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Tribology International 37 (2004) 689699

www.elsevier.com/locate/triboint

Theoretical study of solid back-up rings for elastomeric sealsin hydraulic actuators

George K. Nikas

Mechanical Engineering Department, Tribology Section, Imperial College London, Exhibition Road, London SW7 2AZ, UK

Abstract

The use of back-up rings to support elastomeric seals in high-pressure hydraulic systems is well established in the industry.However, little is known about the operation of such devices and how they affect or interfere in the sealing mechanism of the

seals they accompany. This study is an attempt to model solid, soft back-up rings in terms of elastohydrodynamic lubrication andestablish their exact role in a sealing system in terms of sealing performance (leakage). The model is applied on a typical case of alinear hydraulic actuator for a wide range of sealed pressures (135 MPa) and operating temperatures (55 to +135

v

C), andwith one ring installed on the low-pressure side of the actuator. A system of a rubber seal and a properly selected and installedback-up ring is shown to be often significantly more efficient in terms of fluid leakage than the seal without the back-up ring. Astudy reveals the effect of various parameters of the ring (e.g. the elastic modulus and the surface roughness) on the sealing mech-anism and shows the optimum selection to minimize leakage.Published by Elsevier Ltd.

Keywords:Anti-extrusion ring; Elastomeric seal; Hydraulic actuator

1. Introduction

Back-up rings (BU rings for short) are devicesresembling washers and used in high-pressure sealingsystems to support elastomeric seals and prevent themfrom extruding to narrow gaps when subjected to highsealed pressures. Therefore, BU rings are also knownas anti-extrusion rings. Their role is often very impor-tant in protecting seals from extrusion damage and,thus, maximizing their useful service life. Their appli-cation is extensive in high-pressure linear hydraulicactuators where piston rods perform reciprocating

motion and are sealed from the external environmentwith rectangular, circular or other type of elastomericseals.

Although the role of BU rings is well known in theindustry as anti-extrusion devices, the exact mechanismof their service has not been extensively studied. Forexample, what is the effect of such rings on the leakageof the seals? Do they simply protect the seals fromextrusion without interfering in the normal seal oper-

ation or do they perform some kind of sealing them-selves? Such questions are answered in the presentstudy.

A mathematical model for rectangular rubber sealsfor reciprocating piston rods was developed by theauthor in Ref. [1]. Part of the model was presented inRef. [2] for seals obeying the classic Hookean linearelasticity model. It is that latter basic model which isused in the present study for a solid BU ring mountedon the air-side of a seal, as shown in Fig. 1.

The model assumes a soft ring, as is usually thecase, i.e. a ring with elastic modulus in the order of

0.52 GPa. BU rings are typically made of Polytetra-fluoroethylene (PTFE) reinforced with glass fibres.PTFE has tensile modulus of about 0.5 GPa andPoissons ratio which could be as high as 0.46 or as(negatively) large as 12 (expanded form of PTFE).Extensive information about PTFE and its mechanicalproperties can be found in Refs. [36], including com-posite forms with glass fibres. Reinforced PTFE andsimilar composite materials are, generally, aniso-tropiceither transversely isotropic (mechanicalproperties are the same on one plane in the solid) ororthotropic (there exist three perpendicular planes of

Tel.: +44-207-594-7236E-mail address:[email protected] (G.K. Nikas).

0301-679X/$ - see front matter Published by Elsevier Ltd.doi:10.1016/j.triboint.2004.02.006


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symmetry). The stressstrain equations for transverselyisotropic materials contain five independent elastic con-

stants instead of the usual two constants (elastic modu-lus and Poissons ratio) of isotropic materials.Orthotropic materials on the other hand involve nine

independent elastic constants. These constants are noteasily or readily measured and are affected by tempera-ture. Lack of knowledge of the values of these con-stants dictates that the model of this study becompromised to deal with isotropic, linearly elastic

rings.The author is not aware of any published theoretical

study involving the modelling of BU rings and, evenexperimentally, the work of White and Denny[7] at the

end of World War II offers perhaps one of the very few

insights on this subject. Information will be drawn

from the authors work on seal extrusion modellingRef.[8], the experimental study in Ref.[9], and a study

of nonlinear rubber elasticity in Ref. [10] (a summary

of which is included in Ref. [11]), which will be used

for a more accurate description of the behaviour of the

rubber seal under high sealed pressure and extreme

temperatures.

