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Machinery Requirements for Polar Class Ships(Aug 2006)
1
Application(Rev.1
Jan2007)
The contents of this Chapter apply to main propulsion, steering gear, emergency and(Corr.1
Oct 2007) auxiliary systems essential for the safety of the ship and the crew.
(Rev.2
Jan 2023 The vessel operating conditions are defined in UR I1.
Complete
Revision) The requirements herein are additional to those applicable for the basic open water class ofthe vessel.
2

General2.1

The following drawings and particulars are to be submitted.

2.1.1 Details of the intended environmental operational conditions and the required ice
strengthening for the machinery, if different from ship’s ice class
2.1.2 Detailed drawings and descriptions of the main propulsion, steering, emergency andauxiliary machinery and information on the essential main propulsion load control functions.
The descriptions are to include operational limitations.
2.1.3 Description detailing where main, emergency and auxiliary systems are located andhow they are protected to prevent problems from freezing, ice and snow accumulation andevidence of their capability to operate in the intended environmental conditions
2.1.4 Calculations and documentation indicating compliance with the requirements of thischapterNote:
1.

This UR is to be uniformly applied by IACS Societies on ships contracted forconstruction on and after 1 March 2008.

2.

The “contracted for construction” date means the date on which the contract to build thevessel is signed between the prospective owner and the shipbuilder. For further details
regarding the date of “contract for construction”, refer to IACS Procedural Requirement(PR) No. 29.

3.

Rev.2 of this UR is to be uniformly applied by IACS Societies on ships contracted forconstruction on or after 1 July 2024.

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2.2

System Design

2.2.1 Systems subject to damage by freezing, shall be drainable.
2.2.2 Vessels classed PC1 to PC5 inclusive shall have means provided to ensure sufficient
vessel operation in the case of propeller damage including the Controllable Pitch (CP)mechanism. Sufficient vessel operation means that the vessel should be able to reach safe
haven (safe location) where repairs can be undertaken. This may be achieved either by atemporary repair at sea, or by towing, assuming assistance is available. This would lead
however to a condition of approval.
2.2.3 Means shall be provided to free a stuck propeller by turning it in reverse direction. This
shall also be possible for a propulsion plant intended for unidirectional rotation.
2.2.4 The propeller shall be fully submerged at the ships LIWL.
3

Materials

Materials shall be of an approved ductile material. Ferritic nodular cast iron may be used forparts other than bolts. For nodular cast iron an averaged impact energy value of 10 J at
testing temperature is regarded as equivalent to the Charpy V test requirements defined
below.
3.1

Materials exposed to sea water

Materials exposed to sea water, such as propeller blades, propeller hubs and cast thruster
bodies shall have an elongation not less than 15% on a test specimen according to UR W2.
Charpy V-notch impact testing is to be carried out for materials other than bronze andaustenitic steel. The tests shall be carried out on three specimens at minus 10 ºC, and theaverage energy value is to be not less than 20 J. However, Charpy V impact test
requirements of UR W7 or UR W27 as applicable for ships with ice class notation, shall also
be applied to ships covered by this UR.
3.2

Materials exposed to sea water temperature

Charpy V-notch impact testing is to be carried out for materials other than bronze andaustenitic steel. The tests shall be carried out on three specimens at minus 10 ºC, and theaverage energy value is to be not less than 20 J. However, the Charpy V impact test
requirements of UR W7 as applicable for ships with ice class notation, shall also be applied toships covered by this UR.
This requirement applies to components such as but not limited to blade bolts, CPmechanisms, shaft bolts, propeller shaft, strut-pod connecting bolts, etc. This requirement
does not apply to surface hardened components, such as bearings and gear teeth or sea
water cooling lines (heat exchangers, pipes, valves, fittings etc.). For a definition of structural
boundaries exposed to sea water temperature see UR I2 Figure 6.
3.3

Material exposed to low air temperature

Materials of exposed machinery and foundations shall be manufactured from steel or otherapproved ductile material. An average impact energy value of 20 J taken from three Charpy V
tests is to be obtained at 10 ºC below the lowest design temperature. Charpy V impact tests
are not required for bronze and austenitic steel.

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This requirement does not apply to surface hardened components, such as bearings andgear teeth. For a definition of structural boundaries exposed to air temperature see UR I2
Figure 6.
4

Definitions

4.1

Definition of Symbols
Table 1: Definition of symbols

Symbol
𝑐𝑐
𝑐𝑐0.7
𝐶𝐶𝐶𝐶
𝐷𝐷
𝑑𝑑
𝑑𝑑𝑝𝑝𝑝𝑝𝑝𝑝
𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙
𝐸𝐸𝐸𝐸𝐸𝐸
𝐹𝐹𝑏𝑏

Unit
m
m
m
m
mm
m

𝐼𝐼𝑡𝑡
𝑘𝑘
𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝑚𝑚
𝑀𝑀𝐵𝐵𝐵𝐵
𝑀𝑀𝑀𝑀𝑀𝑀
𝑁𝑁𝑛𝑛
𝑛𝑛𝑛𝑛
𝑁𝑁𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖

kgm2
m
kNm
rev/s
rev/s
-

𝑁𝑁𝑄𝑄
𝑃𝑃0.7
𝑃𝑃0.7𝑛𝑛
𝑃𝑃0.7𝑏𝑏
𝑃𝑃𝑃𝑃𝑃𝑃

m
m
m
m

kN

𝐹𝐹𝑒𝑒𝑒𝑒𝐹𝐹𝑓𝑓
𝐹𝐹𝑖𝑖𝑖𝑖𝑖𝑖(𝐹𝐹𝑖𝑖𝑖𝑖𝑖𝑖 )𝑚𝑚𝑚𝑚𝑚𝑚
𝐹𝐹𝐹𝐹ℎ0(𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖 )
𝐼𝐼

kN
kN
kN
kN
m
m
kgm2

𝑁𝑁𝑅𝑅

-

Definition
chord length of blade section
chord length of blade section at 0.7𝑅𝑅 propeller radiuscontrollable pitch
propeller diameter
external diameter of propeller hub (at propeller plane)
diameter of shear pin
limit value for propeller diameter
expanded blade area ratio
maximum backward blade force for the ship’s service life (negative
sign)
ultimate blade load resulting from blade failure through plastic bending
maximum forward blade force for the ship’s service life (positive sign)
ice load
maximum ice load for the ship’s service life
fixed pitch
depth of the propeller centreline from lower ice waterline (𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿)
Ice block dimension for propeller load definition
equivalent mass moment of inertia of all parts on engine side ofcomponent under considerationequivalent mass moment of inertia of the whole propulsion systemshape parameter for Weibull distribution
lower ice waterline
slope for S-N curve in log/log scale
blade bending momentmaximum continuous rating
number of ice load cycles
propeller rotational speed
nominal propeller rotational speed at MCR in free running conditionreference number of ice impacts per propeller revolution per ice class
total number of ice load cycles on propeller blade for the ship’s service
life
reference number of ice load cycles for equivalent fatigue stress (108cycles)number of propeller revolutions during a milling sequence
propeller pitch at 0.7𝑅𝑅 radiuspropeller pitch at 0.7𝑅𝑅 radius at MCR in free running condition
propeller pitch at 0.7𝑅𝑅 radius at MCR in bollard condition
pitch circle diameter
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(cont)𝑄𝑄(𝜑𝜑)𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴
𝑄𝑄𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒
𝑄𝑄𝐹𝐹 (𝜑𝜑)𝑄𝑄𝑓𝑓𝑓𝑓
𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚

