Dimensions of propulsion shafts and their permissible torsional vibration stresses

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1 (Feb 2005) (orr.1 Mar 2012) (orr.2 Nov 2012) (Rev.1 Aug 2014) (Rev.2 Apr 2015) Dimensions of propulsion shafts and their permissible torsional vibration stresses.1 Sope This UR applies to propulsion shafts suh as intermediate and propeller shafts of traditional straight forged design and whih are driven by rotating mahines suh as diesel engines, turbines or eletri motors. For shafts that are integral to equipment, suh as for gear boxes, podded drives, eletrial motors and/or generators, thrusters, turbines and whih in general inorporate partiular design features, additional riteria in relation to aeptable dimensions have to be taken into aount. For the shafts in suh equipment, the requirements of this UR may only be applied for shafts subjet mainly to torsion and having traditional design features. Other limitations, suh as design for stiffness, high temperature, et. are to be addressed by speifi rules of the lassifiation soiety. Expliitly the following appliations are not overed by this UR: - additional strengthening for shafts in ships lassed for navigation in ie - gearing shafts - eletri motor shafts - generator rotor shafts - turbine rotor shafts - diesel engine rankshafts (see M53) - unproteted shafts exposed to sea water.2 Alternative alulation methods Alternative alulation methods may be onsidered by the lassifiation soiety. Any alternative alulation method is to inlude all relevant loads on the omplete dynami shafting system under all permissible operating onditions. onsideration is to be given to the dimensions and arrangements of all shaft onnetions. Notes: 1. This UR replaes URs M33, M37, M38, M39 and M This UR applies to ships ontrated for onstrution on or after 1 July The ontrated for onstrution date means the date on whih the ontrat to build the vessel is signed between the prospetive owner and the shipbuilder. For further details regarding the date of ontrated for onstrution, refer to IAS Proedural Requirement (PR) No Rev.1 of UR applies to ships ontrated for onstrution on or after 1 July Rev.2 of UR applies to ships ontrated for onstrution on or after 1 January Page 1 of 9 IAS Req. 2005/Rev

2 Moreover, an alternative alulation method is to take into aount design riteria for ontinuous and transient operating loads (dimensioning for fatigue strength) and for peak operating loads (dimensioning for yield strength). The fatigue strength analysis may be arried out separately for different load assumptions, for example as given in Material limitations Where shafts may experiene vibratory stresses lose to the permissible stresses for transient operation, the materials are to have a speified minimum ultimate tensile strength ( ) of 500 N/mm 2. Otherwise materials having a speified minimum ultimate tensile strength ( ) of 400 N/mm 2 may be used. For use in the following formulae in this UR, is limited as follows: - For arbon and arbon manganese steels, a minimum speified tensile strength not exeeding 600 N/mm 2 for use in.5 and not exeeding 760 N/mm 2 in.4. - For alloy steels, a minimum speified tensile strength not exeeding 800 N/mm 2. - For propeller shafts in general a minimum speified tensile strength not exeeding 600 N/mm 2 (for arbon, arbon manganese and alloy steels). Where materials with greater speified or atual tensile strengths than the limitations given above are used, redued shaft dimensions or higher permissible vibration stresses are not aeptable when derived from the formulae in this UR unless the Soiety verifies that the materials exhibit similar fatigue life as onventional steels (see Appendix I)..4 Shaft diameters Shaft diameters are not to be less than that determined from the following formula: d = F. k. 3 p n d d 4 i 4 o where: d = minimum required diameter in mm d i = atual diameter in mm of shaft bore d o = outside diameter in mm of shaft. If the bore of the shaft is 0.40d o, the expression 4 d i 1 may be taken as d o F = fator for type of propulsion installation = 95 for intermediate shafts in turbine installation, diesel installations with hydrauli (slip type) ouplings, eletri propulsion installations = 100 for all other diesel installations and all propeller shafts Page 2 of 9 IAS Req. 2005/Rev

3 k = fator for the partiular shaft design features, see.6 n 0 = speed in revolutions per minute of shaft at rated power p = rated power in kw transmitted through the shaft (losses in gearboxes and bearings are to be disregarded) = speified minimum tensile strength in N/mm 2 of the shaft material, see.3 The diameter of the propeller shaft loated forward of the inboard stern tube seal may be gradually redued to the orresponding diameter required for the intermediate shaft using the minimum speified tensile strength of the propeller shaft in the formula and reognising any limitations given in.3..5 Permissible torsional vibration stresses The alternating torsional stress amplitude is understood as ( max min ) / 2 as an be measured on a shaft in a relevant ondition over a repetitive yle. Torsional vibration alulations are to inlude normal operation and operation with any one ylinder misfiring (i.e. no injetion but with ompression) giving rise to the highest torsional vibration stresses in the shafting. For ontinuous operation the permissible stresses due to alternating torsional vibration are not to exeed the values given by the following formulae: ± =...(3 2. λ 2 K D ) for λ < ± =. K. D.1.38 for 0.9 λ < where: = permissible stress amplitude in N/mm 2 due to torsional vibration for ontinuous operation = speified minimum ultimate tensile strength in N/mm 2 of the shaft material, see also.3 K = fator for the partiular shaft design features, see.6 D = size fator = d o d o = shaft outside diameter in mm λ = speed ratio = n/n 0 Page 3 of 9 IAS Req. 2005/Rev