2. Mathematical model

The seal assembly is shown in Fig. 1. It involves a

hydraulic actuator with a reciprocating piston rod.

Nomenclature

A auxiliary variable (Eq. (2))ca,cb fluid constantsdcyl,Dcyl nominal inner and outer diameter of the actuator cylinderdrod,Drod nominal inner and outer diameter of the piston rod

Ecyl,Ering,Erod elastic moduli of the cylinder, the ring and the rodh local film thicknessp elastohydrodynamic pressurepcyl sealed pressure (Fig. 1)pgap fluid pressure at the sealring lower gappring rodring average (dry) contact pressure (Eq. (9))p0 pringpcyl 0(Eq. (10))q fluid mass leakage rate (Eq. (15))qring,qseal mass leakage rates of the back-up ring and the sealqsystem mass leakage rate of the sealring system (Eq. (14))Ra average surface roughnessSrod,Sring local roughness heights of the rod and the ring

u fluid velocity component (Fig. 1)uucyl;uurod radial surface displacements of the cylinder and the rod (Eqs. (6) and (7))

uurodz ;uu

ringz local normal surface displacements of the rod and the ring (Eq. (15) of Ref.[2])

t fluid velocity component (Fig. 1)V stroking velocity (Fig. 1)a pressureviscosity coefficient at temperaturehacyl,aring,arod thermal expansion coefficients of the cylinder, the ring and the rodDR rodring radial interference at the ring installationDh hh0ex, ey, ez normal strains of the back-up ringg actuator-fluid dynamic viscosity at temperaturehg0 gp 0

h operating temperatureh0 room temperature during the seal and ring installationl boundary friction coefficient at the rodring contactmcyl, mring, mrod Poissons ratios of the cylinder, the ring and the rodq actuator-fluid mass density at temperaturehq0 qp 0rx,ry,rz normal stresses of the back-up ringu circumferential coordinate (angle)

690 G.K. Nikas / Tribology International 37 (2004) 689699


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Sealing is achieved with a rectangular rubber seal, whichis supported by a solid ring of rectangular cross-section.Initially (during assembly), the ring may or may not bein contact with the rod. The computational model hasthe capability to check for actual contact at any stage ofthe operation of the actuator and establish, based onthe thermomechanical expansion or contraction of thesystem elements at differential temperature and sealedpressure, if there is contact or not, and the level of inter-ference between the ring and the rod, if any.

As already explained, the ring is assumed soft, iso-

tropic and linearly elastic, with a typical tensile modulusbetween 0.5 and 2 GPa. The piston rod is made of steeland with a typical elastic modulus of 200 GPa, it is100400 times stiffer than the ring. The rubber seal on theother hand has a typical elastic modulus of 510 MPa atroom temperature and about 100400 MPa at lowsubzero temperatures (e.g. at55

v

C, which is very closeto the lower limit where aircraft hydraulic actuatorsoperate). Therefore, both geometrically and mechani-cally, the BU ring of this study resembles the typical elas-tomeric seal modelled in Ref. [2]. Therefore, the largestpart of the model of Ref. [2] will be used in the present

study for the BU ring as well.The lubrication of the seal is modelled as described

in Section 2 of Ref. [2], except for the thermoelasticstress analysis (Section 2.5 of Ref. [2]), which isreplaced here by the more suitable nonlinear elasticity(MooneyRivlin type) model developed in Ref. [1]andpresented in Refs. [10,11]. For a BU ring that is not incontact with the piston rod, the full model involves theanalysis of seal extrusion, which consists of checking ifthe seal extrudes in the gap between the BU ring andthe rod and, if so, computation of the shape of theextruded part of the seal as well as of the local contact

pressure between the extruded part and the rod. Theextrusion analysis is presented with details in Ref.[8].

