An angular-contact ball bearing provides an easily obtainable, precise mechanical system for rheological tests on thin films under high pressure. The test conditions are by definition similar to those found in practice. Accessible independent variables include size, pressure, bulk temperature, roughness, adsorbed surfactant, fluid type, fluid quantity, fluid supply rate, film thickness, entrainment velocity, transit time, and combined strain. Easily measured or inferred variables include slip, changes in film thickness with time (transients), strain rate, lubricant elastic modulus (thin film, high pressure), tractive force, lubricant chemical degradation rate, and lubricant degradation product. Methods for setting and obtaining these quantities in a bearing are discussed, together with experimental limitations on them

Kingsbury, E.

English

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(VISA-TIM-83570) THE BALL EEABING AS A	 N84-17591
EHEOLQGICAL TEST Di VICE (Ml5k) 13 p
HC A021tlP A01	 CSCL 131
Unclas
G3/37 18336
Edward 'Kingsbury
Lewis Research Center
Clevef and, Ohio
Prepared for the
Tenth Leeds-Lyon Symposium on Tribology
•	 Lyon, France, September 6-9, 1983
THE BALL BEARING AS A RHEOLOGICAL TEST DEVICE
Edward Kingsbury*
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135
SUMMARY
An annular-contact ball bearing provides an easily obtainable, precise
mechanical system for rheological tests on thin fluid films under high pres-
sure. The test conditions are by definition similar to those found in prac-
tice. Accessible independent variables include size, pressure, bulk tempera-
ture, roughness, adsorbed surfactant, fluid type, fluid quantity, fluid supply
rate, film thickness, entrainment ve l ocity. transit time, and combined strain.
Easily measured or inferred variables include slip, changes in film thickness
with time (transients), strain rat,-, lubricant elastic modulus (thin film, high
pressure), tractive force, lubricant chemical degradation rate, and lubricant
degradation product. Methods for setting and obtaining these quantities in a
bearing are discussed, together with experimental limitations on them.
INTRODUCTIGN
Many machine elements, including ball bearings, depend on separation by
an elastohydrodynamic lubrication (EHL) film to prevent seizure and wear. The
rheologic and chemical response of the lubricant within h;gh-pressure,
high—shear tHL contacts is sufficiently complicated (refs. 1 and 2) to justify
an experimental analysis. Bench tests in single—, four—, and five—ball and
crowned roller test devices (ref. 3) may not reproduce the strains, pressures,
volumes, and rates in real bearings. The test devices also require specialized
precision parts that are easily damaged and hard to replace. As an alterna-
tive, an off-the-shelf bearing, slightly modified, can be used to investigate
viscous, tractive, elastic, and chemical effects in lubricants. The rolling
conditions are authentic, and if an experiment s;-,cljld damage the bearing, ano-
ther is quickly available.
This paper presents a collection of formulas from various sources that
allow quick calculation of test conditions. These include formulas for Hertz
contact parameters and for bearing and contact kinematics and dynamics. Also,
some of the rheologic experiments with bearings that have been made (and could
be extended) are briefly described in an attempt to indicate the versatility
of a ball bearing as a rheological test device.
TEST CONFIGURATION
For rheological testing the bearing is run in counterrace rotation at zero
ball orbit rate under pure axial load. No ball retainer (cage) is fitted but
raper Laboratory, Cambridge, Massachusetts 02139 and National Re-
search Council — NASA Research Associate during 1983.
a full complement of balls is provided. Lubricant is supplied ir small, known
amo;:nts to the balls by withdrawal from a dilute solvent dip, the races being
left dry after cleaning. The result is a more or less uniform lubricant film
on the balls that is thin enough to be immobile in the operating centrifugal
field. Its thickness can be established by wzighing and is less than the cal-
culated fully flooded classical thickness, thus insuring controlled starvation.
Thickness can be varied by changing the solvent concentration.
BEARING GEOMETRY
Geometry is shown in figure 1. Nominal properties available from the
bearing manufacturer are
a	 Contai-c angle
CO,CI	 Crossrace curvatures
d	 Ball diameter
E	 Pitch diameter
Y	 Young's modulus
U	 Poisson's ratio
The maximum number of balls in a full complement is
N = int 
1.9
/sin 1(E)
HERTZ PARAMETERS
The test bearing carri,2s an axial load L. Resulting Hertz dimensions
and stress at the ball-race contacts (frcai the Brawe-H amrock approximations
(ref. 4) written in terms of bearing parameters) are
Effective curvatures
Rolling	 Crossrace
direction	 direction
	
