Fluid Mechanics

1) The section of shaft shown in the figure is to be designed to approximate relative sizes of d = 0.75D and r = D/20 with diameter d conforming to that of standard metric rolling-bearing bore sizes. The shaft is to be made of AISI 4140 steel, heat-treated to obtain minimum strengths in the shoulder area of 951 MPa ultimate tensile strength and 834 MPa yield strength with a Brinell hardness not less than285. At the shoulder the shaft is subjected to a completely reversed bending moment of 35 x 10 N.mm, accompanied by steady torsion of 22.5 x 103 N.mm.Surfaces are machined.

1. Choose a diameter at the root groove d, =?

b. Find the size factor, k, = ?

c. Find the Endurance limit S. = ?

d. Find the notch sensitivities and static stress concentration factors

q=?, q_{s}=?, K_{t}=?, K_{t s}=?

Find the fatigue stress concentration factors Kf = ?,Kfs = ?

Using a fatigue factor of safety according ASME-EIliptic, n =nASME = 3.5, estimate the diameter at the root groove, d,

d=\left\{\frac{16 n}{\pi}\left[4\left(\frac{K_{f} M_{a}}{S_{e}}\right)^{2}+3\left(\frac{K_{f s} T_{a}}{S_{e}}\right)^{2}+4\left(\frac{K_{f} M_{m}}{S_{y}}\right)^{2}+3\left(\frac{K_{f s} T_{m}}{S_{y}}\right)^{2}\right]^{1 / 2}\right\}^{1 / 3}

g. With this new calculated, d,, Loop through part b to part f, until you have a converged solution for the diameter at the root groove.

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