KEVOS® MAKEOS · Springs
Extension Spring Designer (Body, Hooks, Initial Tension, Frequency)
Will this extension spring carry its working load without overstressing the body or the hooks, is the initial tension sensible, and how high is its natural frequency?
Design check of a helical extension spring with standard loop hooks: rate, load at the working extension, body shear stress with the Wahl factor (as the extension spring tool), the initial-tension stress against your range, hook bending stress at the loop and torsional stress at the bend radius (Wahl hook formulas), and the natural frequency of the spring fixed at both ends.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Wire diameter | mm | Diameter of the spring wire. |
| Mean coil diameter | mm | Mean diameter of the coils. |
| Active coils | Number of active coils (for loop ends, about the body coils). | |
| Shear modulus | GPa | Shear modulus of the wire. |
| Initial tension | N | Initial tension wound into the spring. |
| Working extension (beyond initial tension) | mm | Extension from the free position at the working load. |
| Allowable body shear stress | MPa | Allowable body shear stress at the working load (your value from the spring maker). |
| Hook loop mean radius | mm | Mean radius of the hook loop (usually half the mean coil diameter). |
| Hook bend mean radius | mm | Mean radius of the bend where the hook leaves the body. |
| Allowable hook bending stress | MPa | Allowable bending stress in the hook (your value). |
| Allowable hook torsional stress | MPa | Allowable torsional stress at the hook bend (your value). |
| Initial-tension stress, low end | MPa | Low end of the initial-tension stress the maker can wind for this index. |
| Initial-tension stress, high end | MPa | High end of the initial-tension stress the maker can wind for this index. |
| Wire density | kg/m³ | Density of the spring wire. |
Method and formulas
- Rate k = G d⁴ ÷ (8 D³ N_a); working load F = F_i + k x; body stress τ = K_w 8 F D ÷ (π d³) with the Wahl factor (as the extension spring tool).
- Hook bending σ_A = F [K₁ 16 D ÷ (π d³) + 4 ÷ (π d²)], K₁ = (4C₁² − C₁ − 1) ÷ [4C₁(C₁ − 1)], C₁ = 2r₁ ÷ d.
- Hook torsion τ_B = K₂ 8 F D ÷ (π d³), K₂ = (4C₂ − 1) ÷ (4C₂ − 4), C₂ = 2r₂ ÷ d.
- Natural frequency (both ends fixed) f = ½ √(k ÷ m_a), m_a = ρ π² d² D N_a ÷ 4.
- Example: the spring carries 56.993 N at 25 mm; the body runs at 509.11 MPa and the hook at 972.48 MPa bending.
Limitations
- Static design stresses; fatigue needs the stress range and the maker’s fatigue data.
- Hook formulas are for standard full loops; other end types differ.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design an extension spring for a return or counterbalance
- Find why springs break at the hook
- Check a spring for surge at a cycling frequency
Who it is for
- Design engineers
- Spring buyers
- Maintenance engineers
What you get
- Rate, working load and body stress
- Hook bending and torsional stresses
- Initial-tension stress and natural frequency
Interpreting the result
- Hooks usually fail first: a larger bend radius r₂ lowers the hook torsional stress the most.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 325–340. 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.
Open the Extension Spring Designer (Body, Hooks, Initial Tension, Frequency) calculator
