Machinery's Handbook, 31st Edition
Bevel Gearing
2263
Rules and Formulas for Calculating Dimensions of Milled Bevel Gears To Find Rule Formula Addendum Divide 1 by the diametral pitch. S = 1 ÷ P Dedendum Divide 1.157 by the diametral pitch. S + A = 1.157 ÷ P Whole Depth of Tooth Divide 2.157 by the diametral pitch. W = 2.157 ÷ P Rules and Formulas for Calculating Dimensions of Milled Bevel Gears (Continued)
Divide 1.571 by the diametral pitch.
Thickness of Tooth at Pitch Line
T = 1.571 ÷ P
Pitch Cone Radius
Divide the pitch diameter by twice the sine of the pitch cone angle. Subtract the width of face from the pitch cone radius, divide the remainder by the pitch cone radius and multiply by the addendum. Subtract the width of face from the pitch cone radius, divide the remainder by the pitch cone radius and multiply by the thickness of the tooth at pitch line. Divide the addendum by the pitch cone radius to get the tangent. Divide the dedendum by the pitch cone radius to get the tangent. Divide the pitch cone radius by 3 or divide 8 by the diametral pitch, whichever gives the smaller value.
sin C D 2 # α = s S C C F # = −
Addendum of Small End of Tooth Thickness of Tooth at Pitch Line at Small End
t T C C F # = −
Addendum Angle Dedendum Angle Face Width (Max.)
C S θ =
tan
C S A
tan
φ = +
F C F P 3 8 or = =
Circular Pitch
Divide 3.1416 by the diametral pitch.
ρ = 3.1416 ÷ P
Face Angle
Add the addendum angle to the pitch cone angle Subtract both the pitch cone angle and the addendum angle from 90 degrees. Subtract the dedendum angle from the pitch cone angle.
γ = α + θ
Compound Rest Angle for Turning Blank
δ = 90 ° − α − θ
Cutting Angle
ζ = α − φ
Angular Addendum Multiply the addendum by the cosine of the pitch cone angle.
K = S × cos α
Outside Diameter
Add twice the angular addendum to the pitch diameter. Multiply one-half the outside diameter by the cotangent of the face angle. Subtract the width of face from the pitch cone radius; divide the remainder by the pitch cone radius and multiply by the apex distance. Divide the number of teeth by the cosine of the pitch cone angle.
O = D + 2 K
Vertex or Apex Distance
cot J O 2 # γ = j J C C F # = −
Vertex Distance at Small End of Tooth Number of Teeth for which to Select Cutter
cos N N ′ α =
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