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Pour l'obtention du grade de

DOCTEUR DE L'UNIVERSITÉ DE POITIERS UFR des sciences fondamentales et appliquées

Pôle poitevin de recherche pour l'ingénieur en mécanique, matériaux et énergétique - PPRIMME (Diplôme National - Arrêté du 7 août 2006)

École doctorale : Sciences et ingénierie en matériaux, mécanique, énergétique et aéronautique - SIMMEA

Secteur de recherche : Génie mécanique Cotutelle : Universitatea politehnica (Bucarest)

Présentée par :

Alex Florian Cristea

Analysis of thermal effects in circumferential groove journal bearings with reference to the divergent zone

Directeur(s) de Thèse :

Michel Fillon, Mircea D. Pascovici, Jean Bouyer Soutenue le 12 décembre 2012 devant le jury

Jury :

Président Alexandru Dobrovicesu Prof.dr.ing., Universitatae Politehnica Bucure ti

Rapporteur Mohammed Jaï Maître de conférences HDR, INSA de Lyon

Rapporteur Dumitru Olaru Prof.dr.ing., Universitatae Tehnic Ia i

Membre Michel Fillon Directeur de recherche, Inst. Pprime, Université de Poitiers

Membre Mircea D. Pascovici Prof.dr.ing., Universitatae Politehnica Bucure ti

Membre Corneliu B lan Prof.dr.ing., Universitatae Politehnica Bucure ti

Membre Jean Bouyer Maître de conférences, UFR des sciences fondamentales et appliquées,

Université de Poitiers

Pour citer cette thèse :

Alex Florian Cristea. Analysis of thermal effects in circumferential groove journal bearings with reference to the divergent zone [En ligne]. Thèse Génie mécanique. Poitiers : Université de Poitiers, 2012. Disponible sur Internet

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pour l’obtention du grade de

DOCTEUR DE L’UNIVERSITE DE POITIERS (Faculté des Sciences Fondamentales et Appliquées)

(Diplôme National - Arrêté du 7 août 2006)

Ecole doctorale : Sciences et Ingénierie en Matériaux, Mécanique, Energétique et Aéronautique

Secteur de Recherche: Génie Mécanique, Productique et Transports

Et pour l'obtention du grade de

DOCTEUR INGENIEUR de l'UNIVERSITE "POLITEHNICA" de BUCAREST (Faculté d'Ingénierie Mécanique et Mécatronique)

Secteur de recherche : Génie Mécanique Présentée par :

Alex Florian CRISTEA

************************ ANALYSIS OF THERMAL EFFECTS

IN CIRCUMFERENTIAL GROOVE JOURNAL BEARINGS WITH REFERENCE TO THE DIVERGENT ZONE

************************

Directeurs de thèse :

Michel FILLON – Université de Poitiers

Mircea D. PASCOVICI – Université "Politehnica" de Bucarest

Codirecteur de thèse :

Jean BOUYER – Université de Poitiers

************************ Soutenue le 12 décembre 2012 devant la Commission d’Examen

************************

JURY

A. DOBROVICESCU Professeur, Université "Politehnica" de Bucarest (Président) M. JAI Maître de Conférences HDR, INSA de Lyon (Rapporteur) D. OLARU Professeur, Université "Gheorghe Asachi" de Jassy (Rapporteur) C. BALAN Professeur, Université "Politehnica" de Bucarest (Examinateur) J. BOUYER Maître de Conférences, Inst. Pprime, Université de Poitiers (Examinateur) M. FILLON Directeur de Recherche, Inst. Pprime, Université de Poitiers (Examinateur) M.D. PASCOVICI Professeur, Université "Politehnica" de Bucarest (Examinateur)

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FONDUL SOCIAL EUROPEAN Investeşte în oameni!

Programul Operaţional Sectorial pentru Dezvoltarea Resurselor Umane 2007 – 2013

Proiect POSDRU/88/1.5/S/60203 – Dezvoltarea de cariere științifice competitive prin programe de burse doctorale (COMPETE)

UNIVERSITATEA POLITEHNICA DIN BUCURE

ŞTI

Facultatea de Inginerie Mecanică şi Mecatronică Departamentul Organe de Maşini şi Tribologie

UNIVERSITÉ DE POITIERS – INSTITUT PPRIME

Département Génie Mécanique et Systèmes Complexes

Nr. Decizie Senat 11463 din 23.07.2012

TEZ DE DOCTORAT

Analiza efectelor termice în lag

ărele radiale alimentate printr-un

canal circumferen

țial, cu referire la zona divergentă

Analysis of thermal effects in circumferential groove journal

bearings with reference to the divergent zone

Autor: Ing. Alex-Florian CRISTEA

COMISIA DE DOCTORAT

Preşedinte Prof.dr.ing. A. Dobrovicescu de la Univ. Politehnica Bucureşti

Conducător de doctorat Prof.dr.ing. M.D. Pascovici de la  Univ. Politehnica Bucureşti

Conducător de doctorat Dr. HDR M. Fillon de la  Université de Poitiers

Conducător de doctorat Dr. MdC J. Bouyer de la  Université de Poitiers

Referent Prof.dr.ing. C. B lan de la  Univ. Politehnica Bucureşti

Referent Prof.dr.ing. D. Olaru de la  Univ. Tehnică Iaşi

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AKNOWLEDGEMENTS

First of all I, the author, would like to thank my thesis advisors, doctors Mircea Pascovici, Michel Fillon and Jean Bouyer, for the entire support provided throughout our ongoing collaboration. Also, I would like to thank my family for the support.

More specifically, the author would like to thank doctors Michel Fillon and Jean Bouyer for coordinating the research at the University of Poitiers – Institute Pprime. They ensured that the author had access to a state of the art test rig, and also enabled it to be upgraded throughout the thesis with new data acquisition and control hardware, a broad array of pressure transducers and an adequate flow rate meter. The author would like to thank them also for the support whilst designing the circumferential groove journal bearing (CGJB) and the groove adapters that have been used in the experimental research part of the thesis. The author appreciates all the financial support provided by University of Poitiers – Institute Pprime through doctors Michel Fillon and Jean Bouyer with respect to the CGJB, test rig and workstation used during the time in Poitiers. The author also appreciates the accommodations and travel expenses support, provided throughout the thesis. For their help during the experimental part of the thesis, in addition to doctors Michel Fillon and Jean Bouyer, the author would like to thank: René Branlé for manufacturing the groove adapters; doctor Pascal Jolly for providing a portable pressure transducers hydraulic calibration rig; Sébastien Sabourin for the transducers connections. The author would like also to thank Mathieu Maillet for ensuring the safe operation of the workstations used during the research. During the time spent in France, the author appreciates also the helpful attitude of doctors Bernard Tournerie and Noël Brunetière, together with the above. A very special thank you from the author is addressed to fellow PhD students / new doctors: Franck Balducchi, Andrei Gherca, Amine Hassini, Yann Henry, Elias Harika and Andre Parfait.

