ON THE LUBRICATION OF MECHANICAL FACE SEALS

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ON THE LUBRICATION OF

MECHANICAL FACE SEALS

Harald Lubbinge

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The research project was sponsored by Flowserve B.V.

and was carried out at the University of Twente.

ISBN: 90-3651240-9

Printed by FEBO druk B.V., Enschede Copyright c 1999 by H. Lubbinge, Enschede

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ON THE LUBRICATION OF MECHANICAL FACE SEALS

PROEFSCHRIFT

ter verkrijging van

de graad van doctor aan de Universiteit Twente, op gezag van de rector magnificus,

prof.dr. F.A. van Vught,

volgens besluit van het College voor Promoties in het openbaar te verdedigen

op vrijdag 15 januari 1999 te 15.00 uur

door Hans Lubbinge geboren op 9 juni 1971

te Giethoorn

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Dit proefschrift is goedgekeurd door:

Promotor: Prof.ir. A.W.J. de Gee Assistent–promotor: Dr.ir. D.J. Schipper

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voor Tineke

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ACKNOWLEDGEMENTS

This research is sponsored by Flowserve B.V., which is gratefully acknowl- edged.

I would like to thank the members of the tribology group, who created a pleasant work environment during the last four years: Ton de Gee, Johan Ligterink, Hans Moes, Wijtze ten Napel, Dik Schipper, Kees Venner, Laurens de Boer, Willy Kerver, Walter Lette, Erik de Vries, Jan Bos, Bernd Brogle, Rob Cuperus, Edwin Gelinck, Rudi ter Haar, Qiang Liu, Henk Metselaar, Elmer Mulder, Dani¨el van Odyck, Patrick Pirson, Matthijn de Rooij, Jan Willem Sloetjes, Ronald van der Stegen, Harm Visscher, Andr´e Westeneng and Ysbrand Wijnant.

Special thanks are deserved by:

Ton de Gee, my promotor, for his valuable contribution to this thesis. Edwin Gelinck, who was my roommate during the last 2 years, for the many useful discussions and suggestions. From Flowserve, Jan Keijer, Seb Bakx, Jan van der Velden and Erik Roosch for the discussions and their support. The employees of Flowserve in Dortmund for lapping and measuring seal faces. Gerrit van der Bult, Willie Olthof and Willie Kerver for making parts for the test rig.

From the Philips laboratories, Bram Pepers and Cor Adema, who accurately prepared the seal faces for testing. Arie de Jong of the Netherlands Foundation for Research in Astronomy for the interference microscope measurements. The employees of the IMC, who made some specific parts of the test rig. Gerben te Riet o.g. Scholten of the former AID, who did a great job with respect to the electronics of the test rig. Laurens de Boer and Erik de Vries for their technical assistance concerning the test rig. Ieke van Gaalen and Peter Wijlhuizen, who worked on my project for their MSc. degree and delivered a significant contribution to my thesis. Marcel de Boer for his help with the design of the test rig. The ladies of the secretariat, Debbie Vrieze, Annemarie Teunissen and Carolien Post for their administrative assistance. Katrina Emmett for her help concerning the English language. Lieselot IJsendoorn for her contribution to the design of the cover.

I especially thank my mentor Dik Schipper, for his stimulating discussions,

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ii Acknowledgements

comments on this thesis and, moreover, his optimism and great support.

Laurens and Erik are also thanked for their assistance as paranimf.

Although he cannot read this, Bob is also thanked, because of his pleasant company during the weekends and the evenings at the university.

I thank my parents for their encouragement and support.

Finally, I thank my girl-friend Tineke for being my best friend, for her love and patience.

Harald Lubbinge Enschede, January 1999

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SAMENVATTING

Om de lekkage van een mechanische asafdichting te minimaliseren, als gevolg van de steeds strenger wordende milieu eisen, dient de separatie zo klein mo- gelijk te zijn. Als gevolg hiervan zal zowel de wrijving (vermogens verlies) als de slijtage (verkorte levensduur) toenemen.

Er dient dus gezocht te worden naar een operationele conditie waarbij de slijtage en de wrijving aanvaardbaar zijn, en de lekkage tot een minimum wordt gebracht. Wanneer gekeken wordt naar de Stribeck curve, waarin de wrijv- ingscoëfficient wordt uitgezet tegen bijvoorbeeld de snelheid of één of ander smeringskental, zijn er drie smeringsregimes te onderscheiden. Dat zijn het grensgesmeerde regime, het gemengde smeringsregime en het hydrodynamisch gesmeerde regime. Grensgesmeerd zou ideaal zijn voor een minimale lekkage, maar is echter niet geschikt met betrekking tot de wrijving en slijtage. Daar- entegen bestaat er onder in het gemengde smeringsregime, in het gebied van de overgang van hydrodynamisch naar gemengd gesmeerd, een situatie die wel geschikt is. Hier is namelijk de separatie klein, zodat de lekkage relatief laag is. Daarnaast zijn zowel de slijtage als de wrijvingscoefficient laag.

In de literatuur bestaan er verschillende modellen die de filmdikte in een mechanische asafdichting bepalen. Een nadeel van deze modellen is dat meestal uitsluitend naar de hydrostatische druk component van de af te dichten vloeistof wordt gekeken, terwijl vaak, zo niet altijd, een hydrodynamische component aanwezig is. De hydrostatische druk component wordt bepaald door de mate van coning die er zich op de afdichting bevindt. Het resultaat van een dergelijk model is dat het theoretisch voorspelde gedrag niet overeenkomt met de prak- tijk situatie.