Because of the length and complexity of the relevantequations and since most have been presented withextensive details in other studies (Refs. [2,8,10,11]),only important and new or modified equations are pre-

sented here. Starting with the elastohydrodynamicaspects of the BU ring model, the appropriate form ofthe Reynolds equation is similar to that for a journalbearing, as was presented in Ref. [2]:

4

D2rod@2p

@u2

@2p

@y2

4

D2rod

3

h@h

@u A

@p

@u

@p

@u

3

h@h

@y A

@p

@y

6 V g

h2 a A

@p

@y

6 g V

h3

@h

@y 1

where p is the local static pressure of the fluid filmbetween the rod and the ring, u is the circumferentialcoordinate (angle of axis Oz and a point on the outersurface of the rod on the xz-plane in Fig. 1), h is thelocal film thickness, Drod is the outer diameter of therod, V is the rod velocity (positive for instrokes andnegative for outstrokes), g is the local fluid dynamicviscosity, and

A ca

1 cbp 1 ca cb p a 2

where ca and cb are fluid constants and a is the fluid

pressureviscosity coefficient at the operating tempera-ture. Constants ca and cb are those used in the densitypressure formula of the actuator fluid, assumed to bethe well-known equation for mineral oils qq0 1 cap=1 cbp, q being the local fluid massdensity at operating conditions and q0 qp 0.Because of the low stroking velocities (less than 1 m/s)and sealed pressures (in the order of 140 MPa), thefluid at the rodring contact is expected to behave in aNewtonian manner without significant viscous shearheating. The dynamic viscosity is then calculated fromthe Barus formula, g g0 e

ap, where g0 gp 0.

The lubrication Eq. (1) is analysed and non-dimen-sionalized as presented in Ref. [2]. The following kine-matic and boundary conditions apply (seeFig. 1):

At z 0: u 0 and t VAt z h: u 0 and t 0

3

The boundary shear stresses are computed as in Ref. [2]:

ssrodzx

h

Drod@p

@u;

ssringzx

h

Drod@p

@u;

ssrodzy

h

2@p

@y

V g

h

ssringzy

h

2@p

@y

V g

h

4

Fig. 1. Seal configuration (half section shown, apart from the rod).

G.K. Nikas / Tribology International 37 (2004) 689699 691


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in areas where h60. At asperity contacts where h 0,the surface tractions are

ssrodzx ssringzx 0 andss

rodzy ss

ringzy

sgnV l p 5

where l is the boundary friction coefficient of the rodring contact and sgn(V) is the sign function of argumentVsgnV 1 if V0 and sgnV 1 if V


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where

p0 Ering

1 m2ring 1 mring aring Dh mring ex ez 10

is the contact pressure for pcyl 0. In Eq. (10),

exDrod

dring

1 11

ez uucyl uurod DR

DR dcyl Drod

2

12where DRis the rodring radial interference given at thering installation. It is assumed that the ring is squeezedbetween the rod and the actuator cylinder, and thatinterference DR is caused by compressing the ring on itsouter circumference. Establishing the level (or lack) ofcontact at the rodring interface is done via Eq. (9): anegative (computed) contact pressure pring implies lackof contact.

The film thickness at the rodring contact is calcu-lated from

h Srod Sring uurodz uu

ringz

uurod;preloadingz uuring;preloadingz 13

where Srod and Sring are the local roughness heights ofthe working surfaces of the rod and the ring, respect-ively,uu

rodz anduu

ringz are the normal elastic surface dis-

placements of the rod and the ring, respectively(computed from Eq. (15) of Ref. [2]), and the last twoterms in Eq. (13) are owed to the rodring pre-loadingfrom the initial interference plus any temperature dif-

ferential, computed using pressure p0 (Eq. (10)).Having analysed the elastohydrodynamics and con-tact mechanics of the system, it is now time to calculateleakage. Both the seal and the BU ring have their ownleakage or interface flow. What is of interest here is thesystem leakage, which is the leakage of the sealringpair. A BU ring in contact with the rod is obviously anobstruction of any fluid flow at the air-side of the sys-tem (Fig. 1). This may be obvious for a ring installedpressurized on the rod but if the (often large) environ-mental temperature variations during system operationare taken into consideration (e.g. temperature varia-tions up to 200

v

C in hydraulic actuators for aircraft

landing gear), then it is computed that the contactpressure between the ring and the rod can vary signifi-cantly from nearly zero (loss of contact) to several MPa.

