Experimental findings of a three mass rotor with four channels of feedback control are reported. The channels are independently controllable with force being proportional to the velocity and/or instantaneous displacement from equilibrium of the shaft at the noncontacting probe locations (arranged in the vertical and horizontal attitudes near the support bearings). The findings suggest that automatic feedback control of rotors is feasible for limiting certain vibration levels. Control of one end of a rotor does afford some predictable vibration limiting of the rotor at the other end

Allaire, P. E.

Bradley, P. L.

Lewis, D. W.

Moore, J. W.

English

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VIBRATIONLIMITII_ OFROTORS BY FEF__ (_
David W. Lewis, J_nes W. Moore, Philip L. Bradley, and Paul E. Allaire
Department of Mechanical and Aerospace Engineering
University of Virginia
Charlottesville, Virginia 22901
SUMMARY
This work reports some experimental findings of a three-mass rotor with four
channels of feedback control. The channels are independently controllable with
force being proportional to the velocity and/or instantaneous displacement from
equilibrium of the shaft at the non-contacting probe locations (arranged in the
vertical and horizontal attitudes near the support bearings).
The findings suggest that automatic feedback control of rotors is feasible for
limiting certain vibration levels. Control of one end of a rotor does afford some
predictable vibration limiting of the rotor at the other end. The next step in the
work is to move from acoustic drivers to electro-hydraulics so that larger force
levels may be experimented with.
INTRODUCTION
High speed turbomachines are subject to lateral vibrations, which may limit their
performance level [1,2]. Machines are often required to operate at least 20% away
from a rotor critical speed. They must also be designed so that, for machines oper-
ating above one critical speed, all clearances in the machine are sufficient to accom-
modate high amplitudes of vibrations near a critical speed. Lastly, machines are
sometimes subject to subsynchronous vibrations, which can lead to machine failures
[I]. One type of neans for reducing these vibrations is that of active vibration
control.
A number of analytical studies of active feedback controls for rotating machinery
have been presented in the literature [3-6]. These have been primarily developed by
researchers in the automatic controls area and the results are normally presented in
terms associated with automatic control theory. A very limited number of experimental
works have reported the use of active control for laboratory test rigs [7-9]. With
the possible exception of the electromagnetic bearing, there has not been an applica-
tion of active feedback control to an industrial rotor at this time.
This work considers unbalances in rotating machinery which might be compensated
by use of active feedback control circuits. With proper algorithms, such closed loop
automatic control devices could permit machinery to be run longer even though the
unbalanced forces grew to significant values. Such an approach would have little
impact for small and noncritical rotors. However, for very important systems for
which an unscheduled shut-down would be costly, an analog or digital closed-loop
feedback controlled force actuator(s) could be justified.
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https://ntrs.nasa.gov/search.jsp?R=19830007385 2020-03-21T23:46:58+00:00Z
Also, for somevery expensive turbines, pumps, and compressors, active feedback
controlled force actuators would allow machinery to pass through the crlticals with
smaller clearances (because of controlled vibration levels) resulting in more effi-
cient running. With such an application, t_e proposed devices would be functioning
only during runup or rundown of the machinery permitting certain advantages for the
designers of the machinery.
Values in the text are given in both SI and U.S. Customary Units. The measure-
ments and calculations were made in U.S. Customary Units.
EXPERIMENTAL UNIT
A small test rotor has been constructed and is generally described by the sche-
matic drawing of Fig. i. It consists of a 12.7 mm (0.5 inch) diameter shaft supported
