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Wiliam R. Jones, Jr. Lewis Research. Center. Cleveland, Ohio. Joseph Prahl and Ralph Jansen. Case Western Reserve University _. Cleveland, Ohio. _. : 7 :.

NASA

Techrfical

Memorandum

104426

Parched Elastohydrodynamic Lubrication: Ins1 and Procedure

Bryan

Schritz

Case Western Reserve Cleveland, Ohio

University

............

Wiliam R. Jones, Jr. Lewis Research Center Cleveland, Joseph

Ohio

Prahl and Ralph Jansen

Case Western Reserve Cleveland, Ohio

Prepared

University _

_ :

for the

:

..........

Annual Meeting of the Society of TfiboLogists •Ptuqadeiphia, Pennsylvania, May 4-7,' !992

NASA

7

m__

andLubrication

Engineers

......

(NA% A-TM1.04_70 ) PARCHFO ELASTOHYDROOYNAMIC LU3_ICATInN: INSTP, UMENT._,TIGN AND PRnCEDURE(_'A_k,) 27 p CSCL

NC_1- 30 469



_?

_._-. -...

20D

G3/34

uricl _S 00373R2

PARCHED

ELASTOHYDRODYNAMIC

INSTRUMENTATION

AND

Bryan Case

Reserve

William

R.

Prahl

and

44135

Ralph

Reserve

Cleveland,

Administration

Center

Ohio

Western

Jr.

Space

Research

Cleveland,

Joseph

44106

Jones,

and

Lewis

University

Ohio

Aeronautics

Case

PROCEDURE

Schritz

Western Cleveland,

National

LUBRICATION:

Jansen

University

Ohio

44106

SUM/MARY

A

counter

transient

rotating

instrumentation ment

bearing

elastohydrodynamic and

systems

and

upgraded.

documents

the

Methods

rig

has

been

lubrication test

capacitance

for

procedures. (film

measuring

designed

and

phenomena. Ball

thickness)

bearing

constructed

This

paper

and

race

speed

measurement

torque

and

race

to

study

describes

new

measure-

system

were

temperatures

were

implemented.

INTRODUCTION

Starvation was

theory,

described

occurring

a

in

build-up

ball

in

calculated

the by

there thin of

no

that

free

practical

torque

The

which

are

also

leads

film

thinning

then

concentrated

in

this

process,

the

resulting

For

retainerless that

a

Hertzian

and

energy

degradation

pressure thinner

spin

is

not

to

than

the

and

so

regime

loss

is

is

eventually

(ref.

stresses, produced

4

and

In

order

due

to

mechanical

chemical

contact

is

(refs.

volumes.

polymerization

film

where are

driving

and

failure.

balance

low

This

least

immobile

irreversible

at

films

axis.

Hertzian

polymeric

bearing

behavior

zone.

transients

increases

and/or

ball

lubricant

the

bearing

smaller

causes

The

thinning

added

operating in-situ

which

this

contact

defined

rate

and

in

(EHL),

situation

thickness

require

contact

shear

smaller

bearings

Hertzian

film be

the

instrument

3).

subsequently

must

film

to

describes

bearings

precisely

occurs,

beneficial

(ref.

parched

oil

in

system

long-term

failure

shear

"parched"

the

supply

a

describe

EHL,

outside

a

oil in

lubrication

relates

2).

adequately

the

most

in

in

lubricant,

suggested

the

make-up

is

in

It

restricted

(ref.

of

since

inside

film

failure,

As

oil

resulting to

to

immobile

have

lubricant out

prevent flow.

bulk

importance

and

squeezed

fails

I).

resulting

theory

subdivision

elastohydrodynamic

(ref.

a

inhibited EHL

theory

of

ago

having

is

classical

they

subdivision years

bearings

Another

is

of

inlet

starvation behavior.

a

number

cross

shear At

some

changes

5),

to

energy point in

the

6).

it which

has

been

yields

a

geometrically perfect, plastic ball separator in just the right location (ref. 7). This is particularly important since elimination of the retainer in a bearing precludes any retainer instability problems which commonlyoccur in gyroscope bearings (ref. 8). To study these concepts, a Transient Elastohydrodynamic Lubrication Apparatus (TEHL) was initially designed and constructed by Kingsbury (ref. 3). Later, modifications by Hunter (ref. 9) allowed for calculation of film thickness from capacitance measurements. The objective of this paper is to describe several new modifications to the TEHLapparatus and to completely document its operation. The ball and race speed measurementsystems and the capacitance measurementsystem were upgraded. Methods for measuring bearing torque and race temperature were implemented. Finally, a computer data acquisition system was installed. TEHLAPPARATUS - BASICOPERATION The overall apparatus is shown in figure i. It consists of the TEHL apparatus itself, inner and outer race drive motors (the latter containing a torque sensor) and a loading mechanism. The TEHLapparatus appears in figure 2. The upper bearing is the test bearing. The outer race of this bearing is driven by a synchronous hysteresis motor through a toothed belt drive. A keyed bushing is press fit into the inner race. The load ring is keyed into the bushing and a spindle, which is driven by a second synchronous motor through another toothed belt drive. This allows the bearing to be run in a counter - rotating mode (the races spin in opposite directions such that the ball complement is stationary). The bearing is loaded with a deadweight axially through the load ring and the central load shaft that extends down through the spindle (fig. 3). The four lower bearings provide support and alignment. Ball-race coupling is followed by measuring the basic speed ratio of the bearing (ref. I0). BSRis defined as: _b