Vaak bevinden er zich op het contactoppervlak van een mechanische asafdichting een tweetal golven (waviness) in omtreksrichting. Deze ontstaan gedurende het voorbewerkingsproces, het vlakleppen van de afdichting. Maar ook tijdens bedrijf onstaan er tengevolge van slijtage, mechanische deformatie en thermis- che effecten, golven in omtreksrichting op het oppervlak. Dergelijke golven met amplitudes van enkele tienden van een micrometer, zijn voldoende om een aanzienlijke hydrodynamische vloeistofdruk te genereren, met als resultaat een grotere separatie en daarmee een hogere lekkage. Een gewenst effect van een dergelijke golving is dat, mocht de hydrostatische component falen om

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iv Samenvatting

´e´en of andere reden, deze golving kan blijven zorgen voor de nodige smering en vloeistofdruk in het contact. Een ander nadeel van de bestaande modellen is dat uitsluitend wordt gekeken naar volle film condities, terwijl juist, onder gemengde smeringscondities, tevens gekeken dient te worden naar een contactmodel.

In dit proefschrift wordt daarom een model gepresenteerd waarmee een volledige Stribeck curve voor een mechanische asafdichting berekend kan worden, en daarmee het overgangsgebied van volle film naar gemengde smering als functie van de operationele condities. Dit model is gebaseerd op de combinatie van een contact model met een filmvergelijking. In dit model, dat overigens isother- misch is, wordt rekenschap gehouden met onder andere de golving, coning, geometrie van de asafdichting, ruwheid, druk van de af te dichten vloeistof en belasting. Uit literatuuronderzoek bleek dat een filmvergelijking voor mechanische asafdichtingen, die ook rekening houdt met hydrodynamische effecten, niet bestond en deze is daarom ontwikkeld en in dit proefschrift beschreven.

Om gebruik te kunnen maken van het contactmodel, diende er een schatting gemaakt te worden van het nominale contactoppervlak. In dit proefschrift is, gebaseerd op numerieke berekeningen, een funktiefit gemaakt voor het nominale contactoppervlak als funktie van de amplitude van de golving, de coning hoek, de elasticiteitsmodulus en de belasting.

Tenslotte, om het model te verifi¨eren, is er een testopstelling ontworpen en gemaakt waarmee Stribeck curves aan mechanische asafdichtingen gemeten kunnen worden. Ook zijn er slijtagemetingen en belasting proeven uitgevo- erd. Slijtagemetingen om de veranderingen in de microgeometrie te kunnen analyseren, en belastingproeven om de belastbaarheid voor de wrijvingsexper- imenten vast te stellen.

Het wrijvingsmodel komt zeer goed overeen met de gemeten wrijvings curves.

Het effect van de operationele conditions, zoals de geometrie (ruwheid, coning en golving), druk van de af te dichten vloeistof en de belasting, op de transitie van volle film smering naar gemengde smering is geanalyseerd. Afhankelijk van de operationele condities, wordt de transitie van volle film smering naar gemengde smering sterk bepaald door onder andere de coning hoek, de belasting en de ruwheid en in mindere mate door de amplitude van de golving, de ruwheidsverdeling en de gereduceerde elasticiteits modulus.

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ABSTRACT

In order to minimize leakage of a mechanical face seal, due to environmental regulations, the separation between the faces should be as small as possible.

As a consequence, an increase of friction (power loss) and wear (reducing life time) occurs. Hence, an operational condition is sought for which wear and friction are acceptable, and, moreover, the leakage is minimized. Taking the Stribeck curve into consideration, in which the coefficient of friction is plotted as a function of the velocity or some lubrication parameter, three lubrication regimes can be distinguished. These are the boundary lubrication regime, the mixed lubrication regime and the hydrodynamic lubrication regime. Boundary lubrication would be the ideal regime regarding leakage, but it is not suitable with regard to friction and wear. In the lower region of the mixed lubrication regime, however, i.e. the transition region from hydrodynamic to mixed lubrication, a suitable operational situation exists. Here, the film thickness or separation is relatively small, and, therefore, the leakage is low. In addition, wear as well as friction are low.

In the literature, different models are described which calculate the film thickness in a mechanical face seal. Unfortunately, these models mostly only con- cern the hydrostatic fluid pressure, which is the result of the pressure of the fluid to be sealed, whereas often, if not always, a hydrodynamic component is also present. The hydrostatic pressure is determined by the amount of coning present on a seal face. The result of such a model is that the theoretically predicted behaviour does not correspond with the practical situation.

Often, a two-wave waviness exists on the circumference of a seal face. These waves develop during the preprocessing, i.e. flat lapping of the face, but also during seal operation when, as a result of wear, mechanical distortion and thermal effects, waves develop on the face circumference. Such waves with amplitudes of a few tenths of a micrometer, are enough to generate a consider- able hydrodynamic fluid pressure, resulting in a larger separation and, hence, a greater leakage. A desirable effect of waviness is that, when the hydrostatic component fails for some reason, lubrication and interfacial fluid pressure of the faces is maintained. Another disadvantage of such models is that they only strictly apply in the full film lubrication regime; for the mixed lubrication regime a contact model must also be incorporated.

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vi Abstract

Hence, in this thesis, a model is presented which is able to calculate a complete Stribeck curve for a mechanical face seal and, as a consequence, the transition from full film to mixed lubrication as a function of the operational conditions.

This model is based on a combination of a contact model and a film thickness equation. The model, which is isothermal, incorporates waviness, coning, face geometry, roughness, pressure of the fluid to be sealed and load. From the literature it appeared that no film thickness equation for mechanical face seals, which also accounts for hydrodynamic effects, exists and this is, therefore, developed and described in this thesis. In order to use the contact model, a nominal contact area is required. In this thesis, based on numerical data, a function fit is made for the nominal contact area as a function of waviness amplitude, coning angle, modulus of elasticity and load.

Finally, in order to verify the model, a test rig was designed and built. With the test rig, Stribeck curves of mechanical face seals were measured. Furthermore, wear measurements and load carrying capacity tests were performed. Wear measurements were carried out to analyze the change in micro-geometry, load carrying capacity tests were performed to determine the maximum applicable load during friction experiments.

