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CHAPTER-I

GENERAL INTRODUCTION

1.1 General Introduction

1.2 Types of Lubricants

1.2.1 Fluid-lubricant Properties

1.3 Mode of Operation

1.3.1 Hydrodynamic Lubrication

1.3.2 Hydrostatic Lubrication

1.3.3 Boundary Lubrication

1.3.4 Elastohydrodynamic Lubrication

1.3.5 Partial (Mixed) Lubrication

1.3.6 Turbulent Lubrication Regime

1.3.7 Magnetohydrodynamic (MHD)

Lubrication

1.3.8 Rarefied Gas Lubrication

1.3.9 Porous Metal Lubrication

1.3.10 Biolubrication

1.4 Types of Relative Motion

1.5 Geometry of Bearing Surfaces

1.6 Types of Loading

1.7 Bearing Design Characteristics

1.8 Review of Related Literature

 

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1.1 GENERAL INTRODUCTION:

The present day machine technology is dependent on mechanisms involving

kinetic pairs where mechanical power has to be transmitted between that are in

relative motion. Two most important inherent phenomena associated with such a

system are those of friction and wear. It is the friction which resists relative motion of

the surfaces and causes wear. It consumes and wastes energy due to noise and

generation of local surface heat. Wear causes changes in dimensions and results in

eventual breakdown of the machine element and consequently the entire machine and

all that depend upon it. The aspect of loss of energy and loss of material due to

friction is astonishingly large.

Professor Vogelpohl (1951) [Hamrock (1994)] has estimated that from one

third to one-half of total energy produced in the world is consumed in friction.

Automobiles, trucks, buses, trains, airplanes, ships and the like, effectively expenses

most of their power in overcoming friction. The automobile engine delivers useful

work only after the friction is reduced. This useful work is then largely consumed in

gear friction, rolling friction of the tires, brake friction, and wind friction etc.

The effect of wear is of equally mementoes significance. Wear may be defined

as deterioration of surface due to use. It occurs in wide variety of operations and in

some industries the annual cost of replacing worn parts is a major expense. Wear

causes the deformation of the machine elements and changes in its dimensions which

may result in seizure of surfaces, reduction in machine life or in its serious break

down thus enormously increasing the running and maintenance cost of machines. For

the conservation of energy and material from natural resources point of view the

reduction of friction and wear through proper means is a basic necessity.

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In 1966 with the publication in England of the “Department of Education and

Science Report”, some times known as the “Jost Report, the word "Tribology" was

introduced and defined as the science and technology of interacting surfaces in

relative motion and of the practice related there to. A better definition of "Tribology"

might be "The integrated study of friction, wear and lubrication".

In order to minimize friction and wear between moving machine elements a

foreign substance known as lubricant is introduced in between them. The lubricant

keeps the machine elements apart and allows them to move relatively with minimum

efforts. Such a system where lubricant is used is called lubricated system and the

process of minimizing the friction and wear using lubricant is called lubrication. The

machine component which serves to achieve the smooth motion of the machine

surfaces using lubricant is called bearing. Bearing is an important component in

machines. It is a support or guide that locates one component with respect to others in

such a way that prescribed relative motion can occur while forces associated with

machine operation are transmitted smoothly and efficiently. It transmits loads and

forces or supports load exerted on the moving machine parts under reduced friction.

Design of bearing requirements are imposed on the mechanical system by the

bearings. There is a continuous demand for better bearing systems to support moving

machine components in regard to improved performances and exacting operation

conditions and research efforts are directed towards achieving these objectives.

Bearings may primarily be classified on the basis of following factors:

(1) Types of lubricants

(2) Mode of operation

(3) Types of relative motion

(4) Geometry of bearing surfaces

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(5) Types of loading

(6) Type of bearing materials

1.2 TYPES OF LUBRICANTS:

Selection of lubricant depends upon the type of the bearing which is used in the machine

elements. Solids, liquids, gases or even plasma are used as lubricants. Commercial lubricants can

roughly be grouped in three generic type namely; solid lubricants, semi-solid lubricants and

liquid lubricants. The bearings using solid lubricants are called dry rubbing bearings, whereas

those using fluid as lubricants are called conformal fluid film bearings. In dry rubbing bearings

the load carrying and frictional characteristics can directly be related to basic contact

properties of the bearing materials and the lubricant used.

Solid lubricants are used in cases where lubricating oils and greases can not be used

because of contamination reasons. Solid lubricants are used in high temperature

conditions or in machines working under high pressure and low speed condition.

Common semi-solid lubricants are greases and polymer thickened oils. Grease

consists of a soap dispersed throughout liquid lubricating oil. Main function of the soap is

of thickening agent so that grease sticks firmly to bearing surface. These are used in variety of

applications like rail axle boxes, paper textile and food producing, machinery and bearings

and gears working under high temperatures like hot rolling machine where it is used to reduce

roll load.

Most liquid oil lubricants can be classified in to vegetable oils, mineral or petroleum

oil, blended oil, synthetic oil and emulsions.

Animal and vegetable oils have good oiliness even under high temperatures and loads.

They undergo oxidation and have tendency to hydrolyze in moist air and are used as blending

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agents with other lubricating oils. They are mainly used for delicate instruments like watches,

clocks, sewing machines etc.

Mineral or petroleum oils are obtained by distillation of petroleum. These type of

lubricants are stable under service conditions but possess poor oiliness. Naphthenic and paraffinic

are the main two types of such oil. The first kind acts as a very good lubricant for almost any

application. It contains very little wax, where as the paraffinic oil is very much waxy and is used in

hydraulic equipment, steam engines, elevators, cranes etc.

