cogging torque reduction of 6s-4p spoke-type...
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COGGING TORQUE REDUCTION OF 6S-4P
SPOKE-TYPE IPMSM USING A NEW
COMBINATION OF ROTOR DESIGN
FATIHAH SHAFIQAH BINTI BAHRIM
UNIVERSITI TUN HUSSEIN ONN MALAYSIA
COGGING TORQUE REDUCTION OF 6S-4P SPOKE-TYPE IPMSM USING A
NEW COMBINATION OF ROTOR DESIGN
FATIHAH SHAFIQAH BINTI BAHRIM
A thesis submitted in
fulfillment of the requirement for the award of the
Degree of Master of Electrical Engineering
Faculty of Electrical and Electronic Engineering
Universiti Tun Hussein Onn Malaysia
SEPT, 2017
This dissertation is dedicated to my beloved mother ROHAYAH BINTI ADNAN and
my father BAHRIM BIN SALIM. My brothers, and sisters, who have always
encouraged me with their love and prayers.
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ACKNOWLEDGEMENT
I am very thankful to Almighty ALLAH for without His graces and blessings,
this study would not have been possible. Since I started my Master research work,
several people and organizations have been involved directly and indirectly with my
project. They have loyally provided me encouragement, motivation, moral, and
financial support. Hereby, I express my gratitude to them. I would like to thank my
supervisor, Prof. Madya Ir. Dr. Erwan Sulaiman and co-supervisor, Dr Zarafi bin
Ahmad for providing the opportunity to be one of their students. His guidance and
support during the entire study made it possible for me to write this thesis. I am
continually amazed by his discipline, research, and scientific skills. This Master
project has been made possible with the financial support from the CGS, Universiti
Tun Hussein Onn Malaysia, and Ministry of Higher Education (MOHE), Malaysia.
My sincere thanks go to all my research group friends for sharing practical and
theoretical knowledge. Furthermore, I wish to express my sincere gratitude to my
family for their moral support and prayers. I would like to thank my father, Mr.
Bahrim bin Salim for his prayers and support, and also to my mother, the one who
had made me successful with her caring and gentle love.
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ABSTRACT
Cogging torque is one of the vital issues in permanent magnet motors (PMM).
Reducing cogging torque, which may cause vibration and acoustic noises, has
become an increasingly critical issue in PMM. Low cogging torque significantly
reduces acoustic noises and vibration, and enhances the positioning control of the
motor for electric vehicle drive application. Therefore, this thesis exemplifies the
significance of various rotor-PM configurations of three-phase 6S-4P Spoke-type
(IPMSM). Initially, conventional cogging torque reduction techniques of skewing
(Sk), notching (Not), radial pole pairing (Pop), and axial pole pairing (App) were
analysed. Then, a new combination such as skewing with pole pairing (SkPop),
skewing with pole axial pairing (SkApp), notching with pole pairing (NotPop), and
notching with pole axial pairing (NotApp) were proposed and compared. The
validity of the proposed designed techniques has been confirmed by 3-D Finite
Element Analysis (FEA) executed in commercial JMAG designer version 14.1,
under open circuit and short circuit conditions. Simulation results showed that the
conventional techniques have reduced the cogging torque of 6S-4P Spoke-type
IPMSM by 70.59%, 21.57%, 32.35%, and 48.04% for Sk, Not, Pop, and App
respectively from the original value of 1.01Nm. The new proposed combination
techniques reduce the cogging torque by 71.86%, 63.55%, 30.93%, and 51.55% for
SkPop, SkApp, NotPop, and NotApp simultaneously. In addition, the cogging torque
in 6S-4P Spoke-type IPMSM has been successfully reduced and the best technique is
NotPop with 30.93% of cogging torque reduction, as well as the highest torque and
power capabilities of 7.643 Nm and 959.03 W respectively. Finally, design analysis
to improve NotPop performance has been done in this thesis. As a result, a new 6S4P
Spoke-type IPMSM with low cogging torque and 19.05% torque improvement has
been successfully designed.
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ABSTRAK
Tork penuggalan adalah salah satu isu penting dalam motor Magnet kekal (PMM)
dan mengurangkan tork penunggalan yang menyebabkan getaran dan bunyi akustik
menjadi isu yang semakin penting dalam PMM. Tork penuggalan yang rendah
dengan ketara mampu mengurangkan bunyi akustik, getaran, dan meningkatkan
kawalan kedudukan motor untuk elektrik aplikasi pemanduan kenderaan. Oleh itu,
tesis ini contoh kepentingan pelbagai pemutar-PM konfigurasi 3-fasa 6S-4P jenis
jejari (IPMSM). Pada mulanya, teknik pengurangan tork penuggalan konvensional
seperti Menyengetkan (Sk) dan mencatat (Not), jejari tiang berpasangan (Pop), dan
paksi berpasangan tiang (App) dianalisis. Kemudian, gabungan baru seperti
Menyengetkan dengan kutub berpasangan (SkPop), Menyengetkan dengan tiang
paksi berpasangan (SkApp) dan mencatat dengan kutub berpasangan (Notpop) dan
mencatat dengan kutub berpasangan paksi (NotApp) dicadangkan dan dibandingkan.
Kesahihan teknik direka yang dicadangkan itu telah disahkan oleh 3-D Finite
Element Analysis (FEA), dilaksanakan dalam komersial JMAG pereka versi 14.1, di
bawah litar terbuka dan keadaan litar pintas. Keputusan simulasi menunjukkan
bahawa teknik konvensional telah mengurangkan tork penuggalan untuk 6S-4P jenis
jejari IPMSM oleh 70,59%, 21.57%, 32.35% dan 48.04% bagi Sk, Not, Pop, dan
App masing-masing dari nilai asal 1.01Nm. Teknik gabungan baru yang dicadangkan
mengurangkan tork penuggalan dengan 71,86%, 63,55%, 30,93%, dan 51.55% bagi
SkPop, SkApp, NotPop dan NotApp serentak. Di samping itu, tork penuggalan
dalam 6S-4P jenis jejari IPMSM telah berjaya mengurangkan dan teknik yang
terbaik adalah NotPop dengan 30.93% pengurangan tork penuggalan serta
ketumpatan tork dan kuasa keupayaan tertinggi masing-masing 7.643 Nm dan 959.03
W. Akhir sekali, analisis reka bentuk untuk meningkatkan prestasi NotPop telah
dilakukan dalam tesis ini. Hasilnya, 6S4P jenis jejari IPMSM dengan tork
penuggalan rendah dan 19.05% peningkatan ketumpatan tork telah berjaya direka.
