Hidrodinamica de Los Cojinetes

7/27/2019 Hidrodinamica de Los Cojinetes

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Hydrodynamic BearingsHydrodynamic Bearings --DesignDesign

Lecture 26Lecture 26

Engineering 473Engineering 473

Machine DesignMachine Design


2/24

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.


3/24

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.


4/24

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).


5/24

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.


6/24

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


7/24

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

=

+=

+=


10/24

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

=

==


12/24

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


14/24

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 =


16/24

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


20/24


21/24

Step 12Step 12Find Side Flow LeakageFind Side Flow Leakage

secin0.142Q

secin0.1770.8Q

0.8Q

Q

3

s

3

s

s

=

=

=


22/24

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

=

=

=

=


23/24

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.


24/24

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.

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