It is possible to improve the typical lubricating properties of petroleum oils by adding

specific materials as additives. Oiliness of lubricating oil can be increased by the addition of

vegetable oils and fatty acids. In many applications the lubricant becomes mixed with air as is

frequently the case. It will begin to oxidize and the rate of oxidation will get accelerated if catalytic

action of metals is present and as the temperature rises. This may produce unwanted products - the

gums, varnishes and the sludge and the lubrication is seriously interfered with.

Synthetic lubricants can extend the life of equipment which operates at extreme

temperatures: some eliminate fires of oxidation with highly reactive materials and they

reduce maintenance and down time. Such lubricants have remained special lubricants for

unusual applications. The important synthetic lubricants are silicon fluids. Most widely

recognized synthetic lubricants are silicones having least change in viscosity, wide temperature

range, good thermal stability and good oxidation stability.

An emulsion is two phase system consisting of a fairly coarse dispersion of two immiscible liquids,

one being dispersed as droplets in other. Oil in-water or water in-oil emulsions are used in several

situations as lubricants. 3 to 20 % water emulsions are used for cutting tools, 40 % water

emulsions are used for compressors and pneumatic tools. High viscosity oil emulsions with

water are used for steam engines. Soap emulsions are used for wet wire drawing.

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Ferro liquids are ordinary liquids containing stable colloidal dispersions of finite

particles. They behave as ordinary liquids except that they experience a body force in the

presence of an applied magnetic field gradient. The use of ferromagnetic fluids as

lubricant in fluid film bearing is mainly attracted by its magnetic sealing effect and boundary

lubricating effect. Under a suitable design of the bearing geometry and magnetic field, the

Ferro fluid lubricated bearing can operate without side leakage, so that mechanical seals

can be eliminated, and bearing friction at both ends can be reduced. The boundary

lubricating effect of the Ferro fluid, retained at the sliding surface by magnetic field, can

reduce the friction and wear between the bearing surfaces under low velocity operating

conditions. [Mikaye and Takahashi (1985)].

Gases are preferred as lubricants on account of its several advantages, like :

(i) Low frictional force and torque due to reduced lubricant viscosity,

(ii) Low power loss, cool running characteristics and very low wear rate,

(iii) Operate over a large range of speed and temperature

(iv) Almost no periodic maintenance, virtually no problem of contamination and therefore no

requirement of seal.

However, a gas lubricated bearing has inferior load carrying capacity compared

to identical oil bearing; besides they are prone to instability. Air is used as lubricant in many

high speed spindles. Wind tunnel balances, torque -meter, machine tool sideways,

gyroscopes, accelerometers, electric motors, refrigerators, liquefies, computer elements,

dental drill machine etc., use air as lubricant because of the advantage of low frictional force.

Gas circulators use gas as lubricant because of its being contamination free. In a number of

chemical plants air is used as lubricant because of high temperature conditions.

Gas bearings are particularly valuable when used with precision instruments because of

low noise characteristics and low frictional losses. When the distance between molecules of

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the gaseous lubricant becomes large enough the fluid no longer acts as if it were continuum,

particularly, in the situations where very small film thickness are involved as in low vacuum

conditions such as magnetic storage devices and gyroscopes etc. The lubricant in these

situations is a rarefied gas [Ramanaiah (1969)].

In addition to their function of reducing friction the lubricants also perform the

function of carrying away a major portion of heat generated by the friction. Thus the theory

of lubrication deals not only with the ways of minimizing the friction and wear, but the

viscous dissipation of heat also.

Most of the lubricants used come from the range of fluids; hence the study of fluid film

lubrication has assumed considerable importance.

1.2.1 Fluid-lubricant Properties:

The lubricant is required to possess certain physical, chemical and

metallurgical properties commensurate with the system where it is required to be

used..

In order that a lubricant is to be effective, it must be viscous enough to maintain a

lubricant film under operating conditions but should be as fluid as possible to remove heat

and to avoid power loss due to viscous drag. A lubricant should also be stable under thermal and

oxidation stresses and have low volatility.

This is the most important single property of fluid lubricant as it determines the fictional

power loss and heat generation in bearing and the flow rate through the bearing. In general,

however, a lubricant does not simply assume a uniform viscosity in a given bearing. This results

form the non uniformity of the pressure and/or the temperature prevailing in the lubricant film.

Indeed, many elastohydrodynamically lubricated machine elements operate over ranges of

pressure and/or temperature so extensive that the consequent variations in the viscosity of the

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lubricant may become substantial and in turn, may dominate the operating characteristics of the

machine element.

It is a well-known fact that many common lubricants, including petroleum -base lubricants,

undergo considerable increase in viscosity when they are subjected to high pressures.

The increase in viscosity due to pressure will raise the friction losses in the bearing.

The viscosity of a lubricating oil decrease with a rise in temperature. In many

important practical applications this variation in viscosity with temperature is very significant as is in

the case of automobile engine crank-case. High viscosity of oil means excessive bearing resistance

during cold starting with heavy demands upon the battery. After the engine has warmed up, the oil

viscosity becomes lower. If this reduction in viscosity is too great, wear, or even seizure may then

result. Hence knowledge at the variation of viscosity with temperature is of great

importance in determining the suitability of a lubricating oil for a particular use.

Besides, the variations of viscosity with temperature, a number of other thermal

properties of fluids as lubricants are important especially, specific heat and thermal conductivity.

Viscosity is sensitive to large variations in both pressure and temperature. This

sensitivity forms a considerable obstacle to the analytical description of the consequent viscosity

changes. Roelands (1966) noted that at constant pressure the viscosity increases more or less

exponentially with the reciprocal of absolute temperature. Similarly, at constant temperature the

viscosity increases more or less exponentially with pressure.

