Machinery's Handbook, 31st Edition
2296 Ratchet Gearing P LSN FM = This formula has been used in the calculation of ratchet gears for crane design. Module System Gear Design.— The module of a gear is equal to the pitch diameter divided by the number of teeth, whereas diametral pitch is equal to the number of teeth divided by the pitch diameter. The module system (see accompanying table and diagram) is in general use in countries that have adopted the metric system; hence, the term module is usually understood to mean the pitch diameter in millimeters divided by the number of teeth. The module system, however, may also be based on inch measurements and then it is known as the English module to avoid confusion with the metric module. Module is an ac- tual dimension, whereas diametral pitch is only a ratio. Thus, if the pitch diameter of a gear is 50 millimeters and the number of teeth 25, the module is 2, which means that there are 2 millimeters of pitch diameter for each tooth. The table Tooth Dimensions Based Upon Module System shows the relation among module, diametral pitch, and circular pitch. German Standard Tooth Form for Spur and Bevel Gears DIN 867
Module x 3.1416
Module
20
The flanks or sides are straight (involute system) and the pressure angle is 20 degrees. The shape of the root clearance space and the amount of clearance depend upon the method of cutting and special re- quirements. The amount of clearance may vary from 0.1 × module to 0.3 × module. To Find Module Known Circular Pitch Known Addendum Equals module 0.31823 × Circular pitch Dedendum 1.157 × module* 1.167 × module** 0.3683 × Circular pitch* 0.3714 × Circular pitch**
Working Depth
2 × module
0.6366 × Circular pitch 0.6866 × Circular pitch* 0.6898 × Circulate pitch**
2.157 × module* 2.167 × module**
Total Depth
Tooth Thickness on Pitch Line
1.5708 × module
0.5 × Circular pitch Formulas for dedendum and total depth, marked (*) are used when clearance equals 0.157 × module. Formulas marked (**) are used when clearance equals one-sixth module. It is common practice among American cutter manufacturers to make the clearance of metric or module cutters equal to 0.157 × module.
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