INDUSTRIAL AIYD ENGINEERING CHEMISTRY
460
journal friction = 0.0069 X 19,500 = 115 pounds. The friction torque is 3 X 111 = 333 inch pounds per Figure 4. The power loss in journal friction is = 19 horsepower 1.81 X (3600)2 X (3)2 X 9 X If the journal carries no load = 0 and the friction scale reading is 1.75 instead of 1.81-i. e., only 3.45 per cent less than if the journal carries 19,500 pollnds. It will be found that the per cent difference is greater for a greater clearance ratio, and conversely. Exan~pZe8. A 2-inch journal runs a t 300 r. 11. m , carrying a unit load of GO pounds per square inch of projected area-i, e,, 120 pounds per inch of axial length. Find characteristics for this journal when running with radial clearance of 0.002 inch in a full bearing, in a central, in a n offset, and in a fitted 120-degree partial bearing. Assume viscosity is 3.4 x 10-6 (150 s. U. v.). For some of the characteristics see Examples 3, 4, and 5. = 0.0022, w / ~ ve 60/300 = 0.2. Hence from Figure 8, while from Figure 12, X = 0.0019. This completes the data for all cases except the fitted partial bearing, which will be studied below. The fitted 120-degree bearing can he studied from Figure 14. Entering the w / N scale with 0.2 we find from the 120-degree capacity curve t h a t CY = 77.4 degrees, 6 = 148.3 degrees, and t h a t e/a = 0.00215, X = 0.0017, and ( h o / a ) = ( s / a ) COS +. L, = 180(77.4 f 148.3 - 120) = 74.3 degrees. ( h o / ~ )= 0.00215 X 02706 = 0.000582 For comparison of results see section under “Comparison of Partial Bearings.’ ’
VoI. 18, No. 5
Example 9. Compare the friction, eccentricity, and nearest approach of surfaces for a journal 6 inches in diameter, 6 inches long, running a t 400 r. p. m., carrying a vertical load of 7200 pounds, ( a ) when supported in a 120-degree fixed fitted bearing, and ( b ) when supported in two adjacent 60-degree fitted pivoted segments. Assume the Oil viscosity p = 3.4 X 10-6 (inches, Pound% seconds). The vertical load will be 7200/6 = 1200 pounds per inch Of length Of the bearing. ( a ) The nominal unit pressure ma = l200/6 = 200. Hence W d L V = 0.5. Entering Figure 14 with this value we find ( € / a ) , = 0.0011. The nearest approach found from = O014 and Equation l3 (hole) = ( € / a ) cos l+b (13) is (ho/a)a = 0,0014 COS 74.3 degrees = 0.00038 inch. ( b ) The vertical load per linear inch (axial) is in this case divided, each segment carrying (1200/2) secant 30 degrees = 693 pounds. Each segment must be studied separately t o avoid confusion. Hence W b = 69316’ = 115.5. Wd,./N = 115.5/400 = 0.29. From Figure 14 we find ( € / a ) b = 0.0006 and that the friction coefficient X b = 0.00135 secant 30 degrees = 0,00156. The nearest approach is found to be: (hole)* = 0.0006 cos 57.1 degrees = 0.000326 (ab) Comparing the two bearings it is found that: Friction coefficient A b = 1.42 A, markedly favoring the single bearing Eccentricity ( ~ / a ) b= 0.43 ( € / a ) , markedly favoring the single bearing Nearest approach (ho/a)* = 0.86 (ho/a),also favoring the single bearing
Oil Flow in Plain Bearings By D. P. Barnard, 4th ENGINELABORATORY, ST.ANDARD OIL Co. (ISDIANA), WXITINC.,IND.
An attempt is made to present the basic laws of fluid lubrication in such a manner that they may be readily used in the correlation of test data. As is well known, these laws are founded upon the properties of the viscous flow of fluids. The work of Reynolds and Harrison has served to outline the laws governing power and film thickness. This paper describes a simple method of development of the approximate laws controlling oil flow through bearings-due both to pressure developed in the film and to oil-feed p r e s s u r e a n d presents some experimental data in substantiation of this method.