Conversely, during the research carried out in Romania at the University “Politehnica” of Bucharest, the author acknowledges the complete support of doctor Mircea Pascovici. The author would like to thank doctor Mircea Pascovici for coordinating the research at the University “Politehnica” of Bucharest. For the support provided during the Rayleigh step

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2 Also the author acknowledges the support of doctors Corneliu Bălan, Aurelia Meghea, and Alexandru Rădulescu during the lubricant rheological measurements. For providing the basic tools for understanding data acquisition and control, the author would like to thank doctors Adrian Pascu and Tom Savu. The author would like to thank doctor Traian Cicone for the teaching assistant opportunity at the Tribology course during the first semester of the third year of the thesis. The author would like to thank fellow PhD student Daniela Coblaş for the collaboration during part of the theoretical research of the thesis. The author would like also to thank doctor Victor Marian for the helpful attitude throughout the thesis, together with the above. A very special thank you from the author is addressed to fellow PhD students / new doctors: Ilie Brânduşa, Mihaela Radu, Mihai Tică and Mihai Vladu. Also, the author would like to thank the doctors Corneliu Bălan, Mohammed Jai and Dumitru Olaru for accepting to referee the thesis and for their output.

The author would like also to thank the also the peers who shared similar and also separate points of view concerning different aspects of the research. This enabled the author to improve the thesis.

The author would like to thank also for the support and helpful attitude of the persons that were not mentioned in the acknowledgement.

Finally, the author acknowledges the financial support of the Sectoral Operational Programme Human Resources Development 2007-2013 of the Romanian Ministry of Labour, Family and Social Protection through the Financial Agreement POSDRU/88/1.5/S/60203. The author also acknowledges the CPER Transport project, which is financially supported by FEDER European Fund, Conseil Régional de Poitou-Charentes, and Conseil Géneral de la Vienne, for the hydraulic system used in this study.

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T

ABLE OF CONTENTS

AKNOWLEDGEMENTS... I TABLE OF CONTENTS...III LIST OF NOTATIONS ... VII

1 CHAPTER 1. INTRODUCTION AND STATE OF THE ART ... 1

1.1 INTRODUCTION... 1

1.1.1 Why study Tribology?... 1

1.1.2 Journal Bearings overview... 2

1.1.3 The Circumferential Groove Journal Bearing ... 4

1.1.4 Hydrodynamic Lubrication with Reynolds’ equation... 6

1.2 STATE OF THE ART ON JOURNAL BEARINGS RESEARCH... 10

1.2.1 The first steps ... 10

1.2.2 A leap forward... 11

1.2.3 The interest on cavitation. Part one: the mass conservation milestone ... 12

1.2.3.1 The Jakobsson-Floberg-Olsson (JFO) mass-conserving model... 13

1.2.3.2 Floberg on bubble theory and tensile strength of liquids... 14

1.2.3.3 Taylor, Coyne and Elrod on stationary bubbles and film separation ... 15

1.2.3.4 Elrod and Adams on (JFO) mass conserving cavitation algorithms ... 18

1.2.3.5 End note of part one ... 19

1.2.4 Thermal aspects of hydrodynamic lubrication. Part one: classical research ... 19

1.2.4.1 From pioneer research towards classic studies ... 19

1.2.4.2 End note of part one ... 27

1.2.5 The interest on cavitation. Part two: film extent, and new cavitation models... 28

1.2.5.1 Some divergence on film separation modes ... 28

1.2.5.2 Film extent and cavitation role in bearing stability... 29

1.2.5.3 Submerged journal bearings research relevant to cavitation... 32

1.2.5.4 Circumferential groove journal bearings research relevant to cavitation... 36

1.2.5.5 Towards a conceptual unification of cavitation ... 39

1.2.5.6 Cavity shape stability to small perturbations ... 42

1.2.5.7 Additional research concerning cavitation ... 43

1.2.5.8 End note of part two ... 45

1.2.6 Numerical models development with respect to thermal effects and cavitation ... 45

1.2.6.1 THD Models developed without Mass Conserving Cavitation ... 46

1.2.6.2 Isothermal Models with (JFO) Mass Conserving Cavitation... 48

1.2.6.3 Isothermal Models with alternative Mass Conserving Cavitation ... 49

1.2.6.4 THD Models development with Mass Conserving Cavitation ... 51

1.2.7 Dynamic operation of journal bearings with respect to thermal effects and cavitation... 54 1.2.8 Thermal aspects of hydrodynamic lubrication. Part two: thermoelastic transients, thermoelastic

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1.2.9 Thermal aspects of hydrodynamic lubrication. Part three: additional research on bearing

performance... 64

1.2.9.1 CGJB THD research... 64

1.2.9.2 Miscellaneous THD research... 65

1.2.10 Further Reading, Summary and Conclusions... 68

2 CHAPTER 2. STEADILY LOADED CGJBS OPERATING UNDER THERMAL EQUILIBRIUM (NOMINAL STEADY-STATE REGIME) ... 81

2.1 EXPERIMENTAL RESEARCH... 81

2.1.1 Institut Pprime Test Rig and Overall Instrumentation ... 81

2.1.2 The Circumferential Groove Journal Bearing (CGJB) ... 87

2.1.3 Modus operandi (experimental data mining) ... 92

2.1.4 Modus operandi (numerical data reconstruction)... 94

2.1.5 Test parameters overview... 96

2.1.6 Sample film pressure and temperature measurements for a low load - low speed test ... 98

2.1.7 Influence of load and speed on film pressure and temperature distributions... 104

2.1.8 Influence of supply parameters and groove geometry on film pressure and temperature distributions... 111

2.1.9 Influence of the operating conditions, supply parameters and groove geometry on bearing performance parameters ... 116

2.1.10 Additional observations concerning bearing operation, with reference to film pressure and temperature measurements variations... 120

2.1.11 Summary and conclusions ... 124

2.2 THEORETICAL RESEARCH... 126

2.2.1 Film extent determined with several theoretical methods available in the literature ... 126

2.2.2 Bearing performance parameters determined with a dedicated design standard for circumferential grooved journal bearings... 131

2.2.3 Summary and Conclusions ... 140

3 CHAPTER 3. STEADILY LOADED CGJBS DURING TRANSIENT REGIMES (START-UP, STEADY-STATE STABILIZATION WITH THERMAL EQUILIBRIUM AND SHUT-DOWN)... 143

3.1 EXPERIMENTAL RESEARCH... 143

3.1.1 Test parameters overview... 143

3.1.2 Start-up, steady-state stabilization, and shut-down transient regime measurements of bearing performance parameters. Influence of load, speed and of acceleration / deceleration ramps. ... 145

3.1.3 Start-up to stabilization transient regime measurements of the land temperature distribution in an unstable case ... 156

3.1.4 Start-up to stabilization transient regime measurements of the pressure and temperature fields in a stable case ... 157

3.1.5 Summary and conclusions... 165

3.2 THEORETICAL RESEARCH... 167

3.2.1 A simple transient lumped thermal mass EHD analysis of the risk of seizure in narrow CGJBs (Seizure Mark 1) ... 167

