Machinery's Handbook, 31st Edition
298 Shafts millimeters; G = torsional modulus of elasticity in newtons per square millimeter; and α = angular deflection of shaft in degrees. According to some authorities, the allowable twist in steel transmission shafting should not exceed 0.08 degree per foot length of the shaft. The diameter D of a shaft that will per mit a maximum angular deflection of 0.08 degree per foot of length for a given torque T or for a given horsepower P can be determined from the formulas: (14a) or (14b) Using metric SI units and assuming an allowable twist in steel transmission shaft ing of 0.26 degree per meter length, Formulas (14a) and (14b) become: . D T 226 4 = or . D N P 1257 4 # = where D = diameter of shaft in millimeters; T = torsional moment in newton- millimeters; P = power in kilowatts; and N = revolutions per minute. Another rule that has been generally used in mill practice limits the deflection to 1 de- gree in a length equal to 20 times the shaft diameter. For a given torque or horsepower, the diameter of a shaft having this maximum deflection is given by: (15a) or (15b) Example: Find the diameter of a steel lineshaft to transmit 10 horsepower at 150 revolu tions per minute with a torsional deflection not exceeding 0.08 degree per foot of length. Solution: By Formula (14b), . . D 46 150 10 2 35 inches 4 # = = This diameter is larger than that obtained for the same horsepower and rpm in the exam ple given for Formula (5b) in which the diameter was calculated for strength consider ations only. The usual procedure in the design of shafting which is to have a specified maximum angular deflection is to compute the diameter first by means of Formulas (13), (14a), (14b), (15a), or (15b) and then by means of Formulas (3a), (3b), (4b), (5b), or (6b), using the larger of the two diameters thus found. Linear Deflection of Shafting.— For steel line shafting, it is considered good practice to limit the linear deflection to a maximum of 0.010 inch per foot of length. The maximum distance in feet between bearings for average conditions, in order to avoid excessive linear deflection, is determined by the formulas: L = . D 895 3 2 for shafting subject to no bending action except its own weight L = . D 52 3 2 for shafting subject to bending action of pulleys, etc. in which D = diameter of shaft in inches and L = maximum distance between bearings in feet. Pulleys should be placed as close to the bearings as possible. In general, shafting up to 3 inches in diameter is almost always made from cold-rolled steel. This shafting is true and straight and needs no turning, but if keyways are cut in the shaft, it must usually be straightened afterwards, as the cutting of the keyways relieves the tension on the surface of the shaft produced by the cold-rolling process. Sizes of shafting from 3 to 5 inches in diameter may be either cold-rolled or turned, more frequently the latter, and all larger sizes of shafting must be turned because cold-rolled shafting is not available in diameters larger than 5 inches. . D T 029 4 = . D = N P 46 4 # . D T 01 3 = . D = N P 40 3 #
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