Analysing the combined mass leakage rate of the seal(qseal) and of the BU ring (qring), the system (sealring) mass leakage rate, qsystem, is

qsystem

0; ifqseal>0 andqring0 andqring>0minfjqsealj; jqringjg; ifqseal>:

14

where mass leakage rate, q, of the seal or the ring is,generally, calculated from

q

2p0

q

h0

h z

h V z

h z

2 g @p

@y

Drod2

z

dz

du 15

The signs for the flow rates in Eq. (14) are based on

the coordinate system ofFig. 1, i.e. negative flow indi-cates fluid transferred from left to right, whereas theopposite is true for positive flow. Thus, negative systemleakage is leakage in the common sense (fluid loss fromthe actuator), whereas positive system leakage is ben-eficial leakage because fluid returns to the actuator(carried by the rod during an instroke). Under theseterms and for positive sealed pressure (pcyl>0), the

condition qring>0 can only hold during an instroke.

3. Application and effects of the back-up ring

The numerical solution of the model presented ear-lier for the BU ring is similar to that for the seal, asdescribed in Section 3 of Ref.[2]. Specifically, the non-dimensionalized and discretized version of Eq. (1) (asin Eq. (3) of Ref. [2]) is solved with the successiveoverrelaxation (SOR) method. For a typical case, thecomplete analysis (elastohydrodynamic solution for thesealring pair and computation of leakage and friction)for steady-state conditions takes about 80 s for roughcontacts with 100 100 gridpoints, using a 1.5 GHzPentium-4 PC, with typical total memory allocation of10 MB during the program execution.

This section is devoted to the study of the effects of atypical solid BU ring in a hydraulic actuator as showninFig. 1, used in aircraft landing gear. The rectangularrubber seal used for this purpose has, typically,remarkably different behaviour at subzero temperaturesthan at room temperature. Fig. 2 shows the stressstrain diagram of such a seal. For the more accuratedescription of the mechanics of this seal, a modifiedversion of the MooneyRivlin nonlinear model of rub-ber elasticity is used, as presented in Refs. [1,10,11].The operating data used in the examples of this sectionare presented next.

. Operating data: h 54, +23 and +135 v

C,

h0 23 v

C, sealed pressure is varied between0.7 MPa (100 lb/in.2) and 27.6 MPa (4000 lb/in.2),V 0:2 m=s, rodactuator clearance at the air-sideof the seal in the absence of a BU ring is 0.2 mm.Assumption:pgap pring (explained in Section 2).

. Piston rod: steel hollow cylinder, drod47 mm,Drod 50 mm, Erod 207 GPa, mrod 0:3, arod

12 106 K1; average roughness Ra 0:20 lm,r.m.s. roughness 0:23 lm, roughness maximumpeak-to-valley height 0:8 lm. Actuator: steel hol-



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low cylinder, dcyl 60 mm, Dcyl 63 mm, Ecyl

207 GPa, mcyl 0:3, acyl 12 106 K1.

. BU ring: solid ring of rectangular cross-section,dring 50 mm,Dring 60 mm, width 2 mm,Ering

1 GPa (except in Fig. 7), mring 0:3, aring 12

106 K1, rodring boundary friction coefficient0:10, rodring initial radial interference 10 lm(except in Figs. 68); average roughness Ra 0:20lm, r.m.s. roughness 0:23lm, roughness maxi-mum peak-to-valley height 0:8 lm (different rough-ness values are used inFig. 9).

. Seal: elastomeric ring of rectangular cross-section,inner diameter 49:9 mm, width 3:5 mm, cornerradius 0:2 mm, stressstrain properties and elasticmodulus given in Fig. 2, Poissons ratio 0:499,

thermal expansion coefficient 2 104 K1, rodseal boundary friction coefficient 0:06, rodsealinitial radial interference 300 lm, glass-transition-

temperature 47 v

C; average roughness Ra 1:50 lm, r.m.s. roughness 1:73 lm, roughnessmaximum peak-to-valley height 6:0 lm.