viii
TABLE OF CONTENTS
TABLE OF CONTENTS viii
LIST OF SYMBOLS AND ABBREVIATIONS xi
LIST OF TABLES xiv
LIST OF FIGURES xv
LIST OF PUBLICATIONS xix
LIST OF AWARDS xxi
CHAPTER 1 INTRODUCTION 1
1.1 Research Background 1
1.2 Problem Statement 2
1.3 Objectives 3
1.4 Scope 3
1.5 Thesis Outline 4
CHAPTER 2 LITERATURE REVIEW 6
2.1 Introduction 6
2.2 Overview of Permanent Magnet Synchronous Motor
(PMSM) 6
2.3 Review of Cogging Torque 8
2.4 Cogging Reduction Method 12
2.5.1 Skewing the Slots/Poles/Magnet 13
2.5.2 Slot Opening Variation 16
2.5.3 Stator tooth Pairing 18
2.5.4 Rotor teeth/pole-pairing and Axial Pole
Pairing 19
ix
2.5.5 Stator/rotor pole displacement design 21
2.5.6 Slot and pole number combination 23
2.5.7 Dummy Slot/Notching 24
2.5.8 Rotor pole-chamfering 27
2.5.9 Magnet shifting 29
2.5.10 Magnet Pole Arc 30
2.5.11 Magnet Optimization 32
2.5.12 Flux barrier 33
2.5.13 Combination Techniques. 34
2.5 Summary 36
CHAPTER 3 RESEARCH METHODOLOGY 37
3.1 Introduction 37
3.2 Design and Investigation using Conventional Skewing,
Notching, Radial Pole Pairing and Axial Pole Pairing
Methods 38
3.2.1. Design Configuration of Conventional
Cogging Torque Reduction Methods 40
3.2.2. Investigation using JMAG-Designer 43
3.2.3. Performance Analysis of 6S-4P Spoke-type
IPMSM 45
3.3 Design and Investigation of New Combination
Method for Cogging Torque Reduction 50
3.3.1 Design Configuration of Proposed Combination
Method for Cogging Torque Reduction 50
3.4 Design Analysis to Improve the Best Cogging Torque
Reduction Method 52
3.5 Summary 52
CHAPTER 4 RESULTS AND DISCUSSION 53
4.1 Introduction 53
4.2 Design Results and Analysis Using Conventional
Skewing, Notching, Radial Pole Pairing and Axial
Pole Pairing Methods 53
x
4.2.1. Open Circuit Analysis Performance on The
Basis of 3-D FEA 55
4.2.2. Closed Circuit Analysis Performance Results
on The Basis of 3-D FEA 58
4.3 Design and Investigation Results of New Combination
Method for Cogging Torque Reduction 61
4.3.1 Open Circuit Analysis Performance on The
Basis of 3-D FEA 62
4.3.2 Closed Circuit Analysis Performance on The
Basis of 3-D FEA 65
4.4 Design Improvement Results of the Best Cogging
Torque Reduction Method 68
4.4.1 Open Circuit Analysis Performance on The
Basis of 3-D FEA 72
4.4.2 Closed Circuit Analysis Performance on The
Basis of 3-D FEA 75
4.5 Summary 78
CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS 79
5.1 Conclusion 79
5.2 Future Works 80
REFERENCES 81
xi
LIST OF SYMBOLS AND ABBREVIATIONS
ωNm - Mechanical angular displacement
m - PM flux linkage
e - Field excitation flux linkage
θ - Angle of rotor position
θm - Rotor mechanical angle
a - Filling factor of armature coil
cog - Electrical angle of rotation
e - Filling factor of excitation coil
f - Filling factor
- Efficiency
- Electrical angular position of rotor
r - Rotational speed
- Copper resistivity
An - Cross sectional area of PM
nB - Magnetic flux density
ef - Electrical frequency
mf - Mechanical rotation frequency
H - Height of coil slot
Ia - Armature coil current
aJ - Armature current density
k - Harmonic order
kW - Kilowatt
- Stack length
L - Coil length
La,e - Stack length of machine
La-end - Estimated average length of armature end coil
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Ld - d-axis inductance
La-end - Estimated average length of field excitation end coil
Lf - Total series inductance of field coil
Lq - q-axis inductance
N - Number of turns
n - Number of skewing steps
Na - Number of turns of armature coil
Nc - Period of cogging torque
Nd - Neodymium
Ne - Number of cogging torque cycle
NL - Least common multiple of slots
Nn - Number of notches
Np - Number of periods of cogging torque
rN - Number of rotor poles
sN - Number of stator slots
p - Pole pairs number
Q - Number of stator slots
aS - Armature coil slot area
T - End time
eT - Electromagnetic torque
τcog - Cogging torque
LT - Load torque
Tmax - Maximum torque
V1 - Volume of coil slot
V2 - Volume of coil end
Vtotal - Total volume of coil
Wm - Energy in the air-gap
Wi - Stored magnetic energy
Wo - Average magnetic energy
xd,q - Components in d-q axis
xu,v,w - Components of U, V, and W phase
AC - Alternating current
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AFFSPMM - Axial Field flux switching permanent magnet machine
BHmax - High energy product
Br - Retentively
DC - Direct current
EV - Electric vehicle
EMF - Electromotive Force
FE - Field excitation
FEA - Finite Element Analysis
FEFSM - Field excitation flux switching machine
FSM - Flux switching motor
HCF - Highest common factor
HE - Hybrid Excitation
HEFSM - Hybrid excitation flux switching machine
HEV - Hybrid Electric Vehicle
IPMSM - Interior permanent magnet synchronous motor
MMF - Magnetomotive force
NdFeB - Neodymium magnet
PM - Permanent magnet
PMSM - Permanent magnet synchronous machine
SPM - Surface permanent magnet
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LIST OF TABLES
1.1 Parameters of 6S-4P Spoke-type IPMSM. 4
3.1 Initial model specifications of the proposed 6S-4P
Spoke-type IPMSM [105]. 39
3.2 Design Parameter for Skewing, Notching, Radial pole
pairing and Axial pairing of 6S-4P Spoke-type IPMSM. 42
3.3 Design specifications of the proposed 6S-4P Spoke-type
IPMSM 44
3.4 Input current of armature coil, Ia of initial IPMSM
design. 48
3.5 Design Parameter for SkPop, SkApp, NotPop and
NotApp method of 6S-4P Spoke-type IPMSM. 51
4.1 Rotor model for existing cogging torque reduction
techniques. 54
4.2 Rotor model for proposed cogging torque reduction
techniques. 62
4.3 Overall performance of all rotor-PM designs of 6S-4P
Spoke-type IPMSM. 68
4.4 Parameters of various stator tooth thickness and rotor
outer radius. 68
4.5 Parameters of various shaft radius and PM length and
width. 70
4.6 Parameters of various rotor bridge thickness. 71
4.7 Final design specifications of the new 6S-4P Spoke-type
IPMSM. 72
xv
LIST OF FIGURES
2.1 Surface Permanent Magnet Synchronous Motor. 7
2.2 Interior Permanent Magnet Synchronous Motor. 7
2.3 Flow path of flux. 9
2.4 One period of a regular cogging torque cycle. 10
