Case study

Propeller Cavitation Vibration Case Study

Naval engineering case study on propeller cavitation, blade-rate vibration, erosion evidence, cavitation number, rpm derating, propeller repair, sea-trial validation, and release decisions.

Propeller cavitation is not only a loss of efficiency. It can create pressure pulses on the hull, blade erosion, underwater noise, bearing load variation, crew discomfort, and fatigue risk in connected structures. A vessel may still reach speed while operating in a damaging condition.

This case study follows a coastal ferry that develops blade-rate vibration and visible propeller erosion after a propeller repair and a change in service loading. The case is hypothetical and intended for engineering education. It shows how a naval engineer should connect cavitation number, wake, shaft speed, vibration evidence, delivered power, operating restriction, repair action, and sea-trial validation.

The central question is:

Can the vessel keep its scheduled rpm because propulsion power is available, or should the operating envelope be restricted until cavitation and vibration evidence are resolved?

The correct decision is to restrict the damaging rpm range, investigate the propeller and wake condition, and release normal service only after measured vibration, cavitation evidence, and performance data agree.

Case Context

The vessel is a twin-screw ferry. One propeller shows higher vibration and faster coating loss than the other. Divers report leading-edge roughness, local pitting, and polished erosion marks near the outer blade radius.

ItemDegraded service value
propeller diameterD=2.2\ \text{m}
number of bladesZ=4
shaft speedn=5.8\ \text{rev/s}
vessel speedV=8.0\ \text{m/s}
wake fraction at propellerw=0.25
shaft-center immersionh=2.4\ \text{m}
seawater density\rho=1025\ \text{kg/m}^3
seawater vapor pressurep_v=2.3\ \text{kPa}
atmospheric pressurep_{atm}=101\ \text{kPa}
measured blade-rate vibration4.5\ \text{mm/s RMS}
vibration review limit at blade rate3.0\ \text{mm/s RMS}
delivered power in degraded run1.80\ \text{MW}
effective power estimate0.98\ \text{MW}

These values are simplified. A real review would use class requirements, propeller drawings, cavitation tunnel evidence, hull wake measurements, shaft-power instrumentation, vibration spectra, underwater noise criteria, blade inspection data, trial corrections, and operating profile.

Field Evidence

The failure mode is supported by several independent observations:

EvidenceEngineering interpretation
vibration peak appears at blade-rate frequencypropeller excitation is a credible source
diver inspection finds blade pitting near outer radiuscavitation erosion is plausible
vibration worsens at high rpm and heavy loadingblade loading and local pressure are involved
delivered power rises without expected speed gainpropulsive efficiency has deteriorated
sister propeller does not show the same vibration levelthe issue is not only sea state or normal hull resistance

The important point is that speed alone is not the acceptance metric. Cavitation damage can grow while the vessel still appears operational.

Wake and Advance Ratio

The advance speed into the propeller is reduced by wake:

V_A=V(1-w)
V_A=8.0(1-0.25)=6.0\ \text{m/s}

Propeller advance ratio:

\displaystyle J=\frac{V_A}{nD}
\displaystyle J=\frac{6.0}{5.8(2.2)}=0.47

The value is not judged by itself; it must be compared with the propeller curve, blade loading, and cavitation margin. Here it indicates a heavily loaded operating point for the measured wake and rpm.

Cavitation Number Screen

Use a common cavitation number form:

\displaystyle \sigma=\frac{p_\infty-p_v}{0.5\rho V_{rel}^2}

where p_\infty is local absolute reference pressure, p_v is vapor pressure, and V_{rel} is a representative blade-section relative speed.

Estimate absolute pressure at shaft center:

p_\infty=p_{atm}+\rho gh
p_\infty=101000+1025(9.81)(2.4)=125{,}100\ \text{Pa}

Use the 0.7R radius:

\displaystyle r=0.7\frac{D}{2}=0.7(1.1)=0.77\ \text{m}

Tangential speed at 0.7R:

V_t=2\pi nr
V_t=2\pi(5.8)(0.77)=28.1\ \text{m/s}

Representative relative speed:

V_{rel}=\sqrt{V_A^2+V_t^2}
V_{rel}=\sqrt{6.0^2+28.1^2}=28.7\ \text{m/s}

Now compute:

\displaystyle \sigma=\frac{125100-2300}{0.5(1025)(28.7^2)}
\sigma=0.291

For this simplified case, the review threshold from prior model evidence is:

\sigma_{review}=0.35

Since:

0.291<0.35

the operating point is inside the cavitation-risk region. The result agrees with the observed erosion and blade-rate vibration.

Blade-Rate Vibration

Blade-rate frequency is:

f_b=Zn
f_b=4(5.8)=23.2\ \text{Hz}

The measured vibration at that frequency is:

v_{RMS}=4.5\ \text{mm/s}

The review limit is:

v_{limit}=3.0\ \text{mm/s}

Utilization against the review limit:

\displaystyle U_v=\frac{4.5}{3.0}=1.50

The vibration evidence does not prove cavitation by itself, but the frequency, rpm dependence, erosion pattern, and cavitation-number screen support the same diagnosis.