kNm
kNm
kNm
kNm
kNm
kNm

𝑅𝑅
𝑆𝑆
𝑆𝑆𝑓𝑓𝑓𝑓𝑓𝑓
𝑆𝑆𝑖𝑖𝑖𝑖𝑖𝑖
𝑟𝑟
𝑇𝑇
𝑇𝑇𝑏𝑏
𝑇𝑇𝑓𝑓
𝑇𝑇𝑛𝑛
𝑇𝑇𝑟𝑟
𝑇𝑇𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘
𝑇𝑇𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘2
𝑇𝑇𝑚𝑚𝑚𝑚𝑚𝑚1
𝑇𝑇𝑘𝑘𝑘𝑘∆𝑇𝑇𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘
𝑡𝑡𝑧𝑧𝑧𝑧𝑝𝑝𝑝𝑝𝑝𝑝
𝛼𝛼𝑖𝑖
𝛾𝛾𝜀𝜀
𝛾𝛾𝑣𝑣
𝛾𝛾𝑚𝑚
𝜌𝜌

m
m
kN
kN
kN
kN
kN
kNm
kNm
kNm
kNm
kNm
m
deg
-

𝜎𝜎𝑓𝑓𝑓𝑓𝑓𝑓
𝜎𝜎𝑓𝑓𝑓𝑓𝜎𝜎𝑟𝑟𝑟𝑟𝑟𝑟1
𝜎𝜎𝑟𝑟𝑟𝑟𝑟𝑟2

MPa
MPa
MPa
MPa

𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚
𝑄𝑄𝑛𝑛
𝑄𝑄𝑟𝑟 (𝑡𝑡)
𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝
𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠
𝑄𝑄𝑣𝑣𝑣𝑣𝑣𝑣

kNm
kNm
kNm
kNm
kNm
kNm
kNm

𝜎𝜎0.2
𝜎𝜎𝑒𝑒𝑒𝑒𝑒𝑒

MPa
MPaTorquemaximum response torque amplitude as a simulation result
maximum engine torqueIce torque excitation for frequency domain calculations
friction torque in pitching mechanism; reduction of spindle torquemaximum torque on the propeller resulting from propeller/ice
interaction
electric motor peak torquenominal torque at MCR in free running condition
response torque along the propeller shaft line
maximum of the response torque 𝑄𝑄𝑟𝑟 (𝑡𝑡)maximum spindle torque of the blade for the ship’s service life
extreme spindle torque corresponding to the blade failure load 𝐹𝐹𝑒𝑒𝑒𝑒
Vibratory torque at considered component, taken from frequency
domain open water TVC
propeller radius
Safety factor
Safety factor for fatigue
Ice strength index for blade ice force
blade section radiusHydrodynamic propeller thrust in bollard condition
maximum backward propeller ice thrust for the ship’s service life
maximum forward propeller ice thrust for the ship’s service life
propeller thrust at MCR in free running condition
maximum response thrust along the shaft line
maximum torque capacity of flexible coupling
𝑇𝑇𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘 at 𝑁𝑁 = 1 load cycle
𝑇𝑇𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘 at 𝑁𝑁 = 5 × 104 load cycles
vibratory torque amplitude at 𝑁𝑁 = 106 load cycles
maximum range of 𝑇𝑇𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘 at 𝑁𝑁 = 5 × 104 load cycles
maximum blade section thickness
number of propeller blades
number of shear pins
duration of propeller blade/ice interaction expressed in rotation angle
the reduction factor for fatigue; scatter and test specimen size effectthe reduction factor for fatigue; variable amplitude loading effectthe reduction factor for fatigue; mean stress effecta reduction factor for fatigue correlating the maximum stressamplitude to the equivalent fatigue stress for 108 stress cycles
proof yield strength (at 0.2% plastic strain) of material
mean fatigue strength of blade material at 108 cycles to failure in sea
water
equivalent fatigue ice load stress amplitude for 108 stress cycles
characteristic fatigue strength for blade materialreference stress 𝜎𝜎𝑟𝑟𝑟𝑟𝑟𝑟1 = 0.6 𝜎𝜎0.2 + 0.4 𝜎𝜎𝑢𝑢
reference stress
𝜎𝜎𝑟𝑟𝑟𝑟𝑟𝑟2 = 0.7 𝜎𝜎𝑢𝑢
or
𝜎𝜎𝑟𝑟𝑟𝑟𝑟𝑟2 = 0.6 𝜎𝜎0.2 + 0.4 𝜎𝜎𝑢𝑢 whichever is lessPage 4 of 44

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MPa
𝜎𝜎𝑠𝑠𝑠𝑠MPa
𝜎𝜎𝑢𝑢(𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 MPa

maximum stress resulting from 𝐹𝐹𝑏𝑏 or 𝐹𝐹𝑓𝑓
ultimate tensile strength of blade material
principal stress caused by the maximum backward propeller ice load

(𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 MPa

maximum ice load stress amplitude at the considered location on theblademean stressblade stress amplitude distribution(𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 MPa
MPa
𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚(𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝐴𝐴 (𝑁𝑁) MPa
4.2

principal stress caused by the maximum forward propeller ice load

Definition of Loads
Table 2: Definitions of loads

𝐹𝐹𝑏𝑏

𝐹𝐹𝑓𝑓

𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠

𝑇𝑇𝑏𝑏

𝑇𝑇𝑓𝑓

Definition
The maximum lifetime backward
force on a propeller blade resulting
from propeller/ice interaction,
including hydrodynamic loads on thatblade. The direction of the force isperpendicular to 0.7𝑅𝑅 chord line. See
Figure 1.
The maximum lifetime forward force
on a propeller blade resulting frompropeller/ice interaction, includinghydrodynamic loads on that blade.
The direction of the force isperpendicular to 0.7𝑅𝑅 chord line.
The maximum lifetime spindle torqueon a propeller blade resulting frompropeller/ice interaction, includinghydrodynamic loads on that blade.
The maximum lifetime thrust on
propeller (all blades) resulting frompropeller/ice interaction. The
direction of the thrust is the propeller
shaft direction and the force is
opposite to the hydrodynamic thrust.
The maximum lifetime thrust on
propeller (all blades) resulting frompropeller/ice interaction. The
direction of the thrust is the propeller
shaft direction acting in the directionof hydrodynamic thrust.