BSR=

where race

_b spin

is rates,

the

ball spin respectively

BEARING

The 4267A

bearing

ply

CAPACITANCE,

capacitance

(1 )

_i

FILM

and sign

measurement

personal

computer

to

bearing

connected a

known

that

is

LCZ

meter

(relative

the

alternating

developed as

shown

to

the

current

across in supply

by

the

figure

four

an

across bearing 5.

current)

the as

a

cables.

result

Measurements of

the

returned

of

of

a

Two and of the

and outer fig. 4).

Hewlett-Packard

interfaced

interface

bearing

in

CONDUCTIVITY

consists

meter,

IEEE-488

coaxial

the inner as shown

AND

system LCZ

through

_o are defined

THICKNESS,

(inductance-capacitance-impedance)

compatible is

rate and (algebraic

(BSR)

this

of

two

carry

back and

made

IBM

LCZ

cables the

current

are

an

The

these

amplitude

voltage

with

bus.

sup-

voltage to

phase by

meter

the

the shift

instrument, and the total impedance across the bearing is calculated. The impedance is resolved into an effective parallel capacitance and conductance, which are the actual values displayed by the meter. The average contact film thickness is then calculated from the capacitance readings by a computer program from a method developed by Dyson et al. (ref. 12) for cylinders but successfully applied to ball bearings by Allen, et al. (ref. 13). Actual electrical connections to the bearings are madethrough two sets of slip rings (fig. 5). The first set carries all four wires from the stationary lab reference frame to the rotating outer housing. Two wires (one current supply and one voltage sense) are attached to a screw, which in turn, is tightened against the outer bearing race. The other two wires pass through the second slip ring assembly (whose stator rotates with the outer housing) to the load ring, where they are attached by a screw. The load ring makes direct metal contact with the inner race, completing the circuit. The whole apparatus is electrically isolated from ground (except for a 5 M_ bleed-off resistor, which drains away static build-up). Isolation from ground is necessary for proper operation of the LCZ meter. Typical capacitance readings are on the order of 500 pF, with an accuracy of about ±2 pF, and conductance readings are in the 1 _s (microsiemens) range, accurate to ±0.i _s. Stray circuit

capacitance

and

readings from the

by

backing

and

conductance

out

the

from the meter. values read from

The

ball

and

rate, the

race

speed

measuring

on

the

rate

order

of

this

system:

ball

complement

in

the

AND

(fig.

±0.001

percent.

the

race

speed

races

drive

driven

To

determine

integer

4).

and

the

ratio

the

driven

of The

the

pulley. power

counters.

The

This

to

the

race

To

measure

and

is

pick-up

ball

then

subtracted

important

in

are

ball

than

considerably the

three

spin

more

the accu-

calculation

basic

of

sections

measurement,

to

and

the

used

to

the

period

I000

is

timing

sufficient

constant pole

(in

pulley

outputs

on are

of

signals

fed

this

case, of

to

the of

into

pulley the the

the

motors,

number

on

the a

and

interface

and

measure

each

motors the

belt to

arrangement

driving

IEEE-488

SPIN

one of

a

the

the

the

rate, made

by

monitor

drive the

through

it

by on

from

through

spin

motors

divide

teeth

measure

coil,

SPEED

determined of

signals

computer

the A

is

There

speed,

BALL

magnetized.

the

taking

complicated

also

the

synchronous

motors,

supplies counters

breaking then

are

more

is

contacts.

the

number The

is

It

measurement,

by

constant

of

frequency information

the

and

controller.

are

frequency

by

screw, readings

circuit

RACE

The

measured

SPEEDS

6).

ball-race

position

arrangements.

are

contact

RACE

measuring

circuit of

slip

race

These stray background the LCZ meter.

BALL

capacitance

values

outer

variable

pair

of

transmit

the

bus.

RATE

of

the turns

bearing of

balls

number

34

is

slightly

A.W.G.

magnet

wire woundon a laminated iron core, is positioned near the magnetized ball. (The ball is stationary in space because of the counter-rotating mode of bearing on

operation,

the

order

frequencies first a

rates of

by

roll-off are

three

sharp gain

The

output

rate. and

12

=

50

a

is the

information

like

the

race

An

important

to

part

controller.

measured

under

complement adjustments during

to

the A

ment

second

a

EMF

each

in

of

coil

that

coil

the

coil The

controller

box

parallel

buffer/damper controller

may

controller

action,

is

then

output

added from

controlled

in race

the

go

the

the

position

rotation

of rate

the

the

filter

through

(Ball

(ref.

is

spin

a

series

ii),

an

detector. the

period

IEEE-488

ball

of

spin

the

wave,

interface

bus,

ball

at

the

ball

to

move

the

the

voltage box.

the

ball

to

return

a

invertor, on

of

coils,

them,

the

the

measurefirst

the

same

in

generated

coil

of

an

the

be

EMF

other

measurement

coil

generating

will

coil, in

rate the

between

both

PID

signal motor

ball

to

preamps

pass

rectifier two

in

will

the

magnetized

one

used

of the

controi

to motor

main

results complement

signal

which

an

the

sent in

from

any

original

a

the

proper output

which

into

adjustment its

obtain

The

turn

the

through

signal,

Thus,

to

to sent

rotation.

is

supply. in

get

into

identical

output

control

generator, power

is

with

fed

sections,

The

necessary,

then through

amplitudes

controller.

form

the are

signals

then

these

if

to

complement the

two

direction

This a

identical

the

and in

into

drive

a

preamp

box,

sections, difference

race

that

gives

spin

frequency one

stationary

from

two

the

minute

coils.

