II2 ~ H 1 p 1 -p 2 g > p ‘

If this inequality is found not to be true in any special comparison, then the cheaper oil should be used. P varies from fd. to over 1⅜d., according to the class of engine and boiler and to the good or bad management of the works, while p 1 — ρ 2 , in comparing the extremes of cheap and expensive commercial lubricants, amounts to 2s. 6d. or more.

To compare the advantages of using a larger or smaller amount of the same oil, let g 1 and g 2 be the quantities used, and the resulting wastes of horse-power be H 1 and II 2 . Then the use of the larger quantity g 1 will be economical if

Γ(H 2 - H 1 ) - 2 ¼ - g, 2 ) > 0; or > ⅛ .

g 1 ~ 9 2 1

Considering the meaning of this inequality in the two cases of a high-priced and of a low-priced oil, in the former case — has a larger value, while — I has also a

P 91-9-2 larger value than in the latter case. In both cases this latter fraction decreases with increase of g 1 ; but it decreases more rapidly in the case of a high-priced than in that of a low-priced oil, because the former is a better lubricator. Thus with the dearer oil the limit beyond which it is uneconomical to increase the consumption of oil is reached sooner than with the cheaper, and it follows that of the cheaper oils it is best to use a large quantity, while of the dearer a smaller amount is what is most usefully employed. If the law according to which H varies with g be found for any oil, by experiment or otherwise, then the exact most economical quantity can be found by differentiating pg + PH with respect to g, and equating the differential coefficient to zero; thus dH_ _p_ dg P ’

<ZH

when — is expressed in terms of g, gives this most economy mical value of g. An example of the actual values of the quantities involved in these formulas is given by an experiment by Van Cleve on ajournai 6 inches in diameter by 7 inches long, in which the coefficient of friction was found to be about ∙077, and there was wasted 3 , 4 horsepower when Ό23 of a gallon was used per hour.

Of the animal oils and fats suitable for lubrication those commonly used are sperm, lard, neats-foot, tallow, and common whale oil. Of vegetable oils olive, cotton-seed, and rape-seed are extensively employed, the first mostly in those countries where the olive is grown, and generally in the pure condition, while the last two are more used for mixing with higher class and more expensive oils. Various fish oils are also much used, and mineral oils now form a large proportion of the many lubricating compositions that are in use. For machinery where considerable pressure is exerted between the bearing surfaces the mineral oils are too thin, or, as it is termed, are too wanting in “body” to be quite suitable without being mixed with an animal or vegetable oil. Unless a lubricant has considerable “body” it is quickly pressed out of the bearing, and an unnecessarily rapid supply has to be provided. The same oil may be used several times over, and several ingenious designs of bearings for rotating shafts, such as Player Brothers’ or Taylor & Challen’s, whereby the shaft itself as it runs round continually pumps up again to the top of the bearing the oil that has once been used, have been very successful in practice. If an automatic arrangement of this sort is not employed, the oil dripping from the bearing should be collected in a pan and used again to fill the oil-cups. The oil gets gradually worn out as a lubricant by becoming filled with dirt, partly the dust of the atmosphere and partly the minute iron and brass dust that is continually rubbed off the bearing surfaces. Oils that have been used two or three times can be to a certain extent repurified by washing in a solution of carbonate of soda or potash and chloride of calcium in boiling water. But it must not be supposed that with repurification an oil may be used an indefinite time as a lubricant. A large portion of it is actually evaporated by the heat caused by the friction at the journal, and the unevaporated portion seems to undergo some chemical change injurious to its lubricating properties. Vegetable oils are peculiarly rich in volatile constituents, and it is this fact probably, even more than the greater cheapness of mineral oils, that has led to the largely increased use of the latter in the lubrication of machinery.

The quality of an oil may be tested by chemical analysis; by measurement of density and viscosity; by observation of the temperature necessary for ignition in the atmosphere, or, as it is called, the “flashing” temperature; by observation of the succession of figured patterns produced when a single drop of the oil is let fall upon the surface of pure water in a clean dish; by the measurement of the temperatures to which a journal rises when running at different speeds and under different pressures, and when supplied with a given amount of the lubricant per minute; and by the measurement of the coefficient of friction at the same journal with varying speeds of rotation and pressures. The last two methods of test are the most interesting and directly useful from a mechanical point of view, i.e., considering the oil as a lubricant simply.