Inner race R R = d(E - d)	 R  = C I d
	
—7F—	2l-T
	
Outer race R = d(E + d)	 R = C 0 d
R	
2r--X 
C— I
Curvature sum
1	 1 + i
7 
= R.R _ffX
Ellipticity (ratio of major to minor contact dimensions)
E
	
2
(1)
(2)
(3)
a
ORIOITOL PAGE TM
OF pOOR QVALI	 0.636
	k = a/b = 1.0339(R/RR )	 (4)X 
Elli ptic integral
	
= 1.0003 + 0.5968	 (5)
R 
x 
/R 
R
From these the semimajor Hertz width is
1/31/3
6k
2
^R(1 - ^^2 1	 L	 (6)
a B-R -	 ,^ Y	 N sIn
and the average contact pressure is
_	 L 1 l
	
P B-R - N s niBJ ,rah	 (>>
At a ball-ball contact carrying load z the area is circular with radius
aB-B, where
1/3
BY
and the average contact pressure is
P B-B W11
 ( 91
B-B
KINEMATICS
A reasonable figure of merit for a rolling contact is surface velocity; in
a ball bearing this is given by
V = wad	 (10)
where a is the ball spin angular velocity.
E
For any combination of race rotations (mode), including counterrace rota-
tion, ball spin rate is (ref. 5)
+c=PS	 (11)
3
_S	 _d co; E)
YO
	
1	 2
Sd cos E
Y I = -^ 1+-2
Inner-race rate (15)
where
	 O POFF OR QUALITY
(basic speed ratio) _ E2 - d 2 Cos 2B-- 2 E d
S (total speed) = 10 - 
YI
P is a constant bearing characteristic number, and S is the algebraic, dif-
ference in race rates.
All modes (including inner, outer, or counterrace rotation) at the same
total speed give the same ball spin rate; they are kinematically equivalent.
This allows counterrace-rotation rheological experiments to be related to the
more common operatin g modes on t l .e basis of total speed and surface velocity:
v = ,rdnS
	
(14)
Specification of v specifies S: for count Trace rotation • n ominal race rates
become
Outer-race rate
(12)
(13)
BALL-RACE SLTP
There are two kinds of slip in a bearin g : kinematic sli7, which i'^ dic-
tated by the motions and shapes of the balls and races; and an additir	 l rheo-
logical slip introduced by the lubricant. Examples of the former are Hfr^th-
cote, pivoting, and transverse precessional slip. These would be pres(iit with-
out any lubricant. They are the main tribological reason for lubricating a
ball bearing, and they can be calculated without knowing anything about the
lubricant.
The most important kinematic slip is produced by pivoting between balls
and races. (Pivoting is the relative angular velocity component of two bodies
in contact normal to their plane of tangency. It is often loosely referred to
as spir.) The sum of the inner- and outer-race pivotings is constant in a
ball bearing, independent of the position or motion of the ball spin vector
(ref. 6).
E _ S sin B
	 (16)
4
ORIGINAL PACE 13
OF POOR QUALITY
The associated pivoting slip u is maximm at the edge of the Hertz area
u - 2-aB-Rye
	
