hamrock fme ch12 bearings

8/13/2019 Hamrock FME Ch12 Bearings

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Hamrock Fundamentals of Machine Elements

Chapter 12: Hydrodynamic andHydrostatic Bearings

A Kingsbury Bearing.

A cup of tea, standing in

a dry saucer, is apt to slip

about in an awkward

manner, for which a

remedy is found inintroduction of a few

drops of water, or tea,

wetting the parts in

contact.

Lord Rayleigh (1918)


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p

ub

p

ub(x)

Figure 12.1 Density wedgemechanism.

Figure 12.2 Stretch mechanism.

Density Wedge and Stretch


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p

ub

p

wa

wb

Physical Wedge and Normal Squeeze

Figure 12.3 Physical wedgemechanism.

Figure 12.4 Normal squeexemechanism.


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ua

ub

p

Heat

p

Figure 12.5 Translation squeezemechanism.

Figure 12.6 Local expansionmechanism.

Translation Squeeze and Local Expansion


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z

ua

Stationary

BA

BA

h

Wz

z

x

B

A

(c)

L M

N

BC J KD

Aua ua ua

H

J

I

B

Moving

StationaryA

E

(a)

B

C DA

ua ua

B

A

(b)

BA

Figure 12.7 Velocity profiles in aparallel-surface slider bearing.

Figure 12.8 Flow within a fixed-inclineslider bearing (a) Couette flow; (b)Poiseuille flow; (c) resulting velocityprofile.

Velocity Profiles in

Slider Bearings


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A AW

t

ro

ri

Lubricant

Thrust bearing

Bearing pad

Bearing pad

Figure 12.9 Thrust slider bearing geometry.

Thrust Slider Bearing


7/31Hamrock Fundamentals of Machine Elements

Wz

ho

qs

sh

q

qs (both sides)

Film pressuredistribution

q

ub

l

ho

ub

z

x

sh

Fb

Fa

Wxa

Wa

Wza

Wzb

Figure 12.10 Force components and oilfilm geometry in a hydrodynamicallylubricated thrust slider bearing.

Figure 12.11 Side view of fixed-incline slider bearing.

Force and Pressure Profiles for Slider Bearing



Design Procedure for Fixed-Incline Thrust Bearing

1. Choose a pad length-to-width ratio. A square pad (!= 1) is generally thought to give good

performance. If it is known whether maximum load or minimum power loss is more

important in a particular application, the outlet film thickness ratioHocan be determined

from Fig. 12.13.

2. Once !andHo

are known, Fig. 12.14 can be used to obtain the bearing numberBt.

3. From Fig. 12.15 determine the temperature rise due to shear heating for a given !andBt.

The volumetric specific heat C

s

= "C

p

, which is the dimensionless temperature rise

parameter, is relatively constant for mineral oils and is equivalent to 1.36 !106N/(m

2C).

4. Determine lubricant temperature. Mean temperature can be expressed as

where tmi

= inlet temperature, C. The inlet temperature is usually known beforehand.

Once the mean temperature tm

is known, it can be used in Fig. 8.17 to determine the

viscosity of SAE oils, or Fig. 8.16 or Table 8.4 can be used. In using Table 8.4 if the

temperature is different from the three temperatures given, a linear interpolation can be

used.

(continued)

tm = tmi+!tm

2



Design Procedure for Fixed-Incline Thrust Bearing5. Make use of Eqs. (12.34) and (12.68) to get the outlet (minimum) film thickness h

0as

Once the outlet film thickness is known, the shoulder height sh

can be directly obtained from sh

= ho/H

o. If in some applications the outlet film thickness is specified and either the velocity u

b

or the normal applied load Wz

is not known, Eq. (12.72) can be rewritten to establish ubor W

z.

6. Check Table 12.1 to see if the outlet (minimum) film thickness is sufficient for the pressurized

surface finish. If ho

from Eq. (12.72) "ho

from Table 12.1, go to step 7. If ho

from Eq. (12.72)

< ho

from Table 12.1, consider one or both of the following steps:

a. Increase the bearing speed.

b. Decrease the load, the surface finish, or the inlet temperature. Upon making this change

return to step 3.7. Evaluate the other performance parameters. Once an adequate minimum film thickness and a

proper lubricant temperature have been determined, the performance parameters can be

evaluated. Specifically, from Fig. 12.16 the power loss, the coefficient of friction, and the total

and side flows can be determined.

h0=

Hol!0ubwt

WzBt



Sliding surfaceor runner

ri Na

ro

l

Pads

0

.2

.4

.6

.8

1.0

1 2

Length-to-width ratio, = l /wt

Maximumnormal

load

Dimens

ionlessminimumf

ilmt

hickness,

Ho=ho

/sh

Minimum powerconsumed

3 4

Figure 12.12 Configuration ofmultiple fixed-incline thrust sliderbearing

Figure 12.13 Chart for determiningminimum film thicknesscorresponding to maximum load orminimum power loss for variouspad proportions in fixed-inclinebearings.

