Design and Modelling Long Stroke Linear Permanent Magnet Machine

by

Ahmad Marwan Bin Mah Hassan

Dissertation submitted in partial fulfilment of

the requirements for the Bachelor of Engineering (Hons)

(Electrical and Electronic)

JUNE 2010

Universiti Teknologi PETRONAS Bandar Seri Iskandar 31750 Tronoh Perak Darul Ridzuan

CERTIFICATION OF APPROVAL

Design and Modelling Long Stroke Linear Permanent Magnet Machine

by

Ahmad Marwan Bin Mah Hassan

A dissertation submitted to the

Electrical and Electronic Engineering Programme

Universiti Teknologi PETRONAS

in partial fulfillment of the requirement for the

BACHELOR OF ENGINEERING (Hons)

(ELECTRICAL AND ELECTRONIC ENGINEERING)

Approved by,

UNIVERSITI TEKNOLOGI PETRONAS

TRONOH, PERAK

June 2010

ii

CERTIFICATION OF ORIGINALITY

This is to certify that I am responsible for the work submitted in this project, that the

original work is my own except as specified in the references and acknowledgement,

and that the original work contain herein have not been undertaken or done by

unspecified sources or person.

AHMAD MARWAN BIN MAH HASSAN

III

ABSTRACT

The awareness for the need of renewable energy has been increasing due to

the environmental impacts from the current power generation system and its

increasing operation cost. With increasing demand of electrical power especially in

Malaysia which is projected to reach 274TWh in 2030, renewable energy will be a

good alternative for fossil fuel energy. One of the promising renewable energy is the

tidal wave energy. Therefore, this project aims to design and model a long stroke

permanent magnet linear generator for tidal wave system. The specific objectives of

this project are to conduct literature review for various types of linear machine, to

propose new topologies design for tidal wave generating system, to design, model

and simulate the proposed new topologies and to choose the best design base on the

analysis result. The literature review on various types of linear machine has been

carried out thorough reading of journals, textbooks and various. Linear permanent

magnet machines come in various topologies such as moving-coil, moving-iron, and

moving-magnet. Then, two new different topologies of linear permanent magnet will

be proposed. Finite element analysis and optimisation of the proposed designs have

been simulated using Finite Element Method Magnetics, FEMM software.

iv

ACKNOWLEDGEMENT

First and foremost, I would like to thank my supervisor, Dr Taib Ibrahim for

the guidance and support during supervising my project from the beginning until present. lie is also being very helpful whenever I encounter any difficulties and problems in doing my project. Besides that, he always encourages me to not giving up searching the solution for such problems and difficulties.

Apart from that, I also would like to take this opportunity to thank all my

colleagues who have directly or indirectly helped me in completing this final year

project. Their assistance in solving some of the problems and their understanding of

my condition has been a great relieve.

V

TABLE OF CONTENTS

ABSTRACT --------------------------------------------------------------------------------------iv

LIST OF FIGURES viii

LIST OF TABLES x

CHAPTER 1: INTRODUCTION I

1.1 Background of Study ...................................................

1

1.2 Problem Statement 2

1.3 Objective and Scope of Study .....................................

3

CHAPTER 2: LITERATURE REVIEW 3

2.1 Linear Motor Concept_________________________________________________ 3

2.2 Linear Permanent Magnet Motor------------------------------- 5

2.3 Finite Element Method 11

CHAPTER 3: METHODOLOGY 14

3.1 Procedure Identification 14

3.2 Methodology .................................................................

j. 6

3.2 Tools and Equipment ....................................... .............

16

CHAPTER 4: RESULT AND DISCUSSION____________ ---------18

4.1 The Proposed Design----------------------------------------------------18

4.2 Finite Element Analysis of Air-cored ..........................

22

Quasi-Halbach Magnetised Machine

With Rectangular Magnet

vi

4.3 Finite Element Analysis of Air-cored ..........................

26

Quasi-Halbach Magnetised Machine

With Trapezoidal Magnet

CHAPTER 5: CONCLUSION AND RECOMMENDATION 28

5.1 Conclusion 28

5.2 Recommendation 28

REFERENCES 29

APPENDICES......... 31

Appendix 1 FYP I Gantt Chart and Key Milestone................. 2

Appendix II FYP 11 Gantt Chart and Key Milestone .............

33

Appendix III Dimension of Air-Cored .....................................

34

Quasi-Halbach Magnetised Machine With

Rectangular Magnets

Appendix IV Dimension of Air-Cored ....................................

