Concept:
Stiffness of the spring is given by:
\(k = \frac{W}{\delta } = \frac{{G{d^4}}}{{8{D^3}n}}\)
Where D is mean diameter of the spring coil, d is the diameter of the spring wire; n is the number of active coils and G is the modulus of rigidity for the spring material.
Calculation:
d2 = 1.02d1
\(k = \frac{{G{d^4}}}{{8{D^3}n}} \Rightarrow k \propto {d^4}\)
\(\frac{{{k_2}}}{{{k_1}}} = {\left( {\frac{{{d_2}}}{{{d_1}}}} \right)^4} = {\left( {1.02} \right)^4} = 1.082\)
k2 = 1.082 k1
\({\rm{\Delta }}k = \frac{{{k_2} - {k_1}}}{{{k_1}}} = 0.082 = 8.2\% \)
