design and
TRANSCRIPT
-
7/27/2019 Design And
1/8
Research article
Design and fabrication of magnetic couplings
in vacuum robotsPinkuan Liu, Yulin Wang and Jun Wu
State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering,Shanghai Jiao Tong University, Shanghai, China
AbstractPurpose The purpose of this paper is to discuss the design and fabrication of magnetic couplings to use for vacuum robots. The permanent magneticcoupling (PMC) is appropriate for torque transmission in ultrahigh vacuum and highly clean environments. However, conventional structures of PMC arealways unsuitable to use for vacuum robots.Design/methodology/approach Two types of design scheme for radial magnetic couplings are introduced and compared. The major characteristicof the novel design scheme is that the inner part uses a nonmagnetic mantle to enclose the magnets and yoke, and the outer part uses two end closuresto position magnets. The locating groove on the end closure may be manufactured as T-shape or dovetail shape.
Findings The 3D finite element analysis simulation results and experimental studies have demonstrated that the proposed Design B had a lowercontamination rate and a higher transmission efficiency than the Design A.Research limitations/implications The limitation of the research to date is that issues of control, path-planning, and communication have not yetbeen addressed.Practical implications The proposed PMC is successfully applied in vacuum robots which uses combined direct drive techniques and magnetictransmit techniques.Originality/value These results suggest that the proposed PMC is suitable for using in vacuum robots.
Keywords Robotics, Magnetism, Power transmission systems
Paper type Research paper
1. IntroductionPermanent magnetic couplings (PMC) are device that
transmitting torque through magnetic force with no
mechanical contact from a primary drive to a secondary
follower. In particular, it is very appropriate for torque
transmission in ultrahigh vacuum, highly clean, hazardous or
corrosive environments, and has been widely used in the fields
of industriy and defense. The PMCs as critical component are
increasingly used in much of developing vacuum robot for
wafer handling related to the field of semiconductor. It is
desirable for transmitting torque or rotary motion from the
atmosphere to the vacuum environment. The wafer holder
arms of vacuum robot, which operate in the reaction
chamber, are magnetically coupled to a directly driving motor
outside of the vacuum area. For example, in ultrahigh vacuum,a coaxial drive mechanism is incorporated to the design of a
compact wafer-transfer robot, in which multiple sets of
magnetic couplings with different configurations are
simultaneously used to couple different axes, a non-magnetic
vacuum partition wall separates the inner and outer rotor to
maintain the high vacuum from atmosphere environment.
Synchronours-type couplings among different types of
PMC can transmit higher torque than others for identical
volum e of m agnetic m aterials. On the basis of the
configuration, these types of couplings can be further
categorized into radial, axial and mixed-type couplings. The
axial-type couplings usually generate considerable axial force,
for example attractive or repulsive force, therefore, they are
only suitable to transmit lower torque. However, they possess
an advantage of easy adjustment of the air gap. On the other
hand, the radial-type couplings can transmit higher torque
level by simply increasing the length of the two concentric
coupling members or increasing the amount of pole-pairs by
augmenting the diameter of couplings. The radial-type
couplings are desirable for application in wafer-transfer
robot. This type of PMC consists of outer and inner rotors,
the outer rotor has permanent magnets of changing polarity
on the inner side and the inner rotor has them on the outside.
The north and south poles of the rotors are opposite to eachThe current issue and full text archive of this journal is available atwww.emeraldinsight.com/0143-991X.htm
Industrial Robot: An International Journal
36/3 (2009) 230237
q Emerald Group Publishing Limited [ISSN 0143-991X]
[DOI 10.1108/01439910910950487]
This paper is an updated and revised version of the paper originallypresented at 2008 International Conference on Intelligent Robotics andApplications (2008 ICIRA), Wuhan, China, October 15-17, 2008. Thiswork was supported in part by the Science & Technology Commission ofShanghai Municipality under Grant 07PJ14051 and 071111008.
230
-
7/27/2019 Design And
2/8
other, the magnetic field is completely symmetric in non-
operative state. When the rotors are twisted over a torsion
angle, the magnetic field line are moved, hence the torque is
transmitted from primary shaft to follower one through the
air gap.
However, conventional PMC are always unsuitable for
vacuum robot because that the robot needs the PMC run in
vacuum environment with an extremely low-contaminationrate and high reliability. It is essential to present some more
feasible designs applied in vacuum condition with pressure
range from 1025 to 1027 Pa. Some considerations related
design and fabrication are involved to suit high vacuum and
ultrahigh vacuum application requirement.
