Spring Set Removal⚠ unverified
Mechanical / Springs · Compute the set-removal (preset) stress limit for a spring
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| F | F | N | 1.0 | Applied axial force |
| d | d | m | 1.0 | Wire diameter |
| D | D | m | 1.0 | Mean coil diameter |
| Sut | Sut | Pa | 1.0 | Ultimate tensile strength of the wire material |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | τset | Pa | Set-removal stress limit, in pascals (Pa) |
The science & history
Understanding the Parameters
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Ultimate tensile strength $S_{ut}$ — the wire's ultimate strength, from which spring allowables are scaled. Spring wire is used at unusually high fractions of $S_{ut}$ (springs are made from very high-strength drawn or music wire), and the presetting threshold sits around $0.65\,S_{ut}$ in shear.
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The coefficient $0.65$ — an empirical fraction. Below roughly $0.65\,S_{ut}$ (in shear) essentially no permanent set occurs; presetting to this level or a little above yields the surface just enough to lock in beneficial residual stress without over-distorting the spring. Different references cite $0.6$–$0.7\,S_{ut}$ depending on material and desired set.
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Unused inputs $F$, $d$, $D$ — would normally give the actual operating stress $\tau = K\,8FD/(\pi d^3)$ to compare against this threshold; here they are placeholders.
Derivation (Approaching a Proof)
The value is an empirical strength ratio, not a closed-form derivation, but its basis is clear. Presetting requires the peak wire shear stress to exceed the material's shear yield strength so that the outer fibres flow plastically while the core stays elastic. On unloading, the elastic core forces the yielded surface into compression — a favourable residual stress.
The threshold is expressed relative to $S_{ut}$ because spring-wire yield data are scattered but $S_{ut}$ is reliably measured and scales predictably with wire diameter (via the Sut-vs-diameter power law for music/hard-drawn wire). Using the distortion-energy relation between shear yield and tensile strength ($S_{sy}\approx 0.577\,S_y$) and typical spring-wire $S_y/S_{ut}$ ratios, the practical set-removal shear stress lands near $0.65\,S_{ut}$. Presetting then permits raising the allowable working shear stress (often from ~0.45 to ~0.6 $S_{ut}$) because the residual stresses subtract from the service stress — directly analogous to autofrettage of gun barrels and pressure vessels.
Dimensional check. $[\tau_{\text{set}}] = [S_{ut}] = \text{Pa}$ (0.65 dimensionless). ✓
History and Development
Presetting (also called "scragging" or "removing set") is a long-standing spring-manufacturing practice, formalised in Wahl's Mechanical Springs and Shigley's design texts. It parallels the autofrettage of thick-walled pressure vessels and the shot-peening of fatigue-critical surfaces: all deliberately induce beneficial compressive residual stress. Modern high-duty valve and clutch springs are routinely preset and shot-peened to reach their high working-stress levels.
Related Concepts: Helical Spring Stress, Spring Index, Fatigue Endurance Limit, Goodman Line, Helical Spring Rate
Notes: Empirical threshold ($\approx 0.6$–$0.7\,S_{ut}$ in shear). The $F$, $d$, $D$ inputs are unused (registry artefact) — compute the actual stress with Helical Spring Stress and compare. Presetting raises allowable working stress via favourable residual stresses.