3.2.2 A simple transient thermal boundary layer with land averaged lubricant temperature EHD analysis of the risk of seizure in narrow CGJBs (Seizure Mark 2)... 174

3.2.3 Simple transient one-dimensional heat transfer with land averaged lubricant temperature EHD analysis of the risk of seizure in narrow CGJBs (Seizure Mark 3)... 177

3.2.4 Summary and conclusions... 188

4 CHAPTER 4. RESEARCH ON RAYLEIGH STEP PINS (RSPS) UNDER TRANSIENT REGIMES... 191

4.1 EXPERIMENTAL AND THEORETICAL RESEARCH... 192

4.1.1 OMTR Test rig and Instrumentation ... 192

4.1.2 Modus operandi (experimental data mining) ... 193

4.1.3 Lubricant(s) properties overview ... 195

4.1.4 Test parameters overview... 196

4.1.5 Transient thrust measurements at start-up for forward and reverse rotation modes. Influence of operating parameters and lubricants on lift, downforce and cavitational effects. ... 197

4.1.6 Comparison of lift peak experimental measurements with constant flow geometry steady-state theoretical models. ... 201 4.1.7 Theoretical transient thrust evaluation for a stepped pin subjected to film-squeeze phenomena.

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4.1.8 Downforce peak experimental measurements at start-up, and cavitation phenomena evaluation

with the theoretical Adapted Stability Criteria for a Rayleigh step (ASC-RS). ... 210

4.1.9 Summary and conclusions... 218

5 CHAPTER 5. CONCLUSIONS, CONTRIBUTIONS AND NEW DIRECTIONS ... 221

5.1 CONCLUSIONS... 221

5.2 CONTRIBUTIONS... 225

5.3 NEW DIRECTIONS... 229

REFERENCES... 233 APPENDIX A. EXTRACT FROM THE CGJB ENGINEERING DRAWINGS...A.1 APPENDIX B. EXPERIMENTAL RESEARCH ON JOURNAL BEARINGS: PRESSURE AND/OR TEMPERATURE MEASUREMENTS POST 1966-1967 OVERVIEW...B.1 APPENDIX C. SAMPLES OF CGJB EXPERIMENTAL MEASUREMENTS TABLES ...C.1

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LIST OF NOTATIONS

Latin symbols

A plate area / surface displacement amplitude at film-squeeze atn start-up ramp / shut-down ramp acceleration

B bearing land width

Bgrv circumferential groove supply width c specific heat capacity

cb specific heat capacity of the bushing cs specific heat capacity of the shaft

cl Specific heat capacity of the lubricant (fluid) C journal bearing radial clearance

C0 initial journal bearing radial clearance / cold clearance

Ca Capillary number

Cgrv circumferential groove supply radial clearance (radial groove depth) Cp coefficient of performance for narrow journal bearings

d diameter of the shaft / pin diameter

D inner diameter of the bushing / nominal bearing diameter De outer diameter of the bushing

Dgrv circumferential groove supply diameter e eccentricity

F force

h film thickness

h* film thickness at film rupture hmin minimum film thickness

hncv natural convection coefficient

k thermal conductivity coefficient

M equivalent total journal bearing mass with respect to thermal effects

Mf friction torque

n rotational speed of the shaft O1 geometric center of the shaft O2 geometric center of the bushing

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2 p fluid pressure (for positive) / tensile stress in the fluid (for negative)

pc cavity pressure / peak tensile stress Pf friction power loss

pgrv fluid pressure in the groove

pm mean bearing pressure ( specific bearing pressure) ps lubricant supply pressure

Q lubricant flow rate / lubricant supply flow rate QHD hydrodynamic lubricant flow rate component QHS hydrostatic lubricant flow rate component

r radial coordinate / radius of the pin / radius of the shaft / change of the cavity radius of curvature along the sliding direction

R0 radius of curvature of free film boundary at separation point Rm pin displacement radius

Re Reynolds number

ReCR critical Reynolds number

s pin step / discontinuous domain step t time

ts time to seizure

T temperature / period of oscillation

T0 initial temperature / reference temperature TC bearing cartridge (bulk) temperature

Tenv environment temperature / temperature in the bearing protective cage Tgrv temperature in the groove

THS hydrostatic bearing temperature Tout outlet temperature of the lubricant

TPP near proximity probes location temperature

Troom environment temperature far from the journal bearing Ts lubricant supply temperature

U sliding surface velocity component along the x-coordinate / linear shaft speed at the nominal radius / radial expansion of bearing components

u, v, w velocity components along the (x,y,z) directions

V surface velocity component along the y-coordinate / squeeze velocity the surface / volume of the components

W applied load / capable load /load carrying capacity / thrust / total bearing load x, y, z rectangular coordinates

Greek symbols

α thermal diffusivity

αLTE linear thermal expansion coefficient

β lubricant property (exponent in Reynolds’ viscosity-temperature relationship)

Γ dimensionless parameter

dimensionless loss of clearance / radial extent of the thermal boundary layer Δ dimensional loss of clearance

Δ radial deformations of the components

eccentricity ratio

ζ dimensionless axial coordinate

θ circumferential (angular) journal bearing coordinate along the direction of shaft rotation / temperature rise

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Θ dimensional temperature rise

Λ dimensionless parameter

dynamic viscosity of the lubricant (fluid) 0 initial viscosity / reference viscosity

Poisson coefficient

dimensionless film thickness

ρ density / radius of curvature of the cavity along the sliding direction ρb density of the bushing

ρl density of the lubricant (fluid) ρs density of the shaft

surface tension of the fluid (with respect to air)

v standard deviation

shear stress / dimensionless time x, y, z shear stress in the (x,y,z) directions

φ film wetting angle of the stationary surface

ϕ attitude angle

bearing clearance ratio / circumferential (angular) journal bearing coordinate along the direction of shaft rotation starting in the divergent zone

0 initial bearing clearance ratio

grv clearance ratio of the circumferential supply groove frequency of oscillation

Subscripts and superscripts 0 initial / reference b bearing C cartridge / cavitation CR critical e exterior / external env environment grv groove L land / left l lubricant (fluid) max maximum min minimum R right / reverse

s seizure / shaft / supply Y 82

superscript in Yoshioka’s model I 62

superscript in Ishii’s model

overbar symbols denote a dimensionless format

Abbreviations and conventions

AG axial groove

AH adhered film

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2 CAD computer aided design

CFD computational fluid dynamics

CG circumferential groove

CGJB circumferential groove journal bearing

CH constant ratio between the bubble cavity height and local gap height

DAQ data acquisition and control

DC direct current

EHD elastohydrodynamic

EL effective length

F forward

FDM finite difference method

FEM finite element method

FFF full (filled) fluid film

FH constant film height adhered to the journal

FVM finite volume method

GB gas bubble

HD hydrodynamic

HS hydrostatic

ICE internal combustion engine

INSA Institut National des Sciences Appliqués (National Institute of Applied Sciences)

JFO Jakobsson-Floberg-Olsson

LHS left hand side

LMS Laboratoire de Mécanique des Solides (Laboratory of Solid Mechanics)

NI National Instruments

OMTR Organe de mașini și Tribologie (Machine Elements and Tribology)

PID proportional-integral-derivative

PP proximity probes / performance parameters

R reverse

r relative to the environment pressure (value)

RSP Rayleigh step pin

RST rolling stream trails

SM 1 seizure Mark 1

SM 2 seizure Mark 2

SM 3 seizure Mark 3

SP supply pocket

TT transducer type / transducer range

TBL thermal boundary layer

TEHD thermoelastohydrodynamic

THD thermohydrodynamic

TPJB tilting pad journal bearing

UP Université de Poitiers (University of Poitiers)

UPB Universitatea “POLITEHNICA” din București (University “POLITEHNICA” of Bucharest)

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C

hapter

O

ne

Introduction and State of the art

C

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1

CHAPTER 1.

