# dnv classification note 51.1: ice strengthening of propulsion

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CLASSIFICATION NOTESNo. 51.1

ICE STRENGTHENING OF PROPULSION MACHINERY

JANUARY 2011

DET NORSKE VERITASVeritasveien 1, NO-1322 Høvik, Norway Tel.: +47 67 57 99 00 Fax: +47 67 57 99 11

FOREWORDDET NORSKE VERITAS (DNV) is an autonomous and independent foundation with the objectives of safeguarding life,property and the environment, at sea and onshore. DNV undertakes classification, certification, and other verification andconsultancy services relating to quality of ships, offshore units and installations, and onshore industries worldwide, andcarries out research in relation to these functions.Classification NotesClassification Notes are publications that give practical information on classification of ships and other objects. Examplesof design solutions, calculation methods, specifications of test procedures, as well as acceptable repair methods for somecomponents are given as interpretations of the more general rule requirements.All publications may be downloaded from the Society’s Web site http://www.dnv.com/.The Society reserves the exclusive right to interpret, decide equivalence or make exemptions to this Classification Note.

BackgroundThis Classification Note was introduced in order to offer design guidance according to revised IACS PolarClass rules and the Finnish-Swedish Ice Class rules for Northern Baltic.

Main Changes January 2011— In section 4.3.5 a formula has been corrected.— In section 4.4.4 a formula has been corrected including changing from small to capital “A” in the formula

and in 4.5.1.— In section 4.5.5 a superfluous formula has been deleted.

AcknowledgmentDNV wish to thank ABB Marine Oy, Berg Propulsion AB and MAN Diesel for their contributions and figures.

The electronic pdf version of this document found through http://www.dnv.com is the officially binding version© Det Norske Veritas

Any comments may be sent by e-mail to [email protected] subscription orders or information about subscription terms, please use [email protected] Typesetting (Adobe Frame Maker) by Det Norske Veritas

If any person suffers loss or damage which is proved to have been caused by any negligent act or omission of Det Norske Veritas, then Det Norske Veritas shall pay compensation tosuch person for his proved direct loss or damage. However, the compensation shall not exceed an amount equal to ten times the fee charged for the service in question, provided thatthe maximum compensation shall never exceed USD 2 million.In this provision "Det Norske Veritas" shall mean the Foundation Det Norske Veritas as well as all its subsidiaries, directors, officers, employees, agents and any other acting on behalfof Det Norske Veritas.

Classification Notes - No. 51.1, January 2011

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CONTENTS

1. GENERAL.............................................................................................................................................. 41.1 Scope.........................................................................................................................................................42. SYMBOLS, NOMENCLATURE AND UNITS .................................................................................. 43. PROPELLER BLADES ........................................................................................................................ 53.1 Ice Interaction Load Models .....................................................................................................................53.2 Finite Element Analysis............................................................................................................................93.3 Propeller blade strength assessment........................................................................................................143.4 Blade Failure Design Loads ...................................................................................................................164. PROPELLER HUB AND PITCH MECHANISM ........................................................................... 174.1 Scope and General Remarks ...................................................................................................................174.2 Applicable load scenarios .......................................................................................................................194.3 Load transmission ...................................................................................................................................194.4 Strength assessment ................................................................................................................................234.5 Stress in components of CP-Mechanism ................................................................................................244.6 Material strength .....................................................................................................................................345. GUIDANCE ON SIMULATION CALCULATIONS ...................................................................... 405.1 The lumped mass-elastic system.............................................................................................................405.2 Damping in the mass-elastic system.......................................................................................................415.3 Excitations...............................................................................................................................................456. PROPULSION SHAFT DESIGN AGAINST FATIGUE ................................................................ 456.1 Nomenclature..........................................................................................................................................456.2 General ....................................................................................................................................................456.3 Method for fatigue analysis ....................................................................................................................467. REDUCTION GEARS ........................................................................................................................ 508. PODDED PROPULSORS / AZIMUTHING THRUSTERS ........................................................... 518.1 Ice loads on pod/thruster body and propeller hub...................................................................................51Appendix A.GENERAL GUIDANCE ON FATIGUE ANALYSIS OF PROPULSION MACHINERY SUBJECT TO ICE LOADS .......................................................................................................................... 54

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1. GENERAL1.1 ScopeThis Classification Note contains procedures and methods necessary for verification of the load carryingcapacity (ultimate and fatigue strength) for the following components in the propulsion plant subject to loadsdue to ice impacts:

— propeller blades, hub and pitch mechanism— shafts— reduction gears— pod/thruster underwater housing.

The assessment of other components together with the general applicability, required safety factors, materialrequirements and design ice loads for the different ice classes are given in the respective sections of the Rulesfor Classification of Ships, Pt.5 Ch.1 Sec.3 (Northern Baltic ice classes: ICE-1A* - ICE-1C) and Pt.5 Ch.1 Sec.8(Polar ice classes: PC-1 – PC-7). Consequently, this document should be read together with the rules referredto above, in order to describe all aspects of the strength assessment. The ice loads described in the Rules for Classification of Ships Pt.5 Ch.1 Sec.3 and Sec.8 are meant to be totalloads, i.e. in general they include the open water hydrodynamic loads (unless otherwise stated). In cases wherethe calculations described herein result in smaller scantlings than derived from other class requirements, thelatter requirements prevail.The calculation methods specified herein are to some extent prepared based on empirical considerations andstudies of conventional design known at the time of writing. This means that they are applicable for “standard”materials and geometrical shapes within a limited range of geometry and size. Hence, the presented formulae should not uncritically be used for novel designs or be transferred to otherapplications.In principle, other relevant calculation methods may be applied for this purpose.

2. SYMBOLS, NOMENCLATURE AND UNITSIn addition to the list presented below, the symbols are explained with their first occurrence in the text or anequation.

Table 2-1 SymbolsSymbol Term Unitā S-N curve parameter, log(ā) is the intercept of the log(N) axis -CP Controllable pitchd Minimum shaft diameter at considered notch mmD Propeller diameter mdi Inner diameter of shaft at considered notch mmFb Maximum backward blade force for the ship’s service life kNFex Ultimate blade load resulting from blade loss through plastic bending kNFf Maximum forward blade force for the ship’s service life kNh0 Depth of the propeller centreline from lower ice waterline mHice Thickness of maximum design ice block entering to propeller mI Number of different load magnitudes (load blocks) considered in Palmgren-Miner’s us-

age factor/”damage sum”-

k Weibull shape parameter -LIWL Lower ice waterline mln() Natural logarithm -log() 10th logarithm -m Slope parameter for SN curve in log/log scaleMbl Blade bending moment kNmMCR Maximum continuous ratingMDR Miner’s accumulated fatigue damage ration Propeller rotational speed rev./sni(τv ice) Number of cycles with a constant stress amplitude τv ice -Nice Number of load cycles in ice load spectrum -

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3. PROPELLER BLADES3.1 Ice Interaction Load ModelsThe design loads described in the rules and listed in Table 3-1 are maximum lifetime forces on a propellerresulting from propeller/ice interaction, including hydrodynamic loads. The methodology presented here is an approach to be more in accordance with the actual, physical contactbetween propeller and ice. It will cover conventional propeller design not limited to a certain blade skew angleas previous. The background for the ice loads is a combination of ice model tests, full scale measurements andDNV's long service experience with ice classed vessels.The requirements for concentrated ice loads affecting the blade tips and edges have been removed from theserules and will give a unique opportunity for the designers to optimise the blade edges and profiles individually.It is however necessary, during design of blades, to take into consideration the blade edges impact strength toavoid local indentations of the edges. This can be done with either old methods or even better with FEA and

Ni(τv ice) Number of cycles to failure due to the constant stress amplitude τv ice -qw Weibull scale parameter NmR Propeller radius mS Safety factor -T Torque NmT0 Torque at maximum continuous power in bollard condition NmTaverage The average torque during an ice milling sequence NmThb Maximum backward propeller ice thrust for the ship’s service life kNThf Maximum forward propeller ice thrust for the ship’s service life kNThr Maximum response thrust along the shaft line kNTpeak The highest response peak torque in the shaft due ice impacts on propeller (probability

for exceeding = 1/Z· Nice) Nm

TA The response torque amplitude on the shaft during a sequence of ice impacts on the pro-peller

Nm

TA max The highest response torque amplitude on the shaft during a sequence of ice impacts on the propeller (probability for exceeding = 1/Z· Nice)

Nm

Wt Cross section modulus torsion = polar moment of inertia divided by distance to the sur-face

mm3

Z Number of propeller blades -αt Geometrical stress concentration factor, torsion -Δσmax Maximum dynamic stress range, is difference in maximum backward bending stress and

maximum forward bending stressMPa

η Palmgren-Miner’s usage factor/”damage sum” -σAmax

Maximum dynamic stress amplitude, MPa

σFat-E7 High cycle mean bending fatigue strength - 107 load cyclesσmean Mean stress MPaσref

Reference stress MPa

σref 2 Reference stress

or

whichever is less

MPa

σu Ultimate tensile strength of blade material MPaσy Minimum specified yield strength of shaft material N/mm2 = MPaτ Nominal mean torsional stress at any load (or r.p.m.) N/mm2 = MPaτv ice Nominal torsional stress on the shaft caused by Tv ice N/mm2 = MPaτv ice max Nominal torsional stress on the shaft caused by Tv ice max N/mm2 = MPaτvHC Permissible high cycle (=3·106 cycles) torsional vibration stress amplitude N/mm2 = MPaτvLC Permissible low cycle (=104 cycles) torsional vibration stress amplitude N/mm2 = MPaτy Yield strength in shear of shaft material (= minimum specified σy/√3) N/mm2 = MPa

Table 2-1 SymbolsSymbol Term Unit

2max

maxσσ Δ

=A

uref σσσ ⋅+⋅= 4.06.0 2.0

uref σσ ⋅= 7.02

uref σσσ ⋅+⋅= 4.06.0 2.02

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local ice pressures on the propeller blade edge and tip. See 3.3.6.

Figure 3-1Ice loads acting on propeller

Table 3-1 Ice interaction loadsLoad Definition Use of the load in design processQsmax The maximum lifetime spindle torque on a propeller blade

resulting from propeller/ice interaction, including hydro-dynamic loads on that blade.

In designing the propeller strength, the spindle torque is automatically taken into account be-cause the propeller load is acting on the blade as distributed pressure on the leading edge or tip area.

Thb The maximum lifetime thrust on propeller (all blades) re-sulting from propeller/ice interaction. The direction of the thrust is the propeller shaft direction and the force is oppo-site to the hydrodynamic thrust.

Is used for estimation of the response thrust Thr. Thb can be used as an estimate of excitation for axial vibration calculations. However, axial vi-bration calculations are not required in the rules.

Thf The maximum lifetime thrust on propeller (all blades) re-sulting from propeller/ice interaction. The direction of the thrust is the propeller shaft direction acting in the direction of hydrodynamic thrust.

Is used for estimation of the response thrust Thr. Thf can be used as an estimate of excitation for axial vibration calculations. However, axial vi-bration calculations are not required in the rules.

Tmax The maximum ice-induced torque resulting from propel-ler/ice interaction on one propeller blade, including hydro-dynamic loads on that blade.

Is used for estimation of the response torque (Tr(t)) along the propulsion shaft line and as ex-citation for torsional vibration calculations.

Fex Ultimate blade load resulting from blade loss through plas-tic bending. The force that is needed to cause total failure of the blade so that plastic hinge is caused to the root area. The force is acting on 0.8R. Spindle arm is to be taken as 1/3 of the distance between the axis of blade rotation and leading/trailing edge (whichever is the greater) at the 0.8R radius.

Blade failure load is used to dimension the blade bolts, pitch control mechanism, propeller shaft, propeller shaft bearing and trust bearing. The objective is to guarantee that total propeller blade failure should not cause damage to other components.

Tr(t) Maximum response torque along the propeller shaft line, taking into account the dynamic behaviour of the shaft line for ice excitation (torsional vibration) and hydrodynamic mean torque on propeller.

Design torque for propeller shaft line compo-nents.

Thr Maximum response thrust along shaft line, taking into ac-count the dynamic behaviour of the shaft line for ice exci-tation (axial vibration) and hydrodynamic mean thrust on propeller.

Design thrust for propeller shaft line compo-nents.

of 1.27 MPa. The load is distributed as Fx = 702 kN, Fy = - 214 kN and Fz = - 185 kN.

Depending on the pitch angle of the 0.7 r/R section, the pressure would need to be increased

Assuming a pitch angle of

Combining hydrodynamic load with ice loads

dur ing these measurements include both the ice loads and the hydrodynamic loads . This is

Hence, it is not necessary t

calculating the safety factor for ice .

bFFresult

0.7R

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The direction of the forces is perpendicular to the plane defined by the generatrix and the 0.7R chord line.Homogenous surface pressure is applied over the part of the blade as specified for the various load cases inTable 3-2 and 3-3. Because the propeller blade is a curved 3-D shape the force resulting from a homogenouspressure, Fresult may act in a somewhat different direction than perpendicular to the plane defined by thepropeller generatrix and 0.7R chord line. Hence the surface pressure shall be scaled so that the component of the resulting force perpendicular to theplane defined by the generatrix and 0.7R chord line equals the design load as derived from formulae in theRules for Classification of Ships Pt.5 Ch.1 Sec.3 J500 and Sec.8 I300 and I400. Hence, the resulting force fromthe ice pressure, Fresult may be somewhat larger than the design ice load but the difference will normally notbe very large.This is illustrated in the example for Fb in Figure 3-1.The tables 3.2, 3.3 and 3.4 are describing the extreme loads a propeller operating in ice is expected to suffer.The load cases 1-5 are given by the rules and are only reproduced here for convenience.

Table 3-2 Ice loads on leading edge and tip region – forward bendingBackward bending force - Fb Use of the load in the design

processFb The maximum lifetime backward force on a propeller blade resulting

from propeller/ice interaction, including hydrodynamic loads on that blade. The direction of the force is perpendicular to 0.7R chord line. See Figure 3-1.

Design force for strength cal-culation of the propeller blade.

Load case 1Open propeller Uniform pressure applied on the back of the blade (suction side) to an

area from 0.6R to the tip and from the leading edge to 0.2 times the chord length.Pressure corresponding to Fb

Ducted propeller Uniform pressure applied on the back of the blade (suction side) to an area from 0.6R to the tip and from the leading edge to 0.2 times the chord length.Pressure corresponding to Fb

Load case 2Open propeller Uniform pressure applied on the back of the blade (suction side) on

the propeller tip area outside 0.9R radius.Pressure corresponding to 50% of Fb

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Figure 3-2Backward bent blade trailing edge tip resulting in too heavy pitch and loss of propulsion until temporarily repaired(source DNV)

Table 3-3 Ice loads on leading edge and tip region – forward bendingForward bending force - Ff Use of the load in the design proc-

essFf The maximum lifetime forward force on a propeller blade resulting

from propeller/ice interaction, including hydrodynamic loads on that blade. The direction of the force is perpendicular to 0.7R chord line. See Figure 3-1.

