Driveshaft Max Length for an Operating Speed
The longest a tube can be before it whips at a target operating speed.
Example
You enter
- Operating speed (RPM) 6385.23
- Tube outer diameter (in) 3.5
- Tube wall thickness (in) 0.083
- Material steel
You get
- Max shaft length 48.0 in
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
ScopeL_max = L_ref x sqrt(0.65 x N_crit_ref / target_rpm), since the first-mode critical speed falls as 1/length^2 and you stay below 0.65 of critical. A 3.5 in x 0.083 in steel tube that has to run at 2,800 RPM can be at most 72.5 in long; halve the RPM and it can grow 41% to 102.5 in. Answers 'how long can I make it' instead of the critical speed of one length. A bare-tube estimate; split a long run with a center bearing. The driveline manufacturer governs.
Formula or tableN_crit falls as 1/L^2, so L_max = L_ref × sqrt(0.65 × N_crit_ref / target_rpm), keeping the running speed at or below 0.65 × critical. The inverse of N_crit (rpm) = (94.25/L^2) × sqrt(E I / (rho A)).
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 namestarget_rpm, od_in, wall_in, material, max_length_in
- 1/L^2 critical speed the first-mode critical speed scales as 1/length^2; L_max = L_ref x sqrt(0.65 x N_crit_ref / target_rpm)Euler-Bernoulli beam theory
- Operating margin keeps the running speed at or below 0.65 x critical (guidance 0.6-0.75)AAM / Spicer engineering manuals
- Bare-tube estimate yokes, slip joint, balance, and support bearings shift the real critical speed; keep margindriveline practice