Control Of 5 DC Motor For Application In Robot Manipulator.

UNIVERSITI TEKNIKAL MALAYSIA MELAKA

CONTROL OF FIVE DC MOTOR FOR APPLICATION IN ROBOT

MANIPULATOR

This report submitted in accordance with requirement of the Universiti Teknikal Malaysia Melaka (UTeM) for the Bachelor Degree of Manufacturing Engineering

(Robotic and Automation) with Honours.

By

SONG CHIEN SHYEN

FACULTY OF MANUFACTURING ENGINEERING 2008

DECLARATION

I hereby, declared this report entitled “Control of Five DC Motor For Application In Robot Manipulator” is the results of my own research except as cited in references.

Signature : ...

Author’s Name :Song Chien Shyen

APPROVAL

This report is submitted to the Faculty of Manufacturing Engineering of UTeM as a partial fulfilment of the requirements for the degree of Bachelor of Manufacturing Engineering (Robotics and Automation) with Honours. The member of supervisory committee is as follow:

(Signature of Supervisor)

...

i

ABSTRACT

This report presents a project entitled “Control of Five Direct Current (DC) Motor for Application in Robot Manipulator”. The idea of conducting this research is to study the ability, functionality and the reliability of DC motor as the actuator for the robots manipulators. The characteristics and types of DC motor are studied. The total of five Shunt DC motor are used to act as the electrical actuating system for the robot arm. Three designs of robot arm are designed and conceptualized to support the five DC motors. The designs are then presented in this report and the best design is being developed. For this project, a 4 axis using 5 DC motors is chosen. The proposed robot arm structure is documented and drawn using Computer Aided Design (CAD) program. The specifications of materials, types of motors and controllers unit are discussed. Upon completion, the robot arm will be mounted on the slider fabricated and available in the Faculty of Manufacturing’s (FKP) Robotics Lab. To build a good robot, the controller is the most important component. For this project, a relay triggered controller is determined. The methods of fabrication and components needed for the relay triggered controller is researched and developed. Using this controller and robot arm, a series of test is designed and tested. From the findings, it is found out that DC motor is suitable to be used as robot manipulator.

ii

ABSTRAK

Untuk projek ini, sebuah laporan yang bertajuk “Control of Five Direct Current (DC) Motor for Application in Robot Manipulator” telah disediakan. Idea untuk menjalankan penyelidikan ini adalah bagi mengkaji keupayaan, kefungsian dan kebolehpercayaan motor DC sebagai penggerak untuk lengan robot. Ciri-ciri bagi setiap jenis motor telah dikaji. Bagi projek ini, sejumlah lima motor DC jenis Shunt telah digunakan sebagai penggerak berelektrik untuk lengan robot. Bagi mengkonsepsi lengan robot yang boleh menyokong lima motor DC, tiga reka bentuk telah direka. Rekaan-rekaan itu kemudiannya dipersembahkan dalam laporan ini. Rekaan lengan robot yang terbaik dan memenuhi ciri-ciri yang ditentukan terlebih dahulu akan dipilih, didokumenkan dan dilukis menggunakan program Computer Aided Design (CAD) lalu difabrikasikan. Penentuan bagi bahan mentah untuk lengan robot, jenis motor dan unit alat-alat kawalan akan dibincang dengan terperinci. Apabila lengan robot telah siap, ia akan dipasang di atas gelangsar yang telah difabrikasi dan boleh didapati di Makmal Robotik Fakulti Kejuruteraan Pembuatan (FKP). Untuk membina satu robot yang cekap, alat pengawal adalah komponen terpenting. Untuk projek ini, alat pengawal yang menggunakan “relay” digunakan. Kaedah dan komponen yang diperlukan untuk memfabrikasi alat pengawal relay akan dikaji. Akhirnya, alat pengawal relay akan diuji untuk kefungsiannya sebelum ia dikaji keatas motor DC yang telah dipasang pada lengan robot. Daripada kajian yang telah diperolehi, didapati bahawa pengawalan lima motor DC untuk tujuan aplikasi pada pengolah lengan robot dapat dicapai dengan lengan robot dan alat pengawal yang direka dan difabrikasi.

