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INTRODUCTION

A hydrodynamic (HD) bearing is a bearing which carriesload by sliding. This bearing is often called a bushing or a

babbit or journal bearing. The HD bearings are very

widely used and appear in most kinds of equipment, e.g.as crankshaft and connecting rod bearings in internal

combustion engines.

The HD bearing may carry load in one of several waysdepending on their operating conditions, load, relative

surface speed (shaft to journal), clearance within the

bearing, quality and quantity of lubricant and temperature

(effecting lubricant viscosity).

If full film conditions apply the bearing load is carried

solely by a film of fluid lubricant, there being no contactbetween the two bearing surfaces. In this condition they

are known as fluid film bearings.

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INTRODUCTION

Crankshaft, Babbitt metal, plain bearing shell

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INTRODUCTION

In mixed or boundary conditions load is carried partly by

direct surface contacts and partly by a film formedbetween the two mating surfaces of components.

Plain bearings are relatively simple and hence

inexpensive. They are also compact, light weight, straight

forward to repair and have high load-carrying capacity.

However, if operating in dry or boundary conditions plain

bearings may wear faster and have higher friction thanrolling element bearings.

Mixed and boundary conditions may be experienced even

in a fluid fi lm bearings when operating outside of itsnormal operating conditions, i.e. at startup and shutdown.

An HD bearing uses a hardened and polished steel shaft

and a soft bronze bushing. In such designs the softerbronze portion can be allowed to wear away, to be

eriodicall renewed.

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INTRODUCTION

The beginnings of theory of the hydrodynamic lubrication

have been done in the last decades of the 19th century.

The main persons were here Beauchamp Tower andOsborne Reynolds.

Tower investigated experimentally the plain lubricatedbearings utilised in British railways. He discovered the

self-acting pressure generation in such bearings.

This phenomenon has been explained by Reynolds who

had developed the theory of hydrodynamic lubrication.

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INTRODUCTION

Towers testing device for experiments on lubrication

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INTRODUCTION

Towers testing device for experiments on lubrication

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INTRODUCTION

Towers measurements of the pressure distribution (7988 vs. 8008 lbf)

INTRODUCTION

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INTRODUCTION

Reynolds general view on the action of lubricant: a) parallel surfaces in

relative motion (Poiseuil le flow); b) approaching parallel surfaces(Couette flow).

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INTRODUCTION

Reynolds general view on the action of lubricant: c) parallel surfaces

approaching with tangential motion (superposit ion of the Poiseuille and

Couette flow).

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INTRODUCTION

Reynolds general view: d); e) inclined surfaces with tangential motion

only.

1

1

VISCOSITY

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VISCOSITY

Viscosity is a measure of internal friction of a fluid that varies with

temperature and pressure and, sometimes, with shear rate (non-Newtonian lubricant). Newton postulated that the viscous shear

stresses were directly proportional to the shear strain rate, i.e. to

the velocity gradient

where

shear stressdu/dz rate of shear

coefficient of dynamic viscosity

hU

dzdu ==

u

du

dzz

x

VISCOSITY

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VISCOSITY

The viscous shear stress is proportional to the shearrate, the dynamic viscosity being the proportionalityfactor. So, thicker oils have a higher viscosity valuecausing relatively higher shear stresses at the same

shear rate.

In SI system is expressed in Ns/m2 (1 Ns/m2 = 1 Pas).This is quite a large unit and it is more common to use

its submultiple, that is mPas.

In CGS system (centimetre/gram/second) the viscosity

was measured in poise 1 P = 1 g/(cms). Practically used

unit was 1 cP = 1 mPas.

VISCOSITY

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VISCOSITY

Dynamic viscosities are usually measured under high shear

conditions, for example, the cone-and-plate viscometer inwhich the viscous shear torque is measured on the cone.

MCM

Cr

M

r

r

dy

du

==

==

= 132

3;

VISCOSITY

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VISCOSITY

The kinematic viscosity is the quotient of the dynamicviscosity and the fluid density

In SI system is expressed in m2/s, which is again a verylarge unit and practically used is mm2/s.

In CGS system a unit used was stokes 1 St = 1 cm2/s and aused one was cSt (1 cSt = 1 mm2/s).

=

VISCOSITY

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VISCOSITY

The physical principle of

measurement of

kinematic viscosity is

based on the rate atwhich a fluid flows

vertically downwards

under gravity through asmall-diameter tube.

Viscosity is measured by

timing the fall of theliquid level between the

etched rings.

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REYNOLDS EQUATION

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REYNOLDS EQUATION

Reynolds equation takes into consideration both theequilibrium of forces in viscous fluid (Navier-Stokes

equation) and continuity of flow. We assume for

simplification that:

- Fluid is incompressible and a Newtonian one (the shear

stress is directly proportional to the shear strain rate)

- Fluid properties remain constant; effects due to variationin temperature and pressure being neglected

- Inertia and gravity forces (mass forces) are negligible in

comparison to friction forces (surface forces)

- The solid bodies remain rigid

- Lubricating film is of sufficiently small thickness that the

fluid pressure can be considered constant through thethickness of the film

- The bearin is infinitel wide

REYNOLDS EQUATION

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REYNOLDS EQUATION

In the situation where surfaces are moving tangentially (in

the x direction) with no normal motion and a fluid between

them, if the above assumptions are made the Reynolds

equation reduces to

where h is the local fi lm thickness, h is the film thicknessat the position of maximum pressure and U1 and U2 are the

tangential velocities of mating bodies.

