Design, Analysis, and Fabrication of a Direct Drive Permanent NdFeB Magnet Synchronous Motor for Precision Position Control

Abstract

Direct drive motors have the excellent ability for precision position control due to their direct connection to load and elimination of the gearbox and pulley backlash. Among the direct drive motors, permanent NdFeB magnet synchronous motors (PMSMs) are the best choice for control systems due to their high efficiency, high power density, good dynamic behaviour, and excellent controllability. This study deals with the design, analysis, and fabrication of a direct drive PMSM for precision position control. To reach this aim, the designed motor should have very low cogging torque and torque ripple to avoid the motor deviation at the target point. To achieve these purposes, at first, a suitable combination of slot and pole has been selected for the motor and then the optimum shape of the magnets has been obtained by using the 2D finite element method. For the magnet shape, two important parameters of the magnet are optimised simultaneously. The designed motor has been fabricated and tested. Both simulation and experimental results show that the designed motor has a very good performance as the point of cogging torque and torque ripple views. Also, the experimental results validate the theoretical calculations.

Full text

IET Electric Power Applications
Research Article
Design, analysis, and fabrication of a direct
drive permanent NdFeB magnet synchronous
motor for precision position control
ISSN 1751-8660
Received on 4th March 2020
Accepted on 20th March 2020
E-First on 1st June 2020
doi: 10.1049/iet-epa.2018.5542
www.ietdl.org
Ali M. Hariri1 , Aliakbar Damaki Aliabad1, Mahdi Ghafarzadeh2, Sadegh Shamlou3
1Electrical Engineering Department, Yazd University, Yazd, Iran
2Mechanical Engineering Department, Sharif University, Tehran, Iran
3Faculty of Electrical Engineering, K.N. Toosi University of Technology, Tehran, Iran
E-mail: am.hariri@grad.kashanu.ac.ir
Abstract: Direct drive motors have the excellent ability for precision position control due to their direct connection to load and
elimination of the gearbox and pulley backlash. Among the direct drive motors, permanent NdFeB magnet synchronous motors
(PMSMs) are the best choice for control systems due to their high efficiency, high power density, good dynamic behaviour, and
excellent controllability. This study deals with the design, analysis, and fabrication of a direct drive PMSM for precision position
control. To reach this aim, the designed motor should have very low cogging torque and torque ripple to avoid the motor
deviation at the target point. To achieve these purposes, at first, a suitable combination of slot and pole has been selected for
the motor and then the optimum shape of the magnets has been obtained by using the 2D finite element method. For the
magnet shape, two important parameters of the magnet are optimised simultaneously. The designed motor has been fabricated
and tested. Both simulation and experimental results show that the designed motor has a very good performance as the point of
cogging torque and torque ripple views. Also, the experimental results validate the theoretical calculations.
1 Introduction
Direct drive motors have very good advantages such as high
precision, robustness, reliability, no backlash and a simple structure
for large diameter applications with respect to the use of gearbox
[1, 2]. These motors are usually designed with a large number of
poles and large diameter and directly connected to the load. The
mentioned advantages have introduced the direct drive motors as a
suitable choice for precession position control where the backlash
is a harmful factor. Among the direct drive motors, permanent
NdFeB magnet synchronous ones have good dynamic behaviour
and excellent controllability. Hence, they are very appropriate for
control applications and in this paper have been selected for
precision position control.
For precision position control, the motor should have very low
cogging torque and torque ripple. Cogging torque is caused by the
interaction between the rotor permanent NdFeB magnets and the
stator teeth and deflects the motor from the target point in position
control. Therefore, it should be decreased as much as possible. The
torque ripple is a periodic increase and decrease in the output
torque of the motor and has three sources in permanent NdFeB
magnet synchronous motors (PMSMs): cogging torque, the
difference between reluctances of the air gap in the d- and q-axis,
and distortion of the magnetic flux density waveform in the air gap
[3]. Minimising this ripple is of great importance in the application
of constant speed or high-precision position control, especially at
the low speed [4–7]. Kano and Matsui[8] present a design approach
of a direct drive permanent-magnet (PM) motor with a
concentrated winding for a low-speed high-torque application. A
genetic algorithm has been used to optimise the lamination design
in order to meet the requirements of the target application.