INTRODUCTION AND STATE OF THE ART

1.1 Introduction

1.1.1 Why study Tribology?

Why should Tribology, a science concerned with friction, lubrication and wear, be important? The first law of thermodynamics states that in a closed system energy is conserved, hence energy is neither produced nor destroyed. Second law of thermodynamics states that you cannot convert one form of energy to another without increasing entropy. A common example is the power plant, where electrical energy is converted from mechanical energy through turbines. Efficiency can never reach unity, and part of the mechanical energy is transferred to the environment through heat, hence not converted electrical energy. From the economical point of view, all energy that cannot be used / recovered is considered a loss. Hence, efficiency is increased by identifying and limiting losses. Though the latter concept is easy to understand, its implementation is not.

While reducing friction losses and minimizing components wear by proper lubrication is the main objective in rotating machinery, it is not the only area where Tribology has an impact. Though, one must not consider friction as the enemy as life would not be possible without it, literally! What is important, on the other hand, is to understand how nature works, to improve technology, and ultimately enhance the quality of life. For a very well documented historical overview on the advances in Tribology, Dowson’s History of Tribology published in 1997

[63] (Do 1997) is highly recommendable.

This thesis is limited to a particular type of rotating machinery components called

circumferential groove journal bearings (CGJB’s), that are lubricated with mineral oils.

However, an introduction concerning journal bearings in general is necessary. Hence, their form, function and purpose are detailed in the following sections. A state of the art on the most relevant research associated with journal bearings is also presented, and represents the foundation on which the thesis was built on.

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1.1.2 Journal Bearings overview

The main role of a bearing is to provide stable support for components in relative motion and under load. Depending on the operating parameters and / or design requirements, one may use rolling element bearings or lubricated sliding bearings as solutions. The first is well-suited for frequent starts / stops, however the lifetime is limited with respect to the operating conditions. The latter can run at high speeds and provide stiffness and damping under dynamic loads through the inclusion of a thin film of lubricant between the journal and bearing surfaces. This solution minimizes friction losses and components wear in during operation. Moreover, a properly designed lubricated sliding bearing may run indefinitely. Though downsides exist also for lubricated sliding bearings, e.g.: components wear at startup / shutdown under mixed lubrication conditions; fluid film breakdown and / or thermoelastic instabilities can occur at improper operation and / or faulty design etc.

If the lubricated sliding bearing supports radial loads, then it is called a journal bearing. If the load supported is thrust, then it is a thrust bearing. Though in form they differ fundamentally, in function they rely on the same concept, namely lubrication. When sufficient pressure is generated within the fluid film under relative motion to separate the surfaces, then one can speak about hydrodynamic (HD) lubrication. If the surfaces are separated through pockets containing fluid that is externally pressurized, and not through hydrodynamic mechanisms, then the concept represents hydrostatic (HS) lubrication. Though, most lubricants are liquids such as mineral or synthetic oils, one can use also gas for fluid film lubrication, depending on the application. Mineral oil characteristics depend on type and area or origin, and various chemicals are added in order to improve some of their properties during bearing operation

[121] (Hi 1976). When it is not possible to use a fluid film for lubrication, such as hip replacements, fans in electronic components, or in outer space, solutions have been developed with antifriction pairs of materials [197](Ne 1995). Even if in lubricated sliding bearings the surfaces are separated by a thin fluid film, it is still necessary that adequate pairs of materials, such as steel with bronze and / or whitemetal, are used to prevent wiping, [47] (Co-JoLe 1976). Most of the times the fixed component, i.e. the bearing, has small overall dimensions and is made from or coated with soft antifriction material; the rotating component, the journal, has large overall dimensions and is made from high hardness steels.

The concept of hydrodynamic lubrication is presented, following a brief classification of journal bearings form based on their purpose.

The design of journal bearings has evolved significantly since interest in the field started with the pioneer works of Tower [277] (To 1883) [278] (To 1885) and Reynolds [236](Re 1886)

in the 19th century. As the design requirements have been varied, several types of journal bearings have been developed and classified according to their strengths, weaknesses, and their ease of manufacturing in Table 1.1.2.1. The classification is based on the Glacier Metal Co. Ltd. tables [303] (Glacier 1973) also presented by Hill [121] (Hi 1976), and later on by Frêne [105](Fr 1995). Only several bearing types are presented in this section.

It is worth mentioning that journal bearings come in all shapes and sizes, and a wealth of design solutions exist outside Table 1.1.2.1. Therefore journal bearings range from medium and large in rotating machinery, such as compressors or power plant turbines, to very small and light bearings in mechatronics. In different parts of the Earth, the journal is also called shaft, and the bearing is called bushing; though the overall assembly is a journal bearing.

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Table 1.1.2.1 Various journal bearing configurations compared with circular bore.

Bearing type Geometry Load

capacity

Rotating load support

Stiffness Damping Stability Manuf.

Circular bore One or two axial grooves (1-AG, 2-AG) Easy Circular bore Circumferential grooves (CGJB) Easy Circular bore

Supply pocket bearing (1-SP, 2-SP) Easy Elliptical bore Two lobes (Lemon bearing) Easy F ixe d ge om et ry Elliptical bore

Offset halves Easy

A da p ta bl e ge o m et ry Tilting-pads (TPJB) Difficult

The performance of tilting-pad bearings can be improved by selecting an appropriate number of pads and by shifting the pivot positions [20] (BoFiNiBa 1995). Lemon bearings have low stiffness in the horizontal direction, offset halve bearings are not suited for reverse rotation, while axial and circumferential groove bearings are unstable at low loads [303](Glacier 1973) [121](Hi 1976) [105](Fr 1995).

Although the gap between theoretical and actual bearing operation has been narrowed due to important research in the field, there are many aspects that have not been fully understood: non-Newtonian fluids, wall slip, cavitation, tensile strength of liquids, thermoelastic instabilities, lubricant supply flow, transients regimes or dynamic operation to name a few. Part of the heat produced through viscous friction in the lubricant film is carried away by the lubricant flow, the rest by the shaft and bushing. As real components are not rigid but elastic, both thermal and mechanical deformations need to be considered. Thermoelastohydrodynamic (TEHD) analysis is standard nowadays in bearing design, though it can still be improved.

