REVIEWPAPER 1 ...

REVIEW PAPER 1

Eighty years of research on hydraulic reciprocatingseals: review of tribological studies and relatedtopics since the 1930sG K NikasMechanical Engineering Department, Tribology Group, Imperial College London, Exhibition Road, London SW7 2AZ, UK.email: [email protected]; [email protected]

The manuscript was received on 21 December 2008 and was accepted after revision for publication on 16 April 2009.

DOI: 10.1243/13506501JET607

Abstract: Hydraulic seals are complicated machine elements. The engineering research onhydraulic reciprocating seals, which commenced roughly in the 1930s, has achieved a basicunderstanding of performance issues. This article provides a review of the experimental andtheoretical research conducted over a period of eight decades, discussing more than 200 of themost significant publications from the related literature. The topics discussed include recipro-cating seal designs, materials, experimental methods, theoretical studies, elastohydrodynamiclubrication, solid and contact mechanics, performance issues, and optimization.

Keywords: seal, reciprocating, elastomer, rubber, polymer, tribology, review

1 INTRODUCTION

Hydraulic reciprocating seals are critical machineelements used in a variety of industrial, automo-bile, aerospace, and medical applications that involvelinear and rotational motion such as in hydraulicactuators [1]. They are usually made of polymericor thermoplastic materials, including elastomers andrubber-like materials (rubber compounds with vul-canized natural rubber as the prototype or syntheticrubbers produced with sulphur or other additives),plastics, polyurethanes, as well as composites. Theseseals normally operate dynamically under broad oper-ating conditions, with sealed pressures of up to 80MPa, sliding speeds of up to 15 m/s, and temperaturesvarying roughly between −70 and +250 ◦C, dependingon application. Figure 1 shows typical hydraulic actu-ators and some reciprocating seals of various shapes,including rod, piston, and rotary-vane seals [1–4]. It ischaracteristic that the depicted seal shapes are just afew of many complex designs that have evolved overdecades of theoretical and applied research.

A hydraulic reciprocating seal is a rather neglectedmachine element in the scientific literature, in spiteof its vital role in many applications. The neglect ispartly attributed to the complexity of seal behaviour,which is owed to the large number of variables sig-nificantly affecting sealing performance. The major

difficulty is attributed to seal flexibility, which pre-cludes obtaining analytical solutions and complicatesany numerical solution process, particularly in tran-sient conditions. Moreover, typical seal materials suchas elastomers obey highly complex, non-linear stress–strain laws of finite elasticity or thermoviscoelasticity,which are strongly affected by temperature. In fact,basic mechanical properties of hydraulic seals suchas the moduli of elasticity and rigidity, Poisson’s ratio,hardness, and compressibility all depend strongly ontemperature. Additional influential factors such aschemical interaction with hydraulic fluids, material(e.g. elastomer or rubber) oxidation, and ageing playmajor roles in sealing performance.

In spite of the difficulties in sealing performanceevaluation, hydraulic seals are met in many criticalapplications with machinery costing hundreds to mil-lions of times more than the seals. A characteristicexample was the dramatic destruction of the NASAspace shuttle Challenger in 1986, which was attributedto the loss of sealing ability of a static elastomericO-ring because of low ambient temperature the nightbefore the shuttle’s launch [5], an engineering errorthat cost several human lives. Therefore, the correctengineering design and evaluation of hydraulic sealsis of paramount importance to avoid costly mistakes.

As far as the author is aware, the scientific researchon hydraulic reciprocating seals was initiated before

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Fig. 1 Hydraulic actuators for linear and rotary motion, and some examples of rod seals (on theright), piston seals (on the left), and rotary-vane seals (top, right) (from references [1] to [4])

World War II; it then rapidly progressed in the 1960sand 1970s. Following one of the early studies on thenetwork theory of rubber elasticity by Meyer et al. [6] in1932, the doctoral thesis of Gronau [7] in 1935 was oneof the earliest known publications on hydraulic seals.However, the first breakthrough probably was the pio-neering work of White and Denny [8, 9] from 1944to 1947, an exhaustive experimental and theoretical

work on reciprocating seals, which remains a sourceof reference. Denny [10–16] continued his pioneeringwork on reciprocating seals in the 1950s and 1960s,dealing – mainly experimentally – with the issues oflubrication, leakage, and friction. Some other note-worthy, early experimental studies during the 1950swere those of Cheyney et al. [17] and Morrison [18]on static and dynamic O-rings, as well as the work

Proc. IMechE Vol. 224 Part J: J. Engineering Tribology JET607 © IMechE 2010



Eighty years of research on hydraulic reciprocating seals 3

of some researchers in Germany [19, 20]. By the late1950s, the foundations of the elastohydrodynamic the-ory of lubrication had been laid [21] and the theory wasswiftly applied to reciprocating seals with increasingsuccess since the 1960s.

The progress in sealing research was continuousbetween 1960 and 2000 with a variety of valuableexperimental [22–29] and theoretical studies [30–46]exploring fundamental issues of friction and leakageperformance on a variety of seal shapes, includingrectangular seals, toroidal seals (O-rings), U-cups,step-seals, tandem seals, and a few others. These arediscussed in later sections of the article, together withmore recent studies in 2000–2008. Very few reviews onreciprocating seals have been published over the past80 years, most notably the general reviews of Nau [47,48] covering some of the work done up to the 1990s, thestudy of Field and Nau [49] on experimental researchup to the 1970s, the general discussions of Flitney[50] in 1982, and Ramsdell [51] in 1986, the detailedreviews of Kanters [52] and Visscher and Kanters [53]in 1990 (mainly on experimental issues), the presen-tations of reciprocating-seal tribology and designs ofBisztray-Balku [54, 55], and, finally, the book chapterin reference [1]. The present article is a review of themajority of the significant theoretical and experimen-tal studies on reciprocating seals and related topics,discussing the major contributions in this field andlisting over 200 references for a complete bibliographyon the subject.

2 REVIEW OF EXPERIMENTAL STUDIES ONRECIPROCATING SEALS AND RELATED TOPICS

Although the work of Gronau [7] in 1935 is one ofthe earliest recorded studies on hydraulic seals, thework of White and Denny [8, 9] between Septem-ber 1944 and December 1946 is probably the firstmajor research contribution on seals. Their 130-pagefinal report [9], containing over 110 figures and draw-ings, was based on an exhaustive experimental studyamidst World War II. In fact, the study was sup-ported by the Ministry of Aircraft Production and theRoyal Aircraft Establishment in the UK in the inter-ests of improving hydraulic system reliability.The workof Deny under the direction of Professor White atImperial College in London dealt with the experimen-tal study of flexible packings, including rectangular,toroidal, and U-cup seals of various polymeric mate-rials. Their measurements at various sealed pressures,speeds, and temperatures involved the friction coeffi-cient and force at the sealing contact, leakage rates,seal wear, and failure mechanisms involving abra-sion and extrusion. They studied the effects of sealmaterial hardness (which they showed to decreaseabrasion and extrusion) and sealed-fluid properties onleakage and friction, and came up with seal housing

arrangements such as back-up rings to avoid extru-sion. Their experiments on interfacial phenomenainvolving surface roughness effects are of great impor-tance because they demonstrated, perhaps for thefirst time in hydraulic seals, the relation between stic-tion, static and dynamic friction on the roughnessvalue and texture. Furthermore, by measuring the fric-tion force in reciprocating motion at various strokingvelocities, they realized the connection with the filmthickness at the sealing contact and the transitionfrom boundary or partial lubrication with roughness–asperity interactions at low speeds to elastohydrody-namic lubrication at higher speeds. The latter wasmuch later explained by the Stribeck curve, althoughsome differences exist between the Stribeck curve ofhard-elastohydrodynamic contacts and that of flexi-ble, reciprocating seals [56, 57]. White and Denny alsomanaged to measure the contact pressure at the seal-ing interface and locate the zone of maximum sealstrain. This provided two important observations:

(a) elastomeric seals are nearly incompressible (thePoisson’s ratio is very close to 0.5), which meansthat the hydraulic pressure exerted on (preloadedby radial interference) seals is readily transferredto the sealing contact, allowing seals to achieveautomatic sealing (Fig. 2);

(b) the mechanism of sealing is hidden in the inletzone of the contact and related to the gradient ofthe contact pressure distribution at the inflexionpoint (more on that later).

