Engine Torsional Vibration Analysis: Marine Shafting

Torsional vibration analysis (TVA) is the engineering discipline that determines whether a marine propulsion shaft system can survive the cyclic torque pulses from cylinder firings without fatigue failure. Every combustion event in a diesel engine produces a periodic torque spike with strong harmonic content. If a harmonic frequency matches one of the shaft system’s torsional natural frequencies, resonance occurs and torsional stresses rise sharply. Left unmanaged, the result is crankshaft or intermediate shaft fracture.

Class societies require TVA for every new-build vessel with a diesel propulsion plant before the shaft system is manufactured, and again after any major modification to the propulsion train. The governing document is IACS Unified Requirement M68 (Rev.3, February 2021), which all ten IACS member societies implement. It defines the shaft stress limits that separate acceptable from barred operating zones, and it mandates sea-trial torsiograph verification before the vessel enters service. This article covers the complete analytical framework, from building the mass-elastic model through sea-trial verification, and explains the operational consequences that flow from the analysis: barred speed ranges, damper requirements, and the separate approvals needed for cylinder cut-out and misfire conditions.

The companion marine propulsion shafting article covers the physical design of the shafting system this analysis governs. The crankshaft and main bearings article covers the engine-side components most at risk from torsional fatigue. For bedplate and alignment effects that interact with torsional behaviour, see engine alignment and bedplate flexure.

The mass-elastic model

A shaft system is not a rigid body. It is a chain of rotating inertias connected by elastic shaft sections, and when any element is disturbed angularly, a torsional wave propagates along the chain. The analyst’s first task is to reduce the physical system to a mathematical model that captures the dominant inertia and stiffness of every element. This model is called the mass-elastic system.

Inertia elements

Each crank throw, comprising the crank pin, two webs, and approximately half of each adjacent journal, is assigned a polar moment of inertia in kg·m². The flywheel is modelled as a single large inertia at the engine’s output end; on a typical slow-speed two-stroke it accounts for 30 to 60 percent of the total rotating mass. The thrust shaft, intermediate shafts, and tail shaft each contribute their own distributed mass, usually lumped at the mid-point of each bearing span. Some analysts split long shafts between bearings into two or three lumped masses to improve accuracy at higher modes.

The propeller introduces a complication. Its dry polar moment of inertia is known from the manufacturer’s drawing, but the water it accelerates during torsional oscillation adds to that value. This hydrodynamic added mass depends on blade geometry and immersion depth. IACS UR M68 requires the entrained water to be included; in practice the added inertia is typically 20 to 30 percent of the dry propeller value for a conventional fixed-pitch propeller, and engineering practice commonly uses empirical coefficients from Burrill or from propeller manufacturers to estimate it. A controllable-pitch propeller (CPP) with hub-mounted servo mechanism adds a further inertia term from the servo mechanism and pitch rods.

Shaft generators, PTOs, and PTI systems appear as additional inertia elements connected to the main line by couplings. The coupling’s own elastic and damping properties enter the model explicitly.

Stiffness elements

Each shaft section between adjacent inertia lumps is a torsional spring. Its stiffness $k$ in N·m/rad is:

where $G$ is the shear modulus of the shaft material (approximately 80 GPa for carbon steel), $I_p = \frac{\pi d^4}{32}$ is the polar second moment of area for a solid shaft of diameter $d$, and $L$ is the section length. For a hollow shaft with outer diameter $d_o$ and inner diameter $d_i$:

Crankshaft sections between throws have an equivalent stiffness that is lower than the journal cross-section would suggest, because the crank webs and crank pin geometry introduce local compliance. Engine builders supply equivalent stiffness data for each engine type from finite element calculations, and these manufacturer data replace the simple shaft formula for the crankshaft spans.

Flexible couplings appear in the stiffness chain with their own rated static and dynamic stiffness values, which differ by a factor of 1.2 to 1.6 in many elastomeric designs because rubber stiffens under dynamic loading.

Model size and modern practice

A complete mass-elastic model for a six-cylinder, direct-drive slow-speed engine with one intermediate shaft and a CPP shaft generator might have 14 to 18 inertia elements and 13 to 17 spring elements. Before digital computing, this was solved by Holzer’s tabular method. Today, dedicated torsional analysis software (Geislinger CRIT, AVL EXCITE, and similar) ingests the model, applies excitation from the engine builder’s database, and returns natural frequencies, mode shapes, and stress responses in minutes.