The friction model agrees very well with the friction experiments performed.

The effect of the operational conditions, i.e. geometry (roughness, coning and amplitude), pressure of the fluid to be sealed and load on the transition full- film lubrication to mixed lubrication is shown. It was found that, depending on the operational conditions, the transition from hydrodynamic to mixed lubrication significantly depends on the coning angle, load, and roughness and to a lesser extent on the waviness amplitude, the height distribution and the reduced modulus of elasticity.

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NOMENCLATURE

a coning angle [rad]

a_i contact radius of an individual asperity [m]

A waviness amplitude [m]

A_c real contact area [m²]

A_c_i area of contact of a single asperity i [m²]

A_f sealing interface area [m²]

A_h hydraulic loading area [m²]

A_H hydrodynamic contact area [m²]

A_nom nominal contact area [m²]

A˜_nom dimensionless nominal contact area A˜_nom = A_nom

b² [–]

Aseal seal area [m²]

b equivalent radius of contact [m]

B_r balance ratio B_r = A_h

A_f [–]

B radial seal width [m]

c compliance [m]

d_d distance between d_s and d_h [m]

d_s mean plane of the summits heights [m]

d_h mean plane of the surface heights [m]

D_b balance diameter [m]

D_i inner face seal diameter [m]

D_m mean face seal diameter [m]

D_o outer seal face diameter [m]

E⁰ reduced modulus of elasticity [Pa]

E_i elasticity modulus of contacting surface i (i = 1, 2) [Pa]

f coefficient of friction [–]

f_c_i coefficient of friction of a single asperity i [–]

f_c coefficient of friction in the boundary lubrication regime [–]

F_C load carried by the asperities [N]

F_f friction force [N]

F˜_f dimensionless friction force F˜_f = F_f B²p_m

rp_m

ηω [–]

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xii Nomenclature

F_i load of an individual asperity [N]

F_H load carried by the hydrodynamic component [N]

F_N axial load [N]

F_s spring load [N]

G duty parameter [–]

h film thickness, separation [m]

H dimensionless film thickness H = h B

rp_m

ηω [–]

h^∗ separation [m]

h_min minimum film thickness [m]

H_min dimensionless minimum H_min = hmin

B

rp_m

ηω [–]

film thickness

k number of circumferential waves on a seal face [–]

k_s specific wear rate [mm³/N.m]

K pressure gradient factor [–]

p pressure [Pa]

P dimensionless pressure P = p

p_m [–]

¯

p mean pressure [Pa]

˜

p dimensionless pressure p =˜ p

p_i− po

[–]

p_a atmospheric pressure [Pa]

p_C asperity pressure [Pa]

p_c_i pressure in a single asperity i [Pa]

p_cav cavitation pressure [Pa]

p_f sealed fluid pressure [Pa]

P_f dimensionless fluid pressure P_f = p_f

p_m [–]

p_h Hertzian contact pressure [Pa]

p_H hydrodynamic pressure [Pa]

p_i pressure at inner seal face diameter [Pa]

¯

p_inside mean pressure of an inside pressurized seal [Pa]

p_m mean pressure [Pa]

p_o pressure at outer seal face diameter [Pa]

¯

p_outside mean pressure of an outside pressurized seal [Pa]

p_s spring pressure [Pa]

p_T total pressure [Pa]

q_c liquid fraction [–]

q_m leakage [m³/s]

Q_m dimensionless leakage Q_m = q_mη

B³p_m

rp_m ηω

3

[–]

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Nomenclature xiii

r radius [m]

˜

r dimensionless radius r =˜ r

r_o [–]

r_b balance radius [m]

r_i inner radius [m]

r_m mean radius [m]

r_o outer radius [m]

R_x radius of curvature [m]

s sliding distance [m]

t time [s]

U velocity [m/s]

U_seal velocity of seal face at mean radius r_m [m/s]

v velocity [m/s]

v_t transiton velocity from HL to ML [m/s]

˜

v_t dimensionless transition velocity v˜_t = v_t_exp

v_t_cal [–]

from HL to ML

v_t_cal calculated transition velocity from HL to ML [m/s]

v_t_exp measured transition velocity from HL to ML [m/s]

V volume [mm³]

w compliance [m]

x cartesian coordinate [m]

X dimensionless coordinate [–]

y cartesian coordinate [m]

Y dimensionless coordinate [–]

z cartesian coordinate [m]

Greek symbols

α dimensionless coning α = a

rp_m

ηω [–]

α_nom dimensionless coning angle α_nom = aR_x

b [–]

β radius of asperities [m]

β_nom dimensionless seal width B

b [–]

γ dimensionless waviness γ = A

B rp_m

ηω [–]

˙γ shear rate [s⁻¹]

γ_{M L} Adaptation parameter for hydrodynamic component [–]

in mixed lubrication regime

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xiv Nomenclature

δ distance [m]

η dynamic viscosity [Pa·s]

η_s density of asperities [1/m²]

θ angular coordinate [rad]

λ dimensionless separation λ = h

σ_s [–]

ν Poisson’s ratio [–]

ξ curvature variable ξ = r_i

r_o [–]

ρ density [kg/m³]

ρ_c cavitation variable ρ_c =

p_cav p_m

[–]

σ standard deviation of the surface height distribution [m]

σ_after standard deviation of the surface height distribution [m]

after the experiment

σ_ini standard deviation of the surface height distribution [m]

before the experiment

σ_s standard deviation of the height distribution of the summits [m]

τ_c_i shear stress at the asperity i [Pa]

τ_H hydrodynamic shear stress [Pa]

φ distribution of the asperities [–]

ψ dimensionless seal face geometry ψ = r_o

B [–]

ω angular velocity [rad/s]