Four experimental studies from the classic sealingconferences organized by the British HydromechanicsResearch Association in the 1960s provided valuablenew information on seal lubrication and friction, usinga variety of measuring techniques. In 1964, Cnops [58]

Fig. 2 Rectangular elastomeric seal with an anti-extru-sion ring in a linear hydraulic actuator (onlythe upper half of the seal, ring and housing depic-ted), demonstrating how the seal automaticallyadjusts to sealed-pressure variations by transfer-ring it to the sealing contact via its nearly incom-pressible material (see arrows)




4 G K Nikas

devised a spring-loaded piston in a hydraulic cylindercontaining brake fluid of harmonically varying volumeto measure the friction of cup, piston, and elastomericseals. With that rig, Cnops observed the mechanismof oil film formation at the sealing contact, the thick-ness of which varied with the stroking speed frompartially collapsed at low speeds to relatively thick athigher speeds. In terms of friction, Cnops observed theeffects of stiction and elastomer relaxation and creep,which characterize the viscoelastic nature of rubber-like materials, particularly after long periods in staticconditions. In fact, these effects had been discussedyears earlier by, for example, Denny [15] in 1959.

The friction and lubrication of natural-rubber, pis-ton seals, were also studied by Lawrie and O’Donoghue[23] in 1964, who utilized displacement transducers fortheir friction and piston-velocity measurements. Theirsealing rig, which consisted of a pump-pressurized,brake-fluid filled cylinder, allowed for simultaneousmeasurement of contact pressure, friction force, andstroking velocity for a complete operating cycle viaa multi-channel recorder. The seal rubber used wasconducting to allow for contact resistance measure-ments and establishing whether the fluid film at thesealing contact had collapsed (zero resistance) or wasfull (infinite resistance). It was thus possible to mea-sure the sealing performance in transient conditionsand identify potential problems with seal abrasivewear for collapsed fluid film or, simply, observe filmdevelopment and variation during an operating cycle.

The development of a fluid film at a sealing contactand the transition from boundary (partially collapsedfilm) to hydrodynamic (full film) lubrication was alsothe focus of Müller’s experimental work [22] in 1964.His experiments with elastomeric toroidal seals andquad (X) rings revealed the effects of the strokingvelocity, seal preloading, and fluid viscosity on seal-ing performance in terms of leakage and friction. Ofparticular importance was his discussion on the film-thickness difference between instrokes and outstrokes(see Fig. 2 for the direction clarification), as well as onthe elastohydrodynamic film thickness of elastomericreciprocating seals.

In 1969, Aston et al. [59] made a significant con-tribution by presenting their experimental work onrubber seal friction at temperatures of up to 200 ◦C.The importance of that work was on the demon-strated relation between temperature and rubber-specimen dimensions, which affected the frictionalforce. Moreover, Aston et al. studied the relaxationand subsequent recovery rate of rubber after peri-ods of inactivity, which caused a reduction of thefrictional force in time. Such viscoelastic phenom-ena are crucial in sealing performance and met inmany hydraulic-seal applications such as those in theaerospace sector. They are also related to the naturalageing of elastomeric materials and can be explainedvia the network theory of rubber [60].

Another significant contribution from the 1960s isthe work of Dowson and Swales [25], who combinedexperimental work with theoretical predictions via theelastohydrodynamic lubrication theory. They deviseda rotating disc machine to test a cylindrical rubberblock, emulating reciprocating seals and very longstrokes. The sealing contact pressure was measuredby a piezo-electric transducer and the film thicknesswas measured via capacitance techniques. The theory,generally, supported the experimental findings show-ing increase of film thickness with speed and decreasewith contact pressure. Moreover, the fundamentalsealing mechanism of reciprocating seals, i.e. the leak-age difference between outstrokes and instrokes, wasrevealed. The latter, obviously, resulted in concludingthat seal leakage-per-cycle (in reciprocating seals, anoperating cycle consists of one outstroke followed byone instroke) is zero if the fluid that leaked duringthe outstroke is fully returned to the sealed chamberduring the instroke.

Moving on to the 1970s, the experimental contribu-tions of Field and Nau [24, 49], focusing on rectangularrubber seals, improved the understanding of seal-ing mechanisms and performance issues. By usingoptical interferometry and electrical transducers tomeasure the film thickness, they produced resultson leakage, friction, and contact pressure. However,those results were characterized by some inconsisten-cies. The reason for the latter, apart from a probablelack of high-precision instrumentation at that time,could be found in a study of Flitney and Nau [61]in the late 1980s, which revealed a scatter in resultsobtained from seven laboratories located in differentcountries, yet based on experiments under controlledconditions. A possible explanation postulated in refer-ence [61] was that the adherence to test specificationswas hindered by the lack of standardized methods insealing technology.

Another significant contribution from the 1970s wasthe experimental work of Hirano and Kaneta [27]in 1971 who measured the friction force and leak-age of nitrile-rubber D-rings in reciprocating motion.They observed how the mixing of air bubbles withhydraulic fluid in the sealing contact affected leakageand friction. (Similar observations about air bubblesindicating cavitation at the edges of the contact andleading to film depletion because of the oil obstruc-tion by the bubbles have been reported by Rana [62],although that was happening in low-load contactsafter long periods of operation (more than 30 min)and the phenomenon was weak when the contact loadwas increased.) Hirano and Kaneta [27] also observedthe now well-known phenomena of rubber stictionat the start-up and the reversal of motion, owing tocollapse of the fluid film at the sealing contact. Theyalso showed how friction and leakage were relatedto the stroking length and how it became unsta-ble in short stroking-length situations. In fact, they





discussed how the development of a stable hydro-dynamic film in the sealing contact depends on theratio of the stroking length to the seal contact width.If the said ratio is >2, sealed fluid, which is trans-ported through the sealing contact at about half thespeed of the contact counterfaces, can reach the out-let zone of the contact and, thus, leakage takes place.This observation is, obviously, of paramount impor-tance in reciprocating-seal leakage, friction, and wear.The same conclusion was reached in an equally sig-nificant study by Field and Nau [29] in 1975, who,additionally, studied the effects of seal hardness andpreloading or initial interference, seal edge (or corner)geometry, and back-up clearance. These parameterswere much later included in theoretical models byother researchers and their effects quantified (moreon that later). What is perhaps most worthy of remem-bering from Field and Nau [29] is their graphs on thevariation of the minimum film thickness and frictionforce of a reciprocating rubber seal during a full cycle(see Fig. 3). The differences between outstroke andinstroke dictate the leakage-per-cycle and explain theseal behaviour during each stroke.

Fig. 3 The variation of the minimum film thickness ofa rectangular rubber seal during outstrokes andinstrokes (from Field and Nau [29])

In the first 40 or so years of sealing research (upto and including the 1960s), the main parametersaffecting sealing performance had been identified andexperimentally studied. Naturally, the quality of theexperimental work was depending on the quality of thelaboratory equipment and the efficiency of the tech-niques used. From the oil weighing for leakage mea-surements in the 1940s to the video-camera recordingof the sealing contact in the late 1990s, there has beena long way of custom-built apparatuses and measure-ment techniques of variable success. Four variablesare of major importance in all of those studies, namelythe contact pressure distribution and width, the con-tact film thickness, the seal frictional force, and theleakage rate.

The measurement of static contact pressure distri-butions [34, 63–70] has been performed by using straingauges, piezo-electric force transducers [24, 25, 71],photoelastic methods [72], as well as inductive trans-ducers for measuring displacements. The latter hasalso been used in film-thickness measurements, inaddition to electrical capacitance [24, 25, 29, 49, 66,71] and resistance methods [23, 67, 73], as well as opti-cal interference and fluorescence techniques [74–76].Recently developed methods on film-thickness mea-surements such as ultrasonic techniques have alsobeen used, although the latter has been applied tomechanical seals [77] and not to reciprocating sealsyet as far the author is aware.

