NASA 

Technical Paper 1547 

AVRADCOM 

Technical Report 79-26 

Correlation of Asperity 

Contact-Time Fraction With 

rodynamic ilm Thic 

illimeter- ore Ball 

John J. COY 

Propulsion Laboratory, A VRADCOM Research and Technology Luboratories 

Lewis Reseurcb Center 

Cleueland, Ohio 

National Aeronautics 

and Space Administration 

Scientific and Technical 

Information Branch 

1979 
SUMMARY 

Elastohydrodynamic film thicknesses and asperity contac t-time fractions were measured for a 20-millimeter-bore ball bearing by using the capacitance and conductance 

techniques. The bearing was thrust loaded to 90, 445, and 778 newtons (20, 100, and 175 

lb). The corresponding maximum stresses on the inner race were 1.28, 2.09, and 2.45 

gigapascals (185 000, 303 000, and 356 000 psi). The test speed ranged from 400 to 15 000 

rpm. The test bearing was mist lubricated with an M1L-L-23699A turbine oil. The test 

temperature was 27O C (80° F). 

fraction) as a function of measured film thickness. Measurements were made for three test 

series that represented the test bearing in various conditions of run-in. The measurements 

show that the percent film changes with bearing run-in time. The experimental results 

agreed well with theoretical predictions based on surface trace analysis for a new bearing. 

For the run-in state, they agreed with previously reported experimental results. The results 

show that asperity contact existed at a film thicknessroughness ratio A of 6.0 or less for 

a new bearing. After run-in, no asperity contact occurred at a A of 3.5 or greater. 

The experimental results were correlated to give the percent film (no-contact-time 

1N TRODUCTlO N 

Elastohydrodynamic ( EHD) lubrication of concentrated mechanical contacts has been 

investigated theoretically and experimentally for several decades (refs. 1 to 16). EHD 

lubrication theory has practical applications in ball and roller bearings, gears, and tractiondrive transmissions. 

fluences the viscosity of the lubricant and (2) the elastic contacts are substantially deformed locally. The net result is the formation of a thiri lubricant film that is beneficial in 

preventing seizure and rapid wear of contacting parts. 

EHD film thickness is difficult to measure because the films are so thin: They are generally of the same order of magnitude as the rms surface roughness. Various measurement 

methods have been developed and used (ref. 17). The X-ray method is restricted to applications where there is an open path for X-rays to the EHD contact, such as in the disk machine. The optical interference method is used for a ball on a transparent disk and in cases 

where the bearing outer race can be filled with a transparent window. The capacitance 

method is suitable for measuring EHD film thickness in an operating rolling-element bearing, as well as in the disk machine. 

Most theoretical models of EHD lubrication assume that smooth surfaces are in contact. However, real engineering requirements of manufacture and economy of production 

result in surfaces that are rough to greater or lesser degrees. There have been experimental and theoretical studies performed for EHD lubrication of rough surfaces. Reference 18 presents a theoretical model for the effect of roughness on average film thickness. 

Reference 19 reports on the experimental determination of film thickness on disks in rolling contact. The theory and experiment showed that surface roughness with longituTwo significant effects occur in elastohydrodynamic lubrication: (1) high pressure in- 
dinal lay has adeleterious effect on film thickness. If the EHD film becomes too thin, 

metal-to-metal contact occurs at the surface asperities. Reference 20 describes a model 

for the average asperity contact-time fraction. This model makes it possible to predict the 

amount of asperity contact as a function of film thickness and surface roughness. 

Asperity contact-time fraction is defined as the expected time fraction during which 

there is metal-to-metal contact in the EHD zone. A contact-time fraction of zero corresponds to full film lubrication, with no contact between surface asperities. In connection 

with this definition, it is important to realize that time averaging rather than spacial averaging is used. A very small percentage of area contact can result in a very large asperity 

contact-time fraction. Indeed, if there were only one asperity contact in the EHD zone at 

all times, the asperity contact-time fraction would be unity, but the percentage of area 

contact would be almost zero. 