There are several methods to reduce the cogging torque and
torque ripple. Jahns and Soong [9] review a wide range of motor-
and controller-based techniques for minimising the generation of
cogging and torque ripple in both sinusoidal and trapezoidal
PMAC motor drives including the motor type and design, skewing,
stator winding types, and rotor and stator magnetic designs. In [10]
the performance of motors fitted with a magnet to magnet recycled
compared with the type of NdFeB which has high magnetic energy
densities and leads to the better torque performance. Using several
magnet segments which are placed in appropriate positions also
lead to the reduction of the cogging torque. In [11], the design of
experiment method has been employed to determine the
appropriate position of the magnet segments in this structure. Islam
et al. [12] reduce the cogging torque and the torque ripple of the
PM motor by skewing of the magnets. Sekerák et al. [13] comprise
synchronous motors with different permanent magnet and winding
types as the point of cogging and torque ripple view.
Among all of the methods, the magnet shaping is a popular and
effective method to reduce the cogging torque, back-electromotive
force (EMF) harmonics and on-load torque ripples [14–22]. Jang et
al. [15] optimise the magnet shape of a PMSM with bread shape
magnet for minimisation of ripple torque. In [16] the magnet
parameters including magnet embrace and magnet bridges have
been optimised for a six-slot/four-pole PMSM. Li et al. [18]
optimise the magnet offset of the PMSM to minimise total
harmonic distortion of the back-EMF waveform. Eom et al. [22]
minimise the cogging torque in permanent magnet motors by teeth
pairing and magnet arc design using a genetic algorithm.
As observed, most of the investigations focus on one of the
mentioned methods to reduce the cogging torque and torque ripple.
However, in this paper a comprehensive design has been performed
to reach a PMSM with minimum cogging and torque ripple. For
this purpose, at first, among all of the possible structures, a suitable
structure as the point of slot and pole combination has been
selected for the motor and then two magnet parameters including
magnet offset and magnet embrace are optimised simultaneously
by using the 2D finite element method. The design procedure has
been done to reach a direct drive motor with an output torque of
45 N m and a speed of 200 rpm. Simulation results show that with
the selected structure and the optimised magnet shape the motor
has very low cogging and ripple torque and sinusoidal back-EMF
which are needed for precision position control. The experimental
results performed on the prototyped motor verify the theoretical
computations and show that the motor has the desired performance.
2 Selection of the motor structure
The first step of the motor design is to determine the motor
structure as the point of the number of slots and poles view. The
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slot and pole combination should be selected in such a way that the
minimum cogging torque and ripple torque are achieved. Since the
ripple torque includes the cogging torque, it is better to consider
the cogging torque as a criterion of slot and pole selection. For this
purpose, all the possible combinations of the slot and poles for the
number of poles between 10 and 20 were investigated. The reason
for a selection of this range (i.e. 10<p < 20) is that the poles
number could not be very low due to the direct drive requirements
and not be very large due to the number of slot limitations in the
distributed winding. Direct drive motor requires a large number of
poles in order to produce a high amount of torque. However, a very
large number of poles in the distributed winding motor lead to a
large number of slots that is impossible due to the mechanical
consideration. Moreover, the large number of poles requires a
supply with high frequency that maybe impossible.
To reach the minimum cogging torque, at first, the greatest
common divisor (GCD) of the poles and slots should be one [23].
Hence, among the possible combinations of slots and poles, the
ones with GCD = 1 have been selected and presented in Table 1. In
the next step, the cogging torque of all the presented slot and pole
combinations has been calculated by using a 2D finite element. To
compute the cogging torque, the stator current has been set zero
and the motor has been rotated with a low constant speed. These
calculations have been done in the same conditions as the motor
dimensions for all the cases. The offset and embrace of the magnets
defined in the next section are 0 and 0.8, respectively, in all
calculations. The peak-to-peak value of the cogging torque for each
slot and pole combination has been presented in Table 2.
As seen from Table 2, the cogging torque of the motor with 14
poles has the lowest values. However, among the various 14-pole
combinations, there is no considerable difference between the
cogging torques. Hence, other criterions of motor performance
such as winding factor and mechanical aspects should be
considered for selecting slot and pole combination. The winding
factors of the 14-pole combinations are illustrated in Table 3. As
seen from this table, the winding factor of the motor with 15, 45,
and 57 slots has the largest values and are equal to about 0.95.
Table 4 shows the space harmonic contents of these three cases. As
seen from this table, the case with 15 slots has high harmonic
contents (due to the concentrated winding) and hence, is not
recommended. The case with 57 is also not recommended due to
the high number of slots that leads to tenuous tooth and weak
mechanical strength. Therefore, the combination of 45-slot and 14-
pole is selected for the motor structure. The winding arrangement
of this structure is illustrated in Fig. 1.