. Actuator fluid: mineral oil, q0 897:0 kg=m3 at

54 v

C, 842.2 kg/m3 at +23 v

C, 762.5 kg/m3

at +135 v

C;g0 0:8073 Pa s at54 v

C, 0.4795 Pa s

at +23 v

C, 2:7069 103 Pa s at +135 v

C; a

20 GPa1, ca 0:6 GPa1, cb 1:7 GPa

1. (The

pressureviscosity coefficient is generally tempera-ture dependent. However, it is assumed constant in

this study due to lack of data. Nevertheless, it isestimated that its variation with temperature, iftaken into account, would not affect qualitativelythe results presented later because of the relativelylow pressures involved.)

The above data are from a real aviation application.The roughness heights of the components were creatednumerically using a pseudo-random number generatorso that the target average roughness was achieved.Typical components (rod, seal and BU ring) were mea-sured with a Talysurf profilometer. Moreover, the sealand the BU ring were measured with a LaserSurfoptical (non-contacting) instrument. The mathematicalroughness simulation described previously gives pro-files symmetric to the mean line with zero skewness.The seal in particular has blunt roughness features witha negative coefficient of kurtosis, equal to 1.2 (thus aplatykurtic distribution, whereas a coefficient of zero

corresponds to the Gaussian distribution). More detailsof the simulation and the measured roughness profilesare included in Ref.[1].

In the lubricated regions, the fluid continuity equa-tion is satisfied through Eq. (1), which is derived fromthe equation of fluid mass conservation. The regions ofsolid contact between roughness asperities are found tobe isolated as in similar studies in the literature dealingwith mixed (partial) lubrication. A representativeexample of the extent of asperity interactions for thestudied type of seal is given in Fig. 10 of Ref. [2].According to the results obtained from the current

study and for the range of operating conditions tested,both the seal and the BU ring operate in the mixed toboundary lubrication regime. Specifically, at themaximum sealed pressure studied (27.6 MPa), strokingvelocity of 0.2 m/s, and with 50,000 gridpoints ineach of the two contacts (500 points along the rod axisand 100 points along the circumference), the compu-tation gives in the worst case scenario in the rodringcontact an average film thickness of 0.14 lm. With thegiven roughness profiles, this corresponds to a lambdaratio (defined as the average film thickness over thecomposite r.m.s. roughness) of 0.44 and a maximumportion of gridpoints in asperity contacts in the region

of 45%. Therefore, in the highest load case, the BUring operates in what is roughly defined as boundarylubrication regime (lambda below 1, as in p. 41 ofHamrock [13]). The seal on the other hand, for theworst case scenario, operates in the mixed or partiallubrication regime (lambda between 1 and 5Ref. [13])but close to the boundary lubrication regime, with acomputed lambda ratio of 1.31 and an average filmthickness of 2.3 lm. These results, although realisticand in agreement with similar theoretical results in theliterature (as for example with Ruskell [14]), do nottake into account possible adhesion effects, which

Fig. 2. Typical stressstrain data of an industrial elastomeric sealmaterial.



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would be expected to reduce the average film thickness,and there is room for improvement in this area.

The most interesting questions to ask are What isthe effect of a BU ring on leakage? and then Howdoes it vary with the sealed pressure and the operatingtemperature?Fig. 3provides an answer to the previousquestions for the low subzero temperature of54

v

C.The sealed pressure is varied from 0.7 MPa (100 lb/in.2)to 27.6 MPa (4000 lb/in.2). The mass leakage rate forinstrokes and outstrokes is shown on the left verticalaxis with the sign convention defined earlier. Similarly,

the mass leakage rate per cycle (a cycle is defined as oneoutstroke followed by an instroke with the same strok-ing velocity and equal stroking length) is shown on theright vertical axis, assuming that the outlet of the systemis always flooded. According to Fig. 3, during an out-stroke without a BU ring, negative leakage increasesrather linearly with the sealed pressure, in the same waythat positive leakage increases during the followinginstroke under the same conditions. However, with theintroduction of the BU ring (with a 10 lm initial inter-ference as quoted earlier), the leakage, both for out-strokes and for instrokes, is dramatically reduced and is

