inch is the maximum limit of safe friction under ordinary circumstances. As the results of this preliminary work indicated that the coefficient of friction varied with all the circumstances, it was necessary to simulate the conditions of specific practical applications to determine the value of a lubricant for such purposes. It was decided to begin these investigations with spindle oils, and therefore the machine was loaded with five pounds to the square inch, and run at about five hundred revolutions per minute, as the oil is then submitted to conditions of attrition, corresponding to those met with in extremes of velocity and pressure, in the case of a Sawyer spindle running at seven thousand six hundred revolutions per minute with a band tension of four pounds, and the results subsequently given refer only to the friction under these conditions, except when definitely stated to the contrary. This particular spindle was selected because, that of the five million ring spindles in the United States, about one and a half million are of this manufacture, and in a large number of the remainder the conditions of lubrication are quite similar. In a Sawyer spindle, the step measures three-eights by fifteen hundredths inches, and receives seven-ninths of the pull due to the band. If that tension is four pounds, three and one-ninth pounds are transmitted to the step, whose projected area is nine-sixteenth square inch. The pressure per square inch is, therefore, five and one-third (say five) pounds. The diameter of the spindle at bolster is .28", or .8976" in circumference. At seven thousand six hundred revolutions per minute, its velocity amounts to 6,685", or 557 feet, per minute; and the mean area of the discs of the oil machine must revolve at this speed. To illustrate, let Router radius of disc=2.656 inches. To give a desired fractional velocity of 6.685 inches per minute, the discs must revolve at 6,685 divided by 13.45=497 (say) five hundred revolutions per minute. To recapitulate: By revolving the disc at five hundred revolutions per minute, with a pressure of five pounds per square inch, the oil is submitted to conditions of attrition, corresponding to those in the extremes of velocity and pressure met with in a Sawyer spindle revolving a seven thousand six hundred revolutions with a band tension of four pounds. My reason for giving such a detailed statement is, because the value of investigations upon this subject must be measured by the precision with which all the conditions are observed. The apparatus is used in the following manner to measure the coefficient of friction of oil. After cleaning with gasoline and wiping carefully with wash leather, the discs are oiled and run for about five hours, being kept cool by a stream of water circulating through the upper disc. From time to time they are taken apart, cleaned, and oiled again. After using any oil, even if the discs are afterwards cleaned, the results with the oil subsequently used give the characteristics of the previous oil, and it is only after thirty-five to forty-five miles of attrition that these results become consistent with each other; each succeeding result, meantime, approaching the final series. This seems to indicate that friction exists at the surface of the two discs, between the film of oil acting as a washer and the globules of oil partially embedded within the pores of the metal. If the dense bronze and steel retain the oil despite attempts to remove it, how much longer must it require to replace the oil in machinery with a new variety whose merits are to be tested? These experiments confirm the wisdom of the increasing use of cast iron for journals, as its porosity enables it to contain and distribute the lubricant. When the discs are ready to test the oil the apparatus is cooled by the circulation of water; the flow of which is stopped when the machine is started. At every degree of temperature, the corresponding resistance is read on the dynamometer. When the thermometer indicates a temperature of sixty degrees, the counter is thrown in gear, and the time noted. When one hundred-and-thirty degrees is reached, inch is the maximum limit of safe friction under ordinary circumstances. As the results of this preliminary work indicated that the coefficient of friction varied with all the circumstances, it was necessary to simulate the conditions of specific practical applications to determine the value of a lubricant for such purposes. It was decided to begin these investigations with spindle oils, and therefore the machine was loaded with five pounds to the square inch, and run at about five hundred revolutions per minute, as the oil is then submitted to conditions of attrition, corresponding to those met with in extremes of velocity and pressure, in the case of a Sawyer spindle running at seven thousand six hundred revolutions per minute with a band tension of four pounds, and the results subsequently given refer only to the friction under these conditions, except when definitely stated to the contrary. This particular spindle was selected because, that of the five million ring spindles in the United States, about one and a half million are of this manufacture, and in a large number of the remainder the conditions of lubrication are quite similar. In a Sawyer spindle, the step measures three-eights by fifteen hundredths inches, and receives seven-ninths of the pull due to the band. If that tension is four pounds, three and one-ninth pounds are transmitted to the step, whose projected area is nine-sixteenth square inch. The pressure per square inch is, therefore, five and one-third (say five) pounds. The diameter of the spindle at bolster is .28", or .8976" in circumference. At seven thousand six hundred revolutions per minute, its velocity amounts to 6,685", or 557 feet, per minute; and the mean area of the discs of the oil machine must revolve at this speed. To illustrate, let Router radius of disc=2.656 inches. 66 66 66 rinner Frictional area of annular disc area of outer half (R'-') = π(R'-n') Length of line bisecting the area=27/47 (R* +r2) 2 √/2π2 (R2 + r2) =V9.87(7.05+2.11) =√19.74 x 9.16 = 180.8184 = 13.45 inches. = 1.12 feet. To give a desired fractional velocity of 6.685 inches per minute, the discs must revolve at 6,685 divided by 13.45=497 (say) five hundred revolutions per minute. To recapitulate: By revolving the disc at five hundred revolutions per minute, with a pressure of five pounds per square inch, the oil is submitted to conditions of attrition, corresponding to those in the extremes of velocity and pressure met with in a Sawyer spindle revolving a seven thousand six hundred revolutions with a band tension of four pounds. My reason for giving such a detailed statement is, because the value of investigations upon this subject must be measured by the precision with which all the conditions are observed. The apparatus is used in the following manner to measure the coefficient of friction of oil. After cleaning with gasoline and wiping carefully with wash leather, the discs are oiled and run for about five hours, being kept cool by a stream of water circulating through the upper disc. From time to time they are taken apart, cleaned, and oiled again. After using any oil, even if the discs are afterwards cleaned, the results with the oil subsequently used give the characteristics of the previous oil, and it is only after thirty-five to forty-five miles of attrition that these results become consistent with each other; each succeeding result, meantime, approaching the final series. This seems to indicate that friction exists at the surface of the two discs, between the film of oil acting as a washer and the globules of oil partially embedded within the pores of the metal. If the dense bronze and steel retain the oil despite attempts to remove it, how much longer must it require to replace the oil in machinery with a new variety whose merits are to be tested? These experiments confirm the wisdom of the increasing use of cast iron for journals, as its porosity enables it to contain and distribute the lubricant. When the discs are ready to test the oil the apparatus is cooled by the circulation of water; the flow of which is stopped when the machine is started. At every degree of temperature, the corresponding resistance is read on the dynamometer. When the thermometer indicates a temperature of sixty degrees, the counter is thrown in gear, and the time noted. When one hundred-and-thirty degrees is reached, the counter is thrown out of gear, and the time noted. This not only gives the velocity of the rubbing surfaces, but the number of revolutions required to raise the temperature a stated number of degrees, and is a close criterion of the oil. The coefficient of friction is the ratio of the pressure to the resistance, and is deduced in the following manner: In the friction of annular discs, the portions of the surface near the perimeter have a greater leverage than those near the center. The mean sum of these moments is found by the calculus. Let e be the radius of any infinitesimal narrow ring or band. Then will The expression for the area of an annular disc is 7 (R2-2). (5) To express the moment of a ring in terms of an annular surface, divide Eq. 4 by Eq. 5, as follows: |