The measurement of friction of rubber-like recipro-cating seals has been the focus of most experimentalstudies. Lack of standardized methods and commer-cial apparatuses dictated the construction of variousrigs and devices to fit specific purposes. The com-plexity and individuality of those approaches make adetailed discussion very difficult but a lot of informa-tion can be found in the doctoral theses and relatedpublication of Kanters and Visscher [52, 53, 78] forstudies conducted up to 1990.

The measurement of leakage of reciprocating seals isusually done by weighing the leaked fluid after remov-ing it from piston rods. This is most likely the oldestmethod and has been used by most researchers [9, 22,24, 27, 71, 79, 80]. A few other methods have also beenused such as measuring the electrical capacitance ofleaked oil layers with one or two electrodes [81] as wellas by measuring the oil flow necessary to maintain aconstant sealed pressure [24, 71, 82, 83].

Other important variables such as the static anddynamic extrusion of elastomeric seals into largeclearances [84] have also been measured but themain focus was on the phenomena taking place ata sealing interface. The use of optical interferometrysince at least the 1960s gave new results to con-sider in the study of hydrodynamic films, involvingthe contacts between polymers (including rubber),steel, and, especially, glass. In this respect, the workof Blok and Koens [74] in 1965 was important because




6 G K Nikas

it addressed the problem of poor reflectivity of rub-ber surfaces (owed to high surface roughness anddark colour) by using an externally aluminized, thin,plastic-sheet cover on the rubber. The method wasapplied to rubber lubrication a few years later byRoberts and Tabor [85], too. Optical interferometry inthe study of sealing contacts has more recently beenused by Kanzaki et al. [86, 87] as well as Kaneta et al.[26]. In the latter study, a mono-chromatic techniquewas used in D-rings and lip-shaped, nitrile-rubber,stationary seals on sinusoidally reciprocating glass.Unfortunately, in order to improve rubber reflectivity,the specimens had to be specially moulded to improvetheir smoothness, which destroyed their natural sur-face roughness. A better solution to this problem (bet-ter still than that in references [74] and [85] discussedearlier) was used by Rana [62]: by applying a goldsputtering method, seal specimens were coated withfour layers of gold, each being 50 nm thick. This gavevery high reflectivity without altering significantly the

original average roughness, which, in the case of elas-tomeric seals, is quite high (typical values in the orderof 1.5 µm [1]).

Apart from optical interferometry, direct observa-tion of lubricating films in sealing contacts was alsodone by cameras and video recording. Schrader [88]in the late 1970s and Kawahara et al. [67] at the begin-ning of the 1980s used high-speed cameras to photo-graph seals sliding on glass cylinders. More recently,Rana [62], in collaboration with seal manufacturersin England [89], developed a test rig for stationaryelastomeric seals on a reciprocating glass plate, whichwas equipped with a microscope and computer data-logging of video-recorded images (Fig. 4(a)). Severaltests of rectangular seals were performed with this rigunder static, dynamic, dry, and lubricated conditions,varying the contact load on the seal, the reciprocatingfrequency, and the stroking length [90]. Substitutionof different seals (of various dimensions and rough-ness profiles) is straightforward. Apart from leakage

Fig. 4 Test rigs for reciprocating seals developed by Rana [62]: (a) the original, simpler version [62,90] and (b) the final, advanced version [62, 91]





and friction results, this type of sealing-contact ana-lysis offered real-time data on the dynamic varia-tion of hydrodynamic films, including cavitation fromhydraulic-fluid starvation, air bubbles at the edgesof the sealing contact, as well as obstruction of fluidreplenishment by the accumulation of debris particles(often fragments of seal material).

Rana’s rig [62, 90] was re-designed to allow forgreater flexibility and experimental precision. Theadvanced rig [62, 91] (Fig. 4(b)) consisted of a hol-low, transparent, and high-strength tube connectedto a motor, which transferred reciprocating motionto the tube via a gear mechanism. Gland, elastomericseals were accommodated by a steel casing envelop-ing and supporting the tube, whereas a hydrauliccircuit supplied red hydraulic fluid to the stationaryseals (refer to Fig. 4(b)) with pressures up to 7 MPa(although the maximum sealed pressure in the testswas kept below 1 MPa for safety reasons). A still, exter-nally mounted boroscope with integral lighting wasfocused on a seal and signalled clear images to a CCDcamera and attached computer for data logging andsubsequent processing. That rig provided an arrayof results on seal leakage, friction, extrusion, cavita-tion, and wear, as well as results on surface-roughnessdeformation in dynamic conditions, fluid film devel-opment and collapse, debris particle entrainment, andso on.Visual observation of the sealing interface showsthat the entrainment of debris particles, including sealfragments and foreign contaminants, increases leak-age by distorting the seal surface. If the debris areharder than the seal material, they stick to the sealand may abrade the contact counterface (e.g. a pistonrod). The thus-created scoring grooves act like micro-channels, allowing pressurized fluid to escape to thelow-pressure side of the seal (similar grooves wereartificially created by White and Denny [9] in theirexperiments to test this hypothesis, which they ver-ified). In the experiments of Tanoue et al. [92] withused lubricating oils, it was found that shaft wearwas significantly affected by sub-micrometre particles(<0.25 µm) and was proportional to the concentra-tion of the particles. Remarkably, significant wear wasobserved even for small particle concentrations, e.g.0.2 per cent by weight.

Another important finding from the work of Rana[62] was that, during the initial running-in period,seals became smoother. Specifically, in Rana’s tests,the average roughness was reduced from 1.8 to 1.1 µmand skewness (a measure of the asymmetry of theroughness profile about the mean line) reduced from1.07 to 0.23 µm, even though the seal was sliding onan (ultra smooth) glass surface. Wear was reducedafter the initial running-in period and was higher atthe end of the strokes because of a reduction of thefilm thickness caused by the lower sliding speed (orinstantaneously zero speed during the reversal of theentrainment velocity). Such results are of importance

in designing optimized seals and should complementglobal optimization algorithms that normally take intoaccount only basic performance parameters [44, 93].

3 REVIEW OF THEORETICAL STUDIES ONRECIPROCATING SEALS, MATERIALS, ANDRELATED TOPICS

The theoretical analysis of reciprocating seals beganwith the pioneering studies of the 1930s and 1940s (forexample, see references [7] and [9]) but was hinderedand delayed by the challenging nature of the elasto-hydrodynamics and contact mechanics problems offlexible seals. The challenges, which are detailed in ref-erence [1] and briefly in reference [94], are explainednext for the sake of completeness, and blended withthe discussion of progression in the theoretical mod-elling of hydraulic reciprocating seals and their perfor-mance evaluation. They concern both the mechanicsand the lubrication modelling of hydraulic seals.

The main problem is the flexible nature of recip-rocating seals, which are made of either polymericmaterials (including elastomers and, generally, rub-ber compounds), thermoplastics such as polytetra-fluoroethylene (PTFE), ultra-high-molecular-weight-polyethylene (UHMWPE), polyurethanes, and com-posite materials such as bronze-filled PTFE in coaxialseals [95], PTFE with glass fibres bonded with elas-tomers as in rotary vane seals (Fig. 1) [4, 96, 97], orPTFE filled with stainless steel or graphite. Even whenthe main sealing element is not really flexible, thesupporting sealing element definitely is in order toallow automatic adjustment of the contact pressureto sealed pressure variations (e.g. observe the glyd-ring rod seal at the bottom-right corner in Fig. 1).Polymeric and composite materials have a non-linearstress–strain behaviour, including viscoelasticity (as inelastomers), viscoplasticity (as in PTFE), and, gener-ally, finite elasticity, involving several experimentallyderived coefficients, which make their mechanicsmodelling a complicated task.