Abbreviations

BL Boundary Lubrication HL Hydrodynamic Lubrication ML Mixed Lubrication

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1. INTRODUCTION

1.1 Mechanical face seals

Mechanical face seals are used to seal a fluid at places where a rotating shaft enters an enclosure. Figure 1.1 shows schematically the configuration of a mechanical face seal. The rotating seal is fixed to the shaft and rotates with it, whereas the stationary seal is mounted on the housing. The secondary seals (o-rings) prevent leakage between the rotating shaft and the rotating seal, and the housing and the stationary seal, respectively. The rotating seal is flexibly mounted in order to accomodate angular misalignment and is pressed against the stationary seal by means of the fluid pressure and the spring. The primary sealing occurs at the sealing interface of both seal faces, where the rotating face slides relative to the stationary face. For proper functioning of a mechanical face seal, a fluid film is maintained between the faces. In the configuration of Fig. 1.1 the sealed fluid may also act as a lubricant. Applications of mechanical

Housing Pressurized fluid

Rotating shaft

Stationary seal Rotating seal

Spring

Secondary seal

Sealing interface

Fig. 1.1: Mechanical face seal, schematically.

face seals are numerous. The most common example of application is in pumps

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2 1. Introduction

for the chemical industry. Also propellor shafts in ships and submarines, com- pressors for air conditioners of cars and turbo jet engines and liquid propellant rocket motors in the aerospace industry require mechanical face seals.

Mechanical face seals have become the first choice for sealing rotating shafts operating under conditions of high fluid pressures and high speeds, at the expense of soft-packed glands. The reason for this is lower leakage, less main- tenance and longer life. A disadvantage of face seals is that when they fail, they do so completely, whereas a soft-packed gland can continue, although less efficiently.

1.2 Problem definition

Due to increasing technical and environmental requirements, operational conditions are becoming more severe. Face seals have to operate at higher pressures and higher speeds, so a sufficient fluid pressure in the sealing interface is vital if excessive wear, friction and temperature rise (frictional heating) are to be avoided and a long seal life is to be ensured. However, a too thick fluid film is unfavourable with regard to leakage, as this is proportional to the cube of the film thickness. Due to environmental demands, leakage must be minimized by reduction of the separation between the faces. From the above it is clear that the demands with regard to optimum sealing are contradictory. Ideally, a mechanical face seal should operate with a fluid film as thin as possible, to reduce the leakage and to restrict wear.

In Fig. 1.2 the coefficient of friction is schematically plotted as a function of a lubrication parameter, which yields the generalized Stribeck curve (Schipper, 1988). Figure 1.2 also shows the separation h. The lubrication parameter is defined in many ways in the literature. It contains, for instance, the viscosity, the velocity of the surfaces, the contact pressure and the roughness of the surfaces, see Gelinck (1999). In this graph, three lubrication regimes can be distinguished, i.e. Hydrodynamic Lubrication(HL), Mixed Lubrication (ML) and Boundary Lubrication(BL). The different lubrication regimes are schematically represented in Fig. 1.3. The faces are hydrodynamically lubricated, when they are fully separated by a fluid film, due to pressure build-up, which is caused by rotation of the faces. The load is transmitted by the fluid.

When the fluid pressure for some reason is not capable of fully separating the mating seal faces, asperity contact will occur. Then, the load on the faces is carried by both the fluid and the asperities. This type of interfacial contact is called mixed lubrication. When there is no fluid pressure build-up at all, the load is completely carried by the interacting asperities and this is called boundary lubrication, i.e. a layer is present which protects the surface. Each

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1.2 Problem definition 3

a b

BL ML HL

Lubrication parameter (log)

Coefficientoffrictionf Separationh

Fig. 1.2: Generalized Stribeck curve; coefficient of friction and the separation are schematically plotted as a function of a lubrication parameter.

lubrication mode is characterized by a typical friction behaviour. In the BL- regime shear takes place in the boundary layers or at the interface of both layers. When the boundary layers are damaged, direct contact between the asperities occurs, and shear takes places at this interface or in the weaker asperities, which results in material transfer from one surface to the other. In the hydrodynamically lubricated regime, the faces are fully separated by a fluid, and all shear, as a result of motion of one of the faces, takes place in the fluid.

In the mixed lubricated regime, shear in both the fluid and the boundary layer takes place. The transitions HL–ML and ML–BL are defined by the inter- sections obtained by extrapolating the curves representing the coefficients of friction of the HL regime and the BL regime, respectively, with the tangent of the ML regime.

For mechanical face seals an optimum operational region would be around the transition from hydrodynamic to mixed lubrication, indicated by position a.

In this region a low coefficient of friction is accompanied by a low wear rate (hardly any interaction between the opposing surfaces is present) and a low leakage, as the separation is rather small. Position b, where face seals may operate as well, will also show a low coefficient of friction and hardly any wear as the faces are fully separated by a fluid film. However, as shown in the graph, position b is accompanied by a much larger separation and hence, a large leakage.

Several researchers performed friction measurements in order to establish the transitions between the different lubrication regimes. Lebeck (1987) collected a

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4 1. Introduction

Boundary lubrication

Mixed lubrication

Hydrodynamic lubrication

Fig. 1.3: Lubrication modes.

lot of these friction measurements and plotted them in a graph as a function of a lubrication parameter, in this case called the “duty parameter” G (Fig. 1.4), which is frequently used. The duty parameter is defined by:

G = ηv∆r

F_N , (1.1)

where η is the dynamic viscosity, v the velocity, ∆r the width of the seal face and F_N the axial load acting on the seal (Lubbinge et al., 1997). Figure 1.4 shows that the friction is not characterized adequately. For example the G–

value for the transition from hydrodynamic– to mixed lubrication differs by at least 2 powers of 10. The reasons for this are that a) the duty parameter G does not contain any surface roughness parameter and b) the load per unit width does not represent the real pressure between the seal faces (Lubbinge

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1.3 Objective of this research 5

Coefficientoffriction

Duty parameter G

Fig. 1.4: Stribeck curves of mechanical face seals [from Lebeck (1987)].

et al., 1997). From this graph it is therefore clear that further investigation of the lubrication of mechanical face seals is required.