Design force for calculation of strength of the propeller blade.

Load case 3Open propel-ler

Uniform pressure applied on the blade face (pressure side) to an area from 0.6R to the tip and from the leading edge to 0.2 times the chord length.Pressure corresponding to Ff

Ducted pro-peller

Uniform pressure applied on the blade face (pressure side) to an area from 0.6R to the tip and from the leading edge to 0.5 times the chord length.Pressure corresponding to Ff

Load case 4Open propel-ler

Uniform pressure applied on propeller face (pressure side) on the propeller tip area outside 0.9R radius.Pressure corresponding to 50% of Ff

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3.2 Finite Element Analysis3.2.1 FE modelThe requirement for the finite element model is that it is able to represent the complex curvilinear geometryand the thickness variation of the blade, in order to represent the complex three-dimensional stress state of thestructure and to predict the local peak stresses needed to assess the fatigue strength of the structure withacceptable accuracy. The load of the propeller blade is dominated by bending, leading to non-constant stressdistribution over the thickness of the blade. Local details such as anti-singing edges etc. are normally excluded.

3.2.2 FE engineering practiceThe use of solid elements is highly recommended for determining the stress distribution of the propeller blades.The use of a very dense parabolic tetrahedron mesh is recommended. Parabolic hexahedron solid elements mayalso be used, but hexahedra require considerable greater modelling effort. Linear elements and, especiallylinear tetrahedrals should not be used in the stress analysis.Well shaped elements are a prerequisite for the stress analysis. The element density should capture stressgradients and good element shape is important in the most loaded areas. It is recommended to show that thesolution is independent of the mesh density.Additional geometric details such as root fillet (see Figure 3-3) may be modelled however these tend to increasethe complexity of the calculation and make it very heavy. This also applies for bolt holes etc. for CP propellerswhere it is recommended to do such studies separate from the propeller blade analysis but with a check ofeventual interaction.

Table 3-4 Ice loads on trailing edge – forward or backward bendingLoad case 5

Open propeller 60% of Ff or Fb, whichever is great-er

Uniform pressure applied on propeller face (pres-sure side) to an area from 0.6R to the tip and from the trailing edge to 0.2 times the chord length

Ducted propel-ler

60% of Ff or Fb, whichever is great-er

Uniform pressure applied on propeller face (pres-sure side) to an area from 0.6R to the tip and from the trailing edge to 0.2 times the chord length.

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Figure 3-3Root fillet of a propeller blade included in the lower blade profiles

A practical workaround would be to model the actual shape of the root fillet included in the sectional geometryof the blade and extend these cylindrical sections inside the propeller hub radius and then neglect the stressconcentrations at the boundary connection.

Figure 3-4A typical parabolic tetrahedron mesh of a propeller blade

The modelling of the tip region is difficult. Thus, it is allowed, for example, to finish discretisation at the0.975R cylindrical section and to make an artificial chord at the tip. In areas where mesh quality areunimportant is it acceptable to use highly skewed elements as these surfaces are only utilized for applicationof load / pressure.

Root profile Fillet

Blade profile

1

APR 6 201015:43:31

ELEMENTS

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Figure 3-5Typical thickness mesh

Where high bending stress occurs is it important to have at least 3-4 elements through the blade thickness asshown in Figure 3-5.

3.2.3 Boundary conditionsThe boundary conditions of the blade model should be given at an adequate distance from the peak stresslocation in order to ensure that the boundary condition has no significant effect on the calculated stress in areasof interest.

3.2.4 Applied pressure loadsThe pressure loads applied on the finite element model can be given either in the normal direction of the curvedblade surface or alternatively as a directional pressure load. The normal pressure approach leads to a loss of thenet applied transversal load as a result of highly curved surface near the edges of the propeller blade. Thesurface pressure shall be scaled so that the resulting force in the perpendicular (normal) direction of the 0.7Rchord line equals the design ice load as derived from formulae in the rules.Whichever approach is used, itshould be ensured that the total force determined in the particular load case is applied on the model. In thenormal pressure case, this can be by scaling the load or, alternatively, by scaling the resulting stresses.

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Figure 3-6One possible way to apply the pressure load to the propeller blade. If the pressure load is given in the normal di-rection of the highly curved blade surface, the resulting net applied load will be less than the intended load andshould be scaled appropriately

Figure 3-7Second alternative: If the pressure load is given in a fixed direction the net applied load is directly the intended load

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3.2.5 Choice of areas for further fatigue analysisThe relevant areas of a FE analysed blade would be where the stress range is largest for the complete lifetimeof the propeller i.e. between the backward load, Fb and the forward load, Ff.

Figure 3-8Typical arrangement of compared results:Top left- Max Principal- Ff, Top center -Max Principal-FbBottom left-Min Principal-Ff, Bottom center-Min Principal-FbTop right-von Mises-Ff, Bottom right – von Mises-Fb

The stresses compared should be Max-Min principal stresses for Ff and Fb respective. It is important that themain principal stress direction is the same in both load cases. This might not be the case in specific areas ofunconventional designs (f. ex. highly skewed propellers) where a lot of torsion occurs. There are in many FEpost processors features available that creates stress plots with two load cases and by that shows the actualstress range on the model itself.

3.2.6 Blade tip and edge strengtheningThe requirements for concentrated ice loads affecting the blade tips and edges have been removed from Pt.5Ch.1 Sec.3 and Sec.8 and will give a unique opportunity for the designers to optimize the blade edges andprofiles individually. Despite correction of an error in the previous formula, the requirement seemed to bedecisive for blade profile, which was not the intended result. It is however necessary, during design of blades,to take into consideration the blade edges impact strength to avoid local indentations of the edges by makingblade edges and tips sufficiently strong to withstand contact with multiyear hard blue ice with pressures thatmay reach 30…40 MPa very locally. This can be done with either old methods or even better with FEA and local ice pressures on the propeller bladeedges and tips applying local ice loads depending on considered local area on the relevant blade edge and tip

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regions. Ice force as a function of considered area may be found as for pod/thruster structures, see 8.1.2.

Figure 3-9Blade tip and edge stress

3.3 Propeller blade strength assessmentThe propeller blade shall be assessed for both fatigue and static loading. The Palmgren-Miner damage theoryand the S-N curve will be restricted for stresses exceeding σref2 / 1.5. A cumulative load spectrum is distributed utilizing the Weibull method for the corresponding σAmax based onthe FEA for selected position(s) on the blade where the stress range (Ff vs. Δσmax Fb) is/are largest.

3.3.1 Propeller materials fatigue strength, S-N curveMaterials fatigue endurance has mainly been found from literature. However majority of these tests wereconducted several decades ago. The presented values in Table 3.5 are strictly “mean fatigue strength values”at 107 cycles and shall not be directly compared to the values shown in the propeller rules Pt.4 Ch.5 Sec.1,Table B1. The values in Table 3.5 are not containing any uncertainties which need to be taken intoconsideration separately.

Endurance values shall reflect the components actual production methods (casting process, welding, heattreatment etc.), loading patterns (bending vs. tension, shear etc) as well as the materials behaviour of changingover time (corrosion etc.). Due to the effect of variable loading with respect of fatigue (stress memory effects)the S-N curve slope of 4.5 from 107 cycles has been extended to 108 cycles and thereafter continues with slope10. Some more details regarding the establishment of S-N curve are given in the rules Pt.5 Ch.1 Sec.8.

3.3.2 Blade fatigue assessmentThe fatigue assessment can be carried out by means of Palmgren-Miner’s theory either utilizing several loadblocks (I) as in Figure 3-10, or by a direct integration method. See Appendix A, Figure A-10, Two Slope S-Ncurve combined with σref2 limitation, extension of slope 4.5 to E8 cycles and the Weibull load function based onk = 1.0.

Series of figures above show how ice load can be applied and corresponding stresses. Pressure on smallest area of 2 mm2 is 30 MPa and decreases to 9.7 MPa at 3700 mm2. Corresponding stresses are from 46 to 340 MPa. The blade section profile is taken from a large propeller where leading edge was found damaged.

Table 3-5 High cycle mean fatigue strengths Bronze and brass (a=0.10) Stainless steel (a=0.05)Mn-Bronze, CU1 (high tensile brass) 80 MPa Ferritic (12Cr 1Ni) 120 MPaMn-Ni-Bronze, CU2 (high tensile brass)

80 MPa Martensitic (13Cr 4Ni/13Cr 6Ni) 150 MPa

Ni-Al-Bronze, CU3 120MPa Martensitic (16Cr 5Ni) 165 MPaMn-Al-Bronze, CU4 105 MPa Austenitic (19Cr 10Ni) 130 MPaAlternatively, σFat-E7 can be defined from fatigue test results from approved fatigue tests at 50% survival probability and stress ratio R = -1, ref. Rules Pt.4 Ch.5 Sec.1 B101.

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Figure 3-10S-N curve, Maximum stress and Load spectre

Maximum dynamic stress range; Δσmax is difference in maximum backward bending stress, σmax b andmaximum forward bending stress, σmax f. The stress amplitude;

Mean stress; σmean should be taken as mean stress due to hydrodynamic propeller load in ice condition (bollardcondition).

Figure 3-11Time series of blade stresses

Investigations have shown that dividing the stress spectrum into minimum I=10 load blocks is necessary toavoid too conservative results. Stress amplitude for block No. i:

No. of cycles in block No. i:

Where Nice is the total number of ice impacts.A Miner sum, MDR < 1.0 is sufficient, since safety factors are included in the values for fatigue strength.The damage rate for a propeller blade can be expressed in the following form:

1 100 1 104

× 1 106

× 1 108

× 1 1010

×10

100

1 103×

S-N curve, Maximum stress & Load spectre

Number of cycles, N

Stre

ss a

mpl

itude

, MP

a

Nice

2max

maxσσ Δ

=A

)11(max Ii

Ai−

−= σσ

∑=

−⎟⎠⎞⎜

⎝⎛ −− −=

i

1i1i

k

Ii11

icei nNn

( )( ) ( ) 0.1)(n1

Nn

1AmaxAmaxi

1 Ami

Ami ≤⋅== ∑∑==

I

i

mI

i ax

ax

aMDR σσ

σσ

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where:

σAmax is a constant stress amplitude of the blade due to ice interaction on the propellerni (σAmax) is the discrete number of cycles with a constant stress amplitude σAmaxNi(σAmax) is the number of cycles to failure of a constant stress amplitude σAmax based on the relevant

part of the design S-N-curve

degree of cumulative “damage” of a constant stress amplitude σAmax

I number of different load magnitudes (load blocks)k Weibull shape parameter = 0.75 for open propellers and 1.0 for nozzle propellersm negative inverse slope of the relevant part (for σAmax) of the design S-N curve ā intercept with the log(N) axis of the relevant part (for σAmax) of the design S-N curve.

3.4 Blade Failure Design Loads

3.4.1 Blade failure load Blade failure load has been applied as one of the main design principles since 1971 in design of propulsionplant pyramidic strength. The blade shall be the weak part and bending of one blade shall not lead to successivedamages if hub or shaft, or any other relevant part, such as thrust bearing, or azimuth thruster structure or itssupport.

Figure 3-12"Pyramide" or selective strength principal = blade failure before shafting failure

3.4.2 Calculation of the bent blade scenario with FE analysisDetermination of the blade failure load Fex can either be made by means of a bending beam based equation, orby means of FEA. In both cases the load shall act on genetric axis at 0.8 radius. The load may be given as apoint load, or a pressure load on defined area with centriod at defined load acting point. One of assumptions isthat blade shall bend near root fillet. This is one reason why load is now defined acting at 0.8R rather than 0.85or 0.9R, as has been case in the previous ice rules.It is further assumed that the same load may act on a certain offset of spindle (genetric) axis. Based on a seriesof FEA we have carried out it has been proven that this load may act at a distance of 1/3 of distance betweenthe spindle axis and leading or trailing edge, which ever is greater. If the distance is made longer a blade startto deform locally and not as assumed.

3.4.3 Plastic hinge methodEven if we consider plastic bending of the blade over a root section, we will accept linear FEA assuming anelastic model. In this respect blade failure load is defined as a force causing von Mises equivalent stresses of1.5 times σref. Because σref (which is a function of ultimate tensile strength, UTS and yield strength, YS) hasbeen determined experimentally for stainless steel and bronze materials by means of measuring real forceneeded to bend rectangular test beam 45o and assuming that plastic section modulus is 1.5 times ditto elastic,we consider this sufficiently proven.σref can either be determined based on known mechanical properties of the considered section, or on basis ofspecified maximum permissible range of the UTS and YS.

( )( )Amaxi

Amaxi

Nn

σσ

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4. PROPELLER HUB AND PITCH MECHANISM4.1 Scope and General Remarks4.1.1 ScopeIn the following it is specified more in detail an acceptable way of assessing the propeller hub and pitchmechanism strength-wise, according to the ice criteria as described in the Rules for Classification of Ships Pt.5Ch.1 Sec.3 and Sec.8.

Figure 4-1CP propeller failure resulting in too heavy pitch and thus total loss of propulsion (courtesy: DNV Turku)

Calculation principles and methodologies are specified, and analytical formulae for stress calculations aregiven as an alternative to more detailed calculations by means of Finite Element Analysis - FEA.

4.1.2 Considered parts in hub and pitch mechanismThe following calculation method is valid only for crosshead type of pitch mechanism as illustrated in Figure4-2 and 4-3. Other types of pitch mechanisms may be assessed on basis of the equivalency principle.

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Figure 4-2Illustration of considered parts in hub and pitch mechanism for some design types: (a) servo cylinder in propeller hub with integrated servo piston and cross head, crank pin on crank disk (b) servo cylinder in propeller hub with separate servo piston and cross head, crank pin on crank disk(c) servo cylinder in shaft line or reduction gear with crank pin on cross head(d) close-up of blade fastening and crank disk of mechanism type (a) and (b)

Figure 4-3Typical controllable pitch propeller mechanism (courtesy of Berg Propulsion Technology AB)

1

8

112

3

5

8

8

9 67

1

4

2

9

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The following components are considered for mechanical strength:

— propeller hub with blade carrier bearings (1) — servo cylinder (2), including clamping bolts (3)— blade bolts (4) and shear pins (5)— crank pin (6)— guide block (7)— retaining wall of slot for guide block (8)— push-pull rod, including fitting to cross head (9).

4.2 Applicable load scenarios

4.2.1 Propeller blade plastic bending (selective strength or “pyramid strength principle”)A propeller blade exposed to an ice load causing plastic bending of blade shall not lead to significant permanentdeformation in the blade fitting arrangement, propeller hub or pitch mechanism. This means that the resultingnominal (excluding local stress concentrations) equivalent (von Mises) tensile stress in each of the componentsshall not exceed the specified minimum yield strength of respective components material (i.e. safety factoragainst nominal yielding is 1.0, as given in Pt.5 Ch.1 Sec.3 and Sec.8. Reference is also given to previouschapter 3.4 “Blade failure design loads”).For blade bolts and hub (blade carriers) the bending moment resulting from the blade failure load, Fex asdescribed in the rules Pt.5 Ch.1 Sec.3 and Sec.8 located at the propeller blade spindle axis shall be considered(i.e. no spindle torque is considered). The torsional capacity of the blade fitting (shear pins and friction capacity in blade bolt connection) andcomponents in pitch mechanism shall be considered on basis of the spindle torque Qsex from the eccentricallylocated Fex (see 3.4.1).