3.1 Studies on hydraulic-seal materials andconstitutive laws

Elastomers suit hydraulic seal applications because oftheir resilience. They accept large tensile, compres-sive, and shear strains without permanent deforma-tion, which is perfect for fitting in different housingsand adapting to pressure variations. This is owedto their low elastic and shear moduli, as well asincompressibility (Poisson’s ratio very close to 0.5,normally >0.490). However, their mechanical prop-erties strongly depend on temperature, the imposedstrain and strain rate, and change in time as theyage. Their Young’s modulus often exhibits up to twoorders of magnitude change when the temperature




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Fig. 5 Stress–strain curves of an elastomer used inhydraulic reciprocating seals, with glass transi-tion temperature of −47 ◦C (see, for example,references [1], [89], [94], [98], and [99])

is changed between positive and sub-zero values [98,99], and is different in tension than in compression(see Fig. 5). The stiffening of elastomers with droppingtemperature is maximized near the glass transitiontemperature (usually between 0 and −70 ◦C, depend-ing on the particular material and signifying the tran-sition from the rubbery to the glassy state), wherepotentially irreversible structural changes ensue [100],which are characteristic of the molecular structure ofelastomers. This fact, in combination with the typi-cally high thermal expansion coefficient of elastomers(10−4 − 3 × 10−4 K−1 [95]) implying large dimensionalchanges with temperature, is critical in aerospaceapplications and can cause sealing failure from lossof contact pressure at low temperatures [1, 4, 94], themost dramatic example of which was the destructionof the NASA space shuttle Challenger in 1986 [1, 5, 94].Dimensional changes of hydraulic seals in the formof swelling are also met in cases where porous sealsabsorb hydraulic fluid.

Further complications in the modelling of elastomermechanics arise by the elastomer not following thesame stress–strain path in loading/unloading (hys-teresis) and by responding to load depending on themagnitude of past acquired strain (memory). Suchnon-linear effects are stronger at temperatures nearor lower than the glass transition temperature andbecome apparent when seals remain stationary (set)for long periods of time. The latter leads to seals adher-ing to their metallic counterfaces and having high fric-tion during the starting up of motion (see, for example,the transient frictional behaviour of the rotary vaneseals in reference [4]; see also the study of Gibsonet al. [101]). It also causes stick-slip and vibration,which is reduced by anti-extrusion rings (Fig. 2) or,practically, avoided by using thermoplastics instead of

elastomers (e.g. the glyd rings in Fig. 1) or twin-lippedseals (Fig. 1), naturally retaining lubricant betweentheir lips and avoiding adhesion. In addition, elas-tomer ageing [102] from oxidation, which is, naturally,faster at higher temperatures, and (sometimes) chem-ical degradation from incompatible hydraulic fluids,cause material hardening and, eventually, embrittle-ment and fragmentation. In fact, rubber ageing hasbeen found to reduce friction and increase abrasivewear in lubricated conditions [102].

A realistic description of the thermomechanics ofelastomeric materials [60] such as those used for recip-rocating seals is based on the statistical–molecularor network theory of rubber elasticity [6], which isquite old but has passed the test of time. According tothe theory, elastomers are compounds of chemicallycross-linked macro-molecules (see section 1.5 in ref-erence [100]), which create a three-dimensional net-work. The macro-molecules (long molecular chains)are folded, kinked, and of three types: linear, branched,and cross-linked. The linear chains move easily recip-rocally, giving elastomers the characteristic softeningwhen heated or stiffening when cooled. The cross-linked chains however resist reciprocal motion, givingelastomers resistance to flow when heated. Ther-mally agitated atoms from said macro-molecules canassume a variety of statistically determined confor-mations [103] (hence the ‘statistical-molecular’ titleof the theory), allowing for continuous variation ofthe free space between the molecular chains. Thisneatly explains the extensibility of elastomers at tem-peratures higher than the glass transition temperatureand their stiffening at temperatures close to or belowthe glass transition temperature when the transientchain motion is slowed down or almost ceases, makingelastomers behave like brittle solids.

Although in a few reciprocating-seal modellingstudies the elastomer mechanics have been mod-elled in the frame of viscoelasticity (e.g. by using ageneralized Maxwell model), nearly all other pub-lished studies have been based on the linear theory ofelasticity. However, according to the present author’swork [89, 98, 99] on comparing the linear and themost popular non-linear (Mooney–Rivlin) model inreciprocating seals at temperatures between −54 and+135 ◦C, the linear theory of elasticity in reciprocat-ing elastomeric seals is adequate for maximum sealstrains up to 10 per cent; above that limit, models offinite elasticity should, ideally, be employed to givemore accurate leakage and friction results.

The most popular phenomenological models onrubber hyperelasticity can be found in some booksdealing with finite elasticity such as Holzapfel’s book[104]. A lot of related material can be found in reviews[60, 103, 105–107], among which the papers of Treloar[103] in 1976 and Ogden [107] in 1986 (both pioneersin rubber thermoelasticity) are of lasting value. Themodels usually deal with incompressible, hyperelastic





(rubber-like) materials and express the mechanicalproperties in terms of the energy function. Specifi-cally, the elastic strain energy per unit volume, W , isexpressed as a function of the three strain invariants,that is W = W (I1, I2, I3), where

I1 = λ21 + λ2

2 + λ23

I2 = (λ1λ2)2 + (λ2λ3)

2 + (λ3λ1)2

I3 = (λ1λ2λ3)2

⎫⎪⎬⎪⎭ (1)

where λi (i = 1, 2, 3) stands for principal stretch (ratioof deformed to reference length). In the Ogden model[108–110] in particular, the strain function is

W =N∑

n=1

µn

αn

(λ

αn1 + λ

αn2 + λ

αn3 − 3

)(2)

where µn and αn (n = 1, 2, . . ., N ) are constant shearmoduli and dimensionless constants, respectively,which are experimentally derived (for typical valuesof these constants, see p. 236 in reference [104]).Additionally, for incompressible materials, λ1λ2λ3 = 1.According to Holzapfel (p. 239 in reference [104]),Ogden’s model for N = 3 (equation (2)) excellentlyreplicates the finite-strain behaviour of rubber-likematerials as proved in references [108] and [111] to[114] among others. However, it should be empha-sized that the difference between Ogden’s model andother phenomenological models becomes apparentonly at high stretches. Based on the present author’sresearch (for example, see references [89], [98]), and[99]), typical polymeric reciprocating seals are usu-ally not strained >15 per cent during operation.This normally justifies the use of the classic linear(Hookean) theory of elasticity [98], which, moreover,is capable of directly accounting for thermal strains,a feature absent from the popular non-linear modelsunless approximately (not rigorously) introduced aswas done by the present author in references [89], [98],[99], and [115] to [117] with a modified Mooney–Rivlinmodel.

Despite the effectiveness of Ogden’s model, theMooney–Rivlin model based on the pioneering workof Mooney [118] in 1940 and Rivlin [119] in 1948 onfinite isotropic elasticity is the most popular, followedby the simpler Neo–Hookean model. In fact, the afore-mentioned models can be derived from Ogden’s model(equation (2)) by setting (N = 2, α1 = 2, α2 = −2) forthe Mooney–Rivlin model and (N = 1, α1 = 2) forthe Neo–Hookean model. Several other constitutiveapproaches for incompressible, rubber-like materialssuch as the Varga model [120] can be found in the lit-erature and some are readily available to use in finite-element commercial software but the Ogden modelwith N = 3 in equation (1), the Mooney–Rivlin, and theNeo–Hookean model, as summarized in equation (3),are met most often and, in this author’s research expe-rience, are deemed sufficient in reciprocating seals,

with preference to the first two

Ogden : W =3∑

n=1

µn

αn

(λ

αn1 + λ

αn2 + λ

αn3 − 3

)

Mooney−Rivlin : W = µ1

2(I1 − 3) − µ2

2(I2 − 3)

Neo−Hookean : W = µ1

2(I1 − 3)

⎫⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎭(3)

Having decided which constitutive model to use, theCauchy (true) principal stresses are given by [104]

σi = λi∂W∂λi

− pc (i = 1, 2, 3) (4)

where pc is a hydrostatic pressure, calculated fromequilibrium equations and boundary conditions (fordetails, see references [1] and [98]). For the Mooney–Rivlin model, a standard engineering stress–straintest of the material in question at the temperatureof interest suffices to derive the necessary constants[98]. Nevertheless, in lack of such results, a reason-able approximation to use is µ1 = −4µ2 (see pp. 7–33in reference [121]). Combining the latter with thecondition of consistency between the Mooney–Rivlinand the classic linear (Hookean) model, expressed byG = µ1 − µ2 (see equation (6.120) in reference [104])where G = E/(2 + 2ν) is the shear modulus with Ebeing the Young’s modulus and ν the Poisson’s ratio,and taking ν = 0.5 for incompressible materials, thefollowing approximation is obtained: µ1

