# Experimental study of the radial and tangential forces in a whirling squeeze film damper

Cyril Defaye, Mihai Arghir, Olivier Bonneau, Philippe Carpentier, Charles

Debailleux, Frédéric Imbourg

► To cite this version:

Cyril Defaye, Mihai Arghir, Olivier Bonneau, Philippe Carpentier, Charles Debailleux, et al. Experimental study of the radial and tangential forces in a whirling squeeze film damper. Tribology Transactions, 2006, 49 (2), pp.271-278. 10.1080/05698190600614916. hal-00214229

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# Experimental Study of the Radial and Tangential Forces in a Whirling Squeeze Film Damper

CYRIL DEFAYE, MIHAȚ ARGHIR and OLIVIER BONNEAU

Laboratory of Solid Mechanics
SP2MI, BP30179

86962 Chasseneuil Cedex, France

PHILIPPE CARPENTIER and CHARLES DEBAILLEUX
Polytech' Lille, Avenue Paul Langevin
59655 Villaneuve d'Ascq Cedex, France
and

FRÉDÉRIC IMBOURG
SNECMA, Rond Point René Ravaud
Réau, 77550 Moissy-Cramayel, France

The present work introduces the main results of a detailed experimental program aimed at investigating the influence of the design parameters and of the working conditions on the global characteristics of squeeze film dampers (SFD) for serial aircraft engines. The SFD is sealed at both ends and is executing circular centered orbits. The results are presented for the tangential and the radial global force in the SFD and the leakage flow rate. The pressure field inside the SFD could also be measured and shows the influence of the inertia force, of the cavitation, and probably of the turbulence regime, as well as the interaction of these effects with the feeding groove. The limits of the existing theoretical models are also demonstrated.

**KEY WORDS** Squeeze-Film Bearing; Inertia Effects; Cavitation; Piston Ring Seal

## INTRODUCTION

During the last four decades SFD technology became widespread among high-speed turbomachinery and a sustained effort was directed to develop an approach for designing an optimum squeeze-film geometry adapted to whole engine dynamics, as stated by Zeidan, et al. (1). Therefore, a relatively large number of theoretical and experimental studies (Della Pietra and Adiletta (2), (3)) dealt with this component. These investigations allowed the underlining of the relative importance and the influence of fluid inertia, lubricant dynamic cavitation, and boundary conditions (the oil feeding system, the end seals). Despite the long and sustained effort and the very large number of publications, industrial practitioners are not entirely satisfied with the predictive capability of existing theoretical models. Real

SFD design and operating conditions are sometimes far from the range of validity of theoretical models that were developed under more or less simplified assumptions. The present experimental study is intended to investigate the global characteristics of an SFD designed and working as close as possible to reality.

Many SFD were studied in the present work and the results enabled underlining the influence of several design parameters: the feeding system (orifices or circumferential feeding groove), the sealing system (piston rings with one slit or with multiple openings), and the radial clearance C (100, 200, and 350 µm). Different working conditions were also tested: the feeding pressure (2...10 bars), the feeding temperature (50...120°C), the whirling speed (17...300 Hz), and the orbit radius (10%...90% relative eccentricity). The SFD is fed with Mobil Jet 2 oil having a dynamic viscosity µ of 1.76·10⁻² and 3.47·10⁻³ Pa·s and a density ρ of 979 and 938 kg/m³ for 50° and 120°C, respectively. These working conditions yield important reduced Reynolds numbers $Re^* = \frac{ρωC^2}{µ}$ up to values of 35. As shown by the present results, for these high values of $Re^*$ inertia effects have a tremendous importance.

Finally, the limits of the existing theoretical models will be enlightened by comparisons to present experimental results and possible improvements are underlined.

## DESCRIPTION OF THE TEST RIG

The test rig is an adaptation of an experimental utility formerly used for hydrodynamic bearings (Defaye, et al. (4)). As shown in Figs. 1 and 2, the journal is supported by two hydrostatic bearings of very high stiffness and the driving electric motor is decoupled. The inner ring of the SFD is serrated on the journal while the outer ring is floating. Two hydraulic shakers mounted at 90° impose a circular orbit to the outer ring. A stinger is mounted between the shaker and the strain gage. Due to its flexibility, the stinger does not perturb the efforts being measured.