One conclusion of reference 20 was that measuring film thickness by the conductance 

(asperity contact) technique is not practical. Notwithstanding this conclusion, conductance 

measurements do reveal asperity contact events and are most useful in determining the integrity of EHD films under varying conditions of operation and surface roughness. 

to 15 000 rpm, at temperatures to 121° C (250° F), and at contact stresses to 2.45 gigapascals (356 000 psi) in four oils. In those tests, the film thickness was measured by the 

capacitance method and compared with theoretically predicted film thickness. In the 

present work, the asperity contact-time fraction has been measured by the conductance 

method and the results have been correlated with measured film thickness. The filmthickness data for test series 3 of this report are the same as those presented in reference 

21. The general objective of the present work was to explore the regime in which asperity 

contact takes place. Therefore, neither an extensive range of test temperature nor a great 

variety of test oils were used. 

The specific objectives of the research described in this report were (1) to measure the 

asperity contact-time fraction for an operating ball bearing, (2) to correlate the results of 

the asperity contact-time fraction measurement with measured EHD film thickness, and (3) 

to compare the asperity contact-time fraction measurements with the theory of reference 

20. 

To accomplish these objectives, we measured EHD film thicknesses and asperity 

contact-time fractions for a ball bearing by the capacitance and conductance techniques. 

The test bearing was a 20-millimeter-bore ball bearing with three balls. It was run in the 

NASA EHD bearing test rig at speeds from 400 to 15 000 rpm. The test bearing was thrust 

loaded to 90, 445, and 778 newtons (20, 100, and 175 lb); this gave maximum contact 

stresses on the inner race of 1.28, 2.09, and 2.45 gigapascals (185 000, 303 000, and 356 000 

psi). The lubricant, an M1L-L-23699 turbine oil, was supplied through a mist system. The 

tests were conducted at room temperature. 

Reference 21 describes tests of a 20-millimeter-bore ball bearing at speeds from 400 

APPARATUS, SP EClMENS, A N D PROC EDU RE 

EHD film-thickness test rig. - The experiments were conducted in the test rig shown in 

figure 1 and described in reference 21. The test rig consists of a rotating driveshaft supported by two bearings running against a test bearing, which is located in a vibrationisolated housing. The shaft is driven with an air turbine. Shaft speed is sensed with a magnetic pickup located near six slots that were milled in the shaft. The speed is held constant 

during a test with an automatic controller. The load is applied pneumatically. The linear 

ball bushing allows the thrust load to be transmitted from the pneumatic loader through the 

shaft to the test bearing. The thrust load is determined from the air pressure acting on. 

2 
the loading cylinder area. All tests reported herein were conducted at room temperature 

(27O 6; 80° F). The bearing temperature remained constant within +3 degrees C (+5 deg F) 

during the tests. Temperatures were sensed by thermocouples placgd on the outerbearing 

race and in the inlet lubrication stream. The support bearings and the test bearing were 

mist lubricated with separate systems. 

Test bearing. - The test bearings for this experiment were 20-millimeter-bore angularcontact bearings with three 7. 15-millimeter- (9/32-in.-) diameter balls. The bearing specifications are given in table 1. The bearing cage was polyimide, and the outer race was 

electrically isolated from the housing. The spring-loaded thermocouple at the outer race 

and the slip rings on the drive shaft provided electrical contact for measurements across 

the test bearing. 

Test lubricant. - The lubricant chosen for this test program is of interest for bearing 

and gear applications. It is an improved type 11 synthetic, aircraft gas-turbine lubricant 

that meets M1L-L-23699A specifications. This lubricant is used in aircraft gearboxes and 

helicopter transmissions as well as in gas-turbine engines. The properties of this lubricant 

are shown in table 11. 

Measurement scheme. - The lubricant film thickness was measured by using the electrical capacitance method, as described in references 3 and ti. A schematic is shown in 

figure Z(a). The electrical capacitance between the inner and outer races of the test bearing is a function of the thickness of the lubricant film and the size of the Hertzian areas of 

contact (table 111). The capacitance across the test bearing was measured with a capacitance bridge, and the film thickness was read from figure 3. During the tests the capacitance-bridge balancing signal was observed on an oscilloscope. Any short circuiting of the 

test+earing capacitance as a result of asperity contact could be observed. 