35

Quasi-Halbach Magnetised Machine With

Rectangular Magnets

vii

LIST OF FIGURES

Figure I Realisation of linear induction motor from rotary induction motor --------- 4

Figure 2 Realisation of linear permanent magnet motor from rotary .................... 4

permanent magnet motor Figure 3 Rectangular ironless moving-coils linear motor

----------- -- -_---------- --- _6 Figure 4 Rectangular iron core linear motor .............................................................

7

Figure 5 Moving-coil linear generator----------------- 8 -----------------------------------------------_-____

Figure 6 Moving-iron linear generator for low power application .........................

9

Figure 7 Axially magnetised cylindrical moving magnet linear motor------------------10

Figure 8 Radially magnetised cylindrical moving magnet linear motor ----------------- 10

Figure 9 Pole piece between two blocks of permanent magnet ..............................

I I

Figure 10 3D cylindrical tube ............................. . _... __..

12

Figure I1 Axisymmetric problem------------- ----------------"----------------------------... ---.. "----------"

12

Figure 12 Planar problem___________________________________ . 12

-----------------------------------------------------__.. Figure 13 Project methodology-. ------- --------------- ---15 Figure 14 Air-cored quasi-hallbach magnetised machine with rectangular

............. 18

magnet

Figure 15 Air-cored quasi-hallbach magnetised machine with trapezoidal .............

19

magnet Figure 16 3D view of air-cored quasi-hallbach magnetised machine with .............

20

rectangular magnet Figure 17 3D view of air-cored quasi-hallbach magnetised machine with.............. 1

trapezoidal magnet Figure 18 Magnetic flux distributions at initial position, z=Omm............................. 22 Figure 19 Magnetic flux distribution at maximum stroke position, z=18mm__-- --23 Figure 20 Magnitude of air-gap magnetic flux density

............................................. 23

viii

Figure 21 Single phase air-cored quasi-hallbach magnetised machine -------------------- 24

with rectangular magnet Figure 22 The graph of machine's efficiency versus TmT/Tp..................................... 25

Figure 23 Magnetic flux distributions at initial position, z=10mm--------------- -----------

26

Figure 24 Magnetic flux distributions at maximum stroke position, z=14mm........ 6

Figure 25 Magnitude of magnetic flux density at the air gap___________________________________ 27

IX

LIST OF TABLES

Table I Design parameters and specification of the machines ------------------------------ 19

Table 2 Comparison of machine's efficiency with varying Tmr/TP .......................

24

X

CHAPTER I

INTRODUCTION

1.1 Background of Study

Renewable energy is becoming popular alternative to the fossil fuels energy

such as petroleum, gas and coal. As the fossil fuels reserve will be extinct and the

environmental impact they have, the renewable energy has a good potential to be

explored. One of the extremely promising energy sources is the ocean wave energy.

The world potential of harnessing the ocean's untapped energy is between 200GW to

5000GW at the offshore, 10GW to 500GW at near shore and I GW to 50GW at the

shoreline [1].

The conversion of ocean wave energy requires a device that will intercept the

linear motion of the wave and converts the portion of the energy into mechanical

energy first and then to electrical energy. Various types of wave energy devices have

been patented, depending on the location of the devices whether shoreline, near shore

or offshore.

Permanent magnet linear generator buoy [2] is an experimental ocean wave device. It employs the vertical motion of ocean wave to move the armature coil (mounted on the buoy) relative to permanent magnet field (mounted on the central translator shaft which is anchored to the sea floor). Then, the voltage is induced in the

coil. Besides that, Surfing Wave Energy Converter (SWEC) [3] employs the wave to

move several paddles horizontally. These paddles are connected to a common drive

train to drive the electrical machines and generating the power. Other mechanism

I

used to absorb wave energy is submerged pressure devices which exploit the pressure

variation on a submerged chamber as wave crests pass to cause the chamber to

expand and contract. (i. e the Archimedes Wave Swing) [3].

The long stroke permanent magnet generator will be designed to harness the

ocean wave energy to generate electricity. In this project, several linear permanent

magnet motor topologies will be studied and analysed using Finite Element Method

and analytical model.

1.2 Problem Statement

The electricity demand of Malaysia will increase by 4.7 percent per year over

the outlook period, to reach 274 TWh in 2030 [4]. As the cost of generating electrical

power from the fossil fuel increases and growing demand of electrical power, there is

a need to overcome this problem through renewable and clean energy.

