Answer to Question #261740 in Mechanical Engineering for Maneesh

Question

shows a 302 stainless steel spring is being applied by a dynamic loading from 150N to

600 N. The spring is peened to induce residual stress on the wire in order to resist fatigue failure. The total number of the coil is shown in Figure Q4 and the spring end is left as squared so that it is able to stand vertically when placed on a flat surface. If the spring index given is 11 and the outer diameter is 66 mm, determine the fatigue factor of safety of this spring. Also, estimate the critical frequency of the spring if the unit weight is given as 76 kN/m².

Answer 1

Factor of safety (Gerber) criteria=$n_{gerber}=\frac{1}{2}(\frac{s_{su}}{z_m})^2(\frac{z_a}{s_{se}})[-1+\sqrt{1+(\frac{2z_us_{se}}{s_{su}z_a}})$

$=\frac{1}{2}(\frac{863.42}{392.38})^2(\frac{235.43}{642.51})[-1+\sqrt{1+(\frac{2*392.38*642.51}{863.42*235.43}})$

=0.7678

Critical frequency, $f=\frac{1}{4}\sqrt{\frac{Kg}{W}}$

$=\frac{1}{4}\sqrt{\frac{3987*9.81}{0.00000411}}$

=770.44Hz