4.2.2 Propeller blade force due to maximum ice load

— When propeller blade is exposed to maximum ice loads (Fb and Ff) as described in the rules Pt.5 Ch.1 Sec.3and Sec.8 the methodology for assessing blade fitting arrangement, propeller hub and pitch mechanism isthe same as in the propeller blade plastic bending case (see also 4.2.1), i.e. nominal stresses are comparedto yield strength.

However, for the maximum ice load case, a safety factor of 1.3 against yielding is required in Pt.5 Ch.1 Sec.3and Sec.8. Safety factor shall be applied on the acting ice load, unless otherwise is explicitly specified.

4.2.3 Propeller blade forces due to dynamic ice load amplitudesWhen exposed to a spectrum of ice loads derived from the maximum ice loads (Fb and Ff) as described in theice rules, the safety factor against fatigue for the influenced parts in propeller hub and pitch mechanism shallbe at least 1.5, according to Miner’s rule, as required in Pt.5 Ch.1 Sec.3 and Sec.8. Safety factor shall be appliedon the acting dynamic ice load amplitudes. The application of ice loads on each component is the same as for the two (static) cases above.

4.3 Load transmission

4.3.1 Transmission of spindle torque into mechanismThe propeller blade spindle torque caused by ice loads acting eccentrically to the spindle axis will betransmitted into the propeller pitch mechanism. However, parts of the spindle torque will be taken up as friction loss due to reaction forces set up in the bladecarrier bearings. In the radial bearing, there will be reaction forces due to ice load on propeller blade, and forceson the crank pin. The reduction in loads due to these frictional losses may be accounted for as mentioned herein.

4.3.2 Geometrical relationsThe geometrical relations between spindle torque and force on crank pin are given as follows: In the case crank pin is fixed in crank disk:

ϕcos1000

crp

crpcrp R

QF = (kN)

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In the case crank pin is fixed in cross head:

where Qcrp is net spindle torque (kNm) transmitted into the mechanism, see next chapter, Rcrp (mm) is crankpin eccentricity and f (rad) is considered angular position of crank pin (normally same as pitch angle).Note that since Qcrp includes the frictional losses and the specified safety factors, this also applies for Fcrp.

Figure 4-4Crank pin in crank disc and in cross head

Further, the force on crank pin is transmitted into a servo, generating a certain increase in servo pressure. Inthis respect, a direct transformation shall be carried out (i.e. no further internal frictional losses except thosementioned in next chapter shall be accounted for). Servo pressure corresponding to a given force on crank pinis then found as follows:In case crank pin is fixed in crank disk:

In case crank pin is fixed in cross head:

Where Aservo is effective pressurised area of the servo piston.

4.3.3 Reduction in transmitted spindle torque due to frictionBending moments taken up by the blade carrier will cause the following friction torque:

Where Mb is bending moment (kNm) including relevant safety factor and may be taken in the same way as forthe blade bolts (see 4.5.4). Dblc is effective blade carrier diameter (mm) carrying the load, Dbfric is effectivefriction diameter (mm) and m is friction coefficient (-). See also Figure 4-5. For lubricated surfaces, the friction coefficient, m shall be taken as 0.10.Pressure distribution may be assumed to be sinusoidal. Then the relation Dblc/Dbfric equals 4/p.Forces taken up radially by the blade carrier will cause the following friction torque, Qfrf:

Where F is considered radial force (kNm) in bearing, including relevant safety factor and Dffric is effectivefriction diameter (mm).

ϕcos1000

crp

crpcrp R

QF = (kN)

Rcrp

Rcrp

CRANK PIN INCROSS HEAD

CRANK PIN INCRANK DISK

servo

crpservo A

Fp

410= (bar)

ϕcos104

servo

crpservo A

Fp = (bar)

μ⎟⎟⎠

⎞⎜⎜⎝

⎛=

bfric

blcfrb D

DMbQ (kNm)

3102 −=

πμffric

frf

DFQ (kNm)

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Pressure distribution may be assumed to be sinusoidal. Then Dffric is 4⋅Diblc/π, where Diblc is inner diameter(mm) of blade carrier (blade thrust) bearing. See also Figure 4-5.Compared to the frictional forces generated by the ice loads, the contribution from centrifugal forces isnormally relatively small and shall be neglected for safety and simplicity. This will contribute to predictedcrank pin forces somewhat more to the safe side, in particular for the high cycle loads.Note that the ice loads specified in the rules include contribution from hydrodynamic propeller load, whenapplicable, and hence no separate friction loss shall be calculated for the hydrodynamic propeller load.Spindle torque transferred into crank pinNet spindle torque transferred into the pitch mechanism (crank pin), Qcrp shall be taken as Qcrp = Qsp -Qfr1(kNm)Where Qsp is the considered blade spindle torque (kNm), including the specified safety factor, Qfr1 (kNm) isthe sum of relevant friction torque reductions due to blade carrier loads, i.e. Q fr1 = Qfrb + Qfrf (kNm).Spindle torque for evaluation of blade flange / crank disk connectionWhen considering the transfer of spindle torque between the blade flange and the crank disk, the following netspindle torque shall be used: Qcrp = Qsp - Qfr1- Qfr2(kNm) Where Qfr2 is the friction torque reduction betweenthe blade flange and crank disk due to bolt pretension forces, to be taken as:

Where σbpre is bolt pre-stress (N/mm2) in section with minimum diameter, Dbblt (mm), Nbblt is number of bolts,and PCD is bolt pitch circle diameter (mm). For non-lubricated surfaces the friction coefficient, m shall betaken as 0.15 unless otherwise is substantiated.The relevant friction torque reduction, Qfr1 should in this respect only include the friction contribution on theblade flange (not the crank disk). I.e. the following applies:

Where khcr is describing the height ratio between blade flange part of radial bearing and total radial bearingheight. I.e. if only blade flange has a radial bearing surface, khcr is 1.0, if only crank disk has a radial bearingsurface, khcr is 0.0. For designs as illustrated in Figure 4-2, khcr would be some 0.5.

4.3.4 Transmission of blade bending moment into blade carrierAssuming that the peripherical pressure distribution due to a bending moment Mbl follows a sinusoidalrelationship, the maximum pressure at the blade carrier is found from:

Where Bblc is breadth of blade carrier bearing (mm). See also Figure 4-5.

622 10

24−=

PCDNDQ bbltbbltbprefrπμσ (kNm)

frfhcrfrbfr QkQQ −= 5.01 (kNm)

(N/mm2)6

2blcblc

blbblcmax 10

DB4π

Mp =

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Figure 4-5Illustration of blade carrier and blade bearing

4.3.5 Transmission of force into blade carrierAssuming that the peripherical pressure distribution due to a force also follows a sinusoidal relationship, themaximum radial pressure at the blade carrier is found from:

Where Tblc is thickness of blade carrier bearing (mm). See also Figure 4-5.

4.3.6 Transmission of load between crank pin and retaining wall for guide blockThe ice loads from the blade are transferred by means of pressure from the crank disk to the crosshead, via theguide block. These components deflect when loaded. This influences on the pressure distribution and hence,the pressure distribution at the contact surfaces deviates from the nominal pressure. This applies in particularwhen the loading is high. The skewed pressure distribution changes the effective point of reaction for thetransmitted force, as well as introduces local strains and stresses.

Figure 4-6Illustration of possible pressure distribution between crack components

In general, the “footprint” of crank pin cylindrical shape is reflected in the pressure distribution on the retainingwall and vice versa.

TblcDi

blc

Bblc

blcD

(N/mm2)6

max 10

4 blcblc

fblc

DiT

Fpπ

=

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Further, a distinct increase in local pressure near the root sections (close to the fillet) of crank pin and retainingwall is normally seen.Apart from the local high pressure near the root sections, the height-wise pressure distribution on the crank pinis normally quite homogenous. For the retaining wall, the height-wise pressure distribution normally showsmore of a triangular shape.Both for the crank pin and the retaining wall, local maximum stresses in fillets are also influenced by the contactpressure occurring at the surface close to the fillets.These effects lead to shortcomings when predicting stresses according to classical cantilever beam theory andshall be accounted for. In particular for local stresses (relevant for fatigue calculations) this influence issignificant. The above is included in the strength assessment chapter (4.4).During the transmission of loads via contact surfaces, there will also be some internal friction. However, forsafety and simplicity the internal friction losses in the crank mechanism shall not be accounted for.

4.3.7 Transmission of loads into cross head, push-pull rod and servoIn general ice loads act at one blade at the time. This introduces a bending moment on the cross head, whichtogether with the radial forces is transmitted into the crosshead bearings. Such bearings may be integrated inthe crosshead arrangement itself or the push-pull rod bearing support may also act as radial journal bearing forthe cross head.The axial component of the crank pin force is transmitted via the crosshead and push-pull rod (if applicable)and into the servo. To some extent, part of the axial load may also be transmitted back into the crank pinsconnected to blades which are not exposed to the ice load (and will be taken up as mass forces and frictionforces in the respective blade carriers). Such a reduction in servo loading is quite uncertain and shall not beaccounted for.There will also be some internal friction in crosshead / push-pull rod bearings. For safety and simplicity thesefriction losses shall not be accounted for.

4.4 Strength assessment4.4.1 Static strengthThe load conditions referred to in 4.2.1 (blade failure load) and 4.2.2 (maximum ice loads) shall be consideredas static load cases. That means that the strength assessment is carried out directly against the loads, includingthe safety factors specified in the rules Pt.5 Ch.1 Sec. 3 and Sec.8.For these load cases, the “worst condition” assumption applies, since the loads in principle may apply in anyoperating condition. For the static strength assessment this means that propeller pitch angle shall be chosen asthe one giving highest loads in the components. In case crank pin is located in cross head this means that pitch angle shall correspond to crank pin in zero angleposition (normally, this equals the geometrical zero pitch position). With the crank pin located in the crank disk, maximum operational pitch angle for ice operation shall be chosen.If not otherwise is substantiated, a pitch angle corresponding to 70% of pitch at ahead free running, MCR shallbe used.In case the design pressure is smaller than the pressure corresponding to blade failure load, the mechanism shalladditionally be checked in a pitch condition corresponding to mechanical stop. The same applies if relief valvearrangement is only provided on the pump side of the directional valves.

4.4.2 Dynamic strength The load conditions referred to in 4.2.3 (dynamic loads) shall be assessed according to fatigue criteria asdescribed in the following chapters. In general, such loads will accumulate under all possible ice operatingconditions, and hence under varying pitch angles. However, in order to simplify the calculations, the complete fatigue assessment shall be carried out for onereference pitch setting:

— In case crank pin is located in crank disk a pitch angle corresponding to 60% of pitch at ahead free running,MCR shall be used.

— In case crank pin is located in cross head a pitch angle corresponding to 40% of pitch at ahead free running,MCR shall be used.

4.4.3 Cumulative fatigue calculationThe hub and pitch mechanism shall be designed to prevent accumulated fatigue when considering loads asdescribed in the rules Pt. 5 Ch.1 Sec.3 and Sec. 8.

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There are locations at the components in the hub and pitch mechanism where dynamic stresses due to ice loadsare significantly higher than in the surrounding material. These stress risers, such as notches or fillets formingthe transition between different shapes, are critical w.r.t. fatigue strength. The same may apply to welded parts, where fatigue strength is reduced due to the welding.In case local stresses at maximum load exceeds yield strength (σy or σ0.2) or 70% of the ultimate tensilestrength (σu) sufficient margin against accumulated fatigue shall be documented using the linear elasticMiner’s rule. The stress spectrum should be divided into minimum I = 10 blocks. A lower number of blocks is tooconservative, whereas increasing the number of blocks beyond I = 20 blocks will not reduce the calculatedfatigue damage significantly.Miner’s rule sum up damage fractions, ni / Ni, where ni and Ni are respective occurring and allowable numberof cycles for the load level (stress block) in question (according to the material SN diagram – see also 4.6.2).Hence the total fatigue damage is given by the Miner sum, MDR (-):

A Miner sum, MDR < 1.0 is sufficient, since safety factors are included in the ice loads and load level for eachblock is chosen conservatively.No. of cycles in block No. i:

Where Zice equals number of propeller blades in case the considered component accumulates ice loads from allblades (for instance push-pull rod). Otherwise Zice = 1. Further, k is the Weibull shape parameter = 0.75 foropen propellers and 1.0 for nozzle propellers, and Nice is the number of ice impacts (-) experienced by thepropeller blade during its life time, as defined in the rules Pt.5 Ch.1 Sec.3 and Sec.8. The formulation isconservative, because each block refers to the nearest load level above.

4.4.4 Fatigue stress amplitudeThe propeller blade ice spindle torque variation spectrum follows a Weibull distribution. However, the relationbetween load and corresponding stress in parts of the pitch mechanism components is not necessarily strictlylinear. This is due to deflections in the mechanism and frictional effects. In the calculation model describedherein, this is neglected, and the calculation models are chosen in order to be representative for typical loadsituations contributing to fatigue damage. Hence, a Weibull distribution for acting stress is assumed as a simplification, and fatigue stress amplitude forblock No. i shall be taken as:

Stress concentration factors, Kt are discussed in subsequent chapters for each component.

4.5 Stress in components of CP-Mechanism4.5.1 Stress calculation in generalStatic stressFormulae for nominal equivalent static stresses are given for each of the components in the sub sections below.Dynamic stress amplitude/ mean stressMaximum dynamic stress range, Δσmax (N/mm2) is defined as the difference in component stress when bladeis exposed to maximum backward load (Fb) and maximum forward load (Ff) for components that will beinfluence by load in both directions. For components influenced by load in only one direction (retaining wall) maximum backward load ormaximum forward load is taken as zero (whichever is less critical). The maximum stress amplitude σAmax= Δσmax/2 (N/mm2). This corresponds to the “once in a life time” iceload situation. For stress range/amplitude distribution, see previous chapter.

∑=

=I

i i

i

NnMDR

1

(-)

(-)( ) ∑=

−⎟⎠⎞⎜

⎝⎛ −− −=

i

1i1i

k

Ii11

icei nNn iceZ

(N/mm2)⎟⎠⎞

⎜⎝⎛ −

−=I

iAi

11maxσσ

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Classification Notes - No. 51.1, January 2011

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Mean stress, σmean (for determination of reduction in fatigue strength due influence of mean stress, Kmean - see4.6.2) shall be taken as a constant = stress due to hydrodynamic propeller load in ice condition (withoutreduction for friction loss in blade bearings), except for components influenced by load in only one direction(retaining wall) where mean stress shall be taken equivalent to the stress amplitude plus stress fromhydrodynamic propeller load in ice condition.The above is a simplification, since the number of cycles related to backward and forward blade load is notnecessarily the same. However due to the conservatism built into the calculation method in total, results willbe somewhat on the safe side.For some components (mainly the retaining wall), the maximum stresses will occur at somewhat differentlocations, depending on pitch angle. However, as the fatigue calculation is carried out for one reference pitchsetting this shall not be accounted for, unless it is substantiated that it will have significant influence on thepredicted Miner sum.Formulae for principal dynamic stresses, including geometrical stress concentration factors, are given for eachof the components in the following sub sections.Stress concentration factors for short beams have in general been derived from the book “Stress concentrationfactors” by R.E. Peterson (1973). Corrections to these formulations have been done on basis of finite elementcalculations and empirical studies.

