Part 9

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.

Take any point in this pitch line of wheel, mark off 3¹⁄₂ inches as represented on scale, mark this around the pitch line, it will be the center of each of the 76 teeth; then the breadth of thickness of each tooth (= pitch × 0.475) must be marked from these centers, then mark from _P L_, length of tooth to point (= pitch × 0.35) and _P L_ to root (= pitch × 0.4), draw circles for outside of teeth _N_ and root of tooth _O_; now with compass set to the pitch (3¹⁄₂) of the wheel, draw the outer portion from pitch line of tooth.

The radius will center in the pitch line of next tooth where thickness of tooth has been marked; after finishing outer portion of both sides of teeth, set the compass from _center_ of tooth with radius to the thickness marked on pitch line and draw the portion of tooth from pitch line to root.

Now mark off with dividers and draw thickness of rim (= pitch × 0.5), divide this line into six parts, draw radii for centers of arms; draw the bore hole 7″ and the thickness of metal for hub same as pitch.

On radii lines of arms, draw the breadth of arm at rim (= pitch and thickness of tooth), increase in breadth approaching the center (1″ per foot), draw the thickness of feather of arm (= pitch × 0.35); draw web on inside of rim (= pitch × 0.375); fill in arcs for the joining of arms in rim and hub (radii = pitch × 0.8) and feather to rim and hub (radii = pitch × 0.37).

Proceed in similar manner, completing the teeth of pinion, and when pencil lines are all in, ink the drawing, erasing all needless lines.

_P P_ shows the pitch line; _B_, thickness of tooth; _c_, breadth of space; _A_, the pitch; _E_, clearance at root; _N_, the addendum of tooth; _O_, the root of tooth; _H_, length of tooth from pitch line to point; _I_, length of tooth pitch line to root; _G_, whole length of tooth; _F_, thickness of rim; _J_, web or feather on rim; _K_, breadth of arm; _L_, thickness of feather; _M_, hub, or thickness round the eye.

NOTE.--It must be remembered that no fixed standard has ever been agreed upon for these proportions, and workshops differ considerably in practice.

The number of teeth, their proportions, pitch and diameter of pitch circle are frequently determined on the “Manchester” principle. This system originated in Manchester (Eng.), and is now generally used in the United States for determining diameters and number of teeth, which, of course, regulate speeds. The principle is not applicable to large wheels, but is limited in its application to small wheels, or wheels having “fine pitch,” as will be seen in the following explanation, which is introduced as very useful and indispensable knowledge for the acquisition of the student in mechanical drawing.

The “pitch” of teeth has already been stated to be the distance from center of one tooth to the center of another on the “pitch line,” measured on the chord of the arc. In determining the number of teeth or pitch of wheels on this principle, the pitch is reckoned on the _diameter_ of the wheel, _in place of the circumference_, and distinguished as wheels of “4 pitch,” “6 pitch,” “8 pitch,” etc. In other words, this means that there are four, six, or eight teeth in the circumference of the wheel for every inch of diameter.

In designing gears to transmit power the stress on a tooth is calculated; it determines the breadth or width and also the thickness of the tooth on pitch line; the space between the teeth is in proportion to the thickness of tooth, and the thickness of both combined (one tooth and one space), measured on the pitch line or circle, is the pitch of the wheel.

From the pitch all the proportions and measurements for the sizes and strength of the parts of the wheel are taken _by rule_, and a symmetrical form is produced.

In machine drawing the practice is to represent wheels by circles only; the teeth are never shown except on enlarged details and then only in very rare instances; the circles drawn are always the _pitch lines_ or the rolling points of contact of the wheels.

The addendum circle is seldom if ever used in practical drawing. Should it be necessary to show it in an exceptional case, the circle would be represented by “dotted” line.

The shape of tooth and mode of constructing it, as practiced in drawing offices, differs from the true theoretical curve of the tooth, although very minutely.

In all calculations for the speed of toothed gears the estimates are based upon the pitch line, the latter standing in the same place as the circumference of a pulley.

To find the _diameter of a gear-wheel_ multiply the number of teeth by the pitch, divide by 3.1416.

To find the _pitch of a gear-wheel_ multiply the diameter by 3.1416 and divide by the number of teeth.

To find the _number of teeth in a gear-wheel_ multiply the diameter by 3.1416 and divide by the pitch.

The _breadth of wheels_, where practicable, should be at least three times the pitch.

Fig. 276 shows a scale for proportions of teeth; it is divided into tenths and used thus:

Say wheel is 2″ pitch, then from pitch circle to addendum will be 3¹⁄₂ tenths, and from pitch circle to root of tooth will be 4 tenths measured at the 2″ line on scale, and so on.

The decimal proportions already given in example, page 210, are adopted in many workshops. Many others use the proportions approved of by Sir William Fairbairn, which are:

Table of proportion of gears:

Depth of tooth above pitch line .35 of the pitch. Depth of tooth below pitch line .40 of the pitch. Working depth of tooth .70 of the pitch. Total depth of tooth .75 of the pitch. Clearance at root .05 of the pitch. Thickness of tooth .45 of the pitch. Width of space .55 of the pitch.

