/P as there are as many brush spindles as the number of poles.

b = 2Ia/(Pδa

)

where δa

is the current density in the brushes which can be taken from Table 3.7

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Table 3.7 Properties of brush materials

Each spindle may have many brushes. The area of each individual brush should be taken so that

it does not carry more than 70 A. It is better to use a larger number of brushes of relatively

smaller width than a few very wide brushes.

Suppose,nb = number of brushes per spindle, and wb and tb are respectively the width and

thickness of each brush respectively.

Contact area of each brush ab = wb tbab

Total contact area of brushes in one spindle Ab = nb ab

The number nb is so selected that each brush does not carry more than 70 A.

Length of commutator Lc = nb (wb+cb)+c1+c

where c

2

b is the clearance between the brushes and depends upon the construction of the brush

holder. It is usually 5 mm. c1 is the clearance allowed for staggering the brushes. This clearance

varies with the size of the commutator, but generally lies between 10 mm for small machines to

about 30 mm for large machines. c2

Type of material

is the clearance for allowing the end play and is usually

between 10 to 25 mm.

Brush contact drop V

Current density A/mm2

Pressure kN/m2

Commutator speed m/s

Co-efficient of friction

Natural graphite

0.7-1.2 0.1 14 50-60 0.1-0.2

Hard carbon 0.7-1.8 0.065-0.085

14-20 20-30 0.15-0.25

Electro graphite

0.7-1.8 0.085-0.11 18-21 30-60 0.1-0.2

Metal graphite

0.4-0.7 0.1-0.2 18-21 20-30 0.1-0.2

28 | P a g e

If this length gives too small a dissipating surface, so that the temperature rise of commutator

exceeds the permissible value, then Lc must be increased to give sufficient surface to dissipate

the heat generated by the commutator losses.

3.5.3 Losses at the commutator surface

The losses at the commutator are the brush contact losses and the brush friction losses. Brush contact loss: The brush contact drop for different materials is given in Table 3.7

However, the brush contact loss also depends upon the condition of the commutator and upon the

quality of the commutation obtained. It is therefore, very difficult to predetermine accurately the

brush contact losses. The brush contact drop is independent of load current. The typical values of

brush drop are 1 V per brush arm for carbon/graphite brushes, 0.25 V for metal/graphite, and 0.1

V foe small machines used for control applications.

Brush friction loss: The brush friction loss depends up on the brush pressure, the peripheral

speed of the commutator and the coefficient of friction between brush and the commutator. It

may be calculated from the following approximate formula:

Brush friction loss Pbf = μPb PAb Vc where μ= co-efficient of fribfction, Pb = brush contact pressure on commutator, N/m

2

The coefficient of friction depends upon the peripheral speeds Vc

, decreasing at high speeds. It

largely depends upon the type of brush used. The coefficient of friction for different brush

materials is given in Table 3.7

The coefficient of friction μ normally varies from 0.1 to 0.3 and typical value of brush pressure,

Pb for industrial machines is 12.5 KN/m2

.

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3.6 Design of Interpoles

The interpoles are the smaller poles placed in between the main poles. The polarity of the

interpole must be that of the main pole just ahead for a generator and just behind for a motor.

The winding of the interpole must produce an mmf which is sufficient to neutralize the cross

magnetizing armature mmf at the interpolar axis and enough more to produce the flux density

required to generate rotational voltage in the coil undergoing commutation to cancel the

reactance voltage.

3.5.1 Width of commutation zone

The width of commutation Zone is the portion of armature circumference where one or more

coils are short circuited. The width of commutation zone is equal to the distance moved by

armature during the effective time of commutation, τc.

For Lap winding

wc = {�u �α +12� − 1� βc + tb − ti)}

DDc

where D and Dc

For Wave winding

wc = {�u2 −

aP

� βc + (tb − ti)}DDc

are respectively the diameter of armature and commutator

Width of interpole shoe: If a straight line commutation is desired,the width of interpole shoe

should not be less than width of commutating zone

Width of interpole shoe wip = wc – (1.5 to 2)Lg

Where L

i

gi = Length of air gap under the interpole. In general Lgi = (1 to 2) L

g

30 | P a g e

3.6.2 Calculation of reactance voltage

The reactance voltage can be calculated by calculating the specific permeance for slot, tooth top

and overhang leakage.

The specific slot permeance is given by

𝜆𝜆𝑠𝑠 = 𝜇𝜇0[ℎ1

3𝑤𝑤𝑠𝑠+

ℎ2

𝑤𝑤𝑠𝑠+

2ℎ3

𝑤𝑤𝑠𝑠 + 𝑤𝑤0+

ℎ4

𝑤𝑤0

The tooth top specific permeance λt for a machine with interpoles is

λt = μ0 wip

6Lgi

The overhang leakge flux is calculated from the following empirical relation

λ0 = L0

L (0.23 logL0

b0+ 0.07) × 10−8

L0

b

= Length of overhang of one coil side

o

If there are T

= is the periphery of the all coil sides in one layer

c

turns per coil in the winding, the average reactance voltage per segment

Erav = 4TcλLIsZs

τc

3.6.3 Length of interpole

The length of interpole should be so chosen that the flux density in the interpole will be below

the saturation point of the material. This is required in order to obtain proper compensation of

reactace voltage at all loads, which is the only possible if the flux density under the interpole

varies linearly with the load current. Hence there should be no saturation in the iron parts of the

interpole magnetic circuit.

For machines designed for large fluctuating loads or for variavle speed motors, which employ

completely laminated core, the length of interpole is taken equal to that of main poles.

31 | P a g e

Flux density under interpole shoe: The mean emf generated in the coils undergoing

commutation, by their rotation in the reversing field under the interpole, must be just equal to the

reactance voltage so that the resultant emf in the coil is zero.

Rotational emf produced in a coil (with Tc

E

turns) by cutting the field under the interpole

gi = 2×Tc

This voltage must balance the reactance emf Erav inn each turns . Hence , the flux density under the interpole is

Bgi = 2IzZsL

LiP

1Va × Tc

λ

×voltage generated in each conductor = 2TcBg Lip Va

3.6.4 Design of interpole winding

The length of air gap under the interpole is relatively large, and the iron parts of the interpole magnetic circuit are worked much below the saturation region, the reluctance of the iron parts may be neglected.

Mmf required for interpole ATi = 800,000Bgi Kgi Lgi + ATa for machines without compensating windings

The interpole winding is connected in series with the armature and the total armature current flow through the interpole winding.

Number of interpole turns Ti = ATi /I

The current density in the interpole winding should be 2.5 to 4.0 A/mm

a

2

; the higher value is

used where ventilation is especially good, and the insulation is thin.

3.7 LOSSES AND EFFICIENCY The losses in a dc machine can be classified into two general types:

(i) Rotational losses (ii) I2

Rotational losses: Rotational losses are made up of:

R losses

(i) Friction and windage losses (ii) iron losses

32 | P a g e

3.6.1 Friction and windage losses The friction losses occur in the bearings and at the commutator. The amount of bearing friction

losses depends upon the pressure in the bearing, the peripheral speed of the shaft at the bearing

and the coefficient of friction between the bearing and the shaft.

The windage losses produced by rotation depend upon the peripheral speed of the rotor, the rotor

diameter, the core length and largly upon the construction of the machine. The windage loss, in

fact, depends upon too many intricate factors and cannot be easily assessed.

Table 3.8 gives the values of windage plus bearing friction losses expressed as percentage of

rated output

Table 3.8 Windage and bearing friction losses.

Peripheral Speed m/s

Losses percentage of output

10 0.2 20 0.4 30 0.6 40 0.9 50 1.2

Iron losses: The iron losses per kg is given by the following relationships

0.06fBm2 + 0.008f2Bm

2t2

0.006fB

for teeth

m2 + 0.005 f2Bm

2t2

B

for core

m

The pulsation loss in the pole faces may be taken as 20 to 50 percent of total iron loss

is expressed in Wb/m2, f in hz and t(thickness of lamination) in mm.

I2R losses. The I2

(i) Main series circuit of armature. They include the I2R losses in

R losses occur in:

(a) The armature winding = Ia2ra (b) The interpole winding = Ia2

(c) The series field winding = Ia

rip 2rs (d) The brush contacts = P

(ii) Shunt field circuit: These losses include the I2R losses in the winding itself and also the I2R

losses in the field regulator.

bc

33 | P a g e

Stray load losses: These are certain types of losseswhich cannot be easily determined. They

appear when the machine is loaded.

The stray load loss may be assumed as 0.5 0r 1.0% of the basic output for machines with and

with out compensating winding respectively.

Effeciency: The percentage of efficiency is given by

η = output

output +losses= 1 − Losses

Output

34 | P a g e

34 | P a g e

4. Design of Induction Motors

4.1 INTRODUCTION

Induction motors are the ac motors which are employed as the prime movers in most of

the industries. Such motors are widely used in industrial applications from small workshops to

large industries. These motors are employed in applications such as centrifugal pumps,

conveyers, compressors crushers, and drilling machines etc.

4.1.1 Constructional Details:

Similar to DC machines an induction motor consists of a stationary member called

stator and a rotating member called rotor. However the induction motor differs from a dc

machine in the following aspects.

1. Laminated stator

2. Absence of commutator

3. Uniform and small air gap

4. Practically almost constant speed The AC induction motor comprises two electromagnetic parts:

• Stationary part called the stator

• Rotating part called the rotor

The stator and the rotor are each made up of

• An electric circuit, usually made of insulated copper or aluminum winding, to carry current

• A magnetic circuit, usually made from laminated silicon steel, to carry magnetic flux

35 | P a g e

4.1.2 The stator The stator is the outer stationary part of the motor, which consists of

The outer cylindrical frame of the motor or yoke, which is made either of welded sheet steel, cast iron or cast aluminum alloy.

The magnetic path, which comprises a set of slotted steel laminations called stator core pressed into the cylindrical space inside the outer frame. The magnetic path is laminated to reduce eddy currents, reducing losses and heating.

A set of insulated electrical windings, which are placed inside the slots of the laminated stator. The cross-sectional area of these windings must be large enough for the power rating of the motor. For a 3-phase motor, 3 sets of windings are required, one for each phase connected in either star or delta. Fig 1 shows the cross sectional view of an induction motor. Details of construction of stator are shown in Figs 4-6.

Fig 4.1: Stator and rotor laminations

4.1.3 The rotor

Rotor is the rotating part of the induction motor. The rotor also consists of a set of slotted silicon

steel laminations pressed together to form of a cylindrical magnetic circuit and the electrical

circuit.

36 | P a g e

Squirrel cage rotor consists of a set of copper or aluminum bars installed into the slots, which are

connected to an end-ring at each end of the rotor. The construction of this type of rotor along

with windings resembles a ‘squirrel cage’. Aluminum rotor bars are usually die-cast into the

rotor slots, which results in a very rugged construction. Even though the aluminum rotor bars are

in direct contact with the steel laminations, practically all the rotor current flows through the

aluminum bars and not in the lamination

Wound rotor consists of three sets of insulated windings with connections brought out to three

slip rings mounted on one end of the shaft. The external connections to the rotor are made

through brushes onto the slip rings. Due to the presence of slip rings such type of motors are

called slip ring motors.

4.2 Introduction to Design

The main purpose of designing an induction motor is to obtain the complete physical dimensions of all the parts of the machine as mentioned below to satisfy the customer specifications. The following design details are required.

1. The main dimensions of the stator. 2. Details of stator windings. 3. Design details of rotor and its windings 4. Performance characteristics.

In order to get the above design details the designer needs the customer specifications

Rated output power, rated voltage, number of phases, speed, frequency, connection of stator

winding, type of rotor winding, working conditions, shaft extension details etc.

In addition to the above the designer must have the details regarding design equations based on which the design procedure is initiated, information regarding the various choice of various parameters, information regarding the availability of different materials and the limiting values of various performance parameters such as iron and copper losses, no load current, power factor, temperature rise and efficiency.

37 | P a g e

Output Equation: output equation is the mathematical expression which gives the relation

between the various physical and electrical parameters of the electrical machine.

In an induction motor the output equation can be obtained as follows Consider an ‘m’ phase machine, with usual notations

Output Q in kW = Input x efficiency

Input to motor = mVph Iph cosΦ x 10-3

For a 3 Φ machine m = 3

kW

Input to motor = 3Vph Iph cosΦ x 10-3

Assuming Vph = E

kW

ph

V

,

ph = Eph = 4.44 f ΦTphKw

= 2.22 fΦ ZphK

f = PN

w

S/120 = Pns

Output = 3 x 2.22 x Pn

/2,

s/2 x ΦZphKw Iph η cosΦ x 10-3

kW

Output = 1.11 x PΦ x 3Iph Zph x ns Kw η cosΦ x 10-3

PΦ = B

kW

avπDL, and 3Iph Zph

Output to motor = 1.11 x B

/ πD = q

avπDL x πDq x ns Kw η cosΦ x 10-3

Q = (1.11 π

kW

2 Bav q Kw η cosΦ x 10-3) D2L ns

Q = (11 B

kW

av q Kw η cos Φ x 10-3) D2L ns

Therefore Output Q = C

kW

o D2L ns

where Co = (11 B

kW

av q Kw η cosΦ x 10-3

)

38 | P a g e

4.2.1 Choice of Specific loadings: Specific Magnetic loading or Air gap flux density Iron losses largely depend upon air gap flux density Limitations : Flux density in teeth < 1.8 Tesla Flux density in core 1.3 – 1.5 Tesla Advantages of Higher value of Bav

• Size of the machine reduced

• Cost of the machine decreases

• Overload capacity increases

For 50 Hz machines, Bav lies between 0.35 – 0.6 Tesla. The suitable values of Bav can be

selected from Table 3.1.

Specific Electric loading Total armature ampere conductor over the periphery Advantages of Higher value of q

• Reduced size • Reduced cost

Disadvantages of Higher value of q

• Higher amount of copper • More copper losses • Increased temperature rise • Lower overload capacity

Normal range 10000 ac/m – 450000 ac/m. The suitable values of q can be selected from

the Table 3.1.

39 | P a g e

Table 4.1 Specfic magnetic and electric loading

Output KW Specific magnetic loading

(Bav) Specific electric loading (q)

1 0.35 16,000 2 0.38 19,000 5 0.42 23,000

10 0.46 25,000 20 0.48 26,000 50 0.50 29,000 100 0.51 31,000 500 0.53 33,000

4.2.2 Choice of power factor and efficiency: Choice of power factor and efficiency under full load conditions will increase with increase in

rating of the machine. Percentage magnetizing current and losses will be lower for a larger

machine than that of a smaller machine. Further the power factor and efficiency will be higher

for a high speed machine than the same rated low speed machine because of better cooling

conditions. Taking into considerations all these factors the above parameters will vary in a range

based on the output of the machine. Similar to Bav and q, efficiency and power factor values can

be selected from Table 4.2.

Table 4.2 Efficiency and power factor

Output KW

Power Factor (PF)

Efficiency (eff)

5 0.82 0.83 10 0.83 0.85 20 0.85 0.87 50 0.87 0.89

100 0.89 0.91 200 0.90 0.92 500 0.92 0.93

40 | P a g e

4.2.3 Separation of D and L: The output equation gives the relation between D2L product and output of the machine. To

separate D and L for this product a relation has to be assumed or established. Following are the

various design considerations based on which a suitable ratio between gross length and pole

pitch can be assumed.

i. To obtain minimum overall cost 1.5 to 2.0

ii. To obtain good efficiency 1.4 to 1.6

iii. To obtain good overall design 1.0 to 1.1

iv. To obtain good power factor 1.0 to 1.3

As power factor plays a very important role the performance of induction motors it is advisable

to design an induction motor for best power factor unless specified. Hence to obtain the best

power factor the following relation will be usually assumed for separation of D and L.

Pole pitch/ Core length = 0.18/pole pitch

or (πD/p) / L= 0.18/ (πD/p)

i.e D = 0.135P√L where D and L are in meter.

Using above relation D and L can be separated from D2L product. However the obtained values

of D and L have to satisfy the condition imposed on the value of peripheral speed.

Peripheral Speed: For the normal design of induction motors the calculated diameter of the motor should be such

that the peripheral speed must be below 30 m/s. In case of specially designed rotor the peripheral

speed can be 60 m/s.

41 | P a g e

4.3 DESIGN OF STATOR 4.3.1 Stator winding: Double layer lap type winding with diamond shaped coils is generally

used for stators. Small motors with a small number of slots and having a large number of slots

turns per phase may use single layer windings.

The three phases of the winding can be connected in either star or delta depending on the starting

method employed. The squirell cage motors are usually started by star delta starters and therefore

their stators are designed for delta connection and the six leads are brought out to be connected

to the starter. The wound motors are started by putting resistance in the rotor circuit and

therefore the stator can be connected either in star or delta as desired

4.3.2 Turns per phase: EMF equation of an induction motor is given by, Eph = 4.44fφTph Kw

Hence turns per phase can be obtained from emf equation, Tph = Eph

4.44fφKw

Generally the induced emf can be assumed to be equal to the applied voltage per phase

Flux/Pole = Bav×πDL/P,

winding factor kw

Number conductors /phase, Z

may be assumed as 0.955 for full pitch distributed winding unless otherwise

specified.

ph = 2 x Tph

Hence Total number of stator conductors Z = 6 T

,

ph and conductors /slot Zs = Z/S or 6 Tph/S ,

where Zs

is an integer for single layer winding and even number for double layer winding.

4.3.3 Conductor cross section Area of cross section of stator conductors can be estimated from the stator current per phase and

suitably assumed value of current density for the stator windings.

Sectional area of the stator conductor is given by as

where δ

= Is / δs

s is the current density in stator windings

42 | P a g e

Stator current per phase Is = Q / (3Vph

cosΦ)

A suitable value of current density has to be assumed from the Table 4.3

Table 4.3 Current densities for squirrel cage and wound rotor

Armature diameter (D) in

cm.

Cage rotor(Jsq) in A/mm2 Wound rotor(Jsr) in A/mm2

10 4 3.8 15 3.8 3.6 20 3.6 3.4 30 3.5 3.3 40 3.5 3.2 50 3.5 3.2 75 3.5 3.2

100 3.5 3.2

Hence higher value is assumed for low voltage machines and small machines. Usual value of

current density for stator windings is 3 to 5 amps.

Based on the sectional area shape and size of the conductor can be decided. If the sectional area

of the conductors is below 5 mm2 then usually circular conductors are employed. If it is above 5

mm2

thickness ratio must be between 2.5 to 3.5.

then rectangular conductors will be employed. In case of rectangular conductors width to

4.3.4 Shape of stator slots: in general two types of stator slots are employed in induction motors

viz, open clots and semiclosed slots. Operating performance of the induction motors depends

upon the shape of the slots and hence it is important to select suitable slot for the stator slots.

i.) Open slots: In this type of slots the slot opening will be equal to that of the width of the slots

as shown in Fig 10. In such type of slots assembly and repair of winding are easy. However such

slots will lead to higher air gap contraction factor and hence poor power factor. Hence these

types of slots are rarely used in 3 induction motors.