∼= 4E/15 andµ2

∼= −E/15.The phenomenological models discussed thus far

refer to rubber-like materials and are suitable forpolymeric reciprocating seals. The basic mechanicsanalysis of such seals, consisting of calculating thethree principal stresses for known strains by equation(4), is sufficient when the seals are of simple shapesuch as rectangular. As far as the author is aware (year:2008), it is surprising that there are no publicationsin the literature utilizing the non-linear models inreciprocating seals and all rely on the linear model,except those of the present author [98, 99, 115–117]. Incases of seal shapes other than simple, e.g. step seals,U-cups, and so on (Fig. 1), a simple mechanics analy-sis is unfeasible. In the latter case, the finite-elementmethod has been utilized, which readily allows theuse of non-linear models, even those that incorporatethermal and compressibility effects. Unfortunately,there are several other properties of rubber-like mat-erials, particularly those filler- or particle-reinforcedcomposites, which make their mechanical analysiseven with commercial finite-element software prob-lematic. Those properties include stress softeningin cyclic loading (Mullins effect), strain stiffeningat large stretch, load-frequency-dependent response,temporal softening at high temperature because of




10 G K Nikas

scission of molecular cross-links that can even causepermanent set of the material, and so on. Some con-stitutive models have been developed to deal withsome of the said effects as in references [122] to [126].However, their applicability may be limited to veryspecific cases and they always require experimentalverification.

Even though the majority of published studies dealwith elastomeric seals, some studies have includedPTFE, UHMWPE, polyurethanes, and composite seals.The main benefits of these materials over elastomersare their increased wear resistance, avoidance of stick-slip motion and extrusion, lower friction, and broaderoperating-temperature range. Zhang’s review [127] onpolymer tribology and related book [100] (ch. 16)comprise an excellent source of reference.

PTFE in particular has been used in hydraulic seal-ing since the 1950s [128–132]. It is a thermoplasticbetter known for its low-friction properties. It has avery high resistance to ageing [129] and may be usedin various compounds for temperatures in excess of250 ◦C [133], i.e. temperatures much higher than thoseallowed in elastomeric-seal applications. Its low fric-tional resistance, apart from its low surface energy, isalso attributed to surface porosity, which results ina small contact area. Moreover, in hydraulic recipro-cating seals, surface pores of PTFE act as lubricantpockets. This results in exceptionally low friction andavoidance of stick-slip and vibration, even after longperiods of inactivity or low stroking velocities. How-ever, the porosity may increase leakage. Moreover,the low stiffness of PTFE leads to accelerated wearbecause of delamination [134] when the material isrubbed against metallic surfaces such as piston rods.In fact, accelerated wear of the PTFE may occur evenwhen piston rods are made very smooth (e.g. superfinished), which results in polishing the PTFE dur-ing extended periods of sliding and in a significantincrease of friction. For these reasons, PTFE is nor-mally met in compounds and composites, e.g. filledwith bronze in coaxial seals [95], filled with stain-less steel, graphite, or glass fibres and elastomericcompounds as in rotary vane seals [4, 96, 135]. Unfor-tunately, PTFE in its various compounds is, mechani-cally, a very complex material, with different responsein tension and compression, whereas its Young’s mod-ulus, yield point, and Poisson’s ratio all greatly dependon its composition [136–138]. Li and Mays [135] haveeffectively demonstrated this complexity in their spe-cially adapted finite-element analysis of PTFE rotaryseals. Other materials used in hydraulic seals pose noless complexity and may only suit particular applica-tions. For example, UHMWPE cannot be used if theoperating temperature normally exceeds 80 ◦C [133].Thus, matching the seals to their intended use andoperating environment is the first priority in seal selec-tion, as is realized by studying product catalogues ofseal manufactures [2, 3].

3.2 Studies on hydraulic-seal mechanics andelastohydrodynamics

As is realized from section 3.1, the mechanical analysisof hydraulic seals is a complicated task. The com-plexity of the available phenomenological models forrubber-like materials precludes (even approximate)analytical solutions in the solid mechanics of hydraulicreciprocating seals in all but the simplest geome-tries such as rectangular. This trend is clear in allrelated literature studies. The older studies resorted toeither approximate analytical solutions for very sim-ple geometries or numerical solutions for seal shapesother than rectangular, yet still rather simple (e.g.toroidal). Moreover, they all used the linear theory ofelasticity or elementary stress analysis to resolve sealstresses and strains in the context of solid mechan-ics. In most recent studies (after the year 2004 or so),commercial finite-element software has been used todeal with complex geometries such as for step andU-cup seals.

The simple, approximate analytical solutions ofolder studies remain valuable as they provide muchclearer understanding of the sealing mechanisms andways to optimize seals. In chronological order, most ofthe significant contributions in this field can be foundin the publications of Hooke et al. [32, 43] (rubberO-rings), Johannesson [34] (rubber O-rings), Drag-oni and Strozzi [139] (rubber O-rings), Field and Nau[31] (perfectly rectangular rubber seals), Strozzi [68](rectangular-rounded, elastomeric seals), Johannes-son and Kassfeldt [140] (elastomeric seals of arbitrarycross-section), Nikas [89, 98, 99, 115–117, 141–143](rectangular-rounded elastomeric seals), Nikas andSayles [97] (rectangular-rounded composite seals),and Nikas [4, 96] (rectangular-rounded, composite,and rotary vane seals in alternating rotation). Inthe aforementioned studies, the contact pressure ata sealing contact is calculated by either assumingplane-strains conditions or via an elementary stressanalysis with strains calculated from the amount ofsurface interference. Shear from contact friction isusually neglected, although shear stresses inside aseal’s body can be taken into account – see for exam-ple Nikas [141]. Simple analytical studies have alsobeen conducted by Karaszkiewicz [144] on O-ringsand composite seals with O-ring and PTFE parts [145].

For seal shapes other than rectangular and/or whennumerical accuracy is of priority, the finite-elementmethod is used [46, 52, 68, 70, 82, 146–160]. A reviewof this method for the period 1976–2003 on rubber-like materials with an extensive bibliography can befound in reference [161]. Various types of hydraulicseals have been analysed with this method includingrectangular with rounded or chamfered ends [46, 52,68, 147, 154, 156], O-rings [147, 149, 156, 158], X-rings[148], U-cups [150, 151, 153, 155, 157, 159, 160], andstep seals [160].





Naturally, the main goal of theoretical models isto evaluate sealing performance in terms of leakageand friction. This requires accounting for the sealed-fluid effect at a sealing contact, which the previouslymentioned computation of the pressure distributionis only a part of. It is established experimentally andtheoretically [1] that a lubricating film of nanometreto micrometre thickness is present at a sealing con-tact under reciprocating conditions. The calculationof that film thickness and its distribution in a contactis based on the theory of elastohydrodynamic lubri-cation [162], which is essentially represented by theReynolds equation in its various forms, depending onapplication. Reciprocating seals are normally axisym-metric, which means that leakage takes place alongthe seal axis of symmetry. Thus, the one-dimensionalform of the Reynolds equation has been employed inalmost all studies [143]

∂

∂x

(ρh3

η

∂p∂x

)= 6V

∂(ρh)

∂x+ 12

∂(ρh)

∂t(5)

where p = p(x, t) and h = h(x, t) are the local pres-sure and the local film thickness at the sealing contact,respectively, V is the sum of the tangential velocitiesof the contact counterfaces, ρ = ρ(p) and η = η(p) arethe local mass density and the local dynamic viscos-ity of the sealed fluid at the sealing contact for a givenoperating temperature, respectively, and t stands fortime. A more general, two-dimensional (2D) form ofthe Reynolds equation was used by Nikas [89, 141]and in subsequent publications [98, 99, 115–117] deal-ing with various issues of reciprocating seals, becausethe intention was to account for fluid transporta-tion between roughness asperities transversely to thedirection of motion in an attempt to improve accuracyin leakage calculations. However, this adds complex-ity to the solution process and is, generally, not reallynecessary.

