Section 2 Torsional vibration

2.1.1 In addition to the shafting complying with the requirements of Pt 5, Ch 1 General Requirements for the Design and Construction of Machinery to Pt 5, Ch 7 Propellers and Pt 5, Ch 20 Azimuth Thrusters (where applicable), approval is also dependent on the torsional vibration characteristics of the complete shafting system(s) being found satisfactory.

2.1.2 Further to the Scope of this Chapter, the requirements of this Section are applicable:

1. to ships that are required to comply with the SOLAS - International Convention for the Safety of Life at Sea , as amended, (SOLAS); and

2. for all other ships where any one main engine has a power output exceeding 500 kW.

2.2.1 Torsional vibration calculations, showing the mass elastic values, associated natural frequencies and an analysis of the vibratory torques and stresses for the full dynamic system.

2.2.2 Particulars of the division of power and utilisation, throughout the speed range, for turbines, multi-engine or other combined power installations, and those with power take-off systems. For multi-engined installations, special considerations associated with the possible variations in the mode of operation and phasing of engines.

2.2.3 Enginebuilder's harmonic torque data used in the torsional vibration calculations, see Pt 5, Ch 8, 2.3 Scope of calculations 2.3.3.

2.2.4 Details of operating conditions encountered in service for prolonged periods, e.g. idling speed, range of trawling revolutions per minute, combinator characteristics for installations equipped with controllable pitch propellers.

2.2.5 Details, obtained from the manufacturers, of the principal characteristics of machinery components such as dampers and couplings, confirming their capability to withstand the effects of vibratory loading including, where appropriate, heat dissipation. Evidence that the data which is used to represent the characteristics of components, which has been quoted from other sources, is supported by a programme of physical measurement and control.

2.2.6 Where installations include electric motors, generators or non-integral pumps, drawings showing the principal dimensions of the shaft, together with manufacturer's estimates of mass moment of inertia for the rotating parts.

2.2.7 Details of vibration or performance monitoring proposals where required.

2.3.1 Calculations are to be carried out, by recognised techniques, for the full dynamic system formed by the engines, turbines, motors, generators, flexible couplings, gearing, shafting and propeller, where applicable, including all branches.

2.3.2 Calculations are to give due consideration to the potential deviation in values used to represent component characteristics due to manufacturing/service variability.

2.3.3 The calculations carried out on engine systems are to be based on the Enginebuilders' harmonic torque data. The calculations are to take account of the effects of engine malfunctions commonly experienced in service, such as a cylinder not firing (i.e. no injection but with compression) giving rise to the highest torsional vibration stresses in the shafting. Calculations are also to take account of a degree of imbalance between cylinders, which is characteristic of the normal operation of an engine under service conditions.

2.3.4 Whilst limits for torsional vibration stress in crankshafts are no longer stated explicitly, calculations are to include estimates of crankshaft stress at all designated operating/service speeds, as well as at any major critical speed.

2.3.5 Calculations are to take into account the possible effects of excitation from propeller rotation. Where the system shows some sensitivity to this phenomenon, propeller excitation data for the installation should be used as a basis for calculation, and submitted.

2.3.6 Where the torsional stiffness of flexible couplings varies with torque, frequency or speed, calculations should be representative of the appropriate range of effective dynamic stiffness.

2.4.1 The symbols used in this Section are defined as follows:

2.4.2 Alternating torsional vibration stresses are to be based on half-range amplitudes of stress resulting from the alternating torque (which is superimposed on the mean torque) representing the synthesis of all harmonic orders present.

2.4.3 All vibration stress limits relate to the synthesis or measurement of total nominal torsional stress and are to be based on the plain section of the shafting neglecting stress raisers.

2.4.4 For a longitudinal slot C_k = 0,3 is applicable within the dimension limitations given in Pt 5, Ch 6, 3.1 Intermediate shafts 3.1.6. If the slot dimensions are outside these limitations, or if the use of another C_k is desired, the actual stress concentration factor (scf) is to be documented or determined from Pt 5, Ch 8, 2.4 Symbols and definitions 2.4.5 or by direct application of FE calculation , in which case:

Note that the scf is defined as the ratio between the maximum local principal stress and times the nominal torsional stress (determined for the bored shaft without slots).

2.4.5  Stress concentration factor of slots. The stress concentration factor (scf) at the ends of slots can be determined by means of the following empirical formulae:

This formula applies to:

• Slots at 120 or 180 or 360 degrees apart.
• Slots with semicircular ends. A multi-radii slot end can reduce the local stresses, but this is not included in this empirical formula.
• Slots with no edge rounding (except chamfering), as any edge rounding increases the scf slightly.

