Numerical calculations and experimental measurements of forces from an actuator of the type used in active magnetic journal bearings are presented. The calculations are based on solution of the scalar magnetic potential field in and near the gap regions. The predicted forces from single magnet with steady current are compared with experimental measurements in the same geometry. The measured forces are smaller than calculated ones in the principal direction but are larger than calculated in the normal direction. This combination of results indicate that material and spatial effects other than saturation play roles in determining the force available from an actuator

Knight, Josiah

Mccaul, Edward

Xia, Zule

English

NASA Technical Reports Server

N91-21207
MEASUREMENT and CALCULATION of FORCES in a MAGNETIC
JOURNAL BEARING ACTUATOR
Josiah Knight, Edward MeCaul, Zule Xia
Duke University
DepartmetLt of Mechanical Engineering and Matcrials Scicnce
Durham
NC 27706
477
https://ntrs.nasa.gov/search.jsp?R=19910011894 2020-03-19T19:08:44+00:00Z
Measurement and Calculation of Forces
in a Magnetic Joumal Bearing Actuator
Josiah Knight
Assistant Professor
Edward McCaul
Zule Xia
Graduate Assistants
Department of Mechanical Engineering
and Materials Science
Duke University
Durham, North Carolina
funded by
NASA Lewis Research Center
presented at
NASA Workshop on Aerospace Applications
of Magnetic Suspension
Langley Research Center
September 1990
Abstract
Numerical calculations and experimental measurements of forces from an actuator
of the type used in active magnetic journal bearings are presented. The calculations are
based on solution of the scalar magnetic potential field in and near the gap regions. The
predicted forces from a single magnet with steady current are compared with experimental
measurements in the same geometry. The measured forces are smaller than calculated ones
in the principal direction but are larger than calculated in the normal direction. This
combination of results indicates that material and spatial effects other than saturation play
roles in determining the force available from an actuator.
478
1. Introduction
Recently, there has been much interest in the use of active magnetic bearings to replace
or augment traditional beatings in turbomachinery. Magnetic bearings offer a number of
potential advantages, including low power loss, suitability for harsh environments, and the
ability to change the beating characteristics to minimize vibration.
This paper presents data on calculation and measurement of forces from a magnetic
actuator similar to those that are used in magnetic journal bearings. The data are for open-
loop, steady conditions only and are part of the development of models for active bearings.
Much research has recently been devoted to magnetic bearings. No extensive literature
survey is attempted in this paper, but from a sampling of the published papers on the topic
[ 1-9 ], and the proceedings of the two international symposia on magnetic beatings [ 10,11 ],
it is clear that the concentration is on control aspects. Although the development of robust
control strategies is important in optimizing magnetic bearing characteristics, particularly
stability characteristics, it is also necessary to understand the forces arising from actuators
in order to optimize fully a magnetic bearing system. This is expected to become
increasingly important when the requirements for peak force and for force to weight ratio
are stringent, which may be expected in aerospace applications. Better understanding of
the characteristics of the journal beating actuator is necessary in order to take advantage of
all available parameters, including gap size, shape and material selection1 in a system
optimization. This paper presents preliminary results of work toward this goal.
2. Theory
A computer program has been written that calculates the force exerted on the journal
by a magnet having a steady current in its coils. The force is found by calculating the
energy stored in the air gaps between the magnet and the journal, then performing a
numerical perturbation to obtain a central difference of the energy change per unit position
change. This gives the force in the direction ofthe perturbation. The force for a magnet at
an arbitrary location can be calculated.
The algorithm includes the following assumptions:
i. The permeability of the metal is infinite compared to that of the gaps, which is
assumed equal to that of free space. This implies that all the energy is stored in
the gaps.
ii. All magnetic flux closes the path through both metal parts. Expansion or
fringing of the field near the gaps is allowed, however.
