INDUSTRIAL A N D ENGINEERING CHEMISTRY
856
Vol. 16, No. 8
Does t h e znip Function Fit t h e Facts?' By A. E. Becker Box 276, ELIZABETA, N. J
I
T IS now generally recognized that there are two general
fields to consider in the study of lubrication-namely, boundary and fluid film lubrication. Boundary lubrication has been investigated recently by Hardya and others, and deals with lubrication phenomena under load and speed conditions such that the only lubricant between the bearing surfaces is the adsorbed surface films. However, under more favorable operating conditions the bearing surfaces are completely separated by a fluid film of lubricant. This condition is known as the field of complete or fluid film lubrication and is the one that should be maintained during the operation of bearings.
P
I O
I O
I O
FIG.1
The mathematical theory of fluid film lubrication has been developed by a number of investigators, more particularly by Reynolds3 and S~rnrnerfeld.~These theories have led to the conclusion that for fluid film lubrication, bearing performance is determined by the viscosity of the oil a t the working temperature of the film of oil in the bearing. Such mathematical reasoning has been developed on the assumption that there are no disturbing boundary conditions and that, therefore, the laws of hydrodynamics apply. These theories have led to the conclusion that the friction developed in a bearing where fluid film lubrication obtains is dependent solely upon the viscosity of the lubricant, and is independent of such other factors as the material of which the bearing surfaces are made or of any action between these surfaces and the lubricant. This line of thought has led to the conclusion by Hersey,6 and more recently by Wilson and Barnard,6 that for a given bearing and a given oil, changes in the coefficient of friction, f , are determined entirely by the modulus x n / p , where z is the viscosity of the oil a t the temperature of the oil film, n is the r. p. m., and p is the nominal pressure on the bearing in pounds per square inch. I n a paper by Barnard, Myers, and Forrest,' the statement is made: 1 2
8 4 6
a
Received May 29, 1924. Phil. Mag., 40, 201 (1920). Phil. Trans., 1886, 160. Z. Math., SO, 97 (1904): Z. tech. Physik, 2, 58, 89 (1921). Trans. Mech. En&, 37, 167 (1915).
Identical values off are obtained for the same value of z n / p , regardless of changes in the individual variables. The soundness of this line of reasoning has been well verified by the experimental data available in the literature.
Let us test this contention by an application to some of the results obtained by Tower,* than which no better data are available anywhere. His experiments were made in such manner that there is no doubt whatever that fluid film conditions were maintained. Also, the question of clearance was not involved, since he used a half bearing which was seated by a thorough running-in before the tests were made. Bath lubrication having been provided, the supply of lubricant to the bearing was always ample. A stable film consistent with the operating conditions was, therefore, readily formed in all his experiments. For the purpose of this article, we will make use of Tower's8 results for lard, sperm, and rape oils. The coefficients of friction obtained by him for various conditions of load and speed are tabulated in Table I. I n each case a steel journal 4 inches in diameter and 6 inches long was used. The bearing was made of gun-metal brass, the chord of the arc of contact being 3.92 inches. The speed and pressure being given for each coefficient of friction, it is only necessary to determine the viscosity of the oil in order to obtain values of x n / p corresponding to the coefficients of friction. Unfortunately, Tower did not record the viscosities of the oils used. I n the case of lard, sperm, and rape oils, however, it is permissible to determine the viscosities of present-day samples without making any serious error. In any case, Tower performed all these experiments a t a bath temperature of 90" F., which he took great pains to maintain within narrow limits. Our calculations are, therefore, legitimate for any one of these three tables, since
FIG. 2
in each case the viscosity remained constant throughout the experiments. The actual data used in these calculations are as follows: Density at BOe F. Saybolt viscosity at 90' F. Centipoises at 90' F.
Lard 0.900 276 54.1
Sperm 0.866 120 21.5
THISJOURNAL, 14, 682 (1922). I b i d . , 16, 347 (1924).
8
Proc. Inst. Mech. Eng. (London), 1883,I or 11, 632.
Rape 0:901 306 60.2
IhTDUsTRIAL A N D ENGINEERING CHEMISTRY
August, 1924 Nominal Load Lbs./Sq. In.
520 415 310 205 153 100 415 310 205 153 100 573 520 415 363 258 153 100
_
_ -__-_-_________ ~ 100
180
.... ..
0.0009 0.0012 0.0014 0.0020 0.0027 0.0042
0 . obi7
0.0022
0.0035
...
0.0015 0.0011 0.0016 0.0019 0.0030
o.ooi3 0.0016 0.0025
... ... ...
