Spring Index: Why a Fat Wire on a Small Coil Fights Back

When a helical spring is pushed along its axis, the wire is not stretched or bent as a whole — it is **twisted**. Each little length of wire carries a torque, and the spring deflects because the whole wire winds up slightly along its length. That gives the simple stress formula, which is just the torsion of a round bar: τ = 8FD/πd³. **Two things make it wrong.** *Direct shear.* The load is also pushing the wire sideways, and that shear adds to the torsional shear on one side of the wire and subtracts on the other. It is a small effect and it always adds where you do not want it — the inside of the coil. *Curvature.* The wire on the inside of a turn is on a shorter radius than the wire on the outside, so for the same twist it is strained more. The tighter the coil relative to the wire, the worse it gets. **The Wahl factor bundles both** into one multiplier that depends only on the index. It is always greater than one, and it is the reason a spring almost always fails on the INSIDE of a coil. **Look at a broken spring and you can see this.** The crack starts on the inner surface, where the stress is highest and where any drawing mark or rust pit is also concentrated. A spring is a component with a known worst point, which is unusual and useful.

**Measure the wire with a micrometer, not a caliper**, and measure it in two places at right angles. Spring wire is round to a tight tolerance, but a spring that has been overloaded can have a flattened coil, and a caliper on a curved wire reads high. **Measure the OUTSIDE diameter of the coil**, because that is the one you can actually reach, then subtract one wire diameter to get the mean: D = D_outside − d **Not two.** This is the commonest arithmetic slip in spring work. The mean diameter runs through the centre of the wire, so it is the outside diameter minus one full wire, or the inside diameter plus one full wire. **Then C = D/d**, and you immediately know three things: roughly how stressed the wire is for a given load, whether the spring could have been wound cold, and whether a replacement you are considering is in the same family. **A quick sanity check on any spring you are handed:** an index under 4 on a cheap mass-produced spring is very unlikely, so if your arithmetic says 2.8, check whether you subtracted the wire diameter twice.

**The mandrel is smaller than the coil you want.** Wire springs back when released, by an amount that depends on the material and the index. A rough starting point for hard-drawn spring steel is a mandrel about 10 to 15% smaller than the mean diameter wanted, and then you adjust by measuring what you actually got. Nobody hits it first time. **Springback grows with index.** A tight coil is mostly plastic deformation and comes off close to the mandrel size. A wide coil is closer to elastic and opens out noticeably. This is why the same mandrel and the same technique give a different error on a different spring. **Hold the wire hard.** The tension in the wire as it feeds onto the mandrel sets the pitch and keeps the coils tight against each other. Loose feed gives uneven pitch, which gives uneven rate along the spring. **Wind in the vice, with the mandrel clamped and the wire led round it** — not the other way about. Turning the mandrel by hand with the wire held is far more controllable than trying to wrap wire round a fixed rod. **Leave the ends long** and cut them afterwards. A coil that ends exactly where you wanted it has never happened. **A hard wire cannot be coiled at a low index and then used as it is.** Below about C = 4 the outside of the bend exceeds the wire's ductility and the surface cracks. Those cracks are on the tension side, which becomes the outside of the coil, so they are visible with a loupe. Look before you fit it. **And a coiled spring made from annealed wire is not a spring yet** — it must be hardened and tempered afterwards, or it will take a set the first time it is used. Music wire and hard-drawn wire are supplied already at strength, which is why they are coiled cold and only stress-relieved after.