HE rate of flow of oil through plain bearings is one of
T
the most important factors entering into bearing design and lubrication. Depending upon the conditions of operation, it may be necessary to give first consideration to film thickness, friction loss, temperatures, or oil consumption. Each characteristic, however, is definitely related to the path of oil flow through the bearing, and therefore to the rate of flow. I n view of the large number of variables which determine the actual quantity of oil flowing, this feature is not ordinarily considered other than in an approximate manner. The method outlined herein will, it is believed, facilitate considerably a more complete study of oil flow and consumption in plain bearings.I I n general, the lubricant flowing through a bearing takes the following course: Oil is admitted a t a point usually mid1Tay between the ends of the bearing, where it is picked up by the revolving journal and dragged through the load supporting part of the film space. The pressure thus developed in the oil film serves to support the bearing load and also to force the lubricant toward the ends of the bearing. All of the oil fed to the bearing eventually escapes through 1 For
further details the reader is referred t o Barnard, J . S O L .Aulomo202 (1926).
l i v e Eng., 12,
end leakage due to the pressure existing in the oil film. This endwise flow may not be due entirely to pressure generated within the film itself, as any existing oil-feed pressure also increases end losses. I n studying the problem, however. it is necessary to consider separately the effects of these two pressures. The effect of the pressure generated within the film, as determined by the operating conditions, will be c o n d e r e d first. Flow Due to Pressure Developed in the Film
The primary factors controlling the pressure developed within the lubricating film are given in Table I, in which rll, L, and T denote, respectively, the physical units mass, distance, and time. Table I-Factors
Controlling Bearing Performance Xotation
Absolute oil viscosity, In centipoises Bearing load (nominal) Diameter of bearing Length of bearing Diametric clearance Journalr p m Rubbing speed (xd,? )
Z
I’ d e c .\
u
Dimensions i-1L - 1 T -1 .ML -1 T - 2 L
L
L 1-1
L1-1
As the motion of the journal tends to carry oil in the direction of rotation only, end leakage must be due solely to the pressure in the film. Furthermore, the clearance space is so narrow that all flow within it must be substantially laminar. This is especially true of the endwise component of flow. Therefore, end flow must conform to Poiseuille’s lam, which states that Flux (volume per unit time) = K [ l p e2/fiZ]
(1)
in which K is dependent on the form of the channel of flow, A p represents the pressure drop between the two points under consideration, a is the area, 1 is the length of the path of flow, and p represents the absolute viscosity of the fluid. Arranging the various bearing factors in this manner gives the relation:
Ii\-D USTRIAL A N D ENGINEERISG CHEMISTRY
M a y , 1926
Rate of flow (volume per unit time) = q5 [P(dc:lz/ZZ]
(2)
Equation 2 indicates that the effective driving pressure is a function of the bearing load. Therefore, the volumetric efficiency of the bearing when considered as a pump-i. e., the ratio of the volume discharged per revolution to the clearance volume-may be expressed by P (dc)’ Pumping efficiency, E =
(3) srdcl 2
used is rather narrow and may be readily covered by experiment. The following experimental data illustrate the utility of the foregoing method of correlation and include a study of the effects of changes in operating conditions (Z-V,’P),clearance (l/’c), and oil-feed pressure on one particular bearing. Unfortunately, data are not available on bearings of different sizes and characteristics. EXPERIMENTAL REsuLTs-The range covered by these oil flow measurements is indicated in Table 11, and the test bearing used is shown in Figure 1. The rate of flow was measured by feeding oil to the bearing from a large buret under the indicated supply pressure. The bearing was of bronze and mas supported on a hardened steel journal, the bearing load being directed downward. Clearance was varied by substituting a journal of different diameter. T a b l e I1 -Range
FACTOR Viscosity ( 2 ) R. p m. ( S J
Diameter ( d I Length
(0
Clearance ( c ) Oil-feed pressure 011 flow
Because E is a pure ratio and therefore dimensionless, i t may be expressed as a function of the variable- grouped as follows :
Covered by Oil-Flow LMeasurements MINIMLX MAXIMUM 12.5 centipoises 43.5 centipoises 2000 200 2.9 kg. per sq. cm. 19 kg. per sq. cm. 41 Ibs. per sq. inch 271 Ib. per sq. inch 1 2.54 cm. 1 1 inch 6.08 cm. 2 inches 0.0015 cm. 0.0028 cm. 0.0006 inch 0.0011 inch 0.7 kg. per sq. cm. 4.9 kg. per sq. cm. 10 Ibs. per sq. inch 70 lbs. per sq. inch 50 cc. per min. 1.25 cc. per min. O.OT5 cu. in. per min. 3 cu. in. per min.