1.3 Objective of this research

In the previous sections it was pointed out that the lubrication of mechanical face seals becomes quite complicated due to the increasing technical and environmental demands. There are many factors that affect the interfacial fluid pressure and thus the transition between the lubrication regimes as made clear by Fig. 1.4. Therefore, the objective of this research is to develop a model which predicts the frictional behaviour of mechanical face seals as a function of the operational conditions. The existing duty parameter is not adequate.

When the lubrication mode under specific conditions can be predicted, it is possible to optimize the seal configuration with respect to leakage, friction and wear. In this thesis the model is restricted to the iso-thermal situation.

Clearly, experimental friction data are required to verify the model. Thus, a new test rig was designed and built to measure the friction of mechanical face seals.

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6 1. Introduction

1.4 Overview

Chapter 2 presents an overview of existing knowledge on the lubrication of mechanical face seals. In Chapter 3 the development of the theoretical model is discussed. The model is based on a combination of a modified contact model and a newly developed film thickness equation. Chapter 4 describes the test rig, which is used to collect experimental data to verify the model. In addition, also wear rate measurements and load carrying capacity tests were performed and analyzed. In Chapter 5, the experimental results are compared with the theoretical results and, finally, in Chapter 6, conclusions and recommendations for further research are presented.

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2. REVIEW ON THE LUBRICATION OF MECHANICAL FACE SEALS

2.1 Introduction

Already a lot of research has been performed on the lubrication of mechanical face seals, particularly with respect to the fluid pressure between the mating faces. The pressure generating mechanisms can be divided into two main categories, i.e. hydrostatic mechanisms and hydrodynamic mechanisms.

The mechanism of hydrostatic pressure generation has been extensively inves- tigated by e.g. Doust and Parmar (1986), Young and Lebeck (1982), Lebeck (1991) and Etsion (1978a; 1978b; 1994), and it is in general well understood.

A more difficult area is, however, hydrodynamic lubrication of mechanical face seals, because when two flat parallel surfaces slide parallel to each other in the presence of a liquid, there is, according to the Reynolds’ equation, no mechanism to generate pressure in the fluid. The Reynolds’ equation is derived from the Navier-Stokes equations (Reynolds, 1886). It describes mathematically full film lubrication and, for surfaces that do not deform in the direction of flow, is given in polar coordinates by:

1 r

∂

∂θ

ρh³∂p

∂θ

+ ∂

∂r

rρh³∂p

∂r

= 6ηrω∂(ρh)

| {z∂θ }

wedge term

+ 12ηr∂(ρh)

| {z∂t }

squeeze film term

, (2.1)

where r and θ are the polar coordinates within the fluid, p is the local pressure within the fluid film, ρ and η are, respectively, the density and the dynamic viscosity of the lubricant, h is the film thickness, and ω the angular velocity of the rotating seal face. For liquids, the density variations are negligibly small and, also because the fluid pressures are relatively low, the density ρ can be omitted entirely from Eq. (2.1).

The physical interpretation of the two terms which describe hydrodynamic pressure generation is as follows:

1. Wedge term — Pressure building as a result of a narrowing gap in the flow direction of the fluid.

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8 2. Review on the lubrication of mechanical face seals

2. Squeeze film term — Pressure building as a result of film thickness chang- ing with time.

When two flat seal faces slide parallel to each other, there is no converging wedge and, under such conditions there is no hydrodynamic pressure generation. If a constant load is present and both surfaces are flat, the squeeze term reduces to zero. Therefore, separation of the flat parallel sliding surfaces can only be achieved by hydrostatic action.

In experiments, however, it has been shown that besides the hydrostatic pressure imposed by the sealed fluid pressure, hydrodynamic pressure often devel- ops, see e.g. Sneck (1969), Pape (1968), Stanghan-Batch and Iny (1973), Anno et al. (1968) and Lebeck (1991). The possible reasons for this are discussed in Section 2.2.4.

2.2 Principle of mechanical face seals

2.2.1 Inside vs. outside pressurized seals

Mechanical face seals can be mounted in two different ways in, for instance, a pump or a sealed vessel:

1. Inside mounting. In this configuration the pressurized fluid is to be sealed on the outside of the seal, which is called an outside pressurized seal , see Fig. 2.1. This is the most common arrangement.

2. Outside mounting. The pressurized fluid is on the inside of the seal as shown in Fig. 2.2 and the seal is called an inside pressurized seal .

A_h

D_b A_f

p_f

D_o D_i p_a

D_h Fig. 2.1: Unbalanced outside

pressurized seal, internally mounted.

D_b A_h

p_a

D_o D_i p_f

D_h A_f

Fig. 2.2: Balanced inside pressurized seal, externally mounted.

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2.2 Principle of mechanical face seals 9

2.2.2 Balance ratio

An important parameter, well known in the sealing industry, is the balance ratio, which for an outside pressurized seal is defined as:

B_r = hydraulic loading area sealing interface area = A_h

A_f = D_o² − Db2

D_o²− D_i² . (2.2) For an inside pressurized seal the hydraulic loading area is given by ¹₄π D_b² − D_i²

, thus

B_r = A_h

A_f = D_b²− Di2

D_o²− D_i². (2.3)

The balance ratio controls the axial load, acting on the seal interface. When B_r is greater than 1, the seal is called unbalanced , whereas a balanced seal has a B_r-value lower than 1. Seals operating at high pressures are mostly of the balanced type, B_r < 1, whereas many low-pressure seals operate at B_r > 1, the unbalanced type.