Forces are measured by stress gauges mounted on top of each shaker. The four accelerometers mounted on the floating external
<figure><img src="image_2.png" /><figcaption>Fig. 1—Squeeze film test stand.</figcaption></figure>

ring enabled the evaluation of the inertia forces. The forces in the SFD can thus be evaluated by subtracting these forces from the one measured by the stress gauges at the top of the shakers. Displacements are measured at both ends of the SFD by two proximity probes orthogonally mounted in each loading plane. Forces and displacements are then simultaneously measured by using a multi-channel recorder. The feeding temperature is measured by five thermocouples and the leakage flow rate is measured by a gear-wheel flowmeter.

As depicted in Fig. 3, two identical SFD are simultaneously tested in order to avoid any misalignment problems. The SFD diameter is 152 mm and its active length, defined by the distance between the two piston rings, is 35 mm. The pressure field inside the two SFD (in the thin film and in the feeding groove) is measured by 11 pressure transducers (Fig. 4). These transducers are flush-mounted and fixed as well as possible. The height of the inevitably resulting cavity is less than 10% of the radial clearance. It

<table><caption>TABLE 1—MEASUREMENT UNCERTAINTY</caption><thead><tr><td>Transducer</td><td>Precision</td></tr></thead><tbody><tr><td>Stress Gauges</td><td>0.12% of the measurement range (i.e., ±12N)</td></tr><tr><td>Kulite Pressures<br>Transducers</td><td>0.5% of the measurement range (i.e., ±0.75 bars)</td></tr><tr><td>Proximity Probes</td><td>0.1% of the measurement range in dynamic regime (i.e., ±0.5 μm)</td></tr><tr><td>Gear-Wheel<br>Flowmeter</td><td>0.3% of the measured value</td></tr><tr><td>Accelerometers</td><td>1.5% of the measured value</td></tr></tbody></table>

is then considered that pressure transducers do not affect significantly the flow in the SFD.

For one test, the results are obtained by averaging over 1000 orbits each with 36 points.

## Uncertainties

Experimental results are affected by uncertainties from the calibration of each transducer and by the resolution of the analog-to-digital conversion process of the data acquisition system. Table 1 gives the uncertainties of each measure.

## THE INFLUENCE OF THE DESIGN PARAMETERS

### The Influence of the Feeding System

Figures 5-7 depict the influence of the feeding system on the tangential forces. Three feeding systems were tested. The first two feeding systems consist of a circumferential groove located at the mid length of the seal (centered groove) or close to one of the two end seals (eccentric groove). The third feeding system consists

<figure><img src="image_3.png" /><figcaption>Fig. 2—Squeeze film test rig.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 3—Two squeeze film dampers configuration.</figcaption></figure>

of three equally spaced orifices. The lowest tangential damping force is obtained for the centered groove and the highest one for the orifice feeding system. This result should be considered in conjunction with the sealing system. If the SFD is sealed at both ends, the pressure builds up rapidly along the seal and is almost constant in the axial direction. Compared to the orifice feeding system, the presence of the circumferential groove introduces a non-negligible drop in the axial pressure variation. This is the reason why the tangential damping force is lower when the SFD is fed by a circumferential groove. Figure 5 also indicates the occurrence of the cavitation with increasing whirl radius. Cavitation appears at lower values of the whirl radius for feeding orifices and at higher ones when the SFD is provided with a centered groove. The reason is that compared to the orifices, a feeding groove ensures a

better circumferential distribution of the flow in the SFD (Arauz and San Andres (5), (6)).

Figure 6 depicts the model of the pressure variation when the SFD is fed by a circumferential groove. The pressure variation is most perturbed for the case of the centered groove and this explains also why the eccentric groove has a better damping force. Figure 7 depicts the tangential and radial forces and the flow rate for the centered and for the eccentric groove. The ratio of damping forces for the eccentric groove and for the centered one is around 1.7. Figure 7 also shows that the flow rate is larger in the case of the eccentric groove. The increased flow rate is due to the proximity between the groove and the piston ring that is sealing the SFD.