Propulsive Efficiency Penalty

Estimate degraded delivered-efficiency boundary:

\displaystyle \eta_D=\frac{P_E}{P_D}
\displaystyle \eta_D=\frac{0.98}{1.80}=0.544

The expected value from the service baseline was about:

\eta_{D,baseline}=0.62

Relative efficiency loss:

\displaystyle \frac{0.62-0.544}{0.62}=0.123=12.3\%

The vessel is using more delivered power than expected for the effective power being achieved. Cavitation, roughness, off-design rpm, wake disturbance, or hull fouling can all contribute, so the efficiency penalty should be used as supporting evidence, not as the sole cause assignment.

Engineering Decision

The vessel should be restricted out of the damaging rpm range until the cause is corrected and verified. The decision basis is:

  1. cavitation number is below the simplified review threshold;
  2. vibration at blade rate is 50\% above the review limit;
  3. diver inspection shows erosion and roughness in a cavitation-consistent region;
  4. delivered efficiency is about 12.3\% below the service baseline;
  5. continued operation can accelerate blade erosion, bearing load variation, hull vibration, and fatigue exposure;
  6. the sister propeller does not show the same response.

The immediate operating instruction is:

Avoid sustained operation above the restricted shaft-speed band, inspect the propeller and shafting, review loading and trim, and release full rpm only after repair and sea-trial evidence confirm acceptable vibration and cavitation margin.

This is a controlled derating decision, not a permanent performance acceptance.

Corrective Configuration

The engineering response includes:

  • polish and repair damaged blade leading-edge areas;
  • confirm blade pitch and cup against the approved propeller record;
  • inspect shaft bearings and stern-tube condition for secondary damage;
  • review loading condition, trim, and immersion during the affected route;
  • update the rpm-speed operating map to avoid the damaging band;
  • repeat vibration and shaft-power measurements during sea trial.

The corrected trial uses:

MetricCorrected trial value
shaft speedn=4.8\ \text{rev/s}
vessel speedV=7.6\ \text{m/s}
wake fractionw=0.24
measured blade-rate vibration1.8\ \text{mm/s RMS}
delivered power1.55\ \text{MW}
effective power estimate0.93\ \text{MW}

Corrected advance speed:

V_{A,new}=7.6(1-0.24)=5.78\ \text{m/s}

Corrected tangential speed:

V_{t,new}=2\pi(4.8)(0.77)=23.2\ \text{m/s}

Corrected relative speed:

V_{rel,new}=\sqrt{5.78^2+23.2^2}=23.9\ \text{m/s}

Corrected cavitation number:

\displaystyle \sigma_{new}=\frac{125100-2300}{0.5(1025)(23.9^2)}=0.420

This clears the simplified review threshold:

0.420>0.35

Corrected blade-rate frequency:

f_{b,new}=4(4.8)=19.2\ \text{Hz}

Corrected vibration utilization:

\displaystyle U_{v,new}=\frac{1.8}{3.0}=0.60

Corrected delivered-efficiency boundary:

\displaystyle \eta_{D,new}=\frac{0.93}{1.55}=0.600

The corrected values do not prove that the propeller is optimal, but they support release from the immediate cavitation-vibration restriction for the tested loading condition.

RPN Screen

A simple risk-priority-number screen helps document the operating decision:

RPN=S \times O \times D

Before correction:

FactorValueRationale
Severity S7Continued cavitation can damage propeller blades, increase vibration, and expose shafting and hull structure to fatigue.
Occurrence O4The damaging rpm range is used regularly in service.
Detection D5Speed and power logs alone may miss cavitation unless vibration and inspection evidence are reviewed.
RPN_{initial}=7(4)(5)=140

After propeller repair, rpm restriction, vibration monitoring, and corrected sea-trial evidence:

FactorValueRationale
Severity S7Consequence remains significant if cavitation returns.
Occurrence O2The repaired propeller and operating map reduce recurrence.
Detection D2Blade-rate vibration and inspection triggers improve detectability.
RPN_{controlled}=7(2)(2)=28

The RPN does not replace naval architecture review. It records why the operational risk is lower after the repair and validation package.

Validation Evidence

A credible release package should include:

Evidence itemWhy it matters
diver or dry-dock blade inspectionconfirms erosion, roughness, and repair quality
propeller geometry and pitch recordchecks that the blade shape still matches the approved basis
shaft-speed and shaft-power dataties performance to operating point
vibration spectrumconfirms whether blade-rate excitation has reduced
loading, draft, and trim recordprevents comparing different immersion conditions
sea state and water-depth notessupports trial repeatability
bearing temperature and oil evidencechecks secondary mechanical effects
post-repair operating mapprevents routine operation in a damaging rpm range

The release should state the tested loading condition, shaft-speed range, allowable vibration trend, inspection interval, and trigger for renewed restriction.

Engineering Lessons

The first lesson is that cavitation is a system condition, not only a propeller defect. Wake, rpm, immersion, loading, blade surface, water temperature, and hull interaction all affect local pressure.

The second lesson is that vibration frequency content matters. A blade-rate peak is more diagnostic than a single overall vibration number.

The third lesson is that performance evidence and damage evidence should be reconciled. A power penalty, erosion pattern, cavitation-number screen, and vibration trend that tell the same story make a stronger diagnosis than any one signal alone.

The final lesson is that release after a cavitation event requires operating-envelope evidence. A polished blade is not enough unless the sea trial proves that the damaging condition has been removed or controlled.

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