1
Design Study of Different Direct-Driven
Permanent-Magnet Motors for a Low Speed
Application
F. Libert, J. Soulard
Division of Electrical Machines and Power Electronics, Royal Institute of Technology
100 44 Stockholm, Sweden, phone: +46 87907757, fax: +468205268,
e-mail: florence@ekc.kth.se
Abstract— The goal of the study is to compare different
designs of direct-driven Permanent Magnet (PM) motors that
should replace an induction motor and its gearbox for an
industrial application requiring 5 kW and 50 rpm. Motors with
surface mounted PM, inset surface mounted PM or buried PM,
with inner or outer rotor are investigated. The best design for the
application is presented.
Index Terms—Permanent magnet machines, direct-drive, low
speed, design, optimisation.
I. INTRODUCTION
As environmental concern increases worldwide, higher
drive efficiency is desirable. Thus, replacing induction
machines with Permanent Magnet (PM) machines has recently
gained great interest as the price of the PM decreases. For low
speed applications, using PM machines may eliminate the
need of the gearbox, which is traditionally coupled to a
standard induction machine. Since the gearbox is costly,
decreases the efficiency of the drive and needs maintenance, a
PM direct drive can provide better performance and/or be
lighter than the traditional solution.
Direct-driven PM machines are nowadays mostly used for
boat propulsion and wind turbines [1]. Since the rated speed is
low, a large diameter and a high number of poles characterize
these machines. This paper focuses on an industrial
application, which requires 5 kW and a rated speed below 50
rpm. In [2], direct-driven surface-mounted permanent magnet
(SMPM) machines for low speed application were studied. In
this paper, rotor configurations with inset surface mounted
permanent magnet motors and buried permanent magnet
(BPM) are analysed. Indeed, inset PM motors produce a
reluctance torque in addition to the torque created by the
magnets, that could improve the performances compared to
the SMPM. Buried magnets generate flux concentration in the
rotor that could allow thinner or cheaper magnets. This article
describes the process leading to the determination of the PM
arrangement which gives the best overall performances and is
therefore the most appropriate for the application.
II. THE
INVESTIGATED ROTOR CONFIGURATIONS
A. Rotors with surface mounted PM
The different rotor geometries with surface PM that are
considered are shown in figure 1. The surface mounted PM
designs with inner and outer rotor (designs 1 and 3 on the
figure) were studied in [2]. Design 2 also presents surface
mounted magnets but with iron pieces between the magnets.
This design is referred as inset permanent magnet motor.
These iron pieces create a saliency.
Fig. 1. Cross-sections of investigated surface mounted PM motors (2 poles
represented)
B. Rotors with interior PM
Another solution is to bury the magnets in the rotor.
Different positions of the magnets in the rotor are investigated
and shown on figure 2.
In the first geometry (design 4), there are two magnets per
pole that are placed with a certain angle taking the form of a
“V”. Between the ends of the V formed by the magnets and
the airgap, there are two iron bridges. Such motors were
studied in [3] and [4].
2
In the last studied configuration (design 5) referred as
tangentially magnetized PM, the rotor consists of different
pieces of iron and magnets that are fixed together on a
nonferromagnetic shaft. With a ferromagnetic shaft, a large
portion of flux from the magnets would leak through the shaft.
geometries.
Fig. 2. Cross-sections of investigated buried PM motors (2 poles
represented)
C. Advantages and drawbacks of the investigated
configurations
The usual advantages of the buried magnet configurations
compared to the surface PM designs are the possible flux
concentration generated by the magnets in the rotor, the
protection of the magnet against demagnetisation and the
mechanical strength. In the case of this study, centrifugal
forces on the surface mounted PM are very low because the
nominal speed is around 50 rpm.
Another property that differs between the investigated
rotors is the saliency of the buried PM designs and of the inset
PM designs. A reluctance torque can be produced in addition
to the torque produced by the magnets.
The drawbacks of the rotors with V-shape magnets are the
iron bridges that cause a high leakage flux. Furthermore the
V-shape rotor is not very adapted for high pole numbers.