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DEDICATION

iv

ACKNOWLEDGEMENT

I would like to thank firstly Encik Muhamad Arfauz Bin A.Rahman for willingly take me as my Final Year Project’s Principal Supervisor for the first semester of academic session 2008/09, and Puan Syamimi Binti Shamsuddin also whom willingly take as my Final Year Project’s Principal Supervisor for the second semester of academic session 2008/09. Without your constant guidance, this project will never be a success. Then I would like to extend my humble gratitude to Encik Hisham bin Nordin, without your advice I would not have completed my controller.

To my panels who took their precious time for themselves off to read about my project, Pn Silah Hayati Binti Kamsani and Dr Zamberi B. Jamaludin, I would like to thank you with all my heart.

To my family and beloved ones, who constantly gives me support morally and financially, thank you so much. Without support from you all, nothing will materialize.

To my friends, especially Parameswara, Tham, Aaron, Denis Chua, Anbalagan, and whomever who have helped me, without your constant pushing and help in ways of your expertise, my project will not be as what it is today.

Thank you…!

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TABLE OF CONTENT

Abstract i

Abstrak ii

Dedication iii

Acknowledgment iv

Table of Content v

List of Tables ix

List of Figures x

List Abbreviations xiv

1. INTRODUCTION 1

1.1 Objective 2

1.2 Scope 2

1.3 Benefit of this Project 3

2. LITERATURE REVIEW 4

2.1 DC Motor 4

2.1.1 Lorentz Force 6

2.1.2 Kirchoff’s Voltage Law 8

2.1.3 Magnetomotive Force (mmf) 8

2.1.4 Induced Voltage 8

2.1.5 Neutral zones 9

2.1.6 Generation of DC Voltage 10

2.1.7 Improvement of DC output Waveform 11

2.1.8 Counter-electromotive force (cemf) 13

2.1.9 Armature Reaction 14

vi

2.2 Mechanical Properties of DC Motor 15

2.2.1 Acceleration of the DC Motor 16

2.2.2 Power and Torque 17

2.3 Types of DC Motor 18

2.3.1 Shunt Dc Motors 19

2.3.2 Series DC Motor 21

2.3.3 Compound DC Motor 22

2.3.4 Advantages and Disadvantages 23

2.3.4.1 Between three types of DC motor 23

2.3.4.2 Between Alternating Current (AC) and DC 26

2.4 Control of DC Motor 29

2.5 Robotic Arm 30

2.6 Control of DC motor in Robotic Arm 35

2.6.1 Relay 36

2.7 Materials 38

2.7.1 What is Stainless Steel? 38

2.7.2 Role of Alloying Elements in Stainless Steel 40

2.7.2.1 Carbon 40

2.7.2.2 Chromium (Cr) 40

2.7.2.3 Nickel (Ni) 41

2.7.2.4 Molybdenum 41

2.7.2.5 Manganese 41

2.7.2.6 Silicon and Copper 41

2.7.2.7 Nitrogen 42

2.7.2.8 Niobium 42

2.7.2.9 Titanium 42

2.7.2.10 Sulphur 43

2.7.3 More about stainless steel 44

2.7.3.1 Martensitic Stainless Steel 44

2.7.3.2 Ferritic Stainless Steel 45

vii

2.7.3.4 Duplex Stainless Steel 46

2.7.4 Nonferrous Alloy Steels 47

2.7.4.1 Aluminum and Aluminum Alloys 47

3. METHODOLOGY 52

3.1 Research 52

3.1.1 Determination of objectives and scopes for first stage of project 54

3.1.2 Research on DC motor 54

3.1.3 Research on control of DC motor, robot arm and controlling DC motor 54 on robot arm

3.1.4 Conceptual Design 55

3.1.5 Determination of Design to Use 56

3.1.6 Technical Drawing of the Design 57

3.1.7 Material Selection 57

3.1.8 Motor Selection 58

3.2 Project tools and equipments 59

4. DESIGN AND DEVELOPMENT 60

4.1 Design Process 60

4.1.1 Design Determination 67

4.2 Material Selection 68

4.3 Motor Selection 72