4 n = speed in revolutions per minute under onsideration n 0 = speed in revolutions per minute of shaft at rated power Where the stress amplitudes exeed the limiting values of for ontinuous operation, inluding one ylinder misfiring onditions if intended to be ontinuously operated under suh onditions, restrited speed ranges are to be imposed whih are to be passed through rapidly. Restrited speed ranges in normal operating onditions are not aeptable above λ = 0.8. Restrited speed ranges in one-ylinder misfiring onditions of single propulsion engine ships are to enable safe navigation. The limits of the barred speed range are to be determined as follows: (a) (b) The barred speed range is to over all speeds where the aeptane limits ( ) are exeeded. For ontrollable pith propellers with the possibility of individual pith and speed ontrol, both full and zero pith onditions have to be onsidered. Additionally the tahometer tolerane has to be added. At eah end of the barred speed range the engine is to be stable in operation. In general and subjet to (a) the following formula may be applied, provided that the stress amplitudes at the border of the barred speed range are less than under normal and stable operating onditions. 16. n (18 λ ). n n 18 λ 16 where: n = ritial speed in revolutions per minute (resonane speed) λ = speed ratio = n / n o For the passing of the barred speed range the torsional vibrations for steady state ondition are not to exeed the value given by the formula: where: ± = 1.7. T K T = permissible stress amplitude in N/mm 2 due to steady state torsional vibration in a barred speed range. Page 4 of 9 IAS Req. 2005/Rev

5 .6 Table of k and k fators for different design features (see.7.2) integral oupling flange 1) and straight setions shrink fit oupling 2) Intermediate shafts with 3) 4) Keyway, tapered onnetion 3) 4) Keyway, ylindrial onnetion radial hole 5) longitudinal slot 6) thrust shafts external to engines on both sides of thrust ollar 1) in way of bearing when a roller bearing is used Flange mounted or keyless taper fitted propellers 8) propeller shafts Key fitted propellers 8) etween forward end of aft most bearing and forward stern tube seal k= K = ) Note: Transitions of diameters are to be designed with either a smooth taper or a blending radius. For guidane, a blending radius equal to the hange in diameter is reommended. Footnotes 1) Fillet radius is not to be less than 0.08d. 2) k and k refer to the plain shaft setion only. Where shafts may experiene vibratory stresses lose to the permissible stresses for ontinuous operation, an inrease in diameter to the shrink fit diameter is to be provided, e.g. a diameter inrease of 1 to 2 % and a blending radius as desribed in the table note. 3) At a distane of not less than 0.2d o from the end of the keyway the shaft diameter may be redued to the diameter alulated with k=1.0. 4) Keyways are in general not to be used in installations with a barred speed range. 5) Diameter of radial bore (d h ) not to exeed 0.3d o. The intersetion between a radial and an eentri (r e ) axial bore (see below) is not overed by this UR. Page 5 of 9 IAS Req. 2005/Rev

6 6) Subjet to limitations as slot length (l)/outside diameter < 0.8 and inner diameter (d i )/outside diameter < 0.7 and slot width (e)/outside diameter > The end rounding of the slot is not to be less than e/2. An edge rounding should preferably be avoided as this inreases the stress onentration slightly. The k and K values are valid for 1, 2 and 3 slots, i.e. with slots at 360 respetively 180 and respetively 120 degrees apart. 7) K = 0.3 is an approximation within the limitations in 6). More aurate estimate of the stress onentration fator (sf) may be determined from.7.3 or by diret appliation of FE alulation. In whih ase: K = 1.45/sf Note that the sf is defined as the ratio between the maximum loal prinipal stress and 3 times the nominal torsional stress (determined for the bored shaft without slots). 8) Appliable to the portion of the propeller shaft between the forward edge of the aftermost shaft bearing and the forward fae of the propeller hub (or shaft flange), but not less than 2.5 times the required diameter..7 Notes 1. Shafts omplying with this UR satisfy the following: 1. Low yle fatigue riterion (typially < 10 4 ), i.e. the primary yles represented by zero to full load and bak to zero, inluding reversing torque if appliable. This is addressed by the formula in High yle fatigue riterion (typially >> 10 7 ), i.e. torsional vibration stresses permitted for ontinuous operation as well as reverse bending stresses. The limits for torsional vibration stresses are given in.5. The influene of reverse bending stresses is addressed by the safety margins inherent in the formula in The aumulated fatigue due to torsional vibration when passing through a barred speed range or any other transient ondition with assoiated stresses beyond those permitted for ontinuous operation is addressed by the riterion for transient stresses in.5. Page 6 of 9 IAS Req. 2005/Rev