2.6 Step-skew rotor design under open circuit condition. 14
2.7 Cogging torque waveform with different rotor skewing
steps [63]. 15
2.8 Prototype of stepped rotor skewing [64]. 15
2.9 Cross sectional views of a PM machine at different
axial-z location. 16
2.10 Slot opening and PM interpolar distance [67]. 17
2.11 Stepped rotor skewing with three modules [67]. 17
2.12 Stator design (a) Conventional stator and (b) Stator
tooth pairing [69]. 18
2.13 Characteristic of cogging torque [69]. 18
2.14 Rotor Teeth-Pairing [73]. 19
2.15 Cogging torque comparison between teeth pairing
design and original design [75]. 20
2.16 Rotor teeth pairing (a) Circumferential pairing and
(b) Axial pairing [76]. 21
2.18 Cogging torque characteristic for various stator
displacement angle[77]. 21
2.17 Stator displacement. (a) Original design and (b) Stator
displacement design [77]. 22
2.19 The rotor pole displacement between two rotors [78]. 22
2.20 Cogging torque comparison of two rotor designs [78]. 23
2.21 The pole-pitch to pole-arc ratio of rotor PM [81]. 23
xvi
2.22 Rotor pole notching [82]. 25
2.23 Stator teeth notching (a) With no notching and (b) With
notching [83]. 25
2.24 Influence of notching on cogging torque. 25
2.25 Notches in for cogging torque reduction. (a) Notches
in stator part and (b) Notches in rotor part [84]. 26
2.26 Cross section of 12S10P motor with segmented PMs. 27
2.27 Comparison between proposed evaluation parameter
and FEM analysis results [85]. 27
2.28 Rotor pole-chamfering [86]. 28
2.29 The initial rotor pole scheme with variable rotor pole
arcs [87]. 28
2.30 Rotor tooth-chamfering [39]. 28
2.31 Shifted PMs in (a) Four pole, (b) Six pole and (c) Eight
pole [88]. 29
2.32 Schematic diagram of different rotor model. 30
2.33 Cogging torque of the 8 pole machine [89]. 30
2.34 Optimization of arc length for PM poles. 31
2.35 PM poles angles that have been used for the
computation. 32
2.36 Cogging torque of different PM shapes[94]. 32
2.38 PM shape (a) Full model, (b) 0.75 model, (c) 0.5 model,
(d) 0.25 model, (e) 0 model [96]. 33
2.39 Cross sectional view and parameters details of Brushless
DC motor design [100]. 34
2.40 Two type of skew (a) Conventional skew and (b) Slot
opening skew [104]. 35
2.41 The stator layers with different slot design which result in
various slot-opening positions to achieve the slot opening
skew. 35
3.1 General flow chart of project implementation. 38
3.2 Flow chart of project design and investigation. 38
3.3 Cross sectional view of 6S-4P Spoke-type IPMSM. 39
3.4 Region radial pattern (a) Stator (b) Armature Coil. 40
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3.5 Extruded part (a) Stator and (b) Armature Coil. 41
3.6 General flow chart of geometry editor. 41
3.7 Flow chart of work flow analysis performance. 46
3.8 Typical torque and power versus speed characteristic of
synchronous motor. 49
3.9 Cogging Torque Reduction Techniques. 51
3.10 Flow chart of design improvement analysis. 52
4.1 Cogging torque cycle of existing cogging torque
minimisation techniques. 55
4.2 Instantaneous cogging torque value. 56
4.3 Percentage of cogging torque reduction. 56
4.4 Flux linkage of existing cogging torque minimisation
techniques. 57
4.5 Back EMF phase comparison of existing cogging torque
minimisation techniques. 58
4.6 Initial torque against armature current density, Ja. 59
4.7 Initial power against armature current density, Ja. 59
4.8 Torque versus speed for existing cogging torque
reduction techniques. 60
4.9 Power versus speed for existing cogging torque
reduction techniques. 61
4.10 Cogging torque of proposed cogging torque
minimisation techniques. 63
4.11 Instantaneous cogging torque value of proposed cogging
torque minimisation techniques. 63
4.12 Percentage of cogging torque reduction. 64
4.13 Flux linkage of proposed cogging torque minimization
techniques. 64
4.14 Back EMF phase comparison of proposed cogging torque
minimisation techniques. 65
4.15 Initial torque performance of proposed cogging torque
minimisation techniques. 66
4.16 Initial power performance of proposed cogging torque
minimisation techniques. 66
xviii
4.17 Torque versus speed for proposed cogging torque reduction
techniques. 67
4.18 Power versus speed for proposed cogging torque reduction
techniques. 67
4.19 Various stator teeth thickness and outer rotor radius. 69
4.20 Torque performance of various stator tooth thickness
and rotor outer radius analysis. 69
4.22 Torque performance of various shaft radius and PM size
analysis. 70
4.23 Various rotor bridge thickness analysis. 71
4.24 Torque performance of various rotor bridge thickness
analysis. 71
4.25 Cross-sectional view of new 6S-4P Spoke-type IPMSM.72
4.26 Cogging torque of Basic, NotPop and new NotPop
design. 73
4.27 Instantaneous cogging torque amplitude. 73
4.28 Percentage of cogging torque reduction. 74
4.29 Flux linkage comparison of new NotPop design. 74
4.30 Induce voltage comparison of new NotPop design. 75
4.31 Torque vs. armature current density, Ja. 76
4.32 Power vs. armature current density, Ja. 76
4.33 Torque against speed for new NotPop design. 77
4.34 Power against speed for new NotPop design. 77
LIST OF PUBLICATIONS
Journals:
(i) Fatihah Shafiqah Bahrim, E. Sulaiman, Laili Iwani Jusoh, M. Fairoz Omar,
Rajesh Kumar “Cogging Torque reduction of IPM Motor using Skewing,
Notching, Pole Pairing and Rotor Pole Axial Pairing.” International Journal
of Applied Engineering Research ISSN 0973-4562 vol.12, no.7, Mar 2017,
pp. 1371-1376. (Scopus,Q3)
(ii) Fatihah Shafiqah Bahrim, E. Sulaiman, L. I. Jusoh, R. Kumar. “Method on
Designing The 3-D Rotor Skewing Using JMAG Software”, International
Journal of Energy and Power Engineering Research (IJEPER), accepted.
Proceedings:
(i) F. S. Bahrim, E. Sulaiman, L. I. Jusoh, R. Kumar. “A new combination
notching and pole pairing method for cogging torque reduction in IPMSM
and PMFSM”, 2nd International Conference on Science and Technology
For Sustainability 2016 (ICoSTechS 2016), 30th November, 2016, accepted
and presented.
