Section 3 Design

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

3.1.2 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.

3.1.3 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.

3.1.4 For a longitudinal slot C _k = 0,3 is applicable within the dimension limitations given in Vol 2, Pt 3, Ch 2, 4.2 Intermediate shafts 4.2.6. 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 Vol 2, Pt 5, Ch 1, 3.1 Symbols and definitions 3.1.5 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).

3.1.5 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:

3.2.1 The following stress limits apply to intermediate shafts, thrust shafts and to screwshafts fully protected from seawater. For screwshafts, the limits apply to the minimum section between the forward end of the propeller boss and the forward stern gland.

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

3.2.3 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:

3.2.4 In general, the tensile strength of the steel used is to comply with the requirements of Vol 2, Pt 3, Ch 2 Shafting Systems. 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 Vol 2, Pt 3, Ch 2, 6 Approval of alloy steel used for intermediate shaft material.

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

3.3.1 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.

3.3.2 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:

3.3.3 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:

3.3.4 The amplitudes of 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.

3.3.5 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.

3.3.6 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.

3.3.7 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 Vol 2, Pt 5, Ch 1, 2.2 Scope of calculations 2.2.3.

3.4.1 The relevant requirements of Vol 2, Pt 5, Ch 1, 3.3 Generator sets 3.3.1, Vol 2, Pt 5, Ch 1, 3.3 Generator sets 3.3.2 and Vol 2, Pt 5, Ch 1, 3.3 Generator sets 3.3.3 are also applicable to other machinery installations such as pumps or compressors.

3.5.1  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 is 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.

3.5.2  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 restriction may be required. Where machinery is not directly related to Mobility and/or Ship Type, disconnection of the branch containing the coupling would be an acceptable action in the event of misfiring.

3.5.3  Gearing:

1. The torsional vibration characteristics are to comply with the requirements of Vol 2, Pt 5, Ch 1, 2.2 Scope of calculations. The vibratory torque should not exceed one third of the full transmission torque 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 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.

3.6.1 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.

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

3.6.3 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.

3.6.4 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:

3.6.5 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.

3.6.6 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 stresses are in excess of τ_c, having regard to tachometer accuracy.

3.6.7 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.

3.6.8 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.

3.6.9 For excessive vibratory torque, stress or amplitude in other components, bases on Vol 2, Pt 5, Ch 1, 3.6 Restricted speed and/or power ranges 3.6.1, the limits of any speed/power restriction are to be such as to maintain acceptable levels during continuous operation.

3.6.10 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.

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

3.6.12 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.

3.7.1 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.

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