Free Engineering Tool — #009
Rotor Critical Speed Calculator
Calculate the first critical speed (natural frequency) of a shaft with central mass or distributed mass using the Rayleigh method. Compare with operating RPM for safety margin.
Results
Second Moment of Area
Central Mass — Simply Supported
For a shaft with a concentrated mass m at mid-span and simply supported ends:
Support Condition Factors
The stiffness coefficient k changes with support type:
| Support | Stiffness k | Factor vs SS |
|---|---|---|
| Simply Supported (central load) | 48EI / L³ | 1.00 |
| Fixed-Fixed (central load) | 192EI / L³ | 4.00 |
| Cantilever (end load) | 3EI / L³ | 0.0625 |
Practical Example
Given: L = 800 mm, d = 50 mm, m = 30 kg, Steel E = 210 GPa, Simply Supported
I = π × 50⁴ / 64 = 306,796 mm⁴
k = 48 × 210,000 × 306,796 / 800³ = 6,040 N/mm
ω_n = √(6,040,000 / 30) = 448.7 rad/s
N_cr = 448.7 × 60 / (2π) = 4,285 RPM
⚠️ Note: This simplified model assumes a massless shaft with a single concentrated mass. For more accurate results on heavy shafts, consider the Rayleigh or Dunkerley methods that account for distributed shaft mass.
The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.
Professional field balancing instruments and software. Measure vibration, find critical speeds, and balance rotors on-site. Used in 50+ countries.
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.