on ball bearings which are 406 mm (16 inches) apart. For these tests, three masses,
uniformly distributed between the bearings were attached to the shaft by simple set-
screws. These disks weighed 8.9 N (2.0 ibs), 13.3 N (3.0 ibs), and 8.9 N (2.0 ibs)
with the larger one at the center. The bearing carriers with the associated hardware
each weighed 4.4 N (i.0 pound). Shaft weight is 4.0 N (0.90 pound).
Each bearing has mechanical springs at 11.7 N/mm (67 pounds per inch) in the ver-
tical and horizontal directions plus loud speaker motors (acoustic drivers) attached
to the bearings directed in the vertical and horizontal attitudes. This test rotor
is unique in that forces may be applied to the bearings, through acoustic drivers
that are independent from one another in the vertical and horizontal directions.
These four acoustic drivers provide four independent routes for applying forces to
the bearings.
The vertical and horizontal displacements near the bearings were measured rela-
tive to the static equilibrium position. A force was generated throuKh an analog
feedback loop in the same attitude but of the directlon opposing the motion. At the
same time, an additional force was generated that was proportional to the instantan-
eous velocity (and also oppositely directed). These forces were then applied to the
shaft, through the ball bearings, by means of the acoustic drivers. These four acous-
tic drivers are independently operable. The controls for setting the constants for
generating the forces, as a function of displacement or velocity or some combination
of displacement and velocity, are also independent one from another.
EXPERIMENTAL RESULTS
A number of experimental runs were made. The ones reported here are for runs
with the rotor fairly well balanced and with no control, a low level of control, and
a high level of control. Control was limited in these cases to the velocity feed-
back loops so that, effectively, only damping was being controlled. In addition,
the system was modelled and theoretical response was obtained on a digital computer.
The results of the first run are shown in Fig. 2. The lines with data points
shown represents the experimental results and the continuous llne is for theoretical
results. There is an excellent match of critical speeds at 700 and 1200 rpm and a
reasonable agreement of results for a critical near 6000 rpm. In the midrange ampli-
435
tudes are not in close agreement. It is noted that the displacement monitoring system
had a limit at about 0.56 mm (22 mils).
For the second run the control loop gains were set to give an effective damping
constant at each bearing of 0.047 N sec/mm (0.27 ib sec/in). This was for all four
control loops. However, just as the run was about to start it was found that the
current amplifier in the free-end vertical control loop was not functioning. The run
was continued with data being taken at the motor end. The results here were very
similar to those of the uncontrolled system except that the critical at 700 rpm is
eliminated. The theoretical response did not agree well except for the location of
the criticals.
A large damping factor was applied in the last experimental and theoretical
runs. The results are shown in Fig. 4. The damping constant was estimated to be
about 0.37 N sec/mm (2.13 ib sec/in), about eight times greater than the previous run.
Results are dramatic over the range of all three criticals.
DISCUSSION AND CONCLUSIONS
This limited set of experiments has shown some of the effects that may be obtained
with the use of feedback control. Here, the analog control signals were applied in
both directions at the motor end and only to the vertical direction at the other end.
For Fig. 4, the motor end resulted in a small circular orbit and simultaneously a very
flat ellipse at the other end. The effects obtained here are through the use of velo-
city feedback only with the velocity gain setting at about one fourth of its full
scale values.
These runs were made using analog control only. The experimental rig has a com-
plete digital control system, also. The full potential for the analog system has yet
to be explored. However, it is known that it would use some adaptive ability, either
speed sensitive or logical, in order to fully develop its potential.
The digital control system is potentially far more flexible. In this experimental
