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 47,' !992
NASA
7
m__
andLubrication
Engineers
......
(NA% ATM1.04_70 ) PARCHFO ELASTOHYDROOYNAMIC LU3_ICATInN: INSTP, UMENT._,TIGN AND PRnCEDURE(_'A_k,) 27 p CSCL
NC_1 30 469
•
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_._. ...
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
buildup
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 insitu
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
longterm
failure
shear
"parched"
the
supply
a
describe
EHL,
outside
a
oil in
lubrication
relates
2).
adequately
the
most
in
in
lubricant,
suggested
the
makeup
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. Ballrace 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).
HewlettPackard
interfaced
interface
bearing
in
CONDUCTIVITY
consists
meter,
IEEE488
coaxial
the inner as shown
AND
system LCZ
through
_o are defined
THICKNESS,
(inductancecapacitanceimpedance)
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_ bleedoff resistor, which drains away static buildup). 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
pickup
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
IEEE488
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).
ballrace
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 counterrotating mode of bearing on
operation,
the
order
frequencies first a
rates of
by
rolloff 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
IEEE488
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
zerocrossing
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
0.071Nm
are
thermocouples
resistances wire system
wires
drop),
source
used
IEEE488
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 Nm
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
fourwire 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
superrefined
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
reallife
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
Nm
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
pte 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 firstorder 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,
NI
:X k=0
ii
(15A)
is
as
continuous
convenient but
known
functions
to
use
as
the
a different Ztransform
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
Zdomain:
Tj(z) Yj(z)
=
(17A) Gj(z)
Transforming tion
of
equation
the
(16A)
transform
in
into
the
equation
Zdomain,
(16A)
and
yields
making
the
end
(tlti_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)
(tlti_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
ti1
change
time
crt
approximately
defini
B
constants, tc,j, and dead time constants, to,j, by runnin G the rig until the temperatures
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
30fold
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.
498502.
Horsch,
Kannel,
Hunter,
3,
of
July
vol.
i,
to no.
Ball
1971,
the
i,
Lubrication.
The
Lees,
ed.,
GyroSpin ASLE
Elasto
June
J.
Jog
Mechanism
1959,
Tribology,
in
McGrawHill,
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.
386394.
Angular
Contact
Element
CP2423,
Bearings.
J.
Bearing.
Bearings
1985,
Measurement in
Ball
pp.
ASLE
259262.
Rolling NASA
Speed 102,
and
Parched
Ratio
no.
Active
3,
227241.
H.;
and
in
and
Homologous
Conference,
Mech.
pp.
in
Space.
20th
121132.
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 CRI05378,
Physical
J.
Ridge
Elastohydrodynamic
Instrument College,
Bearing.
391394.
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
CR179506,
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,
229233.
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.
112124.
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.
615.
vol. 4.
and
J.
349363.
Dowson,
pp.
W.;
pp.
of
119134.
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
connectionskCZ
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 baRrace 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 _
..
,,_111I" _(._
Plexiglass
.4,oc Stainless steel
J*l_ " J, .. Bakelite
"{__3I__ _.. 6 c _TIt •
,__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_sson
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.
E6259 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. 205460001
15,
or Grant
No,
441353191 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 47, 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) 4336051. 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