Angular stiffness, synchronous rotary accuracy and air gap
are of key specifications for design of PMCs. First, angular
stiffness depends on the maximal coupling torque of the
PMC. If maximum coupling torque is exceeded, the power
transmission is interrupted. The synchronous rotary accuracy
is predominately related to quantity of the minimal torsion
angle. The air gap is determined by the thickness of the
vacuum barrier.
Various methods to analyze the transmitted torque of
magnetic couplings have been employed, mainly including
analytical methods (Yao et al., 1995) and finite element
analysis (FEA) methods (Wu et al., 1997). The 3D FEA has
been shown to be a powerful and effective tool for the analysis
and design of synchronous magnetic couplings, taking the
end-leakage effects into account (Wang et al., 2008).
In order to decrease the contamination rate and increase
the reliability, two types of design of radial magnetic couplings
were proposed in this paper. The first type denoted as Design
A has two configurations including first one used screw to fix
the magnets on the yokes and second one used mucilage to
adhesive them. The second type denoted as Design B mainly
include two characteristics: the inner rotor of PMC uses a
nonmagnetic mantle to enclose the magnet blocks and the
yoke which has several locating grooves; the outer rotor ofPMC has two end closures which have the T-shape groove or
the dovetail shape to position magnets. The design and
fabrication of two types of PMC are described and discussed.
The Design A was then compared with the Design B base on
their structural characteristics and fabrication. The
simulations on above two types of design through the 3D
FEA method were carried out. In order to verify the validity of
simulations, a five degrees of freedom (DOF) measuring
equipment for magnetic couplings was also built. The
maximal coupling torques were measured. Results from
FEA and testing were discussed and analyzed. In the end, the
PMC of the proposed Design B was successfully applied in
constructing a novel vacuum wafer transfer robot which used
the combined direct drive motor and magnetic transmit
technique.
2. Design and fabrication on the PMC
2.1 General description
Design scheme in this paper focuses on the typical cylindrical
couplings with iron yokes and magnets located separately
without jointing with each other. The alternate magnetized
poles were allocated circumferentially. The yokes with high
permeability short-circuited the inner- and outer-magnet
rings of the couplings to avoid magnetic leakage, thus
improving the efficiency of torque transmission. In these
designs, maximal coupling torque of the PMCs need be up to
75 Nm, the air gap is defined as width of 5 mm so that it can
allow sufficient thickness of the vacuum barrier to ensure its
high stiffness and strength. The magnet material which was
radially magnetized was of Nd-Fe-B with residual flux density
denoted as Br of 1.19 T, and coercive force as Hc of 835.8 kA/
m in the magnetized direction. In our designs, the sector-
shaped magnets with same arc angle are suit to merge thecylindrical curvature, so that the couplings are capable of
keeping uniformity of the air gap between the couplings and
vacuum barrier. Similarly, the ratio of pole width to pole pitch
denoted as a was set to be 0.72 (Hornreich and Shtrikman,
1978) in order to obtain higher efficiency of magnetic
material. Furthermore, yoke was made of steel ASTM 1045.
The bulk conductivity denoted as k of yoke is 2,000,000 S/m,
and the BH-curve of the relative permeability of yoke can be
seen in Figure 1. The structure of yoke with enough thickness
can carry the required flux without saturation. In these
designs, the thickness of magnets was assumed to be equal for
the inner rotor and the outer one of magnetic couplings.
2.2 Design scheme I
Two types of configuration for Design A were proposed. The
first type through socket head screws to connect a set of
magnets on the yoke as shown in Figure 2, of which
Figure 2(a) is the photograph of the prototype, and
Figure 2(b) is the schematic diagram of the design. From
the figure, we can see that 14 magnets with sector-shaped
were separately located on the inner and outer side at interval
of constant angle. The second type used mucilage to adhesive
them together, as shown in Figure 3, where Figure 3(a) is the
photograph of the prototype, and Figure 3(b) is the schematic
diagram of the design. The yoke of these two types both were
machined locating grooves to position each magnet on the
socket of yoke.
In general, the countersunk hole was cut on the magnet and
the threaded hole was machined on the iron for the type ofusing screws. However, the loss of torque will occur obviously,
because that the countersunk hole decreased the volume of
magnetic material. Besides, the screw would also change the
distribution of magnetic field. Furthermore, overusing the
screw may result in bringing containment and particles into
vacuum and clean environment, then changing the pressure of
vacuum environment.
