Results in Physics 7 (2017) 183–188
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Results in Physics
journal homepage: www.journals.elsevier.com/results-in-physics
Design and analysis of a new axial flux coreless PMSG with three rotors
and double stators
Mehmet Recep Minaz a,⇑, Mehmet Çelebi b
a
b
Siirt University, Department of Electric-Electronic Engineering, Siirt, Turkey
Atatürk University, Department of Electric-Electronic Engineering, Erzurum, Turkey
a r t i c l e
i n f o
Article history:
Received 28 September 2016
Received in revised form 20 October 2016
Accepted 22 October 2016
Available online 24 December 2016
Keywords:
Axial flux generator
Permanent magnet generator
Three rotors
Double stator
a b s t r a c t
In this study, axial flux coreless permanent magnet synchronous generator (PMSG) is designed as double
stators and three rotors and its electromagnetic and structural characteristics are analyzed. Designing
aimed the axial flux generator is placed into the single end of the side rotor in the machine and permanent magnets are placed into the double ends of the middle rotor. One more rotor than the number of
stators here is used. Core is not used in the stator of the machine intended to be designed. Aim of this
study is to provide both reduction of iron loss and making the machine become lighter by reducing
the number of the rotors to be used. Moreover, easiness in the production stage of the machine is provided. Three-dimensioned electromagnetic analysis of the designed machine has been done through
the finite element method and transient solutions are suggested based on this. Within this study,
arrangements have been made depending on certain standards in order that permanent magnets and
coils obtain direct alternating current. The designed new axial flux generator move as permanent speed
of 500 rpm and so maximum voltage of approximately 120 V per phase is obtained. Furthermore, this
PMSG does not need a gear system due to its design structure.
Ó 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND
license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Introduction
Electrical machines have started to be used almost within all
areas nowadays. Every passing day, novel studies take place in literature. New models are developed in these studies done. Within
these developed models, increases in power density of the
machine, change in the shape of design as well as size reductions
and studies done depending on excitation types have gained speed.
Studies have centered on axial flux permanent magnet machines as
different excitation types recently. There have occurred important
developments in researches upon ferromagnetic material field
since 1980s. The most important of these is that through the
advance of neodymium magnets over the past 20 years (NdFeB)
these magnets have been used commonly in electrical machines.
It is quite suitable that permanent magnets are used in direct current machines and synchronous machines.
Permanent magnet axial machines have been aimed to be analyzed due to reasons such as being highly efficient and economic
and having ability to produce energy at low cost. The axial flux permanent magnet generator (AFPMG) of electromagnetic structure
⇑ Corresponding author.
design has a variety of changes in theory [1–3]. As there can be
an increase in the number of poles, we can consider the relevant
generators ideal in terms of direct connections and low speed generators [4]. The use of AFPMG has been studied intensively
recently. In [5,6], low-speed permanent magnet machines with
axial or radial flux structures were proposed. Depending on the
operating environment and design these machines may have core
or be coreless [7,8]. Micro wind turbine application has been conducted in a study by Pop et al. Here it has been found that after a
comparison of axial and radial flux permanent magnet generator,
axial flux permanent magnet has shown the best result. It has been
discovered that axial flux generator is less costly [9]. Reducing noload momentum of the generator has been possible using skewed
magnets in axial flux permanent magnet [10]. It is a huge advantage that AFPMG has high efficiency, compact size and light weight
compared to other applications. Main purpose of this type of
machine design is to obtain the best of output power [11]. Furthermore, axial flux permanent magnet generator with coreless stator
is considered as machines having high power density for energygenerating systems [12]. Rotor is used in the both sides of the stator in traditional machines. As the number of stator increases to
two, the number of rotor, as in reference [13], goes up to 4.
