How to use this calculator
- Enter spring geometry. Enter wire diameter, mean coil diameter, active coils and total coils.
- Pick material. Select spring material to set shear modulus and density.
- Enter moving mass. Enter the attached mass and the spring mass factor used in the effective mass.
- Set operating frequency. Enter the cycle frequency and target separation ratio.
- Review margin. Read natural frequency, maximum operating frequency and frequency ratio.
How it works
A helical spring's first screening frequency can be estimated as a simple
mass-spring system. First calculate spring rate from the same geometry used by
the spring rate calculator:
k = G x d^4 / (8 x D^3 x N_a)
where G is shear modulus, d is wire diameter,
D is mean coil diameter and N_a is active coils.
The spring wire mass is estimated from wire length and density:
L_wire ~= pi x D x N_t m_s = rho x A_wire x L_wire
The moving mass is then m_eff = m_load + eta x m_s. For a spring
with one end fixed and a mass attached to the other, eta = 1/3 is
a common first-pass effective spring mass factor.
Natural frequency follows:
f_n = (1 / (2pi)) x sqrt(k / m_eff)
using k in N/m and m_eff in kg. The frequency ratio
f_n / f_op compares that estimate with your operating cycle
frequency. Use the
compression spring calculator for
stress, solid height and buckling, and the
spring pitch calculator for coil spacing
and travel-to-solid geometry.
Worked example
Verified against the live calculator
A music-wire spring with d = 2 mm, D = 16 mm,
N_a = 6, N_t = 8 and a 0.25 kg moving
mass has rate about 6.45 N/mm. The wire length is about
0.402 m, spring mass is about 0.0099 kg, and with
eta = 1/3 the effective mass is about 0.253 kg.
That gives natural frequency about 25.4 Hz.
Spring material data
The calculator uses shear modulus for spring rate and density for spring mass. Verify production designs against supplier-certified material data.
| Material | Standard | G (GPa) | Density (kg/m3) |
|---|---|---|---|
| Music wire | ASTM A228 | 79.3 | 7850 |
| Oil-tempered | ASTM A229 | 77.2 | 7850 |
| Hard-drawn | ASTM A227 | 77.2 | 7850 |
| Chrome silicon | ASTM A401 | 77.2 | 7850 |
| Chrome vanadium | ASTM A232 | 77.2 | 7850 |
| Stainless 302/304 | ASTM A313 | 69 | 7920 |
Source: MachineCalcs spring material dataset from standard spring-design references and ASTM wire standards.
Frequently asked questions
How do you calculate spring natural frequency?
For a first-pass helical spring and attached mass, calculate the spring rate k, estimate the effective moving mass m_eff = m_load + eta x m_s, then use f_n = (1/(2pi)) x sqrt(k/m_eff).
What is effective spring mass?
Not all of the spring wire moves at the same velocity as the attached load. A common one-end-fixed approximation adds one third of the spring mass to the attached moving mass.
What separation ratio should I use?
A conservative screening target keeps operating frequency several times below the estimated natural frequency. The calculator defaults to a 5:1 target, but the right value depends on duty, damping, response tolerance and test data.
Does this calculate spring surge?
It estimates the first lumped mass-spring natural frequency. True spring surge is distributed vibration in the spring body and depends on end constraints, coil geometry, damping, guides, preload and actual operating motion.
Can I use this for valve springs?
Use it as a screening check only. Valve springs also need cam dynamics, installed loads, open loads, coil-bind margin, retainer mass, damping, harmonics, spintron or test data and manufacturer limits.
Method & assumptions
- Linear helical spring, constant rate, small-displacement first-mode screen.
- Spring wire length is approximated as
pi x D x N_t; pitch helix angle and end detail are not modeled. - Effective spring mass is user controlled;
1/3is a common one-end-fixed approximation. - Spring surge, damping, guides, preload, nonlinear/progressive coils, coil clash, harmonics, fatigue, impact and test correlation are outside this screen.