journal bearing design

7/21/2019 Journal Bearing Design

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Bearings Design Journal Bearing

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Contents Outline...

Bearings

Classifications

Bearing Selection

Lubrication and Viscosity

Basic Terminology

Viscosity and its units

Lubrications and Friction Lubrication Regimes

Hydrodynamic Bearings

Performance of Hydrodynamic Bearings29/09/2015


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Contents Outline...

Hydrodynamic Effect

Pressure development in JB

Expression for film thickness (h)

Petroffs Equation

The Sommerfeld Number

Design Consideration

Angular Speed

Trumplers Criterion

Temperature

Raimondi and Boyd Charts

Problems and References29/09/2015


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Bearing Introduction

Bearing : Two parts moving relative to each other

constitutes a bearing. Sliding, rolling or both

The two parts are always separated, either by lubricant

or rolling elements like steel balls

Friction effects are integral while designing bearings

Study of wear and friction?

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Bearings Introduction ..

Usage: To reduce friction where shafts, gears or wheels are used.

To provide high load tolerance

Applications: Transportation including cars, trucks, heavy trucks, helicopters,

airplanes and trains.

Industries including mills, mining, oil and gas extraction and

production, gear drives, health and positioning control, wind

mills and food processing.

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Bearing Configuration

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Bearing Configuration

Journal Bearing

Provides radial location for a shaft rotating carries radialload

Thrust Bearing

Provides axial location for a shaft rotating carries axial load

Slider Pad Bearing

Provides a load perpendicular to a continuous plane surfacealong which the pad moves (usually in reciprocating motion)

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Bearings Types (according tooperating Mechanisms)

Rolling Element Bearings

Hydrodynamic Bearing (Fluid Film Bearings) Self Acting

Hydrostatic Bearing (externally pressurised)

Oil Impregnated (porous metal)

The mating surfaces are partially separated by an oil filmsupplied from a reservoir of oil within the pores of thesintered metal bearing.

Dry Rubbing

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Bearing Types (Operating Mechanisms)

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Journal Bearing in the shaftarrangement

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Bearing Types (Mostly used)

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Selection of Bearing Types

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Bearing Selection Chart

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Types of Lubricant - Physical

Liquid

Typical lubricants are liquid/fluids

Mineral oil or synthetic oils

Solid Graphite, MoS2

Semi solid

Greases

Gases Atomised 2 stroke oils


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Typical lubricants - Application

Engine oils

Gear Oils

Turbine Oils

Hydraulic Oils

Metal working oils

Cutting oils

Forming Oils

Rust preventives

Heat Treatment Oil

Refrigerating Oils


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Lubricant - Components

Base Oils

Mineral by-products of crude oil refining process.

Base oils are polymerized or synthesized further and calledsynthetic

Additives

Natural

Synthetic


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Function of a lubricant

Lubricate - Reduce friction

Cooling - Heat transfer

Cleaning - Detergency Noise pollution - dampening

Sealing prevent leakage

Protection prevent wear


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Properties of lubricants

Dynamic viscosity

Kinematic viscosity

Viscosity index

Pour Point

Flash Point

Total Base Number (TBN)


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Dynamic viscosity

The unit of dynamic viscosity is Ns/m2

In practice, centi poise use.

1P = 100cP = 0.1Pas

y

u

=


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Kinematic viscosity

The unit of kinematic viscosity is m2

/sIn practice, centi stoke use.

1cS = 1 mm2

/s

=


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Effects of temperature

The viscosity of liquids decreases with increase thetemperature.

The viscosity of gases increases with the increase thetemperature.


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Viscosity Temperature Effect


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Major specifying organizations

SAE Society of Automotive Engineers (USA)

API - American Petroleum Institute

US Military Specs US - MIL 2104 - CCMC European Specification

ISO International Standard Organization ISO 3348

NLGI National Lubricating Grease Institute


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Lubrication with SAE standardbased on Temperature

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SAE viscosity grades for engine oils

Designated

With corresponding viscosity

For high temperature application

Warmer areas/regions SAE 20

SAE 30

SAE 40

SAE 10 SAE 50

SAE 60


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SAE viscosity grades for engine oils

Designated

With corresponding viscosity

For low temperature application

Colder areas/regions SAE 0 W

SAE 5 W

SAE 10 W

SAE 15 W SAE 20 W

SAE 25 W


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SAE viscosity grades for Monogrades - Engine Oils

Mono grades are designated with single SAE number

SAE 10, 20, 30, 40, 50

SAE 5W,10W, 15W,20W,25W

Can be used either in summer season or in winterseasons.

