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COUPLINGS 16.23
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bonded type is torsionally softer than the corresponding toothed type, with windup of 15 to 20 versus 5 to 6 for the toothed type. This coupling is not fail-safe; when the flexible element fails, the driver and driven equipment are no longer connected. The shear clamped or tire (torus) coupling is designed around a tireshaped element, as shown in Figs. 16.31 and 16.32. The tire beads are clamped to a hub on either side, and torque is transmitted by shear and tension in the tire body.These couplings may be reinforced or unreinforced (without cords); in either case, the geometry allows very short overall length for a given torque FIGURE 16.30 Bonded type of a shear capacity at the expense of diameter, unclamped coupling. (Lord Corp., Industrial which becomes correspondingly larger. Products Div.) This large diameter can cause some problems resulting from axial pull from the coupling as it is rotated at high speed. Centrifugal forces on the tire cause the two hubs to collapse inward as the speed is increased. The tire shape allows lower restoring force to larger misalignments than the shear unclamped or compression coupling. The tension coupling shown in Fig. 16.33 is very similar to the link coupling (see Sec. 16.3.1), in that alternate legs (links) are in compression or tension. The links may have reinforcing cords to increase their tensile rating. In this coupling the rating is
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FIGURE 16.31 Tire coupling. (Dodge Div., Reliance Electric.)
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FIGURE 16.32 Torus coupling. (Falk Corp.)
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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 16.24
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determined by the compression buckling of the leg pairs or the tensile strength of the other leg pairs, whichever is less. These couplings may be made of plastic, although rubber treated against ozone, when used with reinforcing cords, is also available. To eliminate the effect of tension on rubber in a design similar to the one in Fig. 16.33, the rubber element is precompressed by assembling the element into a state smaller than the free state. This allows the trailing leg (formerly the tension leg) to stretch almost to neutral but never into tension, which would promote early failure. FIGURE 16.33 Tension coupling. (Lovejoy Inc.) In the radially restrained type, a tight metal band is slipped around the OD of the element while it is being held in a radially compressed state. After assembly to the mating hub, the band is snipped off, and the assembly bolts hold the element in precompression. Alternatively, radial bolts are used to draw the rubber element into compression. See Fig. 16.34. Both these designs use fairly thick cross sections for their flexing elements and are quite compliant in all forms of misalignment. Rubber hardness and type can be changed to alter torque capacity, damping, and chemical-temperature resistance. Alternatively, axial restraint can be used. In this design, the rubber element is installed between two hubs which are set a fixed distance apart, as shown in Fig. 16.35. The rubber element is then installed by means of bolts into this space, which is smaller than the free state of the rubber. This design is also very compliant, but generates an axial force because of the forced axial compression of the element.
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FIGURE 16.34 Precompressed radially restrained coupling. (Lovejoy, Inc.)
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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.
COUPLINGS 16.25
COUPLINGS
16.5 UNIVERSAL JOINTS AND ROTATING-LINK COUPLINGS
Another class of shaft connectors is composed of the linkage types, which include universal joints (U-joints) and rotating-link couplings. These couplings all rely on translating misalignment to relative rotation between parts of the coupling. The simplest universal joint is the one for a compass suspension universal joint described by Geronimo Cardano in the sixteenth century and explained mathematically by Robert Hooke in the seventeenth century. The universal joint basically consists of two shaft connections (yokes) which pivot about a pair of centrally located bearings. See Fig. 16.36. Shafts A and B are inclined to each other at angle (shaft centerlines must intersect); when shaft A is rotated, the center member (spider) causes shaft B FIGURE 16.35 Precompressed axially reto rotate by virtue of the connection. strained coupling. (Koppers Co. Inc., Power Transmission Div.) The output speed of shaft B is not constant when the shafts are at an angle. Specifically, the output velocity is 0 = i cos 1 sin2 sin2 (16.20)
where = rotation position angle and = joint or shaft angle. In addition, the change in velocity peaks twice during every revolution. This leads to a second-order harmonic excitation frequency for the drive system. Specifically, the torsional magnitude of this excitation is = tan 1 (sec )1/2 tan 1 (cos )1/2 (16.21)
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