Slider Bearings:Configuration and Film

Thickness



Surface finish Examples of Approximate Allowable outlet (minimum)(centerline average), Ra manufacturing relative film thicknessa, hom in. Description of surface methods costs m in.

0.1-0.2 4-8 Mirror-like surface Grind, lap, 17-20 2.5 100without toolmarks; and super-close tolerances finish

.2-.4 8-16 Smooth surface with- Grind and lap 17-20 6.2 250out scratches; closetolerances

.4-.8 16-32 Smooth surfaces; close Grind, file, 10 12.5 500tolderances and lap

.8-1.6 32-63 Accurate bearing sur- Grind, precision 7 25 1000face without toolmarks mill, and file

1.6-3.2 63-125 Smooth surface with- Shape, mill, 5 50 2000out objectionable tool- grind andmarks; moderate turntolerances

aThe values of film thickness are given only for guidance. They indicate the film thickness required to avoid metal-to-metalcontact under clean oil conditions with no misalignment. It may be necessary to take a larger film thickness than that

indicated (e.g., to obtain an acceptable temperature rise). It has been assumed that the average surface finish of the padsis the same as that of the runner.

Film Thickness for Hydrodynamic Bearings

Table 12.1 Allowable outlet (minimum) film thickness for a givensurface finish.


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Figure 12.14 Chart for determining minimum film thickness forfixed-incline thrust bearings.

Thrust Bearing - Film Thickness

Dimensionlessminimum

filmt

hickness,

Ho=ho/s

h

Bearing number, Bt

10

.1

2

.2

.4

.6

1

2

4

6

10

4 6 10 20 40 60 100 200 400 1000

Length-to-

width ratio,

2

1

1/2

0

3

4


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Figure 12.14 Chart for determining dimensionless temperature rise dueto viscous shear heating of lubricant for fixed-incline thrust bearings.

Thrust Bearings - Temperature Rise

Dimensionlesstemperatu

rerise,

0.9Cswtltm/Wz

Bearing number, Bt

10

4

2

10

6

20

40

60

200

100

400

600

1000

4 6 10 20 40 60 100 200 400 1000

Length-to-width ratio,

4

3

2

1

1/2

0


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Figure 12.16a Chart for determining friction coefficient for fixed-incline thrust bearings.

Thrust Bearings - Friction Coefficient

Bearing number, Bt

Dimensionlesscoeffic

ientoffriction,l

/sh

10

1

2

2

4

6

10

20

40

60

100

200

400

600

1000

4 6 10 20 40 60 100 200 400 1000

21

1/2

0

34



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Powerlossvariable,

1.5

hp

l/Wzubsh,

W-s/N-m

Bearing number, Bt

10

1

2

2

4

6

10

20

40

60

100

200

400

600

1000

4 6 10 20

(b)

40 60 100 200 400 1000

21

1/2

0

3

4

Length-to-

width ratio,

Figure 12.16b Chart for determining power loss for fixed-inclinethrust bearings.

Thrust Bearings - Power Loss


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Dimensionlessflow,q/wtubsh

Bearing number,Bt

10 2

1

2

3

4

4 6 10 20 40 60 100 200 400 1000

1

0

4

(c)

qsq

qs (both sides)

q


1/2

32

Figure 12.16c Chart for determining lubricant flow for fixed-incline thrust bearings.

Thrust Bearings - Lubricant Flow


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Figure 12.16d Chart for determining lubricant side flow for fixed-incline thrust bearings.

Thrust Bearings - Side Flow

Volumetricflowratio,qs

/q

Bearing number, Bt

10 2

.2

.4

.6

.8

1.0

4 6 10 20 40 60 100 200 400 1000

2

1

1/2

0

3

4



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Wr

Film pressure, p

pmax

e

0

max

hmin

b

00

Journal Bearing -

Pressure Distribution

Figure 12.17 Pressuredistribution around a journalbearing.


