Machinery's Handbook, 31st Edition
Spur Gearing
2217
Formulas for Outside and Root Diameters of Spur Gears that Are Finish-Hobbed, Shaped, or Pre-Shaved Notation
D = Pitch Diameter D O = Outside Diameter D R = Root Diameter P = Diametral Pitch
a = Standard Addendum b = Standard Minimum Dedendum b s = Standard Dedendum b ps = Dedendum for Pre-shaving
14 1 ∕ 2 -, 20-, And 25-degree Involute Full-depth Teeth (19 P and coarser) a D D a P N P 2 2 1 O # = + = + a k . D D b P N P 2 2 1157 R # = − = − a k (Hobbed) b . D D b P N P 2 2 125 R s # = − = − a k (Shaped) c . D D b P N P 2 2 135 R ps # = − = − a k (Pre-shaved) d . D D b P N P 2 2 140 R ps # = − = − a k (Pre-shaved) e 20-degree Involute Fine-pitch Full-depth Teeth (20 P and finer) D D a P N P 2 2 1 O # = + = + a k . . D D b P N P 2 2 12 0002 R = − = − + a k (Hobbed or Shaped) f . . D D b P N P 2 2 135 0002 R ps = − = − + a k (Pre-shaved) g 20-degree Involute Stub Teeth a . D D a P N P 2 2 08 O # = + = + a k D D b P N P 2 2 1 R # = − = − a k (Hobbed) . D D b P N P 2 2 135 R ps # = − = − a k (Pre-shaved) a 14 1 ⁄ 2 -degree full-depth and 20-degree stub teeth are not recommended for new designs. b According to ANSI B6.1-1968 a minimum clearance of 0.157/ P may be used for the basic 20-degree and 25-degree pressure angle rack in the case of shallow root sections and the use of existing hobs and cutters. c According to ANSI B6.1-1968 the preferred clearance is 0.250/ P . d According to ANSI B6.1-1968 the clearance for teeth which are shaved or ground is 0.350/ P . e When gears are preshave cut on a gear shaper the dedendum will usually need to be increased to 1.40/ P to allow for the higher fillet trochoid produced by the shaper cutter; this is of particular importance on gears of few teeth or if the gear blank configuration requires the use of a small diameter shaper cutter, in which case the dedendum may need to be increased to as much as 1.45/ P . This should be avoided on highly loaded gears where the consequently reduced J factor will increase gear tooth stress excessively. f According to ANSI B6.7-1967 the standard clearance is 0.200/ P + 0.002 (min.). g According to ANSI B6.7-1967 the clearance for shaved or ground teeth is 0.350/ P + 0.002 (min.).
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