of teeth, and dividing the result by 3.1416, or, as a formula:

PX N
3.1416

The outside diameter of the worm, O2, is usually assumed. To find the pitch diameter of the worm,

FIG. 175.-Worm-wheel.

The root diameter of the worm can be found first after the full depth of the worm-wheel thread has been found. The full depth of the worm-wheel thread equals the pitch multiplied by 0.6866, or: d = PX 0.6866.

Now the root diameter of the worm thread equals the outside diameter of

the worm minus 2 times the depth of the thread, or:

The throat diameter of the worm-wheel is found by adding 2 times the addendum of the worm thread to the pitch diameter of the worm-wheel, or:

The radius of the worm-wheel throat is found by subtracting 2 times the addendum from the outside diameter of the worm divided by 2, or:

The outside diameter of the worm-wheel (to sharp corners) is found by the formula below:

The angle a is usually 75 degrees.

Finally, the center distance between the center of the worm and the center of the worm-wheel equals the sum of the pitch diameter of the worm plus the pitch diameter of the worm gear, and this sum divided by 2, or:

Find, for an example, the required dimensions for a worm and worm-wheel, in which the wormwheel has 36 teeth, the pitch of the worm thread is inch, and the outside diameter of the worm is 3 inches. We have given P=1; N = 36; 02 = 3.

A

PX N
3.1416

=

× 36 3.1416

=

5.730 inches.

= PX 0.3183

=

=

2

× 0.3183 = 0.15915 inch.

D2 = 02- 2A 3 0.3183 = 2.6817 inches.

2

2

=

CHAPTER XIV

ICONE PULLEYS

WHEN it is desired to have a variable speed ratio between two shafts which are belted together, the method of having reversed conical cylinders or drums mounted on the shafts, as shown in Fig. 176 and 177, is sometimes used.

Пр

These permit any

1

FIG. 176.-Simplest
Form of "Cone-
Pulley."

FIG. 177.—An Im-
proved Form of
"Cone-Pulley."

FIG. 178.-The Modern Type of Stepped Cone Pulley.

desired change of speed, but they have disadvantages which on most work offset this advantage. It would be necessary, in the first place, to use a narrow belt to avoid undue stretching at the edges. Then, as the tendency of a belt is to mount to the largest part of a pulley, this tendency, acting in

the same way on the cones, would produce undue tension on the belt. If a crossed belt is used on such cones their faces would be made straight, as the belt would be equally tight in any position. This may be seen by an inspection of Fig. 179, where circles A and B represent sections of such cones on one line, and circles C and D represent sections on another line. If the cones have the

A

FIG. 179.—Diagram Showing relative Influence of Open and Crossed Belt on Pulley Sizes.

same taper it is evident that the circle D will be as much larger than B as C is smaller than A, the gain in one diameter being offset by the loss in the other. Then, as the circumferences of circles vary directly as their diameters (the circumference of a circle having twice the diameter of another, for instance, will be twice as long as the circumference of the other), whatever is gained on one circumference will be lost on the other. For a crossed belt then, it is only necessary that the cones have the same taper.

When, however, an open belt is used, it becomes necessary to have the cones slightly bulging in the