2.2.3 Hydrostatic lubrication

Mechanical face seals always operate with a radial pressure gradient across the face; the pressurized fluid, p_f, on the one side and the atmospheric pressure, p_a, on the other side, see Figs. 2.1 and 2.2. The pressure distribution in the gap is determined by the shape of the sealing interface and therefore the average pressure is strongly affected by this shape. The average hydrostatic pressure in the gap is expressed as K·pf, the K-factor (or the pressure gradient factor) times the fluid pressure to be sealed. The following sections discuss the effect of different seal face geometries on the hydrostatic pressure distribution.

2.2.3.1 Effect of seal radii on hydrostatic pressure distribution – parallel flat faces

As mechanical face seals are circularly shaped, the radial hydrostatic pressure distribution is affected by the degree of curvature, expressed by the ratio of the inner radius and the outer radius, r_i/r_o.

The hydrostatic pressure distribution across a seal face for the statically loaded, parallel face situation (Fig. 2.3), Eq. (2.1) reduces to:

∂

∂r

r∂p

∂r

= 0. (2.4)

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Integrating this expression yields:

r∂p

∂r = C ⇒ ∂p = C∂r

r ⇒ p = C ln r + D. (2.5) As shown in Fig. 2.3, the boundary conditions for Eq. (2.5) read:

p = p_i at r = r_i

p = p_o at r = r_o. (2.6)

Solving the equation for the integration constants C and D by substituting

p_i p_o r_i

r_o

Fig. 2.3: Boundary conditions in the sealing interface.

these boundary conditions gives the solution for the hydrostatic pressure across the seal face:

p = p_iln rr_o + p_olnr_i r lnr_i

r_o

. (2.7)

By defining ˜r = r

r_o, ˜p = p p_i− po

and ξ = r_i

r_o, Eq. (2.7) can be written as:

˜

p = ln ˜r

ln ξ + p_o

p_i− p_o. (2.8)

Figures 2.4 and 2.5 show the pressure distribution for an outside and an inside pressurized seal, respectively, for different values of ξ. For the sake of com- pleteness, the exact solution for the hydrostatic pressure across a rectangular geometry (Fig. 2.6) is given below:

p = p_o− pi

B y + p_i. (2.9)

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((d (

(x (

(d (n

Dimensionless radius ˜r ξ =

ξ 1

1 0

Hydrostaticpressure˜p

Fig. 2.4: Pressure distribu- tion for different values of ξ for an outside pressurized seal.

((d (n (x ( (

(d

Dimensionless radius ˜r ξ =

ξ 1

1 0

Hydrostaticpressure˜p

Fig. 2.5: Pressure distribu- tion for different values of ξ for an inside pressurized seal.

Here the pressure drops linearly from the higher pressure on the one side to the lower pressure on the other side, which thus results in a mean hydrostatic pressure of ¯p = (p_o+ p_i) /2.

As a result of the seal radii, the average pressure across the sealing interface differs from a rectangular geometry, as shown in Table 2.1 and Fig. 2.7. The difference increases with decreasing value of ξ. Furthermore the following applies:

lim

ξ→0p¯_outside→ 1 and lim

ξ→0p¯_inside → 0. (2.10) In practice, however, the value of ξ is about 0.9, so with regard to the hydro- static pressure, the effect of seal radii is relatively small, see Table 2.1.

As well as the seal radii, a much more important factor with regard to hydrostatic pressure in the contact is the coning of the faces. This is discussed in the next section.

2.2.3.2 Effect of coning on hydrostatic pressure distribution

Another important geometrical feature of the seal face, which affects the hydrostatic pressure distribution between the faces, is the so-called coning or radial taper. Figure 2.8 shows the three possible gaps. The coning is convergent if the sealing gap narrows in the flow direction of the fluid, it is divergent

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p_i p_o

y = 0 y = B z xy

Fig. 2.6: Rectangular geometry.

ξ p¯inside p¯outside

0.01 0.21 0.79 0.1 0.33 0.66 0.3 0.40 0.60 0.5 0.44 0.56 0.7 0.47 0.53 0.9 0.49 0.51

Table 2.1: Mean pressure in the contact for different ratios of the radii, where ¯p_inside and ¯p_outside relate to an inside pressurized seal and an outside pressurized seal, respectively.

if the coning narrows in the opposite direction. When the gap is parallel in the radial direction there is no coning. As for large values of ξ, the effect of curvature on the hydrostatic pressure is relatively small, the hydrostatic pressure distribution has been derived in cartesian coordinates in order to show the effect of coning. In Appendix A the Reynolds’ equation is solved in polar coordinates (ξ << 1), expressed in dimensionless form.

The Reynolds’ equation in cartesian coordinates reads:

∂

∂x

h³ η

∂p

∂x

+ ∂

∂y

h³ η

∂p

∂y

= 6U∂h

∂x. (2.11)

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¯ p

ξ

¯ p_outside

¯ p_inside

¯ p = 0.5

0 0 1

1

Fig. 2.7: Mean hydrostatic pressure as a function of ξ.

After substituting the following dimensionless variables:

X = x B Y = y B P = p p_m H = h

B s

Bp_m ηU

H_min = h_min B

s Bp_m

ηU α = a

s Bp_m

ηU P_f = p_f

p_m,

(2.12)

the Reynolds’ equation can be written in a dimensionless form as follows:

∂

∂X

H³∂P

∂X

+ ∂

∂Y

H³∂P

∂Y

= 6∂H

∂X. (2.13)

With coning only, the solution of the hydrostatic pressure distribution, Eq. (2.13), reduces to:

∂

∂Y

H³∂P

∂Y

= 0. (2.14)

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h_min ∆h hmin ∆h

parallel gap converging gap diverging gap hmin

Fig. 2.8: Three different gap geometries. In each situation the seal is outside pressurized.