The diameter of a wheel or pinion is invariably the diameter measured on pitch circle, except it is specially described otherwise, thus the diameter “over all,” etc.

The shape of the curved face of the teeth of gears extending from the root to the addendum is the curve conforming to the passage of the teeth described on its fellow entering and leaving, as they rotate or roll together on their pitch circles.

The curve of teeth outside the pitch circle is called “the face,” and the curve from pitch circle to root is called “the flank.”

The difference between the width of a space and the thickness of a tooth is called clearance or side clearance.

The play or movement permitted by clearance is called the backlash; clearance is necessary to prevent the teeth of one wheel becoming locked in the spaces of the other.

Wheels are in gear or geared together when their pitch lines engage, _i. e._, when the pitch circles meet.

Wheels to be geared together must have their teeth spaced the same distance apart, or in other words, of the same pitch.

The teeth of spur wheels are arranged on its periphery parallel to the wheel axis, or shaft on which it is hung.

The teeth of a bevel wheel or bevel gears are always arranged at an angle to the shaft.

When the _teeth_ of bevel gears form an angle of 45° they are called miter wheels.

Miter wheels to gear must be of equal sizes.

A crown wheel is a disc that has teeth which are on its side face; that is, teeth on a flat circular surface all parallel to the axis of the wheel.

A rack has teeth on a flat surface or plane all parallel to one another.

A gear cut by machine is called a _cut gear_. It has teeth with less clearance than cast wheels, which are not so true or perfect, and therefore require more clearance.

A worm with even a light load is liable to heat and cut if run at over 300 feet of rubbing surface travel. The wheel teeth will keep cool, as they form part of a large radiating surface; the worm itself is so small that its heat is dissipated slowly.

A worm throws a severe end thrust or strain on its shaft.

_Steel Gears._--There is great economy in the use of cast-steel over cast-iron in gears; the average life of the former is nearly twice as great as of cast-iron gears. And, apart from their longer life and efficiency, there is less danger of breaking.

The most accurate teeth, strongest and most uniform in wearing, are to be found in steel gears cut from solid stock, or made by cutters of proper shape.

Fig. 275 shows an elevation and a vertical section of a spur wheel. From these views the various parts in spur gears can be better understood, as they are represented here in combination, and the wheel in its entirety.

_AA_ is the horizontal center line, _BB_, _BB_ the vertical center lines, _II_ and _II_ the pitch lines, _N_ thickness of tooth, _O_ space of tooth, _D_ total depth of tooth, _C_ breadth of face, _F_ diameter on pitch line, _P_ diameter over all, _G_ diameter of hub, _E_ diameter of hole, _H_ depth of hole, _L_ thickness of rim, _M_ thickness of web.

Much has been and still is being written on gearing. No general rule is followed by the writers; the elementary principles given will enable the student to master spur gearing, and bevel and combinations of many kinds of wheels will afterwards be found easier to delineate than the numerous lines seem to indicate.

Working Drawings.

From the “plans” made in the office are produced “working drawings”--which represent in detail the work to be done to exact measurement and of material, as indicated, by the pattern-maker, the foundry, the forge, the shop, and finally, by the erector of the completed mechanism.

How to satisfactorily fulfill the directions contained in these drawings, representing only a part of the work, so that it will fit, with needed accuracy, to all other parts of the design, is the task before each separate worker.

It is by means of this division of the process of manufacture through these drawings, that scores and hundreds of men can be employed at the same time upon a single engine or machine; thus, while handwork has been superseded by machines in many quarters, the art of drawing has not been narrowed nor diminished, for no drawings or designs have yet been made by machinery, nor are they likely to be.

It is thus that a good designer and draughtsman “projects” or extends himself, to the advantage of many fellow workers.

The drawing, fig. 277, shows a simple form of pillar crane: it consists of an upright cast-iron pillar, which is bolted on a cap stone, under which is the foundation plate not shown in the drawing; the boom is of rolled steel, supported by steel tie rods, and provided with rollers at the base; the hoisting gear is shown in broken lines and circles; all as seen in the drawing.

Figs. 278, 279 and 280 show a drawing of a “hydraulic beam bending machine” in three views; fig. 280 is a plan, fig. 278 is an end elevation, and fig. 279 a side elevation, and a portion of the latter in section shows the interior construction.

NOTE.--These three views are a practical illustration of drawings for a machine of the following dimensions: this machine has a bed 3 × 5 feet in area, with 27 holes in each side for the bending pins. The frame and cylinders are made of cast iron, the rams of machinery steel, and the slides for holding the bending blocks, of steel casting. The distance between the bending blocks is 17 inches. The cylinders are copper lined, 8 inches diameter, and the rams have a 6-inch stroke. The rams, which are independent and single acting, are returned by counterweights placed as shown under the table. The cylinders can be operated independently from either side of the machine by an arrangement of valves and levers. The machine complete weighs about 7,500 lbs.