43 | P a g e

3.3.4 Shape of stator slots: in general two types of stator slots are employed in induction motors

viz, open clots and semiclosed slots. Operating performance of the induction motors depends

upon the shape of the slots and hence it is important to select suitable slot for the stator slots.

i.) Open slots: In this type of slots the slot opening will be equal to that of the width of the slots.

In such type of slots assembly and repair of winding are easy. However such slots will lead to

higher air gap contraction factor and hence poor power factor. Hence these types of slots are

rarely used in 3 induction motors.

ii.) Semiclosed slots: This type of slots assembly of windings is more difficult and takes more

time compared to open slots and hence it is costlier. However the air gap characteristics are

better compared to open type slots.

iii.) Tapered slots: In this type of slots also, opening will be much smaller than the slot width.

However the slot width will be varying from top of the slot to bottom of the slot with minimum

width at the bottom.

Selection of number of stator slots: Number of stator slots must be properly selected at the design stage as such this number affects

the weight, cost and operating characteristics of the motor. Though there are no rules for

selecting the number of stator slots considering the advantages and disadvantages of selecting

higher number slots comprise has to be set for selecting the number of slots. Following are the

advantages and disadvantages of selecting higher number of slots.

Based on the above comprise is made and the number of slots/pole/phase may be selected as

three or more for integral slot winding. However for fractional slot windings number of

slots/pole/phase may be selected as 3.5. So selected number of slots should satisfy the

consideration of stator slot pitch at the air gap surface, which should be between1.5 to 2.5 cm.

Stator slot pitch at the air gap surface = τs= D/Ss,

where Ss is the number of stator slot

44 | P a g e

Total number of stator conductors = 3×2Ts

Conductors per stator slot Zss = 6Ts/Ss

The number of conductors per slot must be an even integer for double layer windings because

one half of the conductors per slot belong to the top layer and other half to the bottom layer.

Area of stator slots: When the number of conductors per slot has been obtained, an approximate

area of the slot can be calculated.

Area of each slot = Copper area per slot

Slot space factor

=Zss × as

space factor

The space factor ordinarily obtained vary from 0.25 to 0.4

Length of the mean Turn: Length of the mean turn is calculated using an empirical formula lmt = 2L + 2.3 τp + 0.24 where

L is the gross length of the stator and τp

is pole pitch in meter.

Resistance of stator winding: Resistance of the stator winding per phase is calculated using the

formula = (0.021 x lmt x Tph ) / as where lmt is in meter and as is in mm2

Total copper losses in stator winding = 3 (I

. Using so calculated

resistance of stator winding copper losses in stator winding can be calculated as

s)2 r

s

Stator teeth: The dimensions of the slot determine the value of flux density in the teeth. A high

value of flux density in the teeth is not desirable, as it leads to a higher iron loss and a greater

magnetisinf mmf. As stated earlier, the maximum value of Bts, the mean flux density in the

stator teeth should not exceed 1.7 Wb/m2.

Minium tooth area per pole = Φm/1.7

Tooth area per pole = number of slots per pole×net iron length×Width of tooth = SS/P×Li×wts

45 | P a g e

Or minimum width of stator tooth

(wts)min

= 𝜑𝜑𝑚𝑚 1.7×𝑆𝑆𝑠𝑠/𝑃𝑃×𝐿𝐿𝑖𝑖

(4.8)

The minimum width of stator teeth is near the gap surface. A check of minimum tooth width

using Eqn. (4.8) should be applied before finally deciding the dimensions of stator slot.

Stator core: The flux density in the core should not exceed about 1.5 Wb/m2. Generally it lies

between 1.2 to 1.4 Wb/m2

.

Flux in stator core = Φm/2

Area of stator core = flux through core

flux density in stator core = φm

2Bcs

Area of stator core = Li×d

Where dcs

cs

Thus d

= depth of stator core

cs = ×L

The outer diameter of stator laminations Do = D + 2(depth of stator slots + depth of core) i

= D+2dss+2d

cs

4.4 Design of Rotor There are two types of rotor construction. One is the squirrel cage rotor and the other is the slip

ring rotor. Most of the induction motor are squirrel cage type. These are having the advantage of

rugged and simple in construction and comparatively cheaper. However they have the

disadvantage of lower starting torque. In this type, the rotor consists of bars of copper or

aluminum accommodated in rotor slots. In case slip ring induction motors the rotor complex in

construction and costlier with the advantage that they have the better starting torque. This type of

rotor consists of star connected distributed three phase windings.

Between stator and rotor is the air gap which is a very critical part. The performance parameters

of the motor like magnetizing current, power factor, over load capacity, cooling and noise are

affected by length of the air gap. Hence length of the air gap is selected considering the

advantages and disadvantages of larger air gap length.

46 | P a g e

Magnetising current and power factor being very important parameters in deciding the

performance of induction motors, the induction motors are designed for optimum value of air

gap or minimum air gap possible. Hence in designing the length of the air gap following

empirical formula is employed.

Air gap length lg

= 0.2 + 2√𝐷𝐷𝐿𝐿 mm (4.9)

4.1 Design of Squirrel Cage Rotor Number of Rotor slots: Proper numbers of rotor slots are to be selected in relation to number of

stator slots otherwise undesirable effects will be found at the starting of the motor. Cogging and

Crawling are the two phenomena which are observed due to wrong combination of number of

rotor and stator slots. In addition, induction motor may develop unpredictable hooks and cusps in

torque speed characteristics or the motor may run with lot of noise. Let us discuss Cogging and

Crawling phenomena in induction motors.

Crawling: The rotating magnetic field produced in the air gap of the will be usually non

sinusoidal and generally contains odd harmonics of the order 3rd, 5th and 7th. The third harmonic

flux will produce the three times the magnetic poles compared to that of the fundamental.

Similarly the 5th and 7th harmonics will produce the poles five and seven times the fundamental

respectively. The presence of harmonics in the flux wave affects the torque speed characteristics.

The Fig. 16 below shows the effect of 7th harmonics on the torque speed characteristics of three

phase induction motor. The motor with presence of 7th harmonics is to have a tendency to run the

motor at one seventh of its normal speed. The 7th

harmonics will produce a dip in torque speed

characteristics at one seventh of its normal speed as shown in torque speed characteristics.

Cogging: In some cases where in the number of rotor slots are not proper in relation to number

of stator slots the machine refuses to run and remains stationary. Under such conditions there

will be a locking tendency between the rotor and stator. Such a phenomenon is called cogging.

Hence in order to avoid such bad effects a proper number of rotor slots are to be selected in

relation to number of stator slots. In addition rotor slots will be skewed by one slot pitch to

47 | P a g e

minimize the tendency of cogging, torque defects like synchronous hooks and cusps and noisy

operation while running. Effect of skewing will slightly increase the rotor resistance and

increases the starting torque. However this will increase the leakage reactance and hence reduces

the starting current and power factor.

Selection of number of rotor slots: The number of rotor slots may be selected using the

following guide lines.

(i) To avoid cogging and crawling: (a)Ss ≠ Sr (b) Ss - Sr ≠ ±3P (ii) To avoid synchronous hooks and cusps in torque speed characteristics ≠ ±P, ±2P, ±5P.

(iii) To noisy operation Ss - Sr ≠ ±1, ±2, (±P ±1), (±P ±2)

4.4.2 Design of rotor bars and slots Rotor Bar Current: Bar current in the rotor of a squirrel cage induction motor may be

determined by comparing the mmf developed in rotor and stator.

Hence the current per rotor bar is given by Ib = 2m Kws TsSr

Is cosφ

For a three phase machine ms = 3

Ib = 6Is TsSr

Kws cosφ

≅ 0.85 ×6Is Ts

Sr

The above relation may be interpreted as that the rotor mmf is about 85 percent of stator mmf.

4.4.3 Cross sectional area of Rotor bar

Sectional area of the rotor conductor can be calculated by rotor bar current and assumed value of

current density for rotor bars. As cooling conditions are

better for the rotor than the stator higher current density can be assumed. Higher current density

will lead to reduced sectional area and hence increased resistance, rotor cu losses and reduced

48 | P a g e

efficiency. With increased rotor resistance starting torque will increase. As a guide line the rotor

bar current density can be assumed between 4 to 7 Amp/mm2

Hence sectional area of the rotor bars can be calculated as Ab = Ib/δb mm2

Where δ

b

is the cross sectional area of rotor bar

4.4.4 Shape and Size of the Rotor slots Generally semiclosed slots or closed slots with very small or narrow openings are employed for

the rotor slots. In case of fully closed slots the rotor bars are force fit into the slots from the sides

of the rotor. The rotors with closed slots are giving better performance to the motor in the

following way. (i) As the rotor is closed the rotor surface is smooth at the air gap and hence the

motor draws lower magnetizing current. (ii) reduced noise as the air gap characteristics are better

(iii) increased leakage reactance and (iv) reduced starting current. (v) Over load capacity is

reduced (vi) Undesirable and complex air gap characteristics. From the above it can be

concluded that semiclosed slots are more suitable and hence are employed in rotors.

4.4.5 Copper loss in rotor bars Knowing the length of the rotor bars and resistance of the rotor bars cu losses in the rotor bars

can be calculated.

Length of rotor bar lb = L + allowance for skewing

Rotor bar resistance = 0.021 x lb / A

Copper loss in rotor bars = Ibb

2 x rb

x number of rotor bars.

4.4.6 End Ring Current All the rotor bars are short circuited by connecting them to the end rings at both the end rings.

The rotating magnetic field produced will induce an emf in the rotor bars which will be

sinusoidal over one pole pitch. As the rotor is a short circuited body, there will be current flow

because of this emf induced. The distribution of current and end rings are as shown in Fig. 17

below. Referring to the figure considering the bars under one pole pitch, half of the number of

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bars and the end ring carry the current in one direction and the other half in the opposite

direction. Thus the maximum end ring current may be taken as the sum of the average current in

half of the number of bars under one pole.

Maximum end ring current Ie(max) = ½ ( Number rotor bars / pole) Ib(av)

= ½ x Sr/P x Ib

/1.11

Hence rms value of Ie = 1/2√2 x Sr/P x Ib

/1.11

= 1/π x Sr/P x Ib

≅ SrIb

πP

/1.11

Area of end ring: Knowing the end ring current and assuming suitable value for the current

density in the end rings cross section for the end ring can be calculated as

Area of each end ring Ae = Ie / δe mm2

Copper loss in End Rings: Mean diameter of the end ring (D

,

current density in the end ring may be assume as 4.5 to 7.5 amp/mm2.

me) is assumed as 4 to 6 cms less than that of the rotor. Mean length of the current path in end ring can be calculated as lme = πDme

. The resistance of the end ring can be calculated as

re = 0.021 x lme / A

e

Total copper loss in end rings = 2 x Ie2 x r

e

Full load slip: The value of full load slip at full load is determined by the rotor resistance.

Areasonable value of rotor resistance to be incorporated in the rotor can be obtained by the

knowledge of reasonal values of full load slip. The value of slip S is derived from the following

relationship.

Equivalent Rotor Resistance: Knowing the total copper losses in the rotor circuit and the equivalent rotor current equivalent rotor resistance can be calculated as follows.

50 | P a g e

Equivalent rotor resistance r'r = Total rotor copper loss / 3 x (Ir' )2

4.5 Design of wound Rotor: These are the types of induction motors where in rotor also carries distributed star connected 3

phase winding. At one end of the rotor there are three slip rings mounted on the shaft. Three ends

of the winding are connected to the slip rings. External resistances can be connected to these slip

rings at starting, which will be inserted in series with the windings which will help in increasing

the torque at starting. Such type of induction motors are employed where high starting torque is

required.

4.5.1 Number of rotor slots As mentioned earlier the number of rotor slots should never be equal to number of stator slots.

Generally for wound rotor motors a suitable value is assumed for number of rotor slots per pole

per phase, and then total number of rotor slots is calculated. The selected number of slots should

be such that tooth width must satisfy the flux density limitation. Generally semiclosed slots are

used for rotor slots.

4.5.2 Number of rotor Turns

Number of rotor turns is decided based on the safety consideration of the personal working with

the induction motors. The voltage between the slip rings on open circuit must be limited to safety

values. In general the voltage between the slip rings for low and medium voltage machines must

be limited to 400 volts. For motors with higher voltage ratings and large size motors this voltage

must be limited to 1000 volts. Based on the assumed voltage between the slip rings comparing

the induced voltage ratio in stator and rotor the number of turns on rotor winding can be

calculated.

Voltage ratio Er/ Es = (Kwr x Tr) / (Kws x Ts )

Hence rotor turns per phase Tr = (Er/Es) (Kws/Kwr) Ts

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Er = open circuit rotor voltage/phase Es = stator voltage /phase Kws = winding factor for stator Kwr = winding factor for rotor Ts

By assuming a suitable value of voltage between slip rings, the rotor turns per phase to be

provided can be calculated.

= Number of stator turns/phase

3.5.3 Area of Rotor Conductors (Wound Rotors) The full load rotor mmf is taken as 85 percent stator mmf .

IrTr = 0.85IsTIr = 0.85I

s sTsT

r

Area of rotor conductor can be calculated based on the assumed value for the current density in

rotor conductor and calculated rotor current. Current density rotor conductor can be assumed

between 4 to 6 Amp/mm2

Ar = Ir / δr mm2

Ar < 5mm2 use circular conductor, else rectangular conductor, for rectangular conductor width

to thickness ratio = 2.5 to 4. Then the standard conductor size can be selected similar to that of

stator conductor.

Size of Rotor slot: Mostly Semi closed rectangular slots employed for the rotors. Based on

conductor size, number conductors per slot and arrangement of conductors similar to that of

stator, dimension of rotor slots can be estimated. Size of the slot must be such that the ratio of

depth to width of slot must be between 3 and 4.

Total copper loss: Length of the mean Turn can be calculated from the empirical formula

lmt = 2L + 2.3 τp + 4ds

m

Resistance of rotor winding is given by Rr = (0.021 x lmt x Tr ) / Ar

52 | P a g e

Total copper loss = 3 Ir2

Rr Watts

Rotor teeth: The width of rotor slot should be such that the flux density in the rotor teeth does

not exceed about 1.7 Wb/m2. The minimum flux density for rotor teeth occurs at their section is

minimum there.

Minimum width of rotor teeth wtr(min) = φm1.7×SrP×Li

Minimum width of tooth actually provided

wtr = rotor slot pitch at the root – rotor slot width = π(Dr-2dsrSr-wsr

where dcr = depth of rotor slot and wsr

= width of rotor slot

4.6 Magnetic circuit Calculation

The flux produced by stator mmf turns passes through the following parts:

(i) Air gap (ii) rotor teeth (iii) Rotor core (iv) stator teeth (v) stator core

The calculation of magnetizing current of an induction motor follows the same general procedure

as the calculation of magnetizing current of a dc machine. The main difference is that in a dc

machine the flux density is assumed to be uniform over any cross section and the same mmf for

all paths, in an induction motor the flux is distributed approximately sinusoidally and the mmf

varies similarly.

The reason for this is that the flux density distribution curve can be approximated too closely by

a sine wave with a third harmonic. The value of flux density at 60° from the interpolar axis is

same whether the third harmonic is present or not. Thus the calculation of magnetizing mmf

should be based upon the value of flux density at 60° as far as the gap and teeth are concerned.

Mmf of air gap: The mmf required for air gap is given by

ATg = 800,000Bg60KgLg

Where Bg60 = 1.36Bav Mmf for stator teeth: The flux density is uniform in the teeth when they are parallel sided but

when parallel sided slots are used, the flux density along the length of teeth is not uniform. The

53 | P a g e

value of mmf for teeth is found out by finding flux density at a section 1/3 height of tooth from

narrow end.

Flux density at 1/3 height of tooth from narrow end Bts 1/3 =

φm

Ss /P × Li × wts 1/3

Where wts1/3

π(D + 2dss

3)

S − wss

= width of stator at 1/3 height from narrow end

The calculation of mmf for stator teeth is based upon Bts60 where Bts60 = 1.36 Bts1/3

The mmf per meter atts for stator teeth can be found from chapter2 curve

Mmf required for stator teeth = atts×d

ss

Mmf of rotor teeth: Flux density in rotor teeth at 1/3 height from narrow end Btr 1/3 =

φm

Sr/P × Li × wtr 1/3

With wtr 1/3 = π(Dr−4dsr /3

Sr− wsr

The mmf per meter, attr, for rotor teeth is found from Fig. 4.2 corresponding Btr60

Mmf required for rotor teeth

ATtr = attr×d

tr

Mmf of stator core: Corresponding to the flux density in the core, the mmf per meter atcs is found from chapter 2 curve. The length of path through the core can be taken as 1/3 pole pitch at the mean core diameter. Length of path through stator core

lcs = π(D + 2dss + dcs )

3P

Mmf of stator core = atcr×L

cs

54 | P a g e

Mmf of rotor core: Corresponding to the flux density in the rotor core mmf per meter atcr is found from Fig. 4.2. Length of flux path in rotor core

lcr = π(Dr − 2dsr − dcr )

3P

Total mmf of rotor core ATcr = atcr×L

Total magnetizing mmf per pole for B60

cr

AT60 = ATg +ATts +ATtr +ATcs+ AT

cr

The magnetizing current is given by

Im = 0.427PAT60

Kws Ts

4.7 Performance Evaluation

Based on the design data of the stator and rotor of an induction motor, performance of the

machine has to be evaluated. The parameters for performance evaluation are iron losses, no

load current, no load power factor, leakage reactance etc. Based on the values of these

parameters design values of stator and rotor can be justified.

Iron loss: The iron loss in induction motors consists of hysteresis and eddy current loss in

teeth and cores, surface loss in teeth due to variation of air gap density, tooth pulsation loss

due to variation of teeth density, loss due to non uniform and loss in end plates.

The iron loss in stator teeth and core is found out by calculating their respective weights. The

loss per kg corresponding to the flux densities can be taken from chapter 2.

The frequency of flux reversal in the rotor is slip times the line frequency. In the case of cage

motors, the value of slip is small and, therefore, the iron loss in the rotor is negligible.

Wound rotor motors may operate at reduced speed by insertion of resistance in the rotor

circuit. Therefore rotor iron loss must be included while calculating the operating

characteristics of a wound rotor machine.

55 | P a g e

Friction and windage loss: Table 3.4 gives the approximate values of friction and windage losses expressed in terms of output.

Table 4.4 Friction and windage loss

Loss component of no load current per phase

IL = Total noload loss

3 × voltage per phase

No load current IL = �Im2 + IL

2

The no load power factor , cosΦ = IL/I

The approximate values of no load expressed as percentage of full load current is given in

table 3.5

o

Table 3.5 No load current

Output KW

No load current percent of full load current

0.75 50 3.0 40

15.00 33 37.00 30 75 and above

27

Output KW

F and W loss Percent of output

0.75 5.5 3.70 3.7 7.50 2.7 37.00 1.5 75.00 1.2

150.00 1.0

56 | P a g e

56 | P a g e

5. DESIGN OF BLDC MOTOR

5.1 Introduction

A brushless motor, as its name suggests, is a motor without brushes, slip rings or mechanical

commutator, such as are required in conventional DC motors or synchronous AC machines for

connection to the rotor windings.