One of the renewable energy is ocean wave energy. Ocean wave has powerful force, but its frequency is extremely low of about 0.1 Hz (equivalent to 6 rpm) [1].

While the success of generating electricity from this source demands the frequency is

raised to equivalent of 500 - 1500 rpm. Therefore, three phase long stroke linear

permanent magnet generator will be designed by analysing its performance as the

motor. This is because the machine can be inter-convertible base on its energy

sources.

2

1.3 Objectives and Scope of Study

The objective of this project is to design and modelling long stroke permanent

magnet linear generator for tidal wave system. The specific objectives of this project

are:

" To conduct literature review for various type of linear machine

" To propose new linear machine design for tidal wave generating system

" To design, model and simulate the proposed design

" To choose the best design base on findings from simulation.

3

CHAPTER 2

LITERATURE REVIEW

2.1 Linear Motor Concept

According to A Dictionary of Physics [5], linear motor is a form of induction

motor in which the stator and armature are linear and parallel, rather than cylindrical

and coaxial. Principally, linear machine configuration can be realised from every

rotary electrical machine configuration. Figure 1 and Figure 2 show the process of

realising linear motor from the induction motor and the permanent magnet motor.

Conventional Motor I Inear Motor

Figure 1 Realisation of linear induction motor from rotary induction motor [6]

Wie; Figure 2 Realisation of linear permanent magnet motor from rotary permanent

magnet motor [7]

4

A conventional rotating induction motor has circular rotor and stator. The

coils in the rotor and stator are mounted in circular array. However, linear induction

motor has both flat or tubular rotor and stator. The linear induction motor can be

realised from the rotary induction motor by slicing and unrolling it as shown in

Figure 1. The same process can be used to obtain either flat or tubular linear

permanent magnet motor as shown in Figure 2.

A linear machine produces linear force to the load without any rotary to linear

transmission devices such as belt and pulley, rack and pinion etc.

2.2 Linear Permanent Magnet Motor

Linear permanent magnet motor reduces the manufacturing and operating cost due to its simplicity of construction. Besides that, it also uses permanent magnet as

the field unit, thus eliminate the need for field winding. These two factors make linear

permanent magnet motor more favourable than other direct linear motor [8].

Linear motor comes with various topology such as iron core, air core and

slotless. The advantages of iron core linear motor are it has high thrust force and good

heat dissipation. By utilizing lamination in the armature, the magnetic flux can be

concentrated to produce high thrust force. Heat generated from the coil can be

dissipated through the iron lamination. Air core linear motor produces high

acceleration moving armature due to low mass moving armature. Slotless and slotted

topologies also can reduce the cogging force and increase the thrust force respectively [9].

5

Generally, linear permanent magnet motor can be categorised into three

configurations, which are [9]:

i. moving-coil

ii. moving-iron

iii. moving-magnet

2.2.1 Moving-coil motor

The structure of moving-coil linear motor consists of coil winding at the

armature and permanent magnet at the stator either axially magnetised permanent

magnet or radially magnetised permanent magnet. Rectangular ironless moving coil linear motor [10] shown in Figure 3 has no cogging forces (the attraction between the

moving coil and the permanent magnet) and lower mass armature due to the ironless

coil assembly.

Steel "Racetrack" coil windings

Block magnets

Figure 3 Rectangular ironless moving coil linear motor [10]

The radially magnetised magnets configuration as in Figure 3 provides faster

returning fluxes and significant in reducing the thickness of steel, thus reduce the

material cost [9].

Figure 4 shows rectangular iron core linear permanent magnet motor. The

slotted iron core significantly decreases the working magnetic air gap, thus yields high thrust force. The cogging force also exists because of the strong attractive force

6

between the permanent magnet and the iron core. However, it can be reduced by

skewing the magnet.

Steel forcer

Figure 4 Rectangular iron core linear permanent magnet motor [10]

A tubular moving coil linear generator [2] shown in Figure 5 can reduce the

cogging force by using annular shape pole piece and permanent magnet. The magnets

are stacked in pairs such that opposing magneto-motive forces (mmfs) drive the flux

through the soft iron. This 0.320m total length generator will produce 25V rated

voltage, 3A rated current and 50W output power.

7

N-35 MAGNETS. DOUBLE STACKED N

ýýý`

SOFT IRON POLE TIPS

ýý _'_. ý

N

S

S

3

04, ý.

N

N

Figure 5 Moving-coil linear generator [2]

2.2.2 Moving-iron motor

Moving-iron permanent magnet linear motors have simpler designs because

they are usually required to have a uni-directional force capability and use a

mechanical spring to reverse the motion of the plunger when the motor is de-

energised [9].