Indeed the higher the pole number, the smaller the place for
the magnets in V-shape, and the smaller the angle between the
two magnets. It can therefore easily get saturated between the
magnets if the angle is too little. Another drawback of the Vshape configuration is the high number of magnets that
increases the production cost. The tangentially magnetised PM
rotor presents the drawback of many iron and magnet pieces
to be manipulated if the number of poles is high. Therefore
some production difficulties can arise. However it does not
present any bridges and the flux leakage is then very low.
III.
THE DESIGN PROCEDURE
A. Description of the procedure
The design of the different PM motors is realised by solving
an optimisation problem, using Sequential Quadratic
Programming methods. The design process is presented in
figure 3. It is applied to all the above-mentioned rotor
Fig3. Procedure followed for the design of a low speed PM motor
The objective function is the active weight of the motor.
The parameters to be optimised are: the number of poles,
some geometrical parameters that define the stator teeth and
the magnets, the air-gap length and the machine length. These
parameters are subject to some non-linear inequality
constraints that should guarantee the mechanical, thermal, and
magnetic behaviour expected. The outer stator diameter is
limited. The copper losses are set to a value that guarantees a
better efficiency and lighter weight than the induction motor
with its gearbox. The magnet weight is also limited to set a
constraint on the cost of the machine.
3
At first, a distributed winding with a number of slots per
pole per phase equal to 1 is considered for all the designs.
B. Influence of PM arrangement
The design process differs between the investigated rotor
configurations in mainly two points: the analytical calculation
of the flux-density in the airgap and the calculation of the
inductances and currents.
1) Flux density in the airgap: The flux-density in the airgap
has to be calculated with accuracy since the design procedure
relies on it (figure 2). The method used for the surface
mounted PM motor is described in [2]. The waveform is
assumed to be rectangular as in figure 4. The maximum value
of the airgap flux-density Bm is computed with (1):
Br
Bm =
(1)
µ r .δ .k c
1+
lm
where Br is the remanence flux density of the magnet, µr the
magnet relative permeability and kc the carter factor, δ the
airgap length and lm the magnet thickness.
For the inset PM designs, Bm is calculated the same way.
However there is more flux leakage between the magnets than
for the SMPM. Instead of crossing the airgap, a part of the
flux created by the magnets can go directly from the magnet to
the iron pieces. According to [5], the flux leakage through the
iron piece is negligible if the distance between the magnet and
the iron piece is more than twice the airgap length. The
waveform of the airgap flux density in figure 4 is based on
this assumption. The difference between the FEM and
analytically calculated values of the fundamental of the flux
density in the airgap is less than 4% for pole numbers between
20 and 80.
The maximum of the airgap flux-density Bm for the V-shape
PM motor is calculated using (2), which is derived in [4].
Figure 5 described the different notations used in the formula.
w 
l 
Br − Bsat Fe 1 + µ r i 
wm 
lm 
(2)
Bm =
 2αDr
wFe k cδ 
li 
k cδ



 pw + 2 l . w 1 + µ r l  + µ r l
m
Fe
m 
m 
m

Bsat is the flux density in the saturated iron bridge.
For the design with tangentially magnetized PM, the
derived formula is:
Bm =
Br α m l m
Dr
p
(4)
2
 Dr 

µ r l m k cδ + α ironα m 
 p 
The differences between the FEM and analytical calculated
values of the fundamental of the airgap flux density are less
than 4% for pole numbers between 20 and 80.
Fig.4. Method to calculate analytically the flux density in the airgap
Fig.5. Definition of the parameters for the buried PM geometries
2) Saliency and inductances: The second main difference
between the designs is due to the saliency of the inset and
buried PM structures, whereas the SMPM is non-salient. The
inductances in the direct and quadrature axis (Ld and Lq) are
not equal and therefore a reluctance torque is created. In order
to utilise this additional torque, a d-axis current id is added (5).
For the SMPM, the d-axis current is equal to zero.
3 p
T=
Ψm iq + Ld − Lq id iq
(5)
22
with p is the pole number, iq the q-axis current, Ψm the flux
from the magnets.
