The Efficiency of Worm Gearing.
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Interesting Tests Made by Brown and Sharpe.
Professor William H. Kennerson, of Providence, R.I., recently presented before the American Society or Mechanical Engineers a most interesting paper, in which he set out the records of investigations made by the Brown and Sharpe Manufacturing Co. relating to the efficiency of worm gearing for motor-vehicle final-drive transmission.
In these tests full account was taken of the heating effect due to continuous running, and for their purpose a 50 h.p. electric induction motor was employed, its designed speed being 870 revolutions per minute at full load. In all the tests, between the motor and the worm gearease, a change-speed gearbox was interposed, so that tests could be made at more than one speed, and between the gearbox and the worm gearcase a trans. mission dynamometer was interposed, and an Alden brake was used to absorb and measure the powers transmitted to the gears.
With this special arrangement of transmission dynamometer and brake, tests were made at various loads, and the torque corresponding to horse-power per 100 revolutions per minute was recorded on the dial of the transmission instrument. Against the indications of this instrument were the records of the brake, so that there were two separate and distinct means of calculating the power which was being transmitted. A thermometer was placed in the oil well at the back of the worm gearcase, and another thermometer was suspended within the test house near the test equipment. The lubricating oil used had a specific gravity of 28 Ba.tune, a viscosity of from 260 to 265 at 212 degrees Fair., and a flashpoint of 625 degrees Fahr., and the worm casing contained about five quarts of this oil.
In all the trials the worm was located underneath the gear, and it is a matter for regret that the investigators .did not try the effect also of placing the worm above the worm wheel ; comparative records would have been most valuable. Ball bearings for both journal and axial loads were employed, and the worms were made of case-hardened steel ; whilst the worm wheels were of phosphor-bronze.
The first worm and wheel tested were similar to those which are used for the driving spindle on Brown and Sharpe's automatic spur-gear-cutting machines. This pair of gears constitutes an unusual example" of worm and worm wheel application ; in general appearance it resembles the T-Tindley worm, but it is not really of that type. Its specification reads as follows
Number of teeth in worm wheel, 43 (left hand); pitch diameter, 10.95 in. ; outside diameter, 11.28 in. ; circular pitch, 0.8; angle of teeth with axis, 45 degrees ; normal circular pitch, 0,5657 in. ; pitch of cutter, 5.553; addendum, 0.1628 in. ; thickness of tooth, 0.282 in. ; whole depth of tooth. 0.3882 in. ; included angle of cutter, 45 degrees.
The second and third pairs of gears tested were entirely different
from the set already mentioned, and they also differed from each other in regard to the shape of the worm threads ; this difference is clearly demonstrated in the accompanying diagram, which shows the cutters for the second (A) and third (B) test worms respectively. The specification for the third worm and worm wheel (B) was as follows :-Number of teeth, 40; pitch diameter, 10.5704 in. ; throat diameter, 10.9964 in. ; circular pitch, 0.8302; angle of teeth with axis, 38 degrees 16 mm.; normal circular pitch, 0.6518; pitch of cutter, 4.8196; addendum, 0.213 in. ; thickness of tooth, 0.3568 in. ; whole depth of tooth, 0.4586 in.; • number of leads in worm, 9; pitch diameter of worm, 3.015 in. ; outside diameter of worm, 3.441 in. ; circular pitch of worm, 1.0524; angle of teeth with axis, 51 degrees 44 min. ; thickness of tooth, 0.295 in. ; lead, 7.4719 in. ; ratio of wheel to worm, 40 to 9.
The shape of the teeth in the second pair of gears was produced with a cutter (A) which had an included angle of 29 degrees, as shown in the diagram, and the depth of the tooth was 0.57 in. This depth was based upon the axial pitch, whereas the usual method on multiple worms is to base the depth of the worm on the normal pitch. The object in using this cutter was to obtain the largest possible number of teeth in contact at the same time, and also a shape that could be ground with a straight-sided emery wheel. The teeth of the third worm were cut with a cutter of the shape indicated by the second figure (B) in the accompanying diagram, the shape of this cutter being an arbitrary one, designed to produce the greatest effective breadth.
In order to increase the value of these tests, comparative tests were made with bevel gears in the same manner, the specification of which was as follows, driving pinion made of 5 per cent, nickel steel casehardened :—Diametral pitch, 5; number of teeth, 14; angle of edge, 15 degrees 4 min. ; angle of face, 71 degrees 5 min. ' • outside diameter, 3.3339 in. ; number of teeth in crown wheel, 52; angle of edge, 74 degrees 56 mm. ; angle of face, 13 degrees 47 win.; outside dia., 10.4627 in. The accompanying table gives the highest and lowest recorded tests in each series, as well as an average for all the tests in each series. In conjunction with the efficiency trials a series of runs was made to determine the heating effect due to continuous running, and in these trials, which were in effect endurance tests, a constant load was transmitted through the gear, and the temperature of the oil in the gearcase, as well as the temperature in the test house, was noted at frequent intervals, and from these observations it was found that at the beginning of the run the temperature of the oil rose rapidly, but somewhat irregularly ; as the run continued, however, the rise became much more gradual and regular, and in the runs where the smaller powers were transmitted a point was reached where the temperature remained constant. This last-named condition indicated that radiation was sufficient to carry away the heat due to power lost through friction in the gearing, or, in other words, that the gears would run indefinitely at that load.