Machinery's Handbook, 31st Edition
2216
Spur Gearing Table 6. Formulas for Tooth Parts—Former American Standard Spur Gear Tooth Forms ASA B6.1-1932
Circular Pitch, p Known
Diametral Pitch, P Known
To Find
2 -Degree Involute Full-depth Teeth
14 1 ∕
Addendum
a = 1.000 ÷ P b = 1.157 ÷ P h k = 2.000 ÷ P h t = 2.157 ÷ P t = 1.5708 ÷ P c = 0.157 ÷ P
a = 0.3183 × p b = 0.3683 × p h k = 0.6366 × p h t = 0.6866 × p t = 0.500 × p c = 0.050 × p a = 0.2546 × p b = 0.3183 × p h k = 0.5092 × p h t = 0.5729 × p t = 0.500 × p c = 0.0637 × p
Minimum Dedendum
Working Depth
Minimum Whole Depth
Basic Tooth Thickness on Pitch Line
Minimum Clearance
20-Degree Involute Stub Teeth
Addendum
a = 0.800 ÷ P b = 1.000 ÷ P h k = 1.600 ÷ P h t = 1.800 ÷ P t = 1.5708 ÷ P c = 0.200 ÷ P
Minimum Dedendum
Working Depth
Minimum Whole Depth
Basic Tooth Thickness on Pitch Line
Minimum Clearance
3 × clearance for 14 1 ∕
2 -degree full-depth teeth and 1 1 ∕ 2 ×
Note: Radius of fillet equals 1 1 ∕
clearance for 20-degree full-depth teeth. Note: A suitable working tolerance should be considered in connection with all minimum recommendations. Fellows Stub Tooth.— The system of stub gear teeth introduced by the Fellows Gear Shaper Co. is based upon the use of two diametral pitches. One diametral pitch, say, 8, is used as the basis for obtaining the dimensions for the addendum and dedendum, while another diametral pitch, say, 6, is used for obtaining the dimensions of the thickness of the tooth, the number of teeth, and the pitch diameter. Teeth made according to this system are designated as 6 ∕ 8 pitch, 12 ∕ 14 pitch, etc., the numerator in this fraction indicating the pitch determining the thickness of the tooth and the number of teeth, and the denominator, the pitch determining the depth of the tooth. The clearance is made greater than in the ordinary gear-tooth system and equals 0.25 ÷ denominator of the diametral pitch. The pressure angle is 20 degrees. This type of stub gear tooth is now used infrequently. Information on the tooth part dimensions may be found in the 18th and earlier editions of Machinery’s Handbook. Basic Gear Dimensions.— The basic dimensions for all involute spur gears may be ob- tained using the formulas shown in Table 1. This table is used in conjunction with Table 3 to obtain dimensions for coarse pitch gears and Table 5 to obtain dimensions for fine pitch standard spur gears. To obtain the dimensions of gears that are specified at a standard circular pitch, the equivalent diametral pitch is first calculated by using the formula in Table 1. If the required number of teeth in the pinion ( N p ) is less than the minimum speci fied in either Table 3 or Table 5, whichever is applicable, the gears must be proportioned by the long and short addendum method shown on page 2227 .
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