Helical Spring Natural (Surge) Frequency
The surge (natural) frequency of a helical spring, and how close the working cycle runs to it.
Example
You enter
- Wire diameter d (in) 0.08
- Mean coil diameter D = OD - d (in) 0.75
- Active coils Na 8
- Wire material hard-drawn
You get
- Natural frequency (Hz) 250.3
- Spring rate 17.45 lb/in (matches helical-spring-rate)
Details, formula, and sources
A spring cycled near its own resonance surges: the coils bunch into a travelling wave, the working force spikes, and the spring floats off the cam or fatigues. Shigley's closed form for a spring held between flat plates is fn = (1/2) sqrt(k g / W), with the standard rate k = G d^4/(8 D^3 Na) and the weight of the active coils W = pi^2 d^2 D Na gamma / 4 (gamma the wire weight density, steel 0.284 lb/in^3). A 0.080 in hard-drawn wire, 0.75 in coil, 8 active coils rings at 250 Hz (15,000 cycles/min) - the rate 17.4 lb/in agrees exactly with the spring-rate formula; music wire raises it to 254 Hz, phosphor bronze drops it to 170 Hz. For a valve spring keep fn 13-20x above the highest valvetrain forcing harmonic. Higher modes are integer multiples; damping and variable-pitch springs are not modeled. A screen; Machinery's Handbook / Shigley and the spring maker govern.
fn = (1/2) sqrt(k g / W); k = G d^4/(8 D^3 Na); W = pi^2 d^2 D Na gamma / 4; g = 386.4 in/s^2. gamma by material: steel 0.284, stainless 0.286, phosphor bronze 0.320 lb/in^3. Higher modes are integer multiples of fn.
The fundamental surge frequency of a helical compression spring held between flat parallel plates, per Shigley's Mechanical Engineering Design and Machinery's Handbook, by name; the rate k is identical to the helical-spring-rate tile and the wire weight density gamma is a published material constant.
The surge-frequency formula is a public machine-design result; the rate and the per-material weight density are published constants. Wire and coil dimensions and material are the user's inputs.
Estimate. AHJ and licensed professional govern.
Field names used by the API: wire_diameter_in, mean_coil_diameter_in, active_coils, material, natural_frequency_hz, spring_rate_lb_in
- Surge frequency fn = (1/2) sqrt(k g / W), both ends against flat parallel platesShigley / Machinery's Handbook
- Active-coil weight W = pi^2 d^2 D Na gamma / 4, gamma the wire weight densitygeometry + material density
- Rate cross-pin k = G d^4/(8 D^3 Na), identical to helical-spring-rateMachinery's Handbook / Shigley