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h= c

2r

u u

Bearing

Journal

wt

Na

u

r

c

Figure 12.18 ConcentricJournal Bearing

Figure 12.19 Developed journal bearing surfaces for a concentricjournal bearing.

Concentric Journal Bearing


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Average radial load per area, Wr

Application psi MPa

Automotive engines:

Main bearings 600-750 4-5

Connecting rod bearing 1700-2300 10-15

Diesel engines:


Connecting rod bearing 1150-2300 8-15Electric motors 120-250 0.8-1.5

Steam turbines 150-300 1.0-2.0

Gear reducers 120-250 0.8-1.5

Centrifugal pumps 100-180 0.6-1.2

Air compressors:


Crankpin 280-500 2-4Centrifugal pumps 100-180 0.6-1.2

Table 12.2 Typical radial load per area Wr*in use for journal bearings.

Typical Radial Load for Journal Bearings


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Figure 12.20 Effect of bearing number on minimum filmthickness for four diameter-to-width ratios.

Journal Bearing - Film Thickness


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40

60

80

100

Attitudea

ngle,

,

deg

Bearing number, Bj

101100101102

20

0

Diameter-to-width ratio,

j

0

1

2

4

Figure 12.21 Effect of bearing number on attitude angle for fourdifferent diameter-to-width ratios.

Journal Bearings - Attitude Angle


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Dimension

lesscoefficient

offriction

variable,rb/c

Bearing number, Bj

101100

100

101

102

2 102

1011020

Diameter-to-

width ratio,

j

2

10

4

Figure 12.21 Effect of bearing number on coefficient of frictionfor four different diameter-to-width ratios.

Journal Bearing - Friction Coefficient


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Dimensionlessvolumetric

flow

rate,Q

=2q/rbcwtb

Bearing number, Bj

101100

2

4

6

8

1011020

Diameter-to-

width ratio,j

4

2

1

0

Figure 12.23 Effect of bearing number on dimensionless volumeflow rate for four different diameter-to-width ratios.

Journal Bearing - Flow Rate


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Dimensionlessm

aximumf

ilm

pressure,Pmax=

Wr

/2rbwtpmax

Bearing number, Bj

101100

.4

.6

.8

1.0

1011020

.2

Diameter-to-width ratio,

j0

1

2

4

Figure 12.25 Effect of bearing number on dimensionless maximumfilm pressure for four different diameter-to-width ratios.

Journal Bearing - Maximum Pressure


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L

ocationofterminating

pressure,

0,

deg

Locationofmaximump

ressure,

max,

deg

Bearing number, Bj

101100

40

60

80

100

101102

20

0

10

15

20

25

5

0

Diameter-to-

width ratio,j

0

max

0 1 24

4

2

1

0

Figure 12.21 Effect of bearing number on location of terminatingand maximum pressure for four different diameter-to-width ratios.

Journal Bearing - Maximum andTerminating Pressure Location


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M

inimumfilmthickne

ss,

hmin;powerloss,

hp;

ou

tlettemperature,tmo

;volumetricflowrate,q

Radial clearance, c, in.

q

tmo

hp

hmin

0 .5 1.0 1.5 2.0 2.5 3.0 103

Journal Bearing - Effect of Radial Clearance

Figure 12.27 Effect of radial clearance on some performanceparameters for a particular case.


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Figure 12.21 Parallel-surface squeeze film bearing

Squeeze Film Bearing

x

Surface b

w=

ho

h

t

Surface a

z

l


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WzBearing runner

Bearing pad

Recess pressure,pr= 0 Flow,

q= 0Supply pressure,

ps= 0

Bearingrecess

Manifold

Restrictor

(a)

Wz

pr>0

ps>0

(b)

p=pl

p=pl

Wz

q= 0

(c)

Wz

p=pr

ho

q

p=ps

(d)

Wz + Wz

p=pr + pr

ho ho

q

p=ps

(e)

Wz Wz

p=pr pr

ho + ho

q

p=ps

(f)

Fluid Film inHydrostatic

Bearing

Figure 12.29 Formation of fluidfilm in hydrostatic bearingsystem. (a) Pump off; (b) pressurebuildup; (c) pressure times recessarea equals normal applied load;(d) bearing operation; (e)increased load; (f) decreased load.


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= 0

hosh

Wz

ro

ri

pr

q

Radial FlowHydrostatic Bearing

Figure 12.30 Radial flow hydrostraticthrust bearing with circular step pad.

hamrock fme ch12 bearings

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