Following a new trend, journal bearings can be classified into reactive and proactive [167] (Ma 2011). As opposed to fixed geometry, compliant and titling-pad journal bearings, proactive bearings incorporate electromechanical components that adapt the geometry in real-time to handle transient instabilities and reduce dangerous shaft whirl.

The research presented in the thesis is mainly focused on a circumferential groove journal

bearing lubricated with mineral oil, i.e. Newtonian fluid. The thesis goal was to narrow the

real - theoretical bearing operation gap, by performing theoretical and experimental research. But, what is a circumferential groove journal bearing, and what are the mechanisms that

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1.1.3 The Circumferential Groove Journal Bearing

Circumferential grooved journal bearings (CGJBs) are capable of handling loads from all radial directions [121](Hi 1976), as lubricant is supplied axially all-around its circumference through a groove significantly larger than the journal bearing clearance. Such bearings can be found in ship gearboxes [121](Hi 1976). Moreover, only by using assembled CGJBs in the

internal combustion engine (ICE) one can provide adequate oil delivery through the

crankshaft between bearings, Figure 1.1.3.1.

Figure 1.1.3.1 Internal Combustion Engine Half-Bearing1 (circumferential supply) (bearings are assembled on the crankshaft).

There is no possibility to install solid bush CGJB’s on ICE crankshafts, hence an assembly of thin-walled split half-bearings is required. The mounting problem is less encountered in rotating machinery such as power plant turbines, as end-shafts are the support elements mostly, hence a solid bush CGJB is considered for the thesis, Figure 1.1.3.2 or Appendix A.

The groove can be either at the mid-plane section, Figure 1.1.3.1 or Figure 1.1.3.2, or shifted axially in which case the CGJB will not be symmetrical. However, little attention has been given on the actual groove configuration and its influence on the lubricant flow regime and journal bearing operation.

When a loaded journal, under its own weight and / or external radial forces, rotates with a sufficient speed, n, a convergent - divergent zone is created circumferentially, Figure 1.1.3.2. By introducing lubricant in the bearing, pressure is generated in the convergent part through a geometric wedge mechanism, balancing the load W. In the divergent part, the film ruptures and separates from itself and from the stationary bush, unable to sustain high tensile stresses. When the pressure is low enough, dissolved gases from the lubricant are released in the divergent zone.

Moreover, if the journal’s center position is varying rapidly, i.e. under dynamic operation, then vaporization of the lubricant occurs in addition to the release of dissolved gases at saturation pressures [26](BrHa 2010).

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Figure 1.1.3.2 The Solid Bush Circumferential Groove Journal Bearing (CGJB) (clearance exaggerated) (axial film parameter variations not represented).

Tensile strength of liquids, film rupture, separation, gas release and vaporization are commonly associated with cavitation phenomena, and detailed in the following sections.

As the fluid film pressure is generated through the convergent wedge, the journal moves round the bearing in the same sense of rotation until it reaches an equilibrium position, Figure 1.1.3.2. The line of centers does not coincide with the loading direction, but is shifted with an attitude angle, ϕ. The distance between the centers, i.e. the absolute eccentricity e, divided to the radial clearance C = (D – d) / 2 represents the relative eccentricity or eccentricity ratio, . For instance, concentricity between rigid journals and bearings are characterised by = 0, while surface contact occurs when = 1.

The film thickness may be written for small clearance ratios = 2 C / D ≈ 10-3 … 10-2, assuming no misalignments and rigid bodies, in cylindrical coordinates as h = C (1 – cos θ). Lubricant is supplied through feed holes to the groove at pressures higher than the environment. The width of the groove, Bgrv, is usually smaller than the bearing land B,

otherwise the load carrying capacity would be compromised if the overall journal bearing dimensions are fixed. The clearance between the bearing’s inner diameter and its circumferential groove, Cgrv = (Dgrv – D) / 2, is several orders of magnitude higher than the

bearing radial clearance, i.e. Cgrv >> C. For a low groove clearance the pressure in the groove

does not remain constant, while at high groove clearances the flow can become turbulent depending on the operating conditions.

As the form of the CGJB and its purpose have been briefly explained, a brief preview on their function is possible. Hence, the mechanism of pressure generation at hydrodynamic lubrication can be explained using several simplifications, and basic journal bearing

D   grv B Lubricant Supply Journal x z y 1 O 2 O W B d G ro o ve n W 2 O 1 O x y z e   Reference Line h Line of Centers min h Convergent Zone Divergent Zone Bearing Attitude Angle grv D

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1.1.4 Hydrodynamic Lubrication with Reynolds’ equation

If the pressure in the oil film can be modeled mathematically, then basic performance parameters such as: capable load, lubricant flow rate or power loss can be estimated. One of

the simplest methods is to use Reynolds equation, named after lubrication pioneer Osborne Reynolds that presented in 1886 [236] (Re 1886) a theory based on the equilibrium and continuity conditions for an infinitesimal fluid element. Reynolds obtained an equation that determines the pressure built-up in an infinite wide plain bearing with the thin fluid film assumption. Sommerfeld [251] (So 1904) continued Reynolds research and proposed a solution for the infinite wide journal bearing. Though the theory has been considerably upgraded hitherto, Jakobsson and Floberg’s 1957 model for a finite journal bearing [131] (JaFl 1957) remains a simple method for explaining hydrodynamic lubrication in journal bearings. Hence, the basic concepts are reproduced herein.

Consider the geometry of the flow, as in the original work of Jakobsson and Floberg [131] (JaFl 1957) given in Figure 1.1.4.1 for left handed rectangular coordinates.

Figure 1.1.4.1 Flow geometry (clearance exaggerated).

The following assumptions have to be made: the fluid is considered thin that there are no variations in pressure throughout its thickness; the fluid attaches to both surfaces, i.e. no slip, and completely fills the gap; the fluid is Newtonian; fluid film temperature and viscosity are constant across and throughout the gap; fluid film is incompressible; the flow is laminar.

Note that all these assumptions are “valid” for monotone convergent wedge geometries only.

For Newtonian fluids, the shear stress x is proportional to the velocity gradient ∂u / ∂y:

y u x     (1.1.4.1)

The constant of proportionality, , in eq. (1.1.4.1) represents the dynamic viscosity of the lubricant. The concept may be defined in reference to Figure 1.1.4.2, where a plate of area A

is propelled with a force F at a velocity U, such that a fluid film of constant thickness h exists

between the moving plate and a stationary plane surface. The shear stress which must act on the plate’s underside is given by x = F / A. The velocity gradient is assumed to be constant

throughout the thickness of the fluid film, and is ∂u / ∂y = U / h. Hence for the case of Couette laminar flow between parallel plates, Figure 1.1.4.2, the shear stress is given by eq. (1.1.4.2):

U x    (1.1.4.2) z y 1 U 2 U V 2 1 x

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Figure 1.1.4.2 Couette laminar flow in a parallel gap.

