Helical spring geometry:\nA closely coiled helical spring has mean coil diameter D and wire diameter d. The spring index is defined as which of the following ratios?

Introduction / Context:
The spring index (C) indicates coil tightness and manufacturability of helical springs. It affects stress concentration, buckling tendency, and ease of coiling, influencing both performance and cost.

Given Data / Assumptions:

• Mean coil diameter = D; wire diameter = d.
• Close-coiled helical spring under typical axial loading.

Concept / Approach:
By definition, spring index C = D / d. Typical design ranges (e.g., 6 ≤ C ≤ 12) balance stress concentration and manufacturability. Very low C increases stress concentration and makes coiling difficult; very high C can cause instability.

Step-by-Step Solution:

Verification / Alternative check:
Standard design equations for Wahl factor and spring stress include C = D/d explicitly, confirming the accepted definition.

Why Other Options Are Wrong:

• 1/d, 1/D, and D * d do not match the accepted definition.
• d/D is the reciprocal and would misrepresent coil tightness.

Common Pitfalls:
Mixing mean diameter with outer or inner diameter; using reciprocal by mistake when calculating stress correction factors.

Final Answer:
D / d