In the case of combination of stationary element withmoving one having tangential velocity U we obtain

321')(6

hhhUU

dxdp +=

3

'

6 h

hh

Udx

dp

=

REYNOLDS EQUATION

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REYNOLDS EQUATION

In the case of the normal approach there is no tangentialmotion of the surfaces (U1 = U2 = 0), but there is movement

normal to the surfaces. Consider the two parallel flat

plates with respective normal velocities V1

and V2

.

Common-sense tells us that a pressure will be developed

in the fluid if the difference V1 V2 is positive, and that the

fluid will flow outwards from the point of maximum

pressure. The Reynolds equation confirms this, sincemaking the same assumptions as before, it becomes

where x is the coordinate of the position of maximum

pressure. This situation is often called 'squeeze filmlubrication.

321

')(12 h

xxVVdx

dp

=

REYNOLDS EQUATION

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REYNOLDS EQUATION

The build-up of pressure in a bearing where both types ofrelative motion are present (combined longitudinal and

normal motion) can be found by a simple superposition of

the two effects, thus

To find the actual pressure distribution it is necessary to

integrate the equation. Two unknown quantities will then

be present, the integration constant and the value ofx.These are determined by the incorporation of two relevant

boundary conditions. The above equation may be applied

to any pair of surfaces, provided that the appropriate

velocity components are resolved to obtain the

appropriate values ofU1, U2, V1 and V2.

321321

')(12

')(6

h

xxVV

h

hhUU

dx

dp

+=

MECHANISMS OF THE FLUID FILM FORMATION

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Two main mechanisms of the pressure generation in the

lubricating film have been demonstrated by Reynolds.

Physical wedge Squeeze film


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Two main mechanisms of the pressure generation in the

lubricating film have been demonstrated by Reynolds:

Physical wedge Squeeze film


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Other pressure generating, which are rarely significant,

are:

Stretch mechanism Density wedge

Viscosity wedge Local expansion

PLAIN JOURNAL BEARINGS

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Example of design of the ring-fed journal bearing


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Scheme of the pressure-fed plain journal bearing

operating under steady load


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Plain journal bearings nomenclature:

F applied loadR bushing radius

r shaft radius

D = 2R bearing diameter

B bearing width

p pressure in oil film

p* pressure in the case of oil inlet in the loaded zone

e eccentricity

h oil film thickness

h0 minimum oil film thickness

angular velocity of journal angular position of the shaft centres = R r radial clearance

S = 2s total clearance

= e/s relative eccentricity = S/D relative clearance


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Friction regimes in plain bearings Stribeck curve:1 T = const; 2 T const.

FRICTION REGIMES

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FRICTION REGIMES

Boundary lubrication

The friction and wear characteristics of the lubricated contact are

determined by the properties or the surface layers (in nanometer scale)

the underlying solids. The fatty acids are often used as additivesforming boundary layers. Viscosity has negligible effect on frictional

behaviour.

FRICTION REGIMES

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FRICTION REGIMES

Mixed lubrication

A very large proportion of lubricated contacts operate with

a mixture of hydrodynamic and boundary lubricationmechanisms at the same instant. In mixed lubrication it js

necessary to consider both the physical properties of the

bulk lubricant and the chemical interactions between theadditives and the adjacent solids.

FRICTION REGIMES

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C O G S

Fluid film lubrication

The best way to minimise wear and friction in rolling and slidingcontacts in machines is to separate the solids by a lubricating film.

The lubricant can be a liquid or a gas and the load supporting film can

be created by the motion of the solids (self-acting or hydrodynamic

bearings) or by a external pressure source (externally pressurised orhydrostatic ones).

FRICTION REGIMES

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Elastohydrodynamic lubrication

A special form of fluid film lubrication in which the

development of effective films is .encouraged by local

elastic deformation of the bearing solids is known as

eIastohydrodynamic (EHD) lubrication (gears, ball and roller

bearings, cams and tappets).

CALCULATION OF PLAIN JOURNAL BEARINGS

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The Reynolds equation for the short journal bearing (shownin above figure) has in cylindrical coordinates the form

where the mean pressure is

and the film profile (without considering deformation ofmating components and their surface roughness) describes

the following equation

=

+

hrU

zph

zrph 6

3

2

3

( ) cos1 += sh

DB

Fpm

=


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The integration of the

Reynolds equation givesin dimensionless form

the Sommerfeld number

as a measure of thehydrodynamic load

carrying capacity

Figure shows the

extended Sommerfeld

number as a function of

the relative eccentricity

with the relative width asa parameter.

=

2

mpSo


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The limiting HD film thickness (that ensures the wear-free

operation of bearing) and recommended roughnessheight (peak-to-valley one) is shown in figure.

JOURNAL BEARINGS DESIGN GUIDELINES

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To prevent overheating, the clearance and operating

viscosity should be chosen to suit the operating speed.


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The viscosity in graph is that at the operating temperature

obtained (assumed not greater than 20C above inlet temperature).


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Figure gives a guide

to the load capacity ofbearings when

operating with the

previous given

speeds, clearancesand viscosities.

Normally, values of

B/D should notexceed 1.


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Figure gives

guidance on the

power loss for abearing with width

equal to diameter

(B/D = 1). It can beassumed that the

power loss is

directly proportionalto the relative width

of bearing.


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Figure gives a very

rough guide for the

volume rate of f low(assuming B/D = 1).

It should be

underlined that thelubricant flow is

sensitive to changes

in some variables,e.g. Clearance,

bearing width etc.

OTHER TYPES OF PLAIN BEARINGS

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Lobed plain bearings:

bi-directional lobed bearing unidirectional lobed bearing


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Multi-pad plain bearing


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Plain thrust bearings (plain axial bearings, Mitchell bearings)


C bi d l i b i f di l d bi di ti l i l l d

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Combined plain bearing for radial and bi-directional axial loads

Date post:	14-Apr-2018
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