4.3.1 Motor Type 73

4.3.2 Operating Voltage and Current 74

4.3.3 Power rating and speed 74

4.3.4 Torque 76

4.4 Development of Robot Arm 77

4.4.1 Base Shaft 78

4.4.2 First Joint Shaft 80

4.4.3 Second Joint Shaft 81

viii

4.4.5 Connector 84

4.4.6 Robot Arm Links 85

4.5 Controller Selection 86

4.5.1 Operation of Standard Controller 87

4.5.2 Development of Controller 89

4.6 Test Design 94

5. RESULT 96

6. DISCUSSION 99

6.1 Work on Project 99

6.2 Second Stage of Project 101

6.3 Result Discussion 102

6.3.1 Robot Arm 103

6.3.2 Controller 105

6.3.3 Testing 105

6.4 Suggestion 107

7. CONCLUSION 108

REFERENCES 109

APPENDICES

A Gantt Chart

B Technical Drawings for Robot Arm

ix

LIST OF TABLES

2.1 Advantages and Disadvantages between Shunt, Series and Compound 26 DC Motor

2.2 Advantages and Disadvantages between AC and DC motor 27 2.3 Typical Robot Application Areas (Rudiger Dillmann, 1990) 31 2.4 Summary of role of elements used in stainless steel 43 2.5 Summary of element content in martensitic stainless steel 44 2.6 Summary of element content in ferritic stainless steel 45 2.7 Summary of element content in austenitic stainless steel 46 2.8 Summary of element content in duplex stainless steel 47 2.9 Typical mechanical properties of various aluminum alloys 50

(Adapted from ASM Handbook Volume 2)

3.1 Properties of DC Motor SPG50-60K 58

3.2 Allow Moment Maximum Wrest Power, Output Power and Weight of 58 DC Motor SPG50-60K

3.3 Reduction Ratio for Shunt DC Motor Used in this Project 58

4.1 Components used for symbols in the Light Dimmer circuit 93

4.2 Bill of material for this project 96

5.1 Criterion on the categories to rate the DC motors for this project 96

x

LIST OF FIGURES

2.1 Figure above shows the similarities of DC generator and DC Motor. 5 (Left) Elementary DC generator construction (Jones and Flynn)(Right) Basic construction of a DC Motor (Siemens Energy and Automation)

2.2 Right Hand Rule applied to determine the direction of force (Siemens 6 Energy and Automation, 2000)

2.3 Maximum force when conductor is perpendicular to the magnetic field 7 2.4 Magnetic field due to magnet and current carrying conductor 7 2.5 Neutral zones located in a DC machine (Wildi, 2000) 10 2.6 Induced voltage obtained from the turning coil of the DC generator 10 2.7 Induced voltage produced for one cycle of DC generator rotation 11 2.8 Schematic diagram of a DC generator having 4 coils in 4 segments and 11

4 commutator bars (Theodore Wildi, 2000)

2.9 A more uniform induced voltage produced than in Figure 2.6(Theodore 12 Wildi, 2000)

2.10 Counter-electromotive force (cemf) in a DC motor (Theodore Wildi, 2000) 13 2.11 Magnetic field produced by the current flowing in the armature conductors 14

(Theodore Wildi, 2000)

2.12 Commutating poles produced an mmf of the commutator that opposes the 15 mmf of the armature (Theodore Wildi, 2000)

2.13 Shunt DC Motor (Shaw) 19

2.14 Torque-speed and torque-current characteristic of a shunt motor (Wildi, 20 2000)

2.15 Series DC Motor (Siemens Energy and Automation, 2000) 21 2.16 Torque vs Speed and current for Shunt and Series DC Motors 22 2.17 Compound DC Motor (Siemens Energy and Automation, 2000) 22

xi

2.18 Typical speed versus torque characteristics of various DC motors (Wildi, 24 2000)

2.19 Graph of efficiency vs speed curves at full load among Brush DC motor, 28 Brushless DC motor and AC motor (Edward C.Lee)