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Use of the load in design process
Design force for strength calculationof the propeller blade.

Design force for calculation ofstrength of the propeller blade.

In designing the propeller strength,
the spindle torque is automaticallytaken into account because thepropeller load is acting on the blade
as distributed pressure on the leadingedge or tip area.
Is used for estimation of the response
thrust 𝑇𝑇𝑟𝑟 . 𝑇𝑇𝑏𝑏 can be used as an
estimate of excitation for axial
vibration calculations. However, axial
vibration calculations are not requiredin the rules.
Is used for estimation of the response
thrust 𝑇𝑇𝑟𝑟 . 𝑇𝑇𝑓𝑓 can be used as an
estimate of excitation for axial
vibration calculations. However, axial
vibration calculations are not requiredin the rules.

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𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚
𝐹𝐹𝑒𝑒𝑒𝑒𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠
𝑄𝑄𝑟𝑟

𝑇𝑇𝑟𝑟

The maximum ice-induced torqueresulting from propeller/ice
interaction on one propeller blade,including hydrodynamic loads on thatblade.
Ultimate blade load resulting fromblade loss through plastic bending.
The force that is needed to cause
total failure of the blade so thatplastic hinge is caused to the root
area. The force is acting on 0.8𝑅𝑅.
Maximum spindle torque resulting
from blade failure load
Maximum response torque along thepropeller shaft line, taking into
account the dynamic behaviour ofthe shaft line for ice excitation(torsional vibration) andhydrodynamic mean torque on
propeller.
Maximum response thrust along
shaft line, taking into account the
dynamic behaviour of the shaft line
for ice excitation (axial vibration) andhydrodynamic mean thrust on
propeller.

Is used for estimation of the response
torque 𝑄𝑄𝑟𝑟 along the propulsion shaft
line and as excitation for torsional
vibration calculations.
Blade failure load is used todimension the blade bolts, pitch
control mechanism, propeller shaft,propeller shaft bearing and trust
bearing. The objective is to guaranteethat total propeller blade failure should
not cause damage to othercomponents.
Is used to ensure pyramid strengthprinciple for the pitching mechanism
Design torque for propeller shaft line
components.

Design thrust for propeller shaft line
components.

Shaft
direction
Back side
𝐹𝐹𝑏𝑏

Direction ofrotation

Figure 1 : Direction of the backward blade force resultant taken perpendicular to thechord line at radius 𝟎𝟎. 𝟕𝟕𝟕𝟕. Ice contact pressure at leading edge is shown with small
arrows.
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5

Design Ice Loads

5.1

General

These Rules cover open and ducted type propellers situated at the stern of a vessel having
controllable pitch or fixed pitch blades. Ice loads on bow-mounted propellers shall receive
special consideration at the discretion of each classification society. The given loads are
expected, single occurrence, maximum values for the whole ship’s service life for normal
operational conditions, including loads resulting from directional change of rotation whereapplicable. These loads do not cover off-design operational conditions, for example when astopped propeller is dragged through ice. These Rules also cover loads due to propeller ice
interaction for azimuthing and fixed thrusters with geared transmission or an integrated
electric motor (“geared and podded propulsors”). However, the load models of the regulations
do not include propeller/ice interaction loads when ice enters the propeller of a turned
azimuthing thruster from the side (radially) or loads when ice blocks hit on the propeller hubof a pulling propeller. Ice loads resulting from ice impacts on the body of thrusters shall be
estimated on a case by case basis, however are not included within the following section.
The loads given in section 5.3 are total loads including ice-induced loads and hydrodynamic
loads (unless otherwise stated) during ice interaction and are to be applied separately (unlessotherwise stated) and are intended for component strength calculations only.
𝐹𝐹𝑏𝑏 is the maximum force experienced during the lifetime of the ship that bends a propeller
blade backwards when the propeller mills an ice block while rotating ahead. 𝐹𝐹𝑓𝑓 is the
maximum force experienced during the lifetime of the ship that bends a propeller blade
forwards when the propeller mills an ice block while rotating ahead. 𝐹𝐹𝑏𝑏 and 𝐹𝐹𝑓𝑓 originate fromdifferent propeller/ice interaction phenomena, which do not act simultaneously. Hence they
are to be applied separately.
5.2

Ice Class Factors

The dimensions of the considered design ice block are 𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖 × 2𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖 × 3𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖 . The design ice
block and ice strength index (𝑆𝑆𝑖𝑖𝑖𝑖𝑖𝑖 ) are used for the estimation of propeller ice loads. Both 𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖
and 𝑆𝑆𝑖𝑖𝑖𝑖𝑖𝑖 are defined for each Ice class in Table 3 below.
Table 3: Design Ice Class Factors

Ice Class
PC1
PC2
PC3
PC4
PC5
PC6
PC7

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𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖 [m]
4.0
3.5
3.0
2.5
2.0
1.75
1.5

𝑆𝑆𝑖𝑖𝑖𝑖𝑖𝑖 [-]
1.2
1.1
1.1
1.1
1.1
1
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5.3

Propeller Ice Interaction Loads

5.3.1 Maximum backward blade force 𝑭𝑭𝒃𝒃 for open propellers
when 𝐷𝐷 < 𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 :𝐸𝐸𝐸𝐸𝐸𝐸 0.3
� ∙ 𝐷𝐷 2
𝑍𝑍

𝐹𝐹𝑏𝑏 = 27 ∙ 𝑆𝑆𝑖𝑖𝑖𝑖𝑖𝑖 ∙ (𝑛𝑛 ∙ 𝐷𝐷)0.7 ∙ �[kN][Equation 1]

𝐹𝐹𝑏𝑏 = 23 ∙ 𝑆𝑆𝑖𝑖𝑖𝑖𝑖𝑖 ∙ (𝑛𝑛 ∙ 𝐷𝐷)0.7 ∙ �[kN][Equation 2]

𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 0.85 ∙ (𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖 )1.4[m]

[Equation 3]

when 𝐷𝐷 ≥ 𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 :where:

𝐸𝐸𝐸𝐸𝐸𝐸 0.3
� ∙ (𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖 )1.4 ∙ 𝐷𝐷
𝑍𝑍

Here 𝑛𝑛 is the nominal rotational speed at MCR in the free running open water condition for
CP-propellers and 85% of the nominal rotational speed (at MCR free running condition) for a
FP-propeller (regardless driving engine type) [rps].
For vessels with the additional notation Icebreaker, the above stated backward blade force 𝐹𝐹𝑏𝑏
shall be multiplied by a factor of 1.1.
5.3.2 Maximum forward blade force 𝑭𝑭𝒇𝒇 for open propellers
when 𝐷𝐷 < 𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 :𝐸𝐸𝐸𝐸𝐸𝐸� ∙ 𝐷𝐷 2
𝑍𝑍𝐹𝐹𝑓𝑓 = 250 ∙ �when 𝐷𝐷 ≥ 𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 :𝐹𝐹𝑓𝑓 = 500 ∙ �
where:

𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = �

1

𝑑𝑑
1−
𝐷𝐷

2

1−

𝑑𝑑
𝐷𝐷

𝐸𝐸𝐸𝐸𝐸𝐸� ∙ 𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖 ∙ � 𝑍𝑍 � ∙ 𝐷𝐷

� ∙ 𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖[kN][Equation 4][kN][Equation 5][m][Equation 6]

5.3.3 Loaded area on the blade for open propellers
Load cases 1-4 shall be covered, as given in Table 4, for CP and FP propellers. In order toobtain blade ice loads for a reversing propeller, load case 5 shall also be covered forpropellers where reversing is possible.