Torsional natural frequencies and mode shapes

Natural frequency of a two-inertia system

The simplest model, capturing the first mode of a direct-drive propulsion system, treats the entire crankshaft as a single inertia $J_e$ and the entire shafting plus propeller as a single inertia $J_s$, connected by a single shaft stiffness $k$. The first natural frequency is:

This two-inertia formula gives the correct order of magnitude for the one-node frequency and is useful as a quick sanity check. It gives approximately 1 to 3 Hz for a typical large slow-speed two-stroke system.

Multi-degree-of-freedom systems: Holzer’s method

Holzer (1921) published the first general method for solving the natural frequencies of multi-inertia torsional chains. The algorithm iterates through the shaft system from one end, building up the torque balance element by element:

1. Assume a trial angular frequency $\omega$.
2. Set the angular displacement at element 1 to $\theta_1 = 1$ (arbitrary normalisation).
3. Compute the cumulative torque residual at element 1: $M_1 = -\omega^2 J_1 \theta_1$.
4. For each subsequent element $i$:

5. At the free end (element $N$), the boundary condition requires $M_N = 0$. Iterate $\omega$ until that condition is satisfied; each root is a natural frequency.

The displacement vector $(\theta_1, \theta_2, \ldots, \theta_N)$ at convergence is the mode shape for that natural frequency. The method is numerically stable and remains the conceptual foundation of modern software, even when the actual computation uses eigenvalue decomposition on the assembled stiffness and mass matrices.

Mode shapes and what they mean for stress

The first (one-node) mode has the propeller oscillating against the crankshaft, with a single angular displacement node somewhere along the shafting, typically close to the flywheel. Torsional stress is maximum where the angular twist gradient is steepest, which is near the node. In the one-node mode this is often on the intermediate shaft or the tail shaft. The crankshaft’s aftmost throw also sees high stress because the engine inertia participates strongly.

The second (two-node) mode places nodes within the engine as well as in the shafting. Stress peaks appear at both nodes. Second and higher modes have natural frequencies of 5 to 15 Hz on typical direct-drive installations and are usually excited by higher-order harmonics, often at speeds well above or below normal operating range. They matter primarily for engine rating checks and for derating analysis.

Excitation harmonics and critical speeds

Excitation spectrum of a two-stroke diesel

Every cylinder’s torque pulse contains a fundamental at the firing frequency plus a rich harmonic series. For a two-stroke engine, each cylinder fires once per revolution, so the firing frequency at speed $n$ rev/s is simply $n$ Hz. Decomposed into Fourier components, the torque pulse contains terms at $n$, $2n$, $3n$, etc. For an $N$-cylinder engine with equal firing intervals, consecutive harmonics at the same order add constructively only at the major orders, which are integer multiples of $N$. For a six-cylinder engine the major orders are 6, 12, 18, 24; for an eight-cylinder engine they are 8, 16, 24. Minor orders (1, 2, 3, etc.) exist but at amplitudes typically ten to fifty times smaller than the major orders.

MAN Energy Solutions’ guidance on its slow-speed two-stroke family notes that four-cylinder engines have particularly strong major-order excitation and typically require dampers because the 4th-order resonance often falls within normal operating speed. Six and seven-cylinder engines generally produce a more manageable torsional picture.

Critical speed formula

A critical speed occurs when an excitation harmonic order $k$ multiplied by shaft speed $n$ matches a natural frequency $f_\text{nat}$:

with $n_\text{crit}$ in rev/s (multiply by 60 for rpm). For the one-node mode at 2.0 Hz on a six-cylinder engine, the critical speed for major order 6 is:

That is well below the minimum operating speed for most direct-drive vessels, so this particular resonance causes no operational problem. But if the one-node frequency is higher, say 4.5 Hz on a lightly shafted vessel with a small propeller, the same order 6 critical falls at:

That is inside the normal operating range of most slow-speed two-stroke installations, triggering a barred speed range.

