Question

The solid steel shaft (Sy = 75 kpsi, Se = 50 kpsi, Sut = 110 kpsi) carrying two-belt pulleys is shown in the figure (reaction force, torques are given as well). Two pulleys are keyed to the shaft where pulley B is of diameter 4.0 in the pulley C is of diameter 8.0 in. Assume the shaft has a uniform diameter d = 1.5 in. 1) Design a key (S, = 60 kpsi) for pulley C using the design factor of 2.0. (Specify W, H and L for the key) 2) Determine the fatigue factor of safety of point C (Assume Ky = 1.25 and Kfs = 1.28). A 10 in 10 in 1600 lbf in 200 lbf Y Bi 200 lbf 10 i 10 in 1600 lbfin 1200 lbf 1000 lbf 10 in 10 in 600 lbf 4001661 400 lbf 500 lbf 100 lbf I 400 lbf (a)

Answer 1

Solution And (1):- Shaft diameter = 1.5 in. Cosiresponding to share diomeen, a square Kay of sin is selected. [From table 7-6] (W) width of key = 3/8in, height of key = 3/8in, The force F at the surface of the staff at c.. F = I= 1600 lbf-in (3.5/2.) PF = 2133.330b6} - By the distortion - energy theory , the shear strength → Ssy = 0.577 ify = 0.577 (60) = 34.62 kpsi failure by shear across (wl) will create a stress of t=f/we, substituting the strength divided by the factor of safety for t gues, Sosie - 34,628103 = 21:33. 33 21.33.33 one-half [l=0.3286 inch] the area of key is used - To the resist face crushing of the re=0.37925 inch] The hub length of a gear is usually greater than the shaft diameter for stability. If the key, in this example, 20 made equal in length to

the since So tub It would ther fore have ample Strength it would probably be 1.5 in or longer for the key tos safe design) W = 78 in, H = 3/8 in L = 1.510 And (2): – From the given figure (b) in question, taking wy plane- Bending moment M2) = 400 lbt) (20 in) = 4000 lbf-in at cc taking xz plane - Bending moment at c (My) = (hoo lbf) (10 in) = 4000 lbt-in Total bending moment at c M = M2 2+ My = 5400o) 2 (1000) NM=5656.85 Ibti-in} Tanque at c, &T=1600 lbf-ing given → Kf = 1.25 $ KES = 1.28 → By using DE- Good naon writerion - the change se [4 (kt MJ? 9'42 - att [3 (Tanya Jobel hasta soprons [4 (1.25 X5656.851) Ver to the [3 (4.28X1600127124 = 0.478479 [n= 2. 103 1 7 fatigue factor of safety of point to

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