t
Load ( P )
F i g u r e 1-Experimental B e a r i n g The bearing was made of bronze and supported on a hardened j o u r nal. T h e bearing load, P,was directed downward, as indicated. The clearance was chanqed b y substituting a journal of different diameter.
461
t i i t
EFFECT OF FEEDPRESSURE-FigUreS 2 and 3 show the results obtained from plotting the experimental data in the form E vs. Z-VylP for the different oil-feed pressures used, a distinct curve of the same general form being obtained for each oil-feed pressure. -4s an example, the actual data for a As each of the three groups in Equation 4 is a 1-limensionless feed pressure of 0.7 kg. per sq. em. (10 lbs. per sq. inch) are ratio, separation in this manner makes possible an entirely shown in Figure 2 . The curves shown by the solid lines in general correlation of the effects of the different factors, Figure 3 resulted from data obtained a t the different indicated and experimental results so correlated are dependent only feed pressures. The drop in pumping efficiency with increasing on geometric similarity and not on the actual dimensions of values of Z-V;lP is exactly in accord with that which would the parts. For convenience in the plotting of data it is be expected, as under these conditions the journal occupies desirable to invert the functions indicated in 1(3),and thus a more nearly central position in the bearing and as less avoid the necessity of dealing with very large numerical pressure is generated in the film itself, the tendency is for dues. the oil to follow more closely the direction of rotation.
F i g u r e 2-Experimental D a t a for 0.7 Kg. p e r Sq. C m . Oil P r e s s u r e Similar data were obtained for feed pressures up to 4.9 kg. per sq. cm.
Effect of Oil-Feed Pressure
Oil flow due to feed pressure also follows Poiseuille’s law, hut as the form of the path of flow is altered by changes in the relative positions of journal and bearing it is impossible to formulate a general expression for the effect of feed pressure in a practical form of bearing. This is not a serious handicap, however, as the range of feed pressures ordinarily
Figure 3-Summary
of E x p e r i m e n t a l Data
Inasmuch as part of the flow wa? due t o feed pressure, the recorded values for E are not true pumping efficiencies. Comparisons should be made rather on the basis of the actual pumping ability of the bearing-that is, with no feed pressure. Unfortunately, no measurements were made under these conditions. However, it is possible to estimate such values fairly closely, as changes in flow due to feed pressure should be proportional to changes in that pressure.
Yol. 18,No. 5
I.VDUS21/21.41, :I .VU I?:VQI-VEERING CIIEMISTRY
462
Figure 4; in which E is pliitt,od ngiiinst, the fced />rossurelor several values of L!,VjP, shows that this is actildl?~the case. Extrspolntion of these lines to zero fced pressiirr gives the ciirve true pumping efficiency of t,hc liraring. The i h in Figire 3 was obtained in this mariiicr. Ob~-iooslya break is to he cxpected in these ciirves a t the vnlne of Z N I P corrcsponding to fiuid film rupture. This niet,liod of corrclation fails at tlia rupture point :uid the cxpcrimrntal data prresrntcil do not inchide this condit.ion. A s no tcnrlciicy is appnrciit, r(jr the ~ a l u e sof E for iiiffcrent.clciirarices to separat,e, it niitst, he c o n c 1u d e d t li n t (4iangecs in this filetor, axcc-
I..
