CHAPTER XI WORM GEARING FOR SIDE SHAFT THE type of gearing used by all the gas engine makers to transmit the power at right angles to the side shaft is a form of worm and worm wheel, geared as 2 is to 1, the friction of which must of necessity be more than that of bevel or spur gearing, but can be reduced to a minimum by the use of welllubricated machine-cut gear. Both the driving and driven wheels are part of multithreaded screws, the cross section of the teeth being the same, but the angle of the threads on the driver being twice that of those on the driven wheel, and double the number of teeth or sections of thread on the same size of wheel. If fig. 102 be taken as an eight-threaded screw, with P as the pitch and D as the diameter, the section C would form a worm wheel of eight teeth. In each wheel there are four distinct pitches: P = the pitch of the helix; p = the circumferential pitch, measured from centre to centre of threads around the circumference ; p' = the normal pitch, measured at right angles with the direction of the threads; p” = the axial pitch. In all worm and worm wheels the normal pitch (p") must be the same in both wheels, and it is upon this pitch that the wheel teeth are designed, and to which templates should be made for working, the other pitches varying in the two wheels. The worm and worm wheels shown in figs. 103 and 104 were designed for a 13-inch x 21-inch engine, the diameter of both wheels at the pitch circle being 9 inches—i.e. the centres of the crank shaft and side shaft were 9 inches apart. There are FIGs. 103, 104 sixteen teeth in the worm and double that number (thirty-two) in the worm wheel. The pitch of the screw thread in the worm equals half the circumference of the pitch circle = 9 inches diameter × 3.1416 = * = 14:13 pitch of screw thread. If 2 caloo WORM GEARING FOR SIDE SH we mark off the pitch of the thread on a horizontal line A B (fig. 105), and on a line perpendicular to A B mark off A C equal to the circumference of pitch circle, and join B C, the angle this line makes with A B gives the angle of thread, which is approximately 63°. t = /4 /3 * l FIG. 106 FIG. 105 In the case of the worm wheel the pitch of the screw thread equals double the circumference of the pitch circle = 9 inches diameter × 3.1416 = 28.27 × 2 = 56-54 inches pitch of screw thread, and drawing this out as in fig. 107, and the angle the line B C makes with A B gives the angle of thread, which is approximately 27°, the angle of thread in the worm plus the angle of thread in wheel equal a right angle. This rule for finding the angle of thread is applicable to any pair of worm and wheel of equal diameter, and geared 2 to 1. Dividing the circumferences into their respective numbers of teeth, as in figs. 106 and 108, making D E equal the width of wheels = 2; inches, and drawing the centre line of teeth parallel to their respective angles, the normal pitch p"—in this case # inches, can be measured off, and it will be found the same in both wheels. From this normal pitch the height of tooth above pitch line (which gives the outside diameter of the wheels) and the depth of tooth below the pitch line and the width of tooth at the pitch line are obtained from fig. 109. As in the case of ordinary spur gears, the contour of the tooth can be struck out either cycloidal or involute, the latter being preferable, as it is not only an easier curve to construct, but works well in practice. Fig. 110 shows the construction of the involute curve. Draw a line at 75° with the centre line of the wheels at the point of contact with the pitch circles, and a circle A B, drawn tangentially to this line will be the describing circle, upon which set off the distances a b, b c, c d, d e from a, the edge of the tooth, and draw tangents to same; then set off the distance b b' equal to the arc b a, the distance c c' equal to the arc c a, the distance d d" equal to the arc da, &c., and the curve drawn through these points will be the involute required. Having set off the pitch, height, depth, and width of teeth, as per figs. 109 and 110, and drawn the flanks by the involute obtained, the root from f to g may be a straight line parallel to the centre of the tooth, with a rounded corner. FIG. 110 The angle of a screw varies according to the distance away from the centre or axis of screw, notwithstanding that the pitch of screw is constant. This will be seen from figs. 111 and 112, where the angle of thread is given at three distances from axis —viz. the diameter at root, the pitch circle, and the diameter at point of teeth. The letters and numbers in figs. 111 and 112 correspond. A B being the axis of screw, P the pitch, D C the height of tooth above pitch line of wheels, and D E the depth of tooth below, divide the circumferences of the transverse section F, also the pitch of screw P, into the same number of equal parts— 1, 2, 3, &c.—and draw lines through the points of intersection, as shown at 1", 2’, 3’ &c. This will give the twist of screw I |