The usual simplification of equation (5) is to ignorethe last term ∂(ρh)/∂t dealing with transient effectsand, thus, treat the lubrication problem for steady-state conditions only. This is applicable only whenthe stroking length is significantly greater than twicethe sealing-contact size and, additionally, both thebeginning and the ending of strokes are ignored. Theremaining Reynolds equation can be solved numer-ically either for film-thickness or for the contact-pressure distribution with appropriate kinematicaland boundary conditions, e.g. the no-slip and thecavitation conditions [143].

The early solutions of the Reynolds equation forreciprocating seals were based on assumed film thick-ness and/or measured contact pressure distributions.For example, White and Denny [9] calculated filmthickness by assuming a tapered film profile and aparabolic pressure distribution. Müller [22] used mea-sured contact pressure distributions and a tapered film

profile, which was different between outstrokes andinstrokes. In fact, the Reynolds equation is normallysolved for the film thickness h because the contactpressure is calculated from a solid-mechanics analy-sis as if the contact were dry. The latter is fully justified[143] by the thinness of typical fluid films in recipro-cating seals, which imposes a radial strain negligiblysmall in comparison with the normal strains from sealinterferences and loading.

The fact that the contact pressure can be con-sidered known has been taken advantage of in theliterature in the so-called inverse hydrodynamic (IH)theory [163]. According to that theory, the Reynoldsequation (5) is developed to a cubic algebraic equationfor the film thickness [162]. However, the applica-tion of this method to elastomeric reciprocating sealsmet numerical obstacles caused by the flexibility ofthe seals. Specifically, in calculating the roots of thecubic polynomial, imaginary roots should be correctlyidentified and resolved, otherwise numerical instabil-ity will quickly destroy the convergence to the correctsolution [37, 40]. Nevertheless, the method has beenextensively applied [30, 32, 33, 35, 36, 38–41, 43, 52,71, 72, 164–166].

A modified version of the IH theory was developedby Nikas [143] and applied in elastomeric and com-posite rod and rotary-vane seals in references [4], [96],[97], and [143] for reciprocating motion in curvedcontact geometries, including transient effects [4, 96].Instead of analytically solving the cubic polynomial ofthe film thickness, the following first-order, ordinarydifferential equation was derived [143]

dHdx

= H 3d2q/dx2

6V − 3H 2dq/dx(6)

where H ≡ ρh and dq/dx ≡ (dp/dx)/(ηρ2). An inletboundary condition was applied [143] (and an addi-tional initial condition in the case of transient analysis[4]). Equation (6) was then solved with a robust numer-ical method, which allowed great numerical stabilityand consistency with sub-nanometre precision in thefilm thickness [96, 97, 143], as well as extremely fast(practically instantaneous) computation.

Apart from the IH method, other numerical meth-ods have also been applied, e.g. the Runge–Kuttamethod [167] and the Petrov–Galerkin method [168].These are iterative methods and vary in complexity.The simplest or most direct ones are those that derivethe contact pressure from an elementary stress anal-ysis of the seal and solve the Reynolds equation forthe film thickness iteratively, until the contact pres-sure and film thickness are in agreement. The study ofField and Nau [31] is representative of this methodol-ogy. However, it is also characteristic of the numericalinstability of the method, which is reflected on the slownumerical convergence rate, the wavy pressure andfilm thickness results, and the inability to derive results




12 G K Nikas

for instrokes [31]. The cause of instability is the sensi-tivity of pressure to film thickness variations, which ischaracteristic of the high non-linearity of the Reynoldsequation. Nevertheless, similar direct approaches canbe found in other studies [71, 141, 167].

In a series of papers [98, 99, 115–117, 141] that dealtwith the 2D form of the Reynolds equation for rod sealsthat included surface roughness effects [141], Nikastackled the instability problem of the ‘direct approach’by separating the effect of pressure ripples created bythe roughness asperities from the bulk contact pres-sure. The bulk contact pressure was left out of theconvergence iterations and only the perturbations ofthe roughness asperities were included.

Continuing with the simpler methodologies in solv-ing the Reynolds equation for reciprocating seals,the efficient techniques of Hooke on soft lubricatedcontacts [169–171] that dealt with the elastohydrody-namic inlet and exit zones provide a useful insight intothe lubrication problem. His work is particularly rel-evant in reciprocating seals because the average filmthickness in the contact is almost completely governedby the conditions at the inlet zone [143]. This is ofmajor importance in both leakage and friction, as wellas during the reversal of the entrainment velocity (endof stroke and reversal of motion in reciprocating seals).The latter causes film thinning [172] and increased sealwear, as has been verified experimentally in severalstudies (for example, see references [62] and [86]).

A method to avoid much of the numerical instabilityfrom the inherent coupling between contact pres-sure and film thickness in the Reynolds equation wasdeveloped by Ruskell [46]. It was applied to rectangu-lar rubber seals with chamfered ends under steady-state conditions and for perfectly smooth contacts.Ruskell adapted the numerical technique developedby Rohde and Oh [173, 174] who used a Newton iter-ation scheme. In Ruskell’s work [46], the elasticityequation of the seal and the Reynolds equation werecombined into a single integrodifferential equation,which was solved iteratively. Thus, convergence wasfast and consistent because the reciprocation betweenthe separate contact pressure and film thickness equa-tions to correct one with the predictions of the otherwas avoided. However, Ruskell’s method still lackedoutright computational speed because the contactpressure had to be calculated separately (for a static,frictionless contact) by a (naturally) time-consumingfinite-element analysis. Prati and Strozzi [72] used asimilar method.

In recent years (2006–2008), some more sophisti-cated numerical methods were developed to tacklethe steady-state elastohydrodynamic problem ofhydraulic seals of various shapes. In the studies ofSalant, Maser, and Yang [153, 155, 157, 159, 160, 175],which are essentially based on the thesis of Maser [153]and built on past research experience of Salant andco-workers on rotary seals, inter-asperity cavitation is

incorporated into the Reynolds equation to deal withrough contacts. So far, only the seal surface roughnesshas been considered; the other contact counterfacehas been assumed to be perfectly smooth. Surfaceroughness is treated approximately in the context ofthe Greenwood–Williamson model [176], i.e. it is sim-ulated, idealized roughness. Finite-element analysishas been used to compute the contact pressure ofthe seals in dry, static contact, which gives freedom indealing with complex seal shapes and utilizing modelsof finite elasticity.

The main deficiency of previous studies is that the‘coupled’ elastohydrodynamic problem has not beentackled, i.e. the deformation of the seals from frictionin the sealing contacts is unaccounted. This meansthat the contact pressure is calculated for station-ary contact counterfaces. However, in hydraulic seals,normally, the motion of a counterface deflects theseal because of contact friction and, thus, changesthe pressure distribution at the contact inlet. This, inturn, affects the development of the hydrodynamicfilm and, consequently, the average film thickness andfriction in the contact. The coupling between pres-sure and film thickness or between stroking velocityand contact friction needs to be resolved iteratively.If this is not done, the sealing performance is essen-tially evaluated only for unrealistic, idealized (static)conditions. From a computational-fluid-dynamics orfinite-element point of view, the said coupling istreated with the so-called fluid–structure interaction.A couple of recent studies began to address this prob-lem for simple seal geometries, namely the study ofÖngün et al. [158] on O-rings, and Stupkiewicz andMarciniszyn [156] on rectangular seals and O-rings.Needless to say that such studies are complicated andstill deal with steady-state conditions, i.e. they areapplicable only for very long strokes.

3.3 Transient lubrication effects

In reality, reciprocating seals exhibit clearly transientbehaviour, particularly at the ends of strokes andduring the reversal of the entrainment velocity. Thetransient elastohydrodynamic problem in reciproca-ting seals, as expressed by equation (5), has beentheoretically studied in around 1970 by Hirano andKaneta [36, 38] for idealized parabolic and Gaussiancontact-pressure distributions. Their work confirmednumerous experimental observations (for example,see reference [27]) regarding the importance of theratio of the stroking length to the contact width inthe development of a full elastohydrodynamic film. Asalready explained, the said ratio must exceed two if itis to allow sealed fluid, which is normally dragged athalf the sliding velocity of the contact, to travel fromthe contact inlet to the outlet.

