Marine engineering · naval architecture

Services · Propulsion shafting · Axial and whirling vibration

Axial and whirling vibration of the shaft line

The two vibration checks that complete a shafting assessment alongside torsion. Axial vibration is the shaft line and engine moving fore and aft as a spring and mass, driven by the variation of propeller thrust at blade rate. Whirling is the shaft bending and orbiting inside its bearings. Both are calculated on the same rotor and geometry as the alignment, with bearing stiffness and damping taken from the film the alignment produces.

Discuss a vibration study The complete shafting service
The axial vibration model: the thrust bearing and its seating as a spring to the hull, the engine and crankshaft as a mass, the shafting as an axial spring, and the propeller with its entrained water, driven by thrust that varies at blade rate. hull thrust bearing and seating engine and crankshaft shafting, axially elastic propeller and entrained water thrust, varying at blade rate
The axial model. The thrust bearing and its seating, the engine and crankshaft, the shafting and the propeller with its entrained water form a spring-mass line, driven by the variation of propeller thrust at blade rate.

Axial vibration

On a long-stroke two-stroke engine the crankshaft is axially flexible, and its axial mode couples with torsion through the throws. Propeller thrust varies at blade rate and its multiples, and where one of these orders meets the axial natural frequency the whole line moves fore and aft, loading the thrust bearing, the crankshaft and the engine structure.

The calculation gives the axial natural frequencies with the thrust bearing and seating stiffness, the crankshaft's axial stiffness and the propeller's entrained water, and the forced response against the guidance limit for axial displacement at the crankshaft's free end. Where an axial damper is fitted, the response is calculated with the damper in service and out of action, because the second case sets what the crew must do if it fails.

Why the damper case matters

On the large crude carrier used to validate the model, the yard's coupled axial and torsional calculation shows the axial displacement within the guidance limit with the damper in service. With the damper out of action it exceeds the limit from about one third of rated speed upward, so the ship would have to bar about two thirds of its speed range. That is why the damper's condition is monitored and its failure is treated as a slow-down condition, not a note in the log.

Whirling vibration

Whirling is the lateral bending of the shaft line as it turns. Its natural frequencies depend on the bearing positions and the propeller overhang, and on the stiffness and damping of the oil or water film in each bearing, which change with load and speed. The propeller's gyroscopic moment splits each mode into a forward and a backward whirl that separate as the shaft speeds up.

The calculation builds the rotor with gyroscopic terms and speed-dependent bearing coefficients taken from the film solution at the load the alignment gives each bearing. It reports the Campbell diagram, the crossings with shaft speed and blade-rate orders, the precessional shape of each mode with its direction of whirl, the damping of each mode and the stability of the rotor across the speed range. The classification societies' guidance on whirling, including the allowance for where along a long stern tube bearing the effective support lies, is applied as a band of frequencies, not a single line.

Two computed precessional mode shapes of the reference shaft line at rated speed, drawn in perspective. Each station traces an ellipse around the shaft axis, largest at the propeller overhang and fading to nothing forward of the intermediate bearings. In the upper mode the orbits run the same way as the shaft turns; in the lower mode they run against it. Forward precession Every station orbits the same way the shaft turns. Propeller unbalance and blade-rate forces can drive this mode. to the engine aft stern tube fwd stern tube intermediate intermediate Backward precession The orbits run against the shaft rotation. Unbalance does not excite this mode in a symmetric line. to the engine aft stern tube fwd stern tube intermediate intermediate shaft rotation the shaft at one instant orbit of each station (relative size) bearing
Two lateral modes of the reference line at rated speed, computed by the in-house shaft-line software with the propeller's gyroscopic moment and the bearing film coefficients. Each station traces its own ellipse about the shaft axis, so the line precesses instead of bending in a fixed plane. The motion is carried by the propeller overhang and the stern tube span and has died away forward of the intermediate bearings. The orbits are drawn to relative size, since a mode shape has no absolute amplitude; the forced response to a stated unbalance gives the amplitude in millimetres.
Two speed-range bars. With the axial damper in service only a short torsional barred range is excluded. With the damper out of action, everything from about one third of rated speed upward is barred. Axial damper in service torsional barred range Axial damper out of action barred: axial displacement over the guidance limit 0 % 25 % 50 % 75 % 100 % shaft speed, per cent of rated Usable speed range of a large two-stroke installation
The usable speed range of the validation ship with the axial damper in service and out of action. The hatched band in the upper bar is the torsional barred range; in the lower bar, everything from about one third of rated speed is barred on axial displacement alone.