Inside

input

ball

complement

rate,

makes

away

halfway

while

from

the 45 °

spin

ball

accurately

complement

between

toward

a

bias

in

the

be

orbital

ball

about

exactly

signals

to

controller

used

is

through

is

rate

the

sits

fed

an

The

one

magnitude

then

CONTROLLER

complement

bearing,

magnitude,

controller

inner

signal

pass

Hz.

as

is

many

This

i000

the

coil

of

zero-crossing

circuitry

keep

two

and

dc

the

sent

frequency

spin

ball

the

through a

low

filters

measures

ball

to

ball

in

depending

to

to the

the

The

oscillator

synchronize

run.

filter

section

then

a

same

a

of

is

through

zero.

speed

6).

amplitudes.

zero

test

output

(fig.

point

then

measuring the

race

in

is

Deliyannis

two

of

begins

between

coil.

£he

and

pass

and which

exactly

generated

ball

second

first

for

difference

position The

If

EMF

dB

POSITION

magnetized

increase

The

speed

near

the

the

will

the

identical

them.

If

decrease.

the

placed

run,

of

each

ball's

is

i00,

band

computer

order

be

inner of

coil,

test

magnitude

the

the

signal

precisely

the

assumption must

course

circuit,

During

the

the

-3

The

COMPLEMENT

of In

velocity

the

counter,

from

components

counters.

BALL

position

a

signal

instrumentation.

around

Deliyannis

of

to

speed

past

output significant

the

of

differentiator,

wave

sent

has

and

gain

Hz.)

i00)

a

square then

a

300

to

sends

just

to

The

and

apparatus with

dB/octave

200

control,

is

This

the

preamp

to

(Q

previously.)

millivolts,

to a

typically

automatic

noted

several

related

boosted

with

as

of

the is

is

voltage

used

to

disturbances of

the

inner

position.

TORQUE ANDTEMPERATURE MEASUREMENTS In setting up bearing torque measurementsystem consideration had to be given to not disturb the other measuring apparatus. In order to accomplish this, it was necessary to use a somewhatunconventional method of torque measurement. It is relatively easy to measure the torque required by the test bearing and the upper support bearing together: Simply measure the torque output of the motor, multiply by the ratio of the number of teeth on the driven pulley to the number on the driver pulley, and subtract losses due to windage, and slip rings. Because of the mechanical coupling between those two bearings, it is necessary to consider thermal effects to determine what fraction of the total torque is actually required by each bearing. Since both bearings rotate at precisely the same speed, the energy dissipated in each bearing is proportional to the torque generated by each bearing. The constants of proportionality are the same. Figure 7 shows the simplified The top and bottom of the housing

can

because

a much

the

the

plexiglas

metal,

or

thin

bakelite

ring,

bearing

directly

and

two

the

thermal the

covers

the

are

difference ratio

and

A

general

the

Motor motor

is

pulley

the

test sum

torque

is

suspended

is

the

treatment

measured

from

counteracted

output, are

which

on

(±0.I

the

is

used

order

of

Temperatures

the also

to

transmit

data

(i0

that

The

and

in

torque any

sensor

is

a

to

the

computer.

and

are

equal

can

be

to

(fig. to

strain

gage

I). the

The drive

type,

has Typical to

the

this

A.

applied

accurate

of the

determined.

appendix

conditioner/indicator

in.-oz)

and

Knowing

sensor

torque

low

ratio

housing,

exactly

a

one

housing

the

torque.

torque

by

extremely

then

is

does

from

the

their

the

bearing

contained

The

used.

of

housing

reaction

so

sensor.

is

0.071N-m

are

thermocouples

resistances wire system

wires

drop),

source

used

IEEE-488

In (test

order

with

a

gold

plated

LCZ

for

relay

to box,

contact

a

meter.

a be

a

known

that

an

so

a

analog

torque ±0.0007

values N-m

Fluke

a

room 8520A

operates

The

DMM

DMM

to

Digital much

current,

direct

two

they

are The

more

the carry

source

is

communicates

(DMM)

LCZ

meter

back

used, with

accurate

thermistor

Multimeter

like

wires

current also

since

temperature.

the

resulting

instead the

four-

four-wire of

computer

the

ac

using

bus.

single

support

have

using

thermistors, near

principle,

carry

interface

bearing, leads

in

except

by

using

temperatures

measured

which,

(two

measured

at

are

system,

voltage

the

a

sensor,

flowing

approximation,

bearing

is

than

separated

from

symmetric,

the

test

also

in.-oz).