The value of a transient analysis is obvious whendealing with seal friction, which is greatly affected by





minute changes (in the order of nanometres) in theaverage film thickness in the contact. Obviously, wearis also significantly affected [62]. In fact, squeeze-filmcollapse during long periods of inactivity or duringthe reversal of entrainment motion can cause fric-tion so high that seals may be rearranged in theirhousings and subsequently fail. The experimentalstudy of Nwagboso [177] on elastomeric-seal rollingis characteristic in this respect.

As far as the author is aware (year: 2008), veryfew other studies have so far dealt with solving thetransient elastohydrodynamic lubrication problem inreciprocating seals, namely his own [4, 89, 96, 117].The problem belongs to the category of ‘soft elas-tohydrodynamics’ in which there are several generalstudies in the literature (for example, see references[178] and [179]). A simple approach, dealing withthe transient elastohydrodynamics of compliant solids(which could be applied to reciprocating seals), was

presented by Ikeuchi et al. [180]. In fact, the solu-tion of the transient problem may be simplified byignoring the left-hand side of equation (5). The result-ing reduced equation is merely a classic, first-orderdifferential equation of wave propagation. The latterapproach has been verified by Chang [181]. It hasalso been applied by the present author in recipro-cating, rotary vane seals [4, 96] as a means of fastcomputations in parametric analyses.

3.4 Surface-roughness effects

Apart from transient effects, there are other aspects ofreciprocating seals that have not been given significantemphasis in theoretical studies. Surface roughness isone of those neglected aspects, except in the previ-ously discussed studies of Salant, Maser, Yang, andNikas. It is worth mentioning that, according to thework of Salant and his co-workers (for example, see

Fig. 6 Examples of film thickness maps at the sealing contacts of rectangular, elastomeric rodseals. (a) Theoretical [141] and (b) experimental [62, 91]: (a) film thickness contour mapsof a rectangular, elastomeric rod seal, showing film collapse (left to right) as the sealedpressure is reduced from 27.7 to 0.07 MPa. Patches of direct contact are seen to increase fromleft to right (from the theoretical work of Nikas [141]), and (b) contact interface betweena rectangular, elastomeric rod seal and glass. High-pressure side is on the left side of bothimages. Sealed pressure: 0.69 MPa on the left with moving rod and less than 0.34 MPa on theright image with stationary rod (from the experimental work of Rana [62, 91])




14 G K Nikas

reference [155]), a critical value of average roughnessis predicted to be the limit between a leaking andnon-leaking seal, which, naturally, depends on theoperating conditions and seal geometry. It is also note-worthy that, according to the modelling work of Nikas[89, 141], reciprocating seals normally operate in themixed lubrication regime but roughness mainly affectsthe maximum and the minimum film thickness, notso much the average film thickness. Figure 6 showsthe theoretical predictions of Nikas [141] on the filmthickness distribution of a rectangular, elastomeric rodseal, and some related experimental results of Rana[62, 91] in accordance with the trend of the theoreti-cal predictions. It is characteristic that the lubricationof the seal is improved at higher sealed pressures aspredicted in reference [141] and verified in references[62] and [91]. A further discussion on the roughnesseffects can be found in section 4 of reference [143].Useful findings have also been reported in the exper-imental and theoretical work on rough, rectangular,elastomeric, and reciprocating seals by Kanters andVisscher [182], and Kanters [183]. In the latter study,Kanters used the average-flow model of Patir andCheng [184, 185] (as has been done by Salant and co-workers more recently) to analyse the effects of sealroughness on seal leakage and friction. He found thatwhen the ‘lambda ratio’ (defined as the central filmthickness for an ideally smooth contact divided by thecomposite RMS roughness of the real contacting sur-faces) is >4, a full hydrodynamic film is developed andseal roughness appears unsuppressed. When the ratiodrops below about 2, the seal operates in the mixedlubrication regime as roughness asperities are partiallybut not completely compressed and engage with thoseof the piston rod.

However, roughness modelling remains simplis-tic because several influential factors have yet tobe accounted, such as the transient elastohydrody-namic inter-asperity interactions, asperity viscoelas-ticity [186], and inter-asperity adhesive forces (suchas van der Waals forces) in mixed lubricated condi-tions [187, 188]. Such parameters should be addressedin order to simulate experimentally observed elas-tomeric seal behaviour including stick-slip phenom-ena [189] and instabilities in the transition betweendry and wet regimes [190], Schallamach waves [191,192], and abrasive wear [100, 127, 193, 194]. The workof Jalisi [195] on the contact mechanics of rough elas-tomeric contacts gives a good idea of a numericalapproach via finite-element analysis. Further insightis gained by the general studies of Jin and Dowson[196] and Kim et al. [197] on the modelling of soft andrough elastohydrodynamic contacts.

Nevertheless, the omission of surface roughnessin theoretical models as a first approximation maybe justified. This is so because elastomeric seals aresmoothened during running-in, even when rubbedagainst glass [62, 91]. Moreover, the typical contact

of dynamic seals is rarely in the state originally con-ceived and simulated: polymeric films from worn orrun-in polymers may be deposited onto hard metallicsurfaces, effectively creating a coating with roughnessdifferent from that of the hard substrate [198–200].

3.5 Other topics (seal extrusion, back-up rings,tandem seals)

There are extremely few studies in the literature thatdeal with specialized topics such as anti-extrusionrings and tandem seals. This is so because, untilrecently, the analysis and evaluation of reciprocating-seal performance was more empirical than scientific.However, such issues are known for decades.

White and Denny [8, 9] in the 1940s discussed sealextrusion as a factor causing seal damage and sealingfailure in the long run. Seal extrusion (Fig. 7) is thesqueezing of a part of a seal into a narrow clearancesuch as the clearance between a seal housing and thepiston rod in a linear hydraulic actuator. It is caused by

Fig. 7 Extrusion of a rectangular, elastomeric, rod seal(top picture). Shape of the extruded part andits contact pressure with the piston rod for twocorner radii of the seal (r = 0 and 0.2 mm) (bot-tom graph). Based on the analytical study ofNikas [142]





the sealed pressure (static extrusion) and the frictionof the seal on its counterface (e.g. a piston rod) duringoutstrokes (dynamic extrusion). When the localizedstrain at the extruded part is repeated hundreds orthousands of times in normal reciprocating motion,permanent deformation may occur, accompanied bysealing failure. The static and dynamic extrusion ofelastomeric seals have been studied by Reddy and Nau[84] in 1984.

Apart from experimental investigations on thecauses and effects of extrusion, an analytical solu-tion to the problem was presented by Nikas [89,142] for elastomeric, rectangular rounded or cham-fered, and reciprocating rod seals. The solution wasalso applied to rotary vane seals under alternatingrotation [4, 96]. In the aforementioned analyticalstudy [142], algebraic equations were derived pre-dicting the shape of the extruded part of a seal andthe pressure on it at its contact with its counterface(piston rod). Moreover, simple criteria in the formof algebraic inequalities were mathematically devel-oped, involving the parameters affecting extrusion andestablishing exactly when extrusion commences. Theconclusion was that the best way to avoid extrusion isto use anti-extrusion or back-up rings. Another poten-tial solution was later investigated by the author [97]and found to be viable, namely the replacement of agiven elastomeric seal with a composite seal of thesame dimensions, comprising a central elastomericpart bonded with two outer PTFE parts along thedirection of reciprocation. The elastomer-PTFE vol-umetric proportion was parametrically optimized toproduce a composite seal outperforming the origi-nal elastomeric seal in terms of leakage, friction, andextrusion resistance.

With regard to anti-extrusion rings (see for exam-ple the Polypac PHD seal in Fig. 1), they are used toprevent not only seal extrusion but also roll defor-mation [177]. However, they normally interfere withthe sealing of the supported seal. The author is notaware of any studies in the literature on the modellingof back-up rings except for his own modelling work[89, 116]. In the latter studies, which are computation-ally complicated, parametric analyses were conductedto quantify the effect of back-up rings of rectangularcross-section and relatively low stiffness on the sealingperformance of rectangular, elastomeric rod seals. Theoperating temperature was varied from −54 to +135 ◦Cand the sealed pressure from 1 to 35 MPa. Among someinteresting conclusions of the study was that the con-tact pressure and the average surface roughness ofthe back-up ring can be optimized to minimize theleakage-per-cycle of the seal–ring pair.