A small linear permanent magnet generator for generating electrical power

was developed by Wang et al [11] as illustrated in Figure 6 [9]. The generator is a two-phase tubular device, the stator having both permanent magnets and coils, while the moving armature is a simple salient iron core. The axially magnetized permanent magnets and the laminated pole-pieces in the stator produce an essentially radial air-

8

gap field. The stator winding flux linkage is modulated by the linear movement of the

armature, and generates an induced electromotive force (EMF). This 48mm axial

stroke linear generator produces 3mJ energy and its average speed is 0.3m/s.

Permanent magnet Lamination

Non-magnetic spacer

Figure 6 Moving-iron linear generator for low power application [9]

Throughout comparison of the previous topologies of moving-iron motor, the

conclusion is the moving-coil motor suffers some disadvantages such as:

i. Heavy weight of moving mass ii. Relatively low thrust force

Therefore, moving-iron topologies will not be considered for designing the long

stroke linear permanent magnet generator.

2.2.3 Moving-magnet motor

There are many topologies for moving-magnet motor. The moving-magnet

motor can have different permanent magnet magnetisation direction which are radially or axially magnetised as shown in Figure 7 and Figure 8. Axially magnetised topology has higher specific force capability than the radially magnetised topology. It

9

also offers lower manufacturing cost, because its permanent magnets are simply

magnetised.

Coll wmtling

Disk magnet

Steel housing

_. ý

Figure 7 Axially magnetised cylindrical moving magnet linear motor[ 10]

Coil winding

Steel core --

Steel housing

Lý1 IL iL i'ý LiL

ý Ring magnets -

ý -- \

Figure 8 Radially magnetised cylindrical moving magnet linear motor [10]

As for the linear motor in Figure 7, the magnetic flux is squeezed through the

pole piece between the oppositely polarized magnets. Thus, it increases the magnetic field (0.6 - 1.2 times the magnet material's B, value) [10]. Figure 9 shows the

magnetic field is channelled from the permanent magnet into the coil by the pole

i V'

I 4-

10

piece. While the linear motor in Figure 8 has very small working magnetic air gap

and yields higher forces via a higher magnetic field.

Stator

Figure 9 Pole piece between two blocks of permanent magnet [4]

Moving-magnet linear motor has some advantages such as higher efficiencies

than moving-coil linear motor. Besides that, it also requires smaller volume of

permanent magnet than the moving-coil linear motor for the same output power. Moving-magnet linear motor also does not have flying leads connected to its

armature, thus making it more reliable, rugged and suitable for higher duty operation

[9].

2.3 Finite Element Method

Finite element method is an engineering analysis of engineering design to

predict the performance of the design by calculating the field, which is defined as a

quantity that varies with position within the device analysed. In this project, the

magnetic field will be analysed together with its potential; magnetic vector potential. The field is related to the potential as its derivatives with respect to position.

The finite element model contains information about geometry (subdivided

into finite elements), materials, excitation and constraints. The material properties are needed to describe materials in electromagnetic problems. There are three

11

electromagnetic material properties which are permeability, permittivity (or dielectric

constant) and electrical conductivity. These material properties may vary with

temperature or frequency or other physical parameters.

In this project, two-dimensional (2D) axisymmetric finite element model of

motor will be developed using open source software. 2D finite element means by

definition, it connects three or more grid points forming a 2D plane, and all potentials

and fields in the element can vary in the two directions of the plane. Figure II and 12

show how three-dimensional (3D) cylinder in Figure 10 is modelled as axisymmetric

problem and planar problem respectively.

Z

xy

Figure 10 3D cylindrical tube

Z

r

Figure 11 Axisymmetric problem Figure 12 Planar problem

12

2.3.1 Boundary Condition

There are five boundary conditions exist for the magnetic and electrostatic problem, which are [121:

a. Dirichlet. In this type of boundary condition, the value of potential A or V is

explicitly defined on the boundary, e. g. A=0. By defining A=0 along a boundary in magnetic problem, keeping magnetic flux from crossing the boundary.

b. Neumann. This boundary condition specifies the normal derivative of

potential along the boundary. In magnetic problems, the homogeneous

Neumann boundary condition, en =0 is defined along a boundary to force

flux to pass the boundary at exactly a 90° angle to the boundary. This sort of boundary condition is consistent with an interface with a very highly

permeable metal.

c. Robin. The Robin boundary condition is sort of a mix between Dirichlet and Neumann, prescribing a relationship between the value of A and its normal derivative at the boundary. An example of this boundary condition is:

OA ön+cA=0

This boundary condition is most often in FEMM to define "impedance

boundary conditions" that allow a bounded domain to mimic the behavior of

an unbounded region. d. Periodic. A periodic boundary conditions joins two boundaries together. In

this type of boundary condition, the boundary values on corresponding points of the two boundaries are set equal to one another.

e. Antiperiodic. The antiperiodic boundary condition also joins together two boundaries. However, the boundary values are made to be of equal magnitude but opposite sign.