insensitive to the sealed pressure variations. What is ofmajor concern in the industry is of course the leakage-per-cycle, which is used for seal performance evaluation.According to Fig. 3 (right axis), the standard leakage-per-cycle (leakage during instroke leakage duringoutstroke) shows an increase when there is nopre-loaded BU ring installed in the system, whereas thepresence of the pre-loaded BU ring gives an almost con-stant leakage rate, regardless of the magnitude of thesealed pressure. Looking at the two relevant leakagelines (leakage-per-cycle with and without a ring), it isseen that those two lines intersect at point P, which

corresponds to pcyl ffi 15 MPa. On the right of point P

(i.e. for pcyl > 15 MPa), the benefit of the BU ring in

reducing the leakage-per-cycle is obvious; but on the leftof pointP(pcyl< 15 MPa), the BU ring actually hinders

the seals operation of reducing leakage. Therefore,under the given conditions, a pre-loaded BU ring is ben-

eficial in reducing the system leakage only if the sealedpressure is kept higher than a critical value.

Such a critical pressure is also obvious in Fig. 4,which refers to the same conditions as Fig. 3, exceptfor the operating temperature, which is now equal to+23

v

C. The appearance of the various curves is simi-lar to that of the curves inFig. 3but, this time, pointPhas moved to the left, signifying a lower critical press-ure of about 7.5 MPa, nearly half that ofFig. 3 refer-ring to 54

v

C. In this case, the ring offers a beneficialreduction of the leakage-per-cycle for a wider range ofsealed pressure. Notice that the leakage-per-cycle with-

out a BU ring has increased significantly comparedwith that in Fig. 3, especially at the high end of thesealed pressure, mainly because the fluid dynamic vis-cosity at +23

v

C is only 59% of the viscosity at 54 v

C.On the other hand, the leakage-per-cycle in the pres-ence of the ring has been significantly decreased at theincreased-temperature case, attributed both to thechanged viscosity and to the changed contact pressureconsidering thermal expansion of the system elements.

Moving on to the high end of the temperature scale,Fig. 5 shows the leakage results at the operating tem-perature of +135

v

C. Observing the curve referring to

leakage for an outstroke without a BU ring, it is clearthat leakage increases with the sealed pressure. Thiscould be attributed to the large reduction of the fluiddynamic viscosity at the high temperature of +135

v

C,

Fig. 3. Effect of the sealed pressure on leakage at54 v

C.

Fig. 4. Effect of the sealed pressure on leakage at +23 v

C.



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which also affects adversely the leakage during aninstroke (again without a BU ring). It is interesting tosee that even during an instroke in the absence of a ring,leakage, despite being positive at low sealed pressure,becomes negative (fluid loss) beyond a sealed pressureof about 6 MPa. The latter could be explained by theincreased Poiseuille-type flow at the rodseal contactbeyond a certain sealed pressure, which overcomes theopposing Couette-type flow in the contact from theretracting rod. However, it must be mentioned at thispoint that the theoretical prediction of the model athigh temperature contradicts experimental results that

show decrease of leakage. This discrepancy could poss-

ibly be explained by an overestimation of the thermal

displacements of the piston rod and actuator cylinder as

derived in the model, although, on the other hand,

experiments done at high temperature are often incon-

clusive because of fluid vaporization, which prevents theaccurate weighing of the fluid that actually leaked.

The high-temperature results make the effect of a BU

ring on leakage seem even more significant, as Fig. 5

Fig. 5. Effect of the sealed pressure on leakage at +135 v

C.

Fig. 6. Effect of the rodring interference on leakage for varioussealed pressures.

Fig. 7. Effect of the rodring interference on leakage for variablering elastic modulus.

Fig. 8. Effect of the rodring interference on the leakage-per-stroke.



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demonstrates that the ring reduces leakage substan-tially, both during an outstroke and during aninstroke, particularly at higher sealed pressures.Regarding the leakage-per-cycle, Fig. 5 shows thatpointP, which corresponds to the position where a BUring under the studied conditions becomes effective (orineffective) in reducing overall leakage, has againmoved to the left. Now, the critical sealed pressure,over which the ring is an effective seal in itself, is about

0.5 MPa, which is quite low. In fact, there is no regionin Fig. 5 where the BU ring hinders the sealing per-formance of the system. On the contrary, it improvesthe performance by a margin directly related to thesealed pressure, and, thus, its presence is essential inminimizing and practically eliminating leakage.