Minor orders can create sub-critical resonances at any speed. Order 1 (once per revolution) can be excited strongly during a single-cylinder misfire, because one cylinder not firing is equivalent to injecting a large once-per-revolution torque asymmetry into the system. This is why misfire conditions require their own analysis.

IACS UR M68 stress limits

IACS UR M68 Rev.3 (February 2021) is titled “Dimensions of propulsion shafts and their permissible torsional vibration stresses.” All ten IACS member class societies (DNV, Lloyd’s Register, ABS, Bureau Veritas, ClassNK, KR, RINA, CCS, IRCLASS, and RS) are bound by it.

Two-tier stress structure

Section M68.5 establishes two distinct permissible torsional vibration stress levels for intermediate shafts, thrust shafts, and propeller shafts made of steel forgings:

• $\tau_1$ (continuous limit): The maximum torsional vibration stress amplitude permitted for unlimited continuous operation at any engine speed. If calculated stresses remain below $\tau_1$ across the entire speed range, no barred speed range is needed.
• $\tau_2$ (never-exceed limit): A higher stress level that must never be reached under any operating condition, including transient passage through a resonance zone. Exceeding $\tau_2$ risks immediate fatigue damage.

The actual numerical values of $\tau_1$ and $\tau_2$ in M68.5 depend on the shaft material’s specified minimum tensile strength $R_m$ and the specific shaft section being assessed. The formulas are:

where $k_1$, $k_2$ are shaft-type factors (different for intermediate, propeller, and thrust shafts), $C_1$, $C_2$ are geometry correction factors, and $S_1$, $S_2$ are safety margins against fatigue failure. The ratio $\tau_2 / \tau_1$ is typically 1.5 to 1.7 depending on shaft type and surface treatment. For a standard carbon-manganese steel intermediate shaft with $R_m = 600 \; \text{MPa}$, $\tau_1$ is in the range of 50 to 70 MPa and $\tau_2$ is in the range of 80 to 110 MPa; exact values require applying the full M68.5 formulas to the actual shaft geometry.

Barred speed range trigger

Wherever the calculated torsional vibration stress on any shaft element exceeds $\tau_1$, that speed band is declared a barred speed range (BSR). The BSR spans from the lower speed where stress first crosses $\tau_1$ on the approach to resonance to the upper speed where it falls back below $\tau_1$ on the far side. A typical BSR for a six-cylinder slow-speed engine with a mid-operating-range resonance spans 4 to 8 rpm.

The BSR is a design result, not a fixed rule. An engine fitted with a well-tuned torsional damper may have no BSR because the damper reduces peak stresses below $\tau_1$ across the whole operating range.

Cylinder misfire condition

M68 specifically requires analysis of single-cylinder misfire, because misfire injects a strong once-per-revolution (order 1) torque disturbance. The permissible torsional vibration stress during misfire is higher than $\tau_1$, because misfire is a temporary fault condition rather than a continuous operating state, but it must stay below $\tau_2$. Class societies may allow restricted operation at reduced power (typically below 80 percent MCR) with one cylinder misfiring, subject to the analysis showing stresses remain within the misfire-condition limit.

What M68 does not cover

M68 covers straight forged shafts of traditional design. Composite shafts, shafts with stress-raising keyways outside the defined geometry, and non-standard propeller arrangements require case-by-case assessment under M68.2, which permits alternative calculation methods provided they address “all relevant loads on the complete dynamic shafting system under all permissible operating conditions.”

DNV and class-specific rule additions

IACS UR M68 is the floor. Each class society adds requirements on top.

DNV RU-SHIP Pt.4 Ch.2 Sec.2

DNV’s rules, revised July 2018, introduced two requirements beyond M68:

Maximum BSR transit time. The designer must calculate, for a vessel accelerating through the BSR, the maximum time that can be spent inside the BSR before cumulative fatigue damage (computed via Miner’s rule, assuming 25 years’ service life and ten BSR transits per week) reaches an unacceptable level. The allowable time decreases exponentially as the calculated stress ratio (actual stress / $\tau_2$) increases. At a stress ratio of 85 percent, the allowed transit time for a shrink-fit or multi-fillet-flange coupling shaft is 26 seconds. Sea trials must verify that actual transit time, accelerating ahead, stays within the approved value.