The brushless dc motor is essentially configured as permanent magnet rotating past a set of

current carrying conductors. In this respect it is equivalent to an inverted dc commuted motor, in

that the magnet rotates while the conductors remain stationary. In both case, the current in the

conductors must reverse polarity every time a magnet pole passes by, in order to ensure that the

torque is unidirectional. In the dc commutator motor, the polarity reversal is performed by

commutator and brushes. In the brushless dc motor, the polarity reversal is performed by power

transistors which must be switched in synchronism with the rotor positions.

5.1.1 Types of BLDC Motor

Brushless motor fall into the two principal classes of sinusoidally excited and square wave

(trapezoidally excited) motors. Sinusoidally excited motors are fed with three-phase sinusoidal

waveforms and operate on the principle of a rotating magnetic field. They are simply called

sinewave motors or PM synchronous motors. All phase windings conduct current at a time.

Square wave motors are also fed with three-phase waveforms shifted by 1200 one from another,

but these waveshapes are rectangular or trapezoidal. Such a shape is produced when the armature

current (MMF) is precisely synchronized with the rotor instantaneous position and frequency

(speed).

On the basis of the direction of field flux BLDC motors can be broadly classified as

1. Radial flux: The flux direction is along the radius of the machine

2. Axial flux: The flux direction is parallel to the rotor shaft

57 | P a g e

The radial flux PM machines are more common where as the axial flux machines are coming in

to prominence in a small number of applications due to their higher power density and

acceleration capacity than its counterpart.

Depending on the PM mounting on the rotor the radial flux BLDC machines can be divided in to

1. Surface mounted PM motors

2. Interior magnet motors

Surface mounted PM motors: If a higher speed is required which is constant or varies only

slightly, an exterior –rotor motor is considered. The feature of these design have to do with the

easy of manufacturing and low cost. The relatively high rotor inertia is desirable for such

applications such as fans and blowers.

Interior magnet motors: If a high torque, low speed machine is required, then an interior rotor design is considered using rare earth magnets and a high pole count. Such motors can be made with a large hole through the center of the rotor, which provides valuable space for other parts of mechanisms, cabling, or cooling media.

5.1.2 Structures of brushless dc motors

PM d.c. brushless and a.c. synchronous motor designs are practically the same: with a

polyphase stator and PMs located on the rotor. The only difference is in the control and shape of

the excitation voltage: an a.c. synchronous motor is fed with more or less sinusoidal waveforms

which in turn produce a rotating magnetic field. In PM d.c. brushless motors the armature current

has a shape of a square (trapezoidal) waveform, only two phase windings (for Y connection)

conduct the current at the same time, and the switching pattern is synchronized with the rotor

angular position (electronic commutation).

The electric and magnetic circuits of PM synchronous motors and PM d.c. brushless motors are

similar, i.e., polyphase (usually three phase) armature windings are located in the stator and

moving magnet rotor serves as the excitation system. PM synchronous motors are fed with three

58 | P a g e

phase sinusoidal voltage waveforms and operate on the principle of magnetic rotating field. For

constant voltage–to–frequency control technique no rotor position sensors are required. PM d.c.

brushless motors operate from a d.c. voltage source and use direct feedback of the rotor angular

position, so that the input armature current can be switched, among the motor phases, in exact

synchronism with the rotor motion. This concept is known as self-controlled synchronization, or

electronic commutation.

5.1.3 Basic Winding Consideration

There are two common electrical winding configurations; the delta configuration connects three

windings to each other (series circuits) in a triangle-like circuit, and power is applied at each of

the connections. The Wye (Y-shaped) configuration, sometimes called a star winding, connects

all of the windings to a central point (parallel circuits) and power is applied to the remaining end

of each winding.

A motor with windings in delta configuration gives low torque at low speed, but can give higher

top speed. Wye configuration gives high torque at low speed, but not as high top speed.

Although efficiency is greatly affected by the motor's construction, the Wye winding is normally

more efficient. In delta-connected windings, half voltage is applied across the windings adjacent

to the driven lead (compared to the winding directly between the driven leads), increasing

resistive losses. In addition, windings can allow high-frequency parasitic electrical currents to

circulate entirely within the motor. A Wye-connected winding does not contain a closed loop in

which parasitic currents can flow, preventing such losses.

5.1.4 Comparison between BLDC motor with and induction and DC commutator motors

Cage induction motors have been the most popular electric motors in the 20th century. Recently,

owing to the dynamic progress made in the field of power electronics and control technology,

59 | P a g e

their application to electrical drives has increased.

The main advantages of cage induction motors are their simple construction, simple

maintenance, no commutator or slip rings, low price and moderate reliability. The disadvantages

are their small air gap, the possibility of cracking the rotor bars due to hot spots at plugging and

reversal, and lower efficiency and power factor than synchronous motors.

The use of PM brushless motors has become a more attractive option than induction motors.

Rare earth PMs can not only improve the motor’s steady-state performance but also the power

density (output power-to-mass ratio), dynamic performance, and quality. The prices of rare earth

magnets are also dropping, which is making these motors more popular. The improvements made

in the field of semiconductor drives have meant that the control of brushless motors has become

easier and cost effective, with the possibility of operating the motor over a large range of speeds

while still maintaining good efficiency.

The armature current of a BLDC motor is not transmitted through a commutator or slip rings and

brushes. These are the major parts which require maintenance. In a d.c. commutator motor

the power losses occur mainly in the rotor which limits the heat transfer and consequently the

armature winding current density. In PM brushless motors the power losses are practically all in

the stator where heat can be easily transferred through the ribbed frame or, in larger machines,

water cooling systems can be used. Considerable improvements in dynamics of brushless PM

motor drives can be achieved since the rotor has a lower inertia and there is a high air gap

magnetic flux density and no-speed dependent current limitation.

5.2 Basic Design Configurations

Before a brushless motor design can begin several important decisions to be made, the reason for

this should be obvious from the discussion regarding the feature of different types of brushless

motors and the availability of different magnetic materials. The motor commutation is also an

important issue which should be considered making the basic decisions about the design. The

choice of different interior rotor, exterior rotor, or axial gap motor must be considered first along

60 | P a g e

with a rough idea of the correct number of stator and winding configuration must be selected.

The rotor permanent magnet configuration is designed. Then the stator winding are determined.

Number of phases:

Brushless DC motors come with different phase numbers out of which 1-phase, 2-phase and 3-

phase motors are commonly used. 3-phase motors are by far the most common choice, due to the

following reason.

1. They have extremely good utilization of copper, iron, magnet, insulating materials and silicon,

in terms of quantity of these material required for a given output power.

2. 3-phase motors have flexibility afforded by wye and Delta connected windings, even unipolar

winding.

3. They have excellent starting characteristics, with smooth rotation in either direction with low

torque ripple.

4. They can work with a very wide range of winding configuration and take advantage of coil

winding technology.

5. They can operate with either square wave drive or sine wave drive and well adopted to the

development of ‘Sensor less’ controllers.

Table 3.1 gives a comparison of brushless motors with different phase numbers and their

conductor utilization, torque ripple percentage and the number of Hall switch requirement.

Table 5.1 Comparison of brushless motors with different phase numbers

No. of phases

Conductor utilization%

Commutation Sensor No. of power switches Torque ripple %

1 50 1 2 100 2 50 2 4 30 3 67 3 6 15 4 75 3 8 10 6 83 4 12 7 12 92 5 24 3

61 | P a g e

Number of stator slots and poles:

The choice of number of poles depends upon many factors, some of which are as follows:

1. Magnet material and grade

2. Interior–rotor Vs. exterior-rotor vs. axial gap rotor

3. Mechanical assembly of the rotor and magnets

4. Speed of rotation

5. Inertia requirements

Number of poles will be selected based on the speed of rotation, commutation frequency and

cogging torque. Increase in the number of poles for the same speed results in increased

commutation frequency, hence increase in switching losses in transistors and iron loss in the

stator. And for the fixed main dimensions, with increase in the number of poles, either the width

of magnet spacer or the magnet fraction will decrease, which will result in decrease in specific

magnetic loading and thereby the developed torque. Also end turn becomes shorter and the

leakage inductance becomes lower for higher pole number. But the reduction in pole number

increases the cogging torque and end copper requirement.

Length of air gap:

Of the three components of the phase-inductance, the air gap inductance is the predominant.

Larger air gap will result in reduced phase-inductance, armature reaction effects, and also the

cogging torque, but will necessitate bigger magnets, thereby increased cost. And as the air gap

increases, the efficiency of the motor reduces. The air gap of a small PM motor can be

considered between 0.3 to 1 mm. The length of air gap can also be calculated by considering the

Air gap mmf ATg varies as (60-70) % of armature mmf ATa

Magnet length (thickness):

Based on the magnetic circuit equations, the length of the permanent magnet can be found by

reducing the difference between the assumed and actual flux densities in the air gap with the

variation of permanent magnet length. In order to reduce the requirement of the ampere

62 | P a g e

conductors to improve efficiency, the magnet length can be increased and hence specific

magnetic loading. But the increase in magnet length requires more magnet material and hence

increased cost of the motor.

The magnet thickness can be calculated by considering the ratio Full load mmf(ATf) to armature

mmf(ATa)

The full load mmf ATf = (0.7− 1.3)ATa

The volume of magnet is given by VM = AT f

Hc

The area is given by Ap = α×τp×L

Where α = Pole arc to pole pitch ratio

τP = Pole pitch

L = Length of armature

By dividing Vm to the area of magnet the thickness magnet can be calculated.

5.3 Permanent Magnet Materials and Circuits

A permanent magnet (PM) can produce a magnetic field in an air gap with no field excitation

winding and no dissipation of electric power. External energy is involved only in changing the

energy of the magnetic field, not in maintaining it. As any other ferromagnetic material, a PM

can be described by its B-H hysteresis loop. PMs are also called hard magnetic materials,

meaning ferromagnetic materials with a wide hysteresis loop.

Demagnetization curve and magnetic parameters

The basis for the evaluation of a PM is the portion of its hysteresis loop located in the upper left-

hand quadrant, called the demagnetization curve. Magnetic characteristics in this region are

called the demagnetization characteristics. The main points concerning the demagnetization

characteristics are as follows:

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Fig. 5.1. (a) The hysteresis loop, and (b) demagnetization curve and energy product.

The general relationship between the magnetic flux density B, intrinsic magnetization Bi due to

the presence of ferrow magnetic material, and magnetic field intensity H may be expressed as

B = μoH + Bi = μo (H + M) = μoμrH (5.1)

Saturation magnetic flux density Bsat and corresponding saturation magnetic field intensity

Hsat . At this point the alignment of all the magnetic moments of domains is in the direction of

the external applied magnetic field.

Remanent magnetic flux density Br , or remanence, is the magnetic flux density

corresponding to zero magnetic field intensity. High remanence means the magnet can support

higher magnetic flux density in the air gap of the magnetic circuit

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Coercive field strength Hc , or coercivity, is the value of demagnetizing field intensity

necessary to bring the magnetic flux density to zero in a material previously magnetized (in a

symmetrically cyclically magnetized condition). High coercivity means that a thinner magnet can

be used to withstand the demagnetization field.

Intrinsic demagnetization curve is the portion of the Bi = f (H) hysteresis loop located in the

upper left-hand quadrant, where Bi = B − μ0 H is according to eqn (2.1). For H = 0 the intrinsic

magnetic flux density Bi = Br .

Intrinsic coercivity iHc is the magnetic field strength required to bring to zero the intrinsic

magnetic flux density Bi of a magnetic material described by the Bi = f (H) curve. For PM

materials iHc > Hc .

Recoil magnetic permeability μrec is the ratio of the magnetic flux density to magnetic field

intensity at any point on the demagnetization curve, i.e., μrec = μo μrrec

Maximum magnetic energy per unit produced by a PM in the external space ie equal to the

maximum magnetic energy density per volume, i.e

Wmax = (BH )max

2 J/m3

For PMs with linear demagnetization curve , i.e NdFeB magnets, the coercive field strength at

room temperature can be calculated on the basis of Br and μrrec as

(5.2)

Hc = Brμoμrec

(4.3)

The magnetic flux density produced in the air gap g by a PM with linear demagnetization curve

and its height hm placed in a magnetic circuit with infinitely large magnetic permeability and the

air gap g is approximately’

Bg = Br

1+μrrec ×ghm�

(5.4)

The above equation (4.4) has been derived by assuming Hchm = Hmhm+Hg g, neglecting

magnetic voltage drop (MVD) in the mild steel portion of the magnetic circuit, putting

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Hc = Bg

μoμrrec and Hg =

Bg

μo (5.5)

4.3.1 Kinds of permanent magnet

There are basically three different types of permanent magnet which are used inPM motors:

(i) Alnico magnet,

(ii) Ferrite or ceramic magnet, and

(iii) Rare-earth magnet (samarium-cobalt magnet SmCo and neodymium-iron-boron NdFeB) .

Alnico Magnets

Alnico magnets are made up of a composite of aluminium, nickel and cobalt with small amounts

of other elements added to enhance the properties of the magnet. Alnico magnets have good

temperature stability, good resistance to demagnetization due to shock but they are easily

demagnetized. Alnico magnets are produced by two typical methods, casting or sintering.

Sintering offers superior mechanical characteristics, whereas casting delivers higher energy

products (up to 5.5 MGOe) and allows for the design of intricate shapes. Two very common

grades of Alnico magnets are 5 and 8. These are anisotropic grades and provide for a preferred

direction of magnetic orientation. Alnico magnets have been replaced in many applications by

ceramic and rare earth magnets.

Positive Negative High Corrosion Resistance High Cost High Mechanical Strength Low Coercive Force High Temperature Stability Low Energy Product

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Ferrite Magnets:

Ferrite, also known as, Ceramic magnets are made of a composite of iron oxide and barium or

strontium carbonate. These materials are readily available and at a lower cost than other types of

materials used in permanent magnets making it desirable due to the lower cost. Ceramic magnets

are made using pressing and sintering. These magnets are also made in different grades.

Ceramic-1 is an isotropic grade with equal magnetic properties in all directions. Ceramic grades

5 and 8 are anisotropic grades. Anisotropic magnets are magnetized in the direction of pressing.

The anisotropic method delivers the highest energy product among ceramic magnets at values up

to 3.5 MGOe (Mega Gauss Oersted). Ceramic magnets have a good balance of magnetic

strength, resistance to demagnetizing and economy. They are the most widely used magnets.

Positive Negative High Corrosion Resistance High Cost High Mechanical Strength Low Coercive Force High Temperature Stability Low Energy Product

Samarium Cobalt Magnets

Samarium cobalt is a type of rare earth magnet material that is highly resistant to oxidation, has a

higher magnetic strength and temperature resistance than Alnico or Ceramic material. Introduced

to the market in the 1970's, samarium cobalt magnets continue to be used today. Samarium

cobalt magnets are divided into two main groups: Sm1Co5 and Sm2Co17 (commonly referred to

as 1-5 and 2-17). The energy product range for the 1-5 series is 15 to 22 MGOe, with the 2-17

series falling between 22 and 32 MGOe. These magnets offer the best temperature characteristics

of all rare earth magnets and can withstand temperatures up to 300° C. Sintered samarium cobalt

magnets are brittle and prone to chipping and cracking and may fracture when exposed to

thermal shock. Due to the high cost of the material samarium, samarium cobalt magnets are used

for applications where high temperature and corrosion resistance is critical.

Positive Negative High Corrosion Resistance High Cost High Energy Product Low Mechanical Strength - Brittle High Temperature Stability High Coercive Force

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Neodymium Iron Boron Magnets Neodymium Iron Boron (NdFeB) is another type of rare earth magnetic material. This material

has similar properties as the Samarium Cobalt except that it is more easily oxidized and

generally doesn't have the same temperature resistance. NdFeB magnets also have the highest

energy products approaching 50MGOe. These materials are costly and are generally used in very

selective applications due to the cost. Cost is also driven by existing intellectual property rights

of the developers of this type of magnet. Their high energy products lend themselves to compact

designs that result in innovative applications and lower manufacturing costs. NdFeB magnets are

highly corrosive. Surface treatments have been developed that allow them to be used in most

applications. These treatments include gold, nickel, zinc and tin plating and epoxy resin coating.

Positive Negative Very High Energy Product Higher Cost (Except from us!) High Coercive Force Low Mechanical Strength - Brittle Moderate Temperature Stability Low Corrosion Resistance (When uncoated) The B-H characteristics of these three types vary greatly as shown in Fig. 5.2. Their features are as follows:

Fig. 5.2. Demagnetization curves for different permanent magnet materials

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Table 5.2. Temperature coefficients and Curie temperature for common PM materials

Magnet Grades: A magnet grade is a good measure of the strength of a magnet. In general, higher numbers

indicate a stronger magnet. The number comes from an actual material property, the Maximum

Energy Product of the magnet material, expressed in MGOe (Mega Gauss Oersteds). It

represents the strongest point on the magnet’s Demagnetization Curve, or BH Curve.

Neodymium magnets are by far the strongest type of permanent magnet available. Magnet

advancements are a history of increasing coercivity. Neodymium magnets are both stronger and

less apt to be demagnetized than other magnet types

Grades of Neodymium The Neodymium magnets have a simple nomenclature. They all start with "N" which simply

stands for "Neo" (industry simplification of Neodymium) and is followed by a two digit number.

This number represents the maximum energy product in Mega-Gauss Oersteds (MGOe). Higher

values indicate stronger magnets and range from N35 up to N52. Letters following the grade

indicate maximum operating temperatures (often the Curie temperature), which range from M

(up to 100 degrees Celsius) to EH (200 degrees Celsius).