The film thickness equation for a seal face with only convergent coning reads:

H = H_min+ αY, (2.15)

whereas for divergent coning the film thickness equation becomes:

H = H_min+ α(1− Y ). (2.16)

Solving Eq. (2.14) with convergent coning results in:

P (Y, H_min, α, P_f) = P_fY (H_min+ α)²(2H_min+ αY )

(2H_min+ α)(H_min+ αY )². (2.17) The hydrostatic pressure distribution in a diverging gap reads:

P (Y, H_min, α, P_f) =−PfY H_min²(αY − 2Hmin− 2α)

(2H_min+ α)(αY − Hmin− α)². (2.18) Besides the coning angle of the gap, the minimum film thickness is also important for the shape of the pressure distribution, as shown by Eqs. (2.17) and (2.18). Furthermore, the local pressure P depends linearly on the fluid pressure P_f.

The effect of different coning angles α on the pressure distribution is shown in Fig. 2.9. Lines are plotted for four different values of α, viz. 0, 0.5, 1 and 5.

The fluid pressure P_f and the minimum film thickness H_min are taken to be constant and set at 1.75 and 1, respectively. With increasing α, the curvature increases. In the case of convergent coning (solid lines), the resistance in the direction of the flow increases with increasing α, resulting in a more convex curve and therefore a higher hydrostatic mean pressure. A divergent coning

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results in a more concave curve (dashed lines) with increasing α. The same effect is observed when the minimum film thickness Hmin is varied; a smaller H_min results in greater curvature. In Fig. 2.10 the pressure P is plotted as a function of the seal face width Y for different values of H_min, viz. 0.1, 0.5, 1 and 5. The constants P_f and α are set at 1.75 and 1, respectively. The solid lines indicate convergent coning, whereas the dashed lines indicate divergent coning.

( d

( d 1

Seal face width Y P

α =

5 5

1 1

0.5 0.5

0

Fig. 2.9: Hydrostatic pressure distribution for different values of α, P_f = 1.75 and H_min = 1. The solid lines indicate convergent coning, whereas the dashed lines reflect divergent coning. In the case of α = 0, the gap is parallel (dotted line).

From the above it becomes clear that the mean pressure ¯p is strongly influenced by Hmin when a certain degree of coning is present, as opposed to the parallel gap case, where ¯p is independent of the film thickness h_min, see Eq. (2.7). For a constantly convergent coning angle, ¯p increases with decreasing h_min, whereas

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( d

( d 1

Seal face width Y P

H_min = 0.1

0.1 0.5

0.5 1

1 5

5

Fig. 2.10: Hydrostatic pressure distribution for different values of H_min, P_f = 1.75 and α = 1. The solid lines indicate convergent coning, whereas the dashed lines reflect divergent coning.

for a constantly divergent coning angle ¯p decreases with decreasing h_min. The same result is valid for the angle of coning; an increasing coning angle results in an increasing ¯p in the convergent case, but results in a decreasing ¯p in the divergent case. It is clear that sealing with a diverging taper leads to an unstable situation. As the face seals operate in equilibrium with the fluid pressure (the balance ratio equals the K-factor), a small disturbance (e.g. as a result of temperature or pressure variations), resulting in decreasing h_min, will lead to a collapse of the fluid film and severe mechanical contact of both seal faces, accompanied by heavy wear and high temperatures.

On the other hand, a convergent coning gives a stable hydrostatic fluid film;

disturbances are immediately compensated for by the increasing mean pres- sure when h_min decreases. However, an excessive convergence is undesirable,

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because it opens up the gap, reduces the stiffness and increases the leakage rate, as shown theoretically by Cheng et al. (1968) and Lebeck (1991) and also experimentally by Snapp and Sasdelli (1973) and Young and Lebeck (1982).

Unfortunately during operation, as a result of thermal effects, pressure distortions and wear, the taper is not constant (Young and Lebeck, 1982). In fact, it can vary from convergent to parallel and even to divergent. Interfacial divergence can also occur as a consequence of misalignment, (Etsion, 1978a).

When this happens, the hydrostatic pressure across the sealing interface is no longer able to restore the seal interface to equilibrium with the surrounding fluid pressure. In that case, it would be beneficial if a hydrodynamic pressure generating mechanism were present, which could still separate the seal faces by a fluid film.

From the literature it appears that a lot of research has been performed on the subject of possible mechanisms which might lead to hydrodynamic pressure building. Among these mechanisms, circumferential waviness seems to be the most prominent one. The next section will discuss briefly the reviewed literature concerning hydrodynamic pressure generating mechanisms in mechanical face seals.

2.2.4 Hydrodynamic lubrication

In the past, many different theories have been developed which describe the mechanisms causing pressure generation in the contact of theoretically flat parallel surfaces. An extensive literature survey and evaluation of the possible mechanisms has been given by Lebeck (1987). Lebeck concludes that deviation from the parallel, like waviness and misalignment, is the strongest effect causing hydrodynamic fluid pressure, but he does not exclude the possibility that there is another, as yet unknown mechanism present (Lebeck, 1991).

Also Nau’s (1967) review on the possible sources of pressure build-up shows that waviness and misalignment of the faces play an important role with regard to hydrodynamical operation.

Stanghan-Batch (1971) demonstrated experimentally that hydrodynamic pressure developed as a result of a sinusoidally shaped two-humped surface profile on one face, produced by the lapping process. Furthermore, carbon faces spon- taneously developed waves during testing, as a result of wear. In the region of diverging film thickness cavitation occurred, so a net hydrodynamic load support remained. The same phenomena were observed by Pape (1968). Film thickness fluctuations at twice shaft speed frequency were measured. Surface topography measurements revealed a two-cycle sinusoidally shaped wave in the circumferential direction. Pape concluded therefore that macroroughness or waviness was the only feasible source of the observed phenomena. Ruddy

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et al. (1982) studied the mechanism of film generation in seals, in which both faces had a circumferential 2-wave waviness. The cyclical variation in film thickness resulted in an axial movement of the face. Hence, also the squeeze- film term (see Eq. (2.1)) was taken into account. It was shown that low amplitude circumferential waviness, combined with relative axial movement of the sealing faces, generated hydrodynamic load support.

