hydrostatic bearings-an introduction

8/7/2019 Hydrostatic Bearings-An Introduction

1/15

Design Procedure for

Hydro-Static Bearings (HSB)

Invented by L. D. Girard (Frenchman).

Completely removal of wear and reduction of coefficientof friction to 1/500.

Machines using hydrostatic support show a betterrotational accuracy within 2 micro-inch (0.051 micron)and RMS surface roughness down to 0.25 micro-inch(0.00635 micron)

Externally Pressurized

CoinedbyFuller


2/15

Features of Hydrostatic support

Surfaces can be separated by full fluid film even atzero speed. No problem with micro roughness and waviness.

Zero friction at zero speed. Useful feature for large size telescopes and radars.

High stiffness Oil film thickness varies as cube root of load.

Why not every bearing is based on Hydrostaticmechanism *K IJ RTGUUWTGUWRRN[4GNK CDK NK V [NK

RTGUUWTGQK NNK PGUCTGCNY C[UK PFQW

3/1Wh

HSB for Large BinocularTelescope Supports for Azimuth and Elevation axes.

Telescope makes a far away object look closer by collecting lightfrom a distant object (objective lens or primary mirror) and bringsthat light (image) to a focus where a second device (eyepiece lens)magnifies the image and brings it to our eye.

A telescope's ability to collect light is directly related to thediameter of the lens or mirror -- the aperture -- that is used togather light. Generally, the larger the aperture, the more light thetelescope collects and brings to focus, and the brighter the finalimage.

Refractors have good resolution, high enough to see details.However, it is difficult to make large objective lenses (greater than4 inches or 10 centimeters) for refractors. Because the aperture islimited, a refractor is less useful for observing faint, deep-skyobjects, like galaxies and nebulae, than reflector types oftelescopes.


3/15

Thrust Bearings Many loads carried by rotating machinery have

components that act in the direction of theshafts axis of rotation. Bearings supporting

such loads are known as thrust bearings.

Elementary 1-D Analysis

Assume a shaft ofradius Ro is locatedco-axially with a

circular recess ofradius Ri.

Assume all the oil in

recess is at thesupply pressure Ps.


4/15

Consider a small element of angular extent d ata radius r and radial width dr.

Elemental flow rate:

If flow is symmetrical to the origin, and radialflow rate is constant, then flow rate:

If film thickness is constant, then on integration:

rddr

dphq .

12

3

=

2..12

3

rdr

dphQ =

)(log6

1

3

CrQph

+=

Using two boundary conditions to findunknown values of C1 and Q

Load carrying capacity:

Substituting expression of pand rearranging

i

i

s Rr

RR

rR

pp = 00

0

Rregionin the

log

log

( )drrdpRpWo

i

R

R

is +=

2

0

2.

( )

=

i

o

o

i

os

RR

R

R

RpW

log.2

1

.2

2

2

=

1

2

11

1log.2

1

r

rCW


5/15

.1 .2 .3 .4 .5 .6 .7 .8 .9

4

6

8

10

12

14

16

18

20

22

load vs ratio

ratio

load

C1 = 10

( )drrdpRpWo

i

R

R

is +=

2

0

2.

)/1log(

1

6 1

30

r

phQ s

=)/1log(

1

1

2r

CQ =

.1 .2 .3 .4 .5 .6 .7 .8 .9

0

20

40

60

80

100

120

140

160

180

200

220

240

flow vs ratio

ratio

flow

C2 = 10

)/1log(1

1

2r

CQ =

Load is not a function of film thickness (h0 ), but flow is a very

strong function of film thickness.

Film thickness is designed based on surface finish & vibration.


6/15

Power loss

Power consumption in the hydrostatic bearingsystem consists of pumping power and frictionlosses.

2

4

00

4

0 12

.