Viscosity also change with shear rate. Liquids whose viscosities are

independent of the shear rate are known as "Newtonian". Liquids whose viscosities vary

with shear rate are known as "non-Newtonian". The pseudoplastic fluids are characterized by

linearity at extremely low and extremely high shear rates. The dilatant fluid exhibits an increase

in apparent viscosity with increasing shear rate.

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For a range for which the effects of temperature and pressure on viscosity are found

to be important, the density changes in case of lubricating liquids are small relative to the

viscosity change. Extremely high pressure exists in elastohydrodynamic films and the

lubricant can no longer be considered as an incompressible medium. It is therefore

necessary to consider the dependence of density on pressure in such cases. The variation of

density with pressure is roughly linear at low pressure but the rate of increase falls off at high

pressure.

The physical and chemical properties of commercial lubricants are

expressed in terms of various parameters like viscosity index, flash point, pour point,

saponification number, neutralization number etc.

1.3 MODE OF OPERATION:

Various aspects of the motion of machine elements in conjunction with the lubricant

give rise to different modes of operation.

1.3.1 Hydrodynamic Lubrication:

Hydrodynamic lubrication implies a process in which two surfaces moving at some

relative velocity with respect to each other are separated by a fluid film in which the pressure

forces that separate the surfaces are generated by virtue of the relative motion only. The

relative motion indeed generates positive pressure only if the geometrical configuration is

favorable. It the relative motion tends to drag fluid from a divergent space towards a

convergent space, positive pressure (pressure above atmospheric pressure) is generated.

If, however, the relative motion tends to drag fluid from a convergent space to a divergent

space, negative pressure (pressure below atmospheric pressure) develops.

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In hydrodynamic lubrication the lubricant film is generally thick so that the machine

elements are prevented from coming into potential contact. However, the main drawbacks of this

mode of lubrication is that at low speeds heavy loads cannot be carried and moreover there is

appreciable wear because of frequent stop and start up and motion reversal.

1.3.2 Hydrostatic Lubrication:

When the pressure to fluid film, which separates two surfaces in motion and which

supports the load, is applied from an external agency (pump, accumulator, etc.), the

bearing is classified as hydrostatic bearing. Hydrostatic bearings can be designed to give

predetermined performance characteristics, e.g., optimization in terms of flow, pressure, load

capacity, stiffness, friction and pumping power. Hydrostatic bearings have been designed to

give, where necessary, extremely low coefficient of friction, and on the other hand, they have

been designed to give extremely high stifles. In large telescopes and radar tracking unit

hydrostatically lubricated bearings are used, where extremely heavy loads an< extremely low

speeds are used. In machine tools and gyroscopes also hydrostatically lubricated bearing are

used as there are extremely high speeds, light loads, and gas lubricants are used. A number

of studies on hydrostatic lubricated bearings have appeared [Raimondi and Boyd

(1957); Ghosh and Majumdar (1978, 1980)].

1.3.3 Boundary Lubrication:

Boundary lubrication occurs when the intervening lubricant film between two sliding

surfaces does not completely separate the surfaces. In practice, boundary lubrication

covers a major portion of lubrication phenomena. Even in bearings which are designed for

hydrodynamic lubrication, boundary lubrication occurs during starting, stopping, and during periods

of severe operation.

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Sometimes due to adverse operating conditions, break down of the

hydrodynamic action takes place. At low speeds or high loads, thickness of lubricant film

decreases until high spots on the mating surfaces begin to rub on another and bearing surfaces no

longer are completely separated by a fluid film but partial metal to metal contact takes place which

increase friction and wear. This may take place in other situations as well e.g. (i) when viscosity of

the lubricant is very low (ii) the system is starved off of the lubricant (iii) converging wedge is not

formed. This mode of lubrication is called boundary lubrication. Boundary lubrication is

not the most desirable operating mode, yet at times, it is completely unavoidable. It is

encountered mainly with slow moving loads where cost of a hydrostatic bearing is

probhibitive. Bearings under start or stop condition, valve without converging wedge,

machine tool slide way, gears etc. are the examples where boundary lubrication conditions

exist. Mechanisms such as door hi operate under conditions of boundary lubrication.

The understanding of boundary lubrication is normally attributed to H and Doubleday

(1922.3, 1922.b) who found that extremely thin films adherir surfaces were often sufficient to

assist relative sliding. They concluded that u such circumstances the chemical composition of

the fluid is important and introduced the term “boundary lubrication". Boundary

lubrication is at opposite end of the lubrication spectrum from hydrodynamic

lubrication, boundary lubrication the physical and chemical properties of thin films

molecular proportions and the surfaces to which they attached determine con behaviour. The

lubricant viscosity is not an influential parameter. Because boundary lubrication the

surfaces are not separated by the lubricant, fluid f effects are negligible and there is

considerable asperity contact. The friction characteristics are determined by the properties

of the moving surfaces and lubricant film at the common interfaces. In boundary lubrication,

the roughness the surfaces plays an important part and has to be considered.

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1.3.4 Elastohydrodynamic Lubrication:

In certain situations distortion of the surfaces due to the heat generation important

which results in the changes in the film thickness which are of the sai order of magnitude as the

film thickness itself and this has a strong effect on the pressure development. Infact, a portion

of load carrying capacity of the parallel surface bearing may be due to this phenomenon.