2.20 Open-loop of the control of DC motor 29

2.21 (a) Symbol of a rotary joint. (b) Symbol of a prismatic joint 32 2.22 (a) Rhino-robot with link and joint labeling. (b) Frame assignment of 33

Rhino-robot

2.23 (a) Comau-robot with link and joint labeling. (b) Frame assignment for 34 Comau-Robot

2.24 The workspace for Rhino-robot and Comau-robot drawn by using Autocad 34 2007

2.25 Control of DC motor in Robotic Arm 35

2.26 Flow of signal from the teach pendant to determine the direction of 36 rotation of the DC motor

3.1 Flow chart for the first stage of project 53

3.2 Flow chart for the development of the conceptual robot design (Groover, 55 2008)

3.3 (Left) Slider board of the slider. (Right) Length and width of the slider 57 Board

4.1 (Top left) M-420iA from Fanuc Robotics, (Top right) Comau-Robot, 61 (Below) Rhino-Robot

4.2 Design of Conceptual Design 1 and Frame Assignment 62 4.3 (a) Workspace for Conceptual Design 1 from Top View, (b) Workspace 63

For Conceptual Design 1 from Side View

4.4 Design of Conceptual Design 2 and Frame Assignment 64 4.5 (a) Workspace for Conceptual Design 2 from Top View, (b) Workspace 65

For Conceptual Design 2 from Side View

xii

4.7 (a) Workspace for Conceptual Design 3 from Top View, (b) Workspace 67 For Conceptual Design 3 from Side View

4.8 CAD Drawing and parts labeling of conceptual design 3 67

4.9 Measurement of hollow square aluminum bar 68

4.10 Stress distribution to the robot arm base 70

4.11 Static equilibrium acting on W1 and W2 71

4.12 The approximate length of robot arm when stretched 74 4.13 The structure and labeling of this project’s robot arm 77

4.14 Robot arm fabricated with respect to design 78

4.15 Design of Base Shaft 78

4.16 Fabrication process for Base Shaft 79

4.17 Base Shaft on Base 79

4.18 Design of First Joint Shaft 80

4.19 Fabrication process for First Joint Shaft 80

4.20 First Joint Shaft 81

4.21 Design of Second Joint Shaft 81

4.22 Fabrication process of Second Link Shaft 82

4.23 Second Joint Shaft 82

4.24 Design of Base 83

4.25 Process for the cutting of stainless steel using Laser Cutting Machine 83

4.26 Base as Fabricated 84

4.27 (From left) 2 point connector, 3 point connector 84 4.28 Connection between hollow square using 2 point connector 85

4.29 Design of links for the robot arm 85

4.30 Schematic circuit for the standard controller using Automation Studio 87 4.31 Flow of the current to actuate the DC1 in clockwise motion 88 4.32 Flow of the current to actuate the DC1 in anti-clockwise motion 88

4.33 Testing on the strip board using multimeter 89

4.34 Soldering Set 90

4.35 The cutting of non required conducting area of a circuit board 90 4.36 Solder metal being suck off from the board upon melting by the solder gun 91

xiii

4.37 Circuit for relay using ISIS Professional 92

4.38 Circuit for relay trigger circuit 92

4.39 Schematic circuit for the Light Dimmer 93

4.40 The circuit of the Light Dimmer 94

4.41 Path of test for the first joint for the robot arm 94 4.42 Test design for movement of Second and Third Joint of the robot arm 95