Though it was the most convenient approach to adhesive
the magnet on the socket of the yoke with mucilage, the
properties such as strength, elasticity and ductility of
Figure 1 The BH-curve of the relative permeability of yoke
Fluxdensity(T)
Magnetic field strength (A/m)
0.0
0.5
1.0
1.5
2.0
2.5
50,000 50,000 1,00,000 1,50,000 2,00,000 2,50,000 3,00,000 3,50,0000
Design and fabrication of magnetic couplings
Pinkuan Liu, Yulin Wang and Jun Wu
Industrial Robot: An International Journal
Volume 36 Number 3 2009 230237
231
-
7/27/2019 Design And
3/8
the adhesive layer are of critical issue. Since the magnetic
coupling torque between inner and outer rotors was
permanently remained while running, the vary load was
exerted on the PMC, failure of strength will potentially occur
in the adhesive layer. On the other hand, it was possible that
the mucilage contaminated the vacuum environment.
Therefore, the above two types of configuration of the
PMCs were undesirable for using in constructing the vacuum
robot. It was essential to design some more reasonablestructures for the special application.
2.3 Design scheme B
Two novel types of configuration for PMC were proposed in
this design. In the improved configuration than Design A, the
inner rotor of PMC used a cover made of un-conducted
magnetic materials enclosing the magnets and yoke as shown
in Figure 4. Rim of the cover mate to the flange of the yoke,
then hold them together through screws. The yoke also had
locating grooves to position each magnet on the socket of
yoke, just was similar to the types of Design A. While using
the insulation shell served as a reliable seal to separate the two
coupling halves from two different medium environments, the
cover will ensure a lower outgas rate and atom contaminationrate than the Design A.
The outer rotor of PMC consists of upper- and lower-end
caps, hollow cylinder and magnets. Two types of end caps are
designed and fabricated. One of the end caps was machined
into T-shaped grooves by EDM, other one of that was cut into
dovetail groove. End caps with T-shaped or dovetail grooves
were separately mounted on upper and lower flange of the
hollow cylinder, and held tightly by screws. Grooves on
upper- and lower-end caps were aligned, and then formed the
locating grooves for retaining the magnet. Magnets were also
adhesive on the yoke by mucilage in order to increase the
fastener strength. The configuration of the PMC with
T-shaped and dovetail groove are, respectively, shown in
F igures 5 and 6 . T he above two figures depict the
configuration of PMC, structure of outer rotor and end cap
and shape of magnet in detail. The yoke was manufactured as
cylinder-shaped without locating grooves.
As we can see by comparing Figures 5 and 6, it was easier to
fabricate magnets and end caps into dovetail shape than
T-shape. However, it was more difficulty to mount the
magnets into the dovetail groove than into the T-shape groove
because of the tolerances of the positioning groove from
machining and assembly. These two types of PMC from
Design B both had a higher material utilization rate and a
lower contamination rate than Design A with screw to fix, and
had higher connection reliability than Design A with mucilage
Figure 2 Design of the PMC using screws to fix magnets on yoke: (a) photograph of the prototype; (b) schematic diagram of the design
Outer rotor
N
SS
SS
S
SS
S
S
N
N
N
N
N
N
N
N
Inner rotor
(a) (b)
Figure 3 Design of the PMC using mucilage to adhesive magnets onyoke: (a) photograph of the prototype; (b) schematic diagram of the
design
(a)
(b)
Outer rotor
Outer rotor
inner rotor
inner rotor
Figure 4 The inner rotor of configuration for PMC and the cover
inner rotor
cover
Design and fabrication of magnetic couplings
Pinkuan Liu, Yulin Wang and Jun Wu
Industrial Robot: An International Journal
Volume 36 Number 3 2009 230237
232
-
7/27/2019 Design And
4/8
to adhesive. Therefore, these two novel types of the PMC
were more suitable for using in constructing a vacuum robot.
The photographs of two prototypes for Design B are shown in
Figure 7.
3. Analysis and experiment
3.1 3D FEA simulation
The 3D FEA module of Ansofts Maxwell 11 was employed
in this study to simulate the PMC. Physical model mainly
includes the outer rotor, inner rotor and air gap, therefore,
the finite element (FE) model is built according to this
physical model. The cross-section view of the PMC is shown
in Figure 7. In which the label H represents for the thickness
of magnet; the label R1 stands for the inner radius of inner
magnetic coupling; the label R2 is denoted as outer radius of
inner magnetic coupling; the label R3 stands for the inner
radius of outer magnetic coupling; the label R4 stands for the
outer radius of outer magnetic coupling; the label air_gap
stands for the length of air gap; and the label L stands for theaxial length of PMC. From Figure 8, we can see that vacuum
barrier, which is applied to separates the atmosphere and
vacuum environment, was not modeled in this FE model
because its permeability is close to air. Similarly, the thickness
of yokes was assumed to be uniformity along radial direction.