(ii) F. S. Bahrim, E. Sulaiman, L. I. Jusoh, R. Kumar. “New Cogging Torque
Reduction Methods for Permanent Magnet Machine” International
Research and Innovation Summit, Melaka, Malaysia, 6th May. 2017,
accepted and presented.
xx
(iii) F. S. Bahrim, E. Sulaiman, L. I. Jusoh, R. Kumar. “Cogging Torque
Reduction Techniques for Spoke-type IPMSM” International Research and
Innovation Summit, Melaka, Malaysia, 6th May. 2017, accepted and
presented.
LIST OF AWARDS
(i) Bronze Medal in Research and Innovation Festival, UTHM Malaysia, [R&I
2016]: Erwan Sulaiman, Mahyuzie Jenal, Fatihah Shafiqah Bahrim, Rajesh
Kumar, Syed Muhammad Naufal Bin Syed Othman,“PMSM Electric
Generator System for Micro turbine Application”.
(ii) Gold Medal in Malaysia Technology Expo 2017 [MTE 2017]: Erwan
Sulaiman, Fatihah Shafiqah Bahrim, Siti Khalidah, Laili Iwani Jusuh, Jaudah
Abd. Rani, “D2 Motor for ECLIMO Electric Scooter”.
(iii) Gold Medal in International Invention and Innovation Johor 2017 [IID2017]:
Erwan Sulaiman, Mahyuzie Jenal, M. Fairoz Omar, Fatihah Shafiqah Bahrim,
“Mobile Power Supply (MoPS)”.
1CHAPTER 1
INTRODUCTION
1.1 Research Background
In recent years, permanent magnet motors (PMMs) have gained significant attraction
in electric vehicles (EVs) application. PMMs were accomplished with other motors
in the market especially for the electric propulsion of EVs. In these EVs, the interior
permanent magnet synchronous motors (IPMSMs) employed rare-earth permanent
magnets (PMMs) as their main source of magnetic flux. In addition to that, the total
weight and volume were considerably diminished for the specified output power [1].
Besides these advantages, the PMs also benefited from the increased power density,
improved efficiency, and extraordinary reliability. Furthermore, the heat produced
could be effectively dissipated to the surroundings. For these reasons, the PMs were
accepted by leading automobile manufacturers such as Toyota, Honda, and M for
their line of Hybrid Electric Vehicles (HEV). These motors show excellent reliability
as they seldom need some kind of sliding contacts. Due to the reliability factor, these
motors were also chosen for sensorless control drive applications. The HEVs
generally require increased motor power density to support the speed and
transmission of the vehicle. The most effective strategy to increase the motor power
density has been to employ a combination of a high-speed machine along with a
reduction gear [2]. Conversely, this combination resulted in some unfavourable
results such as vibration, acoustic noise, large torque pulsation, excessive bus current
ripple, and electromagnetic interference noise generation. This highlights the gap in
the industry and hence research and development of permanent magnet synchronous
2
motors (PMSM) have been gaining importance. The main motives of such PMSM
studies are not only to reduce the material cost, but also to reduce the cogging torque
effect as well as to improve motor performance by improving the quality of the
motor [3].
1.2 Problem Statement
PMMs have been an inevitable part of the industry in general due to their high
performances and effectiveness. There are several types of PMMs and each one of
them is used for a specific purpose. Among the several types of PMMs, the interior-
type PM (IPM) motor is the variety that has been generally employed for variable-
speed drives [4]. The vital element for concern is the separation of permanent
magnets (PM) caused by the centrifugal force at high speed. This separation could be
avoided by inserting the PM inside the rotor core. By performing this insertion, it
achieves high torque density, high efficiency, and their compactness. On the other
hand, due to the unique structure of this interior-type PM motor, the interaction of
the stator permanent magnets with the rotor teeth yielded a cogging torque, which
was found to be relatively higher compared with other types of PM motors. Besides
that, a serious distortion of air-gap flux density distribution resulted in copious
harmonics in the back electromotive force (EMF) as well as high torque pulsations
such as cogging torque and torque ripple [5]. Generally, high torque pulsations cause
undesirable vibration, acoustic noise, poor position, pitiable speed control,
performance degradation, and dangerous running failures [6]. Hence, it becomes
necessary to lower the impact of high torque pulsations so as to minimise the ill
effects arising due to it. Techniques to abate torque pulsations are very inadequate
for spoke-type IPM motors. For the same reason, the techniques to minimise high
torque pulsations has not been investigated thoroughly due to their rotor-PM
configuration. Consequently, in order to address all these mentioned inadequacies,
new techniques to minimise the torque pulsation becomes vital for the PMMs. For
this, a 6S-4P Spoke-type interior permanent magnet (IPM) motor has been a subject
of recent study and new techniques to minimise the torque pulsation including
cogging torque has been proposed. The study also experiments with a rugged rotor
structure suitable for assisted motor applied in EV.
1.3 Objectives
The main objective of this study is to minimise the cogging torque for 6S-4P Spoke-
type IPMSM for assisted motor applied in EV. In achieving the main objective, there
are some specific objectives that have to be fulfilled, which are:
1) To analyse the cogging torque characteristic of 6S-4P Spoke-type IPMSM
using conventional rotor skewing (Sk), rotor pole pairing (Pop), rotor
notching (Not), and rotor pole axial pairing (App) methods for cogging
torque reduction.
2) To design and analyse a new combination of skewing with pole pairing
(SkPop), skewing with pole axial pairing (SkApp), notching with radial
pole pairing (NotPop), and notching with axial pole pairing (NotApp) for
cogging torque reduction.
3) To design and analyse performance of the best cogging torque reduction
method for 6S-4P Spoke-type Interior Permanent Magnet Synchronous
Motor (IPMSM) for performance improvement.
1.4 Scope
The scope limitation of this research is parallel with the objectives.
1) This project is to design three-phase 6S-4P Spoke-type IPMSM for assisted
motor applied in EV.
2) Various conventional and proposed cogging torque minimisation techniques
are used and compared using 3D-FEA solver by JMAG Designer ver 14.1,
released by Japan Research Institute (JRI). Analysis result of motor
characteristic based on open circuit and closed circuit analysis.
3) All the proposed design parameters, restrictions, and target specifications of
the three-phase 6S-4P Spoke-type IPMSM are listed in Table 1.1. The limit
of the current density is set to the maximum 30 Arms/mm2 for the armature
winding.
4
Table 1.1: Parameters of 6S-4P Spoke-type IPMSM.
Parameters Unit 6S-4P Spoke-
type IPMSM
Stator outer radius mm 44.0
Stator inner radius mm 26.0
Motor stack length mm 54.0
Shaft radius mm 13.5
Outer Radius of rotor (mm) mm 25.5
Permanent magnet width (mm) mm 4.2
Air-gap length mm 0.5
PM weight kg 0.83
Speed rpm 4800
1.5 Thesis Outline
This thesis consists of five chapters and the summary of each chapter is as follows:
a) Introduction
The beginning chapter of this thesis gives some introduction regarding the
research including the background of IPSM, problem of existing motors
employing cogging torque effect, research objectives, and research scope.
b) Literature Review
The second chapter is a literature review that summarises the basic theory of
torque pulsation and cogging torque phenomenon in electrical machines.