10 percent power margin at the upper BSR boundary. The engine must retain at least 10 percent reserve driving torque above the load demand at the upper edge of the BSR. This ensures the engine can accelerate through the BSR without stalling, since a stall would force the crew to decelerate back through the resonance zone, extending total time at elevated stress. DNV aligned this requirement with CIMAC’s recommendation for minimum acceleration margin.

Lloyd’s Register Part 5 Chapter 8

Lloyd’s Register addresses shaft torsional vibration in Part 5, Chapter 8 of its Rules and Regulations for the Classification of Ships. The chapter sets stress limits consistent with M68, requires barred speed ranges to be marked on the tachometer in red, and mandates that barred ranges be passed through as quickly as possible. Where calculated stress exceeds 85 percent of $\tau_1$ during continuous operation, LR requires an increase of 1 to 2 percent in the shaft fit diameter to account for the fretting fatigue penalty at shrink-fit joints.

ABS Marine Vessel Rules 4-3-2/7

ABS covers torsional vibratory stress requirements at Section 4-3-2/7 of its Marine Vessel Rules (2024 edition). The section references IACS UR M68 for the stress limits and adds measurement procedures: torsional vibration is to be measured at the free end of the propulsion machinery using a torsional vibration transducer, and on the main shafting using strain gauges bonded at ±45 degrees to the shaft axis (to capture shear strain) with a telemetry system for signal transmission from the rotating shaft. ABS updated its broader Guidance Notes on Ship Vibration in September 2023 with revised recommendations for modelling engine and propeller excitations.

ClassNK

ClassNK revised its shafting rules in 2022 (document 22-4-35e). The revision aligned the permissible stress framework with M68 Rev.3 and added explicit requirements for barred speed range marking on the bridge tachometer and engine room telegraph. ClassNK requires that barred speed ranges be marked in red on the tachometer and passed through as quickly as possible. Like LR, ClassNK increases the fit-diameter requirement where continuous operating stress exceeds 85 percent of $\tau_1$.

The barred speed range in practice

A barred speed range creates a genuine operational burden, particularly on vessels that spend much of their service time at slow speeds close to the resonance zone.

Tachometer markings and bridge displays

Class rules require the BSR to be marked on the engine speed indicator visible to the bridge and in the engine room. The marking is typically a red band on the tachometer scale, with yellow warning bands at the BSR boundaries. Modern electronically controlled engines (MAN ME series, WinGD X-DF series) can implement automatic pass-through logic: when the speed governor detects engine speed entering the BSR lower boundary, it commands a brief increase in fuel injection to accelerate the engine through the zone in the minimum time allowed by the shaft fatigue analysis.

Eco-speed and BSR conflicts

The global trend toward slow steaming on derating plans has brought the BSR into more frequent contact with normal operating speeds. A vessel originally rated at 100 rpm MCR but operated continuously at 70 rpm for fuel efficiency may find that its BSR at, say, 63 to 68 rpm becomes a daily obstacle: every departure requires accelerating from manoeuvring speed through the BSR before settling at the eco-speed. DNV’s 2018 rule revision on maximum BSR transit time was prompted precisely by evidence that eco-derated engines, with lower peak torque available for acceleration, were taking 60 to 90 seconds to traverse BSRs originally designed for ships with full-rating torque margins.

Where a vessel’s normal operating regime permanently sits above a BSR, the BSR is a nuisance only during departure and arrival. Where the BSR sits inside the eco-speed range, the options are a detuning damper, a revised shafting arrangement, or acceptance of a more restrictive operating profile.

Torsional dampers

When the unaided analysis predicts stresses exceeding $\tau_1$ at operating speeds, dampers are added to suppress peak amplitudes. Three main types are used in marine propulsion.

Viscous damper

The most common type in large slow-speed engines, the viscous damper bolts to the crankshaft’s free end (opposite the flywheel), where angular displacement in the one-node mode is largest.

The damper housing is bolted rigidly to the crankshaft. Inside, a free-rotating inertia ring is suspended in a thin film of high-viscosity silicone oil, typically 30,000 centistokes (cSt) at operating temperature. When the crankshaft twists in torsional vibration, the inertia ring lags behind due to its mass, and that lag creates a velocity gradient across the silicone film. The resulting viscous shear force acts as a torque opposing the relative motion, dissipating torsional energy as heat. A correctly designed viscous damper can reduce resonant stress amplitudes by up to a factor of ten.