A separate measurement system was used to determine the asperity contact-time 

fraction. The measurement arrangement is shown in figure 2(b). A 200-millivolt-at200-hertz half-wave rectified signal was applied across the test bearing. The voltage was 

visually observed on the oscilloscope for asperity contact. An asperity contact caused the 

voltage to drop to zero. The signal was also converted in a voltage-to-frequency converter 

and read on a pulse counter. The counter was set up to read 100 000 hertz for a known 100- 

percent lubricant film (no asperity contacts). Any asperity contacts reduced the average 

voltage across the bearing, and less than 100 000 hertz would be registered by the counter. 

The counter reading divided by 1000 is the percentage of film lubrication This reading has 

been commonly called percent film. However, this may be an unfortunate choice because 

of a likely confusion with percentage of area contact through the lubricant film. A very 

small percentage of area contact can result in a very high reading for contact-time fraction. Nevertheless, we shall use the present terminology, that is, Percent film = (1 - 

Contact-time fraction) x 100. The conductance measurement concept has been described 

in reference 6 and used in references 13 and 22. 

Test procedure. - Thrust loads applied to the bearing were 90, 445, and 778 newtons 

(20, 100, and 175 lb). The shaft speed was varied from 400 to 15 000 rpm. Temperatures 

remained constant, with a +3-degree C (+5-deg F) tolerance during each test. The test 

temperature was n0minally27~ C (80° FT. 

During the course of some prior experiments, the percent film was periodically measured. In preparation for running a new bearing in a test series, we noted that, for 100- 

percent film to be developed in the new bearing, it had to be run two orders of magnitude 

faster than the used bearing. We concluded that there must be considerable asperity contact in a new bearing and that asperity contact diminishes with running time. Therefore, in 

the present series of tests the percent film for the test bearing was measured at various 

run-in times. 

3 
Three series of tests were run. The test data are summarized in table 1V. The first 

series was started with a new bearing. The shaft speed was very quickly increased to a 

speed high enough to produce a 100-percent film with the 90-newton (20-lb) load. The 

speed was then slowly decreased to the point where 70-percent film occurred. The testing 

continued by gradually increasing the load at each test speed to obtain a series of data 

points for film thickness and percent film. Care was taken not to operate with less than 

70-percent film for test series 1. 

The second series of tests was run immediately after the first series. In the second 

test series, speed was decreased in steps from 15 000 rpm. Test loads were applied at each 

speed until percent-film readings as low as 50 percent were recorded. 

After the second test was completed, the bearing was run at 27O, 650, and 121O C (80°, 

150°, and 250° F) so that film-thickness data could be obtained for a range of loads and 

speeds. The results of these tests are reported in reference 21. 

film was run, again at room temperature. In the third test series, the speed was rapidly 

increased to 15 000 rpm with minimum load. Then the load was increased at each speed 

selected. Speed was decreased in steps down to the minimum speed of 400 rpm. The data 

recorded at each test point for the three series of tests are given in table 1V. Approximately 1 hour of run time was accumulated on the bearing before test series 3 began. 

After the testing at higher temperatures was completed, a third test series for percent 

R ESU LTS A N D DlSCUSSlO N 

After test series 3 was concluded, the test bearing was removed from the rig and 

examined visually and under the light microscope for evidence of wear. It was expected 

that flattening of the asperities would be seen. None could be seen under XlOO magnification. Then high-resolution surface profile traces of the bearing inner race were made at 

several locations in the cross-groove direction. 

side of the trace shows the run track and the left side shows the unrun portion of the 

surface. Although space does not permit showing all the traces, generally there was no 

observable difference in surface character between the run and unrun portions. There was 

no indication of any surface run-in, such as wear or diminishing of asperities. The large 

curvatures in the trace are due to the inability of the surface tracer to exactly follow the 

radius of the inner race. The surface finish, 0.025 micrometer (1 pin.) rms, was much 

better than the bearing manufacturer's specification given in table 1. 

The film thickness measured by the capacitance method is compared in figure 5 with 

the film thickness predicted by the Hamrock-Dowson EHD film-thickness equation (ref. 