The dimensional parameters of the motor have been calculated
in such a way to reach a direct drive motor with the continuous
torque of 45 N m. The design data of the motor including all
dimensions and motor parameters are presented in Table 5.
3 Global optimisation of the magnet shape
NdFeB magnet shape is a very important parameter in PMSMs and
influences on the motor performances. It influences the cogging
torque, ripple torque, and back-EMF waveform that all of them are
important in the current project. Hence, it should be designed as
Table 1 Possible combination of slots and poles with GCD = 1
Slots Poles
10 12 14 16 18 20
12
15 ✓ ✓
18
21 ✓ ✓ ✓
24
27 ✓ ✓ ✓ ✓
30
33 ✓ ✓ ✓ ✓
36
39 ✓ ✓ ✓ ✓
42
45 ✓ ✓
48
51 ✓ ✓ ✓ ✓
54
57 ✓ ✓ ✓ ✓
60
Table 2 Peak-to-peak value of the cogging torque for the selected slot and pole combinations (N m)
Slots Poles
10 14 16 20
15 — 2.28 22.09 —
21 11.996 — 22.29 14.413
27 11.519 2.22 18.93 13.933
33 12.227 2.53 21.10 16.124
39 11.951 2.80 21.07 15.954
45 — 2.30 21.38 —
51 12.52 3.13 22.20 16.751
57 12.614 2.55 22.10 17.573
Table 3 Winding factors of the 14-pole combinations
slot number 15 27 33 39 45 51 57
winding factor 0.95 0.695 0.928 0.863 0.95 0.918 0.955
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well as possible. The NdFeB magnet shape has two important
parameters; magnet offset and magnet embrace. The magnet offset
is the distance between the centres of the rotor and the magnet arc
as illustrated in Fig. 2. The magnet embrace is the ratio of the
magnet arc to the pole arc according to (1). In this equation the
angles αm and βm are as specified in Fig. 3:
Magnet embrace = αm
βm
(1)
There is a lot of research for optimisation of the NdFeB magnet
shape parameters but some of them only optimised one parameter.
However, in this paper, the aim is to optimise both magnet offset
and magnet embrace simultaneously in order to reach the desired
performance. For this purpose, the cogging torque and ripple
torque are calculated for a range of possible offsets and embraces
by using the 2D finite element method. The finite element method
is based on the magnetic scalar potential formulation governed by
the following differential equations [24]:
∇ × H=J0+Je
(2)
∇ ⋅ B= 0
(3)
B=1
v0
H+MPM
(4)
where MPM is the magnetisation of a permanent NdFeB magnet.
The magnetic vector potential A and the equivalent magnetising
current JPMm are expressed as follows:
B= ∇ × A
(5)
JPMm =v0(∇ × MPM)
(6)
Je=σE=σ−∂A
∂t+v×B+ ∇ϕ
(7)
v0(∇ × ∇ × A) = J0+Je+JPMm
(8)
Table 4 Harmonic contents of the 14-pole structure with different slots
Harmonic number 15-slot 45-slot 57-slot
1 0.0464 0.0345 0.0135
2 0.0951 0.047 0.0278
3 0 0 0
4 0.2166 0.1997 0.0647
5 0.315 0.0685 0.0974
6 0 0 0
7 (main) 1.4193 1.417 1.4315
8 1.2419 0.049 0.1735
9 0 0 0
10 0.1575 0.1511 0.0303
11 0.0787 0.0119 0.0143
12 0 0 0
13 0.0146 0.0119 0.0016
14 0.0033 0.0011 0.0005
15 0 0 0
16 0.0029 0.0017 0.0026
17 0.0111 0.0034 0.0064
18 0 0 0
19 0.0456 0.0141 0.0218
20 0.0787 0.0139 0.0421
Fig. 1 Winding arrangement of the 14-pole 45-slot structure
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When the moving coordinate system is used, the governing
equation in 2D is given as follows:
∂
∂xv0
∂AZ
∂x+∂
∂yv0
∂AZ
∂y= − JZ+σ∂AZ
∂t+σ∂φ
∂z−JPMm
(9)
JPMm =v0
∂MPMy
∂x−∂MPMx
∂y
(10)
where AZ is the z component of the magnetic vector potential, JZis
the current density, v0 is the magnetic resistivity, MPMx and MPMy
are the magnetisations of PM, σ is the conductivity of the rotor bar,
and ϕ is the scalar potential. The rotor and stator meshed regions of
the motor are shown in Fig. 4.
