Budynas ch17

Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)

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Chapter 17 17-1 Given: F-1 Polyamide, b = 6 in, d = 2 in @ 1750 rev/min C = 9(12) = 108 in, vel. ratio 0.5, H nom = 2 hp, K s = 1 . 25, n d = 1 Table 17-2: t = 0 . 05 in, d min = 1 . 0 in, F a = 35 lbf / in, γ = 0 . 035 lbf / in 3 , f = 0 . 5 Table 17-4: C p = 0 . 70 w = 12 γ bt = 12(0 . 035)(6)(0 . 05) = 0 . 126 lbf/ft θ d = 3 . 123 rad, exp( f θ ) = 4 . 766 (perhaps) V = π dn 12 = π (2)(1750) 12 = 916 . 3 ft/min (a) Eq. ( e ), p. 865: F c = w 32 . 17 V 60 2 = 0 . 126 32 . 17 916 . 3 60 2 = 0 . 913 lbf Ans . T = 63 025 H nom K s n d n = 63 025(2)(1 . 25)(1) 1750 = 90 . 0 lbf · in F = 2 T d = 2(90) 2 = 90 lbf Eq. (17-12): ( F 1 ) a = bF a C p C v = 6(35)(0 . 70)(1) = 147 lbf Ans . F 2 = F 1 a F = 147 90 = 57 lbf Ans . Do not use Eq. (17-9) because we do not yet know f . Eq. ( i ), p. 866: F i = F 1 a + F 2 2 F c = 147 + 57 2 0 . 913 = 101 . 1 lbf Ans . Eq. (17-7): f = 1 θ d ln ( F 1 ) a F c F 2 F c = 1 3 . 123 ln 147 0 . 913 57 0 . 913 = 0 . 307 The friction is thus undeveloped. (b) The transmitted horsepower is, H = ( F ) V 33 000 = 90(916 . 3) 33 000 = 2 . 5 hp Ans . n f s = H H nom K s = 2 . 5 2(1 . 25) = 1 From Eq. (17-2), L = 225 . 3 in Ans . (c) From Eq. (17-13), dip = 3 C 2 w 2 F i where C is the center-to-center distance in feet. dip = 3(108 / 12) 2 (0 . 126) 2(101 . 1) = 0 . 151 in Ans .
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Chapter 17 421 Comment : The friction is under-developed. Narrowing the belt width to 5 in (if size is available) will increase f . The limit of narrowing is b min = 4 . 680 in, whence w = 0 . 0983 lbf/ft ( F 1 ) a = 114 . 7 lbf F c = 0 . 712 lbf F 2 = 24 . 6 lbf T = 90 lbf · in (same) f = f = 0 . 50 F = ( F 1 ) a F 2 = 90 lbf dip = 0 . 173 in F i = 68 . 9 lbf Longer life can be obtained with a 6-inch wide belt by reducing F i to attain f = 0 . 50 . Prob. 17-8 develops an equation we can use here F i = ( F + F c ) exp( f θ ) F c exp( f θ ) 1 F 2 = F 1 F F i = F 1 + F 2 2 F c f = 1 θ d ln F 1 F c F 2 F c dip = 3( C D / 12) 2 w 2 F i which in this case gives F 1 = 114 . 9 lbf F c = 0 . 913 lbf F 2 = 24 . 8 lbf f = 0 . 50 F i = 68 . 9 lbf dip = 0 . 222 in So, reducing F i from 101.1 lbf to 68.9 lbf will bring the undeveloped friction up to 0.50, with a corresponding dip of 0.222 in. Having reduced F 1 and F 2 , the endurance of the belt is improved. Power, service factor and design factor have remained in tack. 17-2 There are practical limitations on doubling the iconic scale. We can double pulley diame- ters and the center-to-center distance. With the belt we could: Use the same A-3 belt and double its width; Change the belt to A-5 which has a thickness 0.25 in rather than 2(0 . 13) = 0 . 26 in, and an increased F a ; Double the thickness and double tabulated F a which is based on table thickness. The object of the problem is to reveal where the non-proportionalities occur and the nature of scaling a flat belt drive. We will utilize the third alternative, choosing anA-3 polyamide belt of double thickness, assuming it is available. We will also remember to double the tabulated F a from 100 lbf/in to 200 lbf/in.
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422 Solutions Manual Instructor’s Solution Manual to Accompany Mechanical Engineering Design Ex. 17-2: b = 10 in, d = 16 in, D = 32 in, Polyamide A-3, t = 0 . 13 in, γ = 0 . 042, F a = 100 lbf/in, C p = 0 . 94, C v = 1, f = 0 . 8 T = 63 025(60)(1 . 15)(1 . 05) 860 = 5313 lbf · in w = 12 γ bt = 12(0 . 042)(10)(0 . 13) = 0 . 655 lbf/ft V = π dn / 12 = π (16)(860 / 12) = 3602 ft/min θ d = 3 . 037 rad For fully-developed friction: exp( f θ d ) = [0 . 8(3 . 037)] = 11 . 35 F c = w V 2 g = 0 . 655(3602 / 60) 2 32 . 174 = 73 . 4 lbf ( F 1 ) a = F 1 = bF a C p C v = 10(100)(0 . 94)(1) = 940 lbf F = 2 T / D = 2(5313) / (16) = 664 lbf F 2 = F 1 F = 940 664 = 276 lbf F i = F 1 + F 2 2 F c = 940 + 276 2 73 . 4 = 535 lbf Transmitted power H (or
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