Figure 8 depicts the influence of the three feeding systems on the radial force. Negative values of the radial force are obtained

<figure><img src="image_5.png" /><figcaption>Fig. 4—Pressure transducers arrangement.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 5—Influence of the feeding system on the tangential force.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 6—Influence of the feeding groove position on the axial pressure distribution.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7—Influence of the feeding groove position.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 8—Influence of the feeding system on the radial force.</figcaption></figure>

for a low value of the whirl radius when the SFD is fed by orifices and for a large one when it is fed by a centered groove. This observation is correlated with Fig. 5 because negative values of the radial force indicate the presence of cavitation. Positive values of the radial force are obtained when inertia effects are important. If cavitation is absent, the relative importance of inertia forces can be characterized by the values of the ratio K between the radial and the tangential forces. Figure 8 shows that despite the fact that $Re^* < 1$, the inertia effects have non-negligible values. Also, among the three investigated feeding systems, the orifice one is the most nonlinear.

## The Influence of the Sealing System

All tested SFD were sealed by piston rings. Two types of piston rings were used (Fig. 9). The first had one slit while the second was provided with seven circumferential openings. The equally spaced openings were aimed to ensure a uniformly distributed leakage. The total leakage surface for the second type of piston ring was 3.1 times the slit of the first one. Figure 10 depicts the flow rate

<figure><img src="image_10.png" /><figcaption>Fig. 9—Piston ring seals tested; 1: with one slit; 2: with seven openings.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig. 10—Influence of the piston ring type.</figcaption></figure>

and the tangential and radial forces with increasing orbit radius for these two types of piston rings. The flow rate of the piston ring with equally spaced openings is 3.3 times larger and proves to be proportional to the increase of the leakage surface. However, tangential forces are not very different, the values obtained with the second type of seal being 80% of the ones obtained with a piston ring with one slit. The reason for eventually using the second type of seal can be explained from Fig. 11, which depicts the tangential and radial forces. Over one period of the orbit, the tangential damping force has a sinusoidal variation. The average value is the tangential damping force presented up to now and in the following. The variable part of the tangential force can be either due to a non-centered whirl orbit or due to a hydrostatic effect caused by a localized leakage. The second type of piston ring with equally spaced openings is supposed to eliminate this latter effect. Indeed, Fig. 11 shows that the amplitude of the tangential force is 27% smaller than the one for the piston ring with one slit. It is therefore supposed that the remaining amplitude is due to a non-centered whirl orbit.

<figure><img src="image_12.png" /><figcaption>Fig. 11—Influence of the piston ring type on the variation of the tangential force during one period ($C = 100~\mu\text{m}$).</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 12—Influence of the radial clearance.</figcaption></figure>

## The influence of the Clearance

Figure 12 depicts the influence of the radial clearance. For a reduced whirl frequency, the increase of the clearance from 100 µm to 200 µm lowers drastically the tangential effort. For a high whirl frequency, the same increase of the clearance produces a small increase of the tangential effort. This shows that for high whirl frequencies and for increasing clearances the tangential force is not of only viscous origin. Indeed, for $\Omega = 99$ Hz, the governing Reynolds numbers are $Re^* = 1.7$ and $Re = 1287$ for a clearance of 100 µm, and $Re^* = 6.7$ and $Re = 2573$ for a clearance of 200 µm, respectively. This shows not only that inertia effects have an increasing importance (they are known to influence mainly the radial force) but the turbulence flow regime can appear. Ku and Tichy (7) showed that turbulence has an important effect, mainly on the amplitude of the pressure field and leads to an increase of the tangential force.

## THE INFLUENCE OF THE WORKING CONDITIONS

Figure 13 depicts the influence of the feeding pressure on the tangential and radial force components. The tangential force shows negligible change but the radial component is largely influenced by the feeding pressure. This increase of the feeding pressure delays the appearance of cavitation that is responsible for negative values of the radial force. The SFD can generate a negative dynamic stiffness as a consequence of the cavitation appearing with increasing whirl orbit. This nonlinear stiffness can be the source of jump phenomena for unbalance response of the
<figure><img src="image_14.png" /><figcaption>Fig. 13—Influence of the feeding pressure.</figcaption></figure>

whole rotating machine and of sub- and superharmonic vibrations (Zeidan, et al. (1)). Cavitation appears then as undesirable from the standpoint of the rotordynamics of the whole machine and its extent and influence can be limited by increasing the feeding pressure.

