KEVOS® MAKEOS · Springs
Helical Compression Spring Design Check
What rate, load and stress will this compression spring have at its working length?
Rate, working load, Wahl-corrected shear stress, solid length, stress at solid, natural frequency and buckling ratio of a round-wire helical compression spring.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Wire diameter | mm | Measured or specified wire diameter. |
| Mean coil diameter | mm | Mean coil diameter = outside diameter − wire diameter. |
| Active coils | coils | Coils that deflect; for closed ends this is total coils minus 2. |
| End type | choice | End form of the spring. |
| Shear modulus | GPa | Shear modulus of the wire (about 79 GPa for spring steel, about 69 GPa for stainless 302). |
| Unloaded (free) length | mm | Length with no load. |
| Working (compressed) length | mm | Installed or working length under the maximum load. |
| Allowable shear stress | MPa | Allowable shear stress for the wire material, size and duty (static or fatigue) from the spring maker or design data. |
| Wire density | kg/m³ | Wire material density (steel about 7850 kg/m³). |
Method and formulas
- Rate k = G d⁴ ÷ 8D³Na; index C = D ÷ d; Wahl K = (4C − 1) ÷ (4C − 4) + 0.615 ÷ C.
- Load F = k(L₀ − L_w); stress τ = K × 8FD ÷ πd³.
- Total coils and solid length by end type: closed & ground Nt = Na + 2, Ls = Nt d; closed Nt = Na + 2, Ls = (Nt + 1)d; plain & ground Nt = Na + 1, Ls = Nt d; plain Nt = Na, Ls = (Nt + 1)d.
- Natural frequency (fixed ends) f = ½√(k ÷ m_active), m_active = ρπ²d²DNa ÷ 4.
- Example: 2 mm wire, 16 mm mean diameter and 8 active coils give k = 4.8401 N/mm, 72.601 N at 35 mm and τ = 437.8 MPa.
Limitations
- Round wire, uniform pitch and axial loading; hook or eccentric loads raise stress.
- Buckling depends on end restraint; the slenderness ratio is a screening value only.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a catalogue or custom spring against a duty
- Specify a replacement spring
- Check stress at solid before ordering
Who it is for
- Design engineers
- Spring buyers
- Maintenance engineers
What you get
- Spring rate and working load
- Spring index and Wahl factor
- Corrected shear stress at working length and at solid
- Solid length, total coils and clash allowance
- Natural frequency and buckling ratio
Interpreting the result
- Keep the stress at solid below the allowable so the spring survives being fully compressed; keep C between about 4 and 12 for easy manufacture.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 304–324. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