The oil temperature critically affects damping: the viscosity of silicone oil drops substantially with rising temperature, so an overheated damper becomes less effective. Damper housing temperatures above approximately 85 to 90 °C indicate either overloading (the shaft system is spending too much time at resonance) or loss of oil. Class societies require periodic damper oil inspection on the maintenance schedule. Some builders offer dampers with temperature monitoring wiring, and a rising mean temperature trend is an early indicator of abnormal torsional loads.

Viscous dampers are broad-band: they damp all frequencies to some extent, not just the tuned frequency. This makes them tolerant of off-design conditions like cylinder cut-out, which shifts the dominant excitation order.

Tuned (detuner) elastomeric damper

A tuned damper adds an auxiliary inertia ring connected to the crankshaft by a rubber element rather than an oil film. The rubber acts as a spring, giving the auxiliary inertia a natural frequency that the designer sets to match the target resonance. At that resonance, the auxiliary inertia oscillates approximately 180 degrees out of phase with the crankshaft, cancelling the resonance torque. WinGD’s “Delta Bypass” technique on its X-DF and X-B engines uses precisely this principle to control a specific critical resonance without a BSR.

Tuned dampers are highly effective at the design frequency but offer little benefit at others, typically less than 10 percent stress reduction at frequencies more than 20 percent away from the tuned point. They also require periodic rubber element replacement because elastomers fatigue under the combined heat and cyclic strain. The replacement interval depends on rubber compound and operating load; typical intervals are 2 to 5 years.

Combined viscous-tuned damper

Some installations, particularly on large bore four and five-cylinder engines where the major-order resonance is strong and close to operating speed, combine both mechanisms: a viscous film provides broadband damping while a tuned inertia element cancels the dominant resonance frequency. Geislinger’s ARCUSAFLEX series is an example of a combined product used on large slow-speed installations.

Comparison of damper types

Class approval process

Design submission (new build)

Before any shaft components are ordered for a new build, the shipyard or engine builder must submit a torsional vibration analysis report to the class society for approval. The IACS member societies specify the required content consistently with M68:

• Complete mass-elastic model with source data (manufacturer drawings or published data for each inertia and stiffness element)
• Engine excitation harmonic data: torque harmonic amplitudes at each order and speed, supplied by the engine builder from measured cylinder pressure data
• Modal analysis results: natural frequencies and mode shapes for modes 1 through at least the highest mode with a critical speed within 120 percent of MCR speed
• Critical speed table for all major and significant minor harmonic orders
• Stress response curves at each shaft section versus engine speed, for all-cylinder normal operation
• Barred speed ranges derived from the stress limits
• Separate analyses for each approved cylinder cut-out pattern
• Misfire analysis demonstrating that order-1 excitation from a single dead cylinder does not produce stresses exceeding the misfire allowable
• Damper design report including dimensions, oil type and viscosity, and calculated damper effectiveness

Class society technical reviewers check the model assumptions, the excitation data source, and the stress calculations. They may request revised damper sizing, an additional mode check, or a modified BSR width. Approval is documented in a class certificate or a specific plan approval letter, which the shipyard files with the vessel’s construction dossier.

Sea trial verification with torsiograph

After delivery, the TVA predictions must be verified by measurement at sea. Two measurement approaches are in common use:

Torsiograph on the free end of the crankshaft. A torsiograph is an electromechanical or optical instrument that measures instantaneous angular velocity or angular displacement of the shaft. The Geislinger Monitoring Mk6 system and Binsfeld TorqueTrak systems are typical examples. The instrument mounts on the crankshaft free end and records torsional amplitudes as the engine sweeps from idling to full speed, confirming that the predicted resonance speeds and amplitudes match the actual system behaviour.

Strain gauges on the intermediate shaft or tail shaft. Pairs of foil strain gauges bonded at ±45 degrees to the shaft axis measure shear strain directly. A radio telemetry module (slip rings are an alternative but less common) transmits the gauge signal from the rotating shaft to a static data acquisition system onboard. Strain-gauge measurements give true torsional stress values without the mathematical conversion needed from torsiograph angular velocity data.