The drawing, page 222, shows three views of a power punching press.

Fig. 282 is a side elevation.

Fig. 283 a front elevation.

Fig. 281 a vertical sectional view; from these views the proportion, general arrangement and disposition of the automatic devices can be easily understood; it may be well to call particular attention to the automatic clutch on the top shaft and the tripping device.

This drawing, fig. 284, shows a side elevation in section of a self-adjusting piston-rod packing.

_A_ is the gland, _B_ is the piston rod, _C_ is a brass sleeve which contains the packing _D_, _E_ is the cylinder cover, _F_ is a coil spring. It will be seen that the spring _F_ abuts on a bushing in the bottom of the stuffing box and is prevented from scoring the piston rod by stepping over the ends of the bushing and follower. All as shown in the drawing.

The drawing, fig. 285, shows a sectional view of a large pulley fixed on a “quill,” or hollow shaft: the driving shaft passes through the hollow shaft and is attached to the friction clutch shown at the right-hand end; this friction clutch drives the hollow shaft and pulley.

Fig. 286 shows the mechanism, called the link-motion, employed to reverse an engine, or to enable it to be run in either direction. Many forms of link-motion have been devised, but the Stephenson form, as shown in the figure, is, however, the one in almost universal use.

Figs. 287 to 289 represent a bumping-post for the end of railway tracks, reproduced on an enlarged scale from the columns of the _Engineering News_.

In addition to the lettering and dimensions, admirably shown in the drawings, the following description is appended to show how printed text and mechanical drawings mutually aid in practical--or commercial--usage.

The unique feature of the arrangement shown, is that the center line of the post does not coincide with the track, thus adapting itself to the nature of the blows of a car-bumper, as received in the single-post style of the mechanism.

BUMPING POST FOR RAILWAY TRACKS.

The post is a 15-in. steel I-beam, resting on a base plate ³⁄₄-in. thick, and supported by anchor rods 1³⁄₄ ins. diameter, with upset ends held by nuts on a heavy forging bolted to the top of the post. These rods extend forward and outward to clear the rails, and then pass vertically through a 4 × 6-in. angle iron crosstie, and an ordinary wooden tie, extending down to an anchor block or deadman buried in the ground 6¹⁄₂ ft. below the top of the rail.

Vertical braces or spreaders are fitted between the anchor timber and a longitudinal timber under the ties, so as to prevent the loosening of the anchor rods when the post is struck. The rods are held in position against the rails by steel forgings bolted to the rail with 1-in. turned bolts. An oak striking block, 12 × 12 ins., 3 ft. long, is bolted between angle iron brackets on the face of the post.

To Read Working Drawings.

One of the advantages resulting from a knowledge of practical draughting is, that it enables a mechanic to _read_ a drawing when given him as a guide for his work. It is getting every day more general among draughtsmen to figure exactly and minutely every part of their drawings which are made to a scale.

Drawings are almost always made “finished size,” that is, the dimensions are for the work when it is completed. Consequently all the figures written on the different parts indicate the exact size of the work when finished, without any regard to the size of the drawing itself, which may be made to any reduced and convenient scale.

Even in full size drawings this system of figuring is not objectionable. It is a system which should be followed whenever a drawing is made “to work to,” for it allows the workman to comprehend at a glance the size of his work and the pieces he has to get made. Figuring makes a drawing comprehensible even to those who cannot make drawings.

A working drawing should be made, primarily, as plain as possible by the draughtsman; second, the workman should patiently and carefully study it, so that it is thoroughly understood.

In studying a drawing, the object it is intended to represent should be made as familiar as possible to the mind of the student, so that he may fill out in imagination the parts designedly left incomplete--as in a gear wheel where only two or three teeth are drawn in, that he may see, mentally, the whole.

The following is a description of reading drawings when dimensions are not figured. Here we have a piece of machinery represented by fig. 290, and the information we have is that it is to scale, three inches = one foot. Now, with scale and dividers, we can arrive at its actual dimensions.

Measurements should be first taken _with the dividers from the drawing_, and then the dividers applied to the scale to which the drawing is made; this scale is always marked on the working drawing; if the dividers are set to the length of the base of the example, fig. 290, they will measure, on an ordinary two-foot rule, three and three-fourths inches, _but if applied to the three-inch scale they will read_ one foot three inches, the actual length of the part; the “reading” is from the scale; thus, in both figures the drawings are “three-inch scale.”

Now, 3 inches is one-fourth of a foot, hence 3³⁄₄ × 4 = 1 ft. 3 in., the full size, and so on for all parts of the drawing.

Fig. 291 shows _a side view_ of the “steady rest,” illustrated in front elevation, fig. 290; from the scale as before we get the sizes; the two views combined give length, breadth and thickness of the parts.

In some figures it is necessary to show end views, also section views, to enable all measurements to be read from the drawing.

Patent Office Drawing Rules.

U. S. PATENT OFFICE RULES.

AS APPLIED TO PREPARATION OF DRAWINGS.