Figure 6 represents the phasor diagram of salient and nonsalient motor. The angle γ (or β = -γ + π/2) is chosen so that it
gives the maximum torque for a given current (6).
dT
=0
(6)
dγ
[
(
) ]
4
With using (5) and (7), a second order equation (8) is
obtained from (6).
 I d = I sin γ
(7)

 I q = I cos γ
(
)
(
)
2 Ld − Lq I 2 sin 2 γ + Ψm I sin γ − Ld − Lq I 2 = 0
(8)
Different values of β are tested using a recursion, in order
to find the minimum current together with the angle β that
gives the required torque. The recursion is described on figure
3. Knowing the angle β and the d- and q- current, the number
of conductor per slot can be calculated using the phasor
diagram at base speed. The procedure can be continued as for
a SMPM (figure 3).
B. Weight and choice of pole number
Figure 7 shows the evolution of the total active weight of
the different designs as a function of the number of poles. The
same weight of magnet (5.5 Kg) and the same amount of Joule
losses (700W) were imposed. As can be seen for the V-shape
PM motors with q=2, no solutions were found for a pole
number over 30, the teeth becoming too narrow and getting
saturated.
Fig.7. Active weight as a function of the pole numbers for different PM
motors designs
Fig.6. Phasor diagram at rated speed for salient and non-salient PM
machines
IV. RESULTS AND COMPARISON
The performances of the different PM designs are
compared. The motors should have a maximum outer diameter
of 500 mm and their torque and speed should be 840 Nm and
50 rpm respectively. The total weight of the machine should
not exceed 150 kg.
A. Validation of the analytical procedure
To validate the analytical procedure, the flux density in the
airgap and the torque were checked using FEM, for the
different optimized configurations obtained for the pole
numbers p = 30, p = 50 and p = 68. The fundamental of the
airgap flux density analytically calculated was in most of the
cases less than 2% different from the FEM value, with a
maximum of 4% difference. The mean value of the load
torque simulated with FEM was also maximum 4% different
from the required nominal torque. However for the
configuration with V-shape buried magnets, the torque ripple
obtained was very high due to high harmonics in the airgap
flux density. The V-shape designs were therefore tested with
two slots per pole per phase (q=2) giving lower torque ripple
from a more sinusoidal magneto-motive force.
The configuration that is the lightest for a pole number over
34 is the one with tangentially magnetized PM rotor. Indeed
the flux concentration in the rotor allows a high flux density in
the airgap and thus the machine length is lower (table I). The
flux concentration is therefore a non-negligible advantage.
The total active weight of the inset PM and tangentially
magnetized PM motors reaches a minimum at 70 and 60 poles
respectively. This is due to the constraints that guarantee the
rigidity of the structure [5]. When the limit on one or more of
these constraints is reached, the weight increases. For the inset
PM designs, the tooth width reaches its lower limit. The
length of the motor is then increased to fulfill the torque
requirement and the weight therefore increases.
TABLE I
Fundamental of flux density in the airgap Bδ and length for
different configurations and p = 50
Tangentially
Outer rotor
SMPM
Inset PM
magnetized
SMPM
PM
0.911
0.857
0.906
1.12
Bδ [T]
Length
191
179
199
144
[mm]
As can be seen in figure 7, the outer-rotor SMPM
configuration is lighter than the SMPM. Indeed, an outer-rotor
geometry allows a larger bore diameter and thus a lower
current loading is needed to obtain the same torque.
5
Figure 7 also reveals that the SMPM and the inset PM
configurations have almost the same weight for the same
value of magnet weight and copper losses. The inset PM is
even slightly lighter for a pole number over 50. The inset PM
rotor is heavier than the SMPM due to the iron pieces between
the magnets. However the reluctance torque that represents
more than 5% of the required nominal torque allows a lighter
stator, giving a motor that can be lighter than the SMPM.
torque ripple can be decreased with different methods, the two
configurations giving the lowest active weight, i.e. outer rotor
PM and tangentially magnetized PM motors are chosen.