Table 6 shows the calculated results for the cogging torque. In
this table the embrace is varied from 0.77 to 0.9 by step 0.01 and
the offset is varied from 37 to 54 mm by step 1 mm. The points
Table 5 Design data of the direct drive motor
motor input voltage 220 V
nominal current 3.5 A
continuous power 942 W
nominal torque 45 N m
nominal speed 200 rpm
number of phases 3
number of poles 14
stator outer diameter 260 mm
inner diameter 164 mm
stack length 50 mm
lamination stacking factor 95%
number of slots 45
conductor per slot 100
rotor outer diameter 163 mm
inner diameter 130 mm
inertia 0.044 kg m2
Br of NdFeB magnets 1.2 T
Hc of NdFeB magnets −838,000 A/m
Fig. 2 Illustration of the NdFeB magnet offset
Fig. 3 Illustration of the angles in the NdFeB magnet embrace definition
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specified by pluses are the impossible cases due to the large offset
compared to its embrace. As seen from this table, the cogging
torque has an optimal line with low values <0.035 N m. This value
is very excellent and suitable for position control.
To calculate the ripple torque, the stator has been excited by a
sinusoidal current with nominal amplitude and the motor has been
rotated at the rated speed. Table 7 shows the torque ripple of the
motor for the offset range of 37–49 mm and the embrace range of
0.77–0.90. This table also shows an optimal line for the torque
ripple. The blanked points are belonged to the ripple torques far
from the optimal line and hence have not been calculated. As seen
from this table the optimal line has a low value equal to 0.08 N m.
However, this optimal line is different from the cogging torque
line. Therefore, the intersection of two lines should be considered
for the optimal point. The common point of two lines is the point
with an offset of 46 mm and an embrace of 0.9. The cogging torque
and torque ripple of this point are very desirable and equal to 0.03
and 0.08 N m, respectively. However, because with this offset and
embrace the thickness of the NdFeB magnet corners becomes very
small and impractical, the embrace and offset of 0.87 and 42 mm
are selected as the optimum practical points. The cogging torque
Fig. 4 Rotor and stator meshed regions of the motor
Table 6 Peak-to-peak cogging torque of the motor for various offsets and embraces
Cogging torque (mN m) Offset
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
embrace 0.77 111 102 95 94 85 80 75 68 63 57 55 47 52 49 46 40 39 36
0.78 110 99 96 97 83 75 68 63 46 47 45 47 45 39 39 40 39 +
0.79 108 101 90 82 73 65 58 49 43 43 44 40 38 37 35 30 28 +
0.80 95 90 78 73 69 57 52 48 44 40 38 37 36 34 33 30 55 +
0.81 82 72 63 60 59 55 51 49 42 44 40 36 34 33 32 27 46 +
0.82 73 57 56 54 57 55 52 47 47 44 38 34 32 32 39 44 30 +
0.83 58 56 54 50 48 48 47 49 44 42 35 36 34 36 28 31 59 +
0.84 53 51 47 46 46 46 40 40 41 39 43 40 30 32 38 + + +
0.85 52 48 46 42 40 43 41 39 46 42 40 38 32 41 44 + + +
0.86 65 59 38 38 39 43 44 45 37 37 36 35 29 54 41 + + +
0.87 53 36 34 35 40 40 39 40 40 36 33 33 34 42 + + + +
0.88 45 41 42 42 37 36 35 35 35 32 34 34 51 + + + + +
0.89 39 37 36 36 34 34 34 35 33 33 30 53 45 + + + + +
0.90 36 36 35 38 38 35 35 34 32 30 35 40 25 + + + + +
Table 7 Peak-to-peak torque ripple of the motor for various offsets and embraces
Ripple torque, mN m Offset
37 38 39 40 41 42 43 44 45 46 47 48 49
embrace 0.77 * * 1120 * * 1120 * * 1120 * * 1100 *
0.78 * * * * * * * * *
0.79 * * 860 * * 880 * * 900 * * 950 *
0.80 * * * * * * * * *
0.81 * * 590 * * 650 * * 720 * * 790 *
0.82 * * 450 * * 430 * * 620 * * 810 *
0.83 * * 370 * * 430 * * 520 * * 630 *
0.84 150 190 210 240 280 320 360 400 450 * * 570 *
0.85 130 90 105 120 180 220 260 320 * * * 500 *
0.86 220 180 130 85 90 140 200 230 240 330 390 440 480
0.87 * * 230 170 120 80 110 160 210 260 330 380 460
0.88 * * * 270 200 140 80 80 140 210 260 350 420
0.89 * * * * * 230 160 110 80 140 190 310 370
0.90 * * * * * * 230 160 110 80 180 280 310
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and torque ripple of this point are 0.04 and 0.08 N m that is good
and near to the minimum values.