The effect of the initial rodring radial interference isexamined next in Fig. 6 (referring to h h0 23

v

Cto eliminate any thermal expansion or contractioninterference), having the sealed pressure as a para-meter. It is seen that the leakage-per-cycle increasesalmost linearly with the rodring interference for the

studied range of interference (110 lm), although theleakage differences shown are small (about 4%). On theother hand, increasing the sealed pressure results in areduction of the leakage-per-cycle, which is theopposite of what was observed for the leakage-per-cycle without a BU ring in Fig. 4.However, it must berealized that the seal leakage in the absence of a BUring is directly affected by any increase of the sealedpressure in that the left side of the rodseal contact isdirectly exposed to the sealed pressure; this is not thecase for the left side of the rodring contact, which, asexplained earlier in this study, is under a more-or-less

constant fluid pressure pgap (either zero pressure or, inthe other limiting-case scenario, a pressure approxi-mately equal to the (dry) average contact pressure,pring). What does change for the ring when the sealed

pressure is varied is the radial normal surface displace-ment of the rod and the actuator cylinder (see Eqs. (6)

and (7)), which will affect the rodring contact pressureand the contact film thickness. Higher sealed pressurewill increase uurod anduucyl and, thus, release some of the

rodring contact pressure and reduce the film thick-

ness. The conclusion from Fig. 6 is that, in order tominimize the leakage-per-cycle, a lightly pressurizedBU ring must be used, and this ring will performslightly better at higher sealed pressure.

One important parameter in this analysis is the BUring mechanical behaviour. Although not much is read-ily available about the stressstrain relation and thecontact mechanics of typical BU rings made of com-

posite materials such as glass-fibre reinforced PTFE, ashas already been explained, the present model assumesthat the ring behaves in the classic Hookean manner(isotropic and linearly elastic), with a Poissons ratio inthe order of 0.3 (justifiable by the fact that non-expan-

ded and non-reinforced PTFE has a Poissons ratio of0.46) and with elastic modulus comparable to that ofnon-reinforced PTFE (0.30.8 GPa) to reinforcedPTFE (a roughly estimated 0.52.0 GPa).

Fig. 7 shows the effect of the rodring interferenceon the system leakage-per-cycle, using the ring elasticmodulus as a parameter. The figure refers to room

temperature (+23

v

C) and average sealed pressure(pcyl 6:9 MPa 1000 lb=in:

2). It is seen that by usinga ring with higher elastic modulus, the leakage-per-cycle is reduced proportionately. A stiffer ring willdeform less under the applied elastohydrodynamicpressure and, thus, the film thickness at the rodring

contact will be thinner. Although this argument can beused to predict a reduced leakage-per-stroke, it is notstraightforward to explain the reduction of the leakage-per-cycle. A further insight is provided inFig. 8, whichshows the effect of the rodring interference on theleakage-per-stroke, both for an instroke and for an

outstroke, for the same conditions as in Fig. 7 and fora ring with elastic modulus of 0.5 GPa. The left verticalaxis shows the difference of the system leakage at rod

ring interferenceDRas a percentage of the system leak-age at interference DR 0 for the outstroke, whereasthe right vertical axis shows the same for the instroke.Both axes use the same scale absolute limits. It is seenthat the outstroke leakage is affected more than theinstroke leakage (outstroke/solid curve is abovethe instroke/dashed curve) for DR> 2 lm, whereasthe opposite is true for DR< 2 lm. The vertical-linepattern between the two curves highlights the afore-

Fig. 9. Effect of the ring average surface roughness on leakage.



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mentioned difference (which of course depends onroughness).

Speaking of roughness, it is best to complete thisstudy with a presentation of the effect of the surfaceroughness of the BU ring on the system leakage. Fig. 9shows the effect of the average roughness Raof the ring

on the leakage-per-cycle at three representative sealedpressureslow, average and high. The average rough-ness was varied (with the method described at thebeginning of this section) in order to cover all casesbetween a perfectly smooth ring and a ring which ismuch rougher than the rod. According to Fig. 9, theleakage-per-cycle is only weakly affected by the ringroughness, and this is true regardless of the magnitudeof the sealed pressure (within the studied range of pres-sures). The effect of the sealed pressure is clearer to see:lower sealed pressure results in higher leakage-per-cycle, but the differences are still rather insignificantand more immediate when increasing the sealed press-

ure from low values (i.e. from pcyl 0:7 MPa andupwards). The effect of the ring roughness on leakage-per-stroke (not shown) is linear, with leakage increas-ing with roughness, which is explained by the increaseof the average film thickness at the rodring contact(easily realized from Eq. (13)). The leakage curves inFig. 9 reveal an optimum average roughness tominimize the leakage-per-cycle, which depends onthe sealed pressure. For example, at pcyl 6:9 MPa