Figure 14 depicts the influence of the feeding temperature. Increasing the feeding temperature lowers the dynamic viscosity and the viscous (tangential) component of the force. In the meantime, the decrease of the oil viscosity increases the influence of the inertia effects affecting mainly the radial component. The leakage flow rate is also increased because the rise of the temperature will dilate piston ring seals.

## INERTIA EFFECTS AND CAVITATION IN AN SFD WITH A FEEDING GROOVE

The increase of the clearance and the reduction of the oil viscosity tend to enhance the inertia effects. For a centered orbit, these effects engender a centrifugal component of the radial force. This can be assimilated with the effect of an additional unbalance mass (Della Pietra and Adiletta (2); Tichy (8)). For low and mild precession frequencies (when cavitation is absent or has a limited influence) the radial effort can be written as $F_r = Me\omega^2$. Figure 15 depicts the average radial effort versus the precession frequency.

<figure><img src="image_15.png" /><figcaption>Fig. 14—Influence of the feeding temperature.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 15—Evolution of the radial force versus precession frequency.</figcaption></figure>

The values of the equivalent mass due to inertia effects are added on the figure. One can note that for the same whirl orbit the equivalent mass is increasing with increasing whirl frequency. This result confirms a characteristic trend for temporal inertia effects (Della Pietra and Adiletta (2); Tichy (8)). On the other hand, for the same whirl frequency, inertia effects are also increasing with increasing whirl orbit. The dependence of inertia effects on the whirl radius is a characteristic of convective inertia and is often neglected in theoretical models. These convective effects can be beneficial from the standpoint of the ensemble dynamic because they are opposed to cavitation effects and limit the jump phenomena engendered by a change in the sign of the radial force. In the meantime, they generate an additional unbalance that must be compared to the other unbalances present in the rotating machine. In Fig. 15, the equivalent unbalances corresponding to (1) and (2) are 1.6 cm.g and 13 cm.g, respectively.

Figures 16 and 17 present the pressure variation in the thin film and in the groove for points marked by A and B in Fig. 15. Figure 16 shows that the pressure has a sinusoidal variation not only in the thin film but also in the groove. The usual model of a

<figure><img src="image_17.png" /><figcaption>Fig. 16—Circumferential pressure distribution in the SFD and in the feeding groove, Case A.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Fig. 17—Circumferential pressure distribution in the SFD and in the feed-
ing groove, Case B.</figcaption></figure>

constant pressure inside the feeding groove is then not verified de-
spite the fact that the ratio between the groove depth and the film
clearance is 14.2. The phase lag that exists between the minimum
and the maximum of the pressure in the film and inside the feed-
ing groove shows that the variation inside the feeding groove is
entirely due to inertia forces (Re* = 8.3). Figure 17 depicts the
pressure variation for a highly cavitated case. It can be seen that
cavitation affects not only the thin film but also the feeding groove
in exactly the same proportion. This is an unexpected result that
shows that, for a high whirl radius and frequency, the groove can-
not correctly feed the SFD. It is not expected that the theoretical
models developed up to now can handle the pressure variation or
cavitation effects inside the groove.

COMPARISONS WITH ANALYTIC MODELS

Many theoretical models based on more or less simplifying
assumptions are available in the literature (Della Pietra and
Adiletta (2); San Andrés and Vance (9)). These models can be eas-
ily integrated in a dynamic model of the rotating machine without
leading to excessive computational efforts from the standpoint
of industrial calculations. Figure 18 depicts the results obtained
with a “long SFD” model that is known to be applicable when the

<figure><img src="image_19.png" /><figcaption>Fig. 18—Comparison between experimental and analytical results, Re* = 0.05.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Fig. 19—Comparison between experimental and analytical results, Re* = 20.5.</figcaption></figure>

squeeze is completely sealed and for low and mild orbit radius.
The acceptable agreement between theoretical results and mea-
surements can be explained by the fact that the reduced Reynolds
number is low. This is not the case anymore for large values of
Re*. One of these cases is depicted in Fig. 19 when the clearance
and the whirl frequency are much higher, leading to Re* = 20.5.
In this latter case, the measured tangential and radial forces are
much larger than the theoretical estimated values. The conclusion
is then that the long SFD model cannot predict the forces for high
Re* regimes mainly due to uncertainties in dealing with inertia,
turbulence, and cavitation, and of the interaction of these effects
with the feeding groove.