Both approaches are accepted by all major class societies. The sea trial sweep covers the full speed range from slow ahead through MCR, with a controlled slow acceleration through any predicted BSR to verify transit time. Measurements are taken at every 2 to 5 rpm interval in the vicinity of resonances. If the measured peak stress exceeds $\tau_1$, the BSR width may need to be widened, or a damper added or re-tuned, before the vessel can enter service.

Post-trial class records

The class society archives the sea trial torsiograph or strain-gauge record against the vessel’s hull number. Any subsequent propulsion modification (new propeller, engine derating, addition of a shaft generator, enabling of cylinder cut-out) requires the owner to submit a revised TVA and, where the changes are significant, to carry out new sea-trial measurements.

Cylinder cut-out: changes to the torsional picture

Cylinder cut-out deactivates one or more cylinders while the engine continues running, typically to improve specific fuel oil consumption at part load. See engine derating for slow steaming for the fuel efficiency motivation.

From the torsional analysis perspective, cutting out cylinder $j$ removes its torque contribution and inserts a once-per-revolution asymmetry into the firing pattern. The effect on the harmonic spectrum is:

• The major harmonic orders shift from multiples of $N$ to multiples of $(N - m)$, where $m$ is the number of cut cylinders
• Previously cancelled intermediate orders gain amplitude
• The overall mean torque per revolution decreases, but the peak-to-trough torque variation increases as a fraction of mean torque

For a six-cylinder engine with one cylinder cut out, the firing order goes from 6 equally spaced firings to 5, and order 5 becomes a major order. If the one-node natural frequency, when divided by 5, gives a critical speed within the operating range, a new BSR appears that did not exist in the all-cylinder case.

Class societies require a separate approved TVA for each cut-out configuration before that configuration enters the vessel’s operating procedures. The analysis must cover the specific cut-out cylinder (or combination of cylinders) approved, because the torsional response depends on which cylinder is cut and its crank angle position relative to the node point.

Some engine designs limit cut-out to cylinders far from the mid-ship node (where displacement amplitude in the one-node mode is lowest) to minimise the torsional impact. Engine builders publish specific recommendations on permissible cut-out patterns for each engine series.

Dual-fuel engine considerations

Two-stroke dual-fuel engines, including the WinGD X-DF family, burn natural gas in premix mode with a small pilot diesel injection, or diesel in backup mode. The cylinder pressure trace, and therefore the torque pulse shape and harmonic amplitudes, differs between gas mode and diesel mode.

In gas mode, the combustion is more gradual (lower peak pressure rise rate) and more uniform across cylinders, producing lower peak torque harmonics at the major firing orders. This generally makes the TVA easier in gas mode. In diesel backup mode, the engine behaves like a conventional diesel with higher harmonic amplitudes. Class societies require TVA for both operating modes as independent analyses, though in practice the diesel-mode analysis usually governs the damper design and BSR definition, with the gas-mode analysis confirming that the same damper and the same BSR remain valid in gas mode.

Some dual-fuel installations also carry LNG fuel pump drives on the shaft system. These add a further inertia and stiffness element to the mass-elastic model and may require a modified damper to keep the TVA result valid for both fuel modes and both pump-connected and pump-disconnected states.

Ice-class propulsion: impulsive torsional loading

Propellers on ice-class vessels (IACS Polar Class designations PC1 through PC7, or Finnish-Swedish Ice Class IA Super through IC) encounter ice blocks during transit. A propeller-ice impact produces a rapid, large-amplitude torque impulse on the shaft, effectively a step-function excitation rather than the steady-state sinusoidal excitation that the standard TVA addresses.

The impulse duration for a typical ice impact is 10 to 150 milliseconds. This is comparable to the period of the one-node torsional mode (which runs at 1 to 3 Hz, corresponding to periods of 330 to 1,000 ms), so the impulse does excite the first mode with measurable amplitude. It is short relative to higher modes, so the higher-mode response is smaller.

