Machinery's Handbook, 31st Edition
Spur Gearing 2211 Table 2. Formulas for Tooth Parts, 20-and 25-degree Involute Full-depth Teeth ANSI Coarse Pitch Spur Gear Tooth Forms ANSI B6.1-1968 (R1974) To Find Diametral Pitch, P , Known Circular Pitch, p , Known Fillet Radius (Rack) c r f = 0.300 ÷ P r f = 0.0955 × p Pitch Diameter D = N ÷ P D = 0.3183 × N × p Outside Diameter D O = ( N + 2) ÷ P D O = 0.3183 × ( N + 2) p Root Diameter (Preferred) D R = ( N − 2.5) ÷ P D R = 0.3183 × ( N − 2.5) p (Shaved or Ground Teeth) D R = ( N − 2.7) ÷ P D R = 0.3183 × ( N − 2.7) p Circular Thickness—Basic t = 1.5708 ÷ P t = p ÷ 2 Table 2. (Continued) Formulas for Tooth Parts, 20-and 25-degree Involute Full-depth Teeth ANSI Coarse Pitch Spur Gear Tooth Forms ANSI B6.1-1968 (R1974) a 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. b 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 use of existing hobs or cutters. However, whenever less than standard clearance is used, the location of the TIF diameter should be determined by the method shown in True Involute Form Diameter starting on page 2236 . The TIF diameter must be less than the Contact Diameter determined by the method shown on page 2234 . c The fillet radius of the basic rack should not exceed 0.235/ P for a 20-degree pressure angle rack or 0.270/ P for a 25-degree pressure angle rack for a clearance of 0.157/ P . The basic rack fillet radius must be reduced for teeth with a 25-degree pressure angle having a clearance in excess of 0.250/ P . American National Standard Coarse Pitch Spur Gear Tooth Forms.— The American Na- tional Standard (ANSI B6.1-1968, R1974) provides tooth proportion information on two involute spur gear forms. These two forms are identical except that one has a pressure angle of 20 degrees and a minimum allowable tooth number of 18 while the other has a pressure angle of 25 degrees and a minimum allowable tooth number of 12. (For pinions with fewer teeth, see tooth proportions for long addendum pinions and their mating short addendum gears in Table 7 through Table 9d starting on page 2225 .) A gear tooth standard is established by specifying the tooth proportions of the basic rack. Gears made to this standard will thus be conjugate with the specified rack and with each other. The basic rack forms for the 20-degree and 25-degree standard are shown on the following page; basic formulas for these proportions as a function of the gear diametral pitch and also of the cir cular pitch are given in Table 2. Tooth parts data are given in Table 3. In recent years the established standard of almost universal use is the ANSI 20-degree standard spur gear form. It provides a gear with good strength and without fillet undercut in pinions of as few as eighteen teeth. Some more recent applications have required a tooth form of even greater strength and fewer teeth than eighteen. This requirement has stimulated the establishment of the ANSI 25-degree standard. This 25-degree form will give greater tooth strength than the 20-degree standard, will provide pinions of as few as twelve teeth without fillet undercut and will provide a lower contact compressive stress for greater gear set surface durability.
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