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Grades of Neodymium magnets:

• N35-N52

• 33M-48M

• 30H-45H

• 30SH-42SH

• 30UH-35UH

• 28EH-35EH

Neodymium Magnet Physical Properties

Material Type Residual Flux Density (Br)

Coercive Force (Hc)

Intrinsic Coercive Force (Hci)

Max.Energy Product (BH)max

N35 11.7-12.1 KGs >11.0 KOe >12 KOe 33-35 MGOe

N38 12.2-12.6 KGs >11.0 KOe >12 KOe 36-38 MGOe

N40 12.6-12.9 KGs >11.0 KOe >12 KOe 38-40 MGOe

N42 13.0-13.2 KGs >11.0 KOe >12 KOe 40-42 MGOe

N45 13.3-13.7 KGs >11.0 KOe >12 KOe 43-45 MGOe

N48 13.8-14.2 KGs >11.0 KOe >12 KOe 45-48 MGOe

N50 14.1-14.5 KGs >11.0 KOe >11 KOe 48-50 MGOe

N52 14.5-14.8 KGs >11.2 KOe >11 KOe 49.5-52 MGOe

N35M 11.7-12.1 KGs >11.4 KOe >14 KOe 33-35 MGOe

N38M 12.2-12.6 KGs >11.4 KOe >14 KOe 36-38 MGOe

N40M 12.6-12.9 KGs >11.4 KOe >14 KOe 38-40 MGOe

N42M 13.0-13.3 KGs >11.4 KOe >14 KOe 40-42 MGOe

N45M 13.3-13.7 KGs >11.4 KOe >14 KOe 42-45 MGOe

N48M 13.6-14.2 KGs >11.4 KOe >14 KOe 45-48 MGOe

N50M 14.1-14.5 KGs >11.4 KOe >14 KOe 48-50 MGOe

N33H 11.4-11.7 KGs >10.3 KOe >17 KOe 31-33 MGOe

N35H 11.7-12.1 KGs >10.8 KOe >17 KOe 33-35 MGOe

N38H 12.2-12.6 KGs >11.4 KOe >17 KOe 36-38 MGOe

N40H 12.6-12.9 KGs >11.4 KOe >17 KOe 38-40 MGOe

N42H 13.0-13.3 KGs >11.4 KOe >17 KOe 40-42 MGOe

N45H 13.3-13.7 KGs >11.4 KOe >17 KOe 42-45 MGOe

N48H 13.6-14.2 KGs >11.4 KOe >16 KOe 45-48 MGOe

N30SH 10.8-11.2 KGs >10.1 KOe >20 KOe 28-30 MGOe

N33SH 11.4-11.7 KGs >10.3 KOe >20 KOe 31-33 MGOe

N35SH 11.7-12.1 KGs >10.8 KOe >20 KOe 33-35 MGOe

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N38SH 12.2-12.6 KGs >11.4 KOe >20 KOe 36-38 MGOe

N40SH 12.6-12.9 KGs >11.4 KOe >20 KOe 38-40 MGOe

N42SH 13.0-13.3 KGs >11.4 KOe >20 KOe 40-42 MGOe

N45SH 13.3-13.7 KGs >11.4 KOe >19 KOe 43-45 MGOe

N28UH 10.4-10.8 KGs >9.8 KOe >25 KOe 26-28 MGOe

N30UH 10.8-11.2 KGs >10.1 KOe >25 KOe 28-30 MGOe

N33UH 11.4-11.7 KGs >10.3 KOe >25 KOe 31-33 MGOe

N35UH 11.7-12.1 KGs >10.8 KOe >25 KOe 33-35 MGOe

N38UH 12.2-12.6 KGs >11.4 KOe >25 KOe 36-38 MGOe

N40UH 12.6-12.9 KGs >11.4 KOe >25 KOe 38-40 MGOe

N30EH 10.8-11.2 KGs >10.1 KOe >30 KOe 28-30 MGOe

N33EH 11.4-11.7 KGs >10.3 KOe >30 KOe 31-33 MGOe

N35EH 11.7-12.1 KGs >10.8 KOe >30 KOe 33-35 MGOe

N38EH 12.2-12.6 KGs >10.8 KOe >30 KOe 36-38 MGOe

The thermal characteristics physical and mechanical Characteristics of different grades NdFeB

magnet is given below:

Table 5.3 Thermal characterestics of NdFeB magnets

Neodymium Material Type

Thermal Expansion Coeff.

Maximum Operating Temp Curie Temp Thermal Conductivity

%/°C °C (°F) °C (°F) kcal/m-h-°C

N -0.12 176°F (80°C) 590°F (310°C) 7.7

NM -0.12 212°F (100°C) 644°F (340°C) 7.7

NH -0.11 248°F (120°C) 644°F (340°C) 7.7

NSH -0.10 302°F (150°C) 644°F (340°C) 7.7

NUH -0.10 356°F (180°C) 662°F (350°C) 7.7

NEH -0.10 392°F (200°C) 662°F (350°C) 7.7

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Table 5.4 Physical characterstics of NdFeB Magnets

Platings/Coatings

Neodymium magnets are a composition of mostly Neodymium, Iron and Boron. If left exposed

to the elements, the iron in the magnet will rust. To protect the magnet from corrosion and to

strengthen the brittle magnet material, it is usually preferable for the magnet to be coated. There

are a variety of options for coatings, but nickel is the most common and usually preferred. Our

nickel plated magnets are actually triple plated with layers of nickel, copper, and nickel again.

This triple coating makes our magnets much more durable than the more common single nickel

plated magnets. Some other options for coating are zinc, tin, copper, epoxy, silver and gold. Our

gold plated magnets are actually quadruple plated with nickel, copper, nickel and a top coating of

gold.

Machining Neodymium material is brittle and prone to chipping and cracking, so it does not machine well

by conventional methods. Machining the magnets will generate heat, which if not carefully

controlled, can demagnetize the magnet or even ignite the material which is toxic when burned.

It is recommended that magnets not be machined.

Density 7.4-7.5 g/cm3

Compression Strength 110 kg/mm2

Tensile Strength 7.5 kg/mm2

Young’s Modulus 1.7×104 kg/mm2

Recoil permeability 1.05 Heat Capacity 350-500 J/(kg.°C) Thermal Expansion Coefficient (0 to 100°C) parallel to magnetization direction

5.2 x 10-6 /°C

Thermal Expansion Coefficient (0 to 100°C) perpendicular to magnetization direction

-0.8 x 10-6 /°C

72 | P a g e

Demagnetization

Rare Earth magnets have a high resistance to demagnetization, unlike most other types of

magnets. They will not lose their magnetization around other magnets or if dropped. They will

however, begin to lose strength if they are heated above their maximum operating temperature,

which is 176°F (80°C) for standard N grades. They will completely lose their magnetization if

heated above their Curie temperature, which is 590°F (310°C) for standard N grades. Some of

our magnets are of high temperature material, which can withstand higher temperatures without

losing strength.

5.1 Stator Dimensions:

Fig. 5.3 Slot geometry for radial flux motor topology

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Stator back Iron Thickness

The flux from each magnet splits equally in both the stator and rotor back irons and is coupled to the adjacent magnets. Thus the back iron must support one half of the air gap flux; that is the back iron flux is

φbi = φg

2

If the flux density allowed in the back iron is Bmax, then from the above equation the back iron width must be

wbi = φg

2Bmax KstL

Where Kst is the lamination stacking factor.

Stator tooth Thickness

Since there are Nsm number of slots per magnet pole, the air gap flux from each magnet travels

through Nsm teeth. Therefore each tooth must carry 1/Nsm of the air gap flux. If the flux density

allowed in the teeth is also Bmax, the required tooth width is

Wtb = φg

Nsm Bmax Kst L =2

Nsmwbi

5.2 Shaft diameter

The diameter of shaft for an electrical machine is determined by consideration of stiffness i.e

ability to resist deflection due to weight of rotor or unbalanced magnetic pull than strength to

transmit power.

The shaft of an electrical machine designed properly has to satisfy the following requirements:

1. The shaft most be strong enough throughout its section to withstand all loads without causing

residual strain.

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2. The shaft must have enough rigidity in order that the deflection of shaft under operation of the

machine does not reach a dangerous value as to cause the rotor to touch the stator.

3. Critical speeds of rotation should be different from running speeds of machine.

A convenient formula for diameter of of horizontal shafts under armatures is:

Diameter of shaft is given by

d = 5.5 × (Output in wattrps

)𝟏𝟏/𝟑𝟑 mm (5.6)

The diameter of the shaft in the bearings is less than the diameter under the armature. When the

shaft diameter under armature is 150 mm or more a good rule is to make the shaft diameter in

bearings 50 mm smaller than the maximum diameter. In case of small shafts the diameter in

bearings should be about 2/3 of the maximum diameter.

5.3 Basic Electrical Design:

Sizing Procedure and main Dimensions:

The inner diameter Di can be estimated on the basis of the output coefficient. The apparent

electromagnetic power crossing the air gap is given by

Selm = mEfIa

= π√2fTph KwφfmπDiA

2m√2Tph

= 0.5π2Kw Di2LinsBg A ( 5.7)

Where ns = f/P is the synchronous speed, Kw is the stator winding factor

The electromagnetic torque is given by

Td =Selm

2πns

= π4

Kw Di2LiBg A (5.8)

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The output power is given by

Pout = Pinη

= mVIaη

The output coefficient is

Co = Pout

Di2Lins

For sizing procedure of NdFeB PM BLDC motors can be initially be estimated as

Bg = (0.6..0.8)Br

The airgap between the stator core and rotor poles is advised to be 0.3 to 1.0 mm for small PM

motors.

5.3.1 Calculation of the torque constant and the back EMF constant

The torque constant KT and back-emf constant KE are widely used to match the motor to its

controller, especially when the motor and controller are obtained from different sources. Even

more importantly, KT is used in the control system design of complex servo mechanisms that are

driven by electric motors, because it represents the essential ‘gain’ of the motor in converting

current into torque.

The EMF induced is given by

Ef = √2πfKw Tphφf

= √2πPTph Kwφfns

= CEφfns = KE ns

Where CE = πP√2Tph Kw and KE = CEφf are the EMF constants

The electromagnetic torque developed by the motor is

Td =Pelm

2πns

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=mEfIa

2πns

= m√2

PTph KwφfIa = CTφfIa = KT Ia

Where the torque constant is given by

CT = mCE

2π =m√2

PTph Kw

or KT = CTφf

For a square wave excitation the EMF induced in a single turn is given by

ef = 2Bg Liv

= 4PnBg Liτ

For Tph turns having winding factor Kw emf is given by

ef = 4PnTph Kwφf

For 3-phase motor two phases are conducting at the same time. The EMF contributing to the

electromagnetic power is given by

EfL−L = 2ef = 8PTph Kwφfns

= CEdc φfns = KEdc ns

Where CEdc = 8PTph Kw and KEdc = CEdc φf

The electromagnetic torque developed by the motor is

Td = Pg

2πns=

EfL−L

2πns

= 4πPTph KwφfIa

= CTdcφf Ia = KTdc Ia

Where CTdc = CEdc/(2π) = 4π

PTph Kw , KTdc = CTdcφf

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Ia is actually Ia�32 is the flat –top value of the phase current.

Turns per phase calculation

Turns per phase Tph = Es

4.44Bav fKw

Es = Stator voltage per phase

The above relation is applicable when all the turns per phase are connected in series. But if there are ‘a’ parallel paths per phase,

Eph = 4.44φfTph fKw

= Eph

a × 4.44φfKw f

Total number of conductors Z = m×2×Tph

Conductor cross section:

Area of cross section of armature conductor is given by AZ = Is/δa

Where δa = current density in aramature conductor, A/mm2. For normally cooled machines,

permissible current density in the armature conductor is assumed to be 4-7 A/mm2

Dimensions of Stator slot

Area of slot As = copper area of slot

Slot space factor

The area of slot can be estimated by assuming the values of slot space factor. The value of slot

space factor usually lies between 0.35 -0.4

The width of slot and the depth of slot can be calculated by assuming the slot depth to slot width

ratio, which varies between 3 to 3.5.

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Resistance of stator windings:

Length of mean turn is given by

Lmt = 2L + 2.3τ + 4ds

Resistance of the stator winding is given by

Rs = ρLmt Tph

AZ

Losses and performance of the machine:

The major losses occurring in a BLDC motor are the Copper losses and the Core losses.

The copper losses:

As the two phases carry current at a given time the copper loss is given by

Pcu = 2Is2Rs

Core losses:

As compared to copper losses, core losses are very difficult to calculate as they consist of

hysteresis and eddy current losses which vary nonlinearly with frequency and magnetic flux

density. Fortunately manufacturers provide coreloss/kg data of the steel at various values of flux

density and frequency which we can use to approximately calculate the core losses. Core losses

occur only in stator.

Pc = core loss/kg (fe, Bmax)×Wstator

Temperature rise of machine:

By assuming an initial ambient temperature, the final temperature rise of the machine can be

calculated.Calculation of temperature rise is very important as it determines the safe time of

operation of the motor without getting burned

Heat dissipated = M x S x (T2-T1).

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Where,

M is the mass of the material,

S is the specific heat of the material,

T2 is the final temperature,

T1 is the initial or the ambient temperature,

Density of copper = 8900 kg/m3

Mass of total copper in 3 phases = 0.120 kg.

Specific heat of copper = 0.385 J/g˚C.

Mass of stator material = 0.1 kg.

Specific heat of stator material = 0.1 kJ/kg̊ c.

Mass of Aluminum = 0.2 kg

Therefore heat dissipated is given by

(Mcu x Scu x (T2 -T1) + + Ms x Ss x (T2 - T1))

Total loss of the machine = Copper loss +Iron loss

Now

Energy loss = losses x time (Assuming for a certain time)

Since heat dissipated = energy losses.

If we take certain ambient temperature as 35˚C, then the final temperature can be calculated and

this is in the safe limit for all components

Application of BLDC Motor:

Now a BLDC motors are widely used. Some of the application of BLDC motor is given below

1. Electric and hybrid electric vehicles

2. Variable speed cooling fans

3. Computer hard disc drives

4. CD players

5. Factory Automation

6. X-Y Tables

7. Space mission Tools

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Page | 80

6. Conclusion and scope for future works

6.1 Conclusion

This thesis presents an analytical design method for DC machines, Induction motor and BLDC

motor. For each machine a optimized design tool is developed in MATLAB in ‘c’ language. To

make the design more efficient proper materials are selected. Apart from dimensioning of

different parts the of each machine the design also includes the losses and temperature rise and

efficiency of the machine. For BLDC motor, different grades of NdFeB magnets are considered.

The thermal and physical properties of different grades of NdFeB magnets are provided.

6.2 Scope for future works

The future goal of this study has been to present a comparative analysis of the machine and Synthesizing

of the machines using computer aided design (CAD) software and performance analysis using finite

element analysis (FEA). More recently electromagnetic field analysis has emerged to make the design an

optimizing designs, particularly with respect to the efficient utilization of materials and optimization of

geometry. The most popular methods for analysis are based on the finite-element method. It is most

useful in helping to understand a theoretical problem that is too difficult for conventional analysis, and in

this role it has undoubtedly helped to refine many existing motor designs and improve some new ones.

Page | 81

81 | P a g e

References

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[2] M. G. Say, Performance and Design of Alternating current Machines, Pitman publishing; 3rd

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Publishers, 2004

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[4] J. F. Gieras, Permanent Magnet Motor Technology Design and Applications, third Edition,

CRC press, 2010.

[5] J. R. Handershot and T.J.E Miller, Design of Brushless Permanent Magnet Motors, Magna

Physics publishing and Clarendon press, Oxford, 1994.

[6] D.C. Hanselman, Brushless permanent-magnet motor design, McGraw-Hill, 1994

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Electrical Technologies[ICCEET], 2012

[8] M.J. Soleimani Kesshayeh, S. Asghar, ''Optimum design of a Three-Phase Permanent

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[9] A. Shanmugasundaram, R palani, Electrical Machine Design Data Book, New Age

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[10] AK Steel Product Data Bulletin, Selection of Electrical Steels for Magnetic Cores [online]

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[12] K&J Magnetics, Neodymium Magnet Information{Online}

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[14] Xavier Jannot, Jean-Claude Vannier, Claude Marchand, Mohamed Gabsi, Jacques Saint-Michel, DanielSadarnac, (2011). Multiphysic Modeling of a High-Speed Interior Permanent-Magnet Synchronous Machine for a Multiobjective Optimal Design. IEEE Transactions On Energy Conversion, 26(2). [15] Low, S., Lee, W. H., (1987). Characteristics and Performance Analysis of a Permanent Magnet motor with a Multistacked Imbricated Rotor. IEEE Trans. on Energy Conversion, EC-2(3), 450-457. [16] Petkovska, L., (1991). A Contribution to Analysis of Permanent Magnet Excitation Field Influence on Characteristics of an Electronically Operated Synchronous Motor, via 3D Magnetic Field Calculation. PhD Thesis, Skopje, Macedonia, 214. [17] Toliyat, H. A., Kilman, G. B., (2004). Handbook of Electric Motors, Second Edition. Taylor & Francis Group. [18] Eckart Nipp. (1999). Permanent Magnet Motor Drives with Switched Stator Windings. TRITA-EMD 9905 ISSN-1102-0172. Royal Institute of Technology Department of Electric Power Engineering Electrical Machines and Drives. Stockholm. [19] Takorabet, N., (2004). Materials Regional Workshop on Electrical Motor Design and Actuators. CODE 1A- 005-00. [20] Hamdi, E. S., (1994). Design of Small Electrical Machines. John Wiley & Sons, ISBN-10: 0471952028. [21] Luo, S. H. J., Leonardi, F., Lipo, T. A., (1998). A General Approach to Sizing and Power Density Equations for Comparison of Electrical Machines. IEEE Transactions on Industry Applications, 34(1). [22] Binder, A., Schneider, T., (2008). High-speed inverter-fed AC drives. in Proc. 2007 Int. Aegean Conf. Electr. Mach. Power Electron. (ACEMP), 748–755. [23] Thelin, P., Nee, H. P., (1998). Suggestions regarding the pole-number of inverter-fed PM-synchronous motors with buried magnets. in Proc. 7th Int. Conf. Power Electron. Variable Speed Drives, London, U.K., 544–547. [24] Wikipedia Foundation Inc. (2006). Core loss, Eddy current, Hysteresis. Iron loss [serial online] [cited 2006 Oct 15]. [25] Pham, D. T., Ghanbarzadeh, A., Koç, E., Otri, S., Rahim, S., Zaidi, M., The Bees Algorithm – A Novel Tool for Complex Optimisation Problems. Manufacturing Engineering Centre, Cardiff University, Cardiff CF24 3AA, UK.