5.1 Sequence of results taking for this project 97

6.1 The work done on the first stage of the project 100

6.2 Slider to have robot arm to mount on 101

6.3 The process work flow for stage two of project 102 6.4 A 10mm x 10mm aluminum hollow steel used to widen the gap between 104

links

6.5 Waviness of the stainless steel plate due to sudden cooling after welding 104 6.6 Testing using multimeter for bypass on strip board between columns 105

xiv

LIST OF ABBREVIATIONS

AC Alternate Current

Al - Aluminum

C - Carbon

DC - Direct Current

CAD - Computer Aided Drawing cemf - Counter electromotive force

kg - Kilogram

KVL - Kirchoff’s Voltage Law

Mm - milimeter

mmf - Magneto-Motive force

N - North

NC - Normally Closed

NO - Normally Open76

pu - per unit

rad - radians

r/min (rpm) - Revolutions per minute

S - South

UTeM - Universiti Teknikal Malaysia Melaka

V - Voltage

1

CHAPTER 1

INTRODUCTION

To move a robot, there are several actuating agent such as pneumatic actuator, hydraulic actuator and electric actuator. In this project, electric actuator is used. For electric actuator, there are actuating agent that is far more accurate and reliable to be used such as servomotor, AC motor and stepper motor. The usage of DC motor is seldom talked about due to its inability to produce accurate movements. The aim of this project is to study the ability, functionality and the reliability of the Direct-Current (DC) motor (model: SPG-50-60K and SPG-50-180K) as the actuator for the robots rotational manipulators as compared to the other types of motors that are available. In this project, a total of five (5) DC motor will be used, all representing four (4) degrees of freedom of the robots arm. A standard controller will also be developed to control the motor. The circuit board is designed and developed by using relay to trigger the rotation direction of the DC motor via push button. The circuit board is developed by using strip circuit board and soldering method to secure the electronics components on the circuit board. On top of that, the robot structure is being designed by using CAD designing software. The robot designed must be able to fit onto the slider that is available and has been built by previous students.

2 1.1 Project Aim and Objective

The aim of this project is to control 5 DC motor to be acting as the robot actuating agent. The aim is achieved through these objectives.

(a) To study on the advantages and the functionality of DC Motor and hence its capability as the actuator of robot manipulator

(b) To design and develop a five degree of freedom robot manipulator using DC motor as the actuators.

(c) To design and develop a suitable controller for controlling five DC motor

1.2 Scope

In order to achieve the objectives of this research project, the following are the scope of this research project.

(a) Study on the ability of Cytron DC motor, model 60K and SPG-50-180K, to be applied as the rotational actuator for the robot manipulators.

(b) Study on producing a flexible, reliable and functional relay triggered controller for the robot to determine the direction of rotation for the DC motors.

(c) Design the robot structure by using SOLIDWORKS 2005 as designing software to see whether the robot designed is functional and to determine the amount of raw materials needed to build the robot to be fit onto the slider built by the previous student.

3 1.3 Benefit of this Project

Upon completing of this project, few benefits can be obtained as follows:

(a) 5 degree of freedom robot structure to be mounted onto the slider to create an extra axis to move around

(b) More insight of the capability and flexibility of the DC motor to be used in the high technology industry.

4

CHAPTER 2

LITERATURE REVIEW

This chapter describes the research that has been done on DC motor. The research includes the theory behind DC Motor, DC motor’s properties, types of DC motor and the control of DC motor in robotic arm. Besides that, the theory of robot is also discussed. Then the types of materials, basis on controllers and electronics used to be used to create a functioning robot arm are discussed.

2.1 DC Motor

DC motors have been used in industrial applications for years (Siemens Energy and Automation, 2000). It is used as a purpose of converting electrical power into mechanical power to perform useful work such as turning a fan, and raising a car window. The basic principle of DC motor is similar to the usage of a DC generator where it converts mechanical energy into electrical energy. Commercial DC generators and motors are build in the similar way, which makes dc generators are able to operate as dc motors and vice versa. Due to the similarities in the construction, the fundamental properties of generators and motors are almost identical as shown in Figure 2.1.

