Chapter_12_Solutions

# Chapter_12_Solutions - Chapter 12 12-1 Given d max = 25 mm...

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Chapter 12 12-1 Given: d max = 25 mm, b min = 25.03 mm, l/d = 1/2, W = 1.2 kN, = 55 mPa s, and N = 1100 rev/min. min max min 25.03 25 0.015 mm 22 bd c  r 25/2 = 12.5 mm r/c = 12.5/0.015 = 833.3 N = 1100/60 = 18.33 rev/s P = W/ ( ld ) = 1200/ [12.5(25)] = 3.84 N/mm 2 = 3.84 MPa Eq. (12-7):    3 2 2 6 55 10 18.33 833.3 0.182 3.84 10 rN S cP        Fig. 12-16: h 0 / c = 0.3 h 0 = 0.3(0.015) = 0.0045 mm Ans . Fig. 12-18: f r/c = 5.4 f = 5.4/833.3 = 0.006 48 T =f Wr = 0.006 48(1200)12.5(10 3 ) = 0.0972 N m H loss = 2 TN = 2 (0.0972)18.33 = 11.2 W Ans . Fig. 12-19: Q /( rcNl ) = 5.1 Q = 5.1(12.5)0.015(18.33)12.5 = 219 mm 3 /s Fig. 12-20: Q s /Q = 0.81 Q s = 0.81(219) = 177 mm 3 /s Ans . ______________________________________________________________________________ 12-2 Given: d max = 32 mm, b min = 32.05 mm, l = 64 mm, W = 1.75 kN, = 55 mPa s, and N = 900 rev/min. min max min 32.05 32 0.025 mm c r 32/2 = 16 mm r/c = 16/0.025 = 640 N = 900/60 = 15 rev/s Chapter 12, Page 1/26 Draft

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P = W/ ( ld ) = 1750/ [32(64)] = 0.854 MPa l/d = 64/32 = 2 Eq. (12-7):   3 2 2 55 10 15 640 0.797 0.854 rN S cP        Eq. (12-16), Figs. 12-16, 12-19, and 12-21 l/d y y 1 y 1/2 y 1/4 y l/d h 0 /c 2 0.98 0.83 0.61 0.36 0.92 P/p max 2 0.84 0.54 0.45 0.31 0.65 Q/rcNl 2 3.1 3.45 4.2 5.08 3.20 h 0 = 0.92 c = 0.92(0.025) = 0.023 mm Ans . p max = P / 0.065 = 0.854/0.65 = 1.31 MPa Ans . Q = 3.20 rcNl = 3.20(16)0.025(15)64 = 1.23 (10 3 ) mm 3 /s Ans . ______________________________________________________________________________ 12-3 Given: d max = 3.000 in, b min = 3.005 in, l = 1.5 in, W = 800 lbf, N = 600 rev/min, and SAE 10 and SAE 40 at 150 F. min max min 3.005 3.000 0.0025 in 22 3.000 / 2 1.500 in / 1.5 / 3 0.5 / 1.5 / 0.0025 600 600 / 60 10 rev/s 800 177.78 psi 1.5(3) bd c r ld rc N W P ld  Fig. 12-12: SAE 10 at 150 F, 1.75 reyn μμ 2 6 2 1.75(10 )(10) 600 0.0354 177.78 S Figs. 12-16 and 12-21: h 0 /c = 0 . 11 and P/p max = 0 . 21 0 max 0.11(0.0025) 0.000 275 in . 177.78 / 0.21 847 psi . hA p Ans n s Fig. 12-12: SAE 40 at 150 F, 4.5 reyn Chapter 12, Page 2/26 Draft
0m a x 0 max 4.5 0.0354 0.0910 1.75 / 0.19, / 0.275 0.19(0.0025) 0.000 475 in . 177.78 / 0.275 646 psi . S hc Pp hA pA     n s n s ______________________________________________________________________________ 12-4 Given: d max = 3.250 in, b min = 3.256 in, l = 3.25 in, W = 800 lbf, and N = 1000 rev/min. min max min 3.256 3.250 0.003 22 3.250 / 2 1.625 in / 3 / 3.250 0.923 / 1.625 / 0.003 542 1000 / 60 16.67 rev/s 800 82.05 psi 3(3.25) bd c r ld rc N W P ld  Fig. 12-14: SAE 20W at 150 F,  = 2.85 reyn 2 6 2 2.85(10 )(16.67) 542 0.1701 82.05 rN S cP    From Eq. (12-16), and Figs. 12-16 and 12-21: l/d y y 1 y 1/2 y 1/4 y l/d h o /c 0.923 0.85 0.48 0.28 0.15 0.46 P/p max 0.923 0.83 0.45 0.32 0.22 0.43 max 0.46 0.46(0.003) 0.001 38 in . 82.05 191 psi . 0.43 0.43 o A P n s n s Fig. 12-14: SAE 20W-40 at 150 F, = 4.4 reyn 6 2 4.4(10 )(16.67) 542 0.263 82.05 S From Eq. (12-16), and Figs. 12-16 and 12-21: l/d y y 1 y 1/2 y 1/4 y l/d h o /c 0.923 0.91 0.6 0.38 0.2 0.58 P/p max 0.923 0.83 0.48 0.35 0.24 0.46 Chapter 12, Page 3/26 Draft

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0 max 0.58 0.58(0.003) 0.001 74 in . 8205 82.05 178 psi . 0.46 0.46 hc A pA  n s n s ______________________________________________________________________________ 12-5 Given: d max = 2.000 in, b min = 2.0024 in, l = 1 in, W = 600 lbf, N = 800 rev/min, and SAE 20 at 130 F. min max min 2.0024 2 0.0012 in 22 2 1 in, / 1 / 2 0.50 / 1 / 0.0012 833 800 / 60 13.33 rev/s 600 300 psi 2(1) bd c d rl d rc N W P ld Fig. 12-12: SAE 20 at 130 F, 3.75 reyn μμ 2 6 2 3.75(10 )(13.3) 833 0.115 300 rN S cP       From Figs. 12-16, 12-18 and 12-19: 0 0 / 0.23, / 3.8, / ( ) 5.3 0.23(0.0012) 0.000 276 in . 3.8 0.004 56 833 r fc Qr c N l hA f n s The power loss due to friction is 3 2 2 (0.004 56)(600)(1)(13.33) 778(12) 778(12) 0.0245 Btu/s . 5.3 5.3(1)(0.0012)(13.33)(1) 0.0848 in /s . fW H Ans c N l Ans ______________________________________________________________________________ 12-6 Given: d max = 25 mm, b min = 25.04 mm, l/d = 1, W = 1.25 kN, = 50 mPa s, and N = 1200 rev/min.
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Chapter_12_Solutions - Chapter 12 12-1 Given d max = 25 mm...

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