Machinery's Handbook, 31st Edition
2268 Bevel Gearing opposite direction the same amount from a position central with the cutter, and is rotated to line up the cutter with a tooth space at the small end. A trial cut is then taken, which will leave the tooth being milled a little too thick, provided the cutter is thin enough—as it should be—to pass through the small end of the tooth space of the finished gear. This trial tooth is made the proper thickness by rotating the blank toward the cutter. To test the amount of offset, measure the tooth thickness (with a vernier caliper) at the large and small ends. The caliper should be set so that the addendum at the small end is in proper proportion to the addendum at the large end; that is, in the ratio ( C − F )/ C (see Fig. 2).
S + A
s + A
E
(
C – F ) C
s + A = S
+A
Fig. 2. In taking these measurements, if the thicknesses at both ends (which should be in this same ratio) are too great, rotate the tooth toward the cutter and take trial cuts until the proper thickness at either the large or small end is obtained. If the large end of the tooth is the right thickness and the small end too thick, the blank was offset too much; inversely, if the small end is correct and the large end too thick, the blank was not set enough off center, and, either way, its position should be changed accordingly. The formula and table previously referred to will enable a properly turned blank to be set accurately enough for general work. The dividing head should be set to the cutting angle β (see Fig. 2), which is found by subtracting the addendum angle θ from the pitch cone angle α . After a bevel gear is cut by the method described, the sides of the teeth at the small end should be filed as indicated by the shade lines at E ; that is, by filing off a triangular area from the point of the tooth at the large end to the point at the small end, thence down to the pitch line and back diagonally to a point at the large end. Circular Thickness, Chordal Thickness, and Chordal Addendum of Milled Bevel Gear Teeth.— In the formulas that follow, T = circular tooth thickness on pitch circle at large end of tooth; t = circular thickness at small end; T c and t c = chordal thickness at large and small ends, respectively; S c and s c = chordal addendum at large and small ends, respectively; D = pitch diameter at large end; and C , F , P , S , s , and α are as defined on page 2260 . . cos T P T T D T 15708 c 3 = = − S S c T 2 α = +
4
D
6
2
C T C F t t c − ^ h
cos D F t 2
D F t 3 −
α
s s c
t
=
= −
= +
6 2 ^
sin
4 2 − ^
sin
2
h
h
α
α
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