than

the

the

heat

because

support

concept

surfaces,

resistance are

bearing

and the

using

the by

conditioner/indicator

to

this

order

test

bearing

torques, of

of

thermally

the

torque

bearings

first

is

insulated

thermal

isothermal

housing

support

of

a

be

between

bearing

as

higher

quantities

As to

the

difference

the

ratio, more

If

between

of

other.

treated

The

large

assumed

resistance.

be

insulator.

prevents

to

races

temperature

have

bakelite

which

heat flow diagram of the outer housing.

bearing, switched

using

from

gold

relays

in

read

outer

the

resistance

housing,

one

thermistor

plated

contact

good

condition

5

of

and

to

relays. to

all

ambient

keep

the It the

four

air next. is

thermistors

temperatures), This

important

lead

resistance

is

done

to

use to

a

minimum. Other types of relays, or even gold plated contacts with a little wear, produce variations in lead resistance, which show up as noise in the temperature data. The DMMleads pass through the sameslip ring system as the LCZmeter to get to the outer housing. Screw terminal connections are used to attach the leads from the slip rings to the leads from the thermistors. Because of the limited number of terminals on the slip ring assembly, it was necessary to arrange the thermistors in a "Y" arrangement. The thermal inertia of the bearing housing causes a time lag in the response of the temperature readings to variations in torque. It was assumed that the temperatures (Ki) are r_lated to the bearing torques (T±) through the Laplace domain transformation: Ki(s)

1 _- __

G(s) =__ Ti(s

This

is

some

reason,

to

the

stant from

known

as

a

the

first

order

temperature

governing

lag.

)

When

a

T i =

+ i

step

asymptotically

equation,

(2)

Ts

change

in

approaches

C 1 e -(t/T),

where

torque

its

T

is

and C I is a general constant. It is possible discrete data by applying the transformation:

a

new

occurs

value

response

to

remove

time the

for

according con-

time

lag

K i - e-(t/T)Ki_1

(3)

1 - e -(t/T)

(See

appendix

and t = represents

the

are

Here

the

t i - ti_ I, where the value at

constant. in

A).

This data

is

determined

abruptly

Y t

transformation

from

the

temperature

represents ith discrete

the

is

magnified.

changed,

is

Actual

plots

of

creating

a

the elapsed value, and

differential values

temperature step

in

the

EXAMPLES

Figures

8

to

i0

show

bearing

lubricant

(SRG)

contains

typical

physical

bearing

geometry

The

figures

different tures was

run

and to

motor

the

typical

ranges,

torque)

failure.

and

torques). Failure

T

from

runs

All

The the and

the

lag

subscript response thus,

various

where

the

removed, i time

any

noise

thermistors

bearing

load

was

torques.

generated

with

described for

a

super-refined

instrumentation.

SRG

200.

Table

II

gyro

Table lists

I

the

parameters.

variations,

and race

and

values

(film

were

generated

plots

occurred

nature,

time

DATA

capacitance,

calculated

the

time. T is

for

bearing

data

data

operating

(conductance,

bearing

of

in

for

OF

above

property

nominal

show

measured

and

ratio,

and

examples using

with

at

6

approximately

resolutions ball

thickness, from 18

for

speeds, basic a 000

single sec.

the

temperaspeed test

that

CONCLUSIONS

A be

used

in

the

tive

fully in

instrumented the

parched

results

sequence.

study EHL

and

of

This, materials

systems

which

in

operate

This which

turn,

and

automated

failure

regime.

indicating

bearing

the

should

in

the

help and

parched

.v

angular

real-life

factors

coatings,

bearing

of

are in

test

bearing more the

provide regime.

rig

contact

now

ball

test

should

significant synthesis

valuable

exists

in of

data

that

bearings give the

can

running quantitafailure

new

lubricants

and

for

the

of

design

APPENDIX

The the

sum

test of

bearing

the

sum which expressed

torque

test

and

goes to the as follows:

can

support

test

be

A

viewed

bearing

bearing,

the

torques,

Bt"

T_-

Pt

as

product Y

of

, and

two

the

Mathematically

quantities:

fraction

these

of

quantities

that are

T,

+ Yt

(IA)

" Tt

/Y_,

(2A)

where:

Tt

test

bearing

T

support

torque

bearing

torque

S

T_

is

t_e

ratio

found

by

of

subtracting

measuring

pulley out

the

torque

diameters

losses

due

to to

output

obtain

slip

ring

TZ

of

the

the

drive

torque

friction

motor,

applied and

to

multiplying the

by

housing,

and

windage:

DhY m = __ _ TL Dm

(3A)

where:

T

torque

output

by

the

TL

torque

lost

Dh

diameter

of

housing

D

diameter

of

motor

motor

m

m

Losses the ring

by

to

windage

windage

torque

friction

(0.62

the

due

motor

to

is

and

ring

friction

pulley pulley

can

sensor

slip

be and

a constant,

shown are

to

be

on

neglected

in

experimentally

the

order

of

practice. measured

the

resolution

Loss to

be

due 0.0044

to

of the

slip

N-m

in.-oz).

