Machinery's Handbook, 31st Edition
HELICAL GEARING 2281 5. Shafts at Any Angle, Center Distance Approximate.— The sum of the helix angles of the two gears equals the shaft angle, and the gears are of the same hand, if each angle is less than the shaft angle. The difference between the helix angles equals the shaft angle, and the gears are of opposite hand, if either angle is greater than the shaft angle.
Driven
L.H.
Given or assumed: 1) Hand of helix, depending on rotation and direction in which thrust is to be received 2) C a = center distance 3) P n = normal diametral pitch (pitch of cutter) 4) R = ratio of gear to pinion = n N
5) α = angle of helix, gear 6) β = angle of helix, pinion 7) n = number of teeth in pinion nearest
R C P 2 a n
cos cos cos cos β α α β +
for any angle
R C P 2 a n
cos
α
8) and
when both angles are equal
+
1
9) N = number of teeth in gear = Rn To find: 1) D = pitch diameter of gear = cos P N n α 2) d = pitch diameter of pinion = cos P n n β 3) O = outside diameter of gear = D + P 2 n 4) o = outside diameter of pinion = d + P 2 n 5) T = number of teeth marked on cutter for gear = cos N 3 α 6) t = number of teeth marked on cutter for pinion = cos n 3 β 7) L = lead of helix on gear = π D cot α 8) l = lead of helix on pinion = π d cot β 9) C = actual center distance = D d 2 + Example: Given or assumed (angle of shafts, 60 degrees):
1) See illustration 2) C a = 12 inches 3) P n = 8 4) R = 4 5) α = 30 degrees 6) β = 30 degrees 5) n = . cos R C P 1 2 4 1 2 12 8 0 86603 a n # # # α + = +
= 33 teeth
6) N = 4 × 33 = 132 teeth
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