Various cogging torque minimisation techniques from previous research are
discussed in detail and compared.
c) Research Methodology
This chapter describes the inventive steps of existing and proposed cogging
torque reduction techniques implemented using JMAG-Designer software
version 14.1. The project implementation is divided into three steps including
design and analysis of existing cogging torque reduction method, design and
analysis of new combination method for cogging torque reduction, and finally
design improvement of the best cogging torque combination technique. The
three steps are divided into two parts, which are geometry editor and JMAG-
Designer. The geometry editor is for designing and JMAG-Designer is for
machine analysis, which consists of open circuit and closed circuit analysis
by 3D FEA.
d) Results and Discussion
The design and performance of conventional and proposed cogging torque
reduction technique has been described in this chapter. To validate the
performance of cogging torque reduction with various techniques, the design
was analysed at open circuit and closed circuit conditions. Then, the best
cogging torque reduction techniques is identified and the improvement of
design and analysis of this design is discussed in this chapter.
e) Conclusion and Future work
The final chapter describes the major results and concludes the research as
well as recommendations for future work.
2CHAPTER 2
LITERATURE REVIEW
2.1 Introduction
This chapter reviews the phenomena of cogging torque in PM motor and numerous
studies of cogging torque reduction techniques in electrical motor. The phenomena
of cogging torque in PMSM from the earliest to the latest study also been explained
in this chapter. Furthermore, various methods for cogging torque reduction in PM
motor together with their findings were elaborated. Finally, the pros and cons in
terms of developed structure were also explained in brief at the end of this chapter.
2.2 Overview of Permanent Magnet Synchronous Motor (PMSM)
Recently, the study trend of electric motor is about the miniaturisation of size, high
efficiency, and high power industrial applications. PMSMs are spreading in various
applications because of their high torque density, high dynamic performance, and
energy conversion efficiency. The PMSMs is a cross between an induction motor and
brushless DC motor. Like a brushless DC motor, it has a permanent magnet rotor and
windings on the stator. However, the stator structure with windings constructed is to
produce a sinusoidal flux density in the air-gap of the machine, which resembles that
of an induction motor. PMSM’s power density is higher than induction motors with
the same ratings since there is no stator power dedicated to magnetic field
production. Moreover, the lack of sliding contacts makes them reliable and their
intrinsic characteristics make them suitable for sensorless drive applications [7]. The
permanent magnet type motors are divided according to the location of the
permanent magnet and is usually built with one of the following rotor configurations
as shown in Figure 2.1 and Figure 2.2.
Figure 2.1: Surface Permanent Magnet Synchronous Motor (a) Classical (with salient
poles), (b) Surface magnet rotor, and (c) Inset magnet rotor.
(a) (b) (c) (d)
Figure 2.2: Interior Permanent Magnet Synchronous Motor. (a) Spoke-type/interior
transverse magnet rotor, (b) Split interior magnet rotor, (c) Interior magnet rotor, and
(d) Rotor with buried magnets asymmetrically distributed.
PMSMs can be designed with surface permanent magnets (SPMs) in which
PMs are attached to the circumference of the rotor or with IPMs where the PM is
placed inside the rotor core. Compared with SPMSM, IPMSM has been widely used
because of their better performance in flux weakening operation and achieve higher
flux density. This can be proven by the historical progress in the power density of the
main traction motor installed on Toyota HEVs [8]. One advantage comes from the
position of magnets. Because PMs are embedded in the rotor, the IPMSM can be
utilised at higher speeds without de-bonding of the PM from the rotor due to the
(a) (b) (c)
Permanent Magnet Permanent
Magnet
Permanent
Magnet Permanent
Magnet
8
centrifugal forces. In addition to the mutual torque from the PM, the IPMSM utilises
the reluctance torque generated by the rotor saliency.
Despite their great performances and being well-operated, IPMSMs have
some drawbacks to be solved. Regarding the noise and vibration, IPMSMs have
more sources than the SPM motors. Furthermore, analysis of magnetic field in the
IPMSM is more difficult due to the magnetic saturations, especially in the rotors. In
an IPM motor, the electromagnetic excitation sources can be classified into three
parts: cogging torque, ripples of mutual, and reluctance torque, and fluctuations of
radial attractive force between the rotor and stator. In an SPM motor, only the mutual
torque is generally considered and an analytical method can be used.
Hence, the research for solving this problem is essentially demanded. The vibration
sources on the motor are classified with causes of mechanical and electro-magnetic.
The mechanical causes are rotation of the rotor, uneven distribution of mass within
rotor, the balancing of the motor, the bearing defective, and so on. The electro-
magnetic causes are an unbalance of electric source, the harmonic components of
phase current, and an unbalance of air-gap, etc. The mechanical causes could be
removed with the production, which is precise, and the revision after producing. The
principal electro-magnetic causes are a problem in motor design especially in the
case of IPMSM, which has the structure where the mechanical air-gap and magnetic
air-gap are identical, therefore, the vibration and noise are larger by the cogging
torque. The vibration and noise abrade the motor and decrease performance [9].
Accordingly, it is essential to embody low vibration and low noise.
2.3 Review of Cogging Torque
There are three main components of torque in PMSM including mutual torque,
reluctance torque, and cogging torque. Mutual torque is caused by the interaction of
the rotor field and stator currents. Reluctance torque is due to the rotor saliency and
the interaction between permanent magnets and slotted iron structure raising the
cogging torque. Output torque quality can be improved by reducing the torque ripple
in the mutual torque that is related to the harmonic content in the back-EMF. The
reluctance torque is compounded into electro-magnetic torque then it is able to
increase the total torque [10].
Torque quality in both radial and axial gap PM motors has been investigated
by many researchers merely because of the benefits of the low-speed applications
[11]. The torque pulsations are never considered as a serious issue at high speeds. On
the other hand, it could generate major problems at low speed because of the motor-
driven torque pulsations or the inverter-driven pulsations. Generally, there are a few
torque components in PM motors, out of which, average torque is considered as the
main torque component. This average torque is usually caused by the interaction
concerning the fundamental stator magnetomotive force (MMF) and the PM Field
[12]. On the other hand, the stator MMF harmonics and the PM field interactions
collectively produce a chiefly undesirable torque component termed torque ripple.
The effects of the torque ripple could be severe based on the motor design and the
source current harmonics. The foremost problem of torque ripple emerges at low
speeds despite the fact that the system inertia filters out the torque pulsations at high
speeds. There is another torque component known as reluctance torque, which is
usually considered as part of torque ripple. This reluctance torque can be generated
by the stator MMF, stator slotting, and anisotropy of the rotor.
