Answer
Nested wave springs, which consist of multiple turns wound in parallel, exhibit a distinct hysteresis loop during loading and unloading cycles. This is primarily caused by inter-turn friction. The total load $P_{total} = P_{theoretical} \pm P_{friction}$. During the compression stroke, the friction between coils increases the apparent spring rate, while during the return stroke, friction opposes the spring's restorative force. For a nested spring with $n$ turns, the theoretical rate is $n$ times that of a single turn: $K_{nested} = n \cdot \frac{E b t^3 N^4}{I D_m^3}$. However, engineers must account for a $3\%$ to $5\%$ variation in load due to surface finish and lubrication. In subsea valves, where SAE 1070 carbon steel or Inconel X-750 is used, the coefficient of friction $\mu$ significantly shifts the $P-f$ curve, requiring precise characterization to avoid actuator lag.