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[26] Pham, D. T., Ghanbarzadeh, A., Koç, E., Otri, S., Rahim, S., Zaidi, M., The Bees Algorithm – A Novel Toolfor Complex Optimisation Problems. Manufacturing Engineering Centre, Cardiff University, Cardiff CF24 3AA, UK. [27] Von Frisch, K., (1976). Bees: Their Vision, Chemical Senses and Language. (Revised edition) Cornell University Press, N.Y., Ithaca. [28] Seeley, T. D., (1996). The Wisdom of the Hive: The Social Physiology of Honey Bee Colonies. Massachusetts: Harvard University Press, Cambridge. [29] Camazine, S., Deneubourg, J., Franks, N. R., Sneyd, J., Theraula, G., Bonabeau, E., (2003). Self-Organization in Biological Systems. Princeton: Princeton University Press. [30] Bonabeau, E., Dorigo, M., Theraulaz, G., (1999). Swarm Intelligence: from Natural to Artificial Systems. Oxford University Press, New York. [31] Vahed Kalankesh, H., Sharifian, M. B. B., Feyzi, M. R., Multiobjective Optimization of Induction Motor Slot Design Using Finite Element Method. al of Biotechnology, 10(69), 15662-6. . [32] Bin Zhang, Xiuhe Wang, Ran Zhang, Xiaolei Mou* M. Ehsan 'Cogging Torque Reduction by Combining Teeth Notching and Rotor Magnets Skewing in PM BLDC with Concentrated Windings" IEEE Transaction on Electrical machines and systems,(IC EMS),03 VoU pp. 3 189 - 3 192 .Feb.2009 [33] Kwang-Kyu Han Dong-Yeup Lee Gyu-Hong Kang Ki- Bong Jang Heung-Kyo Shin Gyu-Tak Kim Dept. of Electr. Eng., Changwon Nat. Univ, Changwon "The design of rotor and notch to improve the operation characteristics in spoke type BLDC motor" IEEE Transaction on Electrical Machines and Systems(ICEMS). pp.3121-3125. Feb.2009 [34] R.P. Praveen, M.H. Ravichandran, V.T. SadasivanAchari, Dr. v.P. Jagathy Raj, Dr. G. Madhu, Dr. G.R. Bindu, and Dr. F. Dubas" Optimal Design of a Surface Mounted Permanent-Magnet BLDC Motor for Spacecraft Applications"IEEE Transaction on Emerging Trends in Electrical and Computer Technology (ICETECT). pp 413- 419. May 2011 [35] Y. Diinmezer and L. T. Ergene Informatics Institute, Istanbul Technical University, Istanbul, Turkey. "Cogging Torque Analysis of Interior-Type Permanent-Magnet Brushless DC Motor Used in Washers", ELECTROMOTION 2009 – EPE Chapter 'Electric Drives' Joint Symposium, 1-3 July 2009, Lille, France .. [36] PiotrBogusz, MariuszKorkosz& Jan Prokop" A Study of Design Process of BLDC Motor for Aircraft Hybrid Drive" IEEE Transaction on Industrial Electronics (ISlE). pp. 508 -513. June 2011 [37] G. Lacombe I , A. Foggial, Y. Marechall, X. Brunotte2, and P. Wendling3 USA "From General Finite-Element Simulation Software to Engineering-Focused Software:

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Example for Brushless Permanent Magnet Motors Design"IEEE TRANSACTIONS ON MAGNETICS, VOL. 43, NO. 4, APRIL 2007. [38] Parag R. Upadyay and K. R. Rajagopal, "FE analysis and CAD of Radial-Flux Surface Mounted Permanent Magnet Brushless DC Motors" IEEE Transactions on magnetic, Vol. 41 No. 10, October 2005. [39] Z. Q. Zhu and David Howe, "Influence of design parameters on cogging torque in Permanent Magnet Machines" IEEE Transactions on energy conversion, Vol. 15, No. 4, December 2000. [40] Min Dai, Ali Keyhani and Tomy Sebastian, "Torque ripple analysis of a PM Brushless DC motor using Finite Element Method" IEEE Transactions on energy conversion, Vol. 19, No. 1, March 2004. [41] Jinyun, K. T. Chau, C. C. Chan and J. Z. Jiang, "Design and analysis of a new Permanent Magnet Brushless DC Machine" IEEE Transactions on magnetics, Vol. 36, No. 5, September 2000. [42] P. R. Upadyay, K. R. Rajagopal and B. P. Singh, "Computer aided design of an Axial Field Permanent Magnet Brushless DC Motor for an electric vehicle" Journal of applied physics, Vol. 93, No. 10, 15 May 2003. [43] J. F. Gieras, “Comparison of high-power high-speed machines: cage induction versus switched reluctance motors,” IEEE AFRICON, vol. 2, pp.675-678, 1999. [44] M. Cheng, et al, “Design and analysis of a new salient permanent magnet motor,” IEEE Trans. Magnetics, vol. 37, no, 4, pp. 3012-3020, 2001. [45] Y. Liao, F. Liang and T. A. Lipo, “A novel permanent magnet motor with doubly salient structure,” IEEE Trans. Ind. Applic., vol. 31, no. 5, pp. 1069-1078, 1995. [46] S. F. Gorman, C. Chen, J. J. Cathey, “Determination of permanent magnet synchronous motor parameters for use in brushless DC motor drive analysis,” IEEE Trans. Energy Conversion, vol. 3, no. 3, pp. 674-681, Sept. 1988. [47] A. Cavagnino, et.al, “A comparison between the axial flux and the radial flux structures for PM synchronous motors,” IEEE Ind. Applic. Conference, thirty-Sixth IAS Annual Meeting, vol. 3, pp. 1611-1618, 2001. [48] S. Huang, et. al, “A comparison of power density for axial flux machines based on general purpose sizing equations,” IEEE Transaction on Energy conversion, Vol. 14, Issue 2 , pp. 185-192, June 1999. [49] S. Huang, J. Luo; F. Leonardi, and T.A Lipo, “A general approach to sizing and power density equations for comparison of electrical machines,” IEEE Transactions on Industry

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Applications, vol. 34, no. 1, pp. 92-97, Jan.-Feb. 1998. [50] D. Ishak, Z. Q. Zhu, and D. Howe, “Eddy-current loss in the rotor magnets of permanentmagnet brushless machines having a fractional number of slots per pole,” IEEE Transactions on Magnetics, vol. 41, no. 9, pp. 2462-2469, Sept. 2005. [51] P. Thelin, H. P. Nee, “Analytical calculation of the airgap flux density of PM synchronous motors with buried magnets including axial leakage, tooth and yoke saturations,” IEEE Conference on Power Electronics and Variable Speed Drives, no.475, pp. 281-223, 2000. [52] B. N., and Bolognani, S.: ‘Design techniques for reducing the cogging torque in surfacemounted PM motors’, IEEE Trans. on Ind. Appl., vol. 38, no.5, pp. 1259-1263, 2002. [53] F. Sahin, A. M. Tuckey, and A. J. A. Vandenput, “Design, development and testing of a high-speed axial-flux permanent-magnet machine,” IEEE Ind. Appl. Conf., vol. 3, pp.1640- 1647, 2001. [54] S. Huang, J. Luo; F. Leonardi, and T.A Lipo, “A general approach to sizing and power density equations for comparison of electrical machines,” IEEE Transactions on Industry Applications, vol. 34, no. 1, pp. 92-97, Jan.-Feb. 1998.

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Appendices

A. MATLAB Program for Design of a DC Machine

% For DC machine

Data from standard tables

% Variation of Maximum air gap flux density(Bg) & specific electric loading(q)with KW rating SKW1 = [5 10 20 50 100 200 500 750 1000 2000 3000 4000 5000 10000]; SBg = [.5753 .65 .70 .775 .82 .87 .915 .945 .96 .975 .995 1.01 1.02 1.04]; Sq1 = [15 17.5 19.5 25 27.5 31 35 37.5 40 43 47 48 49.5 51];

% Variation of average efficiency(effav) with KW rating

SKW2 = [0.25 1 3 10 25 50 100 300 500 1000]; effav = [0.55 0.79 0.83 0.87 0.89 0.90 0.907 0.92 0.92 0.92];

%Variation of field current(If1) & armature voltage drop(vd) SPaXrpm =[ 10^4 2*10^4 4*10^4 6*10^4 8*10^4 10^5 2*10^5 4*10^5 6*10^5 8*10^5 10^6]; Svd = [ 6.5 6 5.2 5 4.8 4.7 4 3.6 3.2 2.9 2.8]; SIf1 =[ 2.4 2 1.7 1.5 1.3 1.2 0.8 .51 0.4 0.33 0.29]; % Variation of leakage coefficient(LC)w.r.t KW rating SKW3 = [ 50 100 200 500 1000 1500 2000]; SLC = [1.25 1.22 1.20 1.18 1.16 1.14 1.12]; % Variation Carter's coefficient(CC) for semi closed and open slots Ratio1 =[0 1 2 3 4 5 6 7 8 9 10 11 12]; CC1 = [0 .18 .33 .45 .53 .6 .66 .71 .75 .79 .82 .86 .89];%Semiclosed Slots CC2=[0 .14 .27 .37 .44 .5 .54 .58 .62 .65 .68 .69 .7]; %Open Slots % Variation of flux density(BB)& ampere turn for different types of materials for yoke, pole and teeth BB = [0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2]; Ha = [50 65 70 80 90 100 110 120 150 180 220 295 400 580 1000 2400 5000 8900 15000 24000]; H = [20 30 40 50 70 90 120 130 160 200 250 320 480 850 2200 4400 9000 16000 25000 38000]; Hcs = [180 270 370 440 520 590 670 750 820 920 1030 1230 1600 2200 3200 4800 7700 13000 22000 40000]; % Variation of flux density(SBt) & ampere turn for teeth SBt = [1.8 1.9 2 2.1 2.2 2.3 2.4 2.5]; SATm = [9 12 20 31 51 80 113 155]; % for Ks = 2.0 (for teeth) % Variation windage & friction loss percentage w.r.t armature peripheral speed SVa = [10 20 30 40 50]; % Armature peipheral speed SLP = [0.2 0.4 0.6 0.9 1.2]/100; % Loss percentage

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%Inputs

KW = input('Enter rated output, KW =');

N = input('Enter rated speed, N =');

V = input('Enter rated voltage, V =');

PAbyPP = input('Enter PAbyPP ratio, PAbyPP =');

LbyPA = input('Enter LbyPA ratio, LbyPA =');

MT = input('Type of machine:\nFor Gen Enter 0\nFor Motor Enter 1');

WT = input('Winding type:\nFor Progressive Enter 0\nFor Retrogressive Enter 1');

TPM = input('Types of machine:\nFor Non-interpolar machine Enter 0\nFor Interpolar machine Enter 1');

%Assumptions

% Pole arc to pole pitch ratio is assumed 0.7

% A square pole face is assumed i.e Length to pole arc ratio(LbyPA) = 1

%Assumed flux density in the armature core(Bc) = 1.25 wb/m2 varies between 1.0-1.5 wb/m2.

% The flux density in the pole body(Bp)can be taken between 1.2-1.7 wb/m2

%Bp lies between 1.6-1.7wb/m2 for laminated poles of medium and large size machines.

% Assumed Permissible loss per m2(qf) of cooling surface excluding the top and bottom surfaces = 700 %W/m2.

% The flux density(By) in cast steel yokes is normally equal to 1.2wb/m2

% The current density in the interpole winding should be between 2.5 to 4 A/mm2;

% Clearance between brushes(c) is normally assumed 0.5 cm depends upon the construction of brush holder.

%Clearance allowed for staggering the brushes genrally lies between 1cm for small machines to 3 cm for %large

machines

%Clearance allowed for end play usually between 1-2.5 cm

%Clearance for riser 2-4 cm

% Height of lip(h4) = 1;

%Height of wedge(h3) = 4;

% <-------1) Design of Main Dimensions------>

Bg = interp1 (SKW1, SBg, KW, 'spline'); % Maximum gap flux density

q=interp1 (SKW1, Sq1, KW, 'spline')*1e3; % Ampere conductors per meter

eff = interp1(SKW2, effav, KW, 'spline');% efficiency considered

if MT == 0

Pa = KW/eff;

else if MT == 1

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Pa = (1+2*eff)/(3*eff)*KW; % Power developed by armature(Neglecting rotational losses)

end

end

ns = N/60; % Speed in rps

PaXrpm = Pa*N;

Bav = PAbyPP*Bg; %Average air gap flux density

C0 = pi^2*Bav*q*1e-3; % Output coefficient

DsqL = Pa/(C0*ns); % D2L value

% Slection of Number of Poles

Ps = 2:2:12; Np= length(Ps); for i=1:Np fs(i)=(Ps(i)*ns)/2; end m=1; for i=1:Np if fs(i)>=25 if fs(i)<=50 Pf(m)=Ps(i); m=m+1; end end end

Ia1=(KW*1000)/V; Ib1=(2*Ia1)./Pf; m=m-1; for i=m:-1:1 if Ib1(i)<=400 P=Pf(i); end

end f = (P*ns)/2; D1 = DsqL^(1/3)*(P/(pi*PAbyPP*LbyPA))^(1/3); D = round(D1*100); L1 = DsqL*1e6/D^2; L = round (L1); PP = (pi*D)/P; % Pole pitch Parc = PAbyPP*PP; % Pole arc Va = pi*D*ns*1e-2; % Peripheral speed of armature Li = Ki*L; % Net iron length fprintf ( 'Design of %3d KW,%3d V, Level compound DC Generator\n\n' ,KW, V);

fprintf ( '<-------1) Design of Main Dimensions------>\n\n');

fprintf ('Power developed in armature(Pa) = %4.1f KW\n', Pa);

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fprintf ('Average air Gap Flux-density(Bav) = %4.2f wb/m2\n', Bav);

fprintf ('Specific Electric Loading (q) = %6.0f ac/m\n', q);

fprintf ('Output Coefft (C0) = %4.0f\n',C0);

fprintf ('DsqL Value = %6.3f m3\n', DsqL);

fprintf ('Number of Poles(P) = %d\n', P);

fprintf ('Armature diameter(D) = %4.0f cm\n', D);

fprintf ('Armature Length(L) = %4.0f cm\n', L);

fprintf ('Frequency(hz) = %4.0f hz (Range :25to50)\n', f);

fprintf ('Polearc to PolePitch = %4.2f (Range:0.67 to 0.70)\n',PAbyPP) ;

fprintf ('Peripheral speed of armature(Va) = %4.2f(<= 30) m/s\n', Va);

fprintf ('Peak airGap Flux-density(Bg) = %4.3f wb/m2\n', Bg); fprintf ('PolePitch(PP) = %4.1f cm\n', PP); fprintf ('pole arc = %4.0f cm\n', Parc); fprintf ('Net iron length(Li) = %4.0f cm\n', Li); %<-------2)Design of Armature-Winding-------->

IL = (KW*1000)/V; % Full load current Vd = interp1(SPaXrpm, Svd, PaXrpm, 'spline')/100; If1 = interp1(SPaXrpm,SIf1, PaXrpm, 'spline')/100*IL; if MT == 0 E = (1+Vd)*V; % For Generator Ia = IL+If1; % Armature current else if MT == 0 E = (1-Vd)*V; % For Motor Ia = IL-If1; end end

if Ia > 400 a=P; fprintf('Lap winding is considered\n'); else if Ia < 400 a = 2; fprintf('Wave winding is considered'); end end Iap = Ia/a; fi = Bav*PP*L*1e-4; Z1 = (E*a)/(fi*ns*P); % Number of slots selection %Slot pitch lies between 2.5 cm to 3.5 cm Smin1 = round((pi*D)/3.5); Smax1 = round((pi*D)/2.5);

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% Slots per pole should lie between 9 and 16 Smin2 = P*9; Smax2 = P*16; if Smin1 > Smin2 Smin = Smin1; else Smin = Smin2; end if Smax1 > Smax2 Smax = Smax2; else Smax = Smax1; end range = Smin:1:Smax; N=length(range); j=1; k=1; for i=1:N if rem(range(i),P)==0 LWS(k)=range(i); k=k+1; else WWS(j)=range(i); j=j+1; end

end if a == P RF = LWS.*0.7./P; else if a == 2 RF = WWS.*0.7./P; end end M=length(RF); for m=1:M if RF(m)+0.5==round(RF(m)) S1=LWS(m); S2 = LWS(m-1);

end

end

Zs1 = Z1/S1; Zsf = floor(Zs1); Zfr = Zs1 – Zsf; if (Zfr >= 0.85 && rem(Zsf,2) ==1) S = S1;

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Zs = ceil(Zs1); else if (Zfr <=0.15 && rem(Zsf,2) ==0) S = S1; Zs = Zsf; else S = S2; Zs = floor(Z1/S2); end end Z = Zs*S; Ys = (pi*D)/S; % Slot pitch % No. of coils calculation Cmin = round((E*P)/15); % Minimum number of coils required Tc2=0; for Cmin = Cmin :Z/2 Tc=Z/(2*Cmin); if fix(Tc)==Tc if rem(S,Tc)==0 Tc2=Tc; C = Cmin; break; end end end Ncs = 2*C; % Number of coil sides u = (2*C)/S; % Coil sides per slot Tc = Z/(2*C); % Number of turns per coil SL = (Ia/a)*Zs; % Slot loading % Winding layout if a == P for K = 1:1:3 yb1 = (2*C)/P+K; yb2 = (2*C)/P+K; if round ((yb1-1)/u) == (yb1-1)/u && rem(yb1,2)==1; yb = yb1; else if round ((yb2-1)/u) == (yb2-1)/u && rem(yb2,2)==1; yb = yb2; end end end % Progressive or Retrogressive consideration if WT == 0 yc = +1; Y = +2;

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yf = yb-Y; else if WT == 1 yc = -1; Y = -2; yf = yb-Y; end end % Equalizer connection Yeq = (2*C)/P; %Equpotential pitch m = C/2; %Assuming 8 equilizer rings Yph = (2*C)/(m*P); %Phase pitch end if a == 2 for k = 0.01 :0.01:1 yb11 = (2*C)/P+k; yb1 = round((yb11*100))/100; yb12 = (2*C)/P -k; yb2 = round((yb12*100))/100; if round((yb1-1)/u) == (yb1-1)/u && rem(yb1,2) == 1 yb = yb1; else if round((yb2-1)/u) == (yb2-1)/u && rem(yb2,2) == 1 yb = yb2; end end

end

if WT == 0 yc1 = (C+1)/(P/2); if round (yc1)== yc1 yc = yc1; end end if WT == 1 yc2 = (C-1)/(P/2); if round (yc2) == yc2 yc = yc2; end end Y = 2*yc; yf = Y-yb; end % Design of slot Iz = Ia/a; % Current in each conductor Az1 = Iz/Ja; % Area of each armature conductor calculated

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fprintf ('Calculated area of armature conductor(Az1) = %4.2fmm2\n', Az1); if Az1 <= 10 d1 = sqrt((4*Az1)/pi);

fprintf('Calculated dimeter of conductor(d1) = %4.2fmm\n', d1); d = input('Enter conductor diameter, d ='); Az = (pi*d^2)/4; Kss = 0.35; % Slot space factor else if Az1 > 10 Az = input('Enter Area of conductor, Az = '); dz = input('Enter depth of conductor, dz = '); wz = input('Enter width of conductor, wz = '); Kss = 0.37; %Slot space factor end end As = Az/Kss; % Area of slot if TPM ==1 %(NOninterpolar machine) dsbyws = 3.5; else if TPM == 2 %(Interpolar machine) dsbyws = 3; end end ws = sqrt((As/dsbyws)); % Width of slot = ws in mm

ds = dsbyws*ws; % depth of slot = ds in mm

D1b3 = D-4/3*ds*1e-1; % Diameter of armature teeth at 1/3 height from root

sp1b3 = (pi*D1b3)/S; % slot pitch at 1/3 height of root of teeth

wt1b3 = sp1b3-ws*1e-1; % Width of teeth at 1/3 height of teeth

At1b3 = PAbyPP*S/P*Li*wt1b3*1e-4; % Cross sectional area of teeth

Bt1b3 = fi/At1b3; % Flux density in teeth at 1/3 height

Lmta = (2*L + 2.3*PP+ 4*ds*1e-1)*1e-2; %Length of mean turn of armature winding

Ra = Z/2*(0.021*Lmta)/(a^2*Az); %Resistance of armature

Pca = Ia^2*Ra; % Copper loss in armature = Pcua

fprintf (' <-------2) Armature-Winding-------->\n\n') ;

fprintf ('Induced emf(E) = %4.0f V\n', E);

fprintf ('Armature current(Ia) = %4.0f\n', Ia);

fprintf ('Current per parallel path (Iap) = %4.0f(<=200 A)\n', Iap);

fprintf ('Number of parallel paths(a) = %d\n', a);

fprintf ('Number of Slots(S) = %3.0f\n', S);

fprintf ('SlotPitch(Ys) = %4.2f (range:2.5 to 3.5)\n',Ys) ;

fprintf ('Number of coil sides per slot(us) = %4.0f\n', u);

fprintf ('Conductors per Slot(Zs) = %4.0f\n', Zs);