4.5.2 Propeller hub / blade carrier bearingFor the propeller hub, only the blade carrier bearings need to be documented for sufficient strength due to iceloads. However, this does not discharge the designer to ensure that the complete propeller hub is designed withsufficient strength and rigidity to withstand the ice loads.The blade carrier bearing is exposed to bending and shear due to the bearing pressure when the bearing iscarrying the blade bending moment from the ice loads. A sector strip of the bearing i.w.o. the highest pressure shall be considered. For prediction of bending stresses,the reaction point of the resulting force acting on the bearing may be assumed to be in the centre of theconsidered surface. Static stress (yielding)In order to comply with yielding requirements, a prediction of nominal equivalent static stress, σebc shall becarried out. The combined effect of bending, compression and shear on the bearing shall be considered:

Where pressure distribution correction factor, βcblc, bending stress, σbblc, and shear stress, τbblc, are taken fromthe following formulae:

Where pbblcmax, Bblc and tblc are as defined in 4.3.Dynamic stressIn order to predict the maximum principal stress for fatigue calculation, σpblc, it is relevant to consider theinfluence of (short beam) bending. Hence, σpblc should be taken as for σbblc above.Influence from stress concentration and local compression should be represented in fatigue calculations by thetotal geometrical stress concentration factor Kt =βcblc · αbblc as described in 4.6.2. In this respect, βcblc is to betaken as for the static stress case and αbblc is geometrical (short beam) stress concentration in bending in thebearing notch.

( ) 22 3 bblcbblccblceblc τσβσ += (N/mm2)

2.1=cblcβ (-)

(N/mm2)blc

blcbblcmaxblc t

Bpτ =

(N/mm2)2

blc

2blcbblcmax

bblc

t31

Bpσ =

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The following empirical formulae applies, unless otherwise is substantiated:U shaped notch for O-ring:

Shoulder Fillet:

Where rfblc is radius of bearing fillet.The first part in the stress concentration formulae above represents the stress concentration factor in purebending for flat bar with U-notch / shoulder fillet, respectively, whereas the second part includes the short beamcorrection.

4.5.3 Servo cylinder including clamping boltsThe servo cylinder with clamping bolts need normally be assessed only according to static strength criteria.Static stress servo cylinder / design pressureIn order to comply with yielding requirements, a prediction based on nominal equivalent static stress notexceeding yield stress shall be carried out. I.e. the cylinder minimum thickness, tcyl shall comply with:

Where pservo is servo pressure (bar) as defined in 4.3.2 or design pressure, whichever is higher, Dcyl is servocylinder outer diameter (mm) and Kshape is factor for increased stress due to shape of dished end. Unless otherwise is substantiated, Kshape shall be taken according to the following empirical formulae for thecurved part of the cylinder:

Where Hcyl is height of curved part of servo cylinder (see Figure 4-7). Hcyl needs not to be taken less than0.1Dcyl.Kshape shall not be taken less than 1.0.For the cylindrical part of servo cylinder, Kshape is 1.0.

(-)

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+=

⎟⎟⎠

⎞⎜⎜⎝

⎛+−−−

blctblcB

0.380.12

blc

blc1.85

blc

blc0.7

blc

blcbblc t

rftB0.071

trf0.221α

(-)

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+=

⎟⎟⎠

⎞⎜⎜⎝

⎛+−−−

blctblcB

0.380.12

blc

blc1.85

blc

blc0.5

blc

blcbblc t

rftB0.071

trf0.231α

(mm)shapeycyl

cylservocyl K

Dpt

σ20=

(-)⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

cylt1000cylD

1.13

cyl

cylshape D

H0.2K

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Classification Notes - No. 51.1, January 2011

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Figure 4-7Illustration of curved height of cylinder – two examples

Design pressure of the pitch mechanism system shall be taken as given in Pt.5 Ch.1 Sec.8 J406 Static stress cylinder clamping boltsIn order to comply with yielding requirements, a prediction based on bolt pretension stress plus additionalnominal bolt stress due to pressure in servo cylinder shall be carried out in case servo cylinder is clamped tothe propeller hub. Assuming that the complete force on crank pin is transmitted to the servo, the total clamping bolt stress is foundfrom:

Where σcpre is pre-tension stress in minimum section of bolt (N/mm2), Dcblt is minimum section diameter ofbolt (mm), ncblt is No. of clamping bolts and kcblt is bolt factor describing part of additional load carried by theclamping bolts. Unless otherwise is substantiated, kcblt shall be taken as 0.25 / 0.33 in case of steel / bronzematerial in hub and servo cylinder, respectively.Separation between hub and cylinderThe bolt pre-stress must be sufficient to prevent separation between the mating surfaces between hub andcylinder when servo pressure corresponds to maximum forward, Ff and backward load Fb. This corresponds toa situation where the compression load in the flanges becomes zero. Hence, bolt pre-tension stress must as aminimum be:

4.5.4 Blade bolts and shear pinsThe blade bolts and shear pins need normally be assessed only according to static strength criteria.Static stress of blade boltsThe blade bolt connection shall withstand the blade failure bending moment described in the rules withoutyielding. Stresses in the bolts, σbblt shall be calculated according to the following:

Where σbpre is pre-tension stress in minimum section of bolt (N/mm2), kbblt is bolt factor (-) describing part of

HH

cylcyl

3

210

4 cbltcblt

crpcbltcprecblt

Dn

Fk

πσσ += (N/mm2)

3

210

4

)1(cbltcblt

crpcbltcpre

Dn

Fk πσ −= (N/mm2)

610bblt

exbltbbltbprebblt W

Mk+= σσ (N/mm2)

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additional load carried by the blade bolts. Unless otherwise is substantiated, kbblt shall be taken as follows:

In the case that separation between mating surfaces will occur before yielding of bolt (σybbltis yield strength of bolt material in N/mm2). This is acceptable for the blade failure load, but then kbblt may betaken as 1.0 and σbpre may be taken as 0.0 in the above formula for bolt stress, σbblt, irrespective of actualvalues.Mexbblt is bending moment in way of blade bolts due to blade failure load, taken from:

Where D is propeller diameter (m) and rbblt is radius (m) from shaft centre line to the bolt plane. Safety factor,S = 1.0 (as required in Pt.5 Ch.1 Sec.3 and Sec.8) and ksup is support factor, correcting the bending momentdue to reaction forces in blade carrier bearing and bolts. When blade flange is resting on a blade carrier, ksupshall be taken as:

Where max(Abblt i) is taken as distance (mm) from tilting line to bolt located farthest away (for Abblt i, see alsoFigure 4-8 below), and may normally be taken as equal to the pitch circle diameter, PCD (mm).Wbblt is section modulus (mm3) of bolt connection about the tilting line based on minimum section diameterof bolt. Tilting line is tangent to the pitch circle diameter (or other relevant axis for non circular joints), parallel to theconsidered root section. Tilting line is located on “pressurized” side of the flange, i.e. bolt section modulus maydepend on whether the considered force is acting in forward or backward direction.

Figure 4-8Illustration of tilting line and distance to tilting line (Abblt i) for bolt No. i

Table 4-1 Blade bolt factorsBlade flange material Crank disk material kbbltBronze Steel 0.30Bronze Bronze 0.35Stainless steel Steel 0.25Stainless steel Bronze 0.30

0.1<+ bbltybblt

bpre kσσ

⎟⎠⎞

⎜⎝⎛ −= bbltexexbblt rDkFSM

28.0sup

(kNm)

blc

ibblt

D

Ak

2

)max(5.0sup += (-)

Tilting axis

A bblt i

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Bolt section modulus for circular location of bolts shall be taken from the following expression:

Where Nbblt is number of blade bolts and Dbblt is minimum section diameter of bolt (mm).Separation between mating surfacesThe bolt pre-tension stress must be sufficient to prevent separation between the mating surfaces with maximumforward, Ff and backward load Fb. This corresponds to a situation where compression load in the flangesbecomes zero. Hence, bolt pre-tension stress must as a minimum be:

Where Micebblt is maximum bending moment due to ice load, taken from:

Where F is maximum forward ice load (kN), Ff or maximum backward ice load, Fb, respectively, rice is radiusform shaft centre to acting ice load (m). Safety factor, S is 1.3, as required in Pt.5 Ch.1 Sec.3 and Sec.8.Static stress of shear (dowel) pinsThe rules, Pt.5 Ch.1 Sec.8 specify the minimum required diameter for the shear (dowel) pins, in order to avoidshear yield when blade is exposed to maximum ice load and blade failure load.Formulations for friction torque reductions (Qfr1 and Qfr2) are given in 4.3.3.Note that the pitch circle diameter referred to in the Ice rules (PCD) describes the diametrical location of theshear pins (which may be different from the PCD for the blade bolts).

4.5.5 Crank pinCrank pin is exposed to bending and shear, as well as local compression due to pressure from guide block actingclose to the point of maximum bending stress. For prediction of bending stresses, the reaction point of theresulting force acting on crank pin may be assumed to be half way up the crank pin. Hence, stress in crank pin shall be taken as described in the following. Static stress (yielding)In order to comply with yielding requirements, a prediction of nominal equivalent static stress, σecr shall becarried out. The combined effect of bending, compression and shear on the crank pin shall be considered:

Where pressure distribution correction factor, βccr, bending stress σbcr and shear stress, τcr, are taken from thefollowing formulae:

Where Fcrp is force acting on crank pin (kN), Dcr is crank pin diameter (mm) and Hcr is height of crank pin(mm).Additionally, it must be verified that surface pressure from guide block on crank pin does not exceed yieldstrength. The following formula for surface pressure on crank pin, pcr shall be used.

)max(464 1

224

ibblt

bbltN

iibbltbbltbbltbblt

bblt A

ADDNW

∑=

+=

ππ(mm3)

610)1(bblt

icebbltbbltbpre W

Mk−=σ (N/mm2)

( )bblticeicebblt rrkFSM −= sup (kNm)

( ) 22 3 bcrbcrccrecr τσβσ += (N/mm2)

cr

crccr

DH

4.07.0 +=β (-)

2

4

1000

cr

crpcr

D

Fπ

τ⋅

= (N/mm2)

3

32

5.01000

cr

crcrpbcr

D

HFπ

σ⋅

= (N/mm2)

crcrcr

crpcr DH

Fp β

1000= (N/mm2)

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Classification Notes - No. 51.1, January 2011

Page 30

Where βcr is the peripherical pressure concentration factor (local increase in pressure near the edges of theguide block are not considered). Assuming that the surface pressure has a sinusoidal peripherical distributionover the crank pin, βcr shall be taken as 2.0.In case effective height of guide block is significantly less than height of crank pin (Hcr) due to chamfers orsimilar, a corresponding change in Hcr for calculation purposes shall be done. Dynamic stress and mean stress (fatigue)In order to predict the maximum principal stress for fatigue calculation, σpcr, it is relevant to consider theinfluence of (short beam) bending. Hence, σpcr should be taken as for σbcr above.The above reflects the assumption that when considering local stresses, it is relevant to distribute the load overan area corresponding to the crank pin profile.Influence from stress concentration and local compression should be represented in fatigue calculations withthe total geometrical stress concentration Kt =βccr · αbcr , as described in 4.6.2. Influence of local compression bccr is found as for the static case above, and geometrical (short beam) stressconcentration factor abcr shall be found from the following empirical expression, unless otherwise issubstantiated:

Where rfcr is crank pin fillet radius (mm).The first part in the stress concentration formula above represents the stress concentration factor in purebending for round bar with shoulder fillet, whereas the second part includes the short beam correction.

4.5.6 Guide blockThe guide block is exposed to compression loads and is normally designed without dominant stress risers.Hence a static consideration of the surface pressure inside guide block is sufficient.

Static surface pressure (yielding)In order to verify that the surface pressure inside the guide block does not exceed yield strength of material, itis sufficient to calculate nominal surface pressure. This is because some minor compressive deformations inthe guide block are not considered critical for the function of the pitch mechanism. The following formula shall be used for static nominal surface pressure pgb of guide block:

In case effective height of guide block is significantly less than height of crank pin (Hcrp) due to chamfers orsimilar, a corresponding reduction in Hcrp for calculation purposes shall be done.

4.5.7 Retaining wallThe retaining wall is exposed to bending and shear, as well as local compression due to pressure from guideblock acting close to the point of maximum bending stress. For prediction of bending stresses, the reaction pointof the resulting force acting on retaining wall may be assumed to be at a height 35% up the wall. Hence, stress in retaining wall shall be taken as described in the following. Static stress (yielding)In order to comply with yielding requirements, a prediction of nominal equivalent static stress, serw shall becarried out. The combined effect of bending, compression and shear on the retaining wall shall be considered:

Where pressure distribution correction factor, βcrw, bending stress σbrw and shear stress, τrw, are taken from

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+=

⎟⎟⎠

⎞⎜⎜⎝

⎛+−−−

cr

cr

DH

cr

cr

cr

cr

cr

crbcr D

rfDH

Drf

38.012.085.17.0

07.0117.01α (-)

crcr

crpgb DH

Fp

1000= (N/mm2)

( ) 22 3 rwbrwcrwerw τσβσ += (N/mm2)

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Classification Notes - No. 51.1, January 2011

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the following formulae:

Where trw is thickness of retaining wall (mm) and Bgb is breadth of guide block (mm)The above reflects the assumption that when considering nominal stresses, it is relevant to distribute the loadover an area corresponding to the guide block profile.Additionally, it must be verified that surface pressure from guide block on retaining wall does not exceed yieldstrength. The following formula for surface pressure on retaining wall, prw shall be used.

Where βrw is the height wise pressure concentration factor (local increase in pressure near the edges of the guideblock are not considered). Assuming that the surface pressure has a triangular height wise distribution over thecrank pin, βrw shall be taken as 2.0.In case effective height of retaining wall is significantly less than height of crank pin (Hcr) due to chamfers orsimilar, a corresponding change in Hcr for calculation purposes shall be done. Dynamic stress and mean stress (fatigue)In order to predict the maximum principal stress for fatigue calculation, σprw, it is relevant to consider theinfluence of (short beam) bending. Hence, σprw should be taken as follows:

The above reflects the assumption that when considering local stresses, it is relevant to distribute the load overan area corresponding to the crank pin profile.Influence from stress concentration and local compression should be represented in fatigue calculations by thetotal geometrical stress concentration Kt =βcrw · αbrw , as described in 4.6.2.Influence factor for local compression, βcrw shall be taken as for the static case above, whereas the (short beam)stress concentration factor, αbrw shall be found from the following empirical expression, unless otherwise issubstantiated:

Where rfrw is retaining wall fillet radius (mm). The first part in the stress concentration formula above represents the stress concentration factor in purebending for flat bar with shoulder fillet, whereas the second part includes the short beam correction.

