91Ó°ÊÓ

A helical compression spring is to be designed for infinite life when subjected to a load that fluctuates between 55 and \(110 \mathrm{Ib}\). Steel spring wire having \(S_{a}=180 \mathrm{ksi}, S_{\mathrm{ws}}=144 \mathrm{ksi}, S_{y}=170 \mathrm{ksi}\), \(S_{\text {sy }}=99 \mathrm{ksi}\), and a zero-to- maximum torsional endurance limit of \(80 \mathrm{ksi}\) is to be used. (These values are assumed to apply to the size range and surface finish of the spring.) For a value of \(C=7\), determine the wire diameter theoretically required (safety factor \(=1\) ), (a) if presetting is not used and (b) if presetting is used to maximum advantage.

A semielliptic leaf spring similar to the one in Figure \(12.25\) has four leaves, each made from \(0.1 \times\) 2-in. steel having properties of \(S_{\mathrm{u}}=180 \mathrm{ksi}, S_{\mathrm{y}}=160 \mathrm{ksi}\), and \(S_{n}=80 \mathrm{ksi}\). The latter figure includes appropriate corrections for size and surface. The fatigue stress concentration factor \(K_{f}\) (which is due to stress concentration at the clips and the center hole) is 1.3. Use the simplified "triangular plate" model. (a) What total spring length is needed to give a spring rate of \(75 \mathrm{lb} / \mathrm{in}\). (i.e., \(75 \mathrm{lb}\) applied at the center causes a 1 -in. deflection at the center)? (b) In service, the spring will carry a static load (applied to the center) of \(P\), plus a superimposed dynamic load that varies from \(+P / 2\) to \(-P / 2\). What is the highest value of \(P\) that will give infinite life, with a safety factor of \(1.3\) ? [Ans.: \(20.4\) in., \(130 \mathrm{lb}\) ]