Squeeze film dampers are a means of curing instabilities in rotating shaft assemblies. Their efficiency depends very much on the condition of the oil, which in turn depends on inlet and outlet arrangements, on damper geometry and on the flexibility of the rotor and surrounding structure. Rig investigations in which structural flexibility is included experimentally are discussed. Comparisons are made between measured and predicted results

Dogan, M.

Holmes, R.

English

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INVESTIGATIf._ OF SQU_-FII/vl J__VJPEHS
IN FLEXIBLE SUPI-_I_' _TRLCIIJRES
R. Holmes and iVl. Dogan
University of Sussex
Brighton, England hlNL 9QT
S UMMARY
Squeeze-film dampers are a means of curing instabilities in rotatlng-shaft assem-
blies. Their efficiency depends very much on the condition of the oil, which in turn
depends on inlet and outlet arrangements, on damper geometry and on the flexibility
of the rotor and surrounding structure. The work discussed in this paper concerns
rig investigations in which structural flexibility is included experimentally and
comparisons are made between measured and predicted results.
INTRODUCTION
In two previous papers (refs. 1 and 2), the performance of a squeeze-film damper
unassisted by any retainer spring was examined when interposed between a rigid rotor
and its rigid bearing pedestals. In many gas turbine applications, however, both
rotor and pedestals are flexible, the latter to the extent that the first two rotor-
pedestal critical speeds are essentially bounce modes, in which the rotor does not
bend to any significant degree. Instead, on increase in speed the rotor often
vibrates first in a symmetric and then in an anti-symmetric mode, while the pedestals
are the only elements to show any appreciable degree of dynamic deflection. For such
systems a squeeze-film damper interposed between one or more of the rolllng-element
bearings of the rotor and the pedestals can contribute a degree of damping which may
enable the passage of the system through such critical speeds without vibration
becoming excessive, and inhibit possible rotational instability.
It is not uncommon in gas turbines for the antisymmetric mode of vibration to ex-
hibit a node near one of the rolling-element bearings. With such an application in
mind, a test rig (fig.l) was designed and built, which afforded the investigation of
the squeeze-film damper 1 at one of its two rolling-element bearings 2, the other
bearing 3 being of the self-aligning variety. This constituted a pivot about which
an antisymmetric (i.e. conical) mode of vibration would occur, when the rotor 4 was
acted upon by a force arising from rotation of the unbalance mass 5 The test rig
was provided with flexible bars 6, which simulated the pedestal flexibility of an
actual engine. Alternatively, the housing 7 could be clamped by the special clamps
8 to afford investigation of the squeeze-film damper alone. A heavy foundation
block 9 was provided which represented ground and into which the flexible bars were
screwed. Oil of 21 cp viscosity was supplied to the damper via three supply holes
I0 and a central circumferential groove (fig.2). End plates were attached at the
* Performed under contract to Rolls Royce Limited, England
415
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FLEXIBLE BARS
END PLATE
_,__,___,_/UNBALANCE MASS
Figure 2. - Detail of damper.
ends of the outer element of the damper to afford some sealing, the extent of which
could be varied by the insertion of Spacing shims. The squeeze-film dimensions were
set by the outer diameter of the rolling bearing (136 ram), the damper land length
(9 nun) and its radial clearance (.216 ram).
Proximity vibration pickups were used to measure the vibration of the shaft
relative to the pedestal and relative to ground. A pressure transducer was placed
at a mid-land position at the base of the squeeze film to measure dynamic pressure in
the oll under operating conditions and a thermocouple was also provided there to
record oil-film temperature. The presence of the flexible bars allowed convenient
recording of transmitted force by the provision of strain gauges.
This paper describes investigations into the performance of the dampers and a
comparison of experimental findings with numerical predictions. For the latter, the
numerical method developed in reference (2) was used. This was based on the short-
bearing approximation applied to the Reynolds equation to describe the pressure field
in the squeeze film and required the clearance between the end plates and the inner
member of the damper to be wide enough to enable the assumption of atmospheric press-
ure at the ends of the damper to be used.
In reference (2) it was shown that the independent parameters of the squeeze-film
damper could be presented in terms of three non-dimensional groups, namely
Q = P/mclo 2
Qc = Pc/m(xd2
417
and
nR 3B=--. () ,
mL0
in which P is the static load, usually provided by gravity, which for one land of the
