57 July 25, 1884. THE ENGINEER per minute, between ’779 lb. and 810 lb. Similar varia ­ except at the lowest pressures as before. On the whole, ON THE FRICTION OF SHAFTS OR JOURNALS tions occurred with the other lubricants. The differences, the results go very far to confirm the wisdom of those THOROUGHLY LUBRICATED. considering the necessary difficulties in the observation of railway engineers who have retained the use of grease for By Walter K. Browne , M.A., M. Inst. C.E. such small quantities, are not large, and, what is still more their vehicles in preference to oil, especially for cases In a number of The Engineer near the _ beginning important, they are altogether irregular, their highest where high bearing pressures are to be expected. of the present year, there appeared a leading article, values being sometimes at one end of the series, sometimes We have thus established the fourth law with which we entitled “ What is Friction 1” in which attention was at the other, and sometimes in the middle. On the whole, started, viz., that the coefficient of friction increases with drawn to the new and unexpected light thrown upon it is clear that the law must be admitted as correct for all the velocity, and at a rate which is, approximately at this subject by recent experiments, especially those of ordinary pressures and speeds. At the very high pressures least, the same as the square root of that velocity. The the Institution of Mechanical Engineers. Having carried by the mineral oil and the rape oil, the frictional fifth law— that the coefficient is nearly constant at about watched this course of experiments from the first, I may, resistance showed a decided increase ; and therefore some ­ 100ft. per minute—is a mere deduction from what has perhaps, venture on endeavouring to supply some sort of thing like an approximation to the conditions hitherto preceded. The sixth—the variation of friction with tem­ perature —has been noticed as to its general results by answer to the question. Undoubtedly it will not be com ­ supposed to be normal ones appeared to hold in those rases. plete, probably it may be in some respects capable The third law —that the frictional resistance varies as Professor Thurston and others, and is brought put of improvement, but it will at any rate supply a “ working the area —is merely a deduction from the second, and strikingly by Table IX. of the Institution of Mechanical Engineers ’ experiments, giving the coefficients of friction hypothesis, ” which answers fairly to the facts as they therefore needs no illustration. stand at present, and may serve as a guide in the progress The fourth law —the variation of friction with velocity observed with a bath of lard oil, with a fixed load of of further inquiry. The question will at least gain by the —is of a more complicated character, and requires further 1001b. per square inch, but with speeds varying from clear setting forth of the actual laws which, as a matter examination. With regard to the first part of the law, 105ft. to 471ft. per minute, and temperatures varying of experiment, have been found to govern the phenomena. namely, that for speeds up to, say, 100ft. per minute, the from 120 deg. to 60 deg. Fall. I shall not at the present moment attempt to deal with the coefficient of friction is less at higher speeds, we have un­ The actual law under which the variation takes place question of friction proper, or friction between dry sur­ luckily no complete figures to refer to. Professor Kimball has not been previously stated, so far as I am aware. _ It faces, on which further experiment is still urgently needed. found that with a wrought iron shaft in a cast iron bear ­ is, however, shown very clearly by Table VI., in which Nor shall I attempt to deal with what may be termed ing, an increase of speed from 6ft. to 110ft. per minute Table IX., mentioned just above, is reproduced, with an “ oily ” or “moist ” friction, as in ordinary lubrication; but caused a fall of 70 per cent, in the coefficient of friction. addition of figures given by calculation. The true law is shall content myself with examining the only case that is In another case, with lower pressures, an increase from masked in the original table by the fact that the tempera ­ in a fair condition to be approached by theory, namely, 1ft. to 100ft. per minute gave a fall in the coefficient from tures are given on the Fahrenheit, not the Centigrade that where the supply of the lubricant is practically un­ 0T5 to 0'05, or by 67 per cent., which is a result agreeing scale. When the latter is substituted, it is at once seen limited, and the lubrication is therefore complete. closely with the former. Professor Thurston found in that the figures expressing the coefficients of friction are This is, perhaps, the most important part of the whole some cases similar results, while in others the friction approximately in the inverse proportion of those represent- subject of friction, at least as regards practice;* and it is appeared to increase with the speed continuously from the that to which the recent experiments have chiefly been commencement. On the whole, however, he comes to the Coeffiydjertt^s directed. It is covered especially by the “ oil bath ” conclusion that the friction does diminish with increase of eoofiffruZion, experiments of Mr. Tower, detailed in the recent report velocity up to about 100ft. per minute; but the actual Tig 1. of the Institution of Mechanical Engineers —“Proceed ­ figures on which this conclusion is based are not given in ings ” 1883, p. 632—and also by the earlier experiments of detail. Mr. Tower ’s experiments unfortunately do not Professor Thurston. These agree very closely in their begin before 105ft. per minute, and therefore furnish no 750 main results, and the laws educed may be formulated as information as to lower speeds. Between 105ft. and 159ft. follows: —(1) The coefficient of friction is extremely low, per minute his figures show in all cases a decided rise in amounting in many cases to 0‘00I only, or a mere fraction the friction. On the whole, while the fact of the decrease of the lowest results previously recorded, not merely for dry, at low speeds may be admitted, there is nothing to enable 700 gee A but for wet or oily surfaces. (2) The coefficient of friction for us to define its nature or laws ; and a comprehensive set of moderate pressures and speeds varies approximately as the experiments, embracing all speeds from the highest to the 176, reciprocal of the pressure. In other words, the actual frictional -652 lowest, is thus a desideratum of the future. G5U resistance per surface unit is approximately constant, and We now come to the question of the rise in the coeffi ­ therefore if the load is doubled the coefficient of friction cient of friction, when the speed exceeds the value of "62 —which is the ratio of the resistance to the load —is 100ft. or 150ft. per minute; and here our data are clear ,603 halved. In dry friction, on the other hand, it is the and precise. Professor Thurston, indeed, fails here again eoo coefficient which is constant, and therefore the resistance to give us detailed figures ; and he infers that the increase varies directly as the load. (3) As a consequence of the varies as the 5th root of the velocity. This assertion is above, the frictional resistance, with constant pressure, disproved, however, by the elaborate experiments of the 55 y/ varies as the area of contact. In dry friction it is Institution of Mechanical Engineers, which show quite 550 -549 independent of the area. (4) As the velocity of conclusively that the variation is as the square root of the rubbing increases, say, from 10ft. to 100ft. per second, velocity. To prove this I have taken the first table in the frictional resistance— and therefore the coefficient of their report, that for olive oil, and assuming the speed of friction, the load being constant —diminishes also ; but at 209ft. per minute as the basis— since we are here quite 500 100ft. per second, or thereabouts, a change takes place, and beyond the influence of the supposed change which takes 494 4 94 thenceforward the resistance increases as the square root place at 100ft. per minute, or thereabouts —have calculated of the velocity increases. (5) As a consequence of the the coefficients of friction for the remainder of the speeds 132 above, the resistance at and near 100ft. per minute is given, assuming the variation to be as the square root of 328 approximately constant, or independent of the velocity. the speed. The calculated and observed values are placed "Sli (6) A rise in temperature— within moderate limits—has a below each other for comparison in Table I. It will be 300 '298.,--'' marked effect in lowering the coefficient of friction ; the seen that the two sets of figures agree very closely, and 287 coefficient varying approximately in the inverse propor ­ that the differences are sometimes on one side, sometimes 26! tion to the temperature above freezing point of water. on the other, which is the best proof of their being due '2Ui 250 With regard to the evidence for these laws, No. 1 is merely to errors of observation. The only exception is in S' proved by simple inspection of the tables given in Mr. the last column, relating to the highest speed of 471ft.