E-mail address: mehmetrecepminaz@siirt.edu.tr (M.R. Minaz).
http://dx.doi.org/10.1016/j.rinp.2016.10.026
2211-3797/Ó 2016 The Authors. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
184
M.R. Minaz, M. Çelebi / Results in Physics 7 (2017) 183–188
The number of rotor was reduced to 3 with newly designed
axial flux generators. Aim of this study is that iron losses have
reduced placing permanent magnets into both ends of the middle
rotor with three rotors rather than four rotors. Moreover, reducing the number of the rotor discs used, the machine has been
made lighter. Due to the arrangement of the permanent magnets
in electromagnetic analysis, magnetic flux density of the middle
rotor would be less compared to that of other two rotors. As core
has not been used in the stator windings of the designed machine
with coreless stator, stator iron losses have been eliminated completely. As there has not been used of the core in the stator, stator windings will not be influenced by core warm-ups. As the
surfaces of the windings are in contact with air, it will be able
to take the heat on the surface out more quickly. As the core is
not used for the stator windings in this type of axial machine,
production difficulty to arise from applications in such type of
machines has been reduced. Though copper losses have increased
here as the core has not been used in the stator, this newly
designed machine provides production convenience. Iron losses
have been minimized in this new machine and maximum production convenience has been provided. This design can be used
to obtain alternating current without need for gear system during
wind turbine applications. Besides, it is intended to be used in
electric vehicles both as in-wheel motor and generator. Finite element method has been used for analysis in this study. Finite element method is a numerical method used in solving linear and
nonlinear partial differential equation [14]. Design features of
the designed machine have been given within the second chapter.
The third chapter consists of electromagnetic analysis results of
the machine. Results related to the simulation depending on time
have been given within the fourth chapter. The last chapter
includes the conclusion.
Fig. 1. Appearance of AFPMG. Permanent magnets in dark blue colour, rotors in
grey colour, stator windings, in light blue, red and brown colours. (For interpretation of the references to colour in this figure legend, the reader is referred to the
web version of this article.)
Mathematical model and design features of the machine
Fig. 2. Geometry of side rotors of AFPMG.
The design of the machine was developed with a
mathematical mode of axial flux permanent magnet synchronous
generator.
For equations of voltages of the axial flux permanent magnet
synchronous generator the three-phase stator windings have been
written as
V s1;abc ¼ Rs1;abc :is1;abc þ Ls1;abc :
d
d
is12;abc þ k1PM
dt
dt
ð1Þ
In Eq. (1) V s1 , Rs1 , is1 , Ls1 , is12 and kPM1 represent the first stator three phase voltage matrix, the first stator winding resistance matrix, the first stator phase currents, the inductance
matrix, the first and second stator phase currents, the first stator three-phase magnetic flux matrix of the AFPMG,
respectively.
The first stator phase voltage, the first current matrices, the first
and second current matrices are represented as
V s1;abc ¼ ½ V a1
V b1
and is12;abc ¼ ½ ia1
V c1 t ; is1;abc ¼ ½ ia1
ib1
ic1
ia2
ib2
ib1
ic2 t
ic1 t
ð2Þ
The
first
stator
winding
resistance
matrix
is
2
3
RS 0 0
½Rs1;abc ¼ 4 0 RS 0 5
0 0 RS
The
inductance
matrix
is
½Ls1;abc ¼
2
3
L
M1 M1 M2 M3 M3
4 M1 L
M1 M3 M2 M3 5
M1 M1 L
M3 M3 M2
The first stator three-phase magnetic flux matrix is represented
as
Fig. 3. Geometry of middle rotor of the AFPMG.
2
k1PM
3
k1PM cosðhÞ
k2PM cosðhÞ
k1PM cosðhÞ
6
7
¼ 4 k1PM cos h 23p k1PM cos h 23p k2PM cos h 23p 5
2p
2p
2p
k1PM cos h þ 3
k1PM cos h þ 3
k2PM cos h þ 3
ð3Þ
k1PM represents the fundamental magnet flux of AFPMG.
V s1;abc ¼ V s2;abc
ð4Þ
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M.R. Minaz, M. Çelebi / Results in Physics 7 (2017) 183–188
2
1.8
1.6
1.4
B(T)
1.2
1
0.8
0.6
0.4
0.2
0
0
Fig. 4. Geometry of permanent magnet of AFPMG.