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Table 4: Loaded areas and load case definition for open propellers
Force

Loaded area

Load case 1

𝐹𝐹𝑏𝑏

Uniform pressure applied on theback of the blade (suction side) toan area from 0.6R to the tip andfrom the leading edge to 0.2 times
the chord length.

Load case 2

50% of 𝐹𝐹𝑏𝑏

Uniform pressure applied on theback of the blade (suction side) on
the propeller tip area outside 0.9R
radius.

Load case 3

𝐹𝐹𝑓𝑓

Uniform pressure applied on theblade face (pressure side) to anarea from 0.6R to the tip and fromthe leading edge to 0.2 times thechord length.

Load case 4

50% of 𝐹𝐹𝑓𝑓

Uniform pressure applied on
propeller face (pressure side) on
the propeller tip area outside 0.9R
radius.

Load case 5

60% of 𝐹𝐹𝑓𝑓 or
60% of 𝐹𝐹𝑏𝑏 ,whichever isgreater

Uniform pressure applied on
propeller face (pressure side) toan area from 0.6R to the tip andfrom the trailing edge to 0.2 times
the chord length(cont)

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Right-handed propeller
blade seen from behind

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5.3.4 Maximum backward blade ice force 𝑭𝑭𝒃𝒃 for ducted propellers

when 𝐷𝐷 < 𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 :𝐸𝐸𝐸𝐸𝐸𝐸 0.3
� ∙ 𝐷𝐷 2
𝑍𝑍

𝐹𝐹𝑏𝑏 = 9.5 ∙ 𝑆𝑆𝑖𝑖𝑖𝑖𝑖𝑖 ∙ (𝑛𝑛 ∙ 𝐷𝐷)0.7 ∙ �[kN][Equation 7]

𝐹𝐹𝑏𝑏 = 66 ∙ 𝑆𝑆𝑖𝑖𝑖𝑖𝑖𝑖 ∙ (𝑛𝑛 ∙ 𝐷𝐷)0.7 ∙ �[kN][Equation 8]

𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 4 ∙ 𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖[m][Equation 9]

when 𝐷𝐷 ≥ 𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 :𝐸𝐸𝐸𝐸𝐸𝐸 0.3
� ∙ (𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖 )1.4 ∙ 𝐷𝐷 0.6
𝑍𝑍

where:

𝑛𝑛 shall be taken as in 5.3.1

For vessels with the additional notation Icebreaker, the above stated backward blade force 𝐹𝐹𝑏𝑏
shall be multiplied by a factor 1.1.
5.3.5 Maximum forward blade ice force 𝑭𝑭𝒇𝒇 for ducted propellers
when 𝐷𝐷 ≤ 𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 :𝐸𝐸𝐸𝐸𝐸𝐸� ∙ 𝐷𝐷 2
𝑍𝑍𝐹𝐹𝑓𝑓 = 250 ∙ �when 𝐷𝐷 > 𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 :𝐸𝐸𝐸𝐸𝐸𝐸1� ∙ 𝐷𝐷 ∙𝑑𝑑 ∙ 𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖
𝑍𝑍
�1− �

𝐹𝐹𝑓𝑓 = 500 ∙ �
where:

𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =

2

𝑑𝑑
𝐷𝐷

�1− �

[kN]

[Equation 10][kN][Equation 11][m][Equation 12]

𝐷𝐷∙ 𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖

5.3.6 Loaded area on the blade for ducted propellers
Load cases 1 and 3 shall be covered as given in Table 5 for all propellers. In order to obtainblade ice loads for a reversing propeller, load case 5 shall also be covered for propellers,
where reversing is possible.

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Table 5: Loaded areas and load case definition for ducted propellers

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Force

Loaded area

Load case 1

𝐹𝐹𝑏𝑏

Uniform pressure applied on theback of the blade (suction side) toan area from 0.6R to the tip andfrom the leading edge to 0.2 times
the chord length.

Load case 3

𝐹𝐹𝑓𝑓

Uniform pressure applied on theblade face (pressure side) to anarea from 0.6R to the tip and fromthe leading edge to 0.5 times thechord length.

Load case 5

60% of 𝐹𝐹𝑓𝑓 or
60% of 𝐹𝐹𝑏𝑏 ,whichever isgreater

Uniform pressure applied on
propeller face (pressure side) toan area from 0.6R to the tip andfrom the trailing edge to 0.2 times
the chord length.

(cont)

Right handed propeller
blade seen from behind

5.3.7 Maximum blade spindle torque 𝑸𝑸𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 for open and ducted propellers

The spindle torque 𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 around the axis of the blade fitting shall be determined both for the
maximum backward blade force 𝐹𝐹𝑏𝑏 and forward blade force 𝐹𝐹𝑓𝑓 , which are applied as per
Table 4 and Table 5. If the above method gives a value which is less than the default value
given by the formula below, the default value shall be used.
Default value 𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 0.25 ∙ 𝐹𝐹 ∙ 𝑐𝑐0.7[kNm][Equation 13]

where:

𝐹𝐹 is taken as either 𝐹𝐹𝑏𝑏 or 𝐹𝐹𝑓𝑓 , whichever has the greater absolute value.

The blade failure spindle torque 𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠 is defined under 5.4.

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5.3.8 Load distributions (spectra) for blade loads
The Weibull-type distribution (probability that 𝐹𝐹𝑖𝑖𝑖𝑖𝑖𝑖 exceeds (𝐹𝐹𝑖𝑖𝑖𝑖𝑖𝑖 )𝑚𝑚𝑚𝑚𝑚𝑚 ), as given in Figure 2 isused for the fatigue design of the blade.
𝐹𝐹

𝑃𝑃 �(𝐹𝐹 𝑖𝑖𝑖𝑖𝑖𝑖)

𝑖𝑖𝑖𝑖𝑖𝑖 𝑚𝑚𝑚𝑚𝑚𝑚

where:≥ (𝐹𝐹𝐹𝐹

𝑖𝑖𝑖𝑖𝑖𝑖 )𝑚𝑚𝑚𝑚𝑚𝑚

� = 𝑒𝑒𝐹𝐹
�𝐹𝐹𝑖𝑖𝑖𝑖𝑖𝑖 ��−�

𝑚𝑚𝑚𝑚𝑚𝑚𝑘𝑘

� ∙𝑙𝑙𝑙𝑙(𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 )�

[Equation 14]

𝑘𝑘= shape parameter of the spectrum

𝐹𝐹𝑖𝑖𝑖𝑖𝑖𝑖= random variable for ice loads on the blade, 0 ≤ 𝐹𝐹𝑖𝑖𝑖𝑖𝑖𝑖 ≤ (𝐹𝐹𝑖𝑖𝑖𝑖𝑖𝑖 )𝑚𝑚𝑚𝑚𝑚𝑚 .

𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 = number of load cycles in the spectrum, see 5.3.9
This results in a blade stress amplitude distribution(𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝐴𝐴 (𝑁𝑁) = (𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 ∙ �1 −where:(𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 =1log (𝑁𝑁) 𝑘𝑘�log (𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 )[Equation 15](𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 −(𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏[Equation 16]

2

The shape parameter 𝑘𝑘 = 0.75 shall be used for the ice force distribution of an open propeller
and the shape parameter 𝑘𝑘 = 1.0 for that of a ducted propeller blade.
1,E+00
Propability of exceeding for N=1E7

I3

1,E-01

0

0,2

0,4

0,6

0,8

1

Weibull distribution/k=1

1,E-02

Weibull distribution/k=0.75

1,E-03
1,E-04
1,E-05
1,E-061,E-07
Fice/(Ficemax)

Figure 2: The Weibull-type distribution (probability that 𝑭𝑭𝒊𝒊𝒊𝒊𝒊𝒊 exceeds (𝑭𝑭𝒊𝒊𝒊𝒊𝒊𝒊 )𝒎𝒎𝒎𝒎𝒎𝒎) that isused for fatigue design.

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5.3.9 Number of ice loads
Number of load cycles 𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 in the load spectrum per blade is to be determined according to
the formula:[Equation 17]

𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑘𝑘1 ∙ 𝑘𝑘2 ∙ 𝑁𝑁𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ∙ 𝑛𝑛
where:

𝑁𝑁𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = reference number of impacts per propeller revolution for each ice class (Table 6)
Table 6: Reference number of impacts

𝑘𝑘1

𝑘𝑘2

Ice Class
𝑁𝑁𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

PC1
21 x 106PC2
17 x 106PC3
15 x 106PC4
13 x 106PC5
11 x 106PC7
6 x 106= 1 for centre propeller= 2 for wing propeller= 3 for pulling propeller (wing and centre)= 0.8 - f

when

f<0

= 0.8 - 0.4·f

when

0≤f≤1

= 0.6 - 0.2·f

when

1< f ≤ 2.5

= 0.1

when

f > 2.5

where the immersion function 𝑓𝑓 is:

𝑓𝑓 =

PC6
9 x 106ℎ0 −𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖
𝐷𝐷/2[Equation 18]

If ℎ0 is not known, ℎ𝑜𝑜 = 𝐷𝐷/2.

For vessels with the additional notation Icebreaker, the above stated number of load cycles
𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 shall be multiplied by a factor of 3.
For components that are subject to loads resulting from propeller/ice interaction with all thepropeller blades, the number of load cycles (𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 ) is to be multiplied by the number ofpropeller blades (𝑍𝑍).
5.4

Blade Failure Load for both Open and Ducted Propellers

5.4.1 Bending Force, 𝑭𝑭𝒆𝒆𝒆𝒆

The minimum load required resulting in blade failure through plastic bending. This shall becalculated iteratively along the radius of the blade from blade root to 0.5R using below
Equation 19 with the ultimate load assumed to be acting at 0.8R in the weakest direction.

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𝐹𝐹𝑒𝑒𝑒𝑒 =0.3∙𝑐𝑐∙𝑡𝑡 2 ∙𝜎𝜎𝑟𝑟𝑟𝑟𝑟𝑟1

where:

0.8∙𝐷𝐷−2∙𝑟𝑟

∙ 103

[kN]

[Equation 19][MPa]𝜎𝜎𝑟𝑟𝑟𝑟𝑟𝑟1 = 0.6 ∙ 𝜎𝜎0.2 + 0.4 ∙ 𝜎𝜎𝑢𝑢

𝜎𝜎𝑢𝑢 (minimum ultimate tensile strength to be specified on the drawing) and 𝜎𝜎0.2 (minimum yieldor 0.2% proof strength to be specified on the drawing) are representative values for the blade
material
𝑐𝑐, 𝑡𝑡 and 𝑟𝑟 are respectively the actual chord length, maximum thickness and radius of thecylindrical root section of the blade, which is the weakest section outside the root fillet locatedtypically at the termination of the fillet into the blade profile.
The classification society may approve alternative means of failure load calculation by meansof an appropriate stress analysis reflecting the non-linear plastic material behaviour of theactual blade. A blade is regarded as having failed, if the tip is bent by more than 10% of thepropeller diameter.
5.4.2 Spindle Torque, 𝑸𝑸𝒔𝒔𝒔𝒔𝒔𝒔

The maximum spindle torque due to a blade failure load acting at 0.8R shall be determined.
The force that causes blade failure typically reduces when moving from the propeller centre
towards the leading and trailing edges. At a certain distance from the blade centre of rotation
the maximum spindle torque will occur. This maximum spindle torque shall be defined by anappropriate stress analysis or using equation 20 below.
𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠 = 𝑚𝑚𝑚𝑚𝑚𝑚(𝑐𝑐𝐿𝐿𝐿𝐿0.8 ; 0.8 ∙ 𝑐𝑐𝑇𝑇𝑇𝑇0.8 ) ∙ 𝐶𝐶𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ∙ 𝐹𝐹𝑒𝑒𝑒𝑒
where :

𝐶𝐶𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝐶𝐶𝑠𝑠𝑠𝑠 ∙ 𝐶𝐶𝑓𝑓𝑓𝑓𝑓𝑓 = 0.7 ∙ �1 − �4 ∙𝐸𝐸𝐸𝐸𝐸𝐸 3
� �
𝑍𝑍

[kNm]

[Equation 20][-][Equation 21]

𝐶𝐶𝑠𝑠𝑠𝑠 is non-dimensional parameter taking into account the spindle arm

𝐶𝐶𝑓𝑓𝑓𝑓𝑓𝑓 is non-dimensional parameter taking into account the reduction of blade failure force atthe location of maximum spindle torque.
If 𝐶𝐶𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 is below 0.3, a value of 0.3 shall be used for 𝐶𝐶𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 .

𝑐𝑐𝐿𝐿𝐿𝐿0.8 c is the leading edge portion of the chord length at 0.8R

𝑐𝑐𝑇𝑇𝑇𝑇0.8 is the trailing edge portion of the chord length at 0.8R

The figure below illustrates the spindle torque values due to blade failure loads across thewhole chord length.