Gradual shift to multi grades.

Shift also due to lower oil consumption by multi grades

Available as Engine oil and Gear Oils


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SAE viscosity grades for Multigrades - Engine Oils

Multi grades are designated with two SAE number

Widely in use today

SAE 10w/30, 15w/30, 25w/50

SAE 5W/30, 20W/40

Suitable for use in winter and summer months orseasons

Available in Engine oils & Gear oil


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Petroffs Equation

The first explanation of bearing friction was given by

Petroff in 1883

It defines, groups of dimensionless parameters with

coefficient of friction

Assumptions :

bearing shaft is in concentric

It carries a small load The clearance space is fully filled with oil

Leakages are negligible

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Journal Bearing Geometry

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O

FN

Rf

O C

W

journalbearing

e

C

W

h

No lubrication present

Hydrodynamic load support

journal

lubricant

Bearing


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Journal Bearing Nomenclature

C= centre of the journal

O = the centre of the bearing

W= unidirectional load of the journal (N)

= angular velocity of the journal (rad/s)

Rf= contact force (N)

N= normal contact force (N)

F= frictional force (N)

= coefficient of friction

h = film thickness (m)

= angular position from the position of max film thickness

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Performance parameters

Eccentricity (e) : the distance between the centres of thebearing and journal (OC).

Radial Clearance (c) : difference in radii between thebearing and journal

Eccentricity ratio () : the ratio between the eccentricityand the radial clearance.

Minimum film thickness (hmin) : difference between theradial clearance and eccentricity.

Attitude angle () : the angle between the load W and theline of centres which lie both the maximum and minimumfilm thickness

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Petroffs Equation Derivation

Please refer class lecture notes

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L b i ti R i (St ib k


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Lubrication Regimes (StribeckCurve)

Boundary Lubrication

Contact between

journal and bearing

Mixed-film LubricationIntermittent contact

Bearing Parameter

Hydrodynamic Lubrication

Journal rides on a fluid

Bearing Parameter pfilm. Film is created bymotion of the journal.

the

dynamic viscosity

rotational speed,

ppressure (force/projected area),

CoefficientofFriction

BoundaryLubrication

Mixed-film

LubricationHydrodynamic

Lubrication


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Lubrication Regimes

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Lubrication Regimes

Figure: Film conditions required for lubrication. (a) Fluid film lubrication -

surfaces separated by bulk lubricant film; (b) partial lubrication - both bulk lubricant

and boundary film play a role; (c) boundary lubrication - performance depends

essentially on boundary film.


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Direction of motionof the bottom plate

Bottom layer of fluid moves withsame velocity as the plate

Velocity of top plate = 0

Velocity of bottom plate = U

A is area of the plate

y

Shear force F

There is no pressure buildup in the fluid due to relative motion

Pressure remains constant throughout influenced only by the load factor

The surfaces are move towards each other due to increase in load

Lubricant

Velocity Profile in Parallel surfaces

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Velocity Profile in Converging


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Bottom surface

Top Surface

Surfaces are inclined to each other thereby compressing the fluid as it flows.

This leads to a pressure buildup that tends to force the surfaces apart

Larger loads can be carried

Velocity Profile in ConvergingWedge

Direction of motion of the oil WedgeOil wedge

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Hydrodynamic Bearing Lubrication

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Bottom surface

Top Surface

Oil wedgeDrag Force

NormalForce

Lift Force

The hydrodynamic effect generates a hydrodynamic pressure in the fluid that result inload carrying capacity, i.e. the fluid film has sufficient pressure to carry the external loadon the bearing.


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Reynolds Equation in One Dimension

Oil wedge

UU

B

hi hho

Pmax


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A journal bearing, in its simplest form is a cylindrical bushing made of a

suitable material and containing properly machined inside and outside

diameters. The journal is usually the part of a shaft or pins that rotates inside

the bearing.

It is simply a block of cast iron with a hole for the shaft providing running fit.

An oil hole is drilled at the top for lubrication

The main advantages of this type of bearing are

It handle high load and velocities because metal to metal contact is minimal due tothe oil film.

The journal bearing is remarkably durable and long lasting

The damping effect of the oil film, journal bearing help make engines quiet andsmooth running.