16). Figure S(a) presents the data from test series 1 and figure 5(b), the data from test 

series 3. The greater scatter in the testseries-1 data is due to difficulties in accurately 

balancing the capacitance bridge in the presence of asperity contacts. Under these conditions there was a w.eak bridge sensitivity. It was impossible to take a capacitance reading for less than 90-percent film. 

tance bridge was easy to balance, since there was a definite response null. The data show 

approximately the expected theore tical sensitivity of film thickness to load. The measured 

film thickness was approximately one-third of the theoretically predicted film thickness. 

An inaccurate value of dielectric constant, an error in the pressure-viscosity exponent, or 

surface roughness effects may have caused this disagreement between theory and experiment. 

Figure 4 is a typical trace. Since the bearing was an angular-contact type, the right 

There is little experimental scatter in the test-series3 data (fig. 5(b)). The capaci4 
If a calibration error is taken into account, the data generally follow the theoretically 

predicted trend in film thickness with speed. At high speeds the leveling off of film thickness with speed is predominantly caused by lubricant film starvation (ref. 21). At low 

speeds, the film levels off at a thickness approaching the rms level of the combined surface 

roughness. This effect is in general agreement with results presented in reference 23. 

The percent-film trends with speed and load are shown for the three test series in figure 6. As expected, there is an order-of-magnitude speed difference for equivalent percent-film readings between test series 1 and test series 3. Test series 2, which was run 

immediately after test series 1 without the rig being shut down, shows definite change in 

percent film with speed. Thus, physical changes in the bearing #at affect percent film 

seem to occur immediately after a new bearing is put into operation. 

The percent film is correlated with measured EHD film thickness for the three test 

series in figure 7. For a new bearing, asperity contact and film breakdown begin to occur 

at a ratio of film thickness to rms surface roughness A of 4.25, for the lightest load (fig. 

?(a)). After run-in (test series 3, fig. ?(e)) the test results show no film breakdown at A = 

3.5 for even the heaviest load, which put a 2.45-gigapascal(356 000-psi) contact series on 

the inner race contact. 

Results from other similar work (refs. 20, 23, 24, and 25) are shown in figure 8 and are 

compared here with the present results. In reference 23, Sidik and Coy used surface trace 

data, stored on magnetic tape in digitized form, to statistically predict percent film as a 

function of EHD film thickness. The traces were made from data taken on new surfaces. 

The computed results compare very well with the data taken in test series 1 (fig. ?(a)) for 

the new bearing. In reference 20, Coy and Sidik show that lowpass filtering of the surface 

trace data shifts the percent-film curves to the left. Low-pass filtering would decrease the 

asperity density in the surface records and thus simulate the expected effect of Wmningin" the bearing. That this trend appears in the present data verifies that the percent-film 

curves shift toward the left to lower film thicknesses with increased run time. Data are 

also shown for the experimental results of other researchers (refs. 24 and 25) as reported in 

reference 26. Their data agree well with the present data from test series 3. In general, 

the experimental observations reported herein agree well with the theoretical prediction of 

reference 20; and with increased run-in, the test data approach that of references 24 and 25. 

SUMMARY OF RESULTS 

Film thicknesses and percent films were measured by the capacitance and conductance 

methods for a thrust-loaded 20-millimeter-bore ball bearing operating under a range of 

speeds and loads. The measurements were made on the bearing when it was new and again 

after it had been run through some higher temperature test sequences. The test parameters were thrust loads of 90, 445, and 778 newtons (20, 100, and 175 lb), which gave maximum contact stresses of 1.28,. 2.09, and 2.45 gigapaxals (185 000, 303 000, and 356 000 psi) 

on the inner race, and speeds ranging from 400 to 15 000 rpm. The bearing was mist 

lubricated with an MIL-L-23699A lubricant and run at room temperature (270 c, 800 F). 

lated and compared with other measurements and theore tical predictions. The following 

results were obtained: 

6 or less. For a run-in bearing with a heavy load, less than 2.45-GPa (356 OOO-psi) Hertz 

stress, there was no asperity contact for a A of 3.5 or greater. 

2. The amount of asperity contact in a new bearing rapidly diminished with run time, 

an indication of wear-in. But under visual examination at XlOO magnification, there were 

no obvious physical changes in the test bearing surface. 

The experimental results of film-thickness and percent-film measurements were corre1. In a new bearing, asperity contact existed at a film thicknesproughness ratio A of 

5 
3. There was good agreement between asperity contact theory and the measured percent film for new bearings; however, the mechanism of asperity contact reduction is 

unknown. 