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fprintf ('Total Armature Conductors(Z) = %4.0f\n', Z);

fprintf ('Flux per Pole (Wb/m2) = % 6.4f\n', fi);

fprintf ('Turns per coil(Tc) = %d\n', Tc);

fprintf ('Coil sides per slot(us) = %d\n', u);

fprintf ('Number of armature coils = %d\n', C);

fprintf ('Number of coil sides = %d\n',Ncs);

fprintf ('Conductor cross section = %3.0f X %3.0f cm\n', dz,wz);

fprintf ('Area of conductor (Az) = %4.1f mm2\n', Az);

fprintf ('Slot depth(ds) = %4.1f mm\n', ds);

fprintf ('Slot width(ws) = %4.1f mm\n', ws);

fprintf('flux density at 1/3 height, Bt1b3 = %4.2f(< 2.1wb/m2)\n', Bt1b3);

fprintf ('Length of mean turn(Lmta) = %4.2f m\n',Lmta);

fprintf ('Armature reistance(Ra) = %4.4f ohm\n', Ra);

fprintf ('Armature copper loss (Pcua) = %4.0f W\n\n', Pca);

% <-------3) Design of field system and Ampere turn calculation -------->

ATap = (Ia*Z)/(a*2*P); % Armature mmf per pole if TPM ==1 %(NOninterpolar machine gamma = 1.4; else if TPM == 2 %(Interpolar machine) gamma = 1.3; end end ATfl = gamma*ATap; LC = interp1(SKW3, SLC, KW, 'spline'); % Leakage coefficient

fip = LC*fi; % Flux in pole

Bp = 1.5;

Ap = fip/Bp; % Area of pole

Lp = L-1; %Length of pole

wp = Ap*1e4/Lp; % width of pole

df = (Parc-wp)/2; % Radial depth of field coil

Kfs1 = 0.6;% Field space factor = Kfs(Initially assumed)

qf = 700;

atpm = 1e4*sqrt(qf*Kfs1*(df*1e-2)); % Ampere turns for meter height of field winding

hf = (ATfl/atpm)*1e2; % Axial Height of field coil

% Assuming height of pole shoe hps = 0.01*hp(varies 0.01-0.015 of hpl)

hpl = (hf + 0.1*PP)/0.99; % Height of pole = hp ATg1 = 0.68*ATap; % Assuming airgap mmf (ATg) varies (60-70)% of

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% Armature mmf per pole

kg1 = 1.15; % Gap contraction factor(initially assumed)

Lg = ATg1/(8*1e5*Bg*kg1)*1e2;

w0 = ws; % For parallel sided slots

X1=w0/(Lg*10);

Kcs=interp1(Ratio1,CC1,X1, 'spline');% Carter's coefficient

Kgs = Ys/(Ys-(Kcs*(w0/10))); % Gap contraction factor for slots

Kg = Kgs; %Gap contraction factor

ATg = 8*1e5*Bg*Kg*Lg*1e-2; % Air gap mmf ATg = 800,000*Bg*kg*Lg

atat = interp1(SBt, SATm, Bt1b3, 'spline')*1e3;

ht = ds; % height of teeth(ht) = depth of slot(ds)

ATt = atat*ht/1e3;

fic = fi/2;

Bc = 1.25;

Ac = fic/Bc; % Cross sectional area of armature core

dc = Ac*1e4/Li; % depth of armature core

Di = D-2*(ds/10+dc);% Internal diameter of armature = Di

Lfpc = (pi*(D -2*ht/10-dc))/(2*P); % Mean length of flux path in core atac = interp1 (BB, Ha, Bc, 'spline'); ATc = atac*Lfpc/1e2; atp = interp1(BB, H, Bp, 'spline'); ATp = atp*hpl/1e2; fiy = (fi*LC)/2; % Flux in the yoke FIy = half of pole flux By1 = 1.2; %flux density in the yoke = 1.2 wb/m2 (Assumed initially) Ay = fiy/By1; % Area of yoke Ly = Lp + 2*8; % yoke extends by 8 cm on each side of the pole dy = Ay*1e4/Ly; % depth of yoke Ay =Ly*dy*1e-4; By = fiy/Ay; Dy = D+2*(Lg+hpl+dy); %outer diameter of yoke = Dy aty = interp1(BB, Hcs, By, 'spline'); Lfpy = (pi*(D+2*Lg+2*hpl+dy))/(2*P); % Length of flux path in yoke ATy = aty*Lfpy/1e2; AT = ATg+ATt+ATc+ATp+ATy; %Total mmf per pole fprintf (' <-3) Design of field system and Ampere turn calculation->\n\n');

fprintf ('Armature mmf per pole(ATap) = %4.0f A\n', ATap);

fprintf ('Estimated field mmf = %4.0f A\n', ATfl);

fprintf ('mmf per meter of coil height(atpm) = %4.0f A\n', atpm);

fprintf ('Height of field winding(hf)= %4.0f cm\n', hf);

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fprintf ('Height of pole(hp) = %4.0f cm\n', hpl);

fprintf ('mmf of air gap(ATg) = %4.0f A\n', ATg);

fprintf ('Gap expansion factor(Kg) = %4.2f\n', Kg);

fprintf ('Length of air gap(Lg) = %4.1f cm\n', Lg);

fprintf ('Flux density in teeth at 1/3 height = %4.2f wb/m2\n', Bt1b3);

fprintf ('mmf of teeth(ATt) = %4.2f A\n', ATt);

fprintf ('depth of core(dc) = %4.2f cm\n', dc);

fprintf ('Internal diameter of armature(Di) = %4.0f cm\n', Di);

fprintf (' Area of core(Ac) = %4.2f m2\n', Ac);

fprintf (' Flux density in core(Bc) = %4.2f wb/m2\n', Bc);

fprintf ('Length of flux path in core = %4.2f cm\n', Lfpc);

fprintf (' MMF for core(ATc) = %4.2f A\n', ATc);

fprintf (' Area of pole (Ap)= %4.2f m2\n', Ap);

fprintf (' Width of pole (wp) = %4.1f cm\n', wp);

fprintf (' Length of pole(Lp) = %4.1f cm\n', Lp);

fprintf (' Flux density in pole(Bp) = %4.1f wb/m2\n', Bp);

fprintf (' MMF of pole(ATp) = %4.0f A\n', ATp);

fprintf (' Depth of yoke(dc) = %4.2f cm\n', dy);

fprintf (' Length of yoke(Ly) = %4.2f cm\n', Ly);

fprintf (' Area of yoke(Ay) = %4.3f m2\n', Ay);

fprintf (' Flux density of yoke(By) = %4.2f wb/m2\n', By);

fprintf ('Length of flux path in yoke = %4.2f cm\n', Lfpy);

fprintf (' MMF for yoke = %4.0f\n', ATy);

fprintf ('Outer diameter of yoke(Dy) = %4.0f cm\n', Dy);

fprintf ('Total mmf per pole(AT) = %4.0f A\n\n', AT);

% <--4) Design of Shunt & series field Windings -->

AT0 = 0.85*ATfl; % Mmf required at no load ATsh1 = AT0; Vsh = 0.8*V; % Voltage across the shunt field winding Ef = Vsh/P; % Voltage across each shunt field coil Lmtf = 2*(Lp+wp)+ pi*df+4; %Length of mean turn of field winding Ash1 = (0.021*ATsh1*Lmtf*1e-2)/Ef; %Area of shunt field conductor fprintf('Calculated area of shunt field conductor(Ash1) = %4.2fmm2\n', Ash1); d1 = sqrt((4*Ash1)/pi); d =input('Enter diameter from standard table, d ='); di = input('Enter diameter of the insulated conductor,di = '); %di = 2.375; %Diameter of the insulated conductor(di) = 2.375 mm

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Ash = (pi*d^2)/4;

Kfs = 0.785*(d/di)^2; %field space factor for field winding

Nd = round((df*10)/di); %Number of layers depth wise;

Nh = round((hf*10)/di); %Number of layers height wise

Tsh = Nd*Nh; %Number of shunt field turns

Rsh = (0.021*Lmtf*Tsh*1e-2)/Ash;

Ish = Ef/Rsh; %shunt field current

If = Ish;

ATsh = Ish*Tsh; % MMf provided by shunt field

Qf = Ef*If; % Copper loss in each field coil

DSF = 2*Lmtf*(hf+df)*1e-4; % Cooling surface of each field coil

CCf = 0.16/(1+0.1*Va); % Cooling coefficient

Trf = (Qf*CCf)/DSF; % Temperature rise of shunt field

Jf = Ish/Ash;

Pcsh = V*Ish; % Copper loss in shunt field

% Design of series field ATse = ATfl - AT0; % mmf produced by the series field winding at full load Actually the current through the %series field winding is 80% of Ia and rest 20% is through shund field winding Ise = 0.8*Ia; Tse1 = ATse/Ise; Tse = round(Tse1); Ase1 = Ise/Jse; hse1 = Ase1/(df*1e1); hse = ceil(hse1); Ase = df*hse*10; Rse = 0.021*P*Tse*Lmtf*1e-2/Ase; Pcse = Ise^2*Rse; fprintf ('<--4) Design of Shunt & series field Windings -->\n\n');

fprintf ('Number of shunt field turns(Tf) = %4.0f\n', Tsh);

fprintf ('Area of shunt field conductor(Ash) = %4.2fmm2\n', Ash);

fprintf ('Depth of winding(df) = %4.2f cm\n', df);

fprintf ('Height of field winding(hf) = %4.2fcm\n', hf);

fprintf ('Resistance of each coil(Rsh) = %4.2f ohm\n', Rsh);

fprintf ('Shunt Field current(Ish) = %4.2fA\n', Ish);

fprintf ('mmf provided by shunt field winding(ATsh) = %4.0fA\n', ATsh);

fprintf ('Copper loss in shunt field winding(Pcsh) = %4.2fW\n', Pcsh);

fprintf ('Cooling surface per coil(DSF) = %4.2fm2\n', DSF);

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fprintf ('Temperature rise of field winding(Trf) = %4.2f0C\n', Trf);

fprintf ('Current density(Jsh) = %4.2fA/mm2\n', Jsh);

fprintf ('Series field mmf(ATse) = %4.0fA\n', ATse); fprintf ('Number of series field turns(Tse) = %4.2f\n', Tse); fprintf ('Conductor area (Ase) = %4.2fmm2\n', Ase); fprintf ('Resistance of series field (Rse) = %4.2fohm\n', Rse); fprintf ('Copper loss in series field winding(Pcs) = %4.0fW\n\n', Pcse); % <------5) Design of Commutator and Brushes----->

%Pb = Brush pressure and lies between 1000 and 1500 kg / m2

Dc = 0.80*D; %Diameter of commutator(Dc) = 0.8 times of armature diameter(D) Vc = pi*Dc*ns*1e-2; %Peripheral speed of commutator Ncs = C; %Number of commutator segments (Ncs)= No. of armature coils (C) pitC = pi*Dc/C; % Commutator segment pitch = pitC Ib = (2*Ia)/P; % Current per brush arm TB = input('Type of Brush:\nFor NC Enter 0\nFor EG Enter 1\nFor SG Enter 2\nFor CC Enter 3'); if TB == 0 % Normal carbon Jc = 5.5; Vdc = 2; mu0 = 0.23; Pb = 1200; else if TB == 1 % Electro graphitic Jc = 8.5; Vdc = 1.75; mu0 = 0.23; else if TB == 2 % Soft graphitic Jc = 9.0; Vdc = 1.6; mu0 = 0.18; else if TB == 3; % Copper carbon Jc = 15.5; % Current density Vdc = 0.3; % Brush contact drop mu0 = 0.16; % Brush friction loss end end end end Ab1 = Ib/Jc; %Area of brushes per brush arm % Current carried by each brush shouldn't exceeds 70 A

nbmin = round(Ib/70); %Minimum number of brushes fprintf('minimum number of brushes per spindle(nbmin) = %4.0f\n', nbmin); nb = nbmin+1; ab1 = Ab1/nb; % Area of each brush tbmax = 4*pitC; % Maximum Thickness of brush fprintf('Maximum thickness of brush(tbmax) = %4.2f\n', tbmax);

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tb = floor(tb); wb = ab1/tb; %Width of each brush ab = tb*wb;% Area of each brush Ab = nb*ab;% Area of brushes in each brush arm Atb = P*Ab; % Total area of contact of brushes Lc = nb*(wb + 0.5)+2+2+3; % Length of commutator = Lc Pbc= Vdc*Ia; % Brush contact loss Pbf= mu0*Pb*Atb*Vc*981*1e-6; % Brush friction loss = BFL Ptc= Pbf + Pbc; % Total losses in commutator = Ptc Sm = (pi*Dc*Lc)/1e4; %Heat dissipating surface of commutator Cm = 0.02/(1+0.1*Vc); % Cooling coefficient of commutator(table 3.6) Trc = (Ptc*Cm)/Sm; % Temperature rise of commutator fprintf ( '<------5) Design of Commutator and Brushes----->\n\n') ;

fprintf ('Commutator Diameter(Dc) = %4.0f cm\n', Dc);

fprintf ('No. of commutator segments(CS) = %4.0f\n', Ncs);

fprintf ('Commutator pitch(pitC) = %4.2f(permissible>0.4cm)\n', pitC);

fprintf ('Peripheral speed of commutator(Vc)= %4.2f (Max = 20m/s)\n', Vc);

fprintf ('Current density in brushes(Jb) = %4.0fA/cm2\n', Jc);

fprintf ('Current per brush arm(Ib) = %4.0fA\n', Ib);

fprintf ('Area of brushes per arm(Ab) = %4.0fcm2\n', Ab);

fprintf ('Number of brushes per arm(nb) = %4.0f\n',nb);

fprintf ('Area of each brush(ab) = %4.0f cm2\n', ab);

fprintf ('Thickness of each brush(tb) = %4.1f cm\n', tb);

fprintf ('Width of each brush(wb) = %4.2fcm\n', wb);

fprintf ('Length of commutator(Lc) = %4.0f cm\n', Lc);

fprintf ('Brush contact loss(Pbc) = %4.0f W\n', Pbc);

fprintf ('Brush friction loss(Pbf) = %4.2f W\n', Pbf);

fprintf ('Total commutator Losses(Ptc) = %4.0f W\n', Ptc);

fprintf ('Temp-Rise of commutator (deg) = %4.1f(Max. perm = 50)\n\n', Trc);

% <--6) Design of Interpoles/Compensating-Pole-Winding -->

alpha = C/P - 1/2*(yb-1); %for full pitched winding alpha = 0 wc = (tb+(u/2-a/P+ alpha)*pitC)*(D/Dc); % width of commutating zone Lgi = 1.5*Lg; % Length of air gap under the interpoles (Lgi)is %taken as 1.5 times that under the main poles wip = wc - (1.5*Lgi);% Width of interpole Lip = 0.5*L;% Length of interpole (Lip) = (0.6 to 0.8)L h4 = 1; % Height of Lip h3 = 4; % Height of wedge h1 = ds - (h3+h4); % Height of conductor portion % Specific slot permeance = LDS

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LDS = 4*pi*1e-7*(h1/(3*ws) + (2*h3)/(ws+w0) + h4/w0); % Tooth top specific permeance = LDT % Slot opening = w0 LDT = (4*pi*1e-7*wip)/(6*Lgi); % Tooth top specific permeance Le = 0.3*PP*1e-2 + 1.25*ds*1e-3; % Projection of coil outside the core % Length of overhang of one coil side = L0 L0 = 2* (sqrt ((PP/2)^2 + (Le*1e2)^2)); % Periphery of all the coil sides in one layer = b0 b0 = 2*(dz+4*wz)*1e-2; %Periphery of one coil side in one layer; % Specific permeance = LD0 LD0 = (L0/L)*((0.23*log10(L0/b0))+ 0.07)*1e-6; % Total specific permeance = LD LD = LDS + LDT + LD0; tc = (tb+(u/2 - a/P + alpha)*pitC)/(Vc*1e2);

% Flux density under interpole = Bgi Bgi = 2*Zs*(Ia/a)*LD*(L/Lip)*1/(Va*tc); % mmf of interpole = ATi Kgi = Kg; ATip1 = ATap + 8*1e5*Bgi*Kgi*Lgi*1e-2; Tip1 = ATip1/Ia; Tip = round(Tip1); ATip = Tip*Ia; Jip = 2.4; Aip = Ia/Jip; %Area of interpole winding conductor Lmtip = 2*(wip+Lip)+4*df+4; Rip = (0.021*P*Tip*Lmtip)/Aip*1e-2; Pcip = Ia^2*Rip; % Copper loss in interpole winding fprintf (' <--6) Design of Interpoles/Compensating-Pole-Winding -->\n\n');

fprintf ('Width of commutating zone(wc) = %4.2f cm\n', wc);

fprintf ('Length of interpole air gap(Lgi) = %4.2f cm\n', Lgi);

fprintf ('Width of interpole(wip) = %4.2f cm\n', wip);

fprintf ('Length of interpole(Lip) = %4.2f cm\n', Lip)

fprintf ('Flux density under interpole(Bgi) = %4.2f wb/m2\n', Bgi);

fprintf ('mmf for interpole(ATip) = %4.0f A\n', ATip);

fprintf ('Number of turns on each interpole(Tip) = %4.0f\n', Tip);

fprintf ('Cross sectional area of interpole winding(Aip) = %4.2f mm2\n', Aip);

fprintf ('Resistance of winding(Rip) = %5.3f ohm\n', Rip);

fprintf ('Copper loss in interpole winding = %4.0f W\n\n', Pcip);

% <--7) Losses and overall performance of the machine -->

Pbrg = interp1(SVa, SLP, Va, 'spline')*KW*1000; % friction and windage losses Ptbrg = (Pbf+Pbrg)/1e3; %Total friction and windage losses bmt = (pi*(D-ds/10))/S - ws/10; % Mean width of teeth

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Wt = 7.8*1e3*S*Li*bmt*ds/10*1e-6; %Total weight of armature teeth

Physt = 0.06*f*Bt1b3^2;

Peddyt = 0.008*f^2*Bt1b3^2;

Piteeth = Physt + Peddyt;

Pit = Wt*Piteeth; % Total iron loss in teeth

Dmc = D-dc; % mean diameter of core

Wc = 7.8*1e3*pi*Dmc*Li*dc*1e-6; % Total weight of armature core

Physc = 0.06*f*Bc^2;

Peddyc = 0.005*f^2*Bc^2;

Picore = Physc+Peddyc; % Iron loss in core per kg;

Pic = Wc*Picore; % Total iron loss in core

% Total iron loss(Pi) = iron loss in teeth (Pit)+ iron loss in core(Pic)

Pi = (Pit+Pic)/1e3; % Total iron loss = Pi

% Pulsation loss assumed to be 30% of total iron loss

Ppl = 0.3*Pi;% Pulsation loss = Ppl

% Total copper loss(Pcu) = copper loss in armature winding(Pca)+copper loss in shunt field

winding(Pcsh)%%+Copper loss in series fieldwinding(Pcse)+ Loss in interpole winding(Pcip)+Brush contact

loss(Pbc)

