PROBLEM $3.$

Design a helical compression spring using round steel wire. The spring will actuate a clutch

and must withstand several million cycles of operation and impact $($fatigue and impact$).$ When

the clutch discs are in contact, the spring will have a length of $2\mathrm{.}50$ in and must exert a force of

$F_{\text{m}\text{i}\text{n}}=20lb.$ When the clutch is disengaged, the spring will be $2\mathrm{.}10$ in long and must exert a

force of $F_{\text{m}\text{a}\text{x}}=35lb.$ The spring will be installed around a round shaft having a diameter of $1\mathrm{.}50$

in$.$

$($a$)$ Determine the spring material.

$($b$)$ Determine the minimum hole diameter for the spring to operate in$.$

$($c$)$ Determine the appropriate wire diameter, d $.$

$($d$)$ Determine the type of spring ends.

$($e$)$ Determine an appropriate number of coils, $Nt,Na,$ needed.

$($f$)$ Determine the spring rate.

$B=0\mathrm{.}125$

$($g$)$ Determine the solid length.

$($h$)$ Determine a static factor of safety based on the yielding of the spring if it is compressed.

to its solid length.

$($i$)$ Determine the fatigue factor of safety when repeatedly cycled for the forces max and min.

Using the Goodman$-$Zimmerli fatigue$-$failure criterion. Consider the spring in peened

condition. $F_2=2016,D=1\mathrm{.}50-0\mathrm{.}375-=1\mathrm{.}12$