In steady state conditions, the sum of forces acting on an infinitesimal fluid element, with sides dx, dy and dz, contained in Figure 1.1.4.1 gap is zero, i.e. conservation of momentum:

y z p y p y x p z x                0 (1.1.4.3)

where p is the fluid film pressure; x and z, the shear stress in the x and z directions

respectively; and x, y and z the rectangular coordinates.

Due to flow continuity, the divergence of the velocity field is zero:

0         z w y v x u (1.1.4.4)

with u, v and w representing the velocities of a fluid particle in the x, y and z directions.

Combining eq. (1.1.4.1), adapted for z direction also, and eq. (1.1.4.3), one obtains momentum equations for Newtonian fluids:

z p y w y p x p y u                1 0 1 2 2 2 2 (1.1.4.5)

Reynolds’ momentum equations, eq. (1.1.4.5), represent the thin film flow particular case of the general Navier [196] (Na 1823) – Stokes [254] (St 1845) momentum conservation equations. The Navier-Stokes system of equations is the most powerful tool for characterizing fluid film flow hitherto.

Integrating eq. (1.1.4.5), and considering flow continuity for incompressible fluids, eq. (1.1.4.4), one obtains the partial differential equation for the pressure in the bearing in rectangular coordinates: U F O x y A h

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V x h U U z p h z x p h x 6 1 2 12 3 3                    (1.1.4.6)

For a general-use journal bearing and at steady-state operating conditions: U1 = V = 0, and U2 = U = π D n. Though, most of the assumptions are not valid for a general-use journal

bearing, as heat is generated through viscous friction and fluid flow is not isothermal, nor is it isoviscous. Furthermore, Reynolds equation is invalid in the divergent zone where cavitation occurs and the film is not complete.

The Reynolds equation eq. (1.1.4.6) can be adapted to handle variations of viscosity and temperature, such that it can be used together with the energy equation and heat conduction to the shaft and bushing, with adequate boundary conditions, for thermohydrodynamic (THD)

solutions. Dowson and coworkers [62] (Do 1962) [65](DoMa 1966-1967) [67](DoTa 1979)

had a great contribution in the field, as explained in the following sections.

Generalized forms of the Reynolds equation, depending on the application, and including other pressure generation mechanisms than geometric convergent wedges are available in the literature. Consider the example given for a fluid with variable density and viscosity in the

Fundamentals of Fluid Film Lubrication handbook [112] (HaScJa 2004), written also for a left-handed coordinate system:

t h z h W x h U V V W W h z U U h x z p h z x p h x                                                                2 2 1 2 1 2 1 2 3 3 2 2 12 12 (1.1.4.7)

By reducing the two-dimensional flow into a one-dimensional case, one can explain other pressure build-up mechanisms with a generalized Reynolds equation [112](HaScJa 2004):

                                          expansion Local Squeeze 2 1 2 Couette 1 2 Poiseuille 3 2 12 x h t h U V V U U h x x p h x nal Translatio Normal                                                    (1.1.4.8)

With the Couette term of eq. (1.1.4.8) leading to three separate actions [112](HaScJa 2004):

 

                                wedge Physical 1 2 Stretch 1 2 wedge Density 1 2 Couette 1 2 2 2 2 2 x h U U U U x h x U U h U U h x                        (1.1.4.9)

The physical wedge term, also described throughout this section represents best method for pressure generation. The density wedge term requires density to decrease in the sliding direction for positive pressures to be generated (form of the term is identical to the physical wedge). The decrease of fluid density in the sliding direction can occur when temperature increases in the flow direction, hence the term is sometimes called the “thermal wedge”. The pressure built-up mechanisms given in eq. (1.1.4.8) and eq. (1.1.4.9) can occur simultaneously

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depending on the application. The “thermal wedge” has been sometimes associated with the “Fogg effect” [103] (Fo 1946), where pressure is generated in parallel-surface bearings. Fortunately, research within the last decades has proved that rigid THD solutions are not sufficient, and the “Fogg effect” [103] (Fo 1946) was mainly due to thermoelastic deformations of bearing components that created local physical wedges [92](FiFrBo 1987); though the thermal wedge still occurred, its contribution to pressure build-up was much smaller.

Conventionally, the stretch mechanism is not likely to occur in bearings, as it requires the boundary surfaces to be elastic and to stretch throughout the bearing in a variable way [112] (HaScJa 2004). The mechanism occurs in cold rolling processes where the exit velocity of a slab is higher than at entry, as deformations occur.

A pressure build-up mechanism appears also if wall slip is altered in the sliding direction, i.e. through heterogeneous slip / no-slip surfaces [239](SaFo 2004) [104](FoSa 2005). However, opposed to the plastic deformation stretch mechanism, the pressure build-up appears as the flow rate is modified by changing the stationary surface velocity profiles through alternating slip / no-slip zones. The no-slip boundary condition has been adopted by researchers as a tool for developing lubrication, though there is no reason it should apply to all cases. Fortunately, most lubricants are compatible with usual bearing materials; hence the no-slip case is adequate for conventional bearings [121] (Hi 1976). But, if one can engineer heterogeneous slip / no-slip surfaces, then the decrease in fluid velocity along the flow enables pressure build-up [239](SaFo 2004) [104](FoSa 2005). Such surface engineering can be analogous to the texturing of surfaces intended to create local physical wedges [226](PaMaGă 2004). For fluid local expansion to generate positive pressures, the density must decrease in time. This lubricant swell in time is usually insignificant in bearing analysis [112](HaScJa 2004).

Squeeze can become very important especially at low film thicknesses and / or high surface

approach velocities [17](Bo 1965). For journal bearings running under dynamic loading, it is essential to take into account the changes in flow geometry in time.

From the discussion presented in this section, it is clear that Reynolds equation can be used to

describe the pressure build-up mechanism in journal bearings. Performance parameters are

obtained by solving eq. (1.1.4.8) with appropriate boundary conditions. The approach is valid for the convergent zone where the developed fluid flow is continuous in the radial direction,

however is not valid for the most of the divergent zone. Unfortunately, one cannot simply “remove” the divergent zone for journal bearings. Even so, that would be a mistake as it contributes to bearing stability [100](Fl 1968)[101](Fl 1973a)[102](Fl 1973b). Neglecting

it will lead to inaccurate estimations in thermomechanical performance parameters and in the film extent as mass conservation will not be fulfilled. Though there are some workarounds

developed in the last decades [75] (El 1981), the solution is to study it and try to create

theoretical models based on actual the physical phenomena [26](BrHa 2010).

Reynolds equation is an approximation, and complicated designs might require much more powerful mathematical approaches, e.g. direct Navier-Stokes simulations [204](Or 1970).

Understanding how journal bearings actually work enables improving design efficiently and avoiding errors; it is an ongoing process that started in the 19th century. As science progresses, there are several questions that require answering: what have we learned from the past? what do we know now about their operation? and what can we do to improve our understanding?