Another source of distortion is the pressure itself which, if high enough, can distort the

bearing on slider on both and in so doing change the pressure distribution. The study of

this effect is called elastohydrodynamic lubrication [Dowson and Higginson (1966)]. This

effect is particularly important in the lubrication of gear and roller bearings where very high

pressure can be developed. In order to solve this problem which involves the interaction of elasticity

and fluid flow phenomena, it is necessary to consider the film thickness hi the Reynolds

equation as a function of the pressure. The other equations needed are an elasticity equation that

relates the displacement of the solid surfaces to the stress system [Timoshenko and Goodier

(1955)] and a relationship between viscosity and pressure.

The first problem to be solved seems to have been for rollers deformed by pressure

generated with a fluid whose viscosity was altered by the pressure [Grubin (1949)].

Osterle and Saibel (1958) discussed the performance of the slider bearing with bearing elasticity,

proving that the deflection of the bearing under higft load reduces the load carrying capacity

of the bearing. Ramanaiah (1968) analyzed the effect of bearing deformation hi squeeze

films between two long rectangular plates. It was shown that under high loads the bearing

will deform producing wedge effect in the lubricant film and the deformation decreases the

load capacity of the bearing. It was assumed in the analysis [Osterle and Saibel (1958);

Ramanaiah (1968)] that the deformation under the elastohydrodynamic conditions is the

same as it would be under the static conditions.

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The effect of elastic distortion on the bearing performance have be studied

among others by Carl (1964), Higginson (1965), O'Donoghue et al. (196 Benjamin and

Castelli (1970), Ibrahim and McCallion (1967) and by Oh a Huebner (1973). Some of

these works are experimental in nature, some combination of experimental and

theoretical analysis, and others purely analytic studies.

1.3.5 Partial (Mixed) Lubrication:

Combined mode of action between fluid film and boundary lubrication generally

referred to as "mixed lubrication" or "partial lubrication". For conform surfaces, where

hydrodynamic lubrication occurs if the film gets too thin, tl mode of lubrication goes

directly from hydrodynamic to partial. For nonconform surfaces, where elastohydrodynamic

lubrication occurs if the film gets too thin, tl mode of lubrication goes from elastohydrodynamic

to partial.

1.3.6 Turbulent Lubrication Regime:

Bearings that are operated at very high speeds, with large clearances or wit lubricants having

low kinematic viscosities may achieve sufficiently high values c Reynolds number in the

bearing film so that some departure from laminar conditions may occur. Bearing in such

a situation are said to work under turbulent regimes.

1.3.7 Magnetohydrodynamic Lubrication (MHD):

Liquid metals like sodium and mercury as lubricants offer several advantages

such as ability to with stand high temperatures over conventional lubricants. And hence

the lubrication properties of liquid metals have been studied theoretically as well as

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experimentally. It is advantageous to use them where very high temperature and speed

occur such as those in space entry vehicles. In addition, the high thermal conductivity of

liquid metals means that heat generated by viscous dissipation at high speeds is readily

conducted away form the source of generation, thus resulting in a tendency towards

uniformity of temperature and viscosity of the lubricant film.

If the liquid metals, such as mercury and sodium, could be pumped or held between

the moving surfaces of the bearing, bigger loads could be supported by applying a large

magnetic field.

Because of the large electrical conductivity of liquid metals, the

possibilities of electromagnetic pressurization from the application of an external magnetic

field have been explored and studied. This electromagnetic pressurization results

when a large external electromagnetic field thorough th electrically conducting lubricant is

applied to induce circulating currents, which in turn, interacts with the magnetic field to create a

body force which pumps the fluid between the bearing surface. The study of hydrodynamic

lubrication wi electromagnetic fields is called the mag.ietohydrodynamic lubrication

interesting papers have been published discussing magnetohydrodynai on the bearings.

[Kuzma (1963, 1964, 1965); Kuzma, Maki and Donne Shukla (1963, 1964, 1965, 1970);

Maki, Kuzma and Donnelly (1964); Hughes and Elco (1962.a); Elco and Hughes (1962);

Hugfa 1963.b); Dodge, Osterle and Rouleau (1965); Shukla and Prasi .V; Dudzinsky,

Young and Hughes (1967) Agrawal (1970.a, 1970.b); Rodkiewicz (1973); Sinha and

Gupta (1973)].

It may be noted that during various phases of the operation of a bearing more than

one mode of operation may appear and indeed, in most practical cases this actually happens.

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1.3.8 Rarefied Gas Lubrication:

In the analysis of gas lubricated bearings, it is customary to assume that the lubricant is

a continuous medium. In gas bearing applications there are such as with gyroscopes and

other aerospace designs that the bearings are essentially operated in the so called slip-flow

regime. This can happen either low ambient pressure conditions or extremely thin bearing films

or both.

In a gas, at a considerable low pressure the length of the molecular mean free path can

become comparable to the thickness of the gaseous film. The gas subjected to this condition

does not behave as a continuous fluid but exhibits some Characteristics of its molecular chaos.

These effects may be encountered in regions having very sharp gradients of fluid properties such

that these properties change sufficiently in the space of a few mean free paths, regardless of

whether or not the absolute density of the gas flow is especially low.

Hsing and Malanoski (1969) analyzed spiral grooved thrust bearings, by applying the

proper slip flow corrections separately to the groove and the ridge region. Ramanaiah (1969)

made a study of the influence of molecular mean free path on the performance of a gas lubricated

thrust bearings. It was found that the effect of the slip flow is to decrease the torque on the rotor

and to increase the mass flow rate a t a given feeding pressure. 1.3.9 Porous Metal Lubrication:

Porous bearings have long been used in industry, perhaps since 1920's when the idea of using

porous metals for a bearing bush of a self-lubricating bearing was first suggested probably

originating from the attempts to overcome heat conductivity limitations of oil soaked wooden

bearings. Analysis of porous metal lubrication was initiated by Morgan and Cameron (1957).

