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Hydrodynamic BearingsHydrodynamic Bearings --DesignDesign
Lecture 26Lecture 26
Engineering 473Engineering 473
Machine DesignMachine Design
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Governing EquationGoverning Equation
( ) ( ) ( )
dx
xdh6U
dz
dp
xh
zdx
dp
xh
x
33
=
In the previous lecture, the momentum and continuity
equations were used to develop the following equation
This equation was generalized to include lubricant flowin both the circumferential and longitudinal directions
( ) ( )dx
xdh6U
dx
dp
xh
x
3
=
This equation is generally solved using
specialty computer programs.
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Design VariablesDesign Variables
Independent VariablesIndependent Variables Dependent VariablesDependent Variables
Viscosity, Load, P (W/projected Area)
Speed, NDimensions r, c, , and L
Friction, f
Temperature rise, T
Volumetric flow rate, QMinimum film thickness, ho
The objective of the design engineer is to select the
independent variables necessary to achieve desired
performance criteria. The dependent variables will
be dictated by the selections made for the
independent variables.
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Graphical DataGraphical Data
Albert Raimondi and John Boyd, A Solution for the Finite
Journal Bearing and Its Application to Analysis and Design,Parts I, II, and III, Transactions of American Society of
Lubrication Engineers, Vol. 1, No. 1, in Lubrication Science
and Technology, Pergamon, New York, 1958, 159-209.
Raimondi and Boyd (1958) did extensive numerical studies
on the relationships between the various parameters that
govern the design of fluid film bearings and publishedgraphical data to facilitate the design of such bearings.
The charts presented in this lecture are for long bearings
with =360o
(full bearings).
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ViscosityViscosity--Temperature ChartsTemperature Charts
Shigley, Fig. 12-11
The viscosity of lubricants
used in fluid-film bearings
are very temperaturedependent.
As work is done on the fluid
as it moves through thebearing it heats up.
The viscosity used in the
design/analysis of a fluid-
film bearing should be based
on the average temperature.
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Average TemperatureAverage Temperature
2
TTT
2
TTT
TTT
inave
outinave
inout
+=
+=
+=
An initial T is estimated
at the start of an analysis.
Iteration will be required
based on the actual T.Shigley, Fig. 12-11
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SommerfeldSommerfeld NumberNumber
P
N
c
rS
2
=
The Sommerfeld Number is used extensively
in journal bearing design.
A. Sommerfeld, Zur Hdrodynamischen Theorie der Schmiermittel-
Reibung, Z. Math. Physik, vol. 50, 1904, pp 97-155.
r journal radius
c clearance
dynamic viscosityN rotational speed (rev/sec)
P bearing load/projected area
Note that consistent units must be used. Theunit for the Sommerfeld number is Rev.
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Example ProblemExample Problem
Given design parameters:
SAE 30 OilTin = 150
oF (oil inlet temperature)
N = 30 rev/sec (journal rotational speed)
W = 500 lb (total load acting on bearing)
r = 0.75 in (journal radius)c = 0.0015 in (clearance between journal and bearing)
L = 1.50 in (length of bearing)
Use the Raimondi-Boyd charts to determine the
bearing performance parameters.
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Step 1Step 1Estimate AverageEstimate Average
Lubricant TemperatureLubricant Temperature
Assume a temperature rise in the oil of 34oF.
F1672
F34F150T
2
TTT
ave
inave
=
+=
+=
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Step 2Step 2Find Average ViscosityFind Average Viscosity
reyn2.2 =
Shigley, Fig. 12-11
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Step 3Step 3Compute Force/ProjectedCompute Force/Projected
Area (P)Area (P)
2lb/in222P
in1.5in0.752
lb500
Lr2
WP
=
==
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Step 4Step 4Compute L/D and BearingCompute L/D and Bearing
Characteristic NumberCharacteristic Number
( )( )
0.0743S
lb/in222
rev/sec30sec/inlb2.2x10
in0.0015
in0.75
P
N
c
rS
0.1in)2(0.75
in1.5L/D
2
262
2
=
=
=
==
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Step 5Step 5Find Minimum FilmFind Minimum Film
Thickness and EccentricityThickness and Eccentricity
Shigley, Fig. 12-14
7.0c
e
28.0c
h0
==
=
ContactContact Light LoadLight Load
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Step 5Step 5ContinuedContinued
( )
( ) in00108.0in0.00150.72e
72.0c
e
in0.00042in0.00150.28h
28.0c
h
0
0
===>
==
===>
=
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Step 6Step 6Find Position of MinimumFind Position of Minimum
Film ThicknessFilm Thickness
degrees44 =
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Step 7Step 7Find the Maximum FilmFind the Maximum Film
PressurePressure
psi617222/0.36P
0.36P
P
max
max
==
=
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Step 8Step 8Find Location of MaximumFind Location of Maximum
PressurePressure
=
=
56
18
o
max
p
p
Shigley Fig 12-21
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Step 9Step 9Find Coefficient of FrictionFind Coefficient of Friction
0.005f
in0.75
in0.00152.5f
2.5fc
r
=
=
=
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Step 10Step 10Find Horsepower RequiredFind Horsepower Required
to Overcome Frictionto Overcome Friction
( )
( )
( ) ( )
63,000
rev/minNlbinTPwr(hp)
rev/minN
Pwr(hp)63,000lb-inT
rWfT
=
=
=
( )( )
hp0.054Pwr
63,000
60301.88Pwr
lb-in1.88T
in0.75lb5000.005T
=
=
=
=
W
Wfff =
r
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Step 12Step 12Find Side Flow LeakageFind Side Flow Leakage
secin0.142Q
secin0.1770.8Q
0.8Q
Q
3
s
3
s
s
=
=
=
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Step 13Step 13Find Temperature Rise ofFind Temperature Rise of
LubricantLubricant
It is assumed that all of the frictional energy is
converted to heat and carried away by the lubricant.
p
f
p
ff
f
cm
TT
TcmQTW
QW
=
==
=
p
f
cQNrWf2T
Qm
N2
rWfT
=
=
=
=
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Temperature RiseTemperature Rise(Continued)(Continued)
pcQ
NrWf2T
=
=
=
=
==
=
=
3
3
3f
OH
fp
f
in1728
ft
ftlb
62.4
0.86
RlbBTU0.42c
rev/sec30Nin0.75r
lb500W
0.005f
2
F.416T
BTUin9,338lb
secin0.177Q
f
3
=
=
=
Note that a temperature rise
of 34 oF was assumed when
the average temperature was
estimated.
The analysis needs to be
repeated with an improved
estimate for Tave.
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AssignmentAssignment
A journal bearing has a diameter of 3 in and is 1.5 in
long; it supports a load of 800 lbf. The journal speed is
600 rev/min and the radial clearance is 0.0025 in. Findthe minimum oil-film thickness and the maximum film
pressure for both SAE 10 and SAE 40 lubricants if the
operating temperature is 150 oF.
Discuss why one has a larger film thickness than the
other.