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1.2 State of the art on Journal Bearings Research

The concept of State of the art is defined as the level of knowledge and development achieved in a technique, science [194](NaVé 1984).

1.2.1 The first steps

Tower [277](To 1883) was the first author to experimentally report a pressure increase within the lubricant film during operation, not matching the theoretical average pressure obtained by dividing the load to the bearing area, pm= W / (B D). The second report by Tower [278](To 1885) included measurements of pressure at the fluid-film bearing interfaces. The works of Tower started the interest of hydrodynamic lubrication research, though Reynolds [236] (Re 1886) is credited as the first researcher in the field of hydrodynamic lubrication. Reynolds

[236] (Re 1886) derived mass and momentum conservation equations with the lubrication assumptions, theoretically describing the pressure build-up mechanism reported earlier in Tower’s experiments [277](To 1883)[278](To 1885).

A second step in improving theoretical understanding has been taken by Sommerfeld [251] (So 1904), developing the infinite wide journal bearing analytical model by neglecting the edge effects. It is worthwhile mentioning that the early journal bearings had a very wide aspect ratio, when compared to modern narrow journal bearings, Figure 1.2.1.1.

Figure 1.2.1.1 Wide (left [134](Je 1912)) vs. narrow (right [302](Göttingen 1968)) journal bearing designs (images were scanned from the original sources).

Gümbel [111] (Gü 1914), addressed the negative pressures that appeared with Sommerfeld’s model [251] (So 1904) by setting them all to zero or ambient levels. Simple approaches on handling the divergent zone cavitation phenomena were pursued also by Swift [264] (Sw 1931) and Stieber [253] (St 1933), independently. They [264] (Sw 1931) [253] (St 1933)

considered that the pressure gradient is null at the rupture boundary, in addition to Gümbel’s hypothesis [111] (Gü 1914). Unfortunately these solutions [111] (Gü 1914)[264] (Sw 1931) [253] (St 1933) are inadequate, as they do not conserve mass and do not reflect the actual physical cavitation phenomena. Although, they can approximate capable load with a good agreement as long as tensile stresses can be neglected [52](CoEl 1971).

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Pioneer research concerning power losses has been undertaken also by Petrov [228] (Pe 1883). Stribeck [255] (St 1902) investigated friction in journal bearings, function of loading and speed. He showed that lubricated sliding bearings the friction was high at low speeds, decreased to a minimum as the metal contact was stopped as the speed augmented, and increased again at higher speeds. As Jacobson [130] (Ja 2003) highlights, Stribeck showed

that operating conditions leading to minimum friction exist for lubricated sliding bearings.

A first study concerning heating effects in lubricating films was put published by Kingsbury

[143] (Ki 1933). Assumptions for the thermal model included radial heat flux continuity throughout the film layers and the fluid-surface boundaries, laminar flow etc. Experiments with a variable speed rotational viscometer showed a reduction of shearing stresses, following an internal heat generation temperature increase. Kingsbury was a pioneer in THD research, by considering viscosity variations along and across the film thickness [143](Ki 1933).

McKee and coworkers [169](McMc 1932)[171](McWhSw 1948)[170](McWh 1950)[168] (Mc 1952) studied various bearing designs and lubricant supply and configurations, measured bearing pressure and temperatures, and several performance parameters during the first half of the 20th century. Their experimental research involved bearings with decreasing length to diameter ratios. Though near unity, the shift from wide bearings to narrow bearings started.

Clayton and Wilkie [43] (ClWi 1948) performed measurements of the temperature distribution in the bush of a plain journal bearing at many operating conditions and configurations, by sliding thermocouples axially at various radial locations and extrapolating gradients. Though measurements were not taken at the fluid film-bushing interface, the tests provided important insight on the temperature field in the circumferential and axial directions. The axial gradients far from the supply grooves were moderate as isotherms followed the axial coordinate, except for circumferential groove bearings. For CGJBs the isotherms’ local peaks were shifted towards the environment from mid-land. Barwell [8] (Ba 1956) attributed the shift to misalignments caused by the test rig’s [43](ClWi 1948) cantilever loading.

1.2.2 A leap forward

The research started by DuBois et al. [68] (DuMaOc 1950) in the 1950’s had a profound contribution to the field. Simultaneous measurements [68] (DuMaOc 1950) of film pressure and bearing temperatures have been performed at high load and high speed operating conditions. Though temperature measurements were not taken at the fluid film–bushing interface, but offseted with 1.6 mm radially in the bush. It enabled reconstructions of the pressure and temperature 2 D fields into 3 D surface map plots. Misalignment effects on bearing performance were also investigated. DuBois and Ocvirk [71](DuOc 1952) continued the experimental research on journal bearings supplied through an inlet hole for a broad range of aspect ratios, B / D = 0.25 … 2, lubricants and operating conditions. The focus was shifted towards performance parameters such as: eccentricity ratio, friction torque, oil flow rate and shaft locus. The later studies [69] (DuOcWe 1955) [70] (DuOcWe 1957) also concerned performance parameters and pressure and temperature fields, though not simultaneous as in the first paper [68] (DuMaOc 1950). DuBois and Ocvirk developed also the isothermal narrow journal bearing theory [201] (Oc 1952)[72] (DuOc 1953). The theory had been used extensively until the start of the information age and the development of personal computing.

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Figure 1.2.2.1 Film reformation with lubricant supply (left) vs. film rupture (right), taken from Cole and Hughes [45](CoHu 1956).

journal bearing operation. They conducted an experimental research on axially and circumferentially grooved journal bearings, in addition to classical one supply hole designs. Lubricant flow rates have been measured for a variety of aspect ratios, and flow photographs have been taken for glass bearings with usual clearance ratios. A comparison of friction losses available in the published literature with conventional film extent models, such as Sommerfeld 0 … 2π and DuBois and Ocvirk 0 … π, revealed that the extent of friction generating film rests between the full and half bearing concepts [251] (So 1904) [72] (DuOc 1953). The study [45] (CoHu 1956) stated, more precisely, that considering a full film model

in friction calculations would introduce a 30 % error in the result. Moreover, flow

visualizations showed incomplete films regardless of the groove configurations or supply pressures, left side of Figure 1.2.2.1. The divergent zone photographs showed the breakdown of lubricant film into thinning streamlets, e.g. right side of Figure 1.2.2.1; a well known but not yet fully understood process even today.

A breakthrough in cavitation research came from Dowson [61] (Do 1957), by publishing the first direct comparison of pressure measurements with photographs taken for the flow in the divergent zone. Experiments had been conducted for a stationary spherical cap bearing and a plane slider. Sub-cavity pressures had been measured just before the oil film rupture, invalidating the Swift-Stieber boundary conditions, dp / dx = p = 0, that predicted flat pressure distributions at atmospheric values. The location of film rupture was shifted downstream the minimum film thickness point; this confirmed Cole and Hughes’s [45] (CoHu 1956) earlier finding. Moreover, the experimental pressure field was compared with the theoretical solution. Acceptable agreement was found for the convergent zone, depending on the lubricant. For the low loads investigated, the experimental pressure distribution resembled the full-Sommerfeld solution.