IACS Polar Class rules require transient torsional analysis for ice-class vessels, with the impulse load defined by UR I (Ice class rules for propulsion machinery). The analysis must show that the stress resulting from the maximum design ice impulse, combined with the nominal operating torque, stays below the shaft’s yield strength, not just its fatigue limit, because the impact is a single large event rather than a fatigue accumulation. Ice-class shafts are typically 10 to 20 percent heavier than equivalent open-water designs, and rubber flexible couplings between the engine and the shafting are common to absorb some of the impulse energy before it reaches the crankshaft.

Operational monitoring

Torsional vibration monitoring in service is uncommon on standard commercial vessels but is fitted on icebreakers, specialised naval vessels, and some LNG carriers where the consequences of shaft failure or the cost of a fatigue-induced failure are unusually high.

Torsiograph-based continuous monitoring

A permanent torsiograph installation on the crankshaft free end, combined with a data-logging system, can track torsional vibration amplitude and frequency in real time. A threshold alarm triggers at a preset fraction of $\tau_1$. Some systems also log cumulative exposure time near resonance to provide a Miner’s rule running estimate of accumulated fatigue damage.

The Geislinger Monitoring Mk6 system integrates angle measurement from an optical encoder with onboard signal processing to deliver torsional vibration amplitudes in engineering units (MPa equivalent) for direct comparison with the class-approved limits.

Strain-gauge permanent installations

On high-value propulsion systems, foil strain gauges bonded to the intermediate shaft transmit torsional strain continuously via a slip ring or inductive telemetry system. The advantage over torsiograph measurements is that strain gauges measure the shaft response directly at the highest-stress location, rather than inferring it from crankshaft-end angular data through the mode shape. The disadvantage is vulnerability to gauge debonding, water ingress, and slip ring wear, all of which can interrupt signal continuity.

Condition-based maintenance implications

Gradual deterioration of a viscous damper’s silicone oil (which degrades through thermal cycling and shear) increases the effective damping ratio, initially improving torsional performance. As the oil further degrades it loses homogeneity and damping drops. Periodic oil sampling (analogous to main-engine oil condition monitoring) catches this before the damper ceases to protect the shaft. A rising mean damper housing temperature during normal operation is the most accessible early indicator of degrading damper performance, visible to the engine room watchkeeper without specialised instrumentation.

Limitations

Several factors constrain the accuracy and completeness of standard TVA:

Propeller hydrodynamic inertia is approximate. The entrained water model relies on empirical coefficients that were validated for conventional propeller designs. CPP hubs, highly skewed blades, and Becker twisted trailing-edge rudders all influence the actual hydrodynamic added mass in ways that the standard coefficients do not fully capture. The resulting uncertainty in the one-node natural frequency is typically ±5 to 10 percent, which can shift a predicted critical speed by 2 to 5 rpm.

Engine excitation data depend on cylinder pressure uniformity. The harmonic amplitudes in the class submission are computed from the engine builder’s nominal cylinder pressure data. Real engines have cylinder-to-cylinder combustion variation of ±3 to 8 percent, which changes the harmonic spectrum, particularly at minor orders. This variation is not captured in standard approval calculations.

Non-linear coupling stiffness is linearised. Elastomeric couplings and flexible couplings show amplitude-dependent stiffness and damping. Standard TVA uses linearised values (typically the dynamic stiffness at the expected vibration amplitude). For large amplitude transients, such as BSR passages, the linearisation introduces error.

Higher modes are often underanalysed. The class submission typically covers modes up to the first one whose critical speed falls well above MCR. But second and third modes can be excited by minor harmonics at unusual operating conditions, such as very slow speeds in harbour approach or during anchor operations with reduced power. These conditions are not always covered.

The model is valid only for the submitted configuration. Any modification to the propeller (different diameter, different pitch, different blade count), to the shafting (coupling replacement, shaft sleeve addition), or to the engine (changed injection timing, new fuel system) can shift the mass-elastic parameters enough to move a critical speed into the operating range without triggering a formal re-analysis requirement. Owners and operators should treat the class-approved TVA as a snapshot of the initial configuration and review it whenever propulsion modifications are planned.

See also

• Marine propulsion shafting and stern tube
• Marine engine crankshaft and main bearings
• Engine alignment and bedplate flexure
• Two-stroke marine diesel engine fundamentals
• Engine derating for slow steaming
• WinGD X-DF dual-fuel architecture
• Ship vibration
• Shaft torsional critical speed calculator