Conical spring calculator
Calculate the initial rate, maximum load and deflection of conical (tapered) springs. Enter both end diameters and see the progressive characteristic.
Formula
This is the initial rate. As the spring compresses, the largest coils bottom out first and the rate rises: conical springs are progressive by nature.
Simboli
Esempio calcolato
Calcolato dallo stesso motore del calcolatore sopra, con i valori iniziali del modulo.
Conical springs combine a reduced solid height with lateral stability: the coils can nest into each other and the body resists buckling better.
The rate is not fixed: once the largest coil bottoms, the active portion shortens and the spring stiffens. The calculator shows the initial rate and where the progression starts.
Use the full designer to see the entire force versus deflection curve and get a quote with a technical drawing.
Come misurare la molla
- Measure the wire diameter (d).
- Measure the outer diameter at both ends: the small end and the large end.
- Measure the free length with no load.
- Count the total number of coils.
Moduli e densità dei materiali
| Materiale | Modulo di taglio G | Modulo elastico E | Densità |
|---|---|---|---|
| Acciaio al carbonio (MW) | 11.5 × 10⁶ psi (79.3 GPa) | 29.5 × 10⁶ psi (203.4 GPa) | 7.85 g/cm³ |
| Inox 302 (SS302) | 10.0 × 10⁶ psi (69.0 GPa) | 28.0 × 10⁶ psi (193.0 GPa) | 7.90 g/cm³ |
| Inox 17-7 PH (SS177) | 11.0 × 10⁶ psi (75.8 GPa) | 29.4 × 10⁶ psi (203.0 GPa) | 7.81 g/cm³ |
| Inox 316 (SS316) | 10.0 × 10⁶ psi (69.0 GPa) | 28.0 × 10⁶ psi (193.0 GPa) | 7.98 g/cm³ |
| Temprato in olio (OT) | 11.2 × 10⁶ psi (77.2 GPa) | 29.5 × 10⁶ psi (203.4 GPa) | 7.85 g/cm³ |
| Cromo-silicio (CS) | 11.2 × 10⁶ psi (77.2 GPa) | 29.5 × 10⁶ psi (203.4 GPa) | 7.85 g/cm³ |
| Trafilato duro (HD) | 11.5 × 10⁶ psi (79.3 GPa) | 29.5 × 10⁶ psi (203.4 GPa) | 7.85 g/cm³ |
| Bronzo fosforoso (PB) | 6.0 × 10⁶ psi (41.4 GPa) | 14.9 × 10⁶ psi (103.0 GPa) | 8.86 g/cm³ |
| Rame berillio (BC) | 7.0 × 10⁶ psi (48.3 GPa) | 18.6 × 10⁶ psi (128.0 GPa) | 8.25 g/cm³ |
| Cromo-vanadio (CV) | 11.2 × 10⁶ psi (77.2 GPa) | 29.5 × 10⁶ psi (203.4 GPa) | 7.85 g/cm³ |
Domande frequenti
Why choose a conical spring?
For the low solid height (coils can telescope), for stability without a guide on long strokes, and for the progressive characteristic, useful for absorbing impact.
Is the rate of a conical spring linear?
Only at the start of the stroke. As the larger coils bottom out, the rate rises progressively until the spring is solid. That behavior is desirable in many damping applications.
How is the initial rate calculated?
k = G·d⁴ / (2·Na·(D₁+D₂)·(D₁²+D₂²)), using the mean diameters of both ends. With D₁ = D₂ the formula reduces to the cylindrical spring formula.
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