5

Figure 2.1: Figure above shows the similarities of DC generator and DC Motor. (Left) Elementary DC generator construction (Jones and Flynn) (Right) Basic construction of a DC Motor (Siemens Energy and Automation)

In DC motor and generator, when the armature or coil rotates, the voltage E is induced in each conductor depending on the density of flux when it cuts. The higher the density of flux, the more induced voltage it will be produced. When induced voltage is passed through the conductors in the armature, rotation of the armature will happen. The reason for this is because of several ideologies such as Faraday’s law and Lorentz force. Faraday’s law states that:-

When a time-varying magnetic field passes through a conducting loop or coil, a voltage is induced in the coil. Conversely, when a time-varying voltage is applied to the terminals of the coil, a time-varying magnetic field is generated (Hi-Dong Chai, 1998).

This means when a time varying voltage is applied onto the armature of the DC motor, a time-varying magnetic field is generated. When a current carrying conductor is moved in a magnetic field, a force is produced in a direction perpendicular to the current and magnetic field directions (G. Alciatore, Michael B. Histand, 2007) and can be related to the Lorentz’s force law.

6

2.1.1 Lorentz Force

Michael states Lorentz’s force law as follows:-

F = I x B ………….(2.1) Where:

F is the force vector (per unit length of conductor) I is the current vector

B is the magnetic field vector

This formula applies for one conductor carrying current. If single conductor is replaced by a large number of conductors, the force per unit length is increased by the number of turns in the coil which results in the amount of current induced to be increased.

The force direction acting on the armature of the motor can be determined by using the Right Hand Rule. The same rule applies to the DC generator. The Right Hand Rule can be described using Figure 2.2.

Figure 2.2: Right Hand Rule applied to determine the direction of force (Siemens Energy and Automation, 2000)

Theodore Wildi describes that Lorentz force is also known as the electromagnetic force. Lorentz force happens when a current-carrying conductor is placed in a magnetic field. When the current-carrying conductor is placed in a magnetic field, it will be subjected to a force as determine by the Right Hand Rule (Figure 2.2).

This force is the basic force for the operation of motors, generators and many more electrical instruments. The magnitude of the force depends on the orientation of the

7

conductor with respect to the direction of the field. The force’s magnitude is the greatest when the conductor is perpendicular to the magnetic field and 0 when parallel to the magnetic field.

The maximum force on a straight conductor can be calculated by using:- F = BIl …………. (2.2)

Where

F = force acting on a conductor [N] B = flux density of the field [T] I = current in the conductor [A] l = active length of the conductor [m]

Figure 2.3 shows the maximum force experience by the conductor when it is perpendicular to the magnetic field.

Figure 2.3: Maximum force when conductor is perpendicular to the magnetic field

When a conductor carries a current, it will be surrounded by a magnetic field. From Figure 2.4, the current is flowing into the page; therefore the circular lines of force have the direction as shown in.

Figure 2.4: Magnetic field due to magnet and current carrying conductor

N S

N S

2

1.1 Project Aim and Objective

The aim of this project is to control 5 DC motor to be acting as the robot actuating agent. The aim is achieved through these objectives.

(a) To study on the advantages and the functionality of DC Motor and hence its capability as the actuator of robot manipulator

(b) To design and develop a five degree of freedom robot manipulator using DC motor as the actuators.

(c) To design and develop a suitable controller for controlling five DC motor

1.2 Scope

In order to achieve the objectives of this research project, the following are the scope of this research project.

(a) Study on the ability of Cytron DC motor, model 60K and SPG-50-180K, to be applied as the rotational actuator for the robot manipulators.

(b) Study on producing a flexible, reliable and functional relay triggered controller for the robot to determine the direction of rotation for the DC motors.

(c) Design the robot structure by using SOLIDWORKS 2005 as designing software to see whether the robot designed is functional and to determine the amount of raw materials needed to build the robot to be fit onto the slider built by the previous student.

3

1.3 Benefit of this Project

Upon completing of this project, few benefits can be obtained as follows:

(a) 5 degree of freedom robot structure to be mounted onto the slider to create an extra axis to move around

(b) More insight of the capability and flexibility of the DC motor to be used in the high technology industry.