In the following sections, possible sources of hydrodynamic load support, other than waviness and misalignment, are briefly summarized.

2.2.4.1 Thermal wedge

Fogg (1946) studied hydrodynamic lift in a thrust bearing with nominally parallel faces and explained the lift in terms of a thermal wedge effect. As a result of a temperature gradient in the direction of the sliding motion, a density variation occurred, which led to the generation of hydrodynamic pressure.

When lubricant enters the bearing, it heats up due to viscous friction, which results in a reduction of its density. Since continuity requires that the mass flow rate must be constant, the volume flow rate has to increase, which is only possible if there is an increasingly negative pressure gradient. This requirement plus the boundary conditions, i.e. the pressure must become ambient at each end of the slider, causes a load supporting pressure in the film. In his article Lebeck (1987) shows that only under conditions of high speeds and lubrication with oil, can some load support develop, however, for liquids like water the thermal wedge is negligible. Therefore, the thermal wedge is not strong enough to explain the load support under parallel sliding conditions, see also Cameron (1966). Dowson and Hudson (1963) and Neal (1963) concluded that, rather than a thermal wedge, thermal distortion acts as a source for the observed load support.

2.2.4.2 Viscosity wedge

Cameron (1966) analyzed the effect of varying viscosity caused by temperature gradients across the film. However, Dowson and Hudson (1963) showed that, when considering parallel surfaces, this mechanism will decrease load support rather than enhance it.

2.2.4.3 Microasperity lubrication

In this case an asperity on the surface acts like a step bearing in the fluid. The pressure increases when the asperity is approached and decreases when the asperity is left behind. As the pressure tends to decrease below the cavitation pressure, the fluid starts to cavitate, and a net hydrodynamic load support

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remains. Pape (1969) showed that microasperity lubrication does not appear to be strong enough to explain the observed hydrodynamic load support in flat parallel faces.

2.2.4.4 Asperity-asperity collisions

Pressure load support is supposed to develop when two asperities of the mating rough surfaces collide in the presence of a lubricant film. This mechanism has been studied extensively by Fowles (1975). Although some load support is observed in the thin film lubrication regime, it is not enough to explain the observed hydrodynamic effects in mechanical face seals.

2.2.4.5 Squeeze film

When two faces oscillate in the axial direction, for instance due to vibrations of the machine itself, fluid pressure can be developed, see Eq. (2.1). Cameron (1966) showed that when the medium to be sealed is compressible, a load is carried. However, a large excitation is required, as for small movements the load curve is practically symmetrical, resulting in a zero net load when integrating over a full cycle. At small amplitudes or at low frequencies, the viscous forces dominate the compressible forces. Fluids are hardly compressible, so the net pressure would be near to zero. A little load support is generated by cavitation of the fluid, as shown experimentally by Parkins and May-Miller (1984).

Finally, due to inertia effects, fluid pressure can develop, see e.g. Kuhn and Yates (1964) and Kauzlarich (1972). More recently, Lebeck (1987) showed that in order to develop noticeable fluid pressure, a much higher excitation frequency is needed than is likely for mechanical face seals.

2.2.5 Force equilibrium

In the previous sections the different pressure generating mechanisms are presented, i.e. hydrostatic and hydrodynamic. The following relation applies, see Fig. 2.11:

p_fπ(r_o²− rb2) + F_s = Kp_fπ(r_o²− ri2) + p_restπ(r_o²− ri2). (2.19) The left side of Eq. (2.19) represents the load on the face seal, which consists of the spring load F_s, plus the fluid pressure p_f times the balance area π(r_o²−rb2).

This load has to be supported by the mean hydrostatic pressure in the contact area of the faces, which is defined as the pressure gradient factor K times the fluid pressure p_f times the face area (r_o²− ri2). When the mean hydrostatic fluid pressure is not capable of supporting the load — i.e. when Kp_f < B_rp_f+

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p_s — the rest of the load must be supported by p_rest which consists of material contact and/or hydrodynamic fluid pressure. Equation (2.19) can be solved for p_rest and then reads:

p_rest= p_f(B_r− K) + F_s

π(r_o²− ri2) = p_f(B_r− K) + ps, (2.20) where p_s is the spring pressure and the balance ratio B_r is defined as in Eq. (2.2).

F_s

p_f

Face seal

p_f p_rest

r_o r_o

r_i r_b

+

Fig. 2.11: Equilibrium of forces acting on a mechanical face seal [after Lebeck (1991)].

2.3 Summary and conclusions

As stated in the introduction of this chapter, when two flat parallel faces slide against each other, according to the Reynolds’ equation there is no mechanism present which could generate any hydrodynamic fluid pressure. From the lubrication theory it is known that, at thin film lubrication, only a small variation in the film thickness in the direction of sliding is enough to generate a consid- erable hydrodynamic load support. In fact, if a mechanical face seal operates at a film thickness of 1 µm, a variation of the order of 0.1 µm of the flatness would be sufficient. It was shown by e.g. Pape (1969) and Lebeck (1984) that many factors exist which can cause a variable film thickness. For example, during the lapping of the faces, often some waviness (Fig. 2.12) remains on the surface as a result of non-axisymmetric loading of the face. Waviness may also develop during the running-in period and the wear process afterwards. During operation waviness may also develop as a result of thermal and mechanical distortions, induced by frictional heating and the pressure of the sealed fluid, respectively. So from the above it becomes likely that during operation the

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2.3 Summary and conclusions 21

Fig. 2.12: Seal face with a circumferential two wave waviness (exag- gerated).

seals are not really flat and parallel, and that an accidental source for generating fluid pressure will usually be present. In Chapter 3 hydrodynamic lubrication in mechanical face seals will be analysed further.

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ON THE LUBRICATION OF MECHANICAL FACE SEALS