7 2. Explanation of k and K The fators k (for low yle fatigue) and K (for high yle fatigue) take into aount the influene of: - The stress onentration fators (sf) relative to the stress onentration for a flange with fillet radius of 0.08d o (geometri stress onentration of approximately 1.45) K = sf and k sf = 1.45 x where the exponent x onsiders low yle noth sensitivity. - The noth sensitivity. The hosen values are mainly representative for soft steels ( < 600), while the influene of steep stress gradients in ombination with high strength steels may be underestimated. - The size fator D being a funtion of diameter only does not purely represent a statistial size influene, but rather a ombination of this statistial influene and the noth sensitivity. The atual values for k and K are rounded off. 3. Stress onentration fator of slots The stress onentration fator (sf) at the end of slots an be determined by means of the following empirial formulae using the symbols in footnote 6): ( l e) / d sf = α t( hole) di e 1. d d This formula applies to: - slots at 120 or 180 or 360 degrees apart. - slots with semiirular ends. A multi-radii slot end an redue the loal stresses, but this is not inluded in this empirial formula. - slots with no edge rounding (exept hamfering), as any edge rounding inreases the sf slightly. α t(hole) represents the stress onentration of radial holes (in this ontext e = hole diameter) and an be determined as: 2 2 e e e α t ( hole) = di 2 d d d d α ( hole) = 2.3 or simplified to t 2 Page 7 of 9 IAS Req. 2005/Rev

8 Appendix I Speial approval of alloy steel used for intermediate shaft material 1. Appliation This appendix is applied to the approval of alloy steel whih has a minimum speified tensile strength greater than 800 N/mm 2, but less than 950 N/mm 2 intended for use as intermediate shaft material. 2. Torsional fatigue test A torsional fatigue test is to be performed to verify that the material exhibits similar fatigue life as onventional steels. The torsional fatigue strength of said material is to be equal to or greater than the permissible torsional vibration stress given by the formulae in.5. The test is to be arried out with nothed and unnothed speimens respetively. For alulation of the stress onentration fator of the nothed speimen, fatigue strength redution fator β should be evaluated in onsideration of the severest torsional stress onentration in the design riteria. 2.1 Test onditions Test onditions are to be in aordane with Table 1. Mean surfae roughness is to be <0.2µm Ra with the absene of loalised mahining marks verified by visual examination at low magnifiation (x20) as required by Setion 8.4 of ISO Test proedures are to be in aordane with Setion 10 of ISO Table 1 Loading type Stress ratio Load waveform Evaluation Number of yles for test termination Test ondition Torsion R=-1 onstant-amplitude sinusoidal S-N urve 1 x 10 7 yles 2.2 Aeptane riteria Measured high-yle torsional fatigue strength 1 and low-yle torsional fatigue strength are to be equal to or greater than the values given by the following formulae: 2 1, λ= 0 = K. 6 D K Page 8 of 9 IAS Req. 2005/Rev

9 where K = fator for the partiular shaft design features, see.7 sf = stress onentration fator, see.7.3 (For unnothed speimen, 1.0.) D = size fator, see.5 = speified minimum tensile strength in N/mm 2 of the shaft material 3. leanliness requirements The steels are to have a degree of leanliness as shown in Table 2 when tested aording to ISO 4967 method A. Representative samples are to be obtained from eah heat of forged or rolled produts. The steels are generally to omply with the minimum requirements of UR W7 Table 2, with partiular attention given to minimising the onentrations of sulphur, phosphorus and oxygen in order to ahieve the leanliness requirements. The speifi steel omposition is required to be approved by the Soiety. Table 2 leanliness requirements 4. Inspetion Inlusion group Series Limiting hart diagram index I Type A Fine 1 Thik 1 Type Fine 1.5 Thik 1 Type Fine 1 Thik 1 Type D Fine 1 Thik 1 Type DS - 1 The ultrasoni testing required by UR W7 is to be arried out prior to aeptane. The aeptane riteria are to be in aordane with IAS Reommendation No. 68 or a reognized national or international standard. End of Doument Page 9 of 9 IAS Req. 2005/Rev

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