On the other hand, an area outside both upper and lower end
of the PMCs was included to model the end-leakage effect.
The width of the air layer considered in this model was set as
about three times the magnetic thickness in order to meet the
requirement of sufficient solving accuracy (Wu et al., 1997).
Since the magnetic coupling was periodically symmetrical
for each pole, the fractional FE models were established. The
master and slave boundaries were applied in this paper, which
can simplify model complexity. The magnetic field on theslave boundary was subjected to match the field on the master
boundary. The magnitude of the magnetic field on both
boundaries was equal. The fields on the two boundaries can
either point in the same direction, or in opposite directions, as
specified during the modeling process.
The FE models from the PMCs with four types of
configuration from the Designs A and B were, respectively,
shown in Figure 9(a)-(d). The parameters used in FE
simulation were listed in Table I. Four FE model were
Figure 5 Configuration of PMC using T-shape groove
PMC
T-shaped end cap
outer rotor
T-shaped magnet
Figure 6 Configuration of PMC using dovetail groove
PMC
outer rotor
dovetail end cap
dovetail magnet
Figure 7 The photograph of two prototypes of the PMC
outer rotor
inner rotor
PMC Dovetail shape
T shape
Figure 8 The cross-section view of PMC
R2 H
H
L
R1
R3
R4 air_gap
Design and fabrication of magnetic couplings
Pinkuan Liu, Yulin Wang and Jun Wu
Industrial Robot: An International Journal
Volume 36 Number 3 2009 230237
233
-
7/27/2019 Design And
5/8
analyzed in order to compute thecouplingtorques of thePMCs.
The first model was Design A with screws fixing, the second
model was also Design A using mucilage to adhesive only, and
the third model was Design B with the T-shape groove and the
last model from DesignB used thedovetailgroove. Thematerial
of the end caps for the last two models was aluminum. The
results of each model, which were maximal coupling torque of
PMC, were summarized in Table II in next subsection. The
maximal torque is yielded when the twisted angle is half-a-pole
pitch (Huang et al., 2001).
3.2 Experimental set-up
The experimental set-up in order to measure the static
coupling torques of PMCs was established as shown in
Figure 10. The Z-positioning stage 1 is vertically mounted on
the base 3, and the Z-stage driven and operated by manual, its
stroke can be up to 250 mm in z-direction. The X-Y
positioning stage 2 is stacked on the moving table of the
Z-stage 1, this stage 2 with precision leadscrew and linear
ball bearing can provide linear motion of 25 mm, respectively,
in x- and y-direction. The inner rotor of the PMC 5 is
connected coaxially to shaft of the torque sensor, 4 by mean
of mechanical coupler. The torque sensor is vertically
mounted on the angle bracket, which is fastened to the
moving table of the X-Y positioning stage 2 by mean of a
Figure 9 FE model of the PMCs: (a) FE model with screw fixing; (b) FE model using mucilage to adhesive; (c) FE model with the T-shape groove;(d) FE model with the dovetail groove
(a) (b)
(c) (d)
xz
z
z
y
y
y
y
z
Table I Parameters used in FE analysis
Design A Design B
Screws
fixing
Mucilage
fixing
T-shape
groove
Dovetail
groove
Air_gap (mm) 5
Br (T) 1.19
Hc (KA/m) 835.8
a 0.72k (S/m) 2,000,000
R2 (mm) 40 66 41 66
H (mm) 7 5 6 6
L (mm) 48 30 50 26
n 14 12 12 12
Design and fabrication of magnetic couplings
Pinkuan Liu, Yulin Wang and Jun Wu
Industrial Robot: An International Journal
Volume 36 Number 3 2009 230237
234
-
7/27/2019 Design And
6/8
screw connection. uz, ux positioning stage 6, which can rotate
range from 0 to 3608 about z-axis and from 0 to 58 about
x-axis, respectively. The outer rotor of the PMC 5 is fastened
to the chuck of the stage 6 by mean of a flange adapter. The
torque sensor 4 used in this experiment is the ORT-803 type,
and the controller of torque meter 7 is the TN-2 type of theOriental Technology Company. The A/D acquisition card is
the ADLINK PCI-9221, which is a 16-bit high-resolution
multi-function data acquisition (DAQ) card, with 16-channel
single terminal or eight-channel differential input capable of
up to 250kS/s sampling rate. The schematic diagram of the
working principle of the experiment set-up is shown in
Figure 11.
