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DIAGRAM FOR CAST-GEAR TEETH

THE accompanying diagram (Fig. 2) for laying out teeth for cast gears will be found useful by the machinist, patternmaker and draftsman. The diagram for circular pitch gears is similar to the one given by Professor Willis, while the one for diametral pitch was obtained by using the relation of diametral to circular pitch.

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By the diagram the relative size of a tooth may be easily determined. For example, if we contemplate using a gear of 2 diametral pitch, by referring to line H K, which shows the comparative distance between centers of teeth, on the pitch line, it will be observed that

2 diametral pitch is but little greater than 1 inches circular pitch, or exactly 1.57 inches circular pitch. This result is obtained by dividing_3.1416 by the diametral pitch (3.1416 divided by 2 equals 1.57). In similar manner, if the circular pitch is known, the diametral pitch which corresponds to it is found by dividing 3.1416 by the circular pitch; for example, the diametral pitch which corresponds to 3 inches circular pitch is by the line H K a little greater than I diametral pitch, or exactly 1.047 (3.1416 divided by 3 equals 1.047). The proportions of a tooth may be determined for either diametral or circular pitch by using the corresponding diagram.

Continue, for illustration, the 2 diametral pitch. We have found, above, the distance between centers of teeth on the pitch line to be a little more than 11⁄2 inches (1.57 inches). The hight of tooth above pitch line B'C' will be found on the horizontal line corresponding to 2 pitch. The distance between the lines A' B' and A' C' on this line may be taken in the dividers and transferred to the scale below. Thus we find the hight of the tooth to be 1⁄2 inch. In the same manner the thickness of tooth B' D', width of space B' E', working depth B' F' and whole depth of tooth B' G' may be determined.

The

The backlash or space between the idle surfaces of the teeth of two gear wheels when in mesh is given by the distance D' E'. clearance or distance between the point of one tooth and the bottom of space into which it meshes is given by the distance F' G'. The backlash and clearance will vary according to the class of work for which the gears are to be used and the accuracy of the molded product. For machine molded gears which are to run in enclosed cases, or where they may be kept well oiled and free from dirt, the backlash and clearance may be reduced to a very small amount, while for gears running where dirt is likely to get into the teeth, or where irregularities due to molding, uneven shrinkage, and like causes, enter into the construction, there must be a greater allowance. The diagram is laid out for the latter case. Those who have more favorable conditions for which to design gears should vary the diagram to suit their conditions. This can be done by increasing B D and decreasing B E, and by increasing B C or decreasing B G, or both, to get the clearance that will best meet the required conditions. The same kind of diagram could be laid out for cut gears, but as tables are usually at hand which give the dimensions of the parts of such gears, figured to thousandths of an inch, it would be as well to consult one of these.

LAYING OUT SPUR GEAR BLANKS

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DECIDE upon the size wanted, remembering that 12-pitch teeth are deep and 8-pitch Should as in the drawing-deep, etc. it be 8 pitch, as shown in the cut, draw a circle measuring as many eighths of an inch in diameter as there are to be teeth in the gear. This circle is called the Pitch Line. Then with a radius of an inch larger, draw another circle from the same center, which will give the outside diameter of the gear, or larger than the pitch circle. Thus we have for the diameter of an 8-pitch gear of 24 teeth, 26. Should there be 16 teeth, as in the small spur gear in the cut, the

outside diameter would be 18, the number of teeth being always two less than there are eighths when it is 8 pitch — in the outside diameter.

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The distance from the pitch line to the bottom of the teeth is the same as to the top, excepting the clearance, which varies from the pitch to of the thickness of the tooth at the pitch line. This latter is used by Brown & Sharpe and many others, but the clearance being provided for in the cutters the two gears would be laid out to mesh together just .

These rules apply to all pitches, so that the outside diameter of a 5-pitch gear with 24 teeth would be 26; if a 3-pitch gear with 40 teeth it would be 42. Again, if a blank be 4 (25) in diameter, and cut 6 pitch, it should contain 23 teeth.

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ACTUAL SIZE OF DIAMETRAL PITCHES

It is not always easy to judge or imagine just how large a given pitch is when measured by the diametral system. To make it easy to see just what any pitch looks like the actual sizes of twelve diametral pitches are given on the following page, ranging from 20 to 4 teeth per inch of diameter on the pitch line, so that a good idea of the size of any of these teeth can be had at a glance.

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LAYING OUT SINGLE CURVE TOOTH

A VERY simple method of laying out a standard tooth is shown in Fig. 5, and is known as the single curve method. Having calculated the various proportions of the tooth by rules already given, draw the pitch, outside, working depth and clearance or whole depth circles as shown. With a radius one half the pitch radius draw the semicircle from the center to the pitch circle. Take one quarter the pitch radius and with one leg at top of pitch circle strike arc cutting the semicircle. This is the center for the first tooth curve and locates the base circle for all the tooth arcs. Lay off the tooth thickness and space distances around the pitch circle and draw the tooth curves through these points with the tooth curve radius already found. The fillets in the tooth corners may be taken as one seventh of the space between the tops of the teeth.

Tooth Curve Radius

One quarter of Pitch Radius

One half

Pitch Radius

Clearance or Whole Depth Circle
Working Depth

Base Circle for Tootn Aros

Pitch Diameter

Addendum or Outside Diameter

FIG. 5. Single Curve Tooth

PRESSURE ANGLES

WE next come to pressure angles of gear teeth, which means the angle at which one tooth presses against the other and can best be shown by the pinion and rack, Figs. 6 and 7.

The standard tooth has a 14 degree pressure angle, probably because it was so easy for the millwright to lay it out as he could obtain the angle without a protractor by using the method shown for laying out a thread tool (see Fig. 14). As the sides of an involute rack tooth are straight, and at the pressure angle from the perpendicular, draw the line of pressure at 14 degrees from the pitch line. The base circle of the tooth arcs can be found by, drawing a line from the center of the gear to the line of pressure and at right angles to it as shown, or by the first method, and working from this the tooth

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