Introduction of Journal Bearing

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Journal bearing- process atstartup

Stationary

journal

Instant of starting (tends to

climb up the bearing)

While running (slips due to loss

of traction and settles eccentric tobearing)

e = eccentricityShaft/journal

Bearing

Because of the eccentricity, the wedge is maintained

(lack of concentricity)

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Hydrodynamic theory- journalbearings

Bottom surface

Shaft/journal

Bearing

Oil wedge forms between shaft/journal and bearing due to them not beingconcentric

Top Surface

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Theory of Hydrodynamic Bearings

Velocity Profile in Parallel Plates

Velocity Profile in Converging Wedge

Reynolds Equation in 1-Dimension

Reynolds Equation in 2- Dimensions

Simplifications of Reynolds Equation

Infinitely long bearing

Infinitely short bearing

Different shape of converging-diverging wedge

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Where,

h = fluid film thickness at any point in x-direction

h = fluid film thickness at maximum pressure condition

hi = fluid film thickness at entryho = fluid film thickness at exit

qx = fluid volume flow rate per unit width in x direction

U = velocity of bottom surface

Top surface velocity is zero

Entrainment velocity =

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Reynolds 1D equation continue..

2/2

0U

U=

+


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The flow rate per unit widthT

L

LT

Lqx

23

==

The first term = Uh/2

The 2ndterm is modifier, f(p), which depends on dp/dx, viscosity and film thickness h

( )

( ) ( ) ( )

cb

a

x

Ldx

dppf

pfUh

q

=

=2

To satisfy the units, a = +1, b = -1 and c = 3

( ) 31

hdx

dppf

=


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Thus, the new equation

=

dx

dphk

Uhqx

3

2

Where, k proportionality constant

The boundary conditions is, at some point, (dp/dx) = 0 and at the this point h will be h

2

hUqx =

=

3

2 h

hh

k

U

dx

dp

=

3

6h

hhU

dx

dp

Where, k = 1/12 from experimental value

This is called as One Dimensional Reynolds Equation


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Assumptions:1. The flow is laminar, since Re is low

2. The fluid lubricant is continuous,Newtonian and incompressible.

3. The fluid adheres to the solid surface at the boundary and there is noslip at the boundary.

4. The fluid viscosity is constant.

5. The velocity component, v, across the thin film (y direction) is

negligible than other two velocity components in x and z direction.

6. The pressure,p, across the film in axial direction is constant.

7. The gravity and inertia forces are negligible.

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Reynolds Equation in Two Dimension


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B

A

h

dy

dx

x

z

y

w

v

u

qy

qx

dxx

qq xx .

+

dyy

qq

y

y .

+

u

v

w1

w2


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Where,

h = fluid film thickness

x y = cross section of an incremental column

qx = fluid volume flow rate per unit width in x direction

qy = fluid volume flow rate per unit width in y direction

u,v, w = velocity components in x, y and z directions respectively.

A and B = rigid surfaces

A surface has u and v velocity components with w vertical velocitycomponent

B Surface has no translation rotation but has w vertical velocitycomponent

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In x-direction, the volume flow rate per unit width is =

Where,

the rate of change of flow in the x direction =

The actual flow out is =

In y-direction, the actual flow out is =

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Continuity of flow of a column

xqx

dydxx

qq xx

+ .

dxdy

y

qq

y

y

+ .

dxxqq xx .+


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dxdyww )( 21The volume of the column changes rate =

The total volume flow into the column

dxdywdxdyy

qqdydx

x

qq

y

yx

x 2.. +

++

+

dxdywdxqdyq yx 1++

The total volume flow out from the column

C i i f fl f l


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By equation flow in and out,

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( ) 012 =+

+

ww

y

q

x

q yx

A El f L b i i h Fil


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An Element of Lubricant in the Film

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E ilib i f El


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Equilibrium of an Element

The derivation and theory will be discussed in the lecture.

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x

phUhqx

=

122

3

y

phVhqy

=

122

3

The relationship between volumetric flow rate and pressure gradients

F ll R ld E ti


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The Reynolds equation,

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Full Reynolds Equation

( )

+

+

=

+

12

33

26 wwVhy

Uhxy

ph

yx

ph

x

Since, the viscosity is constant in hydrodynamic lubrication theory,

( )

+

+

=

+

12

3326 ww

y

hV

x

hU

y

ph

yx

ph

x

F ll R ld E ti ti


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In RHS, the third term, W2-W1 is related to the rate of the height ofthe fluid column changes. It could be written as dh/dt and this is

called as Squeeze film action.

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Full Reynolds Equation continue...

When the bearing is running at steady state, squeeze film becomeszero. But in real time, it is not steady state. Thus, squeeze filmneither zero or negligible. But it is small, when compared with thecontribution made to hydrodynamic pressure form the convergentwedge action.

