Part 33

A bevel wheel and pinion must be made to suit one another by both having teeth forming together an angle of 90°, therefore they are pairs, or proportioned in the number of teeth one to the other. Any other proportion used would not exactly gear and would be termed a “bastard” gear.

Fig. 268 represents a pair of miter wheels in gear; it will be noted that the shafts, when connected, will be at right angles to each other, the wheels being in all particulars of the same dimensions; the figure answers the purpose of a much longer description, if given in words.

A miter-wheel can easily be known by putting a square upon the face of the teeth, which are always at an angle of 45° with one another, irrespective of size.

A miter-wheel is a particular kind of bevel-wheel, the bevel being limited to an angle of 45° in each wheel.

The curve of the teeth in bevel-gears, when correctly formed, changes constantly from one end of the tooth to the other, therefore bevel-gears whose teeth are produced with a forced cutter are not theoretically correct.

Fig. 269 represents a rack and pinion: the teeth in this form of gear are shaped similarly to those in the spur wheel, shown on page 198, with the difference that the teeth of one are on a circle and on the rack are made on a straight line.

A flange or addition to the end of a tooth and the rim connecting them together is used to strengthen the teeth. This extends from the root to pitch line when the wheel and pinion are both flanged: if only one is flanged it extends from the root to the addendum.

Fig. 270 illustrates a worm and a worm wheel, sometimes called screw gears. This is a slow but powerful method of transmitting power, one revolution of the worm only moving the wheel the distance of one tooth and space.

A worm gear is a spur wheel with teeth at an angle to the axis, so as to work with a worm which is a screw, or has teeth shaped in the form of a spiral wound round its circumference; the screw or worm is called an endless screw, because it never comes to a stopping place in the circumference of the wheel.

Fig. 271 represents a gear with helical teeth. It is similar to a spur wheel, and is used in place of same in heavy and slow moving machinery, the formation of teeth preventing--in large measure--the jar or concussion noticeable in common spur gears.

In recent years the speed at which gearing is run has been greatly increased. A striking instance is that of a pair of cast-iron helical wheels, 6 ft. 3 in. diameter, 12 in. wide, making 220 revolutions per minute, the speed of the pitch line being 4,319 feet per minute; these wheels are running continuously and with little noise. There is also a cut gear in a mill in Massachusetts, 30 feet in diameter, and the speed of pitch line is 4,670 feet per minute.

An internal or annular gear wheel is one in which the faces of the teeth are within and the flank without the pitch circle, hence the pinion operates within the wheel. See fig. 272.

In internal geared wheels there is almost an entire absence of friction and consequent wear of the teeth, as compared to ordinary spur gearing.

Fig. 273 shows a crown-wheel which has pin teeth which are fixed by one end only, on its side face and gear into a trundle wheel.

A trundle wheel has no teeth, properly speaking. Instead of teeth, it has pins as shown on illustration, fig. 273, arranged like the rungs of a ladder between two walls. See page 201.

Trains of Gears.--When two wheels mesh--that is, engage with each other--as in fig. 263, one axle revolves in the opposite direction to the other; but when internal gears mesh as shown in fig. 272, the shafts revolve in the same direction; three or more gears running together are often called a train of gears.

Maximum speed of gears under favorable conditions for safety is comparatively--

Ordinary cast-iron wheels, 1,800 feet per minute. Helical cast-iron wheels, 2,400 feet per minute. Mortise wood cog wheels, 2,400 feet per minute. Ordinary cast-steel wheels, 2,600 feet per minute. Helical cast-steel wheels, 3,000 feet per minute. Cast-iron machine cut wheels, 3,000 feet per minute.

It is not, however, advisable to run gears at their maximum speeds, as great noise and vibration are caused.

Designing Gears.

This section is introduced into the work for a double purpose; 1, as an exercise in drawing; 2, as a study in accurate measurements. It is a sample of the work that the advanced student in mechanical drawing will be confronted with as he puts in practice the theory of the art of drawing.

Some sample rules are given in the following pages to aid in calculations relating to gears, and still others are given under the section “Useful Rules and Tables” at the end of the volume; these are to be carefully studied.

To accurately divide the pitch circle of a gear wheel by hand requires both patience and skill. On the accuracy of spacing lies the essential requisite of a good gear wheel.

The drawing in plate, fig. 274, illustrates a pair of spur wheels, shown in gear, the office instructions for which being:

“Required, a detail plan of a pair of spur wheels; dimensions: wheel, 76 teeth, 3¹⁄₂ inches pitch, 7-inch eye, 6 arms; pinion, 19 teeth; scale, 1¹⁄₂ inches = 1 foot.”

The drawing, as illustrated, is the result of the above instructions, all pencil lines being removed, and this result is worked out as follows:

76 teeth × 3¹⁄₂ inches, pitch = 266 inches in circum. = 7 ft. 0¹¹⁄₁₆ in. diam. = 3 ft. 6¹¹⁄₃₂ in. radius; with this measurement as represented on scale, draw line P P on drawing. This is called the pitch line.

Draw next diameter line, produce or extend this diameter line for pinion, and with radius of 10¹⁹⁄₃₂ (19 teeth × 3¹⁄₂) from pitch line of wheel, draw pitch line of pinion.