iii. The coil current, therefore the MMF, is constant over a perturbation.
479
In an Isotropie domain not containing currents, where time variations are only of
low frequency, the magnetic field can be represented as the gradient of a scalar field _x,y).
The energy contained in the domain is
where the flux density B is given by
o = IV E3oBdV (I)
g ffi - V_
and the potential _) satisfies the governing equation
(2)
with the boundary conditions
and, because of assumption (i) above
v ,=o (3)
_n
- 0 on free boundaries
(4)
= 4,1 on pole face 1
= 4,2 on pole face 2 (5)
= 0 on journal surface,
as shown in Figure 1.
Initially the boundary values of_on the pole faces, 4,1 and 4,2, are not known,
but must be determined in relation to the datum of<[_=0 on the journal surface. The problem
is made tractable by the fact that the governing equation is a linear one, so that the values of
qbinternally are determined within a multiplicative constant even for an arbitrary choice of
boundary condition values. The fact that the flux must be the same through the two gaps
allows the ratio
K 4,2
= -- (6)
4,1
to be determined.
magnetomotive force,
4,1 -4,2= _
allows determination of the actual surface potentials.
Then the fact that the difference between !he two potentials is the
(7)
480
scalar potential fiehl
boundary value of s:alar pot_:ntial
Figure 1. Boundary conditions for solution of magnetic scalar potential.
481
2.1. Computer Program
The algorithm above is embodied in a FORTRAN computer program, GAPFOR1,
which uses the finite dement method for calculating the magnetic potential in two
dimensions. For a given journal position the program calculates the gap height as a
function of angular location and generates a finite element mesh for each gap. Flux
fringing is allowed by extending the Finite element domain beyond the edges of each pole
face. Then the journal position is perturbed four times, first with positive dx and negative
dx, then with positive dy and negative dy. At each step the mesh is regenerated and the
energies are recalculated. The central difference analog to the derivative of energy is then
computed, which is equal to the force in the perturbation direction.
To achieve rapid computational speed and efficiency, a dedicated finite element
program was written for this application. It includes a grid generation routine as well as a
banded gauss elimination solver for the assembled equations.
Forces from one magnet of a beating
The computer program has been used to predict the forces from one magnet acting on
the journal at various positions of the journal within the clearance space. The geometry
corresponds to that of the experimental apparatus described in Section 3. Half of the entire
clearance space is mapped, since all positions of the journal with respect to a single magnet
can be represented in terms of positions in this half plane. Figures 2 and 3 show a map of
force versus x,y position. The magnet is the upper vertical magnet, and a steady current of
1 ampere through the coils is used. The dimensions and other parameters are the same as
those of the experimental apparatus described below. The figure indicates that the force in
the y-direction (the principal force) varies between 6 and 180 N as the joumal is moved
along the y axis between -0.7 < y/c < 0.7. When the joumal is also given an x-direction
eccentricity, the y-force increases somewhat.
Except at x=0, there is also an x, or normal, component to the force, as shown in
Figure 3. This normal force increases rapidy as x is made larger. At x/c -- 0.7 it is 12% of
the principal force.
3. Experiment
3.1 Design of Apparatus
The apparatus for force measurement is shown in an exploded view in Figure 4. Each
magnet is independent and is wound with 400 turns capable ,ffcarrying current of 2.0 A in
the steady state. In the steady force measurement mode, the rotor is held stationary by
482
FY
240
Upper vertical magnet
Vertical force in N
R = 38 rnm (1.5 in)
L = 19 mm (0.75 in)
¢ = 0.76 mm (0.030 in)
MMF = 400 A-T
180
120
6O
0
O.
x/c -0.35
-0.71
\
, /
.II
I
///
I
/
/
I
I
!
i
I
I
I
I
g
I
'1
, °
035
vB
0.71
Figure 2. Attractive force from one magnet in principal direction.
483
F×
30.0
22.5
Upper vertical magnet
Horizontal force in N
R = 38 mm (1.5 in)
L = 19 mm (0.75 in)
c = 0.76 mm (0.030 in)
MMF = 400 A-T
15.0
7.5
0,0
0.
o
-0.71
0.71
Figure 3. Attractive force from one magnet in normal dircclion.
,I8,1
III
. II /
0
/
/
I "
_c_ "[
X
l
I
I I --
"l
!
L'
i
]1
1
L
I
r_:, ! '-" 1 0o
Flllure 4. ,Amcmbly drawinll of force meaaurement apparatus.
4,%
ORIGINAL PAGE IS
OF POOR QUALITY
pressure from six micrometer heads (three on each end) that are in turn held by cantilever