Reynolds equation in the present case comes out to be a coupled one with the pressure in the

porous region which satisfies Laplace's equation. However, incorporation of an approximation,

that the thickness of the porous facing is small, results in Reynolds equation being uncoupled and

takes the form of a Possion equation . There had been a great deal of interest to study the

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analytical aspect of the porous metal lubrication and a lot of literature has appeared in this

direction.

Externally pressurized porous bearings have been found to be m from several applications

point of view [Sneck (1968)] several investigations have been devoted towards this [Sneck and Yen

(1967); Hsing (1971); Dah-Cl (1975.a, 1975.b, 1975.c); Murti (1974); Chang (1975); Majumdar

(191 Majumdar and Schmidt (1975)]. Inertia effects hi porous thrust bearings been considered. [Hsing

(1971)].

1.3.9 Porous Metal Lubrication:

The porous bearings are very useful in the air craft and automotive

accessories domestic appliances, printing textile and backing industries, synovial

joints etc and there are two sorts of them. The bearings that work without using any

amount of oil or grease. These bearings are made up of plastics, graphite or ceramics

materials. Second is the bearing that contains lubricant either in special storage or in

their own material structure. The best example here is porous metal bearings

manufactured by sintering process.

Most porous metal bearings consist of either bronze or iron which has

interconnecting pores making up to 20 to 30 percent of the total volume. During

operation lubricant is stored in these pores and feeds from the loaded zone of the

bearing are reabsorbed by capillary action. Since these bearings can operate for long

periods of time without additional supply of lubricant, they are used in inaccessible or

inconvenient places where relubrication or frequent maintenance is difficult. High

porosity with a maximum amount of lubricant is used for high speed, high load

applications such as fractional horse motor bearings. A low lubricant content low

porosity material is suitable for oscillating and reciprocating motion. Bronze is used

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as most common porous bearing material. These bearings are wear resistant, ductile

and corrosion resistant with good embeddability which gives them a wide range of

applications from home appliances to domestic machinery. Copper-iron porous metal

bearings are useful in applications involving shocks and heavy loads. Phenolics, actals

and nylons are widely used plastic materials. Phenolic have been replaced by wood

bearings and metals in such applications as propellers, electrical switch gears, rolling

mills and water turbine bearings.

Slider bearings are used in everybody’s day to day life. This can be

understandable because of some advantages that this sort of bearings production is not

so complicated. The price is lower and they can be made in parts and during the

operation processes they produce less noise and vibrations. In case of accurate

lubrication all sort of bearings are very practical for maintenance and they have long

operating life. These are the perhaps the most important reasons for common use.

1.3.10 BIOLUBRICATION:

Bone terminals forming synovial joints covered by a layer material called hyaline

cartilage in humans and animals consist of surfaces contained within a closed cavity which

contains a fluid whose properties are shear dependent. This fluid is known as synovia! fluid an partly

as a nutritional medium, exhibiting thixotropic non pseudoplastic behaviour [Mow (1969)].

The stress - strain behaviour of the synovial fluid may be represented by pseudoplastic power

law mode (1975)]. McCutchen (1961, 1962, 1966) suggested that the porous cartilage plays

an important role in the joint behavior. He proposed has ingeniously provided animals with

hydrostatically lubricated joints. It was suggested that with low elastic modules and

permeability of the cartilage, it is the hydrostatic pressure of the fluid within the pores that

supports a large portion of the external normal traction.

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1.4 TYPES OF RELATIVE MOTION:

Bearings may be classified on the basis of the type of relative motion.

Bearings based on rolling action of the two surfaces over each other are called rolling

element bearings. The rolling elements might be balls, rollers or needles. Some slipping,

sliding or spinning may also take place. The bearings based on sliding action or relative

tangential motion of the surfaces are called plain or slider bearings. If the relative motion of the

surfaces is normal to the bearing surfaces, the phenomena is called squeeze film lubrication.

In such situation the bearing surfaces separated by the lubricant film approach each other and

motion may be cyclic or non-cyclic. A combination of these types of relative motion may

also occur, hi externally pressurized bearings the motion of the lubricant is induced by external

pressurization of lubricants using supply pumps etc. through a recess.

1.5 GEOMETRY OF BEARING SURFACES:

Relative motion indeed generates positive pressures only when geometric

configuration is favourable. If the relative motion tends to drag lubricant from divergent

space towards a convergent space then only positive pressure generated in a slider

bearing. Geometry of the bearing configuration plays an important role besides the ratio

of inlet to outlet film thickness in supporting the load. In slider bearings various

geometrical shapes like plane inclined, composite plane, composite taper, exponential,

secant shaped, parabolic curved, stepped shape, cantenoidal cycloidal and several others have

been investigated [Pinkus and Sternlicht (1961); Gross et al. (1980); Bagci and Singh (1983)].

Relative transverse motion of parallel surfaces however generates a pressure which can

support a transverse load. Common squeeze film bearing configurations are journal bearings

consisting of cylindrical shafts, spherical and conical shapes etc. Parallel plate squeeze

film bearings with circular, annular, rectangular, elliptical, triangular, sector shaped etc.

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have been analyzed [Archibald (1956)]. Murti (1975.b) analyzed curved squeeze film bearing.

In externally pressurized bearings the film shapes have been considered to be uniform as

well as both converging and diverging. In externally pressurized bearings also circular,

rectangular and several other shapes have been investigated.

