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Spring rate, initial tension, force at any length and stress in the body and the hooks for extension springs; torque, angle and stress for torsion springs. Pick the wire and see the spring stretch or wind up to scale.
| Wire d | Coils | Body | C | % limit |
|---|
An extension spring is wound with the coils pressed together and a built-in initial tension Fi: it does not move until the pull exceeds Fi. The hooks, not the body, usually fail first, because the wire is bent sharply where the hook leaves the body.
A torsion spring is loaded by a moment that bends the wire, so the stress is bending, not shear. As it winds up the coil diameter shrinks and the body gets longer, so it needs an arbor with clearance.
Wire strength Sut = A / d^m and the moduli G and E follow Shigley's Mechanical Engineering Design (tables 10-4, 10-5, 10-7, 10-10) and EN 13906-2/-3. Keep the index C between 4 and 12. Results are for static or slowly cycled loads; fatigue-rated springs need lower stresses and shot peening.
This calculator designs and checks a helical extension spring with full loop hooks. Enter the wire diameter, outer diameter, number of body coils, initial tension, material and the installed and working lengths. It returns the spring rate, free length inside the hooks, force at every length, and the stress at the three places an extension spring fails: the body, the bend where the hook leaves the body, and the twist at the hook base. It also gives the initial tension range a spring maker can actually coil, the maximum safe stretch, and alternative wire sizes for the same rate. Switch to torsion mode for springs loaded by a twisting moment.
The spring has a rate of 1.70 N/mm and pulls 37 N at 70 mm. The hook base is the most stressed point at 43 % of its limit, so the spring is safe; the preferred initial tension for C = 7.75 is 10.4 – 16.2 N, and 12 N is inside it.
Extension springs are wound with the coils pressed against each other and a twist locked into the wire. That built-in load, the initial tension, must be overcome before the coils separate. Below it the spring does not stretch at all. How much a maker can put in depends on the spring index: tight springs (low C) can hold more.
Where the hook bends away from the body the wire is curved sharply, which concentrates bending and twisting stress. In most designs the hook stress is higher than the body stress, so the hook should always be checked. A larger bend radius, a reduced hook or a swivel hook lowers it.
Free length is usually measured inside the hooks, from the inside of one loop to the inside of the other, with the spring unloaded. With full loop hooks it equals the body length (Nb + 1)·d plus about one inside coil diameter per hook.
Measure the wire and outside diameters and count the body coils. The rate is k = G·d⁴/(8·D³·Na), where D is the mean diameter and Na is the body coils plus G/E for the hooks. You can also hang two known weights and divide the difference in force by the difference in length; the initial tension then falls out as the force at zero stretch.
Until the most stressed point – body, hook bend or hook base – reaches its static limit. The calculator shows this as the maximum safe length. Unlike a compression spring there is no solid stop, so use a mechanical limit if the load can exceed it.
Aim for an index C between 4 and 12. Below 4 the wire is very hard to coil; above 12 the coils cannot hold much initial tension and the diameter varies from coil to coil.
What you need to build, measure or check the result.
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