Machinery's Handbook, 31st Edition
2278 HELICAL GEARING 3. Shafts at Right Angles, Center Distance Approximate.— Sum of helix angles of gear and pinion must equal 90 degrees. Given or assumed: Driven
1) Position of gear having right- or left-hand helix, depending on rotation and direction in which thrust is to be received 2) C a = approximate center distance 3) P n = normal diametral pitch (pitch of cutter) 4) R = ratio of gear to pinion size 5) n = number of teeth in pinion = . R C P 1 141 a n + for 45 degrees; and cos cos cos cos R C P 2 a n β α α β + for any angle
R.H.
R.H.
6) N = number of teeth in gear = Rn 7) α = angle of helix of gear 8) β = angle of helix of pinion To find: a) When helix angles are 45 degrees, 1) D = pitch diameter of gear = .
P N 070711 n
2) d = pitch diameter of pinion = . 3) O = outside diameter of gear = D + P 2 n 4) o = outside diameter of pinion = d + P 2 n 5) T = number of formed cutter (gear) = . N 0353 6) t = number of formed cutter (pinion) = . n 0353 P n 070711 n
7) L = lead of helix of gear = π D 8) l = lead of helix of pinion = π d 9) C = center distance (exact) = D d 2 + b) When helix angles are other than 45 degrees 1) D = cos P N n α 2) d = cos P n n β 3) T = cos N 3 α 2) t = cos n 3 β 5) L = π D cot α 6) l = π d cot β Example: Given or assumed: 1) See illustration; 2) C a = 3.2 inches; 3) P n = 10; and 4) R = 1.5. 5) n = . . . . R C P 1 141 15 1 141 32 10 a n # # + = + = say 18 teeth. 6) N = nR = 18 × 1.5 = 27 teeth; 7) α = 45 degrees; and 8) β = 45 degrees.
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