13

CHAPTER 3

METHODOLOGY

3.1 Procedure Identification

Literature review of linear machine has been conducted. It is done through

collecting information from electrical and electronic journal, thesis, textbooks and

websites. This literature review covers the linear motor theory, types of linear

machine and the various topologies of linear machine. There are many types of linear

machine such as linear induction machine, linear synchronous machine, linear

switched reluctance machine, linear DC machine and linear permanent magnet

machine. However, the scope of the literature review will focus only on the linear

permanent magnet machine. The topologies of linear permanent magnet machine can be grouped into three major groups which are moving-magnet machine, moving-iron

machine and moving-coil machine.

Through the findings from literature review, two new topologies of linear

permanent magnet machine have been proposed. The performance of the proposed

machine topologies is analysed by using finite element analysis. Finite element

analysis is being carried out to analyse the magnetic flux distribution and motor's

efficiency. Then, optimisation of the motor's parameters will be done base on the

result of the finite element analysis. The project procedures are summarised in the

Figure 13.

14

Design and Modeling Long Stroke Linear Permanent Magnet Motor

t Start

Feasibility studies of tidal wave generating

system

4 Literature review of current

linear motor topologies 4

Propose new linear motor topology

t Design and modeling

using FEMM

T Finite element

analysis of proposed topology

i Optimisation of motor

dimension

i End

Figure 13 Project methodology

15

3.2 Methodology

The important activity in this project is the finite element analysis of the

design. The geometry of the design will be drawn using FEMM and all the material

needed will be assigned to the parts of the machine. The magnetic flux distribution of

the machine under no load condition will be analysed at its initial position and at

maximum stroke length. If the magnetic flux distribution is symmetrical at both tooth

of the stator when the armature is at initial position, then, magnetic flux distribution

of the machine will be analysed when the armature is at the maximum stroke length.

After that, the efficiency of the machine will be calculated. Efficiency of the machine is affected by the power losses which are copper loss, iron loss and eddy current loss.

Based on the finite element result, dimension of the motor will be optimised such as

magnet length, width of back iron, height of the slot, radius of the air-cored, and

width of the stator slot opening.

The future works of this project involves analytical analysis of the machine's

design using the Matlab Simulink. Both results of finite element analysis and

analytical analysis will be validated.

3.3 Tools and Equipment Required

3.3.1 Finite Element Method Magnetic

Finite Element Method Magnetic version 4.2 (FEMM v4.2) will be used to do

finite element analysis of the linear permanent magnet machine design. An analysis in

FEMM involves three distinct steps, which are:

a. Preprocessing: The user provides data such as the geometry, materials and

element type to the program. b. Solution: The user defines the type of analysis, set boundary conditions,

apply loads, and initiate finite element solutions.

16

c. Post processing: The user reviews the results of the analysis through

graphical displays and tabular listing.

Design optimisation of the proposed new topology of linear permanent

magnet machine will be done base on the result of the finite element analysis.

17

CHAPTER 4

RESULTS AND DISCUSSION

4.1 The Proposed Designs

The most important criterion that will be analysed for the long stroke linear

permanent magnet machine are the stroke's length, the magnetic field and its flux

distribution, the thrust force, motor's efficiency and cost-effectiveness. Base on these

criterions, moving magnet topology has been chosen for the design of long stroke linear permanent magnet machine. Two designs have been proposed for further

analysis, which are three phase air-cored quasi-hallbach magnetised machine with

rectangular magnet and three phase air-cored quasi-hallbach magnetised machine

with trapezoidal magnet. Both machine are tubular motors with slotted stator made of

mild steel. Figure 14 and 15 show the air-cored quasi-Halbach magnetised machine

with rectangular magnet and air-cored quasi-Halbach magnetised machine with

trapezoidal magnet, respectively.