In Eq. (3) the first stator voltage is equal to the voltage of the
second stator.
Main purpose in the machine design is to obtain the best of output power. Estimated value of the output power belonging to the
designed machine can be calculated using the equality below;
f
2
Pout ¼ 4p2 ki kp gð1 þ kd Þð1 kd ÞBg D30
p
2000
4000
H(A/m)
6000
8000
Fig. 6. B-H curve of m19 core material.
ð5Þ
In order that output power of the machine reaches maximum,
pffiffiffi
rate between its dimensions should be as in kd ¼ 1= 3 [15]. Statement related to the relationship between the dimension and power
in AFPMSG has been given within Eq. (1) [16]. The kp here is electric wave form factor and calculated as 0:5 in sinusoidal designs
pffiffiffi
where ki is current wave form and calculated as 2 for sinusoidal
wave forms [17]. Bg refers to maximum flux density within the air
gap. P refers to dipole number and f refers to the frequency. D0 and
Di refers to the inner and outer diameter respectively where kd
refers to the assessment of inner diameter based on its ratio to
the outer diameter. The designed axial flux coreless permanent
magnet synchronous generator is given in Fig. 1. There are two
coreless stators and three rotors within this design.
Fig. 7. Distribution of magnetic flux density for AFPMG.
Fig. 5. Appearance of arrangement of the magnets and flux paths as N-S-N-S-N-S.
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5
4.5
4
Power (kW)
3.5
3
2.5
2
1.5
1
0.5
0
0
500
1000
1500
2000
2500
3000
3500
Speed (rpm)
Fig. 11. Power chart of AFPMG according to certain speeds.
Fig. 8. Appearance of magnetic flux path for AFPMG.
Fig. 12. Voltage harmonic of AFPMG at 500 rpm speed.
Fig. 9. Appearance of external circuit for 3 phases of axial flux permanent magnet
generator.
300
Voltage (V)
250
200
150
100
50
Fig. 13. Voltage value for A-B-C phase of AFPMG.
0
0
500
1000
1500
2000
Speed (rpm)
2500
3000
3500
Fig. 10. Voltage ratings of AFPMG according to certain speeds.
There exist three rotor discs in Fig. 1. 12 permanent magnets
have been placed into the single end of the lower and upper rotor
discs. 12 permanent magnets have been placed into the both back
end and front end of the middle rotor for each. One for each stator
winding has been placed between two rotor discs. Each stator
winding consists of 9 coils in total. Each phase in windings corresponds to three coils (Fig. 2).
Rotor steel used for the machine has been made up of M19.
There are 12 magnets in rotor steel. Magnets placed upon the
rotors have been placed between each other with 30 degrees each.
Do and Di values are 145 and 85 mm. Middle rotor geometric
structure of the machine has been given in Fig. 3. 24 permanent
magnets in total have been placed into both ends of the rotor.
M.R. Minaz, M. Çelebi / Results in Physics 7 (2017) 183–188
187
Direction of the flux path within the arrangement of the magnets is shown in Fig. 8. Arrangements of the permanent magnets
here are in the form of N-S-N-S and S-N-S-N. Accordingly, while
flux path of the quadruple magnet group on the z plane is mostly
up, flux path of the permanent magnet group both at its right
and left is the opposite. For a clearer appearance of the flux path,
it had been shown in Fig. 8.
The simulation results for the machine
Fig. 14. Winding flux value for 3 phase star-loaded (connection) of AFPMG.
Fig. 15. Current value for A-B-C phase of AFPMG.
Geometric structure of the magnets is as shown in Fig. 4. These
types of designed magnets are more advantageous to prevent the
heat and more suitable to obtain a straight sinusoidal wave. Permanent magnet used in axial flux permanent generator is Neodymium. Length of the neodymium magnet is 50 mm and its
thickness is 8 mm.