1000 lb=in:2, the leakage-per-cycle is minimized forring roughness Ra 0, something which is not true forthe curve ofpcyl 27:6 MPa. However, the leakage dif-

ferences are, by any standards, negligible and subject tomany external variables, which negates the need to bepreoccupied with special ring selection to meet any spe-cific roughness criteria other than to protect the rodssurface from abrasion.

4. Conclusion

Solid BU rings of relatively low elastic modulus,used in hydraulic actuators to support rubber seals forreciprocating motion (Fig. 1), were shown to behave inan intrusive manner, affecting the sealing performance

of such systems. The rings, originally intended to pre-vent seal extrusion at high sealed pressure and thusprevent seal damage, were shown to actually have seal-ing properties when installed with an initial interferencewith the rod on which they operate. Even an initialinterference of a few microns, in combination with anaverage elastic modulus of the BU ring in the orderof 1 GPa, generates sufficient contact pressure to estab-lish sealing at high sealed pressures. This sealing mech-anism is affected by several factors, e.g. the sealedpressure (transferred to the BU ring via the adjacentrubber seal), the operating temperature, the viscosity of

the actuator fluid, the surface roughness of the ring,etc. Naturally, the ring intrusion is valid both duringoutstrokes and instrokes, and it could very wellincrease or decrease leakage, depending on the strokingdirection.

It was generally found that the leakage-per-strokecould be significantly decreased by using a ratherlightly pressurized BU ring (see for example Figs. 35).The leakage reduction is significant at high operatingtemperature, with the actuator fluid having a very lowviscosity (Fig. 5). However, and for standard perform-ance evaluation purposes, the leakage-per-cycle is theone most relevant in industrial circles. For the leakage-per-cycle then, it was found that, for given operatingconditions, there exist a critical sealed pressure overwhich a BU ring becomes a more effective seal than therubber seal it supports. That critical pressure (corre-sponding to point P in Figs. 35) is inversely pro-portional to the operating temperature, with effect of

being very low (compared with the sealed pressure) atvery high temperaturesee for exampleFig. 5.

The system leakage-per-cycle was found to slightlyincrease with the rodring interference and (alsoslightly) decrease with the sealed pressure (Fig. 6). Theelastic modulus of the BU ring on the other hand has astronger effect on leakage: the leakage-per-cycle exhi-bits a rather significant reduction when using a ringwith higher elastic modulus (Fig. 7).

Finally, the leakage-per-stroke of the sealring sys-tem is found to be linearly affected by the average sur-face roughness of the BU ring and the effect is

significant. However, the leakage-per-cycle is onlyweakly affected by the magnitude of the average sur-face roughness of the ring (Fig. 9), irrespectively of thesealed pressure. An optimum average surface rough-ness of the ring is found to minimize the leakage-per-cycle of the system, but this is readily affected by theoperating conditions (e.g. the sealed pressure), and thebenefit in terms of leakage reduction is negligible topursue this target any further.

For a final comment, it is emphasized that the resultspresented for the leakage per instroke and for the leak-age-per-cycle are based on the assumption of a floodedair-side of the actuator (leaked fluid resting on the rod,

readily available to be picked up during an instroke).Otherwise, negative leakage would be significantlyincreased and, based on the presented results, theadvantage of using a BU ring would be even greater.

Acknowledgements

This study is part of a project which was financiallysupported by Smiths Aerospace Actuation SystemsCheltenham (UK), Smiths Aerospace ActuationSystemsWolverhampton (UK), Polymer SealingSolutions Ltd (UK), and the British Department



11/11

of Trade and Industry through the Civil Aircraft

Research and Demonstration Programme.

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