0.00102 0.00096 0.00093 0.00084 0.00139 0.00200 0.00357
0 . obi07
0.00162 0.00277
857
TABLEI
C O ~ F F I C I E N OF T S FRICTION AT R. P. M. 200 250 300 Lard oil 0.0013 0,0010 0.0011 0.0016 0.0014 0.0015 0,0022 0.0017 0.0020 0.0031 0.0023 0.0028 0.0041 0.0032 0.0037 0.0067 0.0050 0.0060 Sperm oil 0.0019 0.0017 0.0018 0.0016 0.0012 0.0014 0.0023 0.0021 0.0018 0.0030 0.0028 0.0023 0.0051 0.0038 0.0044 RaPe oil 0.00108 0.00118 0.00126 0.00115 0.00105 0.00125 0.00130 0.00107 0.00119 0.00110 0.00122 0.00096 0.00178 0.00195 0.00162 0.00239 0,00267 0.00300 0.00423 0.00503 0.00576
OF
-
350
400
0.0015 0.0018 0.0025 0.0034 0.0050 0.0076
0.0015 0.0019 0.0026 0.0039 0.0081
0.0017 0.0021 0.0029 0.0042 0.0052 0.0090
0.0020 0.0017 0.0024 0.0033 0.0057
0.0021 0.0018 0.0025 0.0035 0.0061
0.0021 0.0019 0.0027 0.0037 0.0064
0.00132 0.00133 0.00140 0.00134 0.00213 0.00334 0.00619
0.00139 0.00142 0.00149 0.00147 0.00227 0,00367 0.00663
0.0051
450
0 , bbi4s 0.00158
0.00155 0,00243 0.00396 0.00714
The absolute viscosities were calculated from the Saybolt tween the various oils are so large that they cannot be attribviscosities according to the formula given by H e r ~ c h e l . ~uted to an error in the viscosities used in making the calcuUsing these values, the value of z n / p corresponding to each lations. Even though these viscosities are incorrect, the coefficient of friction in the tables was calculated. The differences between the curves for the various loads for any results have been plotted for each load used by Tower. one of the three sets of curves (Figs. 1, 2, and 3) hold, since a change of viscosity would only shift the entire set of curves (Figs. I, 2, and 3) and have absolutely no effect upon their relative order. The same argument applies to the question of the actual film temperature as opposed to that of the bath. Towcss FRET OM DATa It will therefore be noted that the plotting of the modulus z n / p against the coefficient of friction simply results in a CONSTRN-I TEMP 90-F curve for each load used. The writer fails to see any substantiation for the broad claims made for this method of presenting results. From the data of Barnard, Myers, and Forrest,' it would appear that a glycerol-water solution should give as good lubrication in the fluid film region as an animal, vegetable, or petroleum lubricant of the same viscosity. I n fact, since they found that all these liquids give minimum coefficients of friction a t values of z n / p which differ from each other but slightly, it is to be presumed that the glycerolwater solution will lubricate almost as satisfactorily as their Velocite B and lard oils-a conclusion hardly in agreement with practical experience along these lines. The data presented herein, therefore, clearly indicate that I the theories which have been advanced in regard to the z n / p FIO.3 relation fail to fit the facts. It may be a useful method of The curves show clearly that the experimental points analysis, but, in the writer's opinion, it would be far better cannot be represented by a single curve in the case of any to present the actual data measured. Certainly, Tower's one of thcse three oils, to say nothing of the very wide varia- experiments, which were very carefully performed, are not tion between the different oils. I n fact, the differences be- in agreement with the mathematical deductions which are the basis of the x n / p relation. e J . SOC.Automotive Eng., 10, 31 (1922). D
I
Record Gasoline Production Petroleum refineries in the United States established another new high-record gasoline production mark in May, when the total output of this commodity amounted to 780,194,019 gallons. This figure surpasses by more than 25,000,000 gallons the highrecord production mark made in April, which had, in turn, passed by 11,000,000 gallons the previous high record set in March. The largest supply of gasoline yet recorded in the history of the country was on hand a t refineries June 1,according to the Bureau of Mines figures, which show total stocks amounting to 1,647,359,835 gallons. The figures represent an increase of 39,573,431 gallons over the supplies on hand May 1, a t which time a new high mark had been recorded. The daily increase in gasoline production in May, 1924, over the corresponding month in 1923 was 4,789,978 gallons, or 23.5 per cent. Compared with the output for April, 1924, there was a slight increase in the daily production amounting to 8441 gallons. Exports of gasoline amounted to 96,879,769 gallons, a decrease of 20,061,479 gallons. Imports showed a total of 14,265,697 gallons for May, an increase of 6,638,398 gallons. Kerosene showed a decrease in production from the previous
month of 3,193,528 gallons, the total production of this product during May amounting to 199,992,393 gallons. Stocks of kerosene decreased 18,372,875 gallons, but increased 15,034,731 gallons over the stocks on hand a t the end of the corresponding period of a year ago. Total stocks on June 1 were 287,707,015 gallons. Total exports during the month amounted to 79,421,026 gallons, a decrease of 9,442,875 gallons during the month. The output of gas and fuel oils in May was 1,155,935,780 gallons, an increase during the month of 39,172,117 gallons. Stocks decreased 25,026,802 gallons, total stocks on hand June 1 being 1,530,112,132 gallons. Exports and imports both increased during the month-exports by 13,508,496 gallons and imports by 20,803,847 gallons. During the month of May, 258 operating refineries reported to the Bureau of Mines. These refineries had an aggregate daily crude oil capacity of 2,217,292 barrels, running to stills a daily average of 1,851,017 barrels of both foreign and domestic crude oil, or 83 per cent of their daily operating capacity, a decrease of 2 per cent compared with the refinery operations of the previous month.