Lewis Kesearch Center, 

National Aeronautics and Space Administration, 

Cleveland, Ohio, July 12, 1979, 

50 5-0 4. 

R EF ER E N C ES 

1. Grubin, A. N .: Fundamentals of the Hydrodynamic Theory of Lubrication of Heavily 

Loaded Cylindrical Surfaces. lnvestigation of the Contact of Machine Components, 

Kh. F. Ketova, ed., Translation of Russian Book No. 30, Central Scientific lnstitute 

for Technology and Mechanical Engineering, Moscow, 1949, Chapter 2. (Available 

from Department of Scientific and Industrial Research, Great Britain, Transl. 

CTS-235, and Special Libraries Association, Transl R-3554.) 

2. Dowson, D.; and Higginson, G. R.: A Numerical Solution to the Elasto-Hydrodynamic 

Problem. J. Mech. Eng. Sci., voL 1, no. 1, June 1959, pp. 6-15. 

3. Dyson, A.; Naylor, H.; and Wilson, A. R.: The Measurement of Oil-Film Thickness 

in Elastohydrodynamic Contacts. Proc. lnst. Mech. Eng., (London), vol. 180, pt. 3B, 

paper 10, 1965-66, pp. 119-134. 

4. Archard, J. F.; and Cowking, E. W .: Elastohydrodynamic Lubrication at Point Contacts. Proc. lnst. Mech. Eng. (London), vol. 180, pt. 3B, 1965-66, pp. 47-56. 

5. Dowson, D.; and Higginson, G. R.: Elastohydrodynamic Lubrication. Pergamon Press, 

lnc., 1966. 

6. Allen, G. E.; Peacock, L. A.; and Rhoads, W. L.: Measurement of Lubricant Film 

Thickness in Hertzian Contacts. (SKF-AL-681'075, SKF Industries, lnc.; NASA 

Contract NAS3-7912.) NASA CR-105378, 1968. 

7. Foord, C. A.; Hammann, W. C.; and Cameron, A.: Evaluation of Lubricants Using 

Optical Elastohydrodynamics. ASLE Trans., voL 11, no. 1, Jan. 1968, pp. 31-43. 

8. Zaretsky, E. V.; and Anderson, W. J.: EHD Lubrication. Mach. Des, vol. 40, Nov. 7, 

1968, pp. 167-173. 

9. Cheng, H. S.: A Numerical Solution of Elastohydrodynamic Film Thickness in an 

Elliptical Contact. J. Lubr. TechnoL, vol. 92, no. 1, Jan. 1970, pp. 155-162. 

10. Tallian, T. E.: Elastohydrodynamic Hertzian Contacts - Part 1. 1Vlech. Eng., voL 93, 

no. 11, Nov. 1971, pp. 14-18. 

11. Tallian, T. E.: Elastohydrodynamic Hertzian Contacts - Part 2. Mech. Eng., voL 93, 

no. 12, Dee. 1971, pp. 17-22. 

6 
12. Parker, Richard J.; and Kannel, Jerrold W .: Elastohydrodynamic Film Thickness Between Rolling Disks with a Synthetic Paraffinic Oil to 589 K (6000 F). NASA TN 

D-6411, 1971. 

13. Parker, Richard J.! and Kannel, Jerrold W .: Elastohydrodynamic Film Thickness 

Measurements with Advanced Ester, Fluorocarbon, and Poly phenyl Ether Lubricants 

to 589 K (600' F). NASA TN D-6608, 1971. 

14. Kannel, J. W.; and Bell, J. C.: Interpretations of the Thickness of Lubricant Films 

in Rolling Contact. 1 - Examination of Measurements Obtained by X-rays. J. Lubr. 

Technol., vol. 93, no. 3, Oct. 1971, pp. 478-484. 

Viscosity Coefficient. J. Lubr. TechnoL, vol. 94, no. 1, Jan. 1972, pp. 35-43. 

15. Cheng, H. S.: lsothermal Elastohydrodynamic Theory for the Full Range of Pressure16. Hamrock, B. J.; and Dowson, D.: lsothermal Elastohydrodynamic Lubrication of Point 

Contacts. Part 111 - Fully Flooded Results. J. Lubr. TechnoL, vol. 99, no. 2, Apr. 