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Figure 3: Schematic figure showing blade failure load and related spindle torque when
the force acts at different location on the chord line at radius 0.8R.
5.5

Axial design loads acting on open and ducted propellers

5.5.1 Maximum ice thrust on propeller 𝑻𝑻𝒇𝒇 and 𝑻𝑻𝒃𝒃 acting on open and ducted propellers
The maximum forward and backward ice thrusts are given by the following formula:
𝑇𝑇𝑓𝑓 = 1.1 ∙ 𝐹𝐹𝑓𝑓

𝑇𝑇𝑏𝑏 = 1.1 ∙ 𝐹𝐹𝑏𝑏

[kN]

[Equation 22][kN][Equation 23]

However, the load models within this UR do not include propeller/ice interaction loads wherean ice block hits the propeller hub of a pulling propeller.
5.5.2 Design thrust along the propulsion shaft line for open and ducted propellers
The design thrust along the propeller shaft line is to be calculated with the formulae below.
The greater value of the forward and backward directional load shall be taken as the design
load for both directions. The factors 2.2 and 1.5 take into account the dynamic magnification
resulting from axial vibration.
In a forward direction
𝑇𝑇𝑟𝑟 = 𝑇𝑇 + 2.2 ∙ 𝑇𝑇𝑓𝑓[kN]

[Equation 24]

𝑇𝑇𝑟𝑟 = 1.5 ∙ 𝑇𝑇𝑏𝑏

[kN]

[Equation 25]

In a backward direction

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If the hydrodynamic bollard thrust, 𝑇𝑇, is not known, 𝑇𝑇 is to be taken as follows:
Table 7: Guidance for bollard thrust values

Propeller type
CP propellers (open)
CP propellers (ducted)
FP propellers driven by turbine or electric motor
FP propellers driven by diesel engine (open)
FP propellers driven by diesel engine (ducted)

𝑇𝑇1.25 𝑇𝑇𝑛𝑛
1.1 𝑇𝑇𝑛𝑛
𝑇𝑇𝑛𝑛
0.85 𝑇𝑇𝑛𝑛
0.75 𝑇𝑇𝑛𝑛

Here, 𝑇𝑇𝑛𝑛 is the nominal propeller thrust at MCR in the free running open water condition.
For pulling type propellers ice interaction loads on propeller hub must be considered inaddition to the above. These will be specially considered by the Classification Society.
5.6

Torsional design loads acting on open and ducted propellers

5.6.1 Design ice torque on propeller 𝑸𝑸𝒎𝒎𝒎𝒎𝒎𝒎 for open propellers

𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚 is the maximum torque on a propeller resulting from ice/propeller interaction.
when 𝐷𝐷 < 𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 :

𝑑𝑑
𝐷𝐷

𝑃𝑃

0.16

𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑘𝑘𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 ∙ �1 − � ∙ � 𝐷𝐷0.7 �
where:∙ (𝑛𝑛 ∙ 𝐷𝐷)0.17 ∙ 𝐷𝐷 3

[kNm]

[Equation 26]

𝑘𝑘𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 = 14.7 for PC1 – PC5; and𝑘𝑘𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 = 10.9 for PC6 – PC7
when 𝐷𝐷 ≥ 𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 :

𝑑𝑑
𝐷𝐷

𝑃𝑃

0.16

𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚 = 1.9 ∙ 𝑘𝑘𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 ∙ �1 − � ∙ (𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖 )1.1 ∙ � 𝐷𝐷0.7 �∙ (𝑛𝑛 ∙ 𝐷𝐷)0.17 ∙ 𝐷𝐷1.9

𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 1.8 ∙ 𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖[m]where:[kNm][Equation 27][Equation 28]

𝑛𝑛 is the rotational propeller speed in rev/s in bollard condition. If not known, n is to be taken
as follows:
Table 8: Guidance for rotational speeds to calculate torsional loads
Propeller type
CP propellers
FP propellers driven by turbine or electricmotor
FP propellers driven by diesel engine

Rotational speed 𝑛𝑛
𝑛𝑛𝑛𝑛
𝑛𝑛𝑛𝑛
0.85 𝑛𝑛𝑛𝑛

For CP propellers, the propeller pitch 𝑃𝑃0.7 shall correspond to MCR in bollard condition. If not
known, 𝑃𝑃0.7 is to be taken as 0.7⋅𝑃𝑃0.7𝑛𝑛 , where 𝑃𝑃0.7𝑛𝑛 is the propeller pitch at MCR in freerunning condition.
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5.6.2 Design ice torque on propeller 𝑸𝑸𝒎𝒎𝒎𝒎𝒎𝒎 for ducted propellers
when 𝐷𝐷 < 𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 :

𝑑𝑑
𝐷𝐷

𝑃𝑃

0.16

𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑘𝑘𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 ∙ �1 − � ∙ � 𝐷𝐷0.7 �
where:∙ (𝑛𝑛 ∙ 𝐷𝐷)0.17 ∙ 𝐷𝐷 3

[kNm]

[Equation 29]

𝑘𝑘𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 10.4 for PC1 – PC5; and𝑘𝑘𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 7.7 for PC6 – PC7

when 𝐷𝐷 ≥ 𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 :

𝑑𝑑
𝐷𝐷

𝑃𝑃
𝐷𝐷

0.16

𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚 = 1.9 ∙ 𝑘𝑘𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 ∙ �1 − � ∙ (𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖 )1.1 ∙ � 0.7 �
where:∙ (𝑛𝑛𝑛𝑛)0.17 ∙ 𝐷𝐷1.9 [kNm][m]𝐷𝐷𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 1.8 ∙ 𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖[Equation 30][Equation 31]

𝑛𝑛 shall be taken as in 5.6.1.

For CP propellers, the propeller pitch 𝑃𝑃0.7 shall correspond to MCR in bollard condition. If not
known, 𝑃𝑃0.7 is to be taken as 0.7⋅𝑃𝑃0.7𝑛𝑛 , where 𝑃𝑃0.7𝑛𝑛 is the propeller pitch at MCR in freerunning condition.
5.6.3 Ice torque excitation for open and ducted propellers

The given excitations are used to estimate the maximum torque likely to be experienced once
during the service life of the ship. The following load cases are intended to reflect theoperational loads on the propulsion system when the propeller interacts with ice and thecorresponding reaction of the complete system. The ice impact and system response cause
loads in the individual shaft line components. The ice torque 𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚 may be taken as aconstant value in the complete speed range. When considerations at specific shaft speeds
are performed a relevant 𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚 may be calculated using the relevant speed.
Diesel engine plants without an elastic coupling shall be calculated at the least favourable
phase angle for ice versus engine excitation, when calculated in time domain. The engine
firing pulses shall be included in the calculations and their standard steady state harmonics
can be used. A phase angle between ice and gas force excitation does not need to be
regarded in frequency domain analysis. Misfiring does not need to be considered.
If there is a blade order resonance just above MCR speed, calculations shall cover therotational speeds up to 105% of MCR speed.
See also Guidelines for calculations given in 5.7

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5.6.3.1

Excitation for the time domain calculation

The propeller ice torque excitation for shaft line transient dynamic analysis (time domain) is
defined as a sequence of blade impacts which are of half sine shape and occur at the blade.
The torque due to a single blade ice impact as a function of the propeller rotation angle isthen defined as:[Equation 32]

𝑄𝑄(𝜑𝜑) = 𝐶𝐶𝑞𝑞 ∙ 𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚 ∙ sin�𝜑𝜑(180/𝛼𝛼𝑖𝑖 )�

when 𝜑𝜑 rotates from 0 to 𝛼𝛼𝑖𝑖 plus integer revolutions.