damper was 147 N, m is the effective mass of the rotor at each land (12.25 kg), c is
the radial clearance in the damper (0.216 ram), R is the radius of the inner member of
the damper (68 mm), _ the damper land length (9 ram) and _ the oil viscosity (21 cp).
is the rotational speed of the shaft carrying the unbalance mass, which provides
the required dynamic force, Pcj causing vibration. An essential requirement in the
numerical computations is the specification of a cavitation pressure below which the
pressure field is curtailed. This pressure was found experimentally.
TESTS WITH CLAMPED HOUSING
Firstly a series of tests was carried out with the housing clamped and details of
these are given in Table 1.
TABLE I, TESTS WITH HOUSING CLAMPED
Q Rotor speed rev/min
C
0.229 4000 4500 5000
0.642 3000 3400 3750
As the value of Q^ was increased the top speed of the rig was successively re-
duced in order to avoid excessive vibration of the rolling-element bearing in the
damper clearance space. The value of speed dictated the corresponding values of the
non-dimensional groups Q and _ and these are given with the appropriate experimental
recordings and numerical predictions shown later. An oil supply pressure of
34.48 KN/m 2 (5 lbf/in 2) was used throughout these tests to avoid excessive outflow
from the ends of the damper through the rather wide end-plate clearances of 1.25 mm.
A set of experimental vibration orbits and pressure recordings is given in figure
3a for Qc = 0.229. Fig. 3b shows the corresponding numerical predictions. Each
numerical hydro-dynamic pressure distribution was curtailed at its experimentally-
observed negative pressure limit before integration to obtain the squeeze-film forces
which acted on the rotor to produce the orbit of vibration. Figures 4a and b show
similar comparisons for a higher value of Q of 0.642, and are typical of many others.
C
Some significant general observations can be made from these comparisons. In
figure 3a, the general sizes and dispositions of the vibration orbits are well pre-
dicted, while both the experimental and numerical recordings show a reversal in
position of the sharp 'tail' between 4500 and 5000 rev/min. The pressure waveforms
also show good agreement in respect of general shape and height. The orbits of
figure 4a are quite well predicted in general shape, size and disposition (even to
the extent of showing a sudden increase in size between 3700 and 3750 rev/min).
Whilst the experimental pressure waveform at 3000 rev/min is fairly well predicted,
the waveform at 3400 rev/min does not show such good agreement in that numerical com-
putations indicate a sharp positive pressure spike, which is not reproduced experi-
mentally. It seems probable that the slightly shallower slopes of the experimental
vibration orbits do not give rise to such pressures, which are very sensitive to
orbit shape. An inspection of the second experimental pressure peak in a given cycle
will, however, indicate a good comparison with the numerical prediction.
418
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TESTS WITH FLEXIBLY MOUNTED HOUSING
The housing was now unclamped, giving an undamped natural frequency of the system
of about 4500 c/m. A series of tests was carried out using a Q_ value of 0.229 at
speeds of 3500, 3800, 4200 and 4500 rev/min. In addition to obtaining vibration
orbits of the rotor relative to the housing,orbits of the rotor relative to ground
and polar diagrams of transmitted force were obtained. For such a configuration the
mathematical model for the structure included the same damper model as previously,
together with the stiffness of the bearing pedestal, but for speed of computation,
neglected the relatively small housing mass which was only 14% of the effective rotor
mass.
Comparisons of experimental and numerically predicted orbits are shown in figures
5 a,b and indicate good agreement. For the case of 3500 rev/min, a distorted figure
of eight pattern is observed in both experimental and numerical recordings. The
double loops visible in the other experimental recordings persisted over the entire
periods of experimentation and those in the numerical predictions persisted up to a
non-dimensional time _0t of 96, that is about 15 revolutions, when the length of
computing time became prohibitive. The general sizes, shapes and dispositions show
good agreement, and the size at 4200 rev/min is observed to be larger than at the
undamped natural frequency of 4500 rev/min. The pressure recordings of figure 5b
also show fair agreement in shape and size. Negative 'spikes' are evident in figure
5a, indicating that the oil can temporarily support tensile forces. Such tensile
forces have been discussed in reference 2.
Turning now to the vibration orbits of the rotor relative to ground (figs. 6a,b),
very good agreement prevails both in size, shape and disposition and a peak vibration
between 4200 and 4500 rev/min is again observed. This suggests that the squeeze-film