1977, pp. 264-276. 

17. Seth, B. B.; and Willis, T.: Techniques for Film Thickness Measurements in Elastohydrodynamic Lubrication. ASM E paper 76-D ET-79, Sept. 1976. 

18. Chow, L. S. H.; and Cheng, H. S.: The Effect of Surface Roughness on the Average ' 

Film Thickness Between Lubricated Rollers. J. Lubr. TechnoL, vol. 98, no. 1, Jan. 

1976, pp. 117-124. 

19. DOW, T. A.; Kannel, J. W .; and Parker, R. J.: Effect of Longitudinal Surface Finish 

on Elastohydrodynamic Lubrication. NASA T N D-7967, 1975. 

20. Coy, J. J.; and Sidik, S. M.: Two Dimensional Random Surface Model for Asperity 

Contact in Elastohydrodynamic Lubrication. Presented at the International 

Conference on Metrology and Properties of Engineering Surfaces, (Leicester, 

England), April 18-20, 1979. 

21. Coy, J. J.; Gorla, R. S. R.; and Townsend, D. P.: Comparison of Predicted and Meas 

ured EHD Film Thickness in a 20-Millimeter-Bore Ball Bearing. NASA TP-1542, 1979. 

22. Kannel, J. W .; and Snediker, D. K.: Elastohydrodynamic Lubrication in an Instrument 

Ball Bearing. J. Lubr. TechnoL, vol. 98, no. 2, Apr. 1976, pp. 244-250. 

in Elastohydrodynamic Lubrication. NASA TP-1130, 1978. 

23. Sidik, S. M.; and Coy, J. J.: Statistical Model for Asperity - Contact Time Fraction 

24. Tallian, T. E.; et al.: Lubricant Films in Rolling Contact of Rough Surfaces. ASLE 

Trans., vol. 7, no. 2, Apr. 1964, pp. 109-126. 

25. Poon, S. Y.; and Hahes, D. J.: Friction Behavior of Lubricated Rolling-Contact 

26. Johnson, K. L.; Greenwood, J. A.; and Poon, S. Y.: A Simple Theory of Asperity ConElements. Proc. Inst. Mech. Engrs. (London), voL 181, 1966-67, pp. 363-376. 

tact in Elastohydrodynamic Lubrication. Wear, vol. 19, no. 1, Jan. 1972, pp. 91-108. 

7 
TABLE I . . TEST BEARING SPECIFICATIONS 

Material. balls and races .............. ai51 M-1 

Outside diameter. mm (in) ............. 47 (1.8504) 

14 (0.5512) 

Pitch diameter. mm (in) ............... 35.5 (1.4) 17 

53 

54 

Ball diameter. mm (in.) ............... 7.15 (9/32) 

Rockwell C hardness (inner race. outer race. and balls) . 62 - 64 

Surface finish (rms). m ( in.> 

Inside diameter. mm (in.) .............. i0 (0.7874) 

Width. mm (in.) ................... 

Nominal contact angle. deg ................. Inner race curvature. percent ................ Outer race curvature. percent ................ Number of balls ........................ 3 

Races ......................... 0.15 (6) 

................... 0.025 - 0.05 (1 - 2) 

Tolerances ....................... ABEC-5 

Balls 

TABLE 11 . . TEST LUBRICANT SPECIFICATIONS 

[Texaco 7730 A2 . improved type 11 synthetic, 

aircraft gasturbine lubricant (MIL-L-2 36 9 9A).] 

Pour point. OCV ............... -60 

Flashpoint. OC ................ 262 

Firepoint. OC ................ .- 

Autogenous ignition temperature. C .... 426 

Density. g/cm3: 

At looo C (212' F) ............. 0.93 

At 380 C (looo F) ............. 0.98 

Pre ssure-viscosity exponent . m2 / N: 

At looo C (212O F) ........... 1.00X10-8 

At 380 C (looo F) ............ 1.37~10.~ 

Kinematic viscosity. cS: 

At 100' C (212O F) .............. 5-2 

At 38O C (looo F) .............. 28 

At 1000 C (2120 F) ............. 2000 

At 38O C (looo F) ............. 1913 

At 100' C (212OF) ............. 

