Answer
In the spring rate formula $k = (E b t^3 n^4) / (D_m^3)$, the mean diameter $D_m$ is raised to the third power. This means that $k$ is inversely proportional to $D_m^3$. If the tolerance on the diameter is large, the resulting spring rate can vary significantly. For instance, a $2\%$ increase in $D_m$ results in approximately a $6\%$ decrease in $k$. In precision medical devices, where constant force is required, $D_m$ must be tightly controlled through specialized coiling techniques. Furthermore, $D_m$ changes as the spring is compressed; as the waves flatten, the spring expands radially. If the design does not account for this expansion (the 'breathing' of the spring), the spring will bind against the housing, causing the rate $k$ to become infinite.