1.6 TYPES OF LOADING:

Bearings are evaluated on the basis of then" load carrying capacity at various

speeds. Rolling element bearings carrying loads perpendicular to the rotational axis are

called radially loaded bearings. Slider bearings carrying such loads are usually journal

bearings. Thrust bearings support axial loads. In practice most bearings carry a combination of

both radial and thrust loads. Load supported may be static, unidirectional one or the bearing

may be dynamically loaded. In some cases transient or periodic forces or displacements

are imposed on the bearings to load variations. Fluid film bearings are a better choice if

the load is dynamic.

1.7 BEARING DESIGN CHARACTERISTICS:

Bearing design requirements are generally established by the restrictions and

environmental conditions imposed by the bearing systems such as choice of lubricant,

bearing material specifications, bearing life, cost, bearing alignment, positioning precision,

direction and magnitude of loads, bearing ambient pressure, supply pressure, flow rate available

from the system, heat flow etc. The assurance of the compatibility of the bearing and its

design requires definition of both the range of imposed bearing requirements and bearing

performance limitations. Following parameters that characterize the performance of a fluid

film bearing are required to be designed and analyzed :

(1) Lubricant flow in the bearing

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(2) Lubricant side leakage from the bearing

(3) Pressure distribution in the film

(4) Load carrying capacity

(5) Centre of pressure (or attitude angle in case of journal bearing)

(6) Friction force (or coefficient of friction)

(7) Film stiffness

(8) Squeeze film versus film thickness relationship (in case of squeeze film bearings)

(9) Range for stability of the bearing both for initial velocity disturbances and initial

position disturbances.

Usually the bearings are designed to perform optimally for parameter. Typically,

one or more of the following functional characteristics are required in bearing design (a)

optimum load capacity (b) minimum control of film thickness within a specified range (d)

aspect of stability of the baring rotor system, (e) minimum power requirement.

1.8 REVIEW OF RELATED LITERATURE:

During the last hundred years of analytical aspects of tribology, a lot of

developments both in terms of analysis, research and developments of bearings have taken

place and now the branch of tribology has gained a prominent independent status. These

developments have been documented in a number of books; few of these have become very

popular and are used as reference texts; are Pinkus and Sternlicht (1961), Fuller (1956), Tipei et

al (1961), Tipei (1962), Dowson and Higginson (1966), Gross et al (1980), Szeri (1980),

Majumdar (1986) and Hamrock (1994). Dowson (1973) describes the early history of

tribology. Few of the import research papers and survey articles include Benes (1970),

Saibel and Ma< Moore (1965), Sneck (1968), Wu (1978), Vinay Kumar (1980), Christensen

and Tonder (1969.a), and Bagci and Singh (1983). There are several investigations in which the

21

generalized form of Reynolds equation is derived. Morgan and Cameron (1957) obtained the

generalized Reynolds equation for porous metal bearing. Shukla (1963) derived the modified

Reynolds equation for bearings working under the influence of electromagnetic fields.

Dowson (1962) obtained a generalized Reynolds equation for gas bearings in which the

density and viscosity variations both across and along the lubricant films were considered and

Berthe and Godet(1973) derived the generalized Reynolds equation considering the bearing

surface to be rough. Kulkarni and Vinay Kumar (1975) obtained the modified Reynolds

equation for anisotropic porous bearings considering the tangential slip velocity at the porous

wall - film interface, while Bhat (1980) generalized it further to include the electromagnetic

effects, Vinay Kumar (1978) obtained the modified Reynolds equation for porous bearings in

turbulent regime. Agrawal (1986) obtained the modified Reynolds equation bearing working with

magnetic fluids as lubricants. Shukla and Kumar (1987) derived the modified Reynolds

equation for bearings working with ferromagnetic fluids. Deheri and Gupta (1996) derived

modified Reynolds Equation on uncoupling of n-layered porous externally pressurized bearing.

Nanduvinamani et. al (2008) derived dynamic Reynolds Equation for Micropolar Fluid

Lubrication of Porous Slider Bearings.

Reynolds (1886) considered the configuration of an elliptical plate approaching

with relative velocity to another flat plate and obtained solution for it. Underwood (1945) first

used the term SQUEEZE FILM for this situation. The first work on the problem appears to

have been done by Stefan (1874), for a circular flat plate. In fact, the subject of film lubrication

drew renewed interest in the sixties because of the possible space applications [NASA report

(1969); Sneck (1968)] of squeeze film bearings such as gyrogimbal bearings. Many of its

important effects have been studied theoretically as well as experimentally. Archibald (1956)

presented the analysis for the squeeze film between flat surfaces. Hays (1963) considered

the squeeze film phenomena between curved plates having curvature of the sine form and

22

keeping minimum thickness as constant. Jackson (1963) included the inertia effects in his

study. Moore (1965) presented an excellent review on the analyses of squeeze film

bearings upto 1965. Gould (1967) investigated high pressure squeeze film for circular disks

considering viscosity as function of temperature and pressure. Murti (1975.b) analyzed the squeeze

film between curved circular plates, curvature being expressed by exponential function with the

assumption that the thickness remains constant. Gupta and Vora (1980) presented an analysis for

the squeeze film between curved annular plates.

The effect of electric and magnetic fields on the flow of conducting lubricants

has been studied for many years. Studies have shown that MHD bearings have several theoretical

advantages over ordinary bearings. Several kinds of MHD bearings have been discussed. The most

common type is the slider bearing, and two general configurations of the slider have been analysed.