The coaxiality between the inner and the outer rotor of the
PMC can be set by the X-Y positioning stage; the coupling
length between the inner and the outer rotor in axial direction
can be adjusted by the Z-positioning stage; the slope angle of
the outer rotor can be regulated by the ux positioning stage;
while the torsional angle is implemented by the uz positioning
stage. The maximal torque can be measured when the
torsional angle was half-a-pole pitch.The torque value measured is output as frequency signal
range from 5 to 15 kHz by mean of the torque sensor, and
then it was translated to the analog voltage signal range from
25 to 5 V by the torque sensor amplifier. Finally, the 16-bit
high-resolution DAQ card was used to convert the analog
voltage positional to digital signals range from 0 to 100 Nm.
3.3 Results and discussion
The testing results from four types of PMC are summarized
and compared with the results from FE simulation in Table II,
and the following conclusions can be drawn:
.
The error between these two methods is less than3 percent, which shows that the 3D FEA has a high
accuracy.. The method of using screws to fix will decrease the
maximal torque of PMC obviously. The countersunk hole
on the magnet made the volume of magnet block
decrease about 5 percent in the example of this paper,
and the screw also changed the distribution of magnetic
field. The result showed that the maximal torque
decreased about 15 percent compared with other models.
In order to discuss the influence of the deviation length
between the inner and the outer rotor in axial direction, and
the slope angle of the outer rotor, the prototype for T-shape
groove of PMC from Design B was taken as an experiment
example. In Figure 12, the deviation length was set as fourcases, which is 0, 5, 15 and 25mm. When the deviation
length changed less than 5 mm in this case, its influence is
small. However, when the deviation length changed more
than 10 mm in this case, the maximal torque and the stiffness
of PMC decreased greatly. Furthermore, the slope angle of
the outer rotor has little influence on the transmitted torque of
PMC when the slope angle changed from 0 to 28 (Figure 13).
4. Application for constructing vacuum robots
The shafting of vacuum robot was designed which combined
used the rotary direct drive technique and the magnetic force
transmission technique. With a direct drive motor system, it is
no need for mechanical linkage (gearbox, belt, etc.) between
the payload and the motor. Thus, it does not exit the
backlash, clearance, friction, or elasticity problems. This
makes for a much stiffer and more easily controlled system.
Furthermore, the direct drive solution reduces the number of
components, simplifies assembly and thus reduces the overall
cost of the system. All this increase the dynamic performance
and precision of the system, and help to create a cleaner robot
with lower particulate contamination. The partial cross-
section view of a drive section of the 2 DOF vacuum robot
can be seen in Figure 14.
In this design, the rotational and radial position of the arm
was dependant upon the motion of the two rotary direct drive
Figure 10 Experimental set-up: (1) Z-positioning stage; (2) X-Ypositioning stage; (3) base; (4) torque sensor; (5) PMC; (6) uz, uxpositioning stage; (7) controller of torque sensor
1
2
3
4
5
6
7
Figure 11 Schematic diagram of experimental design
AEMC
A/D
Acquisition
Card
Torque
Sensor
Amplifier
xx
z
z
y
x
xy
z
Table II The results comparison of different models
Screws
fixing
Mucilage
fixing
T-shape
groove
fixing
Dovetail
groove
fixing
FEA (Nm) 61.4 71.2 70.7 72.2
Experiment (Nm) 60.9 72.3 72.6 70.9
Error (%) 0.8 1.5 2.6 1.8
Design and fabrication of magnetic couplings
Pinkuan Liu, Yulin Wang and Jun Wu
Industrial Robot: An International Journal
Volume 36 Number 3 2009 230237
235
-
7/27/2019 Design And
7/8
system 1, 2, which were arranged co-axially. Each drive
system was functionally identical and mechanically similar,
and each contained three elements: the drive motor, the
rotary position encoder, and the drive shaft. The drive motor
and the drive shaft both had a large, open, inner diameter.