Pcu = (Pca+Pcsh+Pcse+Pcip+Pbc)/1e3; % Total copper loss (Pcu) in KW

% Stray load loss is assumed to be 1% of output

Psl = 0.01*KW;

%Total losses(Ptl) =Total friction and windage loss(Pbrg)+ Net iron

%loss(Pi)+Net copper loss(Pcu)+Pulsation loss(Ppl)+Stray load loss(Psl)

Ptl = Ptbrg+Pi+Pcu+Ppl+Psl; % Total loss at full load = Ptl

Eff = KW/(KW+Ptl); % Efficiency of the machine

S0 = pi*D*L*1e-4; % Out side cylindrical surface

C01 = 0.015/(1+0.1*Va); % Cooling coefficient

LP1 = S0/C01; % Loss dissipated per 0C

Si = pi*Di*L*1e-4; %Inside cylindrical surface

Vai = Va*(Di/D);% Peripheral speed

C02 = 0.015/(1+0.1*Vai);

LP2 = Si/C02; % Loss dissipated per 0C

TLD = LP1+LP2;% Total loss dissipated per degree centigrade

%Total loss to be dissipated(TL) = iron loss including pulsation

%loss(Pi+Ppl)+stray load loss(Psl)+Copper loss in embedded portion

TL = (Pi+Ppl+Psl)*1e3+((2*L)/(Lmta*1e2))*Pca; %Temperature rise of machine = Trm

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Trm = TL/TLD; fprintf ('<--7) Losses and overall performance of the machine -->\n\n');

fprintf ('Total copper loss(Pcu) = %4.2f KW\n', Pcu);

fprintf ('Total iron loss(Pi) = %4.2f KW\n', Pi);

fprintf ('Pulsation loss(Ppl) = %4.2f KW\n',Ppl);

fprintf ('Friction and windage loss(Ptbrg) = %4.2f KW\n', Ptbrg);

fprintf ('Stray loadf loss(Psl) = %4.0fKW\n', Psl);

fprintf ('Toal Losses Ptl = %5.0f KW\n', Ptl);

fprintf ('Efficiency at full load = %5.2f \n', Eff);

fprintf ('Temperature rise = %4.2f 0C\n', Trm);

fprintf (' <----------------End--------------------->\n\n');

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B. MATLAB Program for design of Induction Motor

% Induction motor

% Data from Standard Tables

% Variation of Specific magnetic loading(Bav) & specific electric loading(q)w.r.t KW rating

SKW4 = [1 2 5 10 20 50 100 500]; SBav = [0.35 0.38 0.42 0.46 0.48 0.50 0.51 0.53]; Sq = [16e3 19e3 23e3 25e3 26e3 29e3 31e3 33e3]; % Variation of Power factor(pf) & efficiency(eff) w.r.t KW rating SKW5 = [5 10 20 50 100 200 500]; SPF = [0.82 0.83 0.85 0.87 0.89 0.9 0.92]; SEFF = [0.83 0.85 0.87 0.89 0.91 0.92 0.93]; % Variation of current density for sq. cage & slip ring IM w.r.t diameter SD = [10 15 20 30 40 50 75 100]; SJsq = [4 3.8 3.6 3.5 3.5 3.5 3.5 3.5]; SJsr = [3.8 3.6 3.4 3.3 3.2 3.2 3.2 3.2]; % Variation of carter's coefficient w.r.t ratio of slot opening and air gap length R2 =[0 1 2 3 4 5 6 7 8 9 10 11 12]; CC3 = [0 .18 .33 .45 .53 .6 .66 .71 .75 .79 .82 .86 .89];%Semiclosed Slots CC4 =[0 .14 .27 .37 .44 .5 .54 .58 .62 .65 .68 .69 .7]; %Open Slots % Variation of F&W loss percentage with KW rating

SKW6 = [0.75 3.7 7.5 37 75 150]; FWLP = [5.5 3.5 2.7 1.5 1.2 1];% F&W loss percentage with output %Assumptions

Stator winding factor is initially assumed to be 0.955 slot opening for stator slots Ws0 = 3 mm Slot opening for rotor slots Wr0 = 2 mm Height of Lip = 3 mm Height of wedge = 1 mm Flux density in the stator core is assumed to be 1.2 Wb/m2 Flux density in rotor core is assumed to be same as stator core

% (1) <-----------Main Dimensions----------------------->

Bav =interp1(SKW4, SBav, KW, 'spline'); % Specific magnetic loading q =interp1(SKW4, Sq, KW,'spline'); % Specific electric loading pf = interp1(SKW5, SPF,KW, 'spline'); % Power factor eff = interp1(SKW5,SEFF,KW, 'spline'); % Efficiency

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ns = N/60; P = (2*f)/ns; % No. of poles Q = KW/(pf*eff);%KVA input Kw = 0.955; %Stator winding factor(Assumed initially) C0 = 11*Kw*Bav*q*1e-3; % Output co-efficient = C0 DsqL = Q/(C0*ns); L1 = sqrt(DsqL/(0.135*P)^2); L = round(L1*100); D1 = sqrt(DsqL/(L*1e-2)); D = round(D1*100); PP = pi*D/P; LtoPP = L/PP; v = pi*D*1e-2*ns; Li = ki*L; % Net iron length

fprintf ( 'Design of %3d KW,%3d V, 3phase sq. cage IM\n\n' ,KW, V);

fprintf('Rated output = %4.0fKW\n', KW);

fprintf('Line voltage(V) = %4.0fV\n', V);

fprintf('Frequency(f) = %4.0fhz\n', f);

fprintf('Number of phases = %4.0f\n', m);

fprintf('Efficiency(eff) = %4.2f\n',eff);

fprintf('Power factor(pf) = %4.2f\n', pf);

fprintf('Number of poles(P) = %4.0f\n',P);

fprintf('Rated synchronous speed(ns) = %4.2f\n',ns);

fprintf('KVA input(Q) = %4.2f\n', Q);

fprintf('Specific magnetic loading(Bav) = %4.2fwb/m2\n', Bav);

fprintf('Specific electric loading(q) = %4.0fac/m\n', q);

fprintf('Output coefficient(C0) = %4.2f\n', C0);

fprintf('DsqL Value = %4.2fm3\n', DsqL);

fprintf('Stator bore diameter(D) = %4.2fcm\n', D);

fprintf('Gross core length(L) = %4.2fcm\n', L);

fprintf('Net iron length(Li) = %4.2fcm\n', Li);

fprintf('Pole pitch(PP) = %4.2fcm\n', PP);

% (2)<----Stator Slots and Winding Design----->

SC = input('Stator connection:\nFor DELTA connection Enter 0\nFor STAR connection Enter 1'); if SC == 0 Es = V; % Stator voltage per phase = Es;(For delta connection) fprintf('Delta connection is considered for stator\n'); else if SC == 1 Es = V/sqrt(3); % For STAR connection

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fprintf('Star connection is considered for rotor'); end end Is = (KW*1000)/(3*Es*pf*eff); % Stator current per phase = Is fi = Bav*PP*L*1e-4; % Flux per pole = fi Ts1 = Es/(4.44*f*fi*Kw); % Stator turns per phase (Initially) Z1 = 6*Ts1; % Stator slot calculation Smin = round((pi*D)/2.5); Smax = round((pi*D)/1.5); qp =[2 3 4 5]; N = length(qp); k = 1; j = 1; m = 1; for i = 1:N Sp(k) = 3*P*qp(i); Spmin = min(Sp);

if Spmin>Smax qs = 2; S = 3*qs*P; else if Sp(k)>= Smin if Sp(k)<=Smax Sn(j) = Sp(k); Zs1(m) = Z1/Sn(j); if Is*Zs1(m)<= 500 S(m) = Sn(m); qs = S(m)/(3*P); k = k+1; j = j+1; m = m+1; end end end end end Zsi = round(Z1/S); if rem(Zsi,2)== 0 Zs = Zsi; else if rem(Zsi,2) == 1 Zs = Zsi+1; end end Ys = (pi*D)/S; % Stator slot pitch = Yss

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Z = Zs*S; % modified number of stator conductors Ts = Z/6; % Modified Stator turns per phase Cs = S/P; if rem(Cs,2)==0 Alpha = (1/Cs)*pi; Kp = cos(Alpha/2); else if rem(Cs,2)==1 Kp = 1; end end sgm = pi/3; Kd = sin (sgm/2)/(qs*sin (sgm/(2*qs))); Kw = Kp*Kd; % Conductor size

Jsq = interp1(SD, SJsq, D, 'spline'); Az1 = Is/Jsq; % Area of stator conductor required = Az1(Initially) fprintf('Area of stator conductor calculated, Ae = %4.2fmm2\n', Az1); if Az1 <= 10 d1 = sqrt((4*Az1)/pi); % Diameter of bare conductor = d1 d = input('Enter diameter from table, d = '); Az = (pi*d^2)/4; Sf = 0.35; % For round conductor else if Az1 > 10 dzXwz = Az1; Az = input('Enter the area of conductor from table'); dz = input('Enter depth of conductor from table'); wz = input('Enter width of conductor from table'); Sf = 0.4; % For rectangular conductor end end

As = Zs*Az/Sf; % Area of slot

MT = input('Machine type:\nNOn-Interpolar Machine Enter 0\nInterpolar Machine Enter 1');

if MT == 0

dsbyws = 3.5; % For Non-Interpolar machine else if MT == 1 dsbyws = 3.1; % For Interpolar machine end end ws = sqrt(As/dsbyws); ds = dsbyws*ws; % Check for minimum widthfor stator tooth

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wtsmin = fi/(1.7*(S/P)*Li); % minimum width of stator tooth Lmts = 2*L+2.3*PP+ 4*ds/10; % Length of mean turn(Stator)= Lmts Rs = (0.021*Ts*Lmts*1e-2)/(Az*1e-6); % Stator resistance per phase = Rs Pcs = 3*Is^2*Rs; % Total stator copper loss % Stator core

fic = fi/2; Bc = 1.2; Ac = fic/Bc; dcs = (Ac*1e4)/Li; D0 = D+2*(ds/10+dcs); fprintf('Stator voltage per phase = %4.0fV\n', Es);

fprintf('Flux per pole(fi) = %4.2fwb\n', fi);

fprintf('Stator turns per phase = %4.0f\n', Ts);

fprintf('Stator current per phase(Is) = %4.2f\n', Is);

fprintf('Number of stator slots(Ss) = %4.0f\n', S);

fprintf('Slots per pole per phase(qs) = %4.0f\n', qs);

fprintf('Winding factor(Kws) = %4.3f\n', Kw);

fprintf('Slot pitch(Yss) = %4.3f\n', Ys);

fprintf('Conductor per slot(Zss) = %4.0f\n', Zs);

fprintf('Diameter of Bare conductor = %4.2f\n', d);

fprintf('Area of conductor(Az) = %4.2f\n', Az);

fprintf('Area of stator slot(As)= %4.2f\n', As);

fprintf('Depth of stator slot(ds) = %4.2f\n', ds);

fprintf('Width of stator slot(ws) = %4.2f\n',ws);

fprintf('Length of mean turn(Lmts) = %4.2fcm\n', Lmts);

fprintf('Depth of stator core(dcs) = %4.2fcm\n', dcs);

fprintf('Outer diameter of stator stampings(D0) = %4.0fcm\n', D0);

%<---------------3)Rotor Design------------>

%Design of squirell cage rotor % Rotor slot selection Lg = 0.2+2*sqrt(D*L*1e-4); %Length of air gap; Dr = D-(2*Lg/10); % Diameter of rotor % Rotor slot selection

Smin = round((pi*Dr)/2.5); Smax = round((pi*Dr)/1.5);

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qpr = [2 3 4 5 6]; M4 = length(qpr); k4 = 1; j4 = 1; for i2 = 1:M4 Sp(k4) = 3*P*qpr(i2); if Sp(k4)< S && Sp(k4) ~= S Sr(j4) = Sp(k4); % Number of rotor slots qr(j4) = Sr(j4)/(3*P); end end Ysr = (pi*Dr)/Sr; % Rotor slot pitch PPr = (pi*Dr)/P;

RT = input('Type of Rotor:\n For cage type Enter 0\nFor wound type Enter 1'); if RT == 0 % Rotor Bars Ib = 0.85*(6*Is*Ts)/Sr; % Current per rotor bar = Ib Jsq = interp1(SD, SJsq, D, 'spline'); Ab1 = Ib/Jsq;

%drb = 10; wrb = 5; %Ab = 50; fprintf('Calculated area of rotor bar, Ab1 = %4.2fmm2\n', Ab1); if Ab1 <= 10 d1 = sqrt((4*Ab1)/pi); db = input('Enter diameter from standard table, d = '); Ab = pi/4*d^2; Kss = 0.35; %Slot space factor(For round conductor) else if Ab1 > 10 drb = input('Enter depth of rotor bar, dz = '); wrb = input('Enter width of rotor bar, wz = '); Ab = input('Enter conductor area, Az = '); Kss = 0.37;% Slot space factor(For rectangular conductor) end end Asr = Ab/Kss; MT = input('Machine type:\nFor Non interpolar machine Enter 0\nFor interpolar machine Enter 1'); if MT == 0 dsrbywsr = 3.5; % for Non_interpolar machine) else if MT == 1 dsrbywsr = 3;%For Interpolar machine end end wsr = sqrt(Asr/dsrbywsr); dsr = dsrbywsr*wsr; % Check of flux density at the bottom of slot Ysrtb = (pi*(Dr-2*dsr/10))/Sr; % slot pitch at the bottom of the tooth wtrb = Ysrtb - wsr/10; % width at the bottom of tooth

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Btrb = fi/(Sr/P*Li*wtrb*1e-4); Lb = L+4.5 ; % Length of each rotor bar Rb = (0.021*Lb*1e-2)/Ab; % Resistance of each rotor bar = Rb Pcb = Sr*Ib^2*Rb; %Total copper loss in rotor bars % End ring Ie = (Sr*Ib)/(pi*P); % End ring current Ae1 = Ie/Jsq; % Area of each end ring fprintf('Calculated area of end ring, Ae1 = %4.2fmm2\n', Ae1); if Ae1 <= 10 d1 = sqrt((4*Ae1)/pi); de = input('Enter diameter from standard table, d = '); Ae = pi/4*de^2;

else if Ae1 > 10 de = input('Enter depth of end ring, de = '); we = input('Enter width of end ring, we = '); Ae = input('Enter area of end ring, Ae = '); end end

D0e = D - 1.5; % Outer diameter of end ring Die = D - 2*dsr/10; % Inner diameter of end ring Dme = (D0e+Die)/2; %mean diameter of end ring Re = (0.021*pi*Dme*1e-2)/Ae; % Resistance of each end ring Pce = 2*Ie^2*Re; % Copper loss in two end rings Pcr = Pcb+Pce; % Total rotor copper loss s = Pcr/(KW*1000+Pcr); % slip at full load = s

fprintf('Length of air gap(Lg) = %4.1f\n', Lg);

fprintf('Diameter of rotor(Dr) = %4.2f\n', Dr);

fprintf('Number of rotor slots = %4.0f\n', Sr);

fprintf('slots per pole per phase(qs) = %4.0f\n', qr);

fprintf('Rotor Slot pitch(Ysr) = %4.2f\n', Ysr);

fprintf('Rotor bar current(Ib) = %4.2f\n', Ib);

fprintf('Rotor bar area(Ab) = %4.1f\n', Ab);

fprintf('Length of rotor bar(Lb) = %4.1f\n', Lb);

fprintf('Resistance of each bar(rb) = %4.2f\n', Rb);

fprintf('Copper loss in bars(Pcb) = %4.0f\n', Pcb);

fprintf('End ring current = %4.0f\n', Ie);

fprintf('Mean diameter of end ring(Dme) = %4.2f\n', Dme);

fprintf('Resistance of each end ring(re)= %4.2f\n',Re );

fprintf('Copper loss in end ring(Pce)= %4.2f\n', Pce);

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fprintf('Total rotor copper loss(Pcr) = %4.0fW\n', Pcr);

fprintf('Slip at full load(s) = %4.3f\n', s);

else if RT == 1 % For wound rotor Vsr1 = 400; % Voltage between slip rings on open circuit = 400(Assumed Initially) Er1 = Vsr1/sqrt(3); Csr = Sr/P; if rem(Csr,2)==0 Alpha = (1/Csr)*pi; Kpr = cos(Alpha/2); else if rem(Csr,2)==1 Kpr = 1; end end sgm = pi/3; Kdr = sin (sgm/2)/(qr*sin (sgm/(2*qr))); Kwr = Kpr*Kdr; Tr1 = (Kws/Kwr)*(Er1/Es)*Ts; % Rotor turns per phase Zr1 = 6*Tr1; % Number of rotor conductor (Initially) Zsr = round(Zr1/Sr); % Rotor conductor per slot Zr = Zsr*Sr; % Actual number of rotor conductor

Tr = Zr/6; % Actual number of rotor turns per phase Er = (Tr/Ts)*Es; % Actual rotor voltage per phase at stand still Vsr = sqrt(3)*Er; % conductor size

Ir = 0.85*Is*(Kws/Kwr)*(Ts/Tr); % rotor current per phase Jsr = interp1(SD, SJsr, D, 'spline'); Azr1 = Ir/Jrb; % Area of rotor conductor fprintf('Calculated Area of wound rotor(Azr1) = %4.2f\n', Azr1); if Azr1 <= 10

d1 = sqrt((4*Azr1)/pi); d = input('Enter diameter from standard table, d = '); Azr = pi/4*d^2; Kss = 0.35; %Slot space factor(For round conductor) else if Azr1 > 10 dr = input('Enter depth of rotor bar, dz = '); wr = input('Enter width of rotor bar, wz = '); Azr = input('Enter conductor area, Az = '); Kss = 0.37;% Slot space factor(For rectangular conductor) end end

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Asr = Azr/Kss; MT = input('Machine type:\nFor Non interpolar machine Enter 0\nFor interpolar machine Enter 1'); if MT == 0 dsrbywsr = 3.5; % for Non_interpolar machine) else if MT == 1 dsrbywsr = 3;%For Interpolar machine end end wsr = sqrt(Asr/dsrbywsr); dsr = dsrbywsr*wsr; Lmtr = (2*L+2.3*PPr+ 4*dsr/10)*1e-2; Rr = Tr*(0.021*Lmtr)/Azr; % Rotor resistance per phase Rrs = Rr*(Kws*Ts/(Kwr*Tr))^2; % Rotor resistance referred to stator Pcr = 3*Ir^2*Rr; % Total rotor copper loss fprintf('Rotor turns per phase(Tr) = %4.0f\n', Tr);

fprintf('Rotor voltage per phase(Er) = %4.0f\n', Er);

fprintf('Voltage between slip rings(Vsr) = %4.0f\n', Vsr);

fprintf('Rotor current per phase(Ir) = %4.0f\n', Ir);

fprintf('Area of Rotor conductor(Azr) = %4.2fmm2\n', Azr);

fprintf('Slot space factor(Kss) = %4.2f\n', Kss);

fprintf('Area of slot(Asr) = %4.2f\n', Asr);

fprintf('Depth of slot(dsr) = %4.2f\n', dsr);

fprintf('Width of slot(wsr) = %4.2f\n', wsr);

fprintf('Flux density at the bottom of slot(Btrb) = %4.2f\n', Btrb);

fprintf('Length of mean turn of rotor(Lmtr) = %4.2f\n', Lmtr);

fprintf('Rotor resistance per phase(Rr) = %4.2f\n', Rr);

fprintf('Rotor resistance referred to stator(Rrs) = %4.2f\n', Rrs);

fprintf('Total rotor copper loss(Pcr) = %4.2f\n', Pcr);

end

end

%(4)<---------------AmpTurns and Magnetizing-Current---------------->

ws0 = 3; % Slot opening for stator slots wr0 = 2; % Slot opening for rotor slots Kwr = 1; X1=ws0/Lg; Kcs=interp1(R2,CC3,X1, 'spline'); Kgss = Ys/(Ys-(Kcs*ws0/10));% Gap contraction factor for stator slots X2=wr0/Lg; Kcr = interp1(R2,CC3,X2, 'spline'); Kgsr = Ysr/(Ysr-(Kcr*wr0/10)); % gap contraction factor for rotor slots Kg = Kgss*Kgsr; % Total gap contraction factor

