Spring index explained: why 4 to 12 matters

What spring index is

Spring index is the mean coil diameter divided by the wire diameter. If a spring has a 10 mm mean diameter and 1.6 mm wire, the index is 6.25. Mean diameter is the outside diameter minus one wire diameter, or the inside diameter plus one wire diameter. Using outside diameter by mistake is a common source of a wrong index and a wrong stress figure.

The number is dimensionless, so it describes the proportions of the spring rather than its absolute size. A 2 mm wire spring and a 12 mm wire spring with the same index behave in a similar way in terms of curvature, stress correction and coiling difficulty.

The four things index controls

Index touches almost every property of a helical spring. The most important is the curvature correction used in stress calculation. A coil is not a straight beam, and the inner fibres of the wire carry more stress than beam theory predicts. The correction factor rises steeply as the index falls, so a tight spring runs closer to its limit than the nominal stress suggests.

Index also sets the relationship between wire diameter and coil diameter, which decides how much the spring can deflect before coils close, how sensitive the rate is to diameter tolerance, and how easily the wire can be coiled without cracking. A spring with a low index needs more forming force and has less room for the coiler to work.

• Stress: the curvature correction rises as index falls, reducing the allowable load for the same wire.
• Rate: rate depends on wire diameter to the fourth power and mean diameter to the third.
• Tolerance: a small index amplifies the effect of a diameter error on rate and fit.
• Manufacture: low index springs need tighter tooling and stress relief after coiling.

Why the practical band is 4 to 12

The 4 to 12 band is not a rule in a standard. It is an empirical working range that keeps stress correction, coiling strain, tolerance sensitivity and slenderness within limits that most suppliers can hold at a sensible price.

Below 4, the wire is thick relative to the coil. The curvature correction is high, the inner surface of the coil is strained hard during forming, and the spring is stiff for its size. Cracking at the coil inside, rate scatter and short fatigue life all become more likely. Tooling also costs more because the wire resists bending.

Above 12, the coil is large relative to the wire. The spring is flexible and slender, which makes it prone to buckling and lateral movement. Coiling consistency falls, the free length becomes harder to hold, and small changes in wire diameter move the rate noticeably. Handling and packing damage also increase because the coils are easily deformed.

Reading the index band

The table below describes what each part of the range usually means in practice. The boundaries are guides, not absolute limits, and a spring outside them can still work if the application justifies the risk.

Index and stress: an illustrative check

Take a spring with 1.6 mm wire and a 10 mm mean diameter, giving an index of 6.25. The Wahl correction factor at that index is about 1.24. If the nominal shear stress from the load is 500 MPa, the corrected stress is roughly 620 MPa. The correction is not a small margin; it is a quarter of the answer.

Change the mean diameter to 6 mm and keep the wire, and the index falls to 3.75. The correction factor rises to about 1.43, so the same nominal stress becomes roughly 715 MPa, and the spring is also stiffer because the coil is smaller. Those figures are illustrative; the allowable stress depends on the material and the fatigue requirement.

Index, tolerance and the rate you actually get

Rate is proportional to wire diameter to the fourth power and inversely proportional to mean diameter cubed. That makes index a useful warning sign for tolerance sensitivity. A spring with a low index has a small mean diameter relative to its wire, so a fixed diameter tolerance is a larger percentage of the mean and moves the rate more.

The same logic applies to fit. A low index spring has less radial space between the wire and the shaft or bore, so the same diameter tolerance consumes more of the clearance. A high index spring has more space but is easier to deform, so handling and installation become the risk instead.

This is why tightening the rate tolerance is often the wrong response to a spring that will not repeat. If the index is at the edge of the band, the process has little room, and a tolerance call cannot create room the geometry does not have.

When the design has to leave the band

Sometimes the envelope forces an index outside 4 to 12. A heavy load in a small radial space pushes the index down. A very low rate in a large bore pushes it up. The job then is to manage the consequence.

• For a low index, choose a cleaner spring wire, specify stress relief after coiling and consider shot peening for fatigue.
• For a low index, allow a generous radius and avoid additional bends or nicks that act as stress raisers.
• For a high index, control free length with a fixture and pack parts so coils cannot deform in transit.
• For a high index, check buckling with a guide rod or a bore, and state the installed support in the drawing.
• In both cases, ask for a first article with a rate and load test rather than dimensions alone.

What to put on the drawing

The drawing does not need to state the index, but it should make the index easy to check. Give the wire diameter with its tolerance, the outside or inside diameter with its tolerance and the total and active coil counts. State the rate and the load at a specified length, then let the supplier confirm the index during DFM review.

If the design is close to a boundary, say so. A note that the index is 3.8 and the fatigue life is critical tells the supplier to plan stress relief, wire selection and inspection accordingly.