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CLUTCHES AND BRAKES 8.23
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CLUTCHES AND BRAKES
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FIGURE 8.14 Ventilation factors. (Tol-o-matic.)
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Here o = Therefore, E= 328 (332) = 178.6 103 lb in 2 = 19.1 Btu (20.150 kJ) The average rate of energy generation is found by Eq. (8.16): Hav = 19.1(19) ES = = 0.101 Btu/s (107 W) 3600 3600 2 (315) = 33 rad/s 60 f = 0
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The disk area needed can be calculated by using Eq. (8.21) and setting Hav = Hdiss = 0.101 Btu/s. Thus A= H diss 0.101 = = 37.1 in2 (0.0239 m2) h(Td Ta) (13.6 10 6)(200)
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8.4 FRICTION MATERIALS
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To help in preliminary design, Tables 8.7 and 8.8 have been compiled, principally from data supplied by British and U.S. manufacturers of friction materials. Although these data are representative, they are hardly exhaustive. And they should be used
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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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TABLE 8.7 Characteristics of Friction Materials for Brakes and Clutches
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8.24 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.
CLUTCHES AND BRAKES 8.25
CLUTCHES AND BRAKES
TABLE 8.8 Area of Friction Material Required for a Given Average Braking Power
for preliminary design estimates only. A friction materials manufacturer should be consulted both to learn of additional options and to get more authoritative data. Although Table 8.7 lists maximum recommended values for contact pressure and rubbing velocity, it is not very likely that you can go the limit on both parameters at once. And a careful distinction must be made between the maximum temperature permissible for a short time and the safe temperature level for continuous operation. The temperature limit for continuous operation is much lower than that for a brief temperature peak. Preliminary design of brakes is aided by calculating the lining area needed for the average rate at which energy has to be dissipated by the brakes (braking power). Table 8.8 lists values that are typical of modern design practice. Again, after using these data to make some preliminary design estimates, you will need to contact the manufacturers of the friction materials before making final design decisions.
8.5 TORQUE AND FORCE ANALYSIS OF RIM CLUTCHES AND BRAKES
8.5.1 Long-Shoe Rim Brake One shoe of an internal expanding rim brake is shown in Fig. 8.15. Usually there is a second shoe as well. The shoe is pivoted about the fixed point A. It is actuated by a force F which can be provided in a number of ways: mechanically, hydraulically, pneumatically, electromagnetically, or by some combination of these. The forces on the shoe include the actuating force F, a reaction force R at the pivot, the distributed normal force, and the distributed friction force, the latter two exerted by the drum on the shoe. For purposes of analysis, the distributed normal and frictional forces on the shoe can be replaced by a resultant normal force P and a resultant frictional force fP. Use of these fictional concentrated forces simplifies the analysis. There is one odd consequence, however. The resultant frictional force fP has to be regarded as acting beyond the surface of the shoe at some point C, the center of pressure. Figure 8.16 shows the shoe subjected to this equivalent force system. Pressure Distribution along Lining. A first step in developing an equation for the torque capacity of the shoe is to adopt a model for the pressure distribution along
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CLUTCHES AND BRAKES 8.26
MACHINE ELEMENTS THAT ABSORB AND STORE ENERGY
FIGURE 8.15 Forces on an internal long shoe.
the lining of the shoe. Assuming that the lining is elastic and of uniform thickness, but that the drum is perfectly rigid, the expression for the normal pressure p on the lining at any angular position is p= pmax sin (sin )max (8.23)
In the usual case, the shoe straddles the = 90 position and (sin )max = 1. The variation of contact pressure along the lining is significant. To assume a uniform pressure is to oversimplify. For example, for a shoe extending from = 30 to = 165 , the pressure varies from 0.5pmax at 30 to pmax at 90 , and to 0.26pmax at 165 .
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