α_t(hole) represents the stress concentration of radial holes and can be determined as :

where , in this context, e = hole diameter, in mm (this is independent of slot width)

or simplified to α_t(hole) = 2,3.

2.5.1 The following stress limits apply to intermediate shafts, thrust shafts and to screwshafts fully protected from sea water. For screwshafts, the limits apply to the minimum sections of the portions of the screwshaft as defined in Pt 5, Ch 6, 3.5 Screwshafts and tube shafts.

2.5.2 In the case of unprotected screwshafts, special consideration will be given.

2.5.3 In no part of the propulsion shafting system may the alternating torsional vibration stresses exceed the values of τ_c for continuous operation, and τ_t for transient running, given by the following formulae:

2.5.4 In general, the tensile strength of the steel used is to comply with the requirements of Pt 5, Ch 6, 2 Materials. For the calculation of the permissible limits of stresses due to torsional vibration, σ_u is not to be taken as more than 800 N/mm² in the case of alloy steel intermediate shafts, or 600 N/mm² in the case of carbon and carbon-manganese steel intermediate, thrust and propeller shafts unless, for intermediate shafts only, it is verified that the materials exhibit a similar fatigue life to conventional steels through compliance with the requirements in Pt 5, Ch 6, 5 Approval of alloy steel used for intermediate shaft material.

2.5.5 Where the scantlings of coupling bolts and straight shafting differ from the minimum required by the Rules, special consideration will be given.

2.6.1 Natural frequencies of the complete set are to be sufficiently removed from the firing impulse frequency at the full load speed, particularly where flexible couplings are interposed between the engine and generator.

2.6.2 Within the speed limits of 0,95N _s and 1,05N _s the vibration stresses in the transmission shafting are not to exceed the values given by the following formula:

2.6.3 Vibration stresses in the transmission shafting due to critical speeds which have to be passed through in starting and stopping, are not to exceed the values given by the following formula:

2.6.4 The amplitudes of the total vibratory inertia torques imposed on the generator rotors are to be limited to ± 2,0Q _s in general, or to ± 2,5Q _s for close-coupled revolving field alternating current generators, over the speed range from 0,95N _s to 1,05N _s. Below 0,95N _s the amplitudes are to be limited to ± 6,0Q _s. Where two or more generators are driven from one engine, each generator is to be considered separately in relation to its own rated torque.

2.6.5 The rotor shaft and structure are to be designed to withstand these magnitudes of vibratory torque. Where it can be shown that they are capable of withstanding a higher vibratory torque, special consideration will be given.

2.6.6 In addition to withstanding the vibratory conditions over the speed range from 0,95N _s to 1,05N _s, flexible couplings, if fitted, are to be capable of withstanding the vibratory torques and twists arising from transient criticals and short-circuit currents.

2.6.7 In the case of alternating current generators, resultant vibratory amplitudes at the rotor are not to exceed ± 3,5 electrical degrees under both full load working conditions and the malfunction condition mentioned in Pt 5, Ch 8, 2.3 Scope of calculations 2.3.3.

2.7.1 The relevant requirements of Pt 5, Ch 8, 2.6 Generator sets 2.6.1, Pt 5, Ch 8, 2.6 Generator sets 2.6.2 and Pt 5, Ch 8, 2.6 Generator sets 2.6.3 are also applicable to other machinery installations such as pumps or compressors with the speed limits being taken as 0.95N _s to 1.10N _s.

2.8.1  Torsional vibration dampers. The use of dampers or detuners to limit vibratory stress due to resonances which occur within the range between 0,85N _s and 1,05N _s are to be considered. If fitted, these should be of a type which makes adequate provision for dissipation of heat. Where necessary, performance monitoring may be required.

2.8.2  Flexible couplings:

1. Flexible couplings included in an installation are to be capable of transmitting the mean and vibratory loads without exceeding the makers' recommended limits for angular amplitude or heat dissipation.

2. Where calculations indicate that the limits recommended by the manufacturer may be exceeded under misfiring conditions, a suitable means is to be provided for detecting and indicating misfiring. Under these circumstances power and/or speed restrictions may be required. Where machinery is non-essential, disconnection of the branch containing the coupling would be an acceptable action in the event of misfiring.

