Hybrid-Electric Ferry Drive Train Tuning for Zero-Excitation Crossing

Case Study 2: Hybrid-Electric Ferry Drive Train Tuning for Zero-Excitation Crossing

Scenario: A new-build battery-diesel hybrid ferry operating on the Oslofjord route required certification under ClassNK’s Green Ship guidelines. During commissioning, torsional vibration spikes occurred at 210 rpm—coinciding with the transition point between diesel-only and parallel hybrid mode. Project type: new construction with integrated e-drive; location context: shallow fjord waters requiring frequent acceleration/deceleration (0–240 rpm duty cycle); constraints included zero tolerance for resonance crossings in the operational envelope (0–240 rpm = 0–4 Hz), strict NVH limits (<0.15 rad/s² RMS at thrust bearing), and inability to modify gearbox ratios due to space and certification lock-in.

Given data:

• Torsional stiffness (k): 41,200 Nm/rad (derived from finite element model validated by impact hammer testing on carbon-fiber-reinforced polymer (CFRP) composite shaft section)
• Polar moment of inertia (J): 8.73 kg·m² (sum of motor rotor, clutch assembly, and scaled propeller inertia; measured via inertia dyno)

Calculation: Using the same formula:

$$ f_n = \frac{1}{2\pi} \sqrt{\frac{k}{J}} $$

Substituting values:

• $ k = 41{,}200 , \text{Nm/rad} $
• $ J = 8.73 , \text{kg·m}^2 $
• $ \frac{k}{J} = \frac{41{,}200}{8.73} \approx 4719.36 $
• $ \sqrt{4719.36} \approx 68.70 $
• $ f_n = \frac{68.70}{2\pi} \approx \frac{68.70}{6.2832} \approx 10.93 , \text{Hz} $

Rounded to two decimal places: 10.93 Hz.

Result and decision: The natural frequency (10.93 Hz ≈ 656 rpm) falls well above the full operational speed range (0–240 rpm = 0–4 Hz), confirming no excitation crossing across any engine, motor, or gear mesh frequency harmonics (max relevant harmonic: 8× motor switching frequency = 3.2 kHz → irrelevant torsionally). However, sub-harmonic coupling was suspected. Further investigation revealed a 10.93 Hz peak aligned with the 2nd bending mode of the intermediate bearing support structure—indicating structural-torsional coupling. The solution was not shaft redesign, but localized stiffening of the aft bearing pedestal (adding 12 mm gusset plates), which raised the coupled mode to 13.2 Hz without altering k or J. The analyzer’s output thus served as a diagnostic anchor—not just a pass/fail metric.

Lesson: A 'safe' natural frequency does not guarantee system-level torsional immunity; always correlate torsional results with structural modes and verify coupling paths using multi-physics simulation and on-site modal testing.