Machinery's Handbook, 31st Edition
2262
Bevel Gearing
Vertex Distance = J
Whole Depth of Tooth = W
Angular Addendum = K
Addendum = S Dedendum = S + A
Axis of Gear
VERTEX
Dedendum Angle = φ
Addendum Angle =
θ
Edge Angle = α
δ
Fig. 1b. Bevel Gear Nomenclature The formulas for milled bevel gears should be modified to make the clearance at the bottom of the teeth uniform instead of tapering toward the vertex. If this recommendation is followed, then the cutting angle (root angle) should be determined by subtracting the addendum angle from the pitch cone angle instead of subtracting the dedendum angle as in the formula given in the table. Rules and Formulas for Calculating Dimensions of Milled Bevel Gears To Find Rule Formula
sin
R
=
tan
Divide the sine of the shaft angle by the sum of the cosine of the shaft angle and the quotient obtained by dividing the number of teeth in the gear by the number of teeth in the pinion; this gives the tangent. Note: For shaft angles greater than 90 ° the cosine is negative. Subtract the pitch cone angle of the pinion from the shaft angle. Divide the number of teeth by the diametral pitch.
α
N N
P
cos + For 90 ° shaft angle, tan P G P α =
R
Pitch Cone Angle of Pinion
N N
G P
Pitch Cone Angle of Gear Pitch Diameter
α G = ∑ − α P
D = N ÷ P
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