Specific heat. J/kg K: 

Thermal conductivity. W/m K: 

0.152 

At 38O C (looo F) ............. 0.162 

8 
Race 

lnner 

Outer 

9 

Contact condition Thrust load, N (lbf) 

90 (20) 445 (100) 778 (1 75) 

Maximum Hertzian stress, GPa (ksi) 1.28 (185) 2.09 (303) 2.45 (356) 

Semimajor axis, crn (in.) 0.0510 (0.0200) 0.0840 (0.0330) 0.0990 (0.0390) 

Semiminor axis, ern (in) 0.0066 (0.0026) 0.0110 (0.0043) 0.0130 (0.0051) 

Maximum Hertzian stress, GPa (ksi) 1.13 (164) 1.85 (269) 2.19 (318) 

Semimajor axis, cm (in.) 0.0460 (0.0180) 0.0740 (0.0290) 0.0860 (0.0340) 

Semiminor axis, cm (in.) 0.0086 (0.0034) 0.0140 (0.0055) 0.0170 (0.0065) 
TABLE 1V. - TEST RESULTS 

- 

in. 

--- 

5.3 

5.9 

5.1 

6.2 

5.2 

3.7 

4.0 

5.5 

4.1 

3.7 

4.1 

2.9 

--- 

--- 

--- 

--- 

--- 

--- 

Speed, 

10 000 

15 000 

film 

66 

100 

100 

100 

100 

88 

100 

97 

71 

100 

93 

68 

100 

93 

55 

100 

69 

100 

50 

Load 

20 

Speed, Load 

rPm 

N lb 

15 000 

10 000 

8 000 

6 000 

4 000 

3 000 

2 000 

- 

Capacitance, Film thickness Percent 

PF film 

pm in. 

(b) Test series 2. 

445 

779 

89 

445 

779 

89 

445 

779 

89 

445 

779 

89 

445 

779 

89 

445 

779 

89 

445 

779 

89 

445 

779 

89 

445 

779 

89 

445 

89 

445 

- 

N 

779 

445 

89 

89 

445 

779 

89 

445 

779 

89 

445 

779 

89 

445 

779 

89 

44 5 

89 

445 

- 

- 

100 

175 

20 

100 

175 

20 

100 

175 

20 

100 

175 

20 

100 

175 

20 

100 

175 

20 

100 

175 

20 

100 

175 

20 

100 

175 

20 

100 

20 

100 

175 

100 

20 

20 

100 

175 

20 

100 

175 

20 

100 

175 

20 

100 

175 

20 

100 

20 

100 

----- 

102.2 

39 

442 

88.2 

43.2 

138.2 

53.2 

97.2 

52.2 

137.2 

52.2 

----- 

----- 

----- 

----- 

67.7 

----- 

15 000 

10 000 

8 000 

6 000 

4 000 

3 000 

2 000 

1500 

1000 

800 

600 

400 

89 I 20 37.7 

85 

139.2 

43.4 

93.4 

150.2 

41.2 

106.6 

161.9 

47.4 

107.4 

181.2 

50.4 

119.2 

200.2 

56.9 

131.8 

217.8 

72 

165.2 

227.2 

81 

208.2 

103.2 

275.2 

100.2 

2922 

105.2 

288.2 

107.2 

315.2 

----- 

----- 

----- 

0.15 

.16 

.14 

-13 

-15 

.13 

.14 

.13 

.12 

.12 

.12 

.10 

.11 

.11 

.09 

.09 

.10 

.08 

.07 

.08 

.08 

.06 

.06 

.04 

.05 

.05 

.04 

.04 

---- 

---- 

---- 

6.1 

6.4 

5.4 

5.1 

5.8 

5.0 

5.5 

5.0 

4.7 

4.6 

4.9 

4.1 

4.3 

4.3 

3.6 

3.7 

4.0 

3.3 

2.7 

3.0 

3.1 

2.3 

2.3 

1.75 

1.8 

1.85 

1.7 

1.75 

1.65 

1.65 

1.45 

--- 

--- 

--- 

100 

100 

98 

100 

98 

100 

100 

98 

100 

98 

89 

100 

97 

92 

100 

95 

45 

100 

94 

10 

100 

97 

100 

97 

Film thickness 1 Percent 

Pm 

0.13 

.15 

.I 

.16 

.13 

.09 

.lo 

.14 

.lo 

.09 

.lo 

.07 

__-- 

__-- 

---- 

---- 

__-- 

---- 

lo 
Figure 1. - EHD film thickness measurement rig. 