system it can be brought into play by simply turning it on and flipping a switch. The
digital unit in the control loop is an Intel 8086 single board computer. This offers
a sixteen bit manipulator. We can anticipate some very interesting control algorithms
with this system which at the present time has been used for a simple look-up algorithm
only. There will be a possibility of even employing an algorithm that "learns" what
combination of displacement and velocity (when multiplied by appropriate constants)
will produce the minimum response for the system at each speed for that particular
rotor condition. Then as the rotor condition changes (through erosion, accumulation
of dirt onto the disks, etc.) this "learning" algorithm could accommodate the chang-
ing disturbance.
The acoustic drivers are small, yielding forces that are small. Typically, the
output for the drivers is approximately 15 watts maximum but with the proper phasing
does produce significant results. It is felt that electro-hydraulics will be the
preferred means of applying forces in an industrial atmosphere. Preliminary calcu-
lations indicate that electro-hydraulics will be satisfactory directly for speeds up
through i0,000 rpm. For speeds above that, it will be necessary to employ one or
more revolutions of the shaft to make the necessary calculations as part of the
control algorithm. However, this time delay (or more specifically the rotation delay)
436
will not likely be significant as rotors must go through many cycles before amplitudes
change an appreciable level.
REFERENCES
i.
.
.
.
.
.
.
,
.
Al]aire, P. E., "Design of Journal Bearings for High Speed Rotating Machinery,"
Fundamentals of the Design of Fluid Film Bearings, Fluid Film Bearings Committee
of Lubrication Division (ASME, 1979), pp. 45-84.
Barrett, L. E., Gunter, E. J., and Allalre, P. E., "Optimum Bearing and Support
Damping for Unbalance Response and Stability of Rotating Machinery," Journal
of Engineering for Power, Transactions of the ASME, Vol. i00, No. i (January
1978), pp. 89-94.
Moore, J. W., Lewis, D. W., and Heinzmann, J. D., "Feasibility of Active Feed-
back Control of Rotor Dynamic Instability," Presented at Workschop on Rotor
Dynamic Instabilit_ Problems in High Performance Turbomachinery, NASA/ARO
Conference, Texas A&M University, May 1980, pp. 1-9.
Heinzmann, J. D., "The Implementation of Automatic Vibration Control in a Nigh
Speed Rotating Test Facility," M.S. Thesis, University of Virginia, January
1980.
Stanway, R. and Burrows, C. R., "Active Vibration Control of a Flexible Rotor on
Flexibly-Mounted Journal Bearings," Joint Automatic Controls Conference, Char-
lottesville, Virginia, June 1981.
Allaire, P. E., Lewis, D. W., and Jain, V. K., "Feedback Control of a Single Mass
Rotor on Rigid Supports," Journal of the Franklin Institute, Vol. 312, No. i,
pp. i-ii.
Nikolajsen, J. L. and Holmes, R., "Investigation of Squeeze-Film Isolators for
the Vibration Control of a Flexible Rotor," Journal of Mechanical Engineering
Science, Vol. 21, 1979, pp. 247-252.
Schweltzer, G. and Lang,, R., "Characteristics of a Magnetic Rotor Bearing for
Active Vibration Control," Institution of Mechanical Engineers Conference on
Vibrations in Rotating Machinery, Cambridge, 1976, paper C239/76.
Gondhaleker, V. M., Nikolajsen, J. L., and Holmes, R., "Electromagnetic Control
of Flexible Transmission Shaft Vibrations," Proc. IEEE, Vol. 126, 1979, pp.
1008-1010.
437
Figure 1. - Schematic diagram showing three-mass rotor l, loud speaker motors
2, mechanical support springs 3, non-contacting probe signals for measuring
the position of the shaft at the outboard bearing 4, similar signals for
the motor-end bearing 5, key phasor signal for speed measurement 6, and a
variable soeed motor 7.
50
40
30
B
2o
io
O°
theoretical
"°. ..°
,!
, I ! l ! ! i ! w v ! ! l
I,000 2,000 3,000 4,000 5,000
SPEED in RPM
Figure 2. - No feedback control.
!
6,000
438
2O
"4
I0
_, theoretical _,
1,000 2,000 3,000 4,000 5,000 6,000
SPEED in RPM
Figure 3. - Small velocity feedback contro].
20
.4
experiment_
l _ I l l ! |' I w ! ! w |
1,000 2,000 3,000 4,000 5,000 6,000
SPEED in RPH
Figure 4. - Large velocity feedback control.
439


Vibration limiting of rotors by feedback control

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