Fig. 46.
In an article by Professor Robinson, attention is called to the fact that if the teeth of wheels are not formed to have correct curves when new, they cannot be improved by wear; and this will be clearly perceived from the preceding remarks upon the amount of rolling and sliding contact. It will also readily appear that the nearer the diameter of the generating to that of the base circle the more the teeth wear out of correct shape; hence, in a train of gearing in which the generating circle equals the radius of the pinion, the pinion will wear out of shape the quickest, and the largest wheel the least; because not only does each tooth on the pinion more frequently come into action on account of its increased revolutions, but furthermore the length of flank that has contact is less, while the amount of sliding action is greater. In [Fig. 45], for example, are a wheel and pinion, the latter having radial flanks and the pinion being the driver, the arc of approach is the thickened arc from c to the line of centres, while the arc of recess is denoted by the dotted arc. As contact on the pinion flank begins at point c and ends at the line of centres, the total depth of flank that suffers wear from the contact is that from c to n; and as the whole length of the wheel tooth face sweeps over this depth c n, the pinion flanks must wear faster than the wheel faces, and the pinion flanks will wear underneath, as denoted by the dotted curve on the flanks of tooth w. In the case of the wheel, contact on its tooth flanks begins at the line of centres and ends at l, hence that flank can only wear between point l and the pitch line l; and as the whole length of pinion face sweeps on this short length l s, the pinion flank will wear most, the wear being in the direction of the dotted arc on the left-hand side v of the tooth. Now the pinion flank depth c n, being less than the wheel flank depth s l, and the same length of tooth face sweeping (during the path of contact) over both, obviously the pinion tooth will wear the most, while both will, as the wear proceeds, lose their proper flank curve. In [Fig. 46] the generating arcs, g and g′, and the wheel are the same, but the pinion is larger. As a result the acting length c n, of pinion flank is increased, as is also the acting length s l, of wheel flank; hence, the flanks of both wheels would wear better, and also better preserve their correct and original shapes.
Fig. 47.
Fig. 48.