Why critical speed matters
Rotating shafts exhibit lateral vibration modes. When running speed approaches a natural frequency, unbalance forces amplify deflection, raise bearing loads, and accelerate fatigue. The first critical speed is the most common constraint for pumps, fans, compressors, and spindles. Estimating it early supports layout decisions, avoids costly test failures, and guides bearing selection. This calculator turns measured or estimated stiffness into a usable speed limit.
Interpreting the three methods
The static deflection method uses the classic Jeffcott idea: a rotor behaves like a mass on a flexible support, so frequency relates to how far it sags under weight. The mass–stiffness method fits the same physics to an equivalent spring and effective mass, useful when support data comes from finite‑element or bearing catalogs. The geometry method builds deflection from beam theory and a concentrated disc load.
Selecting inputs and units
Choose the method that matches your evidence. If you have dial‑indicator sag or a test stand measurement, use deflection. If you have lateral stiffness from a model or vendor, use mass and stiffness. If you are sizing a new shaft, use geometry with length, diameters, and modulus. Always keep units consistent; this tool converts common length, mass, stiffness, and material units to SI before calculations.
Safety factor and separation margin
Practical design avoids operating too close to resonance. The safety factor divides critical speed to produce a conservative maximum operating speed. The operating‑to‑critical ratio and separation margin indicate how much distance remains before resonance. Low ratios generally reduce amplification, while values near one demand added damping, stiffer supports, or a redesign. Use trends rather than a single value when varying load, temperature, or bearing condition.
Using results in design reviews
Document the method, assumptions, and chosen safety factor alongside the computed rpm, Hz, and rad/s. Compare the recommended limit with start‑up transients and any overspeed requirements. If the geometry method includes shaft self‑weight, treat the result as a better first estimate, but still validate with detailed rotor‑dynamics analysis for high‑speed machinery. Exported CSV and PDF outputs help share calculations across teams and audits with minimal additional effort today.