Fig. 5 shows the flux density distribution of the motor with the
optimum NdFeB magnet shape at the no-load condition. This
figure shows that the maximum flux density of the motor is about
1.4 T. In Fig. 6 the cogging torque of the motor is presented. As
seen from this figure the peak-to-peak value of the cogging torque
is about 0.04 N m. Fig. 7 illustrates the calculated torque ripple of
the motor under the nominal torque. It shows that the designed
motor has a low peak-to-peak ripple torque equal to 0.08 N m.
Simulation results also show that the designed motor has a
sinusoidal back-EMF that is necessary for the smooth motion of
the motor. Fig. 8 shows the line-to-line-induced voltage waveform
of the motor when it is rotated at the nominal speed. As seen from
this figure, the back-EMF is very close to the sinusoidal waveform
and its total harmonic distortion is about 0.48%.
4 Experimental results
The designed motor has been manufactured according to the
drawings obtained from the simulation. Two precision back-to-
back angular bearings with very less looseness have been used in
order to minimise the mechanical errors in precision position
control. A precision frameless encoder is directly connected to the
shaft to detect the angular position of the motor. Fig. 9 shows the
cross-section of the motor including all components. Fig. 10 shows
the manufactured rotor and stator and Fig. 11 shows the assembled
motor.
Fig. 5 Flux density distribution of the motor at no-load condition
Fig. 6 Cogging torque of the motor obtained from simulation
Fig. 7 Torque ripple of the motor obtained from simulation
Fig. 8 Calculated back-EMF waveform and FFT analysis
Fig. 9 Cross-section of the motor
Fig. 10 Manufactured rotor and stator
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To investigate the motor performance three tests have been
done on the motor. At first, the back-EMF of the motor is measured
at the rated speed by coupling a motor depicted in Fig. 12. As
depicted in Fig. 13, the measured back-EMF has a sinusoidal
waveform and is very close to the simulated one. The fast fourier
transform (FFT) analysis presented in Fig. 14 shows that the total
harmonic distortion of the measured back-EMF is about 0.58%.
The little difference between the simulation and the experimental
total harmonic distortion is due to the speed variation of the motor
and the manufacturing errors.
The second test performed on the motor is the maximum torque
measurement. For this purpose, the motor excited by the nominal
DC current (Ia = 5 A, Ib = −2.5 A, Ic = −2.5 A) and the static
torque was measured at different rotor positions as shown in
Fig. 15. The maximum torque obtained from this test was 45 N m
that is in agreement with the theoretical value.
In the third test, the cogging torque of the motor has been
measured. For this purpose, the motor is connected to a precision
dynamometer illustrated in Fig. 16 and rotated at a low speed. The
measured cogging torque is depicted in Fig. 17. As seen from this
figure the peak-to-peak value of the cogging torque is about 0.24
N m which is larger than the theoretical value. The reason for this
difference can be due to the dynamometer inevitable errors,
coupling backlash, static looseness, and the mechanical errors
occurred in motor construction.
5 Conclusion
In this paper the procedure of design, analysis, and construction of
a direct drive PMSM motor used for precision position control was
described. At first, a suitable structure was selected for the motor
as the point of slot and pole combination. Then, a global
optimisation was performed for the NdFeB magnet shape in order
to reach the minimum cogging torque and torque ripple. For this
purpose, both NdFeB magnet offset and NdFeB magnet embrace
were optimised simultaneously by using the 2D finite element
method. By the optimal design, the cogging torque and torque
ripple of the motor decrease to low values suitable for precision
Fig. 11 Manufactured direct drive motor
Fig. 12 Test setup for back-EMF measurement
Fig. 13 Measured and simulated back-EMF waveform
Fig. 14 Measured back-EMF waveform and FFT analysis
Fig. 15 Measurement of the motor produced torque
Fig. 16 Test setup for cogging torque measurement
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position control. Also, the back-EMF waveform was very close to
the sinusoidal shape. The designed motor was fabricated and
tested. The experimental results were in good agreement with the
theoretical results and validated the optimal design. The authors are
now working on the motor driver and controller and the results will
be presented in the next occasion.
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Fig. 17 Measured cogging torque versus time
8IET Electr. Power Appl.
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