Machinery's Handbook, 31st Edition
2220 Spur Gearing Tooth Thickness Allowance for Shaving.— Proper stock allowance is important for good results in shaving operations. If too much stock is left for shaving, the life of the shaving tool is reduced and, in addition, shaving time is increased. The following figures represent the amount of stock to be left on the teeth for removal by shaving under average condi- tions: For diametral pitches of 2 to 4, a thickness of 0.003 to 0.004 inch (0.0762–0.1016 mm)—one-half on each side of the tooth; for 5 to 6 diametral pitch, 0.0025 to 0.0035 inch (0.0635–0.0889 mm); for 7 to 10 diametral pitch, 0.002 to 0.003 inch (0.0508–0.0762 mm); for 11 to 14 diametral pitch, 0.0015 to 0.0020 inch (0.0381–0.0508 mm); for 16 to 18 diametral pitch, 0.001 to 0.002 inch (0.0254–0.0508 mm); for 20 to 48 diametral pitch, 0.0005 to 0.0015 inch (0.0127–0.0381 mm); and for 52 to 72 diametral pitch, 0.0003 to 0.0007 inch (0.00762–0.01778 mm). The thickness of the gear teeth may be measured in several ways to determine the amount of stock left on the sides of the teeth to be removed by shaving. If it is necessary to measure the tooth thickness during the preshaving operation while the gear is in the gear shaper or hobbing machine, a gear tooth caliper or pins would be employed. Caliper methods of measuring gear teeth are explained in detail on page 2226 for measurements over single teeth, and on page 2315 for measurements over two or more teeth. When the preshaved gear can be removed from the machine for checking, the center distance method may be employed. In this method, the preshaved gear is meshed without backlash with a gear of standard tooth thickness and the increase in center distance over standard is noted. The amount of total tooth thickness over standard on the preshaved gear can then be determined by the formula: t 2 = 2 tan φ × d , where t 2 = amount that the total thickness of the tooth exceeds the standard thickness, φ = pressure angle, and d = amount that the center distance between the two gears exceeds the standard center distance. Circular Pitch for Given Center Distance and Ratio.— When it is necessary to use a pair of gears of given ratio at a specified center distance, it may be found that no gears of standard diametral pitch will satisfy the center distance requirement. Hence, circular pitch gears may be selected. To find the required circular pitch p , when the center distance C and total number of teeth N in both gears are known, use the following formula: . p N C 62832 # = Example: A pair of gears having a ratio of 3 is to be used at a center distance of 10.230 inches. If one gear has 60 teeth and the other 20, what must be their circular pitch? . . . p inch 60 20 10 230 6 2832 0 8035 # = + = Circular Thickness of Tooth when Outside Diameter is Standard.— For a full-depth or stub tooth gear of standard outside diameter, the tooth thickness on the pitch circle (circular thickness or arc thickness) is found by the following formula: . t P = 15708 where t = circular thickness and P = diametral pitch. In Fellows stub tooth gears the diame tral pitch used is the numerator of the pitch fraction (for example, 6 if the pitch is 6 ∕ 8). Example 1: Find the tooth thickness on the pitch circle of a 14 1 ∕ 2 -degree full-depth tooth of 12 diametral pitch. . . t 12 = 1 5708 = 0 1309 inch Example 2: Find the tooth thickness on the tooth circle of a 20-degree full-depth involute tooth having a diametral pitch of 5. . . , . t 5 1 5708 0 31416 0 3142 say inch = =
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