(17)
and zero at its center. Pivoting slip has been suggested as the source of me-
chanically activated lubricant degradation reactirns in starved bearings (see
below).
Drag torques produced by orbit and spin dissipations of the ball set cause
an additional rheologic slip in the lubricant. Its magnitude depends on vis-
cosity and film thickness in the EHL contacts. Since the thickness is set and
known, this slip can be used to study high-pressure viscosity in situ. Drag
slip is always in the rolling direction and cannot presently be calculated.
One methcd of measurement is to measure the ball and race rates (ref. 7) and
then to infer slips (normalized with respect to v) from kinematic equations
connecting running geometry and rates:
Ball - outer race
E
^O = YO/a	 A + cos BA)
A
Ball - inner race
	 (18)
E
^I=YI/A dA -cos  BA
A
Actual pitch and ball diameters E A and dA and contact angle B A in these
equations are not the manufacturer's nominal values. Instead they must be
measured in an auxiliary experiment at low speed and with thin film so as to
minimize drag slips. For zero drag slip they are given by
cos BA = ^Tr (
Y
 I Y
Y OY I
(19)
The actual g all diameter dA is easily measured direct ,. Once established,
these parameters can be used in equation (18) fur running conditions when the
slips are not small.
An artificial rheologic slip can be induced in the counterrace rotation
mode by applying an external torque to the ball group. Race rates are set to
+ 
5
TT+7
ORIGINAL PACE is
OF POOR QUALITY
qive a not-quite-zero "free" orbit rate. A pin inserted axially between two
balls and connected to a straingage dynamometer forces zero orbit rate
(fig. 2). This technique allows a study of tractive effects within EHL films
and also of ball—to—ball load carrying capacity (ref. 8).
BALL DYNAMICS
Bearing balls are forged from drawn wire and usually have an anisotropic
structure and an axis of figure (ref. 9). An artificial axis of figure can ^e
produced with a small diametral hole. Occasionally a bored ball is observed to
precess (ref. 10) such that the hole axis traces out a cone of half-angle e
at rate p, with the ball simultaneously spinning around the axis at rate s.
Figure 3, taken from (ref. 10), shows stroboscopic photographs of a precession;
e, s, and p can all be obtained from figure 3. Conditions leading to pre-
cession are not yet completely understood, but if it is present there must be
a kinematic transverse precessional slip at the ball-race contacts (ref. 11)
given by
j= 
d 
(s sin e sin pt)	 (20)
Both s and a are measured to be small but p is found to be large (= F).
Thus this slip is of small amplitude but high frequency. It has been suggested
(ref. 2) that the slip is accommodated by elastic strain within the lubricant.
If so, precession provides an experimental method for studying elastic behavior
in bearinq lubricants.
T he bored ball rapidly spinning about a fixed point (its center in coun-
terrace rntation) is a classical gyroscope. Its motion can be l ised to infer
the resultant torque acting on the ball through the EHL films (ref. 12)
M = p sin a [I Hs + ( I H — I F )p cos aJ
	
(21)
Here I H is the moment of inertia of the ball about its axis of figure and IE
is the moment of inertia about a normal axis, both easily calculated.
CHEMICAL EFFECTS
If the EHL film is too thin, the (constant kinematic) pivoting sl;p indu-
ces too much shear energy in the lubricant and oxidation or polymerization re-
actions are activated. The fluid lubricant is changed irreversibly into a
solid (ref. 13). Figure 4 shows lubricant degradation products on a race. It
has been suggested (ref. 2) that the rate of these reactions is given by
R = (const) exp (—Ah/uTT)
	