In RHS, the first term two terms, are related to wedge action,which creating the hydrodynamic pressure in the contact surfaces.


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I fi it l l b i


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Infinitely long bearing

36

h

hhU

dx

dp =

In real bearings, for infinitely long, their longer dimension (L) is

at least 4 times bigger than their short dimension (Diameter, D).

Where, is the value of film thickness at which the pressuregradient becomes zero.

h

If the bearing is long in y-direction (infinite length), thus there is noaxial flow or pressure gradient. Then the simples form of Reynolds

Equation

x

hU

x

ph

x

=

6

3

Performance Characteristics of


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Performance Characteristics ofHydrodynamic Bearings

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J l B i G t


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Journal Bearing Geometry

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O

FN

O C

W

journalbearing

e

C

W

h

No lubrication present

Hydrodynamic load support

journal

lubricant

Bearing

J l B i N l t


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C= centre of the journalO = the centre of the bearing

W= unidirectional load of the journal (N)

= angular velocity of the journal (rad/s)

R = contact force (N)

N= normal contact force (N)

F= frictional force (N)

= coefficient of frictionh = film thickness (m)

= angular position from the position of max film thickness

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P f t


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Performance parameters

Eccentricity (e) : the distance between the centres of thebearing and journal (OC).

Radial Clearance (c) : difference in radii between thebearing and journal

Eccentricity ratio () : the ration between the eccentricityand the radial clearance.

Minimum film thickness (hmin) : difference between theradial clearance and eccentricity.

Attitude angle () : the angle between the load W and theline of centres which lie both the maximum and minimumfilm thickness

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Performance parameters contin e


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Performance parameters continue..

c

e=

O e

C

W

h

journal

lubricant

Bearing

RRcb =

Where, Rb= radius of bearing

and R = radius of journal

The radial clearance isrepresented by c which isin the order of 1/1000 ofthe journal diameter.

ce0

Performance parameters continue


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Performance parameters continue...

)cos1(cos +=+=

cech

)1(min == cech

The gap (h) between the solid surfaces, will be related

to circumferential position

The minimum and maximum gap between the solidsurfaces,

If = 0, then there is no load, if = 1, then the shafttouches the bearing surface under externally large loads.

10

)1(max +=+= cech

Jo rnal Bearing Nomenclat re


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is equal to 2 for a

full bearing

If is less than 2, it isknown as a partial

bearing.

We will only be

considering the fullbearing case.



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Infinitely short or narrow bearing means, the length dimension (L)in the y-direction is very much less than the dimension D.

D

p

L

p>>

x

p

y

p

>>

L

D

25.0 L/D > andy, y1, y1 and y1/4 are the variables corresponding to L/Dratios of , 1, , and , respectively.

Tutorials 3: Bearing Problems


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Q1. A journal bearing has a shaft journal diameter of 75mm, with a unilateral tolerance of -0.025 mm. The

bushing bore has a diameter of 75.125 mm with a

unilateral tolerance of 0.1 mm. The bushing bore is 37.5

mm in length and the load is 3.5 kN. The journal rotatesat 900 rpm. For SAE 40 lubricant, find the minimum filmthickness, the coefficient of friction and the maximum

film pressure for an operating temperature of 60 C for

the minimum clearance assembly

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Q2. A 32 32 mm sleeve bearing uses a grade 20 lubricant. The axial

groove sump has a steady state temperature of 45 C. The shaft journalhas a diameter of 31.75 mm with a unilateral tolerance of -0.025 mm.

The bushing bore has a diameter of 31.85mm with a unilateral toleranceof 0.025mm. The journal speed is 1120 rev/min and the radial load is 2.5

kN. Estimata)The magnitude and location of the minimum film thickness

b)The eccentricity

c)The coefficient of friction

d)The power loss rate

e)Both the total and side oil-flow rates

f)The maximum oil-film pressure and its angular location

g)The terminating position of the oil film

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Q3. A full journal bearing has a shaft journal diameter of 25mm with a unilateral tolerance of -0.03 mm. The bushing

bore has a diameter of 25.04 mm with a unilateral tolerance

of 0.03 mm. The L/D ratio is unity. The bushing load is

1.25 kN, and the journal rotates at 1200 rpm. Analyse theminimum clearance assembly if the average viscosity is 50mPa.s to find the minimum film thickness, the power loss

and the percentage of side flow.

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Vogelpohl Equation


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Vogelpohl Equation

= 1000 + 0.4 x

Where,V = Linear velocity of Journal bearing in m/s

journal bearing design

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