By William C. Orthwein

Comfortably accumulating quite a few formulation, analytical tools, and graphs for the layout and choice of a wide selection of brakes and clutches within the car, plane, farming, and production industries, this convenient reference simplifies calculations, acquaints engineers with an expansive variety of purposes, and assists within the collection of parameters for particular layout demanding situations.

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**Extra resources for Clutches and Brakes - Design and Selection**

**Sample text**

1=2 Band brake lever force: P¼ beÀAa À a T rð1 À eÀAa Þ b þ c Band width in terms of torque: w¼ T pmax r2 ð1 À eÀAa Þ REFERENCES 1. Roark, R. , Young, W. C. (1975). Formulas for Stress and Strain. 5th ed. New York: McGraw-Hill. 2. Popov, E. P. (1976). Mechanics of Materials. 2nd ed. Englewood Cliﬀs, NJ: Prentice-Hall. Copyright © 2004 Marcel Dekker, Inc. 3 Externally and Internally Pivoted Shoe Brakes Typical externally and internally pivoted shoe brakes are shown in Figures 1 and 2. In all but extremely rare designs, equal forces act upon both shoes to produce equal applied moments about their pivots.

Relative to the geometry in Figure 3, and with the aid of equation (1-4), this moment may be written as Z f2 Z pmax wrR f2 2 ð pwr dfÞR sin f ¼ sin f df ð1-8Þ Mp ¼ ðsin fÞmax f1 f2 which integrates to pmax wrR Mp ¼ ð2f0 À sin 2f2 þ sin 2f1 Þ 4ðsin fÞmax ð1-9Þ where f0 is given by equation (1-7). This moment is positive in the counterclockwise direction, and its algebraic sign is independent of the direction of drum rotation relative to the brake lever’s pivot point. Reactive moment Mf at pivot A due to the friction force acting on the shoe may be calculated using the geometry sketched in Figure 4.

The torque exerted by the brake is related to the band force according to T ¼ ðF1 À F2 Þr ð1-9Þ Upon factoring out F1 by referring to equation (1-7) and then replacing F1 by the right-hand side of equation (1-8), we get T ¼ F1 rð1 À eÀAa Þ ¼ pmax wr2 ð1 À eÀAa Þ Copyright © 2004 Marcel Dekker, Inc. ð1-10Þ Band Brakes 21 which gives the brake’s maximum restraining torque as a function of its dimensions and its maximum compressive pressure. This equation may be applied if the leading link can withstand the force F1 = rwpmax and if the band is strong enough to support the force given by equation (1-6) for 0 Q u Q a.