Machinery's Handbook, 31st Edition
Shafts
297
For main power-transmitting shafts:
. N P 177 10 6 3 #
. P D N 177 10 6 3 # =
D
(10a)
or
(10b)
=
For small, short shafts:
. N P 083 10 6 3 #
. P D N 083 10 6 3 # =
D
(11a)
or
(11b)
=
where P is in kilowatts, D is in millimeters, and N = revolutions per minute. Example: What should be the diameter of a power-transmitting shaft to transmit 150 kW at 500 rpm? . D 500 1 77 10 150 81 millimeters 6 3 # # = = Example: What power would a short shaft, 50 millimeters in diameter, transmit at 400 rpm?
50 400 60 kilowatts 6 3 # # =
. P 083 10 =
Torsional Deflection of Circular Shafts.— Shafting must often be proportioned not only to provide the strength required to transmit a given torque, but also to prevent torsional deflection (twisting) through a greater angle than has been found satisfactory for a given type of service. For a solid circular shaft the torsional deflection in degrees is given by: (12) Example: Find the torsional deflection for a solid steel shaft 4 inches in diameter and 48 inches long, subjected to a twisting moment of 24,000 inch-pounds. By Formula (12), , , , . 4 11 500 000 584 24 000 48 0 23 degree 4 # # # α= = D G Tl 584 4 Formula (12) can be used with metric SI units, where α = angular deflection of shaft in degrees; T = torsional moment in newton-millimeters; l = length of shaft in millimeters; D = diameter of shaft in millimeters; and G = torsional modulus of elasticity in newtons per square millimeter. Example: Find the torsional deflection of a solid steel shaft, 100 mm in diameter and 1300 mm long, subjected to a twisting moment of 3 3 10 6 newton-millimeters. The torsional modulus of elasticity is 80,000 newtons/mm 2 . By Formula (12) α=
, 100 80 000 584 3 10 1300 0 285 degree 4 6 # # # # . =
α=
The diameter of a shaft that is to have a maximum torsional deflection α is given by: (13) Formula (13) can be used with metric SI units, where D = diameter of shaft in millimeters; T = torsional moment in newton-millimeters; l = length of shaft in G α . D = Tl 49 4 #
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