𝑄𝑄(𝜑𝜑) = 0

when 𝜑𝜑 rotates from 𝛼𝛼𝑖𝑖 to 360 plus integer revolutions.

Where
𝜑𝜑 =

rotation angle starting when the first impact occurs

𝐶𝐶𝑞𝑞 and 𝛼𝛼𝑖𝑖 parameters are given in the Table 9 below. 𝛼𝛼𝑖𝑖 is the duration of propeller blade/ice
interaction expressed in propeller rotation angle.
Table 9: Ice impact magnification and duration factors for different blade numbers
Torque excitation
Excitation case 1
Excitation case 2
Excitation case 3
Excitation case 4

Propeller/
ice interaction
Single ice block
Single ice blockTwo ice blocks (phaseshift 360/(2· 𝑍𝑍 ) deg.)Single ice block

𝐶𝐶𝑞𝑞

0.75
1.0
0.5

𝛼𝛼𝑖𝑖 [deg]𝑍𝑍=3 𝑍𝑍=4
90
90
135
135
45
45

𝑍𝑍=5
72
135
36

𝑍𝑍=6
60
135
30

0.5

45

36

30

45

The total ice torque is obtained by summing the torque of single blades, taking into accountthe phase shift 360 deg./𝑍𝑍.
At the beginning and at the end of the milling sequence (within calculated duration) linear
ramp functions shall be used to increase 𝐶𝐶𝑞𝑞 to its maximum within one propeller revolution
and vice versa to decrease it to zero (see examples for different 𝑍𝑍 numbers in the appendix).
The number of propeller revolutions during a milling sequence shall be obtained from theformula:[Equation 33]

𝑁𝑁𝑄𝑄 = 2 ∙ 𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖

The number of impacts is 𝑍𝑍 ∙ 𝑁𝑁𝑄𝑄 for blade order excitation.

An illustration of all excitation cases for different blade numbers is given in the Appendix.
The dynamic simulation shall be performed for all excitation cases starting at MCR nominal,
MCR bollard condition and just above all resonance speeds (1st engine and 1st blade
harmonic), so that the resonant vibration responses can be obtained. For a fixed pitch
propeller plant the dynamic simulation shall also cover bollard pull condition with acorresponding speed assuming maximum possible output of the engine.
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If a speed drop occurs down to stand still of the main engine, it indicates that the engine may
not be sufficiently powered for the intended service task. For the consideration of loads, themaximum occurring torque during the speed drop process shall be applied. On these cases,
the excitation shall follow the shaft speed.
5.6.3.2

Frequency domain excitation

For frequency domain calculations the following torque excitation may be used. The
excitation has been derived so that the time domain half sine impact sequences have been
assumed to be continuous and the Fourier series components for blade order and twice theblade order components have been derived. The frequency domain analysis is generally
considered as conservative compared to the time domain simulation provided there is a first
blade order resonance in the considered speed range.
[kNm]

𝑄𝑄𝐹𝐹(𝜑𝜑) = 𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚 ∙ �𝐶𝐶𝑞𝑞0 + 𝐶𝐶𝑞𝑞1 ∙ sin(𝑍𝑍 ∙ 𝐸𝐸0 ∙ 𝜑𝜑 + 𝛼𝛼1 ) + 𝐶𝐶𝑞𝑞2 ∙ sin(2 ∙ 𝑍𝑍 ∙ 𝐸𝐸0 ∙ 𝜑𝜑 + 𝛼𝛼2 )�

[Equation 34]

where :
𝐶𝐶𝑞𝑞0

= mean torque component

𝐶𝐶𝑞𝑞2= second blade order excitation amplitude

𝐶𝐶𝑞𝑞1= first blade order excitation amplitude

𝜑𝜑= angle of rotation

𝑍𝑍= number of blades

𝛼𝛼1,2 = phase angle of excitation component
Table 10: Coefficients for simplified excitation torque estimation
Torque excitation
Excitation case 1
Excitation case 2
Excitation case 3
Excitation case 4
Torque excitation
Excitation case 1
Excitation case 2
Excitation case 3
Excitation case 4
Torque excitation
Excitation case 1
Excitation case 2
Excitation case 3
Excitation case 4

𝐶𝐶𝑞𝑞0
0,375
0.7
0.25
0.2

𝐶𝐶𝑞𝑞1
0.375
0.33
0.25
0.25

𝛼𝛼1
-90
-90
-90
0

𝐶𝐶𝑞𝑞0
𝐶𝐶𝑞𝑞1
0.45
0.36
0.9375
0
0.25
0.251
0.2
0.25

𝛼𝛼1
-90
-90
-90
0

𝐶𝐶𝑞𝑞0
0.45
1.19
0.3
0.2

𝛼𝛼1
-90
-90
-90
0

𝐶𝐶𝑞𝑞1
0.36
0.17
0.25
0.25

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𝑍𝑍=3

𝐶𝐶𝑞𝑞2
0
0.05
0
0.05

𝛼𝛼2
0
-45
0
-90

𝐸𝐸0
1
1
2
1

𝐶𝐶𝑞𝑞2
0.06
0.0625
0
0.05

𝛼𝛼2
-90
-90
0
-90

𝐸𝐸0
1
1
2
1

𝛼𝛼2
-90
-90
-90
-90

𝐸𝐸0
1
1
2
1

𝑍𝑍=4

𝑍𝑍=5

𝐶𝐶𝑞𝑞2
0.06
0.02
0.048
0.05

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Torque excitation

I3(cont)

Excitation case 1
Excitation case 2
Excitation case 3
Excitation case 4

𝐶𝐶𝑞𝑞0
0.45
1.435
0.3
0.2

𝐶𝐶𝑞𝑞1
0.375
0.1
0.25
0.25

𝛼𝛼1
-90
-90
-90
0

𝑍𝑍=6

𝐶𝐶𝑞𝑞2
0.05
0
0.048
0.05

𝛼𝛼2
-90
0
-90
-90

𝐸𝐸0
1
1
2
1

Torsional vibration responses shall be calculated for all excitation cases.
The results of the relevant excitation cases at the most critical rotational speeds are to be
used in the following way:
The highest response torque (between the various lumped masses in the system) is in thefollowing referred to as peak torque 𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 .

