Question

The shaft shown in Figure Q7.21 is proposed for the application defined in Prob. 3-73, p 138. The material is AISI 1018 cold-drawn steel. The gears seat against the shoulders, and have hubs with setscrews to lock them in place. The effective centers of the gears for force transmission are shown. The keyseats are cut with standard endmills. The bearings are press-fit against the shoulders. Determine the minimum fatigue factor of safety.

Answer 1

- 111 Har The Q.7.21 has been proposed for the application. in problem 3-73. P. 138 for l. Som of torque about thadt is zero IT =0; -11000 Cop 20 (3) + Co 125/156)=0 fo=22810N Free body diagram for plane A u ↑ Mo=0; hoof damen -> - 110000 in 20 (401) - 22810 (xin 25) (750) + Rey (1050)=0 Roy 508 N to Rey = 0 Rey=8313N Jy=0; fry-lico fin 20 - 27870 Rin25 +8319 = 0 Roy = 5083N 9. 3762N 2073N Momente; Me = 50 83 x 0.4 = 2033 Nm MB = 931980.3= 2495.7 Nm For Hane B; Roz-494N 2 Mozo; 110o Cop 20 (400)-22 810 6 x 2517501 I to f 35: -Rez (1050) =0 10 337 Rez=-1083 I &q=0; Roz - 11000 66126 +22810 667 25-108.30 = 0 Roz= 494 N P 300 Ke-10830N . Momenty, MA = 494x 0.4 = -198 Nm MR = 10830 x0.3 = 3249 Nm. He it in clear that moment in max at Bi critical at B.: M = 2496²+ 32492 = 4097 Nm. : location B in

-1.265 los que tranxmitted through chaft from A to B; T= 11000 Cox 20 (0-3) =3101 Nm Ma = 4097 Nm 1. bending in reverted ) 1 Tm = 3101 Nm While m = Ta = 6 How From table; for 1018 co teedi Sut = 460 MPa, sy = 370 MPa. Y 5 - 0-5 94+ = 220 MPa . por face factor; Karasuth fox given ustace = 4.51 (440) a=4.5) = 0.9. b = -0.265 at A; old = 0.02 : d=50 t r = 6.02 x d = 0.02X 50 1mm. .. for end milled key reat from given profile key way; K+ = 2.148 K+x=3. - for large nutch radis, q=0.66 Correnbond to 4 914=0.72 8=0.16 in (4mm). Ks itu (ke-1) = 1+0+66 (2-16-1) = 18 Kepa Ital Kex-1) = 1 + 72 (3-1) = 24 fire factor kg = 1 / 3 ) - 0.10 7 50 .107 = 0.818. r. Se= kaks ke se = 0.98 (0.818) x 220 = 162 MPa.

From Gerber Bitzian; here; A = JA ( ky Mar - fx (18 (4097))² - 14751 Nm BEBU, T) 312-4 (30) 2 12890 Nm - from A; 8 (14756) [sor 128 I (05) (162) (108) 71 14750 h=0.25 cl Intinite life is not possible. It /21289 1 14750 x 440 x 10 132 kg Mo 12 /16 max = d3 3 / + 37 - $2 x 1-8 x 4097 1² 8 16 x 2.4x31 01 12 / 2 (05 [ 11.053 = 718 MPa. factor of patety n= Hly) - 5 max h 370 798 = 0.4636 10 - 0.46] As