Whirling Shaft Critical Speed Calculator

• •Use the Whirling Shaft Critical Speed Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations — instant feedback helps identify arithmetic errors before they propagate.
• •Use it during the early design phase to rapidly iterate on parameters and narrow down feasible configurations before committing time to detailed finite element simulations or full design packages.
• •Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility — a quick sanity check can prevent costly downstream errors.
• •Use it to generate reference data for a technical report or presentation without manual computation, ensuring consistent, reproducible numbers throughout the document.
• •Use it in the field when a quick estimate is needed and a full engineering software package is not available.

The Whirling Shaft Critical Speed Calculator is a precision engineering calculation tool designed for students, engineers, and technical professionals. Critical whirling speed of a shaft with mounted disks using Rayleigh's energy method, with deflection shape plot All calculations are performed using established engineering formulas from the relevant scientific literature and standards. Inputs support both metric (SI) and imperial unit systems, with unit conversion handled automatically — simply select your preferred unit from the dropdown next to each field. Results are computed instantly in the browser without sending data to a server, ensuring both speed and privacy. This calculator is intended as a supplementary tool for learning and design exploration; always verify results against authoritative references for safety-critical applications.

Whirling is the lateral vibration of a rotating shaft, where the shaft's center of mass orbits the bearing axis. Critical whirling speed occurs when the rotation rate equals the shaft's natural lateral bending frequency, causing large amplitudes. For a shaft with mounted disks, Dunkerley's method gives 1/ω_c² = 1/ω_shaft² + 1/ω_disk_i² for each disk i, where ω_shaft is the natural frequency of the shaft alone (treating as beam) and ω_disk is the natural frequency with only that disk. Rayleigh's method uses energy balance: ω_c² = g·Σ(W_i·δ_i) / Σ(W_i·δ_i²), more accurate than Dunkerley. Both methods estimate the first (lowest) critical speed. For a simply supported shaft of length L with disk at position a, the static deflection at disk is δ = W·a²·(L − a)²/(3·E·I·L), and the natural frequency is ω = √(g/δ). For multiple disks, superposition of static deflections at each mass location is used. Shafts operated above the first critical speed ('supercritical') must pass through it quickly at startup and shutdown to avoid excessive vibration. Multiple critical speeds exist for real shafts; usually only the first matters for machine design because operating speeds stay below the second critical speed.

• •Turbine shaft design: large turbine rotors (steam, gas) operate near critical speeds and require careful Rayleigh analysis to verify margins.
• •Gearbox shaft analysis: shafts supporting multiple gears must have first critical speed above maximum operating speed.
• •Pump rotor dynamics: multistage pump shafts with multiple impellers have complex mode shapes and multiple criticals.
• •Balancing machine verification: unbalance detection relies on shafts operating well below first critical where rigid rotor theory applies.
• •Automotive driveshaft design: 2-piece driveshafts are used when single-piece would have first critical below maximum speed.