Driveshaft Critical Speed
Euler-Bernoulli first-mode critical RPM with safety-factor recommendation.
Example
You enter
- OD (in) 3.5
- Wall (in) 0.083
- Length between U-joints (in) 48
- Material steel
You get
- Critical RPM 9,823
- Recommended max (0.65x) 6,385 rpm
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
Formula or tableEuler-Bernoulli first-mode whirl (simply-supported, eigenvalue (βL)² = π²): N_crit = (60 / 2π) × (π² / L²) × sqrt((E × I) / (ρ × A)) RPM (the bracketed term is rad/s). Recommended max operating = 0.65 × N_crit (engineering-practice safety margin).
Source and editionEuler-Bernoulli beam theory by name; AAM (American Axle) and Spicer / Dana driveshaft engineering manuals by name.
Free accessBeam-theory principles free in mechanics-of-materials texts at university OCW.
What governsEstimate. AHJ and licensed professional govern.
API field namesod_in, wall_in, length_in, material, critical_rpm, recommended_max_rpm
- Material moduli / densities steel E = 200 GPa (29.0e6 psi) and 7,850 kg/m^3 (0.284 lb/in^3) by default, or user-suppliedengineering reference
- Operating margin 0.65 × N_crit recommendedAAM / Spicer engineering manuals