4.5.8 Push-pull rodThe push-pull rod may include many design features which need to be assessed for the axial load. Dependingon the direction of the load and the crank pin arrangement, the push-pull rod may be exposed to bothcompression and tension loads.Static stressThe push-pull rod needs to be checked for yielding at static peak loads. This may be critical for the followingparts:

(-)

rw

crcrw

tH0.60.6β +=

(N/mm2)

gbrw

crprw Bt

1000Fτ =

(N/mm2)

gb2

rw

crcrpbrw

Bt61

0.35H1000Fσ

⋅=

rwgbcr

crprw BH

Fp β

1000= (N/mm2)

(N/mm2)cr

2rw

crcrpprw

Dt61

0.35H1000Fσ

⋅=

(-)⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟

⎠

⎞⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅⎟

⎟

⎠

⎞⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+=

⎟⎟⎠

⎞⎜⎜⎝

⎛+−−−

rw

cr

tH0.380.12

rw

rw

1.85

rw

cr

0.5

rw

rwbrw t

rftH0.071

trf0.231α

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Classification Notes - No. 51.1, January 2011

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— minimum section diameter— threaded connections— bolted connections.

Further, under the same condition the push-pull rod shall not be exposed to buckling, and if the crosshead isshrink-fitted onto the push-pull rod, the connection must be able to take the crank pin force without slipping. Stresses in the minimum section diameter, σppmin are calculated according to:

Where Dppmin is minimum section diameter of push-pull rod (mm) and Dppo is inner diameter of push pull rod(mm). In case parts of the push-pull rod are connected by sleeves, stresses in sleeves are calculatedcorrespondingly, using outer and inner diameter of sleeves instead.For threaded connections, the same approach is used to find stress in threaded section, σppthr (N/mm2) as forthe minimum section diameter, replacing Dppmin with the thread diameter Dppthr (mm). In case of a sleeve, therelevant diameters for sleeve and sleeve threads shall be used.When considering shear yielding of all threads, the following formulation shall be used for allowable stress:

Where σppy (N/mm2) is yield strength of push-pull rod (or sleeve as relevant), Lppthr is length of threaded part(mm) and rppthr is part of thread carrying load, found from the following empirical relation:

Stresses in push-pull rod bolts, σppblt are calculated according to:

Where σpppre is bolt pre-tension stress (N/mm2) in minimum section diameter, Dppmin (mm), Kppblt is boltfactor for part of external load taken up as tension in bolts – to be taken as 0.25, unless otherwise issubstantiated and Nppblt is number of clamping bolts.In order to avoid buckling of the push-pull rod, the distance between radial support points, Lppsupport (mm) mustnot be less than derived from the following formula:

Where Epp is E-modulus of push pull rod (= 2.05⋅105 N/mm2 for steel) and Dpp is representative diameter ofpush-pull rod.If the connection between the cross head and push-pull rod is by means if shrinkage only, the minimumshrinkage pressure shall be:

Where Ssf is additional safety factor for shrink fit = 1.25, μ is friction coefficient, to be taken as 0.15 for dryconnections, Dpp is push-pull rod diameter in way of shrink fit (mm) and tcrh is effective cross head thickness(mm). The reason for including the additional factor of 1.25 is because slippage will happen immediately upon anoverload, and the general safety factors (if any) applied on the crank pin force as described in the rules refer toyielding criteria, and are considered too small for shrink fit connections.General formulations for cylindrical shrink-fitted connections shall be used as follows:

( )22min

min

4

1000

ppopp

crppp

DD

F

−=

πσ (N/mm2)

ppthr

ppthrppyppthrppthr

D

L

43 π

σρσ ≤ (N/mm2)

15.037.01 −− ppthrppthr Dρ (-)

2min4

1000

ppppblt

crpppbltpppreppblt

DN

FK

πσσ += (N/mm2)

( ))(

64000

443

sup mmF

DDEL

crp

ppoppppportpp

−=

π

(N/mm2)crhpp

crpsfmin tDπμ

F1000Sp =

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— Diameter of outer member, Dhub (cross head) shall for simplicity and safety be taken as the width of thecross head, not including retaining walls for guide block or crank pin (as relevant)

— For maximum allowable interference / shrinkage pressure between push-pull rod and cross head, themembrane stresses due to the shrinkage pressure shall not exceed 70% of cross head material yield strength.

Figure 4-9Illustration of diameter of outer member for push-pull rod shrink fit

Dynamic stress and mean stress (fatigue)The push-pull rod needs to be checked for fatigue in way of significant stress risers. This is typically criticalfor the following parts:

— fillets— radial borings.

Figure 4-10Typical stress raisers in push-pull rod

Principal stresses in way of the stress riser, sapp are calculated as for the static case with minimum sectiondiameter, using relevant diameters.:Influence from local stress concentration should be represented in the fatigue calculations with geometricalstress concentration, Kt = αapp, as described in 4.6.2.Unless otherwise is substantiated αapp shall be taken as 3.0 for radial borings and according to the followingempirical formulation (relevant for axial loading) for shoulder fillets:

Where rfpp is shoulder fillet radius (mm) and Dpps is diameter of shoulder/flange (mm).Also for welded connections of various types, the push-pull rod needs to be checked for fatigue. Principal

DhubDhub

25.0

1

12.023.1−

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜

⎝

⎛

−

−=pp

pp

pp

ppsapp D

rf

DD

α (-)

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Classification Notes - No. 51.1, January 2011

Page 34

stresses may be calculated as above, excluding the influence of stress risers (influence of increased stress inweld is included in the fatigue strength, see 4.3.2).

4.6 Material strength

4.6.1 Static strengthStatic strength vs. yielding (maximum ice load) criterionWith reference to chapter 4.2.2, the yielding criterion for maximum ice load is complied with when thepredicted nominal equivalent stress for the considered component is less than yield strength, σy. A safety factorof 1.3 (as specified in Pt.5 Ch.1 Sec.3 and Sec.8) is included in the maximum ice load.Static strength vs. permanent deflection (blade bending) criterionWith reference to chapter 4.2.1, the yielding criterion for blade failure load is complied with when the predictednominal equivalent stress for the considered component is less than yield strength, σy.

4.6.2 Fatigue (dynamic) strengthFatigue strength basic formulationWith reference to chapter 4.2.3, the fatigue strength criterion is complied with when the Miner sum is less than1.0. The safety factor of 1.5 (as specified in Pt.5 Ch.1 Sec.3 and Sec.8) is then applied on the acting dynamicice load amplitudes.Fatigue strength for components in pitch mechanism is influenced by a number of effects. In general, thefollowing applies for fatigue strength in non-corrosive environment at Ei number of cycles:

Where σfatEi is fatigue strength in rotating bending in air for un-notched test piece, frough is influence factor forinfluence of surface roughness (-), q equals the notch sensitivity factor (-), Kt is the geometrical stressconcentration factor (-) as found in previous chapters, Kmean is correction factor for influence of mean stress,Ksize is correction factor for influence of size, Kvar is correction factor for influence of variable loading andKload is correction factor for other type of loading than bending. These factors are addressed in the following.For welded connections (push-pull rod), none of the above influence factors shall be included.

Fatigue strength at given No. of cyclesThe initial fatigue strength, σfatEi for common materials applied in components for hub and pitch mechanismnot exposed to sea water is derived from SN-curves as described below, unless otherwise is substantiated. The initial SN-curves are limited to / described by linear curves in a log-log diagram as described in thefollowing:σfatEi ≤ σuWhere σu is ultimate tensile strength of material.The SN curve is determined with two slopes, which may be different above and below a defined knuckle point,NHC.

Where Ni is considered number of cycles, σFat E7 is material fatigue strength in rotating bending at 107 cyclesfor un-notched test piece, σFat NHC is corresponding fatigue strength at knuckle point and σFat Ei iscorresponding fatigue strength at 10i cycles. Slopes of SN curve, mLC (low cycle) and mLH (high cycle) arematerial dependent (see table 4.2 below).For parts exposed to sea water, such as propeller hub and blade carrier bearing in way of- or outside of sealing,fatigue properties are to be taken as for propeller blades (see 3.3.1).

( ) loadsizemeantrough

fatEiEi KKKK

Kqf var11 −++=

σσ (N/mm2)

LCm

HCEFatNHCFatHCi N

cyclesNN/17

7

10: ⎟⎟⎠

⎞⎜⎜⎝

⎛== σσ (N/mm2)

LCm

iEFatEiFatHCi N

cyclesNN/17

7

10: ⎟⎟⎠

⎞⎜⎜⎝

⎛=< σσ (N/mm2)

HCm

i

HCNHCFatEiFatHCi N

NcyclesNN

/1

: ⎟⎟⎠

⎞⎜⎜⎝

⎛=> σσ (N/mm2)

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Classification Notes - No. 51.1, January 2011

Page 35

For welded connections (push-pull rod) made of steel the fatigue strength for Ni No. of cycles shall be taken asfollows:

Where the welding parameters Awld and Bwld are tabulated in table 4.3.σFat Ei ≤ σu of the base material.Material parameters for calculation of S-N curveFatigue parameters for some materials commonly applied in propellers and pitch mechanisms are tabulated intable 4.2. These parameters correspond to mean fatigue strength in rotating bending (R=-1) for un-notched,polished specimen with a diameter of 25 mm or less.

Fatigue values for other materials may be agreed upon special consideration.Slope of SN curve in the low cycle part, mLC is calculated from the following:

Slope of the S-N curve in the high cycle part, mHC shall be taken as 50 for all materials. Note that for nodular cast iron, no knuckle point is defined. Hence the low cycle slope applies for the wholecycle range. Also note that Pt.5 Ch.1 Sec.3 and Sec.8 call for a Charpy V impact strength of minimum 20J at -10 deg. C. for propeller materials. Nodular cast iron will normally not comply with this requirement, but isincluded in table 4.2 for the sake of good order. The above formulations include the effect of variable loadingby moving the knuckle point from 107 to 108 cycles for bronze and cast steel materials. For forged steel, theinfluence of variable loading is small and hence knuckle point is taken at 107 cycles. Hence Kvar is taken as 1.0 for all materials.For typical material parameters, an example of initial S-N curves is given in the figure below:

Figure 4-11Example of typical initial S-N curve for some materials

Table 4-2 Material fatigue parameters for some common materialsMaterial σFat E7 NHCBronze alloy 0.30 σu 108

Cast steel 0.40 σu 108

Forged and rolled steel 0.50 σu 107

Nodular cast iron 0.35 σu ∝

wldBiwldEiFat NA=σ (N/mm2)

⎟⎟⎠

⎞⎜⎜⎝

⎛=

7

log

4

EFat

u

LCm

σσ (-)

Example of initial SN Curves

10

100

1000

1,0E+02 1,0E+03 1,0E+04 1,0E+05 1,0E+06 1,0E+07 1,0E+08 1,0E+09 1,0E+10

N

S

BronzeCast steelForge SteelNod. Cast iron

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Classification Notes - No. 51.1, January 2011

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For welded connections, the SN curve is generated (depending on welding type) from the following weldingparameters, unless otherwise is substantiated:

Figure 4-12S-N curve for welded connections (tensile strength taken as 600 N/mm2)

Influence factor for surface roughnessThe influence factor for surface roughness shall be taken from the following empirical formula, unlessotherwise is substantiated:

Where Ra is average surface roughness (mm) and σu is ultimate tensile strength of material (N/mm2). Forprediction of roughness influence, number of load cycles, Ni shall not be taken lower than 103 or higher than107.

Table 4-3 Fatigue parameters for common types of welded connectionsWeld type Awld BwldButt weld, grinding + NDT

8100 -0.29

Butt weld, general 10500 -0.33Transverse butt weldgrinding + NDT 8500 -0.33

Other / unspecified weld5300 -0.33

Example of SN curves for welded connections

1.0

10.0

100.0

1000.0

1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E+09

N

S

Butt weld, grind + NDT

Butt weld, general

Transverse butt weld, grind + NDT

Other

(-)( )( ) 4au

irough 10logR0.8200σ

1000Nlogf −+−⎟

⎠⎞

⎜⎝⎛=

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Classification Notes - No. 51.1, January 2011

Page 37

Figure 4-13Illustration of influence factor for surface roughness

Influence factor for notch sensitivityBasis for the prediction of notch sensitivity, q is the Neuber-equation for high cycle axial/bending fatigue. Thisis used for all materials relevant for propeller hub and pitch mechanism.The Neuber-equation is modified to include an empirical dependency of number of cycles, Ni, taking intoaccount that high tensile materials show some notch sensitivity even at very low number of cycles:

Where Nq is Number of cycles below which material is assumed to have zero notch sensitivity, taken as:

For prediction of notch sensitivity, Ni shall not be taken lower than Nq or higher than 107. In the same way,yield strength σy shall not be taken less than 400 N/mm2.Further, r is notch radius (mm) and is material parameter, empirically depending on material yield strength,σy (N/mm2). Unless otherwise is substantiated, the values of shall as a simplification be based on reported values forsteel according to the following empirical formulation:

The formulations for notch sensitivity may be somewhat on the safe side for some materials such as copperalloys and nodular cast iron, in particular when notches are very sharp.