1.2.3 The interest on cavitation. Part one: the mass

conservation milestone

What is worthwhile mentioning is that despite several congresses and countless papers on the subject, e.g. [304](Leeds-Lyon 1974) [305] (STLE Sp. Publ. 28 1990), cavitation is has not been solved, though there are some milestones and important research in the field; this is detailed during the current section.

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1.2.3.1 The Jakobsson-Floberg-Olsson (JFO) mass-conserving model

Jakobsson-Floberg-Olsson (JFO) [131] (JaFl 1957) [98] (Fl 1961c) [203] (Ol 1965) theory development started with a research for infinite-wide bearings [94](Fl 1957). JFO is the first

cavitation theory that respected conservation of mass. Floberg [94](Fl 1957) measured a flat

pressure distribution in the divergent zone of the bearing, and stated that the lowest pressure for an ideal oil film is its vapor pressure. The vapor pressure of ideal oils is near vacuum [131] (JaFl 1957). If air is present in the oil, the lowest pressure in the film was attributed to the air saturation pressure. Later experimental studies revealed that liquids can reach tensile

stresses lower than absolute zero [100](Fl 1968).

Maintaining the assumptions for the infinite wide bearing and with the aid of Jakobsson, a cavitation model for finite bearings has been developed [131] (JaFl 1957). They adopted for film separation, i.e. the onset of cavitation, vanishing pressure derivatives boundary conditions, i.e. dp / dx = dp / dz = 0. The cavitation model assumed that the lubricant film separates from itself into streamers at the rupture point, and the streamers are attached to both journal and bearing surfaces. For conserving mass, the Couette flow at rupture, i.e. start of separation, needs to be balanced with the Couette and Poiseuille flows at reformation. Mathematically this leads to a differential equation linking the film thicknesses at rupture and at reformation to the pressure gradients in the circumferential and axial directions. Main drawbacks of the approach remain: the unknown film thickness at rupture location; flat pressure distribution in the cavitated region; the convergence criteria of the numerical model.

Figure 1.2.3.1 Film separation and reformation with JFO model (axial groove supply bearing).

Comparing Figure 1.2.2.1 with Figure 1.2.3.1, one can see a clear resemblance between the experimental observations and the theoretical model of JFO theory: appearance of streamlets; the streamlets are narrowing in the direction of rotation to conserve mass flow.

The impact of the JFO theory was first highlighted at power loss calculations. The resistance of air fingers in the divergent zone are negligible due to low viscosity, therefore viscous drag is only due to oil streamlets [95] (Fl 1959). Estimating how many oil streamlets appear in a journal bearing is not a simple problem, and guess values ranging from zero to infinity have been used for theoretical comparisons with experimental measurements.

oil air se p a ra ti o n b o u n d a ry re fo rma ti o n b o u n d a ry

journal rotation oil streamer span decreases cavitated region

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Another important discovery was that cavitation is not tied to the atmospheric pressure [96] (Fl 1961c); it occurs when the pressure becomes lower than the pressure where the oil is in contact with air or gases. Further experimental studies on cavitation [97] (Fl 1961b) enabled selecting arbitrary pressures for cavitation in theoretical models; they range between atmospheric pressure and absolute zero. As general comments: Floberg rarely performed tests outside a 25-30 °C temperature range, hence the isothermal approaches; the experimental bearing was enclosed in a oil bath, and supplied with lubricant by in-flow at the sides.

Olsson [203](Ol 1965) studied cavitation phenomena in dynamically loaded journal bearings with similar boundary conditions as in the works of Floberg and Jakobsson, though independently at the same university. His contributions for describing the flow continuity relative to a moving cavity boundary have been very important, hence the JFO acronym.

Researchers avoided using the JFO model due to its complexity, until Elrod and Adams [77] (ElAd 1974) came up with an algorithm based on the mass continuity conditions similar to JFO. The algorithm was later refined by Elrod [75] (El 1981). Both algorithms [77] (ElAd 1974) [75] (El 1981) are still in use today, though they do not agree with the actual flow observations and pressure measurements in the divergent zone. Other researchers in the field showed that: a thin layer of lubricant adheres to the rotating journal and detaches from the

stationary bearing surface [51](CoEl 1970)[52](CoEl 1971), contradicting JFO separation;

strong reverse flow exists, and flows attached to the bushing from the reformation boundary towards the separation [191] (MoMiAbFu 1967) [82] (EtLu 1982); the film separates both

from itself and from the stationary surface [119](He 1991), i.e. an unifying conceptual model of the flow based on experimental visualizations. These studies are detailed in a following subsection. What is rarely commented by other researchers in the field is that Floberg also a

worked on cavitation theory considering bubbles in the divergent zone [100](Fl 1968).

1.2.3.2 Floberg on bubble theory and tensile strength of liquids

To sort a contradiction between measurements of sub-ambient pressure loops upstream the separation and the flat pressure distribution assumption in the divergent zone, Floberg [100] (Fl 1968) published another paper on infinite wide journal bearings. He mentioned that for

normal to heavy loaded bearings, the performance is not affected by the sub-ambient pressure loop. For bearings operating with low loads, the extent of the cavitation zone and the pressure distribution has an influence on their performance.

In a previous research [99](Fl 1965), Floberg showed a connection between the number of oil streamers in the cavitation region and lowest pressure in the film. Small gas bubbles are contained in liquids, and the higher is the pressure of the gas that is in contact with the liquid, the more gas is dissolved.

As the pressure lowers, some of the gas will leave the liquid. Floberg [100] (Fl 1968)

describes cavitation as a bubble growth process in a liquid supporting tensile stresses. Assuming that adhesion and cohesion stress strength in the liquid are of a higher order than of the bubble, it is the size of the bubble that sets the tensile strength of the liquid. The main problem is to know the size of bubbles at equilibrium in a liquid. While the pressure in the gas bubble is higher than ambient pressure, the molecules of gas will move into towards the surroundings, passing through the liquid in a slow process. Furthermore if cavitation pressure is considered the pressure of the surrounding gas, the sub-cavity pressure is a pressure drop

Figure

Figure 1.2.4.1 Experimentally determined temperature distribution in a bearing bush,   taken from Dowson et al
Figure 1.2.4.2 Experimental and theoretical bush isotherms in degrees Celsius,   taken from [184] (MiHoTa 1986) (several isotherms re-colored)
Figure 1.2.5.1 Submerged journal bearing axial pressure measurements,   taken from Etsion and Ludwig [82] (EtLu 1982) (adapted)
Figure 1.2.5.3 Oil flow with the inlet groove in the cavitated region   (a – axial supply, b – circumferential supply),
+7

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سداسلا لصفلا ع ضر جئاتنلا ةشقانمو ليلحتو 82 اهلكشب ةيكرحلا ةراهملا ملعت ؟حيحصلا لا 11.76 % 8 - نكمي هنا دقتعت له بلغتلا ملعتلا يف تابوعصلا