SUMMARY AND CONCLUSIONS

The present work is the summary of the results of an experi-
mental program aimed to investigate the influence of the design
parameters and of the working conditions on the tangential and
radial force of a squeeze film damper (SFD) executing circular
centered orbits. The main conclusions are:

* The orifice feeding system gives the largest tangential (damping) force but the radial force is highly nonlinear.

* An eccentric feeding groove gives better characteristics than a centered one.

* A piston ring sealing system with many openings leads to a more uniform tangential force but the leakage rate is higher compared to the same piston ring with one slit.

* The clearance has a strong influence for purely viscous regimes (low whirl frequencies); regimes dominated by inertia forces (large *Re*\*) are less influenced.

* The increase in the feeding pressure has an important influence on the radial force (cavitation is delayed) but a negligible one on the tangential force.

* The tangential force is decreased with increasing the feeding temperature; the increase of Re* increases the inertia effects influencing the radial component.

* For low and mild regimes (when cavitation is not dominant) inertia effects can be described as an additional unbalance depending on both the whirl frequency and the orbit radius.
* For high Re\* regimes, inertia and cavitation can have a paramount impact on the pressure distribution in the SFD by affecting not only the thin film zone but also the feeding groove. There is no theoretical model capable of dealing with a non-constant groove pressure.

* Theoretical models (long SFD with inertia) are in agreement with measurements only for low Re\*. New or improved theoretical models need to be developed for sealed SFD with a feeding groove working at large Re\* regimes.

ACKNOWLEDGMENTS

The authors thank the financial support of Snecma Moteurs and Techspace Aéro.

REFERENCES

(1) Zeidan, F. Y., San Andres, L. and Vance, J. M. (1996), "Design and Application of Squeeze Film Dampers in Rotating Machinery," Proceedings of the Twenty-Fifth Turbomachinery Symposium.

(2) Della Pietra, L. and Adiletta, G. (2002), "The Squeeze-Film Damper Over Four Decades of Investigations. Part 1: Characteristics and Operating Features," *The Shock and Vibration Digest*, **34**, 1, pp 3-26.

(3) Della Pietra, L. and Adiletta, G. (2002), "The Squeeze-Film Damper Over Four Decades of Investigations. Part 2: Rotordynamic Analyses with Rigid and Flexible Rotors," *The Shock and Vibration Digest*, **34**, 2, pp 97-126.

(4) Defaye et al. (2004) "Squeeze Film Damper Predictions for Simulation of Aircraft Engine Dynamic," presented at the ASME TURBO EXPO 2004, Vienna, Austria.

(5) Arauz, G. L. and San Andres, L. (1996), "Experimental Study on the Effect of a Circumferential Feeding Groove on the Dynamic Force Response of a Sealed Squeeze Film Damper," *Journal of Tribology*, **118**, pp 900-905.

(6) Arauz, G. L. and San Andres, L. (1997), "Experimental Force Response of a Grooved Squeeze Film Damper," *Tribology International*, **30**, 1, pp 77-86.

(7) Ku, C. P. and Tichy, J. A. (1987), "Application of the k-ε Turbulence Model to the Squeeze Film Damper," *Journal of Tribology*, **109**, 1, pp 164-168.

(8) Tichy, J. A. (1983) "The Effect of Fluid Inertia in Squeeze Film Damper Bearings: A Heuristic and Physical Description," ASME paper, No. 83-GT-177.

(9) San Andrés, L. and Vance, J. (1987) "Force Coefficients for Open Ends Squeeze Film Dampers Executing Small Amplitude Motions About an Off-Centered Equilibrium Position," *ASLE Transactions*, **30**, 1, pp 63-68.