Journal Bearing Design
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Transcript of 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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Reynolds 1D equation continue..
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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Reynolds 1D equation continue..
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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Reynolds 2D equation continue..
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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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Reynolds 2D equation continue..
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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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Continuity of flow of a column
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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Continuity of flow of a column
( ) 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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Journal Bearing Nomenclature
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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Journal Bearing Nomenclature
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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.
Infinitely short bearing
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Infinitely short bearing
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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Tutorials 3: Bearing Problems
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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Tutorials 3: Bearing Problems
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Tutorials 3: Bearing Problems
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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Tutorials 3: Bearing Problems
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Tutorials 3: Bearing Problems
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