Representation of flux paths of the magnets have been given in
Fig. 5. Two types of flux paths can be generated depending on
arrangement of these magnets. Changing the arrangement of the
magnets used in the middle rotor, flowing of the flux in the middle
rotor can be made possible. If arranged in this way, wall thickness
of the medium steel is required to be approximately doubled. To
prevent this, arrangement of the magnets and their flux paths
should be as follows.
Generator stator designed within this study has a coreless
structure. For the rotor core, steel which is of M-19 class and frequently used in electric machines. The steel used for core is not a
linear material. While making solution, the analysis program
applied makes solution using B-H curve. B-H curve of M19 steel
is shown in Fig. 6.
48 trapezoidal permanent magnets (NdFeB) and 18 coreless
coils in total have been used in the machine shown in Fig. 1. 12
magnets have been placed into the single end of the two rotors
for each. 24 magnets in total have been placed into both ends of
the two rotors. There an air gap of 1 mm between the magnets
placed upon the stator and rotor. Average magnetic flux density
is approximately 0.7 T. As a consequence of all these parameters,
power estimated according to equality 1 is approximately 1.9 kW.
Electromagnetic properties of the machine
Distribution of magnetic flux density for the 3D model is given
in Fig. 7. Flux density values formed around the magnet have been
given. Flux density in windings and steels has been measured as
0.8–0.9 T.
Current, voltage and flux values according to the simulation
results of the new designed machine have been given below. They
have been given according to the angular velocity at 500 rpm of the
machine. Circuit of the stator windings is shown in Fig. 9.
Within the Fig. above, coils belonging to each phase and their
relationships with each other have been given. There are three
coils per phase for each stator winding here. 6 coils in total have
been used for each phase. Resistance has been determined as
1.72 ohm in total for one phase of each stator.
It is seen in Fig. 10 that the voltage increased up to 1500 rpm.
There was no change in voltage after this speed. Maximum voltage
was observed to be 1500 rpm (Fig. 11).
Maximum power of the generator goes up to approximately
4.5 kW at 1500 rpm. There is no increase in the power of generator
after this speed.
Harmonic analysis of AFPMG was made in Fig. 12. It was
observed that value of this harmonic analysis was sub-standard. .
Within the design of the generator whose stator windings are
attached in Fig. 7 and in which permanent magnets used are trapezoidal, phase voltage, flux and current wave form to be obtained
time-dependently have been shown in Figs. 13–15 respectively.
It is observed that within the simulations results the output signal is in the form of alternating current. One of the advantages of
the new designed machine is that generated wave form is at quite
a good level.
Data to be obtained at speed of 500 rpm, roughly 120 V voltages
and roughly 10 A current are in Figs. 13 and 15 respectively. Fig. 14
shows a complete sinusoidal magnetic flux. In this case, it is understood that the selection of permanent magnet has been made properly and coil type has been correctly selected.
That magnetic field of the windings is properly dispersed has
been observed from the above curve. The machine did not have
abnormal fluctuations in terms of the design, flux, the current
and voltage curves. In addition, this machine is being used more
efficiently and safely.
Conclusion
In this study, iron losses of the machine were reduced by 25%
reducing the number of rotor used for a 4-rotor machine to three.
Total rotor weight of the machine was reduced by. In addition to
this, the structurally different and alternating-current generating
axial flux coreless permanent magnet synchronous generator
design was analyzed through finite element method to present
its performance. Application of axial flux coreless permanent magnet synchronous generator with three rotors and two stators has
been given. Within this study, due to the form of design there will
be much convenience in production. Though the designed machine
is coreless, a high power density has been obtained. That the output wave forms are close to sinusoidal reveals that design data
related to the machine have been properly chosen. 18 coils and
48 magnets have been used in the machine and according to the
simulation results at 500 rpm, the machine generates approximately 1.8 kW power. It was observed that there was no distortion
in harmonic analysis at 500 rpm speed. Moreover, this machine
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M.R. Minaz, M. Çelebi / Results in Physics 7 (2017) 183–188
generates maximum voltage at 1500 rpm. Approximately 4.5 kW
power is generated from this speed. The designed generator within
this study offers the solution for both in-wheel motor-generator in
electric vehicles and wind power applications.
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