Influence factor for surface Roughness

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08

N

F rou

gh

UTS = 400 MPa, Ra = 0.6

UTS = 400 MPa, Ra = 3.2

UTS = 800 MPa, Ra = 0.6

UTS = 800 MPa, Ra = 3.2

( ))log(71

log

q

q

i

Nra

NN

q−⎟⎟

⎠

⎞⎜⎜⎝

⎛+

⎟⎟⎠

⎞⎜⎜⎝

⎛

= (-)

1304102.2y

q eNσ

−⋅=

(-)

a

a

150082.0 ya

σ−= )( mm

DET NORSKE VERITAS

Classification Notes - No. 51.1, January 2011

Page 38

Figure 4-14Illustration of Notch sensitivity factor

Influence of mean stressInfluence factor for mean stress, Kmean shall be found according to the Goodman formulation for all materials, i.e.:

Where σmean is nominal mean stress (N/mm2), i.e. not including geometrical stress concentration, Kt and σu isultimate tensile strength (N/mm2). Note that for prediction of mean stress, safety factor needs not to be addedon the acting load.Influence of component sizeUnless otherwise is substantiated, the following empirical formulation shall be used for size influence, Ksizefor bronze, cast steel and nodular cast iron:

Where the component thickness, t shall refer to a representative thickness or diameter of the loaded part of thecomponent (thickness of bearing/retaining wall, diameter of crank pin/ push-pull rod diameter, etc), not to betaken less than 25mm.For prediction of size influence, number of load cycles, Ni shall not be taken lower than 103 or higher than 107.The influence of component size on fatigue strength for cast materials is illustrated as follows:

Notch sensitivity factor Including low cycle correction for high tensile materials

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08

N

q

Yield = 300MPa, r = 0.5mm

Yield = 300MPa, r = 4mm

Yield = 300MPa, r = 25mm

Yield = 700MPa, r = 0.5mm

Yield = 700MPa, r = 4mm

Yield = 700MPa, r = 25mm

u

meanmeanK

σσ

−= 1 (-)

⎟⎠⎞

⎜⎝⎛⎟

⎠⎞

⎜⎝⎛−=

25ln

1000log03.01 tN

K isize (-)

DET NORSKE VERITAS

Classification Notes - No. 51.1, January 2011

Page 39

Figure 4-15Influence of component size for cast materials

For forged steel, Ksize is closely connected to mechanical properties and shall therefore be taken as 1.0.Influence of variable loadingThe effect of variable loading on fatigue strength is included by extending fatigue curve with low cycle slope(mLC) from 107 cycles to 108 cycles for materials influenced by variable loading. Hence Kvar is taken as 1.0.Influence of loading typeFor components where bending stresses are not dominating, this shall be compensated for. If axial stresses are dominating:

For prediction of load type influence, number of load cycles, Ni shall not be taken lower than 103 nor higherthan 107.This is illustrated in the following figure:

Influence on component size on fatigue strength

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0 50 100 150 200 250 300

t (mm)

K siz

e

Ni <= 1000Ni = 1E4Ni = 1E5Ni = 1E6Ni >= 1E7

⎟⎠⎞

⎜⎝⎛−=1000

log04.01 iload

NK (-)

DET NORSKE VERITAS

Classification Notes - No. 51.1, January 2011

Page 40

Figure 4-16Influence of load type (axial load)

If shear stresses (τ) are dominating:

over the whole cycle range. Then shear stresses may be compared directly against the criteria described herein.Note that type of loading also influences on other factors, mainly geometrical stress concentration factor, whichis dealt with separately.

5. GUIDANCE ON SIMULATION CALCULATIONS5.1 The lumped mass-elastic systemSimulation of responses in a propulsion shafting system, which are caused by ice impacts on the propellerblades, shall be made by solving differential state-equations in the time domain. The basis for the mass-elasticsystem is found in the ordinary torsional vibration calculations (TVC). Since the step time in a numeric timeintegration should not exceed a few % (<5%) of the period of the highest natural frequency (of numeric stabilityreasons), it is strongly advised to simplify the model into a minimum of lumped masses.This simplification process should aim at the following:

— Keeping the total inertia constant (in order to have a representative deceleration of the system during iceimpact loads).

— Maintain the lowest natural frequencies (the separation margins between the resonance speeds and the realspeed are important).

— To minimise total computer calculation time and to avoid numeric challenges introduced by local highfrequent vibrations.

This would lead to some corrections (normally an increase) of the stiffness between the various new lumpedmasses. For elements with linear stiffness this is no problem. However, for nonlinear elements care should betaken.

— A progressive stiffness may be slightly increased, but in such a way that the coefficients describing theprogressive characteristics also are modified in the same proportion.

— An element with a twist limiter such as a buffer in a steel spring coupling or an emergency claw device ina rubber coupling should be described as correctly as possible. Hitting such limiters can cause extra high

Influence of axial load (rel. bending) on fatigue strength

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09

N

K loa

d

31

=loadK (-)

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Classification Notes - No. 51.1, January 2011

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peak torque in adjacent elements. Thus the torque-twist characteristic should not be altered, unless it isensured that the highest twist will not reach the limiter.

The simulation of ice impacts starts from a steady state condition, normally at full load. The coupling twist atthis full load is determined by the torque and the static coupling stiffness (use of the dynamic stiffness wouldlead to a faulty initial twist). During the impact vibrations it would be correct to use the dynamic stiffness forthe dynamic part and the static stiffness for the static part. This is hardly possible in practice and it is advisedto calculate with the static stiffness only. Alternatively the calculation may be performed with the dynamicstiffness, but then the twist angle when reaching the buffer/claw device must be reduced correspondingly.All essential branches must be included, e.g. PTO/PTI. On the other hand, a torsional vibration damper branchin a 4-stroke engine can simply be added to the engine mass because it hardly will have any influence on thelow frequent ice shock vibrations.The propeller inertia in a TVC will include the entrained water relevant for operation in open water or bollardcondition. When hitting large ice blocks the effective propeller inertia may be altered, but due to lack ofknowledge it is suggested to keep the inertia as given in the TVC.

5.2 Damping in the mass-elastic system5.2.1 Relative damping - GeneralRelative damping, i.e. damping between masses (parallel with the springs), is modelled as in ordinary TVC. Ifany modification of the stiffness is made in order to have the correct natural frequencies, the dampingcoefficient should be altered proportionally. With this recipe all “linear” elastic couplings are covered (“linear”means a torque-twist characteristic that is reasonably straight. The fact that most rubber couplings becomemuch softer when subjected to high amplitudes can be dealt with by a “memory function" of the lastoscillation). If desired, steel shafts can also be modelled with a small damping (e.g. magnifier M=180) but thiswill have negligible influence on the results.For non-linear couplings the stiffness is not often described in such a way that it may be used directly in asimulation calculation. It is convenient to model the torque-twist function as a polynomial function with twist(ϕ) to the power of 1, 3, 5 etc. (Power of 2, 4, etc. should be avoided as problems would occur with negativetwist.):Tel = A·ϕ + B·ϕ3 + C·ϕ5

The stiffness (K) is the derivative of this torque-twist function K = A + 3·B·ϕ2 + 5·C·ϕ4

The damping coefficient (DRel) can relate to that stiffness:DRel = K/(M·ω)where “M“ is the magnifier, i.e. M ≈ 2π/ψ ≈ 1/κ ≈ 1/tanε ≈ 1/2ζ etc., and w is the major excitation frequency(rad/s).

5.2.2 Absolute damping - GeneralAbsolute damping, i.e. damping on mass, is not directly modelled in a system that has a variable rpm. Adamping torque is the product of the damping coefficient and the vibration velocity. This works well in asystem with constant speed and a superimposed vibration. However, when the speed is altered the systemcannot clearly distinguish between a vibration and a change in speed, see Figure 5-1.

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Figure 5-1Rotational speed incl. vibrations as function of time

Incorporating absolute damping requires therefore a filtering of the speed signal. Figure 5-2 shows the samereal speed as above, but now the (new) blue curve represents the filtered signal.

Figure 5-2Filtered rotational speed as function of time

A filtered signal has a time lag (as can be seen above). The damping torque is determined as the product ofdamping coefficient DAbs (kNms/rad) and the difference between unfiltered and filtered speed signal, i.e.:

Ideally the filtered signal should have been in the middle of the oscillating speed signal. The difference between

[ ])()()( ttDtT filteredabsD ϕϕ && −⋅=

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the real filtered (blue) signal and this ideal filtered signal (when multiplied with DAbs) will represent a torque.Due to the necessary sign in the above equation, this torque will act as a kind of friction during deceleration ofthe system. Its magnitude will not be very significant for the final result, but nevertheless the filtercharacteristics should be chosen so as to minimise this “friction”. On the other hand, the filter must not allowany oscillating output signal as that would falsify the damping action.

5.2.3 Propeller damping and demand torque characteristicsFor a propeller the damping is also a consequence of its torque-speed characteristic. Modelling the propellerdemand torque as the square of the rpm or (e.g. close to bollard condition would be relevant in ice) willautomatically result in a damping action (corresponding to an Archer coefficient of about 20), see Figure 5-3.(For any driven component the damping coefficient is the tangent to the demand torque versus speedcharacteristic).

Figure 5-3Propeller torque characteristics

In open water the propeller damping coefficient is 20 – 40% higher than the value corresponding to an Archercoefficient of 20. It is uncertain if higher Archer coefficients than 20 are justified in the context of iceinteraction, and thus it is advised to keep to 20. However, If it is desired to take a higher coefficient intoaccount, it is necessary to use the trick with filtered speed signal as described in 5.2.2. Using this trick for apropeller would also require a continuous updating of DAbs as a function of actual speed.It is of course important to ensure that the propeller damping is not “doubled” in the way that the demand torqueis described together with the damping using the DAbs and the difference between unfiltered and filtered speed.Since the propeller demand torque characteristic is needed anyway, it would be suitable to use the trick offiltering the speed signal for implementation of higher damping than “Archer factor of 20” only.Last but not least it is unknown how the propeller damping works when in contact with ice blocks.

5.2.4 Diesel engine damping and torque characteristicsEngine damping is hard to describe correctly. Physically it is neither a relative nor an absolute damping.Damping caused by oil squeezing in journal bearings comes closer to relative than absolute damping. Enginedesigners sometimes have damping characteristics that are substantiated by measurements, but these areusually applicable for high frequencies such as “crankshaft modes”.An absolute damping coefficient may be described as in 5.2.2. However, using experience values from highfrequent (“crankshaft”) vibrations would lead to highly over-estimated engine damping. It is therefore advisedto abstain from attempts to describe engine damping as absolute damping.Since the real engine damping is more a kind of relative damping (even though TVC often wrongly describethe engine damping as absolute damping), this may be modelled. When the engine masses are added togetherto one mass, this relative damping cannot be modelled. If the engine masses are added to two or more masseswith springs in between, it is possible to model relative engine damping. However, the relative engine dampingis not a high damping compared to the propeller damping, and disregarding it for the benefit of simplificationhas a negligible influence on the results.

ϕ&

0

20

40

60

80

100

120

10 20 30 40 50 60 70 80 90 100 110

Speed

Torq

ue

Bollard Pull Propeller Law

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It is very important that an engine torque characteristic is not made so as to introduce negative damping. If adriver is modelled with a torque that increases with speed, and no special measures are taken to preventoscillations to influence the driving torque directly, this will function as negative absolute damping, see Figure5-4.

Figure 5-4Increasing engine torque capacity with rotational speed

This action is similar to the description of propeller damping above, but now with opposite sign because theelement is a driver. It is necessary to model the torque of the driver in order to simulate the drop of speed duringice interaction, but the vibration velocity of the engine inertia must not be allowed to introduce negativedamping. This must be arranged by filtering that parameter before it is used to update the driving torque.Appropriate filtering also introduces a time delay which is to some extent representative for a diesel engine’sfiring delays.The torque characteristic of a diesel engine depends to a large extent on the turbocharger lay out. The “static”characteristic may be available from the engine manufacturer and may have a shape as given on Figure 5-4. Ingeneral the maximum torque is the torque at MCR (Trated) which is limited by the blocking of the fuel rackposition. At lower speeds the turbocharger cannot feed the engine with sufficient air to prevent excessiveexhaust temperatures. Of that reason the maximum fuel rack position is often limited (controlled) by the chargeair pressure.In the context of ice interaction causing sudden overloads with consequential speed drops, the “dynamic”characteristic will be somewhat higher. The engine is assumed to run at full power when the ice shocks occur.The engine speed will be reduced, but due to the kinetic energy of the turbocharger rotor the engine will be fedtemporarily with more air than in the “static” case. This can be described as a temporary hump on thecharacteristic given in Figure 5-4.To make an accurate simulation model of this is very complicated, and such extreme efforts are hardly justifiedby the slightly more accurate result of the simulation process. A rough empirical approach may be justified,and may be laid out as follows:Engine torque as a function of speed (n) and time (t):T(n;t) = Tstatic(n) + ΔTdyn(t)Where Tstatic(n) is the torque as shown in Figure 5-4 and ΔTdyn(t) is the temporary hump.ΔTdyn(t) is assumed to enable the engine to maintain the Trated for a short duration. This can be described as:ΔTdyn(t) = (Trated – Tstatic)·(1 – t/3) where t starts at 0 when Tstatic < Trated and ends after 3 seconds.

5.2.5 Electric-motor damping and torque characteristicsAn Electric-motor damping is associated with its torque characteristic. When viewed in a torque-speeddiagram, a characteristic increasing from left to right in the diagram will correspond to a “negative” damping.A characteristic decreasing from left to right will correspond to “positive” damping.

0

20

40

60

80

100

10 20 30 40 50 60 70 80 90 100 110

Speed

Torq

ue

Engine Torque

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Figure 5-5Possible torque characteristics of electric motors (constant power or torque)

The above statements are valid for immediate torque response as a function of the momentary velocity. Anytime lag will alter this and introduce a phase angle that may change “negative” to “positive” damping and viceversa. (That is similar to diesel engines where the speed governor and firing system introduce a phase shift ofan oscillating fuel rack that can lead to negative, positive or 0 damping.)Unless the torque response is immediate, it is advised to filter the speed signal and therewith the dampinginfluence.E-motors may have an overload capacity when the rated speed is suppressed, e.g. having constant power asindicated in Figure 5-5 with the hyperbolic shape. However, using this overload capacity may lead to motoroverheating within short time. The simulation model utilising such overload capacity should also include a timelimit function corresponding to the automatic action in the monitoring system.

5.3 ExcitationsThe major excitation source is the ice interaction. The ice impacts in the rules are described as sequences ofhalf-sinus waves of blade passing frequency as well as the double frequency.The start and end of these waves are ramped up respectively down over a given angle of rotation.

A simple way of describing this excitation is to multiply the (constant) sinus waves with a ramp function from0 to 1 over the specified ramp length. A similar ramp function from 1 to 0 applies at the end.

If the ordinary torsional vibrations cannot be disregarded, e.g. as for direct coupled crosshead engines, it isnecessary to have this superimposed to the ice interaction. Such engines usually have a barred speed range or,if not barred, a range where the vibration response is quite significant. These speed ranges are usually below60% of MCR speed and an engine speed drop into these ranges should (or must) be avoided. It is thereforeimportant to model the available driving torque as a function of rpm (ref. Figure 5-5) as correctly as possible.The main engine excitation (normally of the order equal to the number of cylinders) is applied at the lumpedengine inertia.

6. PROPULSION SHAFT DESIGN AGAINST FATIGUE6.1 NomenclatureOnly SI units are used.

6.2 GeneralThis section describes a recommended method for fatigue analysis of propulsion shafts considering theexpected long term ice loads as defined in the Rules Pt.5 Ch.1. The other design criteria involving ice loads, which also have to be fulfilled like “pyramid bending strengthcriterion” for the propeller shaft and prevention of shaft bending/yielding due to peak ice torque, are consideredto be self explanatory in the Rules Pt.5 Ch.1 and are not elaborated further here. Even though propulsion shafts

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are exposed to a wide spectrum of other “open water”-loads (torsion and bending loads), just a few of thedominating load cases need to be considered instead of including them all in the Palmgren-Miner cumulative“damage sum”. The applicable “open water” load cases and their respective acceptance criteria are describedin Classification Note No. 41.4. For most of the propulsion shaft designs and applications known in marineapplications, only one of these load cases will really form the design condition (i.e. the load case that will bedecisive for the dimensions and material properties of the considered shaft). Therefore, it is normally adequateto assess the strength capacity of these load cases separately. However, in cases where two or more of theseload cases are close to their acceptable limits, their degree of cumulative “damage” must be added by usingPalmgren-Miner’s approach. The fatigue analysis is based on the permissible stress levels as presented in thedesign S-N-data/curves in Classification Note No. 41.4 and the validity of the method is given in the samereference.