Finally, another majorly undesirable torque component is known as cogging
torque and this is generated by the interaction amongst the magnetic field and the
stator slotting or it could be just caused by the air-gap reluctance variation. The
prescribed value for average cogging torque must be zero and its variation can be
obtained with no stator excitation in the coils [13].
(a) (b)
Figure 2.3: Flow path of flux. (a) Stable detent position, (b) Generating cogging
torque.
Cogging torque is generated in PM motors at the air-gap between the rotor
and the stator. Figure 2.3 displays the path and the cogging torque generation. The
reluctance varies in the air-gap as the rotor rotates due to the slots that created the
10
cogging torque. While the magnetic flux travels through the rotor to the stator,
reluctance shows variation inevitably. The path of the magnetic flux originates from
the magnets and the rotor, and later it follows the air-gap and the stator; and then it
returns in the same manner [14].
The circumferential component of attractive force attempts to maintain the alignment
between the stator teeth and the permanent magnet poles [15]. Figure 2.4 indicates
the four positions of the magnet pole with the stator teeth and one period of typical
cogging torque waveform. In Figure 2.5(a), the PM is aligned in an unstable detent
position. In this position, there is maximum air-gap space between the rotor and the
stator. Thus, the maximum amount of air-gap reluctance exists and hence, the
resultant cogging.
(a)
(b)
(c)
(d)
Figure 2.4: One period of a regular cogging torque cycle. (a) An unstable detent
position, (b) A peak cogging torque position, (c) A stable detent position, and (d) An
unstable detent position [15].
By rule of thumb, one of the main requirements for a new motor design in an
industry application is the desire for low torque ripples and low cogging torque. As a
result, a good PM electric motor design should emphasise high amplitude torque
output as well as reduction of cogging torque [16]. Specifically, for automobile
applications, both the torque ripple and cogging torque should be lower than 5% and
0.5% of the nominal torque, respectively. Cogging torque, which can be called as the
c
θm a
ω
τcog
(Nm)
θm a b
ω
τcog
(Nm)
τcog.pk
θm a b
ω
τcog
(Nm)
τcog.pk
θm b a c d
ω
τcog
(Nm)
τcog.pk
detent torque, and ‘no-current’ torque act as disturbances as they superimpose over
the electromagnetic torque that is produced during the operation of the machine
operation. This could even produce zero networks. As discussed earlier, cogging
torque could cause unacceptable vibrations, acoustic noise, poor position, pathetic
speed control, performance degradation, and dangerous running failures. Cogging
torque has also been found to be detrimental to the performance of position control
systems such as robots and to the performance of speed control systems particularly
at low speed. The interactions between PMs mounted on the rotor and the anisotropy
originated by stator windings slots raised the cogging torque and variations of the
magnetic field energy during the rotation, according to:
W mcog
(2.1)
where τcog, δWm, and δϴ, are the cogging torque, energy in the air-gap, and angle of
rotor respectively. Cogging torque produces zero network, yet it acts as a
disturbance, superimposing over electromagnetic torque created in the course of
machine operation [17]. From the time when the cogging torque was caused by the
interaction between the PM on the rotor and the stator slot openings, the cogging
torque period has been linked with the number of slots and poles by:
NsNrHCFNrN p (2.2)
Nr
NsN pNe (2.3)
Ne refers to the number of cogging torque cycles, Np is constant, Nr refers to the
number of rotor poles, and HCF is the highest common factor. The resulting cogging
torque is the sum of the elementary torque produced by the interaction between each
magnet and the edge of the slot opening [18]. Therefore, this clearly shows that a low
value of Np will lead to high cogging torque while a high value of Np will lead to a
relatively low cogging torque. Cogging torque can be expressed by means of Fourier
series as:
12
kmkQ
k
x
sin
1 (2.4)
Since the magnetic energy could be expressed as a function of permeance and
squared MMF, many methods attempt to reduce the amplitude of the main harmonics
by acting on one or both of these physical quantities, which defines the magnetic
energy [19].
2.4 Cogging Reduction Method
Minimisation of cogging torque has always been a major concern in PM machine
design, mainly for applications where low speed or position control is mandatory.
Cogging torque is one of the main sources of torque and speed fluctuations in many
applications. It is also a significant criterion for the superiority of the PM motor
design. For that reason, cogging torque minimisation techniques can be separated
into two leading categories: control-side methods and design-side methods. Control-
side techniques are grounded on the harmonic current injection to eliminate the
cogging component of the torque. Meanwhile the design-side methods generally are
based on the design optimisation of the geometric parameters of the machine.
Typically, the design-based techniques were considered to be more effective as well
as economical than the control-based ones. The control-side methods invariably
involved costly, reliable, and accurate sensors [20].
Since the minimisation of cogging torque has become an increasingly critical
issue in the research and development of electrical motors, numerous approaches
were designed to minimise the cogging torque effect. The proposed approaches were
investigated on both radial and axial type PM machines [21]. In general, a well-
known cogging torque minimisation for design method can be accomplished by two
aspects, which include modifications on the rotor and the stator side as illustrated in
Figure 2.5.
Cogging torque minimization methods
Stator side
modification
Dummy
Slots
Stator Pole
Ratio
Rotor side
modification
Displaced
SlotSlot Opening
Rotor
Pairing Chamfering Notching Skewing
Classic
Triangular
Parallel Side
Trapezoidal
Radial
Axial
Round
Dual Skew
Magnet &
Pole Arc
Step Skew
Flux barrierSlot Pairing
Flange
Magnet
Optimization
Slot
Optimization
SkewingFractional
SlotMagnet
Shifting
Figure 2.5: Cogging torque minimisation methods.
Basically, the stator side modification comprises the stator pole ratio [22]–[24], stator
tooth pairing [25], slot opening [26]–[29], dummy slots [30], [31], and displacement
slot [32]–[35]. In contrast, the rotor side modification consists of rotor pole radially
and axially paired [36]–[38], chamfering [39][40], magnet pole arc [41]–[44],
magnet shaping or shifting [45]–[47], skewing [48]–[53], flux barrier [54], and
notching [57]–[62]. Modification in rotor side has been widely used compared with
the stator part as it complicates the stator manufacturing and consequently increases
the manufacturing cost of the machine. Therefore, modifications from the stator side
were considered not to be practical in a majority of the machines and hence this
approach was not preferred.
2.5.1 Skewing the Slots/Poles/Magnet
One of the famous methods to reduce the cogging torque effect is to skew either the
rotor or the stator stack. This method is to influence the interaction between rotor PM
and the stator slots. Skewing can be executed on either the PM or the slots. Stator
skew or rotor skew, which is characterised as creating an angle between the sides of
the PM and the stator slots, is one of the most effective techniques to reduce the
cogging torque in PM motor. This technique can be applied by different means such
14
as conventional skew, triangular skew, parallel-sided skew, trapezoidal skew,
circular skew, and dual-magnet skew. However, both sides have disadvantages.