Iron

Coil f--Air

Figure 14 Air-cored quasi-hallbach magnetised machine with rectangular magnets

18

Iron

Coil

-. T 4-- 1 i/-+\i/'- i-AiC

Figure 15 Air-cored quasi-halbach magnetised machine with trapezoidal magnets

The design parameters and specification of tubular long stroke linear

permanent magnet machine are shown in Table 1. Details of the design parameters for both machines are included in the Appendix III and Appendix IV.

Table 1: Design parameters and specification of the machines Item Value Units Outer diameter of stator 300 mm Axial length of machine 400 mm Length of pole-pitch 10 mm Height of the air-gap 1 mm Height of the magnet 10 mm Permanent magnet material Sintered NdFeB Remanence of permanent magnet

1.045 T

Coercivity of permanent magnet

891300 A/m

19

4. ]JA ir-cored Quasi-Hallbach Magnetised Machine with Rectangular Magnet

The advantage of air-cored machine is it has low mass moving armature.

Thus, the machine will produce high thrust force. Besides that, it also has low iron

loss and no eddy current loss in armature. The slotted stator also provides good heat

dissipation and reduces the working magnetic air gap. Therefore, it will produce high

force. The quasi-hallbach arrangement of the permanent magnet reduces the magnetic

flux leakage because the axially magnetised permanent magnet provides a returning

path for the radial air gap magnetic flux linkage. This will reduce the magnetic flux

linkage in the back iron and the width of the back iron will also be reduced.

Therefore, the cost of the stator's material will be reduced. However, this topology

suffers high cogging force due to the slotted stator but it can be reduced by skewing

or stepping the magnet, and optimize the permanent magnet width and axial length

[13].

Figure 16 shows the three dimension (3D) view of the air-cored quasi- hallbach magnetised machine with rectangular magnet.

Coil

Figure 16 3D view of air-cored quasi-hallbach magnetised machine with rectangular

magnet

20

4.1.2 Air-cored Quasi-Hallbach Magnetised Machine with Trapezoidal Magnet.

In the second design, the trapezoidal NdFeB permanent magnets are used

instead of rectangular magnet. The advantage of trapezoidal magnet is it will

eliminate or reduce the irreversible demagnetization at the top corner of axially

magnetised permanent magnet and the bottom corner of radially magnetised

permanent magnet [141. Figure 17 shows the three dimensional (3D) view of air-

cored quasi-hallbach magnetised machine with trapezoidal magnet.

Coil

Figure 17 3D view of air-cored quasi-hallbach magnetised machine with trapezoidal

magnet

21

42 Finite Element Analysis of Air-cored Quasi-Halbach Magnetised

Machine with Rectangular Magnet

Figure 18 and 19 show the magnetic flux distribution for the air-cored quasi- hallbach magnetised machine with rectangular magnets when the moving magnet is at initial position, z=Omm and at maximum stroke position, z=l8mm, respectively. In

both cases, the frequency is set to zero and no load is applied to the motor. From the figure below, the magnetic flux is almost symmetry at both tooth of the iron core. This shows that the configuration of the permanent magnet is correct. There is no

magnetic flux passing through the back iron of the stator because the magnetisation

vector of permanent magnet set A is cancelling the magnetisation vector of

permanent magnet set B.

0

A B

Figure 18 Magnetic flux distributions at initial position, z=0mm

:0

"

22

Figure 19 Magnetic flux distribution at maximum stroke position, z=l8mm

Figure 20 shows the magnitude of air-gap magnetic flux density. There is a drop of magnitude of air-gap flux density at several points along the axial length of the machine. This is due to the slot effect of the machine. Besides that, the selection

of good size of mesh will determine the accuracy of the result of finite element

analysis of the generator especially the size of the mesh of the air gap between the

stator and the moving permanent magnet. In this analysis, air gap region is divided

into four regions with mesh's size of 0.2mm of each region.

Magnitude of B, T 1.40E+00

1.20E+00

1.00E+00

8.00E-01

6.00E-01

4.00E-01

2.00E-01

0.00E+00

A jv7vý1

yýJýýý 8 . -'I NM

tD N 00 O . -r Mý

. O-1 1-4 rpl

pN NNNNNN

+ýýýTý? Q%

NO0 M Ný! ' ýO

ý Q1 m al

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WWW eWý

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Q1 ONM tJ1 00 NNNNNMMMMM M)

Armature length, mm

Figure 20 Magnitude of air-gap magnetic flux density

23

The design parameter of the machine has been optimised in terms of the ratio

of radially magnetised magnet's length, Tm, over pole's length, T. The optimum Tmr 1'p

ratio is determined by analysing the efficiency of the machine. The analysis of the

machine output power is done as per phase. That means the first phase of the machine

only is analysed using finite element method (single phase of the motor is shown in

Figure 21). This is because in three phase system, the total output power of the

machine is three times the power of single phase machine. 2.5A current is supplied to

the machine at the frequency of 50Hz while the number of turns of the coil is set to

1680 turns. The result of the simulation is shown in Table 2 and Figure 22.

