Machinery's Handbook, 31st Edition
302 Shafts where S t is the maximum allowable tensile stress in pounds per square inch and the other quantities are as previously defined. The formula can be used unchanged with metric SI units, where D = outside diame ter of shaft in millimeters; S t = the maximum allowable tensile stress in newtons per millimeter squared; M = maximum bending moment in newton-millimeters; and T = maximum torsional moment in newton-millimeters. The factors K m , K t , and B are unchanged. Critical Speed of Rotating Shafts.— At certain speeds, a rotating shaft will become dy- namically unstable and the resulting vibrations and deflections can result in damage not only to the shaft but to the machine of which it is a part. The speeds at which such dynamic instability occurs are called the critical speeds of the shaft. On page 205 are given for- mulas for the critical speeds of shafts subject to various conditions of loading and support. A shaft may be safely operated either above or below its critical speed, good practice indi- cating that the operating speed be at least 20 percent above or below the critical. The formulas commonly used to determine critical speeds are sufficiently accurate for general purposes. However, the torque applied to a shaft has an important effect on its critical speed. Investigations have shown that the critical speeds of a uniform shaft are decreased as the applied torque is increased, and that there exist critical torques which will reduce the corresponding critical speed of the shaft to zero. A detailed analysis of the effects of applied torques on critical speeds may be found in a paper, “Critical Speeds of Uniform Shafts under Axial Torque,” by Golomb and Rosenberg, presented at the First US National Congress of Applied Mechanics in 1951. Shaft Couplings.— A shaft coupling is a device for fastening together the ends of two shafts, so that the rotary motion of one causes rotary motion of the other. One of the most simple and common forms of coupling is the flange coupling Fig. 1a and Fig. 1b. It consists of two flanged sleeves or hubs, each of which is keyed to the end of one of the two shafts to be connected. The sleeves are held together and prevented from rotating relative to each other by bolts through the flanges as indicated. Flange Coupling
Fig. 1a. Fig. 1b. Flexible Couplings: Flexible couplings are the most common mechanical means of compensating for unavoidable errors in alignment of shafts and shafting. When correctly applied, they are highly efficient for joining lengths of shafting without causing loss of power from bearing friction due to misalignment, and for use in direct motor drives for all kinds of machinery. Flexible couplings are not intended to be used for connecting a driven shaft and a driving shaft that are purposely placed in different planes or at an angle but are intended simply to overcome slight unavoidable errors in alignment that develop in ser vice. There is a wide variety of flexible coupling designs; most of them consist essentially of two flanged members or hubs, fastened to the shafts and connected by some yielding arrangement. Balance is an important factor in coupling selection or design; it is not suffi cient that the coupling be perfectly balanced when installed, but it must remain in balance after wear has taken place.
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