Skewing the PM increases the magnet cost and skewing the slot increases the copper
loss due to increased slot length, resulting in longer wire. Skewing the rotor PM
continuously is not convenient and even impractical for the prototype machine
because of its bread loaf-shaped magnet poles. Therefore, skewing the rotor magnet
stepwise is more preferable to ease fabrication and assembly. The skewing angle for
this method is between two adjacent steps, which is equal to:
QNcnskewing
2
(2.5)
Where n is the number of skewing steps, Q is the number of stator slots, and Nc is the
period of cogging [31]. Various numbers of skew steps are analysed under no-load
condition in [63].
(a) (b)
(c) (d)
Figure 2.6: Step-skew rotor design under open circuit condition (a) Two steps, (b)
Three steps, (c) Four steps, and (d) Five steps [63].
Figure 2.6 shows four rotor step-skew designs with various number of steps. The
overall cogging torque results of the machine with conventional rotor skewing steps
are illustrated in waveforms as shown in Figure 2.7. The waveforms are ranging from
two to five and the corresponding step skewing angles has been anticipated by 3D
FEA and compared. The outcomes affirm that the cogging torque can be lessened
adequately in the machine with conventional rotor step skewing method.
Nonetheless, there are as yet evident fundamental harmonics in the cogging torque
because of the considerations of the end impacts and axial interactions in the 3D
FEA results. The cogging torque continuously drops as the number of step increased,
and the machines with conventional skewing steps of four and five produces similar
cogging torque waveforms.
Figure 2.7: Cogging torque waveform with different rotor skewing steps [63].
Furthermore, an experimental analysis of step skewed has been discussed in [64].
This technique was chosen due to their simplicity and simple implementation that
also led to the reduction of PM eddy current losses. Skewing can be designed by
placing the PM axially skewed by discrete steps, as illustrated in Figure 2.8. With the
skewing angle between the adjacent sections and rotor of ±2.5 mechanical degrees,
the cogging torque effect was reduced up to 54%.
Figure 2.8: Prototype of stepped rotor skewing [64].
27
9
0
-9
-18
18
-27
0 5 15 10 20 25 30
C3-step (3D)
C5-step (3D)
C2-step (3D)
C4-step (3D)
Rotor Position [deg.e]
Coggin
g T
orq
ue
(m.N
m)
16
Three cross sections of a PM machine with the stator core skewed by a skewing
angle of α is shown in Figure 2.9 [65]. Stator skewing changed the relative position
between the stator and rotor along the axial length of the machine. Therefore, the
parameters of the machine were not constant along the motor axis as well as
variation of magnetic field distribution. Taking into account, the skewing effect of
the machine parameters were presented in 3-D function of the rotor position, θ and
axial length of the machine. Therefore, the flux-linkage per length due to magnets of
a PM machine with skewed stator or rotor topology can be described in this paper.
Furthermore, skewing has the impact of enhancing stator windings distribution and
significantly reduced higher order back-EMF harmonic, thus creating more
sinusoidal back-EMF wave-shapes.
(a) (b) (c)
Figure 2.9: Cross sectional views of a PM machine at different axial-z location.
(a) z= laxial / 2, (b) z= 0, and (c) z= laxial / 2 [65].
2.5.2 Slot Opening Variation
Since cogging torque is generated by the interaction of the stator teeth and the rotor
magnetic field, slot opening has an effect on the cogging torque. Various researchers
are interested in this technique. For example, an analytical technique for accurately
determining the optimal slot opening for minimum cogging torque in PM machines
has been presented in [66]. Then, it was utilised to determine the relationship
between slot opening and cogging torque for machines having different combinations
of slot numbers and pole numbers, N. Levin in [67] also reduced the cogging torque
effect using this technique as shown in Figure 2.10 and concluded that the wider
Stator u-axis
Rotor d-axis
-αskew /2
u u u` u`
Rotor q-axis
Stator u-axis
Rotor q-axis
Rotor d-axis
αskew = 0
u
Stator u-axis Rotor q-axis
Rotor d-axis
αskew /2
u`
opening of slot, the greater value of cogging torque based on the graph in Figure
2.11.
Figure 2.10: Slot opening and PM interpolar distance [67].
Figure 2.11: Stepped rotor skewing with three modules [67].
However, it should be noted that the value of slot opening width is determined by
industrial requirements and it depends on the cross section of armature conductors
[68].
Basically, when the slot opening becomes smaller, the cogging torque and the
harmonic content of the back-EMF decreases but the slot opening method suffers
from a trade-off between cost and total rating usage. If the slot opening is minimum,
the motor cannot be used to its full potential and only 70% of it can be utilised.
Hence, minimal possible value of slot opening width needs to be considered to
optimise the machine design.
Permanent
magnet
Interpolar
distance
Slot
Opening
Stator
Rotor
Slot Opening width, mm
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0
Max
imal
coggin
g t
orq
ue,
Nm
3.0 3.5 4.0 4.5 5.0 5.5
18
2.5.3 Stator tooth Pairing
The stator tooth pairing is a method by pairing the stator tooth with different size and
width. The equation for optimal stator tooth pair width in which two paired stator
tooth widths of a and b are presented in Equation 2.6, where n is constant and NL is
the least common multiple of slots and PM numbers [69].
02
sin2
sin b
nNLa
nNL (2.6)
Figure 2.12 shows the optimal stator tooth pairing and Figure 2.13 shows one cycle
of the cogging torque according to the stator tooth paring design. The analysis result
showed that the smallest cogging torque occurred at the combination of 6.5 [deg.(m)]
to 11.5 [deg.(m)].
(a) (b)
Figure 2.12: Stator design (a) Conventional stator and (b) Stator tooth pairing [69].
Figure 2.13: Characteristic of cogging torque [69].
9.0-9.0 [deg.(m)]
7.6-10.4 [deg.(m)]
7.0-11.0 [deg.(m)]
6.5-11.5 [deg.(m)]
Rotor Rotation [deg.(e)]
0 15 30 45 60
Stator teeth pairing widths
a and b
4
3
2
1
0
-1
-2
-3
-4
Coggin
g T
orq
ue
[Nm
]
N S
Inner
stator
Outer
stator
Rotor N S
Rotor
Outer
stator
Inner
stator N
N S
D
D
S
Two methods for reducing cogging torque in flux reversal machine, namely the
segment rotor method and the stator poles pairing have been proposed in [70] and the
cogging torque was successfully reduced. Daohan Wang, in [71] introduced a model
for cogging torque mechanism and a Fourier analysis. Results verified that suitable
considerations must be ensured to enhance the performance of a given technique.
Since the cogging torque can be presented by partial differentiation, the expression to
obtain an optimal tooth width was analysed in [72]. Based from the expansion, the
cogging torque was reduced by 85%.