One configuration uses a tangential magnetic field with a tangential electric field. Each of these

configurations has been tried with various geometrical shapes of the bearing surfaces [Snyder

(1962); Elco and Hughes (1962); Hughes (1963.a, 1963.b)]. A number of theoretical and

experimental studies [Maki et. al. (1966); Snyder (1962); Hughes and Elco (1962.a, 1962.b);

Hughes (1963.a, 1963.b); Shukla (1965) etc.] have been devoted to magnetohydrodynamic

lubrication.

Mostly, the analysis of bearing problems, the lubricant inertia is neglected in

comparison to viscous forces. In most of the operations the Reynolds numbers are small

enough, so that this assumption may be considered valid. However, with the continuing trend

in machine design for high speeds and the use unconventional lubricants the question

of how important the effect of inertia will be at high Reynolds numbers in the laminar

regime itself is of growing interest [Slezkin and Targ (1946)]. If the Reynolds number

becomes sufficiently large, turbulence may develop and the governing equations may not apply

even when the inertia terms are included. Several contributions including inertia effects have been

23

made. Saibel and Macken (1974) have extensively reviewed the literature existing till that time.

Inertia effects are also important because of the interest in assessing the important of possible

viscoelastic effects in lubricant behaviour and inertia both of which become important in

highly unsteady conditions. Tichy and Winer (1970) studied this aspect in parallel circular

squeeze film bearings and included the effect of lubricant inertia and used regular perturbation

techniques. Tipei and Constantinescu (1956) for the first time used spherical polar coordinate

systems for the development of the Reynolds equation for squeeze film in a spherical

bearings working with gas as the lubricant. Pan (1963) has analyzed the problem of the

hemispherical squeeze-film bearing with the spherical rotor rotating at a constant speed

and also moving with a constant load. In both of the above analyses, the bearing surfaces

were assumed to be smooth. Although, it has been realized for a long time that most sliding

surfaces are rough, theoretical analysis often ignores this fact. This seems to be surprising since it

is well established that the separation of the sliding surfaces in a bearing and the amplitude

of the roughness are comparably in magnitude. However, bearing surfaces, particularly after

having some run-in and wear, develop roughness. It has now been well established that the

roughness of the surfaces significantly affects the bearing performance, especially, in bearings

working in the boundary lubrication regime.

Davies (1963) used a saw-tooth curve for modeling the roughness. Burton (1963) made

use of a Fourier type series approximation for representing a surface roughness. An example of

this approach is the Michell's theory of rugolose lubrication. [Michell (1950)], where he

assumes that the roughness can be represented by a lone high frequency sine wave. Tipei and

Pascal (1966) extended this method by including several terms in the series approximation.

However, this method is, perhaps more suitable in an analysis of the effect of waviness rather than

the roughness. The basic difficulties with these methods lie in performing the actual

computations. Besides the integration of Reynolds equation poses the problem. The

24

random character of the surface roughness was recognized by several investigators who

used a stochastic approach to mathematically model the roughness of the bearing

surfaces [Tzeng and Saibel (1967.a, 1967.b), Christensen and Tonder (1969a, 1969b, 1970.a)].

In actuality Tzeng and Saibel (1967.a) used a method of random analysis which avoided the

computational difficulties in a calculation of an infinitely wide slider bearing. However,

their method had only a restricted application and could not be used with surfaces of arbitrary

dimensions. It appears that the intentions behind the work of Christensen and Tonder

(1969.a, 1969.b), Christensen (1970) were somewhat different in that sense that they aimed

towards the construction of a theory of lubrication suitable to the analysis of rough sliding

surfaces in general, rather than the analysis of a particular type of rough bearing. Their

approach which was based upon the concept of viewing the film thickness as a stochastic

process resulted in a Reynolds type equation in the mean or expected pressure. Since this

Reynolds type equation had a formed which was similar to the ordinary Reynolds equation

but contained only smooth functions of film thickness, integration of Reynolds equation

did not pose any problem. Christensen and Tonder (1970.a) demonstrated the power

of the above theory in applying it to the analysis of a rough slider bearing of finite

width. By comparing the results for different width/length ratios they concluded that the

influence of surface roughness on bearing response could not be decided by the

consideration of roughness alone; but that the effects of roughness were being modified bye

the nominal geometry as well as operational factors. In this article they concluded that

roughness could increase or decrease the load capacity, influenced the frictional properties

to the better or worse as compared with bearing having smooth sliding surfaces. Further the

results indicated that roughness might influence the bearing characteristics considerably.

Tonder (1972) theoretically analyzed the transition between surface distributed waviness

and random roughness. Further he claimed that the application of average type relations

25

was the only way for dealing with this kind of problem particularly in the case of two-

dimensional Christensen disturbances. Christensen and Tender (1970.b) proposed a

mathematical theory of mixed lubrication based upon the stochastic theory of

hydrodynamic lubrication. They developed the expressions for various bearing

characteristics valid under mixed lubrication conditions. In order to illustrate some of the

effects the theory was then applied to the analysis of a no side lickage, constant inclination

sliding bearing. This analysis demonstrated the profound effect that transition into the

mixed lubrication regime has especially on the friction dependent properties. Tzeng and

Saibel (1967.a, 1967.b) used a beta probability density function for the random variable

characterizing the roughness. This distribution is symmetrical in nature with zero mean

and approximates the Gaussian distribution to a good degree of accuracy for certain

particular cases. Christensen and Tonder (1969.a, 1969.b, 1970.a) further developed this

approach and proposed a comprehensive general analysis both for transverse as well as

longitudinal surface roughness based on a general probability density function. In squeeze film

bearings when the plates are having rotatory motion also, the linear inertia may be neglected but the

convective inertia due to rotatory motion may be of importance [Wu (1971); Ting(1975),

Prakash and Vij (1976)]. Na (1966) obtained inertia less solution for non-Newtonian

squeeze films. Ramanaiah (1967) analyzed the problem of squeeze film with power law fluid

considered as lubricant and the inclusion of inertia effects. He did not include the local

inertia and part of the convective inertia in the equation of motion. Elkough (1976)

accounted for all the inertia terms in the equation of motion for a laminar non-Newtonian

squeeze film. Ramanaiah (1966.b) analyzed the problem of squeeze film between circular

plates with axial current induced pinch effect using power law fluid as lubricant,

neglecting lubricant inertia. Gupta and Vora (1982) considered the effect of rotational inertia on

the squeeze film load between porous annular curved plates.