=

=

+=

R

R

h

RP

PQP

PPP

if

sh

fht

2

4

00

4

0

2

2

0

3

0

112

1

)/log(6

11

+= R

R

h

R

PRR

h

Pi

s

i

t

==

=

=

03

0

2

0

0

2

)(

R

iR

ff drrh

PrFP

rAh

rF

h

UAF

Petroff equation

Example: W = 1000 N, =5000 rpm, R0=100

mm, Ri=50 mm, =0.01 Pa.s, 1=0.6, 2=0.9.Optimize minimum film thickness for minimumpower loss

2

4

00

4

0

2

2

0

3

0

1

12

1

)/log(6

11

+=

R

R

h

RP

RR

hP is

i

t

( )

=

io

o

i

os

RR

R

R

RpW

log.2

1

.2

2

20

23

01 hC

hCPt +=

( )Pa824,58

5.01

)2log(.2

1.0*

1000

rad/s6.52360

5000*2

22=

=

==

ss PP

sC

C

/N.m448.0

)N/(s.m10*35.4

2

2

211

1

=

=


7/15

.0004 .0006 .0008 .001 .0012 .0014 .0016 .0018 .002

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

Power loss vs film thickness

Film thickness

Powerloss

Example: W = 1000 N, =5000 rpm, R0=100 mm,=0.01 Pa.s, 1=0.6, 2=0.9, h0=1mm. Optimize ratio(Ri/R0) for minimum power loss

( )( )4

221*7.478

1

)/1log(5.353 r

r

rPt +

=

.1 .2 .3 .4 .5 .6 .7 .8 .9

500

550

600

650

700

750

800

850

Power loss vs ratio

ratio

Powerloss


8/15

.1 .2 .3 .4 .5 .6 .7 .8 .9

280

300

320

340

360

380

400

420

440

460

480

500

Power loss vs ratio

ratio

Powe

rloss

speed = 2500 rpm

.1 .2 .3 .4 .5 .6 .7 .8 .9

200

225

250

275

300

325

350

375

400

425

450

475Power loss vs ratio

ratio

Powerloss

Speed = 1250 rpm

Step hydrostatic bearing to support vertical turbo-charger inpower plant.


9/15

Restrictor In earlier slides, it was assumed that recess pressure

was equal to supply pressure.

This means change in load requires change inperformance of pump.

Pump performance can be regulated:

Manually

Automatically

To automat the pump performance one needs

sensor, amplifier, controller, etc. To reduce cost, often self regulating called restrictor

is used.

( )

=

i

o

o

i

os

RR

R

R

RpW

log.2

1

.2

2

2

Restrictor Constant flow restrictor

If flow is constant, recess pressure and film thicknessare related.

Increase in load, is balanced by increase in recesspressure and corresponding decrease in filmthickness.

Constant supply pressure restrictor Recess pressure is kept lower than supply pressure

Drop in pressure, from supply pressure to recesspressure, depends is controlled by the fixed restrictorplaced between supply manifold and the bearing.

Increase in load, reduces the flow by decreasing filmthickness, recess pressure increases and equilibriumis restored.

)/1log(

1

6 1

3

0

r

phQ s

=


10/15

Constant supply pressurerestrictors

Most commonly used restrictorsare capillary and orifice. Capillary is relatively long and

narrow opposed to and orifice whichis short in the direction of flow.

In a capillary, flow occurs due toshearing and is dependent onviscosity of fluid, whereas flow inorifice is due to inertia and dependson density.

Flow in capillary is directlyproportional to pressure differenceand that in an orifice is dependent onsquare root of pressure difference.

Although the pumping power lossesare higher for these types ofcompensation devices, the initialcost is much less.

c

cc

l

RPQ

8

4=

/.24

2

PCd

Q Do

O =

A smaller flow

produces a

smaller pressure

drop.

Hydrostatic Bearing Film Stiffnesswith Constant Feed Rate

)/log(

1

6

3

0

io

s

RR

phQ

=

( )

=

i

o

o

i

os

RR

R

R

RpW

log.2

1

.2

2

2

3

22

3

0

2

22

*)5.01(*)1.0(*01.0*31.3oo

io

h

Q

h

Q

R

RRW

=

00

13StiffnesshW

dhdWK ==

If W is doubled, and Q is kept constant, what will be

relative change in film thickness?