order to render uisihle the path of flow. In both figures the dircction of rotation is away from the observer a t the top of the journal. Tlie effect of reducing t h e value of % N I P is t,o leiisen the abilhy of the journal to carry lubricant through the load-supporting portion of the film spare. 'I'hix results in a thiniiing out of this part of the oil film with aii accompanying tendency of the oil to leak 01
of % N / P results in an inelore an incrciiscd factor of rafet.y iii the loiid-carrying sbility of the bearing, and a t t,Ilc sainc tiirrc :I dei:re:iavi pumiing efficiency. In beariiigs whir~llarc not prcn%led wit11 nileqitate nieaiis for heat dissi-
:unount of oil flowing, lrave little or n o influence oil tlie liump-
A n o t b e r inrpvrtant factor not included in the experirrients is that of oil grooving. It would seem, howe v e r , t,hrit t.lie effiFigure 4 - S u m m a r y of Experimental ciencies f o u n d at Data in Which E l a Plotfad against the OilFeed P T ~ J ~ U I - F zero feed p r e s s u r e would a p p l y fairly closely to any plain Lcaring with it sirnple oil groove in the unloaded side, although widening of the groove should increase the slope of the lines shown in Figure 4. Tlie effect of oil grooving in the loaded side of the bearing is open to considerable speculation, but it is highly improbable t.hat it would result in any particidar benefit. hs is well known.
Fisure 6~-~Pal11Taken by Oil Flowing shmugh a BellrlSp. T h e operiiting conditiom were ~iipl>tiy above the ban\ition point. the value oi Z N / P being rbuut 500. The film was alinosf completely ruptured.
pation by metallic conduction, this may give rise to some interesting problems in securing a satisfactory film thickness and a t the same time sufficient oil flow to carry away frictioiial heat. Large clearances and high f e d pressures both help iii this, of course. In such cases a compromise may be necessarv and it is believed that the foreeoine ., .nrocedure will be of considerable value in connection with lubrication studies on high-speed bearings such as are used in turbines, electricul machinery, and high-speed internal conibustion engines having large joiirnals carried in bearings supported by thin webs.
-
Acknowledgment
The writer wishes to express his appreciation to the Department of Chemical Engineering of the Massachusetts Institute of Technoloiy for permission to publish the data contaiiied in this paper.
Lubrication at Low Temperatures Figure 5-Psfh
Taken b y Oil Flowias rhruush a Bearing
such grooving is certain to diminis11 the normal hnd-sustainiiie ahilitv of the bearine. In addition to the me;lsurernenta alead? recorded, a motion study was made of flowin a glass bearing, I ,
Two views reproduced from this film are shown in Figures 5 and 6. In this work the bearing was supported by the journal and thc load applied by ineans of weights attached to cords looped Over the bearing' AS the thickness was less than 0.05 em. it was necessary to introduce a small amount of a dyed glycerol solution dong with the oil in
The characteristics of lubricants and lubrication systems,
authori;ation $rum the Bureau of Aeronautics of the Navy Dcpnrtment. An air-cooled radial engine has been mounted in one of the altitude chambers in which the necessary low trmneraturcs can rcadilv be obtained. The eneine is movide.d wit< complete equipmekt for measuring oil flaw unde; various conditions. Measurements with this engine itie being paralleled b y an experimental study of the pump and other elements of the lii~,ricatio,l system. This work is of fuiidamciital importance because at Ion tcmveratures the transfcr of the oil from the supply t?nk to the p u m j ~ and thence to the bearing surfaces 1s attended with a great deal of difficulty. The dimensions of the pump and feed lines must be sltfficient to insure lubrication and yet prevent overcooling when the oil Rows freely.