The hollow design allowed for tubing, fixtures, rotary unions
and wiring to travel up through the center of the shaft and the
motor. The rotation of the arm was driven by the drive shaft
6, while the radial motion was driven by the shaft 7. The drive
shaft 6 runs through the hollow shaft 7 and the direct drive
system 2.The two concentric hollow drive shafts 6 and 7 connected
the two outer parts of the PMC 3, 4, respectively, and the
outer parts of PMC transmited torque to the inner parts by
magnetic force through the insulation shell 5, which separated
the atmospheric region and the vacuum region. The drive and
control mechanisms for the arm were completely outside the
insulation shell. The structure of the insulation shell was
designed as a novel stepped type. It was helpful to
simultaneously use two sets of magnetic couplings with
different dimension to couple different axes, and the cross-
coupling of multiple sets of PMC will decrease greatly
because of obviously different demension. In order to insure
the dem and of ultrahigh vacuum and highly cleanenvironment and a higher reliability for the vacuum robot,
the proposed Design B of T-shape groove and dovetail shape
groove of PMC were used. Finially, the robot arm rotated and
extended through the rotation of the two concentric hollow
drive shafts 8 and 9 which attached to the inner parts of PMC.
5. Conclusion
Based on the analysis, simulations and measurement of all
above PMC structure types, the conclusion can be obtained
that the proposed Design B both had a lower contamination
rate than the Design A; and they also had a higher
transmission efficiency than the screws fixing type of Design
A, and had higher connection reliability than the mucilage
fixing type of Design A. The maximal torque decreased about
15 percent for the screws fixing type compared with other
types.
Besides, the influences of the deviation length and the slope
angle between the inner and the outer rotor were discussed.
The results showed that when the deviation length changed
less than 5 mm in this case, its influence is small. However,
when the deviation length changed more than 10 mm, the
maximal torque and the stiffness of PMC decreased greatly.
The slope angle of the outer rotor has little influence on the
transmitted torque of PMC when the slope angle changed
from 0 to 28.
Figure 12 The influence of deviation length
80
70
60
50
40
30
20Torque(Nm
)
10
0
10
2 0 2 4 6
Torsion angle ()
8 10 12 14
0 mm
5 mm
15 mm
25 mm
Figure 13 The influence of slope angle
80
70
60
50
40
30
20Torque(Nm)
10
0
10
0 2 4 6
Torsion angle ()
8 10 12 14
2 degree
0 degree
Figure 14 The partial cross-section view of a drive section of the 2 DOFvacuum robot: (1), (2) rotary direct drive system; (3), (4) outer parts ofthe PMC; (5) insulation shell; (6)-(9) concentric hollow drive shaft
8
9
5
4
3
2
1
6
7
Design and fabrication of magnetic couplings
Pinkuan Liu, Yulin Wang and Jun Wu
Industrial Robot: An International Journal
Volume 36 Number 3 2009 230237
236
-
7/27/2019 Design And
8/8
Furthermore, the shafting of vacuum robot was introduced,
and the proposed Design B of PMC was verified to be feasible
and can be applied in the vacuum robot successfully.
References
Hornreich, R. and Shtrikman, S. (1978), Optimal design of
synchronous torque couplers, IEEE Transactions on
Magnetics, Vol. 14, pp. 800-2.
Huang, S.M., Chen, W.L., Yau, C.H. and Sung, C.K. (2001),
Effects of misalignment on the transmission characteristics
of magnetic couplings, Proceedings of the Institution of
Mecha nical Engi neers, Part C: Jour nal of Mechan ical
Engineering Science, Vol. 215 No. 2, pp. 227-35.
Wang, Y.L., Liu, P.K. and Wu, J. (2008), Near-optimal
design and 3D finite element analysis of multiple sets of
radial magnetic couplings, IEEE Transactions on Magnetics,
Vol. 44 No. 12, pp. 4747-53.
Wu, W., Lovatt, H.C. and Dunlop, B. (1997), Analysis and
design optimisation of magnetic couplings using 3D finite
element modelling, IEEE Transactions on Magnetics,
Vol. 33, pp. 4083-94.Yao, Y.D., Chiou, G.J., Huang, D.-R. and Wang, S.-J. (1995),
Theoretical computations for the torque of magnetic
coupling, IEEE Transactions on Magnetics, Vol. 31,pp. 1881-4.
Corresponding author
Pinkuan Liu can be contacted at: [email protected]
Design and fabrication of magnetic couplings
Pinkuan Liu, Yulin Wang and Jun Wu
Industrial Robot: An International Journal
Volume 36 Number 3 2009 230237
237
To purchase reprints of this article please e-mail: [email protected]
Or visit our web site for further details: www.emeraldinsight.com/reprints