26

In recent years there has been a great deal of interest both from analytical and

experimental point of view in the operation of bearings beyond the laminar regime. High

velocity and low viscosity lead to high Reynolds numbers and departure from laminar flow.

Macken and Saibel (1972) reviewed the work in this aspect.

In certain situations distortion of the surface due to heat generation and heavy

loading may take place and this may result in the changes in the film shape which may be of

the same order of magnitude as the film thickness itself. The study of this effect is called

elastohydrodynamic lubrication. This effect is particularly important in the lubrication

of gear and roller bea rings where high pressures develops. Osterle and Saibel (1958)

discussed the performance slider bearing with considering the elastic deformation of the

bearing. Ramanaiah (1968) analysed the elastic deformations in hydrodynamic squeeze

films. Ting (1975) investigated the problem of engagement of porous plates simulating it by

annular plates incorporating the effects of elastic deformation and the surface roughness of

the bearings.

In most of the theoretical studies of bearing lubrication, it has more or less explicitly

been assumed that the bearing surfaces can be represented by smooth mathematical planes.

It has, however long, been recognized [Halton (1958)] that this might be an unrealistic

assumption, particularly, hi bearing working with small film thickness. Several devices such

as postulating a sinusodial variation in film thickness [Burton (1963)] have been introduced

in order to seek a more realistic representation of engineering rubbing surfaces. However, this

method is perhaps, more appropriate in an analysis of the influence of waviness rather than

roughness. Tzeng and Saibel (1967.a) have introduced stochastic concepts and have

succeeded in carrying through an analysis of a two dimensional inclined slider bearing with

one dimensional roughness in the direction transverse to the sliding direction. However,

bearing surfaces, particularly, after they have received some run-in and wear, seldom exhibit a

27

type of roughness approximated by this model. On the contrary recent investigations

demonstrate that running in and wear tend to produce a one dimensional type of roughness

running in the direction of sliding or longitudinal direction [Christensen and Tonder (1969.a)].

The effect of surface roughness on the load supporting ability, friction force and oil flow

has been the subject of conjecture for some time [Burton (1963); Michell (1950)], but the

recent studies [Christensen and Tonder (1969.a, 1969.b, 1970.b, 1971, 1972), Citron (1962),

Tzeng and Saibel (1967.b), Tipei and Pascal (1966), Tonder and Christensen (1972.a, 1972.b),

Dowson and Whomes (1971), Christensen (1971) have proved its importance. A general form

of the Reynolds equation has been obtained by Berthe and Godet (1973) by assuming one of

the two moving contact surfaces as either rough or deformed..

In 1975, Christensen et al [Christensen, Shukla and Kumar (1975)] obtained a generalized

Reynolds equation applicable to rough surfaces by assuming that the film thickness function

follows a stochastic process. Tonder (1977) gave a mathematical treatmet of the

problem of lubrication of bearing surfaces depicting two dimensional distributed

uniform or isotropic roughness. Prakash and Tiwari (1982) discussed various types

of rougheness patterns on the bearing surfaces and solved the problem of squeeze

film between porous circular parallel plates. Guha (1993) investigated the effect of isotropic

roughness on the performance of journal bearings.

The development of magnetic fluid as lubricant has not only aded to the long range of

already available lubricants but also added to new characteristics of the lubricant, namely, its

fluidity and magnetic property. Magnetic fluid is a multi component and multiphase system. It

consists of fine magnetic particles coated with a surfactant and dispersed in a non-

conducting and magnetically passive solvent which prevents them from aggregating. The

advantage of magnetic fluid lubricant over the conventional one is that it can be retained at the

desired location by appropriate application of magnetic field. In sealed systems

28

contamination due to lubricants can be prevented if the use of magnetic fluid as lubricant is made.

Under the term of magnetic fluid, a variety of liquid magnetic media, ranging from coarse

dispersion to fine colloidal suspension or even molecular solution and from dielectric to very

good conductors are all included. It is therefore natural that mathematical descriptions of such a

variety of magnetic fluids may differ from each other. Shukla and Kumar (1987)

obtained the generalized Reynolds equation for ferromagnetic lubricants and used it for slider

bearing and squeeze film bearing. Zahn and Rosenweigh (1980) describe the motion of magnetic

fluids through porous media under the influence of obliquely applied magnetic field. This paper became

the basis for many research analyses on the performance of porous bearings working with magnetic fluid

as lubricant. Use of magnetic fluid as lubricant modifying the performance of the bearing has

now been recognized. Agrawal (1986) analyzed the problem of porous slider bearing working

with the magnetic fluid as the lubricant. Bhat and Deheri (1991, 1995) also studied the

problem of slider bearings lubricated with magnetic fluid. They found that slider bearings

with magnetic fluid was performing better than the corresponding one lubricated with

conventional lubricant. More detailed literature reviews are provided in chapter-2 in this direction.