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 thesection“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 planof a pair of spur wheels; dimensions: wheel, 76 teeth, 31⁄2inches pitch, 7-inch eye, 6 arms; pinion, 19 teeth; scale, 11⁄2inches = 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 × 31⁄2inches, pitch = 266 inches in circum. = 7 ft. 011⁄16in. diam. = 3 ft. 611⁄32in. radius; with this measurement as represented on scale, draw lineP Pon 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 31⁄2inches 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 fromP L, length of tooth to point (= pitch × 0.35) andP Lto root (= pitch × 0.4), draw circles for outside of teethNand root of toothO; 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 fromcenterof 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 Pshows 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.
Note.—It must be remembered that no fixed standard has ever been agreed upon for these proportions, and workshops differ considerably in practice.
Spur wheelsFig. 274.
Fig. 274.
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.
GearFig. 275.
Fig. 275.
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 ofthe arc. In determining the number of teeth or pitch of wheels on this principle, the pitch is reckoned on thediameterof 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 takenby 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 thepitch linesor 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 thediameter of a gear-wheelmultiply the number of teeth by the pitch, divide by 3.1416.
To find thepitch of a gear-wheelmultiply the diameter by 3.1416 and divide by the number of teeth.
To find thenumber of teeth in a gear-wheelmultiply the diameter by 3.1416 and divide by the pitch.
Thebreadth of wheels, where practicable, should be at least three times the pitch.
ProportionsFig. 276.
Fig. 276.
Fig. 276shows 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 31⁄2tenths, 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:
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 theteethof 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 acut 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. 275shows 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.
AAis the horizontal center line,BB,BBthe vertical center lines,IIandIIthe pitch lines,Nthickness of tooth,Ospace of tooth,Dtotal depth of tooth,Cbreadth of face,Fdiameter on pitch line,Pdiameter over all,Gdiameter of hub,Ediameter of hole,Hdepth of hole,Lthickness of rim,Mthickness 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
CraneFig. 277.
Fig. 277.