The highest torque amplitude during a sequence of impacts is to be determined as half of therange from max to min torque and is referred to as 𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 .
An illustration of 𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 is given in Figure 4. It can be determined by
𝑚𝑚𝑚𝑚𝑚𝑚�𝑄𝑄𝑟𝑟 (𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡)�−𝑚𝑚𝑚𝑚𝑚𝑚�𝑄𝑄𝑟𝑟 (𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡)�

𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 = �

2

�

[kNm]

[Equation 35]

Qpeak

Qr

Qe

2·QAmax
Figure 4: Interpretation of different torques in a measured curve, as example

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5.6.4 Design torque along shaft linea) If there is no relevant first order propeller torsional resonance in the range 20% (of 𝑛𝑛𝑛𝑛 )above and 20% below the maximum operating speed in bollard condition (see Table 8), thefollowing estimation ([Equation 36] and [Equation 37] respectively) of the maximum response
torque can be used to calculate the design torque along the propeller shaft line.
𝑄𝑄𝑟𝑟 = 𝑄𝑄𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 + 𝑄𝑄𝑣𝑣𝑣𝑣𝑣𝑣 + 𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚 ∙

𝐼𝐼
𝐼𝐼𝑡𝑡

[kNm]

[Equation 36]

Equation 36 is to be applied for directly coupled two stroke Diesel engines without flexible
coupling.
For all other plants:
𝑄𝑄𝑟𝑟 = 𝑄𝑄𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 + 𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚 ∙where:

𝐼𝐼
𝐼𝐼𝑡𝑡

[kNm]

[Equation 37]- 𝐼𝐼 = equivalent mass moment of inertia of all parts on engine side of component underconsideration and- 𝐼𝐼𝑡𝑡 = equivalent mass moment of inertia of the whole propulsion system.

All the torques and the inertia moments shall be reduced to the rotation speed of the component
being examined.
If the maximum torque, 𝑄𝑄𝑒𝑒𝑚𝑚𝑎𝑎𝑎𝑎 , is not known, it shall be taken as follows:

Table 11: Guideline for the determination of maximum motor torque
Propeller type
Propellers driven by electric motor
CP propellers not driven by electric motor
FP propellers driven by turbine
FP propellers driven by diesel engine

Here 𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 is the electric motor peak torque.

𝑄𝑄𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒
𝑄𝑄𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚
𝑄𝑄𝑛𝑛
𝑄𝑄𝑛𝑛
0.75 𝑄𝑄𝑛𝑛b) If there is a first blade order torsional resonance in the range 20% (of 𝑛𝑛𝑛𝑛 ) above and 20%
below the maximum operating speed (bollard condition), the design torque (𝑄𝑄𝑟𝑟 ) of the shaft
component shall be determined by means of a dynamic torsional vibration analysis of theentire propulsion line in the time domain or alternatively in the frequency domain. It is thenassumed that the plant is sufficiently designed to avoid harmful operation in barred speed
range.
5.7 Guideline for torsional vibration calculation
The aim of torsional vibration calculations is to estimate the torsional loads for individual shaft
line components over the life time in order to determine scantlings for safe operation. The
model can be taken from the normal lumped mass elastic torsional vibration model(frequency domain) including the damping. Standard harmonics may be used to consider thegas forces. The engine torque - speed curve of the actual plant shall be applied.

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(cont)For time domain analysis the model should include the ice excitation at propeller, the mean
torques provided by the prime mover and the hydrodynamic mean torque produced by thepropeller as well as any other relevant excitations. The calculations should cover the variationof phase between the ice excitation and prime mover excitation. This is extremely relevant for
propulsion lines with direct driven combustion engines.
For frequency domain calculations the load should be estimated as a Fourier component
analysis of the continuous sequence of half sine load peaks. The first and second order blade
components should be used for excitation. The calculation should cover the whole relevant
shaft speed range. The analysis of the responses at the relevant torsional vibration
resonances may be performed for open water (without ice excitation) and ice excitation
separately. The resulting maximum torque can be obtained for directly coupled plants by thefollowing superposition:[kNm]

𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = 𝑄𝑄𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 + 𝑄𝑄𝑜𝑜𝑜𝑜𝑜𝑜 + 𝑄𝑄𝑖𝑖𝑖𝑖𝑖𝑖[Equation 38]

where:

𝑄𝑄𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 is the maximum engine torque at considered rotational speed

𝑄𝑄𝑜𝑜𝑜𝑜𝑜𝑜 is the maximum open water response of engine excitation at considered shaft speed
and determined by frequency domain analysis
𝑄𝑄𝑖𝑖𝑖𝑖𝑖𝑖 is the calculated torque using frequency domain analysis for the relevant shaft speeds,
ice excitation cases 1-4, resulting in the maximum response torque due to ice excitation
6

Design6.1

Design Principle

The propulsion line shall be designed according to the pyramid strength principle in terms of
its strength. This means that the loss of the propeller blade shall not cause any significant
damage to other propeller shaft line components.
The propulsion line components shall withstand maximum and fatigue operational loads withthe relevant safety margin. The loads do not need to be considered for shaft alignment orother calculations of normal operational conditions.
6.2 Fatigue design in general
The design loads shall be based on the ice excitation and where necessary (shafting)
dynamic analysis, described as a sequence of blade impacts (5.6.3.1). The shaft response
torque shall be determined according 5.6.4.
The propulsion line components are to be designed so as to prevent accumulated fatigue
failure when considering the relevant loads using the linear elastic Miner’s rule as defined
below.
𝑛𝑛

𝑛𝑛

𝑛𝑛[Equation 39]

𝐷𝐷 = 𝑁𝑁1 + 𝑁𝑁2 + ⋯ + 𝑁𝑁𝑘𝑘 ≤ 1
or

1

2

𝑘𝑘

𝑗𝑗=𝑘𝑘 𝑛𝑛𝑗𝑗

[Equation 40]

𝐷𝐷 = ∑𝐽𝐽=1 𝑁𝑁 ≤ 1
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Where:
is the number of stress levels

𝑘𝑘

𝑁𝑁1…𝑘𝑘 is the number of load cycles to failure of the individual stress level class

𝑛𝑛1…𝑘𝑘 is the accumulated number of load cycles of the case under consideration, per class
Miners damage sum

𝐷𝐷

Guidance:
The stress distribution should be divided into a frequency load spectrum having minimum 10stress blocks (every 10 % of the load). Calculation with 5 stress blocks has been found to be
too conservative. The maximum allowable load is limited by 𝜎𝜎𝑟𝑟𝑟𝑟𝑟𝑟 2 for propeller blades andyield strength for all other components. The load distribution (spectrum) should be inaccordance with the Weibull distribution.
6.3

Propeller blades

6.3.1 Calculation of blade stresses due to static loads
The blade stresses (equivalent and principal stresses) shall be calculated for the design loads
given in section 5.3. Finite element analysis (FEA) shall be used for stress analysis as part of
the final approval for all propeller blades. The von Mises stresses, taken as 𝜎𝜎𝑠𝑠𝑠𝑠 , shall comply
with Equation 42.

Alternatively, the following simplified [Equation 41] can be used in estimating the blade stresses
for all propellers in the root area (r/R < 0.5) for final approval
𝑀𝑀

𝐵