I { -- f -- + 0 0 0

I 435,0000

Figure 21 Single phase air-cored quasi-hallbach magnetised machine with rectangular

magnet

Table 2 Comparison of machine's efficiency with varying TmrITp

TmýTP Tmr (mm) TP (mm) Pin (W) Piou (W) Pouc (W) Efiiciency, rl (%)

0.4 18 45 1358.93 295.72 1063.20 78.24 0.45 20.25 45 1363.75 296.10 1067.65 7829 0.5 22.5 45 1354.68 259.02 1095.66 80.88 0.55 24.75 45 1358.22 295.59 1062.63 78.24 0.6 27 45 1365.19 296.35 1068.84 78.29

24

ý V G !! U

ý W

81.50

81.00

80.50

80.00

79.50

79.00

78.50

78.00

77.50

77.00

76.50

0.4 0.4S 0.5 0.55 0.6

Tmr/Tp

Figure 22 The graph of machine's efficiency versus T,,, T/Tp.

25

4.3 Finite Element Analysis of Air-cored Quasi-Halbach Magnetised

Machine with Trapezoidal Magnet

Figure 23 and 24 show the magnetic flux distribution for the air-cored quasi- hallbach magnetised machine with trapezoidal magnets when the armature is at initial

position (z=0mm) and at the maximum stroke position (z=14mm). In both cases, the frequency is set to zero and no load is applied to the motor.. From the figure below,

the magnetic flux is almost symmetry at both tooth of the iron core. This shows that

the configuration of the permanent magnet is correct.

Figure 23 Magnetic flux distributions at initial position, zOmm

Figure 24 Magnetic flux distributions at maximum stroke position, z=14mm

26

Figure 25 shows the graph of magnitude of air-gap magnetic flux density

versus the length of the machine. The maximum magnitude of magnetic flux density is about 1.27T. It is higher than the maximum magnitude of magnetic flux density of air-cored quasi-Halbach magnetised generator with rectangular magnet which is

1.20T. Therefore, trapezoidal quasi-hallbach magnet increases the magnetic flux

density at the air gap.

Magnitudeaf B, T 1.40E+00

1.20E+00

1.00E+00

8.00E-01

6.00E-01

4.00E-01

2.00E-01

0.00E+00

ý-l 14 +ý °+ u., ww 8IRN d 1-4

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Mý OýO

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FOM1O Ný Mh 01 ON

co nO^ý

.... . -. I

............. e} %p pp 01 -i M . -ý rl . -1 ri NNNNNNMMMMMM

Armature length, mm

Figure 25 Magnitude of magnetic flux density at the air gap

27

CHAPTER 5

CONCLUSION AND RECOMMENDATION

5.1 Conclusion

Literature review on various linear machine topologies has been done and the

topologies can be grouped into three groups which are moving-coil, moving-iron and

moving-magnet machine. Based on that information, moving-magnet topology has

been selected for designing two designs of long stroke linear permanent magnet

machine which are air-cored quasi-hallbach magnetised machine with rectangular

magnet and air-cored quasi-hallbach magnetised machine with trapezoidal magnet.

Finite element analysis has been conducted on both machines and optimisation of the

t, n, Jtp has been done to air-cored quasi-hallbach magnetised machine with rectangular

magnet. Therefore, air-cored quasi-hallbach magnetised machine with rectangular

magnet can be further developed for generating electricity from the ocean wave.

5.2 Recommendation

Base on the findings, further optimisation of the design will be focused on

these parameters which are: i. radius of the air-cored

ii. height of the permanent magnet

Besides that, further analysis will be carried out using analytical model to

validate the finite element analysis result.

28

REFERENCES

[1] L. Freris and D. Infield, Renewable Energy in Power Systems, United

Kingdom, John Wiley & Sons Ltd, 2008.

[2] K. Rhinefrank, E. B Agamloh, A. von Jouanne, A. K. Wallace, J. Prudell, K.