11 
r--- - ---- 1 

Osci I lator 

I 

L - - - - - - - - J 

Capacitance bridge 

(a) Film thickness. 

Oscilloscope 8 frequency Counter 

- 

(b) Percent film. 

Figure 2 - Measurement schematics. 

12 
1- 

E .l- 

.08 

.06 

.04 

ii- - 

- 

- 

I I 11 I I I II 

loo0 

.02 

10 100 

Capacitance, pF 

Figure 3. - Calculated capacitance for test bearing as function of load and film thickness. 

13 
d 

I 

m 

14 
10 

.a 

p .4 

C Y V 

E 

.a 

Speed, rpm 

b) Test series 3. 

Figure 5. - Film thickness measurements compared with theory. 

15 
(a) Test series 1. 

1 

(b) Test series 2. 

a 

100 

/ 

4 6 8 10 ZoX103 0 

.4 .6 .8 1 2 

Speed, rpm 

(e) Test series 3. 

Figure 6. - Percent film measurements. 

16 
100 

80 

60 

20 

20 

(b) Test series 2. 

- 

- 

- 

40- 

- 

17 
1 2 3 4 5 

Film thickness roughness ratio, A 

6 

Figure 8. - Percent film - theoretical results for different thrust loads and amounts of filtering. Experimental 

points included for comparison with figure 7. 

18 
AVRADCOM TR 79-26 I 

4. Title and Subtitle CORRELATION OF ASPERITY CONTACT-TIME 

FRACTION WITH ELASTOHYDRODYNAMIC FILM THICKNESS 

IN A 20-MILLIMETER-BORE BALL BEARING 

7. Author(s) 

5. Report Date 

6. Performing Organization Code 

October 1979 

8. Performing Organization Report No. 

John J. Coy E-9936 

10. Work Unit No. 

9. Performing Organization Name and Address 505-04 

NASA Lewis Research Center and 

AVRADCOM Research and Technology Laboratories 

Cleveland, Ohio 44135 

12. Sponsoring Agency Name and Address 

National Aeronautics and Space Administration 

Washington, D. C . 20546 and U. S. Army Aviation Research and 

Development Command, St. Louis, MO 63166 

11. Contract or Grant No. 

13. Type of Report and Period Covered 

Technical Paper 

14. Sponsoring Agency Code 

16. Abstract 

Elastohydrodynamic film thicknesses and asperity contact-time fractions were measured for 

a 20-mm-bore ball bearing by using the capacitance and conductance techniques. The bearing 

was thrust loaded to 90, 445, and 778 N (20, 100, and 175 lb). The corresponding maximum 

stresses on the inner race were 1.28, 2.09, and 2.45 GPa (185 000, 303 000, and 356 000 psi). 

The test speed ranged from 400 to 15 000 rpm. The test bearing was mist lubricated with an 

MIL-L-23699A turbine oil. The temperature was 27' C (80' F). The experimental results 

were correlated to give the percent film (no-contact-time fraction) as a function of measured 

film thickness. Measurements were made for three test series that represented the test bearing in various conditions of run-in. The measurements show that the percent film changes 

with bearing run-in time. The experimental results agreed well with theoretical predictions 

based on surface trace analysis for a new bearing. For the run-in state, they agreed with 

previously reported experimental results. The results show that asperity contact existed at a 

film thickness-roughness ratio A of 6.0 or less for a new bearing. After run-in, no asperity 

contact occurred at a A of 3.5 or greater. 

17. Key Words (Suggested by Authorls)) 

Bearings; Lubrication; Elastohydrodynamics; 

Surface roughness 

18. Distribution Statement 

Unclassified - unlimited 

STAR Category 37 

19. Security Classif. (of this report) 

Unclassified 

20. Security Classif. (of this page) 21. NO. of Pages 22. Price' 

Unclassified 21 A02