Figure 8 shows the geometries of the optimized 60-pole
designs. Table IV gives different characteristics and
performance of the two designs. The iron losses are calculated
using FEM as described in [2].
Figure 7 can be used to choose an optimal pole number.
However it should be kept in mind that the higher the pole
number, the higher the number of magnets and the production
cost. Therefore a compromise should be found between the
weight and the magnet number. For pole numbers over 50, the
decrease of the weight is slower due to the constraints on the
structure. A minimum weight of 80 kg is reached for 60 poles
for the tangentially magnetized PM design.
C. Torque ripple
The torque ripple differs between the configurations and the
pole numbers. Table II gives the ratio between the torque
ripple and the mean torque for 3 different pole numbers and
for the different rotors. As can been seen, the torque ripples
for the buried PM and outer PM are very high. The cause of
this high ripple can come from the harmonics in the airgap
flux density. The harmonics 5 and 11 for the outer PM and
buried PM designs are indeed very high as shown in table III.
TABLE II
Ratio between the torque ripple and the mean torque
Tangentially
Outer rotor
SMPM
Inset PM
magnetized
SMPM
PM
p=30
0.16
0.48
0.30
0.49
p=50
0.14
0.40
0.35
0.40
p=68
0.20
0.58
0.24
0.59
Fig.8. Geometries of 60-pole outer rotor PM and tangentially magnetized PM
optimal designs
TABLE IV
Comparison between outer rotor design and buried magnet
design for p=60
Tangentially
Outer rotor
magnetized
SMPM
PM
Total active weight [kg]
87.1
80.1
Stator active weight [kg]
71.3
66.0
Magnet weight [kg]
5.5
5.5
Length [mm]
189
154
Fundamental of airgap
0.838
1.1
flux density Bδ [T]
Mean torque [p.u]
0.993
0.997
Ratio of torque ripple
0.42
0.46
over mean torque
Copper losses [W]
700
672
Iron losses [W]
110
100
Efficiency [%]
81.6
82.4
TABLE III
Relative value of harmonic 5 in the airgap flux density
Tangentially
Outer rotor
SMPM
Inset PM
magnetized
SMPM
PM
p=50
12.9
19.5
8.5
18.3
p=68
11.7
17.6
6.3
17.6
Finding a half pole angle that decreases both the 3rd and
5th harmonics can decrease the torque ripple. Another
solution is to use a concentrated winding with a good
combination between the pole number and the slot number or
to have stator teeth with different widths [6].
D. Chosen designs
Two designs with 60 poles are further described. Since the
The results in the table show that the tangentially
magnetized PM design has better performances and is lighter
than the outer rotor SMPM design. Using a tangentially
magnetized PM with outer-rotor might improve the
performances even more. The current design fulfills the
requirements in weight and dimensions and presents an
efficiency around 10% higher than the system induction motor
and gearbox to be replaced.
V. CONCLUSION
A procedure to design low speed radial PM motors was
presented. Different types of rotors were investigated. The
advantages and drawbacks of the different rotors used for the
low speed application were given. The methods to calculate
the airgap flux density and the inductances and currents,
which depend on the rotor configuration investigated, were
6
introduced.
The results show that the rotor with V-shape magnets is not
appropriate for design with high pole numbers. Outer rotor
designs are lighter than inner rotor designs. Furthermore the
inset PM motors are slightly lighter than a SMPM thanks to
the reluctance torque. In the considered application, the
configuration with tangentially magnetized PM gives the best
performances. As the obtained total active weight is rather
low, it would be interesting to check if a decrease of the
allowed weight of PM can lead to reduced cost for the
complete motor. However, a prototype is required to confirm
experimentally the results.
This study showed that it is possible to design direct-driven
PM motors with better efficiency and less weight than the
induction motor and its gearbox.
VI. ACKNOWLEDGMENT
This work has been carried out within the Permanent
Magnet Drive Program of the Competence Center in Electrical
Engineering at the Royal Institute of Technology in
Stockholm. Flux2D, software from Cedrat has been used for
the finite element simulations.
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[2]
[3]
[4]
[5]
[6]
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