4

CHAPTER 2

LITERATURE REVIEW

This chapter describes the research that has been done on DC motor. The research includes the theory behind DC Motor, DC motor’s properties, types of DC motor and the control of DC motor in robotic arm. Besides that, the theory of robot is also discussed. Then the types of materials, basis on controllers and electronics used to be used to create a functioning robot arm are discussed.

2.1 DC Motor

DC motors have been used in industrial applications for years (Siemens Energy and Automation, 2000). It is used as a purpose of converting electrical power into mechanical power to perform useful work such as turning a fan, and raising a car window. The basic principle of DC motor is similar to the usage of a DC generator where it converts mechanical energy into electrical energy. Commercial DC generators and motors are build in the similar way, which makes dc generators are able to operate as dc motors and vice versa. Due to the similarities in the construction, the fundamental properties of generators and motors are almost identical as shown in Figure 2.1.

5

Figure 2.1: Figure above shows the similarities of DC generator and DC Motor. (Left) Elementary DC generator construction (Jones and Flynn) (Right) Basic construction of a DC Motor (Siemens Energy and Automation)

In DC motor and generator, when the armature or coil rotates, the voltage E is induced in each conductor depending on the density of flux when it cuts. The higher the density of flux, the more induced voltage it will be produced. When induced voltage is passed through the conductors in the armature, rotation of the armature will happen. The reason for this is because of several ideologies such as Faraday’s law and Lorentz force. Faraday’s law states that:-

When a time-varying magnetic field passes through a conducting loop or coil, a voltage is induced in the coil. Conversely, when a time-varying voltage is applied to the terminals of the coil, a time-varying magnetic field is generated (Hi-Dong Chai, 1998).

This means when a time varying voltage is applied onto the armature of the DC motor, a time-varying magnetic field is generated. When a current carrying conductor is moved in a magnetic field, a force is produced in a direction perpendicular to the current and magnetic field directions (G. Alciatore, Michael B. Histand, 2007) and can be related to the Lorentz’s force law.

6 2.1.1 Lorentz Force

Michael states Lorentz’s force law as follows:-

F = I x B ………….(2.1) Where:

F is the force vector (per unit length of conductor) I is the current vector

B is the magnetic field vector

This formula applies for one conductor carrying current. If single conductor is replaced by a large number of conductors, the force per unit length is increased by the number of turns in the coil which results in the amount of current induced to be increased.

The force direction acting on the armature of the motor can be determined by using the Right Hand Rule. The same rule applies to the DC generator. The Right Hand Rule can be described using Figure 2.2.

Figure 2.2: Right Hand Rule applied to determine the direction of force (Siemens Energy and Automation, 2000)

Theodore Wildi describes that Lorentz force is also known as the electromagnetic force. Lorentz force happens when a current-carrying conductor is placed in a magnetic field. When the current-carrying conductor is placed in a magnetic field, it will be subjected to a force as determine by the Right Hand Rule (Figure 2.2).

This force is the basic force for the operation of motors, generators and many more electrical instruments. The magnitude of the force depends on the orientation of the

7

conductor with respect to the direction of the field. The force’s magnitude is the greatest when the conductor is perpendicular to the magnetic field and 0 when parallel to the magnetic field.

The maximum force on a straight conductor can be calculated by using:- F = BIl …………. (2.2)

Where

F = force acting on a conductor [N] B = flux density of the field [T] I = current in the conductor [A] l = active length of the conductor [m]

Figure 2.3 shows the maximum force experience by the conductor when it is perpendicular to the magnetic field.

Figure 2.3: Maximum force when conductor is perpendicular to the magnetic field

When a conductor carries a current, it will be surrounded by a magnetic field. From Figure 2.4, the current is flowing into the page; therefore the circular lines of force have the direction as shown in.

Figure 2.4: Magnetic field due to magnet and current carrying conductor

N S

N S