Machinery's Handbook, 31st Edition
296
Shafts
For small, short shafts:
P 38 3 =
P D N 38 3 =
(6a) (6b) Shafts that are subjected to shocks, such as sudden starting and stopping, should be given a greater factor of safety resulting in the use of lower allowable stresses than those just mentioned. Example: What should be the diameter of a lineshaft to transmit 10 horsepower if the shaft is to make 150 revolutions per minute? Using Formula (5b), . . D 150 535 10 153 1 16 9 or, say, inches 3 # = = or Example: What horsepower would be transmitted by a short shaft, 2 inches in diameter, carrying two pulleys close to the bearings, if the shaft makes 300 revolutions per minute? Using Formula (6a), P 38 2 300 63 horsepower 3 # = = Torsional Strength of Shafting, Calculations in Metric SI Units.—The allowable twist ing moment for a shaft of any cross section such as circular, square, etc. can be cal culated from: (7) where T = torsional or twisting moment in N-mm; S s = allowable torsional shearing stress in N/mm 2 ; and Z p = polar section modulus in mm 3 . For a shaft delivering power of P kilowatts at N revolutions per minute, the twisting moment T being transmitted is: (8a) or (8b) where T is in newton-millimeters, and ω = angular velocity in radians per second. The diameter D of a solid circular shaft required to transmit a given torque T is: (9a) or (9b) . D S T 51 s 3 = . D NS P 487 10 s 6 3 # = D N T S Z s p # = . N P 955 10 6 # T = T P 10 6 = ω
. S P 51 10 s 6 # ω
3
D
or
(9c)
=
where D is in millimeters; T is in newton-millimeters; P is power in kilowatts; N = revolutions per minute; S s = allowable torsional shearing stress in newtons per square millimeter, and ω = angular velocity in radians per second. If 28 newtons/mm 2 and 59 newtons/mm 2 are taken as the generally allowed stresses for main power-transmitting shafts and small short shafts, respectively, then using these allowable stresses, the power P transmitted by a shaft of diameter D , or the diameter D of a shaft to transmit a given power P may be determined from the follow ing formulas:
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