2.8.3  Gearing:

1. The torsional vibration characteristics are to comply with the requirements of Pt 5, Ch 8, 2.3 Scope of calculations. The sum of the mean and of the vibratory torque should not exceed four-thirds of the full transmission torque, at MCR, throughout the speed range. In cases where the proposed transmission torque loading on the gear teeth is less than the maximum allowable, special consideration will be given to the acceptance of additional vibratory loading on the gears.

2. Where calculations indicate the possibility of torque reversal, the operating speed range is to be determined on the basis of observations during sea trials.

2.9.1 Where calculations indicate that the limits for torsional vibration within the range of working speeds are exceeded, measurements, using an appropriate technique, may be taken from the machinery installation for the purpose of approval of torsional vibration characteristics, or determining the need for restricted speed ranges, and the confirmation of their limits.

2.9.2 Where differences between calculated and measured levels of stress, torque or angular amplitude arise, the stress limits are to be applied to the stresses measured on the completed installation.

2.9.3 The method of measurement is to be appropriate to the machinery components and the parameters which are of concern. Where shaft stresses have been estimated from angular amplitude measurements, and are found to be close to limiting stresses as defined in Pt 5, Ch 8, 2.5 Limiting stress in propulsion shafting, strain gauge techniques may be required. When measurements are required, detailed proposals are to be submitted.

2.10.1 Where calculations and/or measurements have indicated the possibility of excessive vibratory stresses, torques or angular amplitudes in the event of a malfunction, vibration or performance monitoring, directly or indirectly, may be required.

2.11.1 Restricted speed and/or power ranges will be imposed to cover all speeds where the stresses exceed the limiting values, τ_c, for continuous running , including one cylinder misfiring conditions if intended to be continuously operated under such conditions. For controllable pitch propellers with the possibility of individual pitch and speed control, both full and zero pitch conditions are to be considered. Similar restrictions will be imposed, or other protective measures required to be taken, where vibratory torques or amplitudes are considered to be excessive for particular machinery items. At each end of the restricted speed range the engine is to be stable in operation.

2.11.2 The restricted speed range is to take account of the tachometer speed tolerances at the barred speeds.

2.11.3 Critical responses which give rise to speed restrictions are to be arranged sufficiently removed from the maximum revolutions per minute to ensure that, in general, at r = 0,8 the stress due to the upper flank does not exceed τ_c.

2.11.4 Provided that the stress amplitudes due to a torsional critical response at the borders of the barred speed range are less than τ_c under normal and stable operating conditions the speed restriction derived from the following formula may be applied:

2.11.5 Where calculated vibration stresses due to criticals below 0,8N _s marginally exceed τ_c or where the critical speeds are sharply tuned, the range of revolutions restricted for continuous operation may be reduced.

2.11.6 In cases where the resonance curve of a critical speed has been derived from measurements, the range of revolutions to be avoided for continuous running may be taken as that over which the measured vibration stresses are in excess of τ_c, having regard to the tachometer accuracy.

2.11.7 Where restricted speed ranges under normal operating conditions are imposed, notice boards are to be fitted at the control stations stating that the engine is not to be run continuously between the speed limits obtained as above, and the engine tachometers are to be marked accordingly.

2.11.8 Where vibration stresses approach the limiting value τ_t, the range of revolutions restricted for continuous operation may be extended. The notice boards are to indicate that this range must be passed through rapidly.

2.11.9 For excessive vibratory torque, stress or amplitude in other components, based on Pt 5, Ch 8, 2.8 Other machinery components 2.8.1 to Pt 5, Ch 8, 2.8 Other machinery components 2.8.3, the limits of any speed/power restriction are to be such as to maintain acceptable levels during continuous operation.

2.11.10 Where the restrictions are imposed for the contingency of an engine malfunction or component failure, the limits are to be entered in the machinery Operating Manual.

2.11.11 Restricted speed ranges in one-cylinder misfiring conditions on ships with single engine propulsion are to enable safe navigation whereby sufficient propulsion power is available to maintain control of the ship.

2.11.12 There are to be no restricted speed ranges imposed above a speed ratio of r = 0,8 under normal operating conditions.

2.12.1 Where restricted speed ranges are imposed as a condition of approval, the tachometer accuracy is to be checked against the counter readings, or by equivalent means, in the presence of the Surveyors to verify that it reads correctly within ± 2 per cent in way of the restricted range of revolutions.

2.13.1 Where there is a significant critical response above and close to the maximum service speed, consideration is to be given to the effect of temporary overspeed.