Question

The shaft shown in the figure is driven by a gear at the right keyway, drives a fan at the left keyway, and is supported by two deep-groove ball bearings at locations A and B. The shaft is made from AISI 1045 cold-drawn steel. At steady-state speed, the gear transmits a radial load of 300 lbf and a tangential load of 700 lbf at a pitch diameter of 8 in. Assume that the weight and axial load of the fan is negligible this allows for combining the forces of the gear into a single plane. Determine fatigue factor of safety at location D of the keyway using the DE-Goodman failure criterion with a 90% reliability. 12.87 8.30 0.20 2.20 2.75 0.75 0.485 1.750 1.181 1.40 2.0 1.000 1.70 + 11.181 IA 2.0 B HER. V R. 0.15 0.IR x keyway R x keyway R. |-1.02 -1.37-4 6.98 3.14 0.38 Sut=91 kpsi Sy=77kpsi Ka=0.75

Answer 1

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solution: Material of shaft - AZSS 1045 CD Steel Wr=300 ebf, Wt = 700 ebf. PCD = 8 in Rz90% ko 6.98 1761.6 ebr c Ay' (Simplified drawing) By on the shaft, resultant since only one wad is acting had is given by Rz = 761.6 Ubat W2²+ WE2 (300)2+(70012 Ev=0 ... +9 EMA =0 Ay + By = 761.6 : By X 10.12 - 761.686.98 - 0 Ay = 761.6-5.25.3=236.3 esf =) By = 525.3 ils Moment at D,MD= 236.3x6.98 = 1649.4 ebf.in Torque transmitted from D ID A of T = 700x8/2 = 2800 Obtin. Moment and torsion diagrams is shown below. from figure, Maximum bending moment Mo MD=1649.4 ebfin

C D A Mo = 1649.4 T- 2800 с A D of the for End-mill keyseat , for worst end spectrum assuming 2/d = 0.02 ( from table 7.1) ( Abore values are taken from textbook "shigleys Mechanical Engineering design by Nisbelt, et al") kt = 2.14 Its = 3.0 For AISI 1045 CD Sleel, given values are: Sut = 91 kpsi, sy = 77 kpsi ka=0.75 As per figures given below, value of a and as : q=0.65, 93 = 0.7

05 1.0 3.0 3.5 4.0 1.0 Notch radius, mm 1.5 2.0 2.5 (1.4 GPa) (10) Sw=200 hp (0.7) 150 (04) 100 Notch sensitivity 0.4 Steels Alum, alloy 0.2 S. 200 kpsi (1.4GPa) Figure 6-20 Notch-sensitivity charts for steels and UNS A92024-T wrought aluminum alloys subjected to reversed bending 0.8 or reversed axial loads. For larger notch radii, use the G.65 0.6 values of q corresponding to the r = 0.16-in (4-mm) ordinate. (From George Sines and J. L Waisman (eds.), Metal Fatigue, McGraw-Hill, New York. Copyright © 1969 by The McGraw-Hill Companies, Inc. Reprinted by permission.) 0.02 Figure 6-21 1.0 Notch-sensitivity curves for 1.0 materials in reversed torsion For larger notch radii, use the values of shear corresponding to r=0.16 in (4 mm). 0 0.04 0.12 0.14 0.16 0.06 0.08 0.10 Notch radius r. in Notch radiusr, mm 1.5 2.0 2.5 0.5 3.0 3.5 4.0 0.8 150 (10) 100 (0.7) 600.4) 0.6 Oberon 0.4 Steels Alum, alloy 0.2 0 0 0.02 0.04 0.12 0.14 0.16 0.06 0.08 0.10 Notch radius rin

Kf = 1+ 9 (let 1) = 1+0.65(2.14-1) = 1.741 190 = 1 +90 (2xs-1) = 1 +0.7(3-1) = 2.4 -0. 107 Kb=6 0.3 0.11 < d < 2 in -0.107 :: kb (bit) - 0.828 Ке Reliability faction = 0.897 (For got reliability) .: Se z0.750 0.828 x 0.897x 0.5x91 Se z 25.345 kpsi Tato In the given problem, Mm=0, fatigue factor of safety as per DE- Goodman criteria, { to cry fma)²+ [414 mm7 +36kf Time) 36 ñ = 16 16 Tid 3 +3(lefs Ta ) ²] 2 - sut :* the most estus (461746 1649.97 ile oko 3(2-4x28002)"} = 0.95077 (0.2266 +0.127905) i. =0.337 h :. na 2.967 factor of safety = 2.967