Another interesting topic in sealing research con-cerns the use of tandem (dual) seal arrangements(Fig. 8). Those consist of a primary seal, which doesthe major sealing job at the sealed-pressure side, anda secondary seal, which wipes off fluid leaking from the

Fig. 8 Tandem seal arrangement (top) and an exampleof its theoretical analysis (bottom diagram) show-ing the interseal-pressure abrupt rise after about1600 strokes (Nikas and Sayles [115])

primary seal and, also, prevents dirt ingression into thesystem in the absence of a scraping element.

The performance of tandem seals has been exper-imentally investigated in very few studies [80, 201–203]. All concluded that sealing is mainly controlledby the primary seal but it is influenced by the intersealpressure (Fig. 8) and, naturally, by the edge geometry ofboth seals at their low-pressure sides. Moreover, leak-age and friction are also influenced by any back-uprings present in the system [202]. Field and Nau [201,202] in the early 1970s discovered that in some tandemseal arrangements (mainly those of identical seals), anabrupt pressure rise in the interseal space takes placeafter a number of operating cycles. This is caused byleaked fluid flooding the interseal space. They foundthat this phenomenon can cause seal extrusion andeven complete failure of the system if the intersealpressure is not vented before abruptly exceeding thesealed pressure (see Fig. 4 in Field and Nau [201]).

The phenomenon of interseal-pressure rise hasbeen theoretically analysed by Nikas and Sayles [115]by accounting for a compressible mixture of air andleaked fluid in the interseal space, and using the vander Waals equation of state for air to simulate the




16 G K Nikas

temporal change of pressure with the leaking fluidand the number of strokes. A result of this simu-lation is shown in the bottom diagram of Fig. 8,which depicts the interseal pressure rise and inter-seal gas-volume reduction with the number of strokes.This way, the number of strokes before the pres-sure starts to peak is predictable. The simulation alsoincluded back-up rings on both elastomeric sealsin a complex, quasi-steady elastohydrodynamic andnon-linear mechanics analysis with surface rough-ness effects on all elements, followed by performanceanalysis in terms of leakage and friction for operatingtemperatures between −54 and +135 ◦C, and sealedpressure between nearly 0 and 35 MPa. The tandemseal arrangement showed clear benefits in terms ofleakage and friction and could be optimized for givenoperating conditions.

The phenomenon of the interseal pressure rise isalso met in twin-lipped seals. Kanzaki et al. [204]investigated this experimentally for sinusoidally recip-rocating motion. They found that the interlip pressureincreases with the sealed pressure and the oil trappedbetween the seal lips lubricated the seal, reducing fric-tion. This is a well-known benefit of twin-lipped seals[2] and the stored lubricant not only reduces frictionbut also prevents the seal from running dry (evenafter periods of inactivity), thus eliminating stick-slipmotion and vibrations [94]. The operation of scrapingelements [205] should also be seen under the samelight and as influential of the overall performance of asealing system.

4 EXPERIENCE GAINED FROM SEALINGRESEARCH AND THE FUTURE

The knowledge and experience gained from pastresearch on hydraulic reciprocating seals has ben-efited the sealing industry immensely. The topicsdiscussed in the previous sections covered the fun-damental aspects of sealing performance, i.e. leakage,friction, and wear. It was shown that seals can beoptimized to offer better sealing performance withincreased reliability and longer service lives. This con-cerns both existing seal designs and new, innovativedesigns for future applications.

With regard to existing seal designs (shapes), pastresearch has proved the value of paying attention todetails. Some examples are listed next.

1. The values of surface-roughness parameters suchas the average and the RMS roughness are critical inachieving zero leakage under given operating con-ditions. An ‘optimal’ seal roughness value exists andit should be targeted to produce non-leaking seals,at least in the first half of a seal’s life.

2. The effect of temperature on sealing performance ismajor. Seal preloading has to take this into account

to avoid a sealing failure at low temperatures, e.g.in aerospace applications.

3. Seal extrusion is a problem, which can and shouldbe avoided. Anti-extrusion rings (separate or inte-gral to the seals), composite (e.g. elastomeric/PTFE-glass-fibre), and multi-component seals (e.g.the polypac PHD seal in Fig. 1) have been designedto avoid this problem based on past experience andresearch.

4. The corner geometry of reciprocating seals at seal-ing contacts has the greatest influence on leak-age, friction, and wear. Experimental research andexperience had already shown how this couldbe improved before theoretical research showedmathematically that the corner geometry can beoptimized. See for example the application of thisresearch in the design of the step seal and thetwin-lipped U-cup seal in Fig. 1.

5. Seal materials have improved as a result of exper-imental research. Material properties such as stiff-ness, hardness, and general stress–strain mechani-cal behaviour have been under scrutiny in order toproduce seals that suit particular applications, i.e.specific range of operating conditions.

6. As a final but probably most convincing example ofthe gain from applied research is the evolution ofseal design based on tribological and mechanicalprinciples learned from research and experience.The seals depicted in Fig. 1, particularly the left-bottom two, utilize a number of innovations such asanti-extrusion rings, energizing O-rings, compos-ite materials for low-friction and high-wear rate,and asymmetrical corner geometry optimizationsto minimize leakage. Such innovations are notproducts of imagination but of applied research.

With regard to future seal design, it can be pre-dicted that this will be a matter of optimizing existingdesigns and selecting the best seal for a given appli-cation based on end-user requirements. For example,different or conflicting requirements would be min-imum leakage, minimum friction, and/or minimumwear. Unfortunately, scientific research has shown thatthe aforementioned constraints cannot be simultane-ously satisfied. There will always be a compromisebetween leakage, friction, and wear. It is a matter ofend-user priorities which one performance variableshould be optimized. This is exactly where advancedtheoretical research comes hand-in-hand with pastindustrial experience to solve a problem, which is byall means, very complex. The days of empirical solu-tions in sealing research are numbered because thecompetition is stiff and customers are intolerable (andrightly so) to sealing partial or total failures. There-fore, sealing research will continue on a more scientificbasis, taking advantage of improved computing equip-ment and numerical models capable of more realisticpredictions.





The fields where research is lagging and is moreurgently needed include those of surfacial (e.g.abrasive) wear of reciprocating seals, and estimationof life expectancy. Ideally, the latter should be in theform of a performance-degradation curve depictingthe temporal reduction of sealing ability (e.g. increaseof leakage in time). Given the complexity of seal designand countless performance issues, it would be opti-mistic to expect a reliable lifetime prediction methodsuch as that adopted in, e.g. the rolling-bearings indus-try. Nevertheless, some form of prediction methodmay, eventually, be developed, even if it is restrictedto very specific operating conditions. In pursuit of thistarget, engineers may have to rely, once again, on semi-empirical methods. In this authors’ experience, sealingresearch has still a long way to go.

5 CONCLUSIONS

After 80 years of scientific research and developmenton reciprocating hydraulic seals, the main perfor-mance issues have been identified and relatively wellunderstood. Nevertheless, flexible hydraulic seals areelements of complex mechanical behaviour and pre-dicting their performance in real (variable) operatingconditions with satisfactory precision is a very chal-lenging task. A significant amount of work remains tobe done on the modelling front to produce realistic andreliable computational models of the seal mechanicsand tribology, not suitable for the average user yet (thisis rather ambitious) but for the engineer who wants todesign or optimize such seals. Experiments performedover a period of decades as well as practical experiencesuggest that there are many parameters that have to beaccounted for in order to have a good understanding ofsealing performance. Engineering errors such as thatwhich led to the destruction of the NASA space shuttleChallenger in 1986 should not be repeated.

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APPENDIX

Notation

E modulus of elasticityG shear modulush local film thicknessH auxiliary variable, H ≡ ρhI1, I2, I3 strain invariants (equation (1))

p local pressurepc hydrostatic pressureq auxiliary variable defined implicitly by

dq/dx ≡ (dp/dx)/(ηρ2)

t timeV sum of the tangential velocities of the

contact counterfacesW elastic strain energy per unit volumex axial coordinate

α1, α2, α3 dimensionless constantsη local dynamic viscosityλ1, λ2, λ3 principal stretchesµ1, µ2, µ3 shear moduliρ local mass-densityσ1, σ2, σ3 Cauchy principal stresses

(equation (4))




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