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Lge = 1.33*Lg; % Effective length of air gap Ag = PP*L*1e-4; % Area of air gap Bg = fi/Ag; % Flux density in the air gap

Bg60 = 1.36*Bg; ATg = 800000*Bg60*Kg*Lg*1e-3; % mmf for air gap % Stator teeth

wts13 = pi*(D+2/3*ds/10)/S - ws/10; Ats = S/P*Li*wts13*1e-4; Bts13 = fi/Ats; %Flux density at 1/3 height from narrow end Bts60 = 1.36*Bts13; atts = 900; ht = ds; ATts = atts*ht*1e-3; % mmf required for stator teeth % Stator core

fic = fi/2; Acs = fic/Bc; dcs = Acs/Li; atcs = 280; % Length of path through stator core Lcs = pi*(D+2*ds/10+dcs)/(3*P); % Length of flux path through stator core ATcs = atcs*Lcs*1e-2; %mmf required for stator core = ATcs D0 = D+2*ds+2*dcs; % Outside diameter of stator laminations % Rotor teeth

wtr13 = (pi*(Dr-4/3*dsr/10))/Sr- wsr/10; % Width of rotor teeth at 1/3 height from narrow end Atr = Sr/P*Li*wtr13*1e-4; % Area of rotor teeth per pole Btr13 = fi/Atr; %flux density in rotor teeth at 1/3 height Btr60 = 1.36*Btr13; htr = dsr; attr = 900; ATtr = attr*htr*1e-3; %Mmf required for rotor teeth % Rotor core

Acr = Acs; Bcr = Bc; atcr = 280; dcr = dcs; Lcr = pi*(D-2*dsr/10-dcr)/(3*P);% Length of magnetic path in rotor core ATcr = atcr*Lcr*1e-2; % mmf required for rotor core Dir = Dr-2*(dsr/10+dcr);% Inner diameter of rotor stamping AT60 = ATg+ATts+ATcs+ATtr+ATcr; % Total ampere turns Im = (0.427*P*AT60)/(Kw*Ts); % magnetising current per phase

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fprintf('Ampereturns and magnetising current calculation\n\n');

fprintf('Gap contraction factor(Kg) = %4.2f\n', Kg);

fprintf('Mmf required for air gap(ATg) = %4.2f\n', ATg);

fprintf('Flux density at 1/3 height from narrow end(Bts13) = %4.2f\n', Bts13);

fprintf('Mmf required for stator teeth(ATt) = %4.2f\n', ATts);

fprintf('Length of flux path through stator core(Lcs) = %4.2f\n', Lcs)

fprintf('Mmf required for stator core(ATc) = %4.2f\n', ATcs);

fprintf('Outer diameter of stator laminations(D0) = %4.2f\n', D0);

fprintf('Flux density in rotor teeth at 1/3 height from narrow end(Btr13) = %4.2f\n', Btr13);

fprintf('mmf required for rotor teeth = %4.2f\n', ATtr);

fprintf('Inner diameter of rotor stampings(Dir) = %4.2f\n', Dir);

fprintf('Length of magnetic path in rotor core(Lcr) = %4.2f\n', Lcr);

fprintf('mmf required for rotor core(ATcr) = %4.0f\n', ATcr);

fprintf('Total ampere turns(AT60) = %4.2f\n', AT60);

fprintf('Phase magnetising current(Im) = %4.0f\n', Im);

%(5) <-----------Short-Circuit-Current-------------------->')

h3 = 3; % Height of wedge h4 = 1; % Height of Lip h1 = ds - (h3+h4); % Conductor height % Specific permeance of stator slots = Lmdss Lmdss = 4*pi*1e-7*(h1/(3*ws)+(2*h3)/(ws+ws0)+h4/ws0); % Specific permeance of rotor slots = Lmdsr Lmdsr = 4*pi*1e-7*(h1/(3*ws)+(2*h3)/(ws+wr0)+h4/wr0); % Specific permeance of rotor reffered to stator = Lmddsr Lmddsr = Lmdsr*(Kw^2*S)/(Kwr^2*Sr); % Total specific slot permeance = Lmds Lmds = Lmdss+Lmddsr; % Slot leakage reactance = Xs xs = 8*pi*f*Ts^2*L*1e-2*(Lmds/(P*qs)); L0Lmd0 = (4*pi*1e-7*(PP*1e-2)^2)/(pi*Ys*1e-2); %Overhang leakage reactance = x0 x0 = 8*pi*f*Ts^2*L0Lmd0/(P*qs); Xm = Es/Im; % magnetizing reactance xz = 5/6*Xm/m^2*(1/qs^2+1/qr^2); % Zigzag leakage reactance = Xs Xs = xs+x0+xz; % Total leakage reactance referred to stator = Xs %Rrs = Rotor resistance referred to stator per phase Rrs = Pcr/(m*Ib^2); Rss = Rs+Rrs; %Total resistance referred to stator

Zs = sqrt(Xs^2+Rss^2); % Total impedance per phase Isc = Es/Zs; % Short circuit current pfsc = Rs/Zs; % Short circuit power factor

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fprintf('Short circuit current calculation\n\n');

fprintf('Slot leakage reactance(xs) = %4.1fohm\n', xs);

fprintf('Overhang leakage reactance(xe) = %4.1fohm\n', x0);

fprintf('Zigzag leakage reactance(xs) = %4.1fohm\n', xz);

fprintf('Total leakage reactance(Xs) = %4.1fohm\n', Xs);

fprintf('Total resistance refered to stater(Rs) = %4.1f\n', Rss);

fprintf('Short circuit impedance(Zs) = %4.1f\n', Zs);

fprintf('Phase circuit circuit current(Isc) = %4.2f\n', Isc);

fprintf('Short circuit power factor(pfsc) = %4.3f\n', pfsc);

%(6)<--------------Performance-------------------->');

PitpKg = interpl(B,WpKg,Btmax, 'spline'); %Iron loss in teeth per kg

PicpKg = interpl(B,WpKg,Bc, 'spline');% Iron loss in core per kg

wts = pi*(D+ds/10)/S - ws/10; % Mean width of stator teeth

Wts = 7.6*1e3*S*ds*wts*Li*1e-7; %Weight of stator teeth

Pit = Wts*PitPkg; % Iron loss in teeth

Dmc = pi*(D0-dcs); %Mean diameter of stator core

Wc = 7.6*1e3*Dmc*dcs*Li*1e-6; % Weight of stator core

Pic = Wc*PicPkg; % Iron loss in stator core

Pi = Pit+Pic; % Total iron loss

WLP = interp1(SKW6, FWLP, KW, 'spline')/100;

Pfw = WLP*KW*1000; % Friction and windage loss

Pnl = Pi+Pfw; % Total no load loss

Iw = Pnl/(3*Es); % Loss component of no load current per phase

I0 = sqrt(Im^2+Iw^2); % No load current

pf0 = Iw/Im; % no load power factor

Ptl = Pnl+Pcs+Pcr; % Total loss at full load = Ptl

Eff = KW/(KW+Ptl); % Efficiency of the machine

s = Pcr/(KW*1000+Pcr); % slip at full load = s

% Stator temperature rise

S0 = pi*D0*L*1e-4; % Outside cylindrical surface of stator core

C0 = 0.03; % Colling coefficient for outer surface(table 3.6)

LD0 = S0/C0; %Loss dissipated per 0C from outer surface

Si = pi*D*L*1e-4; % Inner cylindrical surface

Va = pi*D*ns*1e-2; % Peripheral speed

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Ci = 0.033/(1+0.1*Va); %Cooling coefficient for inner surface

LDi = Si/Ci; %Loss dissipated per 0C from inner stator surface

TLD = LD0+LDi; %Total loss dissipated per 0C

LDss = Pi+Pcs*(2*L)/Lmts; % Loss dissipated from slot portion of stator

Trm = LDss/TLD; % Temperature rise of machine

fprintf('Losses and performance of the machine\n\n');

fprintf('Iron losses of machine(Pi) = %4.0fW\n', Pi);

fprintf('Friction and windage losses(Pfw) = %4.0fW\n', Pfw);

fprintf('Total losses at full load(Pt) = %4.0fW\n', Ptl);

fprintf('Efficiency at full load(Eff) = %4.1fperc\n', Eff);

fprintf('Temperature rise of machine(Trm) = %4.1f0C\n', Trm);

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C. MATLAB program for the Design BLDC Motor

Input Specifications

Rated Output Power, P0 = 1 KW Rated Voltage, V = 24 V Rated Speed, N = 1500 rpm Frequency, f = 50 hz No. of poles, P = 8 No. of slots, S = 24 Magnet Specification Remanent flux density, Br = 1.21 Coercive force, Hc = 915 Maximum energy product, (BH)max = 279 kj/m Assumptions

Stator winding factor is assumed initially as 0.955 Pole arc to Pole pitch ratio is assumed to be 0.66(varies between 0.65-7) Relative Permeability, mur = 1.05 Bav = (0.6-0.8)Br for NdFeB magnets

% Variation of Power factor(pf) & efficiency(eff) w.r.t KW rating

SKW5 = [1 5 10 20 50 100 200 500]; SPF = [0.81 0.82 0.83 0.85 0.87 0.89 0.9 0.92]; SEFF = [0.83 0.85 0.87 0.89 0.91 0.92 0.93]; % <----------1)Design of Main dimensions-------------> ns = N/60; % rated speed in rps PF = interp1('SKW5, SPF, KW, 'spline'); eff = interp1('SKW5, SPF, KW, 'spline'); Q = KW/(PF*eff); % Apparent electromagnetic power C0 = 11*Kw*q*1e-3; % Output coefficient DsqL = Q/(C0*ns); % DsqL value D1 = DsqL^(1/3)*(P/(pi*LbyPP))^(1/3); Dr0 = round(D1*1e3); % Rotor outer diameter in mm L1 = (DsqL*1e9)/Dr0^2; L = round(L1); % Stack length in mm PP = pi*Dr0/P; LbyPP = L/PP; Li = ki*L; % Net iron length Lg = 0.015*PP; % Length of air gap Dsi = Dr0 +2*Lg PP = (pi*D)/P; % Pole pitch Parc = LbyPP*PP; % Pole arc fprintf('Design of 3 phase radial flux permanet magnet BLDC motor\n\n');

fprintf(' Output coefficient, C0 = %4.2f\n', C0);

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fprintf('DsqL value, DsqL = %4.5fm3\n', DsqL);

fprintf('Diameter of armature(Rotor outer diameter), Dr0 = %4.0fmm\n',Dr0);

fprintf('Stack length of armature, L = %4.0fmm\n', L);

fprintf('Pole pitch value in mm, PP = %4.2fmm\n', PP);

fprintf('Flux per pole, fi = %4.5fWb\n', fi);

fprintf('Air gap length, Lg = %4.2f mm\n', Lg);

% Magnet thickness calculation ATa = (Bav*Lg)/mu0; % mmf required to produce Bav ATf = ATa*1.3; % mmf to be produced by the magnet Ag = PAPP*PP*L; % Aera of area gap Vm = ATf/Hc; % Volume of magnet Lm = Vm/Ag; % Magnet thickness Bg = Br/(1+murrec*Lg/Lm); % Air gap flux density fig = PAPP*PP*L*Bg*1e-4; % Flux per pole = fig Hg = Hc*(1-Bg/Br); %The air gap magnetic field strength wg = (Bg*Hg)/2; % The usefull energy per magnet volume Wg = wg%Vm; % The useful energy per pole pair % Stator Dimensions Btmax = 1.9; % Maximum allowable flux density in stator core(Taken as 1.9) Kst = 0.9; % Lamination stacking factor, Kst wbi = fi/(2*Bmax*Kst*L); % Stator back iron thickness, wbi wtb = (Bg*pi*D)/(S*Bmax); % Tooth thickness, wtb Ds0 = Dsi+2*ds+2*wbi; % Stator outer diameter fprintf(' Area of air gap, Ag = %4.2f\n', Ag);

fprintf('Volume of magnet, Vm = %4.5fm3\n', Vm);

fprintf('Diameter of armature(Rotor outer diameter), Dr0 = %4.0fmm\n',Dr0);

fprintf('Thickness of magnet, Lg = %4.0fmm\n', Lg);

fprintf('Airgap flux density, Bg = %4.2f\n', Bg);

fprintf('Air gap Flux per pole, fig = %4.5fWb\n', fig);

fprintf('Air gap magnetic field strength, Hg = %4.2f \n', Hg);

fprintf('The useful energy per pole pair, Wg = %4.2f\n', Wg);

fprintf('Stator back iron thick ness, wbi = %4.2fmm\n', wbi);

fprintf('Tooth thickness, wtb = %4.2fmm\n', wtb);

fprintf('Stator outer diameter, Ds0 = %4.2fmm\n', Ds0);

% (2)<----Stator Slots and Winding Design----->

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SC = input('Stator connection:\nFor DELTA connection Enter 0\nFor STAR connection Enter 1'); if SC == 0 Es = V; % Stator voltage per phase = Es;(For delta connection) fprintf('Delta connection is considered for stator\n'); else if SC == 1 Es = V/sqrt(3); % For STAR connection fprintf('Star connection is considered for rotor'); end end Is = (KW*1000)/(m*Es*pf*eff); % Stator current per phase = Is Ts1 = Es/(4.44*f*fi*Kw); % Stator turns per phase (Initially) Z1 = 6*Ts1; Zsi = round(Z1/S); if rem(Zsi,2)== 0 Zs = Zsi; else if rem(Zsi,2) == 1 Zs = Zsi+1; end end Ys = (pi*D)/S; % Stator slot pitch = Yss Z = Zs*S; % modified number of stator conductors Ts = Z/6; % Modified Stator turns per phase Az1 = Is/Jsq; % Area of stator conductor required = Az1(Initially) fprintf('Area of stator conductor calculated, Ae = %4.2fmm2\n', Az1); Sf = 0.35; % For round conductor As = Zs*Az/Sf; % Area of slot MT = input('Machine type:\nNOn-Interpolar Machine Enter 0\nInterpolar Machine Enter 1'); if MT == 0 dsbyws = 3.5; % For Non-Interpolar machine else if MT == 1 dsbyws = 3.1; % For Interpolar machine end end ws = sqrt(As/dsbyws); % Width of slots ds = dsbyws*ws; Lmts = 2*L+2.3*PP+ 4*ds/10; % Length of mean turn(Stator)= Lmts Rs = (0.021*Ts*Lmts*1e-2)/(Az*1e-6); % Stator resistance per phase = Rs Pcs = 3*Is^2*Rs; % Total stator copper loss fprintf('Stator voltage per phase = %4.0fV\n', Es);

fprintf('Flux per pole(fi) = %4.2fwb\n', fi);

fprintf('Stator turns per phase = %4.0f\n', Ts);

fprintf('Stator current per phase(Is) = %4.2f\n', Is);

fprintf('Slot pitch(Yss) = %4.3f\n', Ys);

fprintf('Conductor per slot(Zss) = %4.0f\n', Zs);

fprintf('Diameter of Bare conductor = %4.2f\n', d);

fprintf('Area of conductor(Az) = %4.2f\n', Az);

fprintf('Area of stator slot(As)= %4.2f\n', As);

fprintf('Depth of stator slot(ds) = %4.2f\n', ds);

fprintf('Width of stator slot(ws) = %4.2f\n',ws);

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fprintf('Length of mean turn(Lmts) = %4.2fcm\n', Lmts);

Calculation of torque constant and back emf constant Ce = pi*(P/2)*sqrt(2)*Tph*Kw Ke = Ce*fig; % back emf constant Ct = m*Ce/(2*pi); Kt = Ct*fig; % Torque constant HA = 360/(m*P/2); % Hall sensor angle fprintf('Back emf constant, Ke = %4.2f\n', Ke);

fprintf('Torque constant, Kt = %4.5f\n', kt);

fprintf('Mass of stator core material, Msm = %4.2f\n', Msm);

fprintf('Hall sensor angle,HA = %4.2f\n', HA);

% Losses and performance of the machine Pcu = Ia^2*Ra; % Copper losses per phase f = (P*ns)/2; % Frequency of magnetic flux Vsc = (pi/4*(Ds0^2-Dsi^2)*L - S*As*L)*1e-9; % Volume of stator core material = Vsc rh0 = 8150; % Density of stator core,rh0 = 8150 Kg/m3 Msm = rh0*Vsc; % Mass of stator core = Ms WpKg = 80; % Iron loss per Kg Pi = WpKg*Msm; % Total iron loss Pfw = 0.3/100*P0; % Friction & windage losses are taken 3% of output power Pt = Pcu+Pi+Pfw; % Total losses eff = P0/(P0+Pt); % Effeciency of the machine % Temperature rise EL = Pt*t; % Energy loss (Time taken for 20 seconds) Mcu1 = Lmt*Az*rh0*a; % Mass of copper per phase Mcu = 3*Mcu1; % Mass of copper in 3 phases Scu = 0.385; % Specific heat of copper Ssm = 0.1; % Specific heat of stator material %Hd = [Mcu*Scu+Msm*Ssm]*(T2-T1)% Heat dissipated Kd = Mcu*Scu+Msm*Ssm; T2 = EL/Kd+T1; % Temperature rise of machine fprintf('Total copper loss, Pcu = %4.2f\n', Pcu);

fprintf('Volume of Stator core material, Vsc = %4.5f\n', Vsc);

fprintf('Mass of stator core material, Msm = %4.2f\n', Msm);

fprintf('Total iron loss,Pi = %4.2f\n', Pi);

fprintf('Friction & windage loss, Pfw = %4.2f\n', Pfw);

fprintf('Total losses, Pt = %4.2f\n', Pt);

fprintf('Effeciency of the machine, eff = %4.2f\n', eff);

fprintf('Energy loss of the machine, EL = %4.2f\n', EL);

fprintf('Mass of copper in 3 phases, Mcu = %4.2f\n', Mcu);

fprintf('Temperature rise of machine, T2 = %4.2f\n', T2);