Spring index is-

Concept:

The spring index is defined as the ratio of the mean diameter of the coil to the diameter of the wire. Mathematically,

Spring index, \(C=\frac{D}{d}\)

Deflection of Helical Springs of Circular Wire:

\(\delta = \frac{{8W{D^3}n}}{{G{d^4}}} = \frac{{8W{C^3}n}}{{Gd}}\)

Stiffness of the spring or spring rate

\(k = \frac{W}{\delta } = \frac{{G{d^4}}}{{8W{D^3}n}}\)

\(k = \frac{{G{d^4}}}{{8{D^3}n}} = \frac{{G{d^4}}}{{8{{\left( {2R} \right)}^3}n}} = \frac{{G{d^4}}}{{64{R^3}n}}\)

Where D = Mean diameter of the spring coil, d = Diameter of the spring wire, n = Number of active coils, G = Modulus of rigidity for the spring material, W = Axial load on the spring