11/15

.001 .002 .003 .004 .005 .006 .007 .008 .009 .010

250

500

750

1000

1250

1500

1750

2000

2250

Load vs film thickness

film thickness, mm

load,

N

Blue line --> 0.0001 flow

Red line --> 0.001 flow

Green line --> 0.01 flow

Capillary Compensation

174B--)/log(

1

6

33

0 =>== roio

r PhBQRR

PhQ

( )

cc

rscc

c

crsc

rlmm

PPkQl

RPPQ

50,15.0r

0.01assume)(8

c

4

==

=>=

=

( )

039.0A

log.2

1

.

eff3

2

2

2

=+

=

=

co

cseff

reff

i

o

o

i

or

kBh

kPAW

PA

RR

R

R

RPW

co

c

s

r

c

kBh

k

P

P

QQ

+

=

=

3

co

o

oo

co

o

co

cseff

o

kBh

Bh

h

W

h

W

kBh

Bh

kBh

kPAh

W

+=

++=

3

3

3

2

3

3or,

3

Lower value of kc

increases stiffness


12/15

.001 .002 .003 .004 .005 .006 .007 .008 .0090

.2

.4

.6

.8

1

1.2

1.4

1.6

W vs h

film thickness, m

Load,

N

Lower value of kc reduces load

Carrying capacity

.001 .002 .003 .004 .005 .006 .007 .008 .009

0

200

400

600

800

1000

1200

1400

W vs h

film thickness, m

Load,

N


13/15

Orifice Compensation

)(/).(24

2

rsoOrsDoO PPkQPPCd

Q ==

ro

io

r PhBQRR

PhQ 3

3

0

)/log(

1

6==

( )

++=

=

62

6222

2

2

2

2

4

log.2

1

.

o

soooo

eff

reff

i

o

o

i

or

hB

PhBkkkAW

PA

RR

R

R

RPW

262

2

oro

o

s

r

o

kPhB

k

P

P

QQ

+=

=

Hydrostatic Lift Useful to avoid metal to metal

contact under heavy static load

conditions. Ex. Synchronous

condenser, rolling mills, etc.

How to estimate load capacity ?

Trial and error method

Good for first of its kind.

Numerical modeling and simulation

Assume a shaft of radius r being floated in a bearing of radius R by

oil pumped through a slot at pressure PS

cosCh

.12

rateflowElemental

r

3

e

brd

dph

q

=

=


14/15

Hydrostatic lift..

rCee

/)cos1(ChcosCh rr

===

( )b

rd

dpCq r .

12

cos1.

rateflowElemental

33

=

( )331

cos1

12

risepressureElemental

=

d

bC

qrdp

r

( )( ) ( ) ( )

+

++

= D

bC

qrP

r

cos1

coscos

1.2

2

cos1.1.2

cos3-4.sin.12

solutionGeneral

1

5.22

2

222

2

3

1

( )( ) ( )

( )

++

=

==

1

5.22

2

22

2

0

cos1.2

2

1.2

-4.

90at0PusingevaluatedbecanD,n,integratioofconstant

D

( )( ) ( )

( )

++

=

==

1

5.22

2

22

2

3

1

0

ss

cos1.2

2

1.2

-4.120atPPusingdeterminedbecanPpressuresupply

r

sbC

qrP

-1 -.8 -.6 -.4 -.2 0 .2 .4 .60

20

40

60

80

100

120

140

160

180

200

220Pressure versus eccentricity ratio

eccentricity ratio

Supplypressure

Negative value of eccentricity ratio, describe the journal

position when it is above the bearing center.


15/15

Load Carrying Capacity

=2

0

.dpcosbr2W

Wloadappliedthebalancewill

.b.cosprdforceofcomponentverticaland.brdareaonactspPressure

( )( ) ( ) ( )

dC

qrW

r

.coscos1

coscos

1.2

2

cos1.1.2

cos3-4.sin.24 15.22

2

222

22

03

1

2

++

=

( )

=

23

1

2

1

212

rC

qrW

-1 -.8 -.6 -.4 -.2 0 .2 .4 .60

20

40

60

80

100

120

140

160

180Load versus eccentricity ratio

eccentricity ratio

Load

hydrostatic bearings-an introduction

Documents