Rotor Dynamics — validation & limitations

What it calculates

• Lateral critical speeds via a multi-DOF beam-FEM eigensolver with Timoshenko shear and rotary inertia (undamped rotor model; cross-checked against closed-form beam and rigid-body limits)
• Gyroscopic splitting into forward and backward whirl branches
• Mode shapes at each critical speed — the computed whirl shape on your shaft and bearing positions, gyroscopic stiffening included, checked against ROSS by the modal assurance criterion
• Campbell diagram with 1×, 2×, and 3× engine-order excitation lines and API 684 separation-margin check
• Unbalance response vs. speed, solved on the whole rotor — every mode, both planes, gyroscopic coupling — reporting the largest orbit on the shaft and where it occurs
• Optional bearing damping (N·s/m): per-mode damping ratio, logarithmic decrement and amplification factor from a damped complex eigensolution — excluding destabilising cross-coupling, so the log decrement is an upper bound rather than an API 684 stability result
• Bearing orbit plot with keyphasor and clearance circle
• ISO 1940-1 balance quality grade (the full G0.4 to G4000 ladder) — permissible eccentricity, unbalance, and correction mass

Standards this tool applies

• ISO 1940-1 — Computes the achieved balance grade (banded G0.4–G4000, per ISO 1940-1:2003; ISO 21940-11:2016 is the successor), permissible eccentricity and single-plane correction mass for a target grade, alongside critical-speed and Campbell-diagram analysis. It does not implement API 684 acceptance or the ISO 21940-11 procedures beyond this relation.

Validation evidence — independent reference cases (2)

Each case runs the tool's engine on a worked example whose values come from a published source or a hand derivation from the cited equations, and an automated regression test asserts the engine against those values within the stated tolerance. "Conservative" means the engine is known to sit on the safe side of the reference and the test asserts that side. Sources are cited; their text is not reproduced.

• Critical speeds of a bare pinned-pinned shaft and API 684 margin

  Agrees

  Source: Blevins, Formulas for Natural Frequency and Mode Shape, 1979, Table 8-1 (pinned-pinned uniform beam, λ_n = nπ); API 684 2nd ed. separation-margin rule

  Inputs: shaft Ø40 × 1000 mm, 42CrMo4 (E 206 GPa, ρ 7850), no disc, rigid supports 1e7 N/µm, ζ 0.03, 3000 rpm and 4000 rpm cases

  Quantity	Reference value	Tolerance
  1st critical speed	4828.03 rpm	0.5 % relative
  2nd critical speed	19 312.1 rpm	1.5 % relative
  Required separation margin (ζ 0.03)	25.561 %	1e-4 relative
  Actual margin at 3000 / 4000 rpm	60.93 % (pass) / 20.70 % (fail)	0.7 / 1.0 percentage points

  Conservative simplification: The engine's Timoshenko finite-element model reads 0.10 % (mode 1) and 0.38 % (mode 2) below the Euler-Bernoulli closed form, which is the conservative side.

  tests/golden/REF-dynamics-critical-speed.golden.test.ts

• ISO 1940-1 balance quality grade G from residual unbalance

  Agrees

  Source: ISO 1940-1:2003 (now ISO 21940-11:2016): specific unbalance e = U/m, balance quality G = e·Ω, Table 1 grades

  Inputs: Case 1: 10 kg rotor, 3000 rpm, 2.005 g and 2.100 g at 100 mm; Case 2: defaults Ø80 × 360 shaft + 8 kg rotor, 0.5 g at 40 mm, 15 000 rpm

  Quantity	Reference value	Tolerance
  G for 200.5 g·mm at 3000 rpm	6.298893 mm/s (G6.3)	1e-6 relative
  G for 210 g·mm at 3000 rpm	6.597345 mm/s (G16)	1e-6 relative
  Rotor mass basis, defaults	22.20503 kg	1e-6 relative
  G, defaults	1.414812 mm/s (G2.5)	1e-5 relative

  tests/golden/REF-dynamics-iso1940-grade.golden.test.ts

Limitations

Conservative simplifications

• Critical speeds of a bare pinned-pinned shaft and API 684 margin — The engine's Timoshenko finite-element model reads 0.10 % (mode 1) and 0.38 % (mode 2) below the Euler-Bernoulli closed form, which is the conservative side.

Not checked by this tool

• Damped unbalance response with bearing and seal coefficients (API 684) — This is a screen; a compliance analysis needs a damped rotordynamic model with fluid-film bearing and seal coefficients
• Rotor stability (cross-coupled stiffness, oil whip, seal forces) — Log decrement comes from bearing damping only; run a stability analysis for turbomachinery
• Torsional critical speeds of the drive train — Lateral analysis only; check torsional modes with the coupling and motor inertias
• Foundation and pedestal flexibility — Bearings are springs to rigid ground; include pedestal stiffness when it is not much stiffer than the bearings
• Non-steel shafts — Steel modulus and density are used; for other materials use a general rotordynamics code
• Shaft stress and bearing life — Use /shaft and /bearings