Part 34

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.