(22)
where A is an activation energy, u is the pivoting slip velocity, h is film
thickness, T is a limiting shear stress and T is contact transit time, As
the film thins, the degradation rate increases exponentially, without any me-
tallic film penet.ration being required.
6
It is possible to increase the rate at constant thickness by treating the
metal parts with a surfactant (ref. 13). This would have the effect of de-
creasing A.
CONCLUDING REMARKS
These various tests have been made on bearin g s ranging in pitch diameters
between 1 and 5 cm with basic speed ratios t.etwee , ; 2 and 6. Races and balls
of chromium steel and stainless steel have been used. Stainless steel parts
can be final cleaned with concentrated H2SO4 to remove all or g anic contam-
inants. This step is necessary if adsorbed surfac t ants are to be evali,ited.
So far only race finishes as received from the mantfacturers have been run.
There is no reason why artificially rou ghened (etc!ed or sandblasted) surfaces
could not be used.
A variety of organic fluids have been tested. Mineral oils ranging in
visco ity between 0.02 and 4 N s/m2 have been deposited in films between
5x10 	 and 25x10'6 cm thick. A suitable inert solvent for mineral oils is
hexane.
Ball-race contact pressures as high as 240 9 Pa have been used at sur-
face velocities up to 500 cm/sec. Transit tires of 1x10-5 sec arc 'ypical,
with pivoting slips as high as 5 cm/sec.
It is easy to control bulk temperature for small bearings at typical ser-
vice loads and speeds. Larger bearings tend to run above room temperature.
In summary, a ball bearing usec' as a rheological test device gives useful
experimental access to the regimf,
 of EHL where physical and chemical effects
in the lubricant blend together. T l, e simple geometry and motions of t;le bear-
ing parts allow easy determination of the rel , vant test parameters.
REFERENCES
1. Johnson, K. L. and Tevaarwerk, J. L. 'Shear Behavior of Elastohydrodynamic
Oil Films', Proc. R. Soc. London Ser. A, 1977, 356, 215-236.
2. Kingsbury, E. 'Transient EHL Effects in Starved Ball Bearings', presented
at the Tribology in the 80's conference, NASA Lewis Research Center, 1983.
3. Benzig, R., et al 'Friction and Wear Devices', 2nd Edition 1976 (ASLE,
Park Ridge, I11).
4. Brewe, D. E. and Hamrock, B. J. 'Simplified Solution for Elliptical Contact
Deformation Between Two Elastic Solids', J. Lubr. Technol., 1977, 99,
485-487.
5. Kingsbury, E. P. 'Basic Speed Ratio of an Angular Contact Bearing', J.
Lubr. Technol., 1980, 102, 391-394.
6. Kingsbury, E. 'Pivotingar..: Slip in an Angular Contact Bearing', ASLE paper
no. 83-LC-lb-2, 1983 (NASA TM-83408, 1983).
7. Kingsbury, E. P. 'Slip Measurement in an Angular Contact Ball Bearing', J.
Lubr. Technol., 1983, 105, 162-165.
8. Kingsbury, E. P 'Ball ^aTl Load Carrying Capacity in Retainerless Angular
Contact Bearings', J. Lubr. '_chnol., 1982,
  104. 327-329.
rAL
7
9, Kingsbury, E. P. 'Ball Contact Locus in an Angular Contact Bearing', J.
Lubr. Technol., 1983, 105, 166-170.
10. Kingsbury, E. P. 'Ball-otion in Angular
Contact Bearings', Wear, 1968, 11, 41-50.
11, Kingsbury, E. P. 'Precessional Slip in an Angular Contact Ball Bearing',
Wear, 77, 105-114.
12. Kingsbury, E. 'Ball Motion Perturbation in an Angular-Contact  Ball '3ear-
ing', ASLE Trans., 1982, 25, 279-282.
13. Kingsbury, E. P. 'Lubricant Breakdown in Instrument Ball Bearings', J.
Lubr. Technol., 1978, 100, 386-394.
ORIGINAL PACEc 10'
OF POOR QUALITY
8
fit` POOR V 14 l i Y
OUTER
RACE
E/2	 . .—
BEARING AXIS
CROSSRACE CURVATURE C - r/d
Figure 1. - Ball bearing geometry.
Figure 2. - Induced-slip apparatus.
0
I a
N
C
E	 c
N
fp	 U
U	 L-
•^	 G
m
-^	 m
L
N M
Q;	 L
C U
tU^
Ln
^o
co
u
ORIGINAL PAC-- F1
OF POOR QUALITY
4176
ORIGINAL PAGe fb
OF POOR QUALITY
Figure 4. - Solid-lubricant degradation proeucts.


The ball bearing as a rheological test device

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