Figure 6-1Typical load cases to be assessed for an ice classed vessel with direct coupled 2 stroke plant

6.3 Method for fatigue analysisFatigue design of propulsion shafts subject to variable amplitude stresses due to ice loads are assessed by usingthe Palmgren-Miner linear damage hypothesis:

where:

τv ice is a constant stress amplitude in the shaft due to ice interaction on thepropeller

ni(τv ice) is the discrete number of cycles with a constant stress amplitude τv ice Ni(tv ice)is the number of cycles to failure due to the constant stress amplitude τv ice based on therelevant part of the design S-N-curvedegree of cumulative “damage” of a constant stress amplitude τv ice

I number of different load magnitudes (load blocks)m negative inverse slope of the relevant part (for τv ice) of the design S-N curve

T0

103 1010

Tv

Cycles Log(N)

Torque

Tpeak

104 10 105 106 107 108 109 102 Z·Nice

- Ice load amplitudes (cumulative spectrum) - Transient load amplitudes (running through barred speed range) = load case C in C.N. No. 41.4

- Steady state load amplitudes for continuous operation = load case B in C.N. No. 41.4

Taverage

Tv ice

( )( ) ( ) η)(ττn

a1

τNτn

MDRk

1i

micevicevi

k

1i icevi

icevi ≤⋅== ∑∑==

( )( )icevi

icevi

Nn

ττ

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ā intercept with the log(N) axis of the relevant part (for τv ice) of the design S-N curve. η accept usage factor or “damage sum” = 1Applying a histogram to express the stress distribution, the number of stress blocks, I, is to be large enough toensure reasonable numerical accuracy, and should not be less than 10. If integration is used, due considerationshould be given to selection of integration method as the position of integration points may have a significantinfluence on the result. The stress cycles interaction effect is taken into account by conservative safety factors and continuous slope inthe high cycle end of the S-N curve.

6.3.1 Ice loadsThe ice load spectrum (exceedance diagram of ice load history) is by the Rules Pt.5 Ch.1 postulated by a two-parameter Weibull distribution with shape parameter k = 1 and scale parameter , see Figure 6-2:

The corresponding Weibull probability density function:

The highest shaft response torque in the load spectrum, ΤA max shall be based on the transient torsionalvibration analysis of the propulsion system (simulation calculations) as described in Sec. 5.

Figure 6-2Example of an ice load spectrum (cumulative distribution) with total number of ice loads; Z·Nice = 3·108, presentedin a semi-log scale

With , the same can be expressed in terms of stress: Weibull scale parameter:

Stress amplitude distribution:

)Nln(ZT

qice

maxAW ⋅

=

⎭⎬⎫

⎩⎨⎧

⋅−⋅=

)Nlog(Zlog(N)1T(N)T

icemaxAA

⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅⋅−⎟

⎟⎠

⎞⎜⎜⎝

⎛−

⋅⋅

=⋅= maxA

iceA

maxAw

A

T)Nln(ZT

maxA

ice)(TqT

maxAwmaxAA e

T)Nln(Z

e)(Tq

1)T,f(T

( )44

33 101610

iT ddTd

WT

−⋅⋅⋅⋅

=⋅

=π

τ

)NZln(τ

qice

maxicevW ⋅

=

⎭⎬⎫

⎩⎨⎧

⋅−⋅=

)log()log(1)( maxiceviceviceNZ

NN ττ

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Stress amplitude probability function:

6.3.2 Design S-N curveThe design S-N curve for the shaft section in question is established according to Classification Note No. 41.4,which takes into account the materials fatigue strength including the mean stress influence, geometrical stressconcentration (if any), notch influence/sensitivity, size factor and the required safety factors for low and highcycle fatigue respectively. For each shaft section and load case, this lead to a set of 3 points describing the bi-linear design S-N curve, see Figure 6-3:

τvLC Permissible low cycle torsional stress amplitude corresponding to 104 cycles (with safety factor1.25)

τvHC Permissible high cycle torsional stress amplitude corresponding to 3·106 cycles (with safety factor1.5)

τf/S Fatigue strength amplitude corresponding to 109 cycles (with safety factor 1.5) τf/S → τf includesa safety factor of 1.5.

The rest of the S-N- curve is found by linear interpolation/extrapolation in a log(t)-log(N) scale.

Figure 6-3Example of a design S-N curve for steel in air condition

The following bi-linear S-N curve can be used for fatigue assessment:For N ≤ 3·106 cycles:

For N > 3·106 cycles:

⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅⋅−

⋅⋅

= maxicev

icev )ln(

maxicevmaxicevicev

)ln(),( ττ

τττ

iceNZ

ice eNZf

1icev1icev1 )( maN −⋅= ττ

2icev2ice v2 )( maN −⋅= ττ

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where

6.3.3 Fatigue damage due to ice interactionThe degree of damage accumulated from the stress amplitudes due to ice loads may be calculated by a directintegration of each part of the S-N curve:In terms of torsional stress:

Figure 6-4Example of a typical ice stress distribution and design S-N curve for steel in air condition

Since the permissible ice stress amplitude below 1000 cycles is limited by the shaft bending/yielding criterion:

and the shape of the Weibull distribution is as indicated in Figure 6-4, it can be seen that the fatigue damagedue to ice will by far be dominated by the second integral:

⎟⎟⎠

⎞⎜⎜⎝

⎛≈

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

=

vHC

vLC

vLC

vHC

m

ττ

ττ log

477.2

log

10310log 6

4

116

1 103 mvHCa τ⋅⋅=

⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅≈

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅

=

f

f

9

6

2 5,1log

523.2

5,1log

10103log

ττ

ττ vHC

vHC

m 262 103 m

vHCa τ⋅⋅=

( ) ( )∫∫ ⋅⋅+⋅⋅=maxicev

vHC

vHCτ

τicev

icev1

maxicevicevice

τ

0icev

icev2

maxicevicevice dτ

τN)τ,f(τ

NZdττN

)τ,f(τNZMDR

( )∫⋅⋅≈maxicev

vHC

τ

τicev

icev1

maxicevicevice dτ

τN)τ,f(τ

NZMDR

( )∫⋅⋅≈maxice

vHC

icevicev1

maxicevicev ),(v

dN

fNZD iceice

τ

τ

ττττ

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If the highest response torque amplitude on the shaft during a sequence of ice impacts on the propeller, tv ice max,is lower than the design knee point of the design resistance S-N curve,tvHC, the fatigue life of the shaft due to iceimpacts can be assumed as verified and no ice damage calculation is necessary.It is also possible to calculate an equivalent constant ice stress amplitude, teq ice associated with a certainaccumulated number of cycles, which will give the same fatigue damage, Dice as the long term stressdistribution calculated above. The equivalent ice stress amplitude associated with 106 accumulated stresscycles will be, see Figure 6-5:

Figure 6-5Equivalent ice stress amplitude, teq ice associated with 106 accumulated stress cycles giving the same fatigue damageas the ice stress distribution tv ice(N)

6.3.4 Bending stress influenceThe influence on the fatigue damage by significant bending stresses due to ice impacts should be considered inthe following shafts:

a) In propeller shafts aft of the 2nd aftermost bearing caused by maximum propeller blade forces Fb/Ff. b) In gear- and thruster shafts due to the coupled torsional-lateral mode through the gear mesh.

7. REDUCTION GEARSThe general procedure in appendix A1 may be used in combination with Classification Note CN41.2 for toothroot fracture and pitting of flanks. Scuffing calculations may be carried out according to CN41.2 based on themaximum response torque. Subsurface fatigue safety can be roughly estimated by the following:

1) Apply the response torque according to the Weibull distribution at 3x106 cycles.2) Calculate high cycle subsurface safety factor according to CN41.2.3) If the calculated safety factor is somewhat higher than required by the Rules Pt.5 Ch.1, further detailed

subsurface calculations can be omitted.

1

1m

1

6m1

1

6

iceeq aMDR10

aMDR10τ

⋅=⎟⎟

⎠

⎞⎜⎜⎝

⎛

⋅=

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8. PODDED PROPULSORS / AZIMUTHING THRUSTERS8.1 Ice loads on pod/thruster body and propeller hub

Figure 8-1Typical podded propulsor

8.1.1 IntroductionAfter introduction of the new IACS UR I - Polar Class as a tentative new Section 8 in the DNV Ice RulesJanuary 2008, it became obvious that the ice loads calculated according to E 700 Podded propulsors andazimuth thrusters were realistic for only a very limited ship size range. DNV has in cooperation with ABB OYin Finland developed a new method for calculation of structural ice loads on pods and azimuth thrusters.Calculation method presented here will significantly simplify the ice load calculations. Further, it will givereduced and more realistic ice load level for actual ice classes compared to loads calculated according to themethod from early 1990ties. Ice loads may be calculated for the entire exposed area of pod/thruster, or any other actual partial area separately.The method may also be applied on icebreakers and deeply submerged “under bottom mounted” units.These ice loads are also applicable for the Baltic ice classes ICE-1C…1A* , see Pt.5 Ch.1 Sec.3 J1402. Howeverdue to the start-up of the new project at TraFi “Development of technical background for Finnish-Swedish iceclass rules for azimuthing main propulsion” have we decided to exclude these from the Table 8.1 in this editionfor eventual elaboration at a later stage.The new ice load calculation method as described herein shall also be applied for respective ice loads accordingto Section 4, i.e. ICE-05…15 and POLAR-10…30 w/o or with ICEBREAKER notation. Both axial and transversal ice load cases shall be covered. Following cases shall normally be calculated:

1) transversal force on strut2) transversal force on pod3) axial force on strut4) axial force on pod, or propeller hub for pulling propeller5) transversal force on nozzle if any6) axial force on nozzle if any.

In addition, total transversal and axial forces using the sum of projected areas for pod, strut and nozzle (ifapplicable), shall be considered. In calculation of total axial force for pulling propeller case, the projected propeller blade area and ditto hub areashall be used.

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Figure 8-2Illustration of actual load cases to be considered

8.1.2 Ice load definitionIce load on a defined area may be expressed by:F = po

0.8 (A C0.3)exp C1 C2 C3 C4 [MN]where:po= Ice pressure (MPa), see table 8.1

A = considered projected area exposed to ice pressure in m2 if less than 2Hice2

= 2Hice2

otherwise exp = 0.3 when area is 1 m2 and more = 0.85 when A < 1 m2

Table 8-1 Reference ice thickness and –pressure. Ref. technical background note and rules for IACS UR I2 Ice Class Hice (m) p0 (MPa)

PC-1 4.0 6PC-2 3.5 4.2PC-3 3.0 3.2PC-4 2.5 2.45PC-5 2.0 2PC-6 1.75 1.4PC-7 1.5 1.25

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C = A / 2Hice2, or = min. 1

Hice = Reference ice thickness for machinery strength design, see table 8.1 D= propeller diameter C1 = location and propeller type factor for hub and strut loads = 1 in general = 1.5 for pulling and pushing “front propeller” strut loads and pushing propeller axial pod loads = 2.2 for pulling propeller axial load (“hub load”) calculated based on projected hub area C2 = this factor reduces pod ice loads by 1/3 for under bottom mounted units = 1 in general = 2/3 for “deeply submerged” under bottom located propellers C3 = ship type factor = 1 in general = 1.25 for icebreaker and ice management vessel C4 = is statistical factor for expected maximum load during 20 years lifetime = 1.2 in general.Dynamic loadAxial load on the propeller hub exceeding propeller thrust will push the shaft “backwards” and cause dynamicresponse in the thrust bearing in excess of what is reflected in the factor C1 above. The magnitude is dependingon thrust bearing design and axial clearance. For a spherical roller bearing this factor shall be taken minimum1.1. This load is normally transmitted from the thrust bearing to its supporting structure and shall be includedinto the peak load transmitted via thruster support bearing (slewing bearing) to supporting hull structure.Deep submerged under bottom located propellers – C2Maximum ice load on propeller is not depending on submerged depth of propeller, only on total number of iceloads. This is reasonable for propellers, where ice impacts are mainly caused by propeller blades hitting iceblocks and not reversely. Propeller blade rotational speed is much higher than ship speed - normally tip speedis in the range of 20 to 40 m/s. Therefore it will not make any difference for a propeller blade if it hits ice underthe bottom, or close to the surface. The selected 1/3 load reduction reflects to some degree reduction applied to ice loads acting on ship bottom.However, since a thruster penetrating ship hull forms an obstruction for ice moving mutually along the bottom,there will always be crushing of ice against the thruster strut, pod and propeller hub. The given load reductionis not based on measurements, but is selected based on our best knowledge.A deep submersion must also be seen in relation to ice class. The following may be applied as criterion for whena unit may be considered as “deeply submerged”:Depth of propeller shaft centreline at LIWL (ho) > Hice + D Where D is propeller diameter in m.Propellers located in areas Mb, Sb and Bib (see Figure 1 in Pt.5 Ch.1 Sec.8) are considered as “under bottomlocated propellers” for PC. Propellers located under bottom, but in area BIl, or B shall be specially considered.For such thrusters, pod and strut parts may belong to different location categories.For Baltic ice classes similar definitions for locations do not exist. A propeller may be considered as locatedunder bottom when it is in flat bottom area, “5 frame spacings” or equivalent distance aft from “fore foot” asdefined in Figure 1 in Pt.5 Ch.1 Sec.3.

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Appendix AGENERAL GUIDANCE ON FATIGUE ANALYSIS OF PROPULSION MACHINERY SUBJECT TO ICE LOADSA.1 Cumulative Damage by Palmgren-Miner’s RuleIn general, fatigue design of machinery components may be carried out by methods based on fatigue tests (S-N data) and estimation of cumulative damage ratio (Linear Damage Rule or Palmgren – Miner’s Rule). Thetheory of the Palmgren – Miner’s linear cumulative damage rule is that the total damage of the consideredcomponent or more precise the considered section of a component, may be expressed as the accumulateddamage from each load cycle at different stress levels, independent of their sequence of occurrence:

where:

MDR Miner Palmgrens accumulated fatigue damage rationi number of cycles in stress block i with constant stress amplitude (component stress history, see

A3)Ni number of cycles to failure at constant stress amplitude (design S-N curve, see A2)I total number of stress blocks in the components stress historyThe damage ratio (MDR) also called usage factor, represents the ratio of the consumed life of the component.Theoretically, a MDR = 0.35 means that 35% of the component’s life is consumed. Ideally, failure due tofatigue occurs when the damage ratio exceeds 1.0. The general procedure to calculate the damage ratio is as shown in Figure A-1:

1) establish the relevant S-N curve for the section of the component in question, taking into account therequired safety factor, material of the component, mean stress and notch influence, size effect, stressinteraction effect, etc., see A2

2) establish the long term stress amplitude distribution (stress amplitude exceeding spectrum) by relevantWeibull parameters, which are calculated based on the ice impact loads prescribed by convention for theapplicable ice class notation and their response to the component in question, duly taking care of thedynamic properties of the system where the component is installed, see A3

3) check if detailed fatigue analysis can be omitted, see A54) depending on item 3. collate the S-N curve and the Weibull distributed stress amplitudes from step 1 and

2, respectively, by calculating the resulting damage ratio by Palmgren-Miner’s rule (MDR), see A4.