2.5.4 Rotor teeth/pole-pairing and Axial Pole Pairing
Rotor teeth or pole pairing is similar to stator tooth pairing except that this method
was applied in the rotor part of the machine. In this method, two different pole sizes
or widths were assembled alternately in the rotor design in either radial or axial
condition. This method requires an even number of rotor teeth to mechanically
balance the motor. The variable magnetic resistance of air-gap and rotor not only
changed the waveform of cogging torque, but was also reduced in the amplitude. The
cogging torque waveform varied with the rotor tooth width, βr. As an example, if the
width of all rotor teeth was set to 8o, the cogging torque has almost the same
waveform as the case when the width at all rotor teeth was set to 11o, in opposite
phase [73]. Therefore, two types of rotor teeth with different widths of βr at 8 and βr
at 11, were alternatively employed as shown in Figure 2.14. Thus, the overall
cogging torque can be significantly reduced by 13%, as verified by FEA results.
Figure 2.14: Rotor Teeth-Pairing [73].
βr = 8 βr = 11
20
An experimental result shows pairing rotor pole reduced the cogging torque by 85%
along with an acoustic noise of 3.1 dB [74]. Meanwhile, a tooth pairing for an axial
field flux-switching permanent magnet machine (AFFSPMM) was designed and
analysed in [75]. Results showed that the cogging torque was reduced by 21%
compared with the original design. The cogging torque comparison between tooth
pairing design and the original design is shown in Figure 2.15. To obtain smaller
amplitude of the cogging torque, it was also necessary to choose the proper width
ratio of armature teeth to PM pole.
Figure 2.15: Cogging torque comparison between teeth pairing design and original
design [75].
Another way of applying rotor teeth-pairing was by altering the stack length of
design, corresponding to the magnitude of cogging as well as by changing the pole
arc. The stacks length was fixed and only pole arc was varied so that cogging torque
using axial pole arc pairing can be examined. It is a new technique to enable coils to
be connected in parallel, and can comprise different axial lengths as well as different
pole arc widths. Figure 2.16 shows the difference between rotor teeth circumferential
pairing and rotor teeth axial pairing [76]. An improved pole pairing considering axial
stack length using analytical formulas is proposed, which reduces the cogging torque by
71.98%. By selecting the optimal rotor pole arc and stack length, the effect of cogging torque
not only can be reduced, but also results in improved harmonic content of the back-EMF.
1.5
1.0
0.5
-1.0
-1.5
-0.5
0
0 6 12 18 24 30 36
Teeth pairing Original
Coggin
g T
orq
ue
(Nm
)
Rotor position (mech.deg)
(a) (b)
Figure 2.16: Rotor teeth pairing (a) Circumferential pairing and (b) Axial pairing
[76].
2.5.5 Stator/rotor pole displacement design
Stator and pole displacement design is normally applied with dual-rotor or dual-
stator machine. The objective of the stator displacement design is to reduce the
cogging torque by placing the inner and the outer stators in a staggered pattern as
shown in Figure 2.17. An analytical expression as the sum of the total cogging
torques can be made equal to zero by transitioning the cogging torque phase, which
is generated in the outer stator, by 180° [77].
(a) (b)
Figure 2.18: Cogging torque characteristic for various stator displacement angle [77].
Since the Np and Ns of the machine in this study are 30 poles and 20 slots separately,
the optimal value of stator displacement was set to 30°. As a result, the cogging
torque was reduced by 86.6% as shown in Figure 2.18.
Permanent
magnet
Inner Stator
Outer
Stator
Rotor
αt αsde αsde
22
Figure 2.17: Stator displacement. (a) Original design and (b) Stator displacement
design [77].
Furthermore, when the rotor pole staggered a little angle between two rotors as
shown in Figure 2.19, the peak cogging torque on both sides of the stator staggered
some angles too, which avoided the overlapping of the peak cogging torque [78].
Hence, the cogging torque was decreased. The influence of the rotor pole
displacement angle on the cogging torque and the comparison of the cogging torque
are shown in Figure 2.20. For the result, the minimum cogging torque was obtained
when the rotor pole displacement angle equaled to 2 degrees. The cogging torque
was reduced by 59%.
Figure 2.19: The rotor pole displacement between two rotors [78].
Coggin
g t
orq
ue
[Nm
]
0 15 30 45 60
Rotor rotation [deg.(e)]
Stator displacement angle
0 [deg.(e)] 10 [deg.(e)] 20 [deg.(e)]
30 [deg.(e)]
40 [deg.(e)] 60 [deg.(e)]
50 [deg.(e)]
1
0
2
3
4
-1
-2
-4
-3
Figure 2.20: Cogging torque comparison of two rotor designs [78].
2.5.6 Slot and pole number combination
Slot and pole number combinations play an important role in suppressing vibration
and noise for low-speed PM machines [79]. Basically, the appropriate combination
of the slot and pole number, magnet arc, and thickness can significantly reduce the
cogging torque. The smaller the number of slots or poles and the larger the common
multiple between the slot number Q and the pole number, the smaller the amplitude
of the cogging torque [80].
Figure 2.21: The pole-pitch to pole-arc ratio of rotor PM [81].
In order to gain a relationship between the slot/pole combination and the torque
ripple, air-gap field was analysed. An integer number of slots per pole and a
fractional number of slots per pole can be treated. Moreover, the changes in the
number of cycles depend on pole number and slot number combinations. In general,
Rotor pole
displacement
No rotor pole displacement 1.5
1.0
0.5
0
-0.5
-1.5
-2.5
-2.0
Rotor pole position [mech. Deg] 0 2 4 6 8 10 12
Coggin
g T
orq
ue
(Nm
)
Permanent
magnet
Pole Arc Pole pitch
αp
Rotor
yoke
24
the more the cycles, the smaller the cogging torque amplitude. As shown in Figure
2.21, the pole-arc ratio αp of rotor PM is p represented as in Equation 2.7 [81].
p
mp (2.7)
Where, τp is the rotor pole pitch and τm is the magnet pitch. The optimum magnet
pole-arc ratio a for the minimum αpo cogging torque in the radial field as in (2.8):
1..2,1,
Nk
N
kNpo (2.8)
where, N = Nc /2, p is the pole pair number, Nc is LCM of the rotor pole numbers and
the stator slots numbers. Practically, the optimal value of αp would be a little larger
than the calculated p number because of the leakage flux of the stator [81].
2.5.7 Dummy Slot/Notching
Cogging torque can be effectively reduced by introducing notches in either the stator
or in the rotor. Notches in stator slots are normally known as dummy slots. Some
specialised notches featuring in various shapes, width, length, and numbers, which
attempted to increase the utilisation of magnetic flux lines. These notches as in
Figure 2.22 were solely on the stator or the rotor but not both. Furthermore,
utilisation of notches on both the stator and the PMs has been reported in the past. It
is a well-known fact that there exists a trade-off between the cogging torque
reduction and magnetic flux decrement on the PMs through the use of notches [82].
Notching is normally applied in the rotor side as it gives advantages in terms of easy
implementation and low manufacturing costs.
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