Worked example

The reference line: axial modes and the whirl band

Results from the in-house shaft-line software for the reference installation: 39.2 m of shafting, 18 660 kW at 91 r/min, and a 7.6 m five-bladed propeller, so blade rate is 7.6 Hz at rated speed.

Bar chart of the first four axial natural frequencies of the reference line, 20.2, 66.2, 110.6 and 168.6 hertz, against blade-rate and twice blade-rate excitation drawn as dashed lines. The nearest coincidence is 33 per cent clear.
Axial modes against blade-rate excitation. The first axial mode, at 20.2 Hz, is the one to watch. It sits 33 % clear of twice blade rate at rated speed, so no axial resonance falls in the operating range of this line.
Campbell diagram of damped lateral natural frequency against shaft speed for four whirl modes, each drawn with a band for the uncertain support point in the aft stern tube bearing, crossed by the five-times and ten-times blade orders. A shaded band near 60 revolutions per minute marks a critical span.
Whirling modes with the support-point band. Each mode is drawn as a band, because the effective support inside the 1.35 m aft stern tube bearing moves with load. The bands are crossed by blade-rate orders below rated speed; the shaded span near 60 r/min is the one assessed for response, and the rated speed is clear.

Deliverables

What you receive

  • Axial natural frequencies and forced response, with the damper in service and out of action where one is fitted.
  • Thrust bearing load variation and crankshaft free-end displacement against the guidance limits.
  • The whirling Campbell diagram with forward and backward modes, the support-point band and the damping of each mode.
  • The precessional shape of each mode: where along the line the shaft moves, and which way it whirls.
  • Rotor stability across the speed range.
  • Any speed range to be avoided, and the measures that would remove it.

Input data

What the study needs

  • The shafting arrangement drawing and the alignment calculation, if one exists. If not, the alignment is calculated as part of the study.
  • The engine designer's axial data: crankshaft axial stiffness, thrust bearing and seating stiffness, and the axial damper particulars.
  • Propeller mass, inertia, diameter and number of blades.
  • Bearing dimensions, clearances and lubricant.

Questions from owners and yards

Frequently asked

The thrust bearing shows high temperature or fretting. Can axial vibration be the cause?

It can. The study calculates the thrust variation at the thrust bearing across the speed range and identifies whether an axial resonance falls near the speeds the vessel runs at. If it does, the measures to move it or damp it are set out and calculated.

Is whirling a concern on a conventional merchant ship?

On most lines the first whirling mode is well clear of the operating range, and the calculation confirms that with a stated margin. It needs closer attention with a long propeller overhang, a single stern tube bearing, a widely spaced intermediate bearing, or a soft bearing material whose film stiffness is low.

Are the bearing coefficients taken from a handbook?

No. They are calculated from the film in each bearing at the load and misalignment the alignment gives it, so a change to the alignment is reflected in the vibration result.

Can you compare the results with vibration measured on board?

Yes. Measured axial or lateral vibration from trials or a survey is compared with the calculated response, and any difference is reported and explained in terms of the inputs that would account for it.

Commissioning

Start with the drawings you hold

Send the shafting arrangement drawing and whatever machinery data is to hand. An initial technical response follows within two working days, then a written scope and proposal: the conditions to be calculated, the data still needed, the deliverables, the fee and the schedule. A non-disclosure agreement can be put in place before any drawing is exchanged. The calculation is then carried through to a report a yard, a superintendent or a classification society can follow and reproduce, and questions raised on it are answered by us until the review is closed.

Send an enquiry How a study is run

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