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COUPLINGS 16.6
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torque at a frequency of not more than 60 per hour. Vibratory torque ( Tkw) is the coupling vibratory rating at 10 hertz (Hz) for elastomeric couplings. The rotary output of the coupling may be uniform (constant velocity) or cyclic (e.g., Hooke s joint). All drive systems experience some vibration. Vibration can exceed the limits of design, which can cause system failure. Flexible couplings are one method of dampening the amount of vibration from either the driver or the driven equipment. When a flexible coupling is used, the vibration is transferred to a material which is designed to absorb it rather than transmit it through the entire drive. Soft materials, such as natural rubber, can absorb greater amounts of vibration than stiffer materials, such as Hytrel or steel. As a comparison, the relative vibration damping capabilities of Buna N rubber, Hytrel, and steel are shown in the transmissibility chart of Fig. 16.1. If a system has misalignment, there are two factors to consider. First, you must use a coupling that can operate between two misaligned shafts. Second, you must be sure that the coupling does not exert excessive forces on the equipment because of misalignment. Perfect alignment between the driver and the load is difficult to obtain and maintain over the life of the system. A cost-effective alternative to precise alignment is a coupling that can accommodate misalignment between two shafts. The amount of misalignment a coupling can accept varies. Steel drive plates, for example, can accept only misalignment equal to their machining tolerances, frequently as little as 0.005 inch (in) parallel. Other couplings can accommodate mis-
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Hytrel is a trademark of E.I. du Pont de Nemours.
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FIGURE 16.1 Effect of damping ratio on torque transmission. A, steel, = 0.01; B, Hytrel, = 0.03; C, Buna N rubber, = 0.13, where Tr is the transmitted torque and Ti the input torque.
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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COUPLINGS 16.7
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alignment up to 45 . The maximum allowable misalignment is a function of the percentage of torque capacity being utilized and the amount of vibratory torque the system is transmitting under perfect alignment. If there is system misalignment, the material used in the coupling is important. Misalignment may cause radial forces to be exerted on the system. If the radial forces are too great, components such as bearings, seals, and shafts can experience undue stresses and fail prematurely. Different materials exert different radial forces; softer materials typically exert less radial force than stiff materials. The natural frequency of a system can be altered by changing either the inertia of any of the components or the stiffness of the coupling used. See Chap. 31. Generally, after a system is designed, it is difficult and costly to change the inertia of the components. Therefore, coupling selection is frequently used to alter the natural frequency.
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16.2 RIGID COUPLINGS
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The solid coupling does not allow for misalignment, except perhaps axial, but enables the addition of one piece of equipment to another. In its simplest form, the rigid coupling is nothing more than a piece of bar stock bored to receive two shafts, as shown in Fig. 16.2. Its torque-handling capacity is limited only by the strength of the material used to make the connection. The coupling is installed on one shaft before the equipment is lined up, and the mating equipment is brought into position without much chance of accurate alignment when the equipment is bolted into position. The maximum shear stress occurs at the outer radius of the coupling and at the interface of the two bores. This stress can be derived from the torsion formula (see Chap. 36) and is max = TDo 2J (16.1)
where J, the polar second moment of the area, is J= 4 (D o D 4 ) i 32 (16.2)
The coupling must be sized so that, typically, the stress given by Eq. (16.1) does not exceed 10 percent of the ultimate tensile strength of the material, as shown in Table 16.2; but see Chap. 28.
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