arms instrumented with strain guage bridges. Thus all mechanical force on the rotor passes
through the micrometer pushers and the strain guage arm transducers To minimize any
tangential force on the pusher ends Teflon ball sockets with steel spheres were used
between the pusher micrometers and the support disks. A full assessment of the
uncertainty due to friction has not been completed.
3.2 Results of Measurements
Forces were measured at several locations and for several values of steady current.
The figures referred to below display dimensional data as measured, with forces in
Newtons plotted against y/c, the eccentricity ratio in the vertical direction. All of the forces
presented are from the lower vertical magnet, so the vertical forces are in the negative y-
direction. The eccentricites in the x-direction are all positive. Three traverses of the y-
direction were made, at x/c positions of approximately 0.0, 0.24, and 0.45. Assessments
of the errors in measurement are not complete; however, it is expected that the error in
position measurement is no greater than plus or minus 0.05 in y/c and Xr/C,and that the
error in force measurement is no greater that plus or minus 5 N. Errors in current level
control are within 0.1 A. A larger series of measurements that were made before the
addition of the balVsocket contacts was eventually discarded because the measurement error
due to friction appeared to be significant.
The data support some of the anticipated relationships among the position, current and
force variables but appear to disagree with other aspects of the present theory. Figure 5
shows the vertical force as a function ofy/c for several values ofcurre_t. The force tends
to increase roughly as the inverse square of the gap. The magnitudes ofthe forces,
however, are considerably lower than those predicted either by the linear finite element
theory or by the traditional theory based on assumption ofuniform gaps, and the ratio
between measured and predicted forces is not constant. Figure 6 is a comparison ofthe
measured forces with those predicted by the finite element calculation. The results indicate
that at large gap and/or small current the ratio between the measured an.t predicted forces is
about 1.5, but at smaller gaps and/or higher currents this ratio increases, eventually
exceeding 2.0 for all the three values of current that are plotted.
Several mechanisms may be operating to cause these discrepancies, including flux
leakage, non-uniform permeability of the materials and magnetic saturation. Some part of
the disagreement is likely the result of measurement errors, but the differences appear to be
significant even after allowing for reasonable experimental error. These disagreements
reinforce the need for additional work, already planned, on force calculation.
,186
o.o_///
-150 I 2.OA
-200 I Lower vertical magnet
0.0 < x/c < 0.1
y/c
Figure 5. Vertical force from lower vertical magnet at diffcrent values of current.
4_7
Z
LL
0
-100
-150
-200
Figure 6. Measured forces and forces predicted by linear FEM calculation.
,188
The linear finite element theory predicts the existence of forces from a magnet that are
normal to its axis of symmetry when the rotor is displaced from this symmetry axis, but the
forces that are measured are considerably stronger than those predicted by calculation.
Figure 7 shows the x component of force when the rotor is placed as closely as possible on
the y-axis. The normal force appears to be somewhat stronger at higher current levels but
all these forces are small, on the order of 5 % or less of the principal force, so it is difficult
to attribute much significance to this ratio in view of the experimental uncertainty. At
higher values of x/c, however, the normal force becomes much more significant. Figures 8
through 11 show the vertical and horizontal components of force when the x/c value is 0.24
or 0.45, and Figure 12 shows the value of the x force as a function of position for several
values of x/c while the current is held constant at 1.0 A. In general it appears that the
normal force increases significantly with increasing x/c, and at x/c = 0.24 and 0.45 the
horizontal force is about 10 % ofthe principal force. Theory predicts a ratio of about 2 %
to4 %.
Figure 13 indicates that within measurement uncertainty there are not significant
differences in the y-components of force at the three different values of x/c. This is in
general agreement with the theoretical predictions, which show some increase in the y-
component of force as the x-eccentricity is increased.
489
2O I ! I ! ! ! ! I I
"7
LL
15
10
