T H E JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
682
Vol. 14,No. 8
The Mechanism of Lubrication-II’ [ABSTBAOT]
By Robert E. Wilson* and Daniel
P.Barnard, 4th
RESEARCH LABORATORY OB APPLIEDCHEMISTRY. MASSACHUSETTS INSTITUTE O F TECHNOLOGY, CAMBRIDGE, MASS,
LTHOUGH a large number of investigators have pub-
A
lished data bearing on the subject of lubrication, the wide variations in their operating conditions have thus far prevented any satisfactory correlation of their results, or the establishment of definite conclusions as to the effect of such important factors as the smoothness and clearance of the bearing, the “oiliness” of the lubricant, etc. The basic difficulty lies in the fact that f, the coefficient of friction, is, in the case of a journal bearing, some unknown function of at least nine variables-z, n, p , c, d , I , S, M, and 0, where z = Viscosity of the lubricant at the operatifig temperature. n = Revolutions per minute. p = Pressure on bearing. G = Diametrical clearance of bearing. d = Diameter of journal. I = Length of bearing. S = Surface conditions (kind of metal, smoothness, etc.). M = Method (and amount) of oiling. 0 = “Oiliness” factor of the lubricant.
1-The right-hand portion, which is the region of perfect fluid film lubrication, in which the friction coefficient is roughly proportional to zn/p. 2-The critical point of minimum friction where the speed or viscosity becomes so low, or the pressure so high, that the fluid film begins to rupture. 3-The sharply rising portion of the curve to the left of the critical point, which is the region of partial lubrication, in which there is increasing friction, metal to metal contact, and abrasion, as zn/$ decreases below its critical value. Many of the contradictory statements in the literature are due to failure to realize in which of these regions a given set of experiments were being conducted.
However, making use of dimensional reasoning as first suggested by Hersey,Sit can be shown thatf, a factor without dimensions, cannot be an independent function of all these variables, but only of their combination in such forms that all dimensions are canceled out. We may therefore write: en c 1 0.2
of which only the first two are important or primary variables, and indeed the first one includes the only three important variables involved in making tests on a given bearing under varying conditions. If, then, all the observed values of f obtained on a given bearing by varying the load, speed, and viscosity of lubricant, are plotted against the modulus z n / p , they should approximate a line which represents the unknown functional relationship. For the ideal case of a centrally operating bearing with perfectly smooth surfaces, no end leakage, etc., this function would be represented by a straight line passing through the origin, with a slope inversely proportional to the ratio c/o?. For actual bearings this simple relationship would certainly not hold, but the shape and location of the curve which best represents the observed results should give valuable information as to the effect and importance of the other, or secondary variables in bearing design. All the published results which contained adequate data have been plotted on a large scale by the above-recommended method, and most of the plots are reproduced in the original article. Within the limits of this abstract it is possible to show only a typical figure, based on the results of Stribeck using two kinds of bearing metal. Each of these curves may be considered as made u p of two regions divided by a point, as follows: 1 Abstract of paper appearing in J . Soc. Automotive Eng., July 1922. This paper was published as Contribution No. 47 from the Research Laboratory of Applied Chemistry, M. I. T. 2 Director, Research Laboratory of Applied Chemistip, M. I. T. a J . Wush. Acad. Sci., 4, No. 19 (1914).
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RESULTSOBTAINED BY PLOTTING OBSERVED VALUES O F f AQAINST en/# FOR T W O DIFFERENT BEARINGS
The design of bearings and selection of lubricants may dow become a definitely calculable matter. Bearings should not be designed to operate precisely a t the point of minimum friction, because any momentary decrease in z n / p would carry them into the unstable region of partial lubrication, where serious abrasion and overheating are certain to result unless the journal is stopped. The safe average operating value of z n / p should therefore be obtained by multiplying the value of z n / p at the critical point by a suitable factor of safety-say around 5-depending upon the degree of variability of the service conditions. The problem is then merely to adjust the size of the bearing and the viscosity of the lubricant to give the desired value of z n / p . The importance of the precise location of the critical point should be emphasized. For example, in the figure the casual observer would consider that Bearing A was the better because it gave the lower coefficients of friction over most of the normal operating range; but actually its critical point is so much higher than that of B that its value off under safe operating conditions (factor of safety=5) is twice that of B. I n spite, however, of the great importance of the critical point, very little experimental work has ever been done to determine the effect of various factors on its location. The more important tentative conclusions drawn from a careful study of the available data may be summarized as follows :