damper has had some effect in reducing the critical speed of the system. The polar
diagrams of total dynamic load transmitted from both lands show striking agreement in
many respects, such as size, shape and disposition. In particular the kink in each
experimental polar diagram for 3800, 4200 and 4500 rev/min is predicted by numerical
computation. These latter results give extra confidence in accepting the short bear-
ing model of reference 2 for the squeeze film, albeit with a negative pressure cur-
tailed at an experimentally recorded limit.
Also shown in figure 6b are circles representing total displacements and trans-
mitted forces when no damper is present. The effect of gravity on the flexible bars
increased displacements by about 0.04 mm and all forces by about 274 N. It can be
seen that, at the lower speeds the damper is not really beneficial. However, at
speeds approaching the critical speed, its benefits become apparent, especially at
the undamped critical speed of 4500 rev/min where, without the damper the amplitudes
of vibration and transmitted force would theoretically be infinite.
CONCLUSIONS
Continuing on from experience gained on test rigs involving open-ended squeeze-
film dampers interposed between rigid rotors and rigid bearing pedestals (refs.l,2),
this paper has described experimental and numerical work on weakly sealed dampers
with flexible pedestals. Good agreement has been observed between experimental ob-
servations and numerical predictions over a wide range of operating parameters. These
observations included vibration of rotor relative to bearing housing and relative to
ground, dynamic pressure in the squeeze-film damper and transmitted force to ground.
The work shows that, given the correct interpretation of boundary conditions in the
427
damper, reliance can be placed on a mathematical model incorporating the short-
bearing approximation. The benefits of such a damper can also be readily seen.
This work will shortly be extended to include the effect on the damper of
tighter sealing and the use of higher supply pressures and very low oil viscosities,
in keeping with present-day operational practice with gas turbines.
REFERENCES
I. Humes,B. and Holmes,R.: The role of sub-atmospheric film pressure in the
vibration performance of squeeze-film bearings. Jnl Mech.Eng.Sci., vol.20, no.5,
pp. 283-289.
2. Holmes,R. and Dede,M.: Dynamic pressure determination in a squeeze-film damper.
Proc. I.Mech.E. Paper C260/80. Second International Conference on Vibrations in
rotating machinery. Cambridge, Sept. 1980.
428
ADDITIONAL MATERIAL PRESENTED AT THE WORKSHOP
Linear theory as a Qualitative predictor
Although the squeeze-film bearing is a highly non-linear element, it is worth
examining its contribution to the damping of a system against a linear assessment.
_'0"
0-! _b_
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Figure 7(a). - Rotor vibration amplitude Figure 7(b). - Rotor vibration amplitude
relative to the engine frame, relative to the bearing housing.
• F = mu_¢
""  P:TF
3[ // \\ = Figure 7(c).
0-4, O.B 1-2 1.5 2.0 2-_. m/m n
If we consider a linear structure consisting of a series combination of mass,
damper and spring, the graphs shown in Fig.7 are readily obtained. The most notable
features of these graphs are, in Fig. 7a, the cross-over point (l/v/2, 1), and the
increase in vibration amplitude with damping at a frequency ratio of 1; in Fig.7b,
the independence of vibration with damping at _/c0 A = 1; in Fig. 7c, the increase in
transmissibility with damping at _0/c_l = 1.
- Transmissibility.
Figs. 8a, b, c show results obtained from the test rig when running at the
critical speed of 4500 rev/min i.e. _/_ = 1. In these figures, damping is increased
in three separate ways:
429
and
l) by tightening the end sealing (Fig. 8a)
ii) by increasing the lubricant viscosity from 6 to 21 cp (Fig.8b)
ill) by increasing the lubricant supply pressure from 5 to 45 psi (Fig.8c).
In each of these figures the photographs may be identified as follows:
a) Vibration orbit relative to bearing housing
b) Vibration orbit relative to ground
c) Pressure recording
d) Polar load diagram of transmitted force.
It may be seen that in all cases the results support the qualitative conclusion of
the linear treatment, namely that at the critical speed an increase in damping by
whatever means results in an increase in rotor vibration relative to ground, and
an increase in transmissibility, but little change in the rotor vibration relative
to the squeeze-film container.
430
(a) (b)
.(c) Ca)
(a) (b)
(c) (d)
Figure 8[a). Effect of sealing.
Upper four figures loose sealing
Lower four figures tight sealing
431
(a) (b)
(c) (d)
(a) (b)
(c) (d)
Figure 8(b). Effect of lubricant viscosity.
Upper four figures 6 cp
Lower four figures 2] cp
432
(a) (b)
(c) (d)
(a)
(b)
(c)
Figure 8(c).
(d)
Effect of lubricant supply pressure.
Upper four figures 5 psi
Lower four figures 45 psi
433


Investigation of squeeze-film dampers

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