0.11

≤= ∑=

I

i i

i

NnMDR

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Figure A-1The Palmgren-Miner’s rule for one particular stress block i with stress exceedance diagram according a) and de-sign S-N curve b)

Considerable test data has been generated in an attempt to verify Palmgren-Miner's Rule. Most of the “original”test cases for this rule have been using a two step stress history. This involves testing at an initial stress levelS1 for a certain number of cycles and then the stress level is changed to a second level S2 until failure occurs.If S1 > S2, often referred to as a “high-low” stress test, and opposite if S1 < S2, a “low-high” stress test. Theobserved results of these tests are that the damage ratio - MDR corresponding to failure ranged from 0.61 to1.45. Other researchers have shown variations as large as 0.18 to 23.0, with most results tending to fall between0.5 and 2.0. In most cases, the average value is close to Palmgren-Miner's proposed value of 1.0.One problem with two-level step tests is that they do not accurately represent many service load/stress histories.Most load/stress histories do not follow any step arrangement and instead are made up of a random distributionof loads of various magnitudes. However, tests using random histories with several stress levels show goodcorrelation with Miner's rule. The Palmgren-Miner’s linear damage rule has two main shortcomings when it comes to describing observedmaterial behaviour:

1) Load sequence and interaction effects are ignored. The theory predicts that the damage caused by a stresscycle is independent of where it occurs in the load history. Fatigue is a consequence of cycle-by cycleplastic strains locally at a notch. The state of stress and strain in the damage area is a result of the precedingstress-strain history. Hence, the damage in one cycle is not a function of that stress cycle only, but also ofthe preceding cycles, leading to interaction or stress memory effect. An example of this discrepancy wasdiscussed above regarding “high-low” and “low-high” tests. It has also been demonstrated by such two steptests that the stress state at the end of the last cycle of first “high” cycles before the second “low” cyclesstarts has a considerable influence on the total number of cycles to failure, see Figure A-2.

Stre

ss a

mpl

itude

, Sa

1

Sai

ni 10 103 105 106

Stress cycles, n (logarithmic scale)

a)

107

Str

ess

ampl

itude

, Sa

(lo

garit

hmic

sca

le)

1

Sai

Ni 10 103 105 106

Cycles to failure, N (logarithmic scale)

b)

107 104

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2) The rate of damage accumulation is independent of the stress level. However, observed behaviour indicatesthat a crack initiate in a few cycles at high strain amplitudes, whereas almost all the life is spent on initiatinga crack at low strain amplitudes (i.e. very little propagation fatigue).

Despite these limitations, the Palmgren-Miner’s linear damage rule is still widely used. This is due to itssimplicity and the fact that more sophisticated methods do not always result in better predictions. The proposedvalue of MDR = 1.0 can be used as long as the above limitations are acknowledged by taking them into accountwith conservative estimates of the design S-N curve for the component. In this respect by extending the slopeof the S-N curve, m1 (i.e. adjusting the fatigue limit at the “knuckle point”), introducing a proper second slopem2 in the high cycle end (see Figure A-5 in A2) and selecting a proper safety factor.

Figure A-2Stress interaction effect

A.2 Design S-N curveAn illustrative S-N curve is shown in Figure A-3. The Y-axis represents the alternating stress amplitude (Sa)and the X-axis represents the number of cycles (N) required to cause failure.

Figure A-3Schematic S-N curve (semi-logarithmic scale)

Time

Stre

ss, S

St

ress

, S

Δt

Mean fatigue life at stress S1

Mean fatigue strength at N2 cycles

Cycles to failure, N (logarithmic scale)

103

Sa1

N2 104 105 107 108

Result of test samples

Stre

ss a

mpl

itude

, Sa

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S-N curves are normally presented for small test specimens as mean fatigue life (50% probability of failure) orfor a given probability of failure. Generating an S-N curve for a certain material requires many tests tostatistically vary the stress (regular sinusoidal) and count the number of cycles to failure. The type of stressvariation has a major effect on the fatigue performance and the S-N curves are normally determined for onespecific stress ratio value, which is defined as minimum peak stress divided by the maximum peak stress,

.The mean stress, Sm and stress amplitude, Sa is then defined as

It is most common to test at a ratio close to 0, e.g. 0.1 (≈ pulsating load) or -1 (= alternating load, e.g. push-pull). However, it is to be noted that testing with mean stress Sm = constant and stress ratio R = constant willin general give different S-N curves. Therefore, it is important that the experimental basis for the reference S-N curve corresponds to the type of alternating stress applicable for the component in question.

Figure A-4Definition of terms related to fatigue testing

The design S-N curve for the considered section of the component in question is then derived by adjusting themean S-N curve with the following as found relevant:

— notch influence:

a) geometrical stress concentrationb) notch sensitivity/stress gradient influence.

— surface condition (roughness)— surface hardening— mean stress influence— size influences:

a) metallurgical (if the mechanical properties used for the fatigue limit is not achieved from representativetest specimens)

b) statistical (if not already accounted for by a reduction of the mean S-N curve for probability of failure≠ 50%, i.e. reduction by one or more standard deviations).

— required safety factor.

The design S-N curve is then linearised into a curve with two slopes in a double logarithmic chart (log-logscale), see Figure A-5. The bi-linear S-N curve for N ≥ 103 stress cycles may be expressed as:

max

min

SSR =

2R1S +

=m 2R-1S =a

and , see Figure A-4.

Time

Smax

Sa

Sa

Sm

Smin Cycle

0 < R < 1

Stre

ss, S

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or:

where

Sa stress amplitudeā1 the intercept of the logN axis for Ni1 < Nxā2 the intercept of the logN axis for Ni2 > Nxm1 the inverse negative slope of the S-N curve for Ni1 < Nx (i.e. actual slope is -1/m1)m2 the inverse negative slope of the S-N curve for Ni2 > Nx (i.e. actual slope is -1/m2)Nx the number of cycles to the “knuckle point” of the bi-linearised S-N curve (i.e. where the S-N

curve flattens out and changes slope).In the low cycle end of the S-N curve, a cut-off is introduced for N < 103 stress cycles by the stress amplitudeSa resulting in a peak stress Smax = Sm + Sa equal to the yield strength of the material, see Figure A-5. This isintroduced in order to prevent permanent deformation of the component.

Figure A-5Schematic bi-linear S-N curve (log-log scale)

A.3 Long term stress amplitude distribution due to ice loadsAccording to the Rules Pt.5 Ch.1, the ice load spectrum and correspondingly the ice stress amplitude spectrum(exceedance diagram of ice load/stress history) is postulated by a two-parameter Weibull distribution, seeFigure A-6:

where:

Sa(n) load/stress amplitude spectrum as a function of load/stress cycles

( ) 111m

aai SaSN −=

( ) 222m

aai SaSN −=and

( )[ ] aai SmaSN logloglog 111 −=

( )[ ] aai SmaSN logloglog 222 −=and

Cycles to failure, N (logarithmic scale)

103 104 105 107 108106 Nx 1 109 ā1

m1

1

m2

1

Fatigue limit ”knuckle point”

Stre

ss a

mpl

itude

, S

(loga

rithm

ic s

cale

)

Sax

a

1/k

00aa )log(n

log(n)1S(n)S

⎭⎬⎫

⎩⎨⎧

−⋅=

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k Weibull shape parameter as given by the Rules Pt.5 Ch.1n number of load/stress cyclesn0 total number of load/stress cycles in the Weibull distribution as calculated for the component in

question according to the Rules Pt.5 Ch.1qw Weibull scale parameter is defined from the highest stress amplitude, Sa0, as:

Sa0 the highest stress amplitude out of n0 cycles, i.e. the highest stress amplitude in the Weibulldistribution calculated for the component in question according to the Rules Pt.5 Ch.1. This load/stress has a probability for being exceeded equal to 1/n0, see Figure A-7 b).

Figure A-6Weibull stress distribution with k = 1.0 and n0 = 5·107 cycles

The corresponding probability density function and probability of exceedance function of the two-parameterWeibull distribution are:

where:

f(Sa) Probability density function of the stress amplitude Sa, see Figure A-7 a)Q(Sa) Probability for exceedance of the stress amplitude Sa, see Figure A-7 b)

[ ]1/k0

0aW )ln(n

Sq =

Sa/Sa0

log n 5·107

( )⎥⎥

⎦

⎤

⎢⎢

⎣

⎡⋅⎟

⎟⎠

⎞⎜⎜⎝

⎛−−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−

⋅⋅⋅=⋅⎟⎟⎠

⎞⎜⎜⎝

⎛⋅=

)ln(nSS

0k0a

1ka

k

qS1k

W

a

Wa

0

k

0a

a

W

a

enlnSSke

qS

qk)f(S

( )⎥⎥

⎦

⎤

⎢⎢

⎣

⎡⋅⎟

⎟⎠

⎞⎜⎜⎝

⎛−

⎟⎟⎠

⎞⎜⎜⎝

⎛−

===⋅−= ∫)ln(n

SSk

qS

0

S

0aaa

0

k

0a

a

W

aa

eenndSSf1)Q(S

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Figure A-7Probability density and Probability functions of Weibull distribution with k = 1.0, n0 = 5·107 cycles and qw = 3.38

A.4 Calculation of the Palmgren-Miner’s damage sum

A.4.1 By using stress histograms If the general procedure described in A1 for calculating the damage sum is to be applied, the Weibull stressdistribution described in A3 must be transformed to a representative histogram with I columns (i.e. discretefrequency spectrum). The numerical accuracy of the damage sum depends on the transformation method(distribution of columns) and the total number of columns, I used. For the method described below, the total number of columns, I, should not be less than 10, see Figure A-8. The ordinate (stress amplitudes) of the Weibull stress distribution is divided into z equidistant stress columns.The stress amplitude in each of the column will then be:

which for 10 columns become: where:

Sai the stress amplitude of column iI total number columns in the stress distribution histogram

Probability density

Sa Sai

Q(Sai )

f(Sa )

a)

Sa

Probability of exceedance Q(Sa )

1/n0

b)

0aia SI

1i1S ⋅⎟⎠⎞

⎜⎝⎛ −

−= ( ) 01.01.1 aia SiS ⋅⋅−=

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Sa0 the highest stress amplitude out of n0 cycles, i.e. the highest stress amplitude in the Weibulldistribution calculated for the component in question according to the Rules Pt.5 Ch.1. This load/stress has a probability for being exceeded equal to 1/n0, see Figure A-7 b).

Since the Weibull stress distribution is an accumulated continuous spectrum, the individual stress amplitudesof the columns are then calculated by:

where:

ni number of stress cycles in column in0 total number of stress cycles in the Weibull distribution as calculated for the component in

question according to the Rules Pt.5 Ch.1I total number columns in the stress distribution histogramk Weibull shape parameter as given by the Rules Pt.5 Ch.1.The calculation of the damage sum will be on the safe side since the number of cycles in each of the columnsin the histogram is higher than given by the Weibull distribution, i.e. the height of the columns exceeds theWeibull distribution, see Figure A-8. Consequently, the fewer stress blocks used the more conservative is thecalculated damage sum.

Figure A-8Stress amplitude distribution divided into I=10 stress blocks k = 1.0 and n0 = 8.8·107 cycles

A.4.2 By using closed form solutionIf the component is subject to n0 number of randomly distributed stress cycles in total with a Weibullprobability function f(Sa), the number of cycles with stress amplitudes within Sa and (Sa + dSa) is n0· f(Sa) ·dSa.Since the mathematical expression for the S-N curve S(Ni) is known, the fatigue damaged ratio MDR can beexpressed in a closed form by direct integration of damage below each part of the bi-linear S-N curve, seeFigure A-9:

where:

n0 total number of load/stress cycles in the Weibull distribution as calculated for the component inquestion according to the Rules Pt.5 Ch.1.

Sax the fatigue limit (stress amplitude) at the change of slope (“knuckle point”), see Figure A-5Sa0 The highest stress amplitude out of n0 cycles, i.e. the highest stress amplitude in the Weibull

distribution calculated for the component in question according to the Rules Pt.5 Ch.1.

∑=

−⎟⎠⎞⎜

⎝⎛ −− −=

i

1i1i

k

Ii11

0i nnn

( ) ( ) ⎥⎥⎦

⎤

⎢⎢⎣

⎡+⋅=

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⋅=

⋅== ∫∫∫∫∫∑ −−

∞∞=

=

0

12

0

10 20

10 20

0

0

1

)()()()()(

)()()( a

xa

xaa

xa

xa S

Sam

a

aS

ama

aS

Sa

ai

aS

aai

aa

ai

aI

i ai

ai dSSaSfdS

SaSfndS

SNSfdS

SNSfndS

SNSfn

SNSnMDR

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Classification Notes - No. 51.1, January 2011

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f(Sa) probability density function of the stress amplitude Sa, see A3Ni1(Sa) S-N curve for 103 ≤ N ≤ Nx stress cycles, see A2Ni2(Sa) S-N curve for N ≥ Nx stress cycles, see A2Nx the number of cycles to the “knuckle point” of the bi-linearised S-N curve (i.e. where the S-N

curve flattens out and changes slope), see A2.These definite integrals can be numerically evaluated by various methods, e.g. Recursive Trapezoid rule,Romberg algorithm or Adaptive Simpson’s rule.

Figure A-9Direct integration of damage below each part of the bi-linear S-N curve

A.5 Guidance to when detailed fatigue analysis can be omittedA detailed fatigue analysis can be omitted if the largest stress amplitude in the Weibull distribution for theactual detail (section of the component in question) is less than the fatigue limit at the “knuckle point”, seeFigure A-10 a).For components where a yield criterion is introduced, it would be meaningless to carry out detailed fatigueanalysis when the peak stress = largest stress amplitude in the Weibull distribution + the mean stress is higherthan the yield strength of the component (including the effect of any stress concentrations), see Figure A-10 b).

Cycles to failure, N (logarithmic scale)

ā2

103 104 105 107 1081061 109 ā1

m1

1

m2

1

Sax

Sa0

Stre

ss a

mpl

itude

, S

(loga

rithm

ic s

cale

)

Part I of MDR-integral

Part II of MDR-integral

Ni2(Sa)

Ni1(Sa)

Σni(Sa)

n0

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Figure A-10Stress distribution where a detailed fatigue assessment can be omitted

Fatigue limit ”knuckle point”

Stre

ss a

mpl

itude

s, S a

Number of cycles

Weibull stress distribution

S-N curve

Number of cycles

Stre

ss a

mpl

itude

s, S a

S-N curve

Weibull stress distribution

a)

b)

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