Worm gearing . Fig. 20 be the length of the worm = g; AC k theoutside circumference of the worm. From the point A, ADis drawn so that the angle DA C =a. From 5, the Ime BEis drawn perpendicular to AD. The distance A E is the lengthof the arc of the worm which must be subtended by the wormwheel in order that some part of every thread of the worm inthe length AB will touch one of the wheel teeth; from thisdiagram, the following equation is obtained from which thevalue of /? is at once found for any example. 360^ tan a (g2) P = 7:{d + i:So) THE WIDTH OF THE WORM WHEEL 49 when g is the total lengt
Worm gearing . Fig. 20 be the length of the worm = g; AC k theoutside circumference of the worm. From the point A, ADis drawn so that the angle DA C =a. From 5, the Ime BEis drawn perpendicular to AD. The distance A E is the lengthof the arc of the worm which must be subtended by the wormwheel in order that some part of every thread of the worm inthe length AB will touch one of the wheel teeth; from thisdiagram, the following equation is obtained from which thevalue of /? is at once found for any example. 360^ tan a (g2) P = 7:{d + i:So) THE WIDTH OF THE WORM WHEEL 49 when g is the total length of the worm = nP 2Xo = P = .6366P (63) Hence the equation becomes 360 g tan a (64) ^ nid+.63mP) In Fig. 21 the cross-section of the worm wheel is shown. Itwill be observed that the width of the wheel can be measuredat three points, viz., at the pitch line, at the root of the teeth,and at the outside, this last being somewhat deceptive as it hasno natural connection with the width of the working Fig. 21. Each dimension may be expressed as the chord of the angle/? measxired at different radii. The radius of the pitch line being - that of the root of the teeth ;;-|-«. Sufficient thickness of metal must be left in the rim to prop-erly support the teeth of the wheel as in the case of a spur gear. The subject of worm contact has been very fully investigatedby Mr. Robert A. Bruce (Prbc. Inst. Mech. E., Jan., 1906), andthe reader is referred to this for a very complete geometricalanalysis of the subject; the present writer, however, takesexception to some of his reasoning which is somewhat confusingby his method of illustrating the contact by the use of verticalparallel planes cut through the worm teeth. Such planes donot follow the lines of pressure between the contact surfaces andare consequently distorted sections through what is admittedlya very difficult section to correctly illustrate upon paper. 50 WORM GEARS He points out, however, that every part of the outHn
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