Lower vertical rna_net
0.0 < x/c < 0.1
2.0 A
-1.0 -0.8 -0,6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
y/c
Figure 7. Horizontal force from lower vertical magnet at different values of current.
490
Ztl
0
-5O
-100
-150
-200
-250
03
• 1.0 A et
I I I I I I I I I
,0 -0,8 -0,6 -0.4 -0 2 0,0 0.2 0,4 0.6 0.8
y/c
.0
Figure 8. Vertical force from lower vertical magnet when x/c = 0.24.
491
Z
X
LL
20 l I l I I l I I I
Lower vertical magnet
2.0 A x/c I 0.24
15
10
1.0 A
5 -
0 'l I
-0.8 -0.6 -0,4 -0.2 0.0 0.2 0.4 0.6 0.8 .0
y/c
Figure 9. Horizontal force from lower vertical masnet when x/c = 0.24.
.19"J
-50
-10o
Z
u_
-150
-2O0
-250
IOA
2.0 A
Lower vertical rr agnet
x/c = 0.45
I I I I I I I ! I
.0 -0.8 -0.6 -0.4 -0.2 0.0 0,2 0.4 06 0,6
y/c
.0
Figure 10. Vertical force from lower vertical magnet when x/c = 0.45.
,193
"7
:=<
LL
2O
15
I0
I I I I I I I I I
0 i
- 1,0 0.8
Lower vertical magnet
x/c - 0.45
2.0 A
1.0 A
0.3 A
I _ i I_I I I I
-0.8 -0.6 -0.4 -0.2 0.0 0,2 0.4 0.6
y/c
.0
Figure 11. Horizontal force from lower vertical magnet when x/c = 0.45.
494
'°1 ! I I I
x/c =0.24 x/c =0.45
Lower vertical magnet
i= 1.0A
Z
x
LL
4
2 x/c =0_
Figure 12. Horizontal force at different x positions with 1.0 A current.
495
I ! ! !
Z -60
x/c=0,45
X/C=O
- I00 Lower vertical magnet
i= 1.OA
0.0 0,2 0.4 0.6 0.8
y_
Figure 13. Vertical force at different x positions with 1.0 A current.
,1911
4. Conclusig9
Numerical calculations and experimental measurements of forces in a magnetic journal
bearing actuator are presented.
In summary, the general trends of the measured principal forces agree with the
predictions of the theory while the magnitudes of forces are somewhat smaller than those
predicted. The measured forces in the normal direction appear to be significantly larger
than those predicted by theory when the rotor has an x eccentricity. The accuracy of the
measured results has not been firmly established, and these conclusions should be
reexamined as later measurements are made. It appears, however, that these effects will be
significant even after considering experimental uncertainty, and both of these phenomena
warrant further study.
Additional work is planned that will include force calculations considering the finite
permeability of metals, and further force measurements using other materials. A new
apparatus is being constructed that will allow more precise position control and force
measurement.
5. Acknowledgments
The authors gratefully acknowledge the support of this work by NASA Lewis
Research Center under research grant NAG 3-968, and the advice and assistance of the
grant technical officer, Dr. G. V. Brown.
497
5. REFERENCES
1. Habermann, H. and Liard, G., "An Active Magnetic Bearing System," Tribology
International, April 1980, pp. 85-89.
,
.
.
.
.
,
.
.
Schweitzer, G. and Lange, R., "Characteristics of a Magnetic Rotor Beating for
Active Vibration Control," First International Conference on Vibrations in Rotating
Machinery, Institution of Mechanical Engineers, London, Cambridge, 1980.
10.
Nikolajsen, J. L., Holmes, R., and Gondhalekar, V., "Investigation of an
Electromagnetic Damper for Vibration Control of a Transmission Shaft," Institution
of Mechanical Engineers, Vol. 193, No. 31, 1979, pp. 331-336.
I1.
Allaire, P, E,, Lewis, D. W., and Knight, J. D., "Active Vibration Control ofthe
Single Mass Rotor on Flexible Supports," Journal of the Franklin Institute, Vol. 315,
1983, pp. 211-222.
Kelm, R. D., "Analysis and Testing of a Magnetic Bearing for Flexible Rotors,"
M.S. Thesis, University of Virginia, 1986.
Chen, H. M. and M. S. Darlow, "Magnetic Bearing with Rotating Force Control,"
ASME ,inl, of Tribology, paper 87-Trib-7.
Walowit, J. A. and Pinkus, O., "Analytical and Experimental Investigation of
Magnetic Support Systems. Part 1: Analysis," ASME Jnl. of Lubrication
Technology, Vol. 104, No. 2, July 1982, pp. 418-428.
Albrecht, P. R., Walowit, .i. and Pinkus, O., "Analytical and Experimental
Investigation of Magnetic Support Systems. Part 2: Experimental Investigation,"
ASME Jnl. of Lubrication Technology, Vol. 104, No. 2, July 1982, pp. 429-437.
Keith, F. J., Williams, Rd. D. and Allaire, P. E., "Digital Control of Magnetic
Bearings Supporting a Muitimass Flexible Rotor," STLE preprint 89-AM- 1B-3.
Schweitzer, G., (ed), Magnetic Bearings: Proceedings o_f the First International
Symposium, ETH Zurich. Switzerland, June 6-8.198___88,Springer-Verlag, Berlin,
1989.
Higuchi, T. (ed), "Proceedings of the Second International Symposium on Magnetic
Bearings," Tokyo, July 1990.
498


Measurement and calculation of forces in a magnetic journal bearing actuator

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