Free Engineering Tool
Spring Critical Speed Calculator
Calculate the critical surge frequency of a helical compression spring — the resonant frequency at which standing waves form along the coils, causing surging.
Results
Surge Frequency
The critical surge frequency of a helical compression spring (fixed-fixed / free-free boundary, fundamental mode):
- d — wire diameter (m)
- D — mean coil diameter (m)
- nₐ — number of active coils
- G — shear modulus of the wire material (Pa)
- ρ — wire material density (kg/m³)
Spring Stiffness
Spring Index & Fixed-Free Frequency
The spring index C should typically be between 3 and 15 for practical spring designs.
Practical Example
Given: d = 5 mm, D = 30 mm, nₐ = 7, Spring steel (G = 79.3 GPa, ρ = 7850 kg/m³)
√(G / 2ρ) = √(79.3×10⁹ / (2 × 7850)) = 2247.4
f_surge = 0.005 / (2π × 7 × 0.030²) × 2247.4 = 283.9 Hz (17,032 RPM)
k = 79.3×10⁹ × 0.005⁴ / (8 × 0.030³ × 7) = 32.8 N/mm
C = D/d = 30/5 = 6.0 (good, within 3–15 range)
f_fixed-free = 283.9 / 2 = 142.0 Hz
⚠️ Rule of thumb: The surge frequency should be at least 13× the operating frequency for valve springs, and 15–20× for general industrial applications.
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Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