The machine designed and used by Professor Thurston of the Stevens Institute of technology is the best that has yet been constructed to carry out these tests. In it a spindle is revolved in horizontal bearings by a belt from the main shaft of the workshop of the Institute. On the overhanging end of this spindle is formed a journal from which is hung a heavily-weighted rod. The bearings in this rod by which it hangs on the journal are of brass, and the two halves are pressed down upon the journal with any desired pressure by means of a spiral spring placed in the centre of the rod. The weight of this pendulum prevents it revolving along with the spindle, but the friction at the journal deflects the pendulum from the vertical through an angle whose sine is a measure of the frictional effort. There is also inserted in the bearings a thermometer by which the effect of the friction in increasing the temperature is observed. With this machine Professor Thurston has obtained extremely interesting results regarding the variation of the coefficient of friction with temperature, pressure, and velocity of rubbing. These are summar.zed as follows. With great intensity of pressure and low velocity, the friction increases as the temperature is raised; but for each low velocity the rate of increase of friction with temperature becomes slower as the pressure diminishes, and becomes zero at a certain limit of pressure which is higher the higher the velocity is. With high velocities the variation of friction with temperature is in the opposite direction within the limits of pressure commonly used. Again at a given temperature and a given pressure the friction first decreases very rapidly with increase of velocity, and then above a certain limit of velocity increases again slowly with further increase of velocity. The limit of velocity at which the direction of variation changes from · negative to positive does not appear to depend on the intensity of pressure, but the change occurs at much lower velocity-limits with low than with high temperatures. Thirdly, with a given temperature and a given velocity the coefficient of friction, i.e., the ratio of friction to normal pressure, at first decreases rapidly with increase of pressure at low pressures, and then at higher pressures increases again with the pressure. This law seems to hold for all temperatures and all velocities; but how the limit of pressure at which the variation changes in direction is altered by alteration of temperature and velocity is not as yet certainly determined.

It is thus seen that the variation of friction at lubricated journals is extremely complicated, and has no resemblance to the simple law of constant proportionality between the friction and the normal pressure which until lately was commonly believed to hold good for unlubricated flat surfaces. This simple law is really true for many unlubricated surfaces and through a tolerably wide range of conditions, but is not true for all such surfaces, or under all, and especially extreme, conditions of pressure, velocity, and temperature.

Professor Thurston has endeavoured to represent these results in algebraic formulae, but the number of his experiments seems hardly sufficient to establish any general mathematical law which will be trιιe under all circumstances, and the particular formulae which he has adopted give values differing very considerably from those given by some of his experiments.

The friction at a lubricated journal depends really much more on the viscosity of the lubricant than on the frictional properties of either of the solids, which never come in contact when the lubrication is carefully attended to. The layer of oil immediately in contact with either solid probably does not move at all relatively to the solid. The rubbing, therefore, in all probability takes place between two surfaces, or rather between an indefinitely large number of pairs of surfaces, ρf oil. The viscosity of the oil, which hinders this relative motion, is, however, very likely affected by the adhesive force between the solid and liquid surfaces, because, especially if the intensity of bearing pressure be great and the film of lubricant consequently very thin, some at least of the liquid motion will take place within the sphere of action of the cohesive forces.

It is of the greatest importance in order to secure economy in the use of lubricants to maintain the supply to each journal at a constant uniform rate. To effect this, numberless “automatic lubricators” have been invented. The common syphon oil-cup is very efficient so long as the rate of working is steady; but the supply does not automatically vary with the requirements. The “needle” lubricator allows the oil to How down to the journal through a small straight tube in which is placed a wire which nearly blocks up the tube. When the wire is motionless the dimensions of the space between the wire and the tube are capillary, and no oil flows. When the shaft runs, however, its surface scraping on the end of the wire throws it into continual vibration, and this allows a slow stream of oil to pass downwards which is automatically regulated in accordance with the speed of revolution. The necessity of very perfect lubrication of the cylinders of gas engines, which run at a high speed and at a high temperature, has led to the adoption by Messrs Crossley Brothers of an extremely neat and perfect arrangement. A small crank on the end of a spindle, driven at a rate proportional to that of the engine, has suspended from the crank pin a short wire pendulum. At the lower part of the revolution this pendulum dips into a basin of oil and lifts a drop from it. In the upper half of the circular motion, the wire is dragged over a little scraper extending over the open mouth of a pipe. This scrapes the drop off the pendulum, and the drop falls from the scraper into the tube, along which it flows to the surface to be lubricated. The number of drops is thus accurately proportioned to the speed of the engine, and the size of drop can be varied by using smaller or larger wire for the pendulum.

Table of Coefficients of Friction on Cast-Iron Journals at Temperature 70° F. and Velocity 750 Feet per Minute {from Thιιrston). [table]

Other mineral oils than the kerosine and paraffin give a smaller coefficient. For mineral oils generally the lowest coefficient appears to occur at from 30 to 40 lb pressure per square inch. The supply of oil in the experiments was intermittent, and must have been insufficient for the best lubrication.

Table of Coefficients of Friction between Steel Journals and Bronze Bearings lubricated with Sperm Oil, and run at different Pressures, Velocities, and Temperatures (from Thτιrston). [table]

The journal upon which the above results were obtained was 1} inches in diameter and 1⅜ inches long. With a larger journal the results would probably not be exactly the same. (B. H. S.*)