Kimble, J. Aills, E. Schmidt, P. Chan, B. Sweeny, and A. Schacher, "Novel

ocean energy permanent magnet linear generator buoy, " Renewable Energy

31, pp. 1279 - 1298, September 2005.

[3] B. D. Hazlett, I. I. Inculet and D. R. Inculet, "Electric power generation by

`Surfing' water waves, " Renewable Energy 34, pp. 2510-2514, March 2009.

[4] Asia Pacific Energy Research Center,

<http//www. ieej. or. jp/aperc/2006pdf/Outlook2006/Whole Report. pdf, 2006.

1s1 "linear motor" A Dictionary of Physics. Ed. John Daintith. Oxford University

Press, 2009. Oxford Reference Online. Oxford University Press.

[6] V. N. Hoang, "Design of a single-sided linear induction motor", Degree

Thesis, The University of Queensland, Australia, 2003.

[7] 1. Boldea and Syed A. Nasar, Linear Electric Actuators and Generators,

Australia, Cambridge University Press, 1997.

29

[8] R. C. Okonkwo, 2006, "Design and performance of permanent-magnet dc

linear motors", IEEE Transactions on Magnetics, vol. 42, No. 9, pp. 2179 - 2183, September 2006.

[9] T. Ibrahim, "Short-stroke, single phase tubular permanent magnet motor for

refrigeration applications", PhD Thesis, University of Sheffield, 2009.

[10] A. C. Morcos, "The straight attraction, part two", Motion Control, pp. 24 - 28, July/ August 2000.

[11] J. Wang, W. Wang, G. W. Jewell, and D. Howe, "A low-power, linear,

permanent-magnet generator/energy storage system", IEEE Transactions on Industrial Electronics, vol. 49, No. 3, pp. 640 - 648, June 2002.

[12] D. Meeker, Finite Element Method Magnetics version 4.2 User's Manual,

2009.

[131 N. Bianchi, S. Bolognani, D. D. Corte, and F. Tonet, "Tubular linear

permanent magnet motor: an overall comparison", IEEE Transactions on Industry Application, vol. 39, No. 2, pp. 466 - 475, March/ April 2003.

[14] J. Wang, W. Wang, K. Atallah, and D. Howe, "Demagnetization Assessment

for Three-Phase Tubular Brushless Permanent-Magnet Machines", IEEE

Transactions on Magnetics, vol. 44, no. 9, pp. 2195 - 2203, September 2008.

30

APPENDICES

31

APPENDIX I" Planned Milestone for the First Semester of Final Year Project

No. De 111 Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 Selection of Project Topic

2 Preliminary Research Work Feasibility study of tidal wave generating system (tidal power, cost, energy policies and environmental effects)

3 Submission of Preliminary Report

4 Seminar 1

5 Project Work i. Literature review of current linear machine

topologies

6 Submission of Progress Report

7 Seminar 2

8 Project work continues i. Identify factors that reduce machine

efficiency ii. Proposed new topology

iii. Analysis of magnetic flux distribution

9 Submission of Interim Report Final Draft

10 Submission of Interim Report

11 Oral Presentation

p Process Suggested Milestone

32

APPENDIX II - Planned Milestone for the Second Semester of Final Year Project

No. Detxi /Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 19 20 21

1 Project Work Continue Learn using FEMM Refine the desi geometry of the linear machine

2 Submission of Progress Report 1 1 01

3 Project Work Continue Finite element analysis of the proposed design

w

4 Submission of Progress Report 2

5 Project work continue i. Optimise the design parameter of the machine

E

ti

6 Poster Exhibition O

7 Submission of draft report

8 Submission of Dissertation (soft bound) O 9 Oral Presentation

10 Submission of Project Dissertation (I-lard Bound)

Progress Suggested Milestone

33

APPENDIX III - Dimension Of Air-Cored Quasi-Halbach Magnetised Generator With Rectangular Magnets

+ lomm

4

400mm go .

90mm ý

10mm E E

ý 0 ý 20 3

1

50mm i-º } ý-t i -ý * ý-t iý fti

Mýº ýI If ý- T., T., 1T. T. J2

- 90mm ý

-º Tý i

Timm

f39mm

34

APPENDIX IV - Dimension Of Air-Cored Quasi-Halbach Magnetised Generator

With Trapezoidal Magnets

400mm

f q- - 90mm

s --o

20mm 0 E

ý: zz z_ -: sxý -1 ý 1o

-e-y 1 -4 ýe_ Q4

-T-i, -6 j+-a- ;

E ý 0 ý

39mm

35