To determine support bearing the

Bt, to

it is useful to the test bearing

define a torque.

new quantity The ratio

is

_t' the related

ratio of to Bt

expression: 1

#_ . __ 1 +_t

(4A)

Since

both

bearings

rotate

at

identical

speeds,

T,

QB/_s

Q8

Tq

Qt/_t

Qt

(5A) _t

"

by

support

by

test

where:

rate

of

heat

dissipation

rate

of

heatdissipation

bearing

e8

Qt

n

support

bearing

bearing

speed

5

n

test

bearing

speed

this

relationship

t

From

it

follows

that:

et

(6A) Qt

In the network heat

determination of thermal

transfer

thermal are

of _t' resistances

theory

resistance

neglected,

and of

since

than

the

of all between

the parts are the metallic

races,

respectively.

is convenient (fig. AI), and

electrical

the

circuit

bearing

their

higher

it

or

similar. part of R

races

thermal

plexiglass

+ Qs

to to

theory.

and

the

conductances

bakelite

of the housing on an analogy In

this

metallic are

parts,

RI and the housing

think draw

while

R2 represent and the test

model,

part

of

two

orders

the

geometric

the and

as a between the

the

of

housing

magnitude dimensions

thermal support

resistance bearing

represents

the

thermal

resistance

between

the

represents

the

thermal

resistance

between

the

X

bearing

races,

while

R C

metallic the model bearing

part to

of the account

R 3 heat

and R4 are dissipation

included from the

in

races.

Ideally, Qs

housing and ambient air. for other minor means of

and

Qt

R 1 = are

R2,

given

and

Rj,

R 4,

R

and

would

be

infinite.

In

this

case,

X

by T a - Th (7A) es R

1

Tt - Tb Qt

(8A)

= R I

where: T

t

T B

T

h

temperature

of

the

test

bearing

temperature

of

the

support

bearing

temperature

of

the

metallic

part

race race of

the

housing

It

follows

that

Pt

is

given

by

pt-e where

8

is

the

temperature

difference

(9A)

ratio

defined

by:

Tt - Th

(zOA)

88 T t + T.

Since case

of

the

idealized

figure

AI,

_t as a function sion yields the

case

with

all

of 8. following

is the

- 2T h

not

realized

R's

finite

A Taylor polynomial

series in

in and

practice, different

expansion 8.

of

the is

the

more

used

general to

resulting

solve

for

expres-

(IIA) _t

=A

+ [I

+ B +C].

where: (X 2 -)h)(1 a

+ 81 )

i

[i +12(2

211(1

+.2)](1

+ "I)+

+ 81 ) - 12(2

I,(I

+ '2)

+ 6 2 + 6_62)

+ 261

- 8213

- 81

Bm I + 12(2

(i + ,1)(12

+ 82)](1

- _I) {6111

+ 81)

+ 13(1

+ 82)

+ _2 (2

+ I_)]

+ 62)_,3}

C-, [i

+12(2

+82)](1

+61)

+13(1

+62)}

2

8111÷ 12(2÷ 62)]÷62L m

I

i + 12(2

where

+ _2)](I

+ _i)

the

dimensionless

= R2/R x ;

"leakage 81

are

the

dimensionless

tions given parameters equation

following

and

Under asymmetry expression

12

-1

"asymmetry

more

R 4, are

obtained

from

i0

- R1/R 3

62 - (R3/R4)

Under

and zero, set

are

13

and:

and

reaiis£1c

parameters is

;

and

parameters."

R2, and R3, parameters

the

= Re/R 3 ;

parameters,"

= (RI/R2)

above (R I = and asymmetry

(9A},

parameters the

+ e2)

: 11

are

+ 13(1

-1

the

Rx infinite), and equation of

nonzero, equation

assumptions but

small (IIA):

idealistic all (IIA)

assump-

the leakage reduces to

that compared

the

leakage to

unity,

As expected, this expression is very similar to equation (9A), except for a small correction to the linear term, a small constant, and a small nonlinear term. A combination of theoretical and experimental considerations have shown that: _2 - _I < Using tion

these limits, the maximum (9A) is less than 9 percent.

analysis.

Though

this

changing

conditions,

response

of

the

system

i0

To

deal

with

min.

Y, and Yh" respectively

related

into to

the

These would

Transformed

s

indices of

the

is t,

the s,

problem,

three

domain,

h.

by

transform

for

the

new

that inertia

the a

was

steady

housing

on

variables

are

dynamic

order

of Yt'

Tt, T, and was negligible. are

assumed

Gj(s)

as

the

be

follows: (13A)

and

j

transfer

represents

functions

any are

of

assumed

the to

be

form:

-Sto,J (14A)

Gj(s) = to,iS

+ 1

This time,

represents a simple first-order lag with t .' Knowing the actual temperatures, o,3 found from the expression:

Yj(s)

time,

T h, to

= Gj(s)Yj(s)

e

be

data

slowly

introduced:

temperatures function

or

the

the

the temperature of the system

transfer

Pt equaused for

state

makes

constants

actual

variable

Furthermore,

< 0.02

the simplified equation (9A)

time

the values the thermal

temperatures

Laplace

or

of

with

Tj(s)

where

I_iI

effective

inertia poor,

Laplace

ideal

quite

thermal

this

and

error in using Therefore,

is

rather

represent have if the

these

method

0.03

Since

the

but

rather

transformation, and defined:

temperatures as much

are

discrete like

data the

not

and dead can then

Tj(s) = __ Gj(s)

actually

points,

LaPlace

time constant to, , the ideal temperaturesJ

known it

transform,

N-I

:X k=0

ii

(15A)

is

as

continuous

convenient but

known

functions

to

use

as

the

a different Z-transform

of

where:

N

number

of

time

k

between

points

integer

points

ideal

points

interval

an

The

data

are

assumed

temperatures,

to an

be

taken

analogy

at

to

uniform

intervals,

equation

(15A)

is

used

_.

To

in

the

determine

the

Z-domain:

Tj(z) Yj(z)

=

(17A) Gj(z)

Transforming tion

of

equation

the

(16A)

transform

in

into

the

equation

Z-domain,

(16A)

and

yields

making

the

end

-(tl-ti_l)/tc,

Tj(ti) yj (ti)

ti

It _.

be

can

the

equation

various time experimentally

reached the

a

steady

bearing.

reach

63.2

the

percent

time

cation

time

(18A)

-(tl-ti_l)/tc, j

time

at

which

the

(18A)

is

valid

even

of

required the

then

its for

load

creating

constant of

is

new the

step.

i TM

temperature

if

t

550

reading

-

a

sudden

simply

steady

the

is

was

not

state

temperature

In

this

to

case,

t

sec

and

t

to

be

700

the

takes

load

for

while

begin ,

in

it

value,

the

t

a

to

are have

applied

time

after

are

to

temperature

dead

responding

and

taken.

equal

ti-1

change

time

crt

approximately

defini-

B

constants, tc,j, and dead time constants, to,j, by runnin G the rig until the temperature-s

state,

A

the

j

i

The determined

is

represents shown

of

- Tj(ti_l)e 1 --e

where

use

result:

the

found

to

constant

to

appli-

be

CsS

sec,

while

the

dead

time

con-

c,h

stants

are

substantially

Equation the

inertia. place with

of a

the

more

the

means

is

data

gets of

from

that

effects

merit between

small for

larger

slow

to

have

resulted

multiplied

the

a

30-fold

sec

resulting are

and

be

obtain

thus

negligible.

actual

temperature

if

system

the

data

had

substituted

into

a test

bearing

method

of

to

obtain

negligible

thermal

equation

(10A)

torque

in

measurement

time.

a

and

to

this

factor

of

a

constant

time

increase

in

idealized

obliterated.

effects,

response

to

by

20

the

can

drawback

=

and

applied

response

notable

T

T,

temperatures

rapid

approximately

calculated

than

temperatures

one

time

be

would

ideal

actual

much

sampling

can

that

These

There

in

(18A)

temperatures

less

however, substantial

I

and

the noise

data.

12

removal.

I - e

the

of

. t

noise.

temperature This

lag

method

T_e data

of

lag

this

noise

nominal

sec,

torque tend

effort

a

600

removal

experimentalist in

For

=

Any

this

values

to

be

so

still

noisy has

some

is

left

to

choose

to

interpret

the

REFERENCES i. Wedeven,L.D.; Bearing pp.

2.

Evans,

Starvation.

D.;

and

hydrodynamic

3.

5.

E.:

107,

Space

pp.

498-502.

Horsch,

Kannel,

Hunter,

3,

of

July

vol.

i,

to no.

Ball

1971,

the

i,

Lubrication.

The

Lees,

ed.,

Gyro-Spin ASLE

Elasto-

June

J.

Jog

Mechanism

1959,

Tribology,

in

McGraw-Hill,

Axis

Trans.,

and

Dufrane,

Oil

Ball

vol.

Bearing

6,

Gyroscopes.

1963,

no.

Performance

2,

Apr.

with

1963,

Dyson,

E.P.:

Naylor, in

G.E.;

Peacock,

L.D.; an

Instrument

1978,

in

an

pp.

386-394.

Angular

Contact

Element

CP-2423,

Bearings.

J.

Bearing.

Bearings

1985,

Measurement in

Ball

pp.

ASLE

259-262.

Rolling NASA

Speed 102,

and

Parched

Ratio

no.

Active

3,

227-241.

H.;

and

in

and

Homologous

Conference,

Mech.

pp.

in

Space.

20th

121-132.

Analysis

for

Elastohydrodynamic

an

Angular

1980,

an

Angular

Lubrication.

A.

R.:

The

L.A.;

and

Hertzian

Rhoads,

Contacts.

E.E.:

Series Dartmouth

of

The

13

Books,

Blue

vol.

Measurement

180,

W.L.: NASA

pt.

3B,

of

Oil

and Oils.

Hanover,

Films

Lubrica-

1966,

Measurement CR-I05378,

Physical

J.

Ridge

Elastohydrodynamic

Instrument College,

Bearing.

391-394.

TAB

Contacts. London,

Contact

pp.

Handbook.

Wilson,

Eng.

Klaus,

of July

Filter

pp.

Elastohydrodynamic

Thickness

Bearings

The

1979,

Inst.

of

K.F.:

Thickness

Basic

Proc.

Dromgold,

Slip 1984,

Operating

vol.

F.P.:

A.;

Allen,

Film

in

July

1986.

Technol.,

PA,

July

Symposium,

Bearing

CR-179506,

3,

and

3,

Mechanics

Ball

no.

Pivoting

J.W.;

Tedeschi,

tics

no.

Solution

Sci.,

Breakdown

lO0,

no.

S.D.:

tion,

14.

Numerical

B.P.:

of

27,

Kingsbury,

Film

Analysis

93,

229-233.

S.

Lubricant vol.

E.P.:

Thickness

13.

pp.

Blasingame,

vol.

Summit, 12.

Eng.

Films.

E.P.:

Kingsbury,

Lubr. ii.

A

Mech.

1985,

Correlation

Technol.,

contact

i0.

Optical vol.

112-124.

Kingsbury,

NASA

A.:

Technol.,

G.R.:

Instruments,

Lubricating

Aerospace

9.

Cameron,

Elastohydrodynamic

Apr. and

and

J.D.:

Trans.,

8.

2,

F.R.;

Air,

Lubr.

7.

J.

Parched

no.

Archibald,

Dynamic

6.

Higginson,

Problem.

Kingsbury,

pp.

Lubr.

6-15.

vol. 4.

and

J.

349-363.

Dowson,

pp.

W.;

pp.

of

119-134.

Lubricant

1968.

Chemical Presented NH,

Sept.

Characterisat 5,

2nd 1968.

TABLEI.

-

PHYSICAL

PROPERTIES

OF

[Reference Kinematic

viscosity,

38

°C

....................

at

99

°C

...................

Pour

index

point,

Flash

TABLE Bore, Ball

m

Ball

m

diameter,

contact

108 -7

.................

BEARING

GEOMETRY

288

AND

OPERATING

PARAMETERS

deg

complement load,

0.04

....................... m

angle,

Nominal

750 42.2

..............................

" dlameter,

Pitch

-

200)

14.]

..................

°C

II.

(SRG

.................

°C

point,

LUBRICANT

CS

at

Viscosity

TEST

-3

7.9375x10

.......................

5.40xi0

.........................

-2

12.7

........................... N

21

..........................

891

Mean

outer

race

stress,

N/m 2

..................

l.OxlO

9

Mean

inner

race

stress,

N/m 2

..................

1.2xlO

9

Contact

dimensions

Outer

semimajor

axis,

m

...................

4.98xi0

-4

Outer

semiminor

axis,

m

..................

1.22xi0

-4

Inner

semimajor

axis,

m

...................

5.13xi0

-4

Inner

semiminor

axis,

m

...................

1.04xlO



14

,,--TORQUE

SENSOR

/ /

lOAf, E ..... MOTOR--

_, |J='! 11_ -::'-- _ '1'_1 tBqil,.ll_/, .... 'llm=::f_k_' '..' ' "_kl_ " ";_::,. "_,'_1_ _--_": "' ' '!-:

tiillill ?k:;

RACE MOTOR--

_|_,_:..z:. --_'11/

LOADING

t1_"'%

_

7._;_!

"-"'=

-.1'_',__

MECHANISM-_

.

"_'_

It

tl I Figure

1 --Overall

experimental

apparatus.

10 CHANNEL MAIN SL 2 CHANNEL INNER SLIP TERMINAL

BEARING

OUTER RACE DRIVE GE/

UPPORT BEARING ONE

INNER RACE DRIVE

lENT TEMPERATURE PROBE IPPORT BEARING TWO IUPPORT BEARING THREE "SUPPORT BEARING FOUR

LOAD PIN Figure

2.--TEHL

15

apparatus.

COUNTER

cc,

INSULATED

LOAD MECHANISM

I

LOAD

LOAD

ADJUSTMENT

Figure 3.--Loading

Figure 4.--Geometry

PAN mechanism.

of an angular contact ball bearing with a full ball complement.

]6

PICTORIAL

Figure 5.--Electrical

connections-kCZ

17

meter 1o _es! bearing.

FILTER

BOX U

stage 2

stage 3

D/DT

Li_ro

J

crossing j detector

Computer I

I

|

J_.j

I oh'.racei Coil 1

Magnetized ball --x

Timing belts

I

Outer race drive motor

P_ -

I _nte_

_

Motor control Start/ stop/ direction

power supply Coil 2

Inner race drive motor

1 s,, _

gem ,rater vol ;, li'l I

I indicator otel direction

BALL COMPLEMENT

i1- ,

H

I !I _I Fi?r H I I I

POSITION

CONTROLLER

Amplitude detector 1

detector Amplitude 2

+1

I_J-.f I

'

'_

-P"

Figure 6.--Ball

_.

'

= ' P,,I +,--:Cont. I _!_

and race speed measuring system.

18

/_"= acti°n _

>

Insulator Conductor Indicates substantial heatflow

_- Test ,_ bearing

High temp. High temp. gradient gradient

r

' High temp. gradient

"-- Support bearing

Figure 7.--Heat

flow in outer housing.

]9

2.6

2.0 4)

.| O3 0

|

J '10

1.0

,

,

,

.

=1

....

_

!

.....

I

,

. _ ....

(a) Conductance across the bearing versus elapsed time. Bearing fau'iureoccurs at 18 000 seconds. IOO0

8OO

LL ¢1.

L_

6OO

4OO

200

....

1 5000

....

I

....

10 00t3

I 15 000

Elapsed time, sec (b) Capacitance across the bearing versus elapsed time. Figure 8.--Electrical

20

measurements.

....

I 2O 000

.3O

.25

E

.t5

....

.10 0

I 5000

....

] ..... 10000

1

.

,

15000

Elapsed time, sec (c) Calculated film thickness versus elapsed time. Film thickness was calculated from capacitanoe data assuming smooth surfacas in the baR-race contact (no surface roughness). Figure 8._onduded.

=,

2]

I 2OOOO

45.08

45.07

! __45._

45.05

45.04 (a) Inner race speed versus elapsed _me, The inner race Speed Is varied by b"teball complement controller as required to keep the ball complement stationary. 33.78

m

33.77

"_. 33.76

8 33.75 0

33.74

--

33.73

.... 0

.

.



I

....

I

5000

,

10 000

,

,

I 15 000

....

I 20 000

Elapsed time, sec (b) Outer race speed versus elapsed time. The spikes are due to noise in the power supply oscillator causing frequency shifts. Figure 9.--Speed

22

measurements.

263.26-

263.20

-T

"_" 263.15

263.10

263.06

,

,

, , I .... I .... [ .... (c) Ball spin rate (spinning of the ball about its own axis) versus elapsed time•

3.3392

3.3390

3.3380

3.3378

,

,

....

0

I fO 000

5000

.........

Elapsed lime. sec ._ •

_

(d) Basic speed ratio versus elapsed time. ,

Figure 9._Concluded.

23

15 000

I 2O 000

70 Test bearing outer race

J

60 Support bearing outel' race J

Housing

o

_,

50

a O.

E 40

Ambient

3O

....

20

1

.....

(a) Actual measured temperatures .092

I

....

I

,

,

,

,

I

of various test rig components versus elapsed time.

m

.090

E.080 Z

d E ,9o O

.070

|

,

.063 0

5000

10000

15000

Elapsed lime, sec (b) Torque output of outer race drive motor versus elapsed time. Figure lO.'Temperature

24

and torque measurements.

I 20OO0

._-:

.14

) Test bearing

./

.10 E d

| ,05

Support bearing

|

!

,

I

I

....

I

5000

....

10 000

I

,

,

Elapsed Ume, sec (c) Bearing torques calculated from motor torque and temperature data. Figure 10.--Concluded,

Model of housing

Detail of housing e3

/

r

_---_'-I Test bearing _

..

,,-_111-I" _(._

Plexiglass

.--4,oc Stainless steel

J*l_ " J, ..--- Bakelite

"{__3I__ _-.. 6 c _T-I-t •

,-_-_11 -_t_ "--'lum'num Support bearing J

a I

, . _---_,exig,a=

n,_.

*4 Figure A1.--Electrical

analogy to heat transfer in bearing housing.

25

I 2O 000

15 000

I

.,. Spm_ 1. Report

4.

No.

2.

NASA

TM- 104426

Title and

Subtitle

Parched

7.

Report Documentation

Page

A_nlnistr a_on

Elastohydrodynamic

Lubrication:

Government

Acx_ss|on

Instrumentation

No.

3.

Recipient's

5.

Report

6.

Performing

Organization

Coda

Performing

Organization

Repod

8.

R. Jones, Jr., Joseph

No.

Date

and Procedure

Author(s)

Bryan Schritz, William and Ralph Jansen

Catalog

Prahl,

No.

E-6259 10.

Work

Unit

No.

505 - 63 - 1A 9.

Performing

Organization

Name

and

Address 11.

National Aeronautics and Space Administration Lewis Research Center Cleveland,

Ohio

Sponsoring

Agency

Name

and

Supplementary

Type

of Report

Technical

Address

National Aeronautics and Space Administration Washington, D.C. 20546-0001

15,

or Grant

No,

44135-3191 13.

12.

Contract

14.

Sponsoring

and

Period

Covered

Memorandum

Agency

Code

Notes

Prepared for the Annual Meeting of the Society of Tribologists and Lubrication Engineers, Philadelphia, Pennsylvania, May 4-7, 1992. Bryan Schritz, Case Western Reserve University, Cleveland, Ohio 44106; William R. Jones, Jr., NASA Lewis Research Center; Joseph Prahl and Ralph Jansen, Case Western Reserve University, Cleveland, Ohio 44106. Responsible person, William R. Jones, Jr., (216) 433-6051. 16.

Abstract

A counter rotating bearing rig has phenomena. This paper describes ment systems and the capacitance torque and race temperatures were

17.

Key Words

(Suggested

been designed and constructed to study transient elastohydrodynamic lubrication new instrumentation and documents test procedures. Ball and race speed measure(film thickness) measurement system were upgraded. Methods for measuring bearing implemented.

by Author(s))

18.

Distribution

Elastohydrodynamics Bearings

19.

Security

Classif.

Subject

(of the report)

Unclassified NASAFORM 1626OCT86

Statement

Unclassified

20.

Security

Classif.

(of this

page)

Unclassified

- Unlimited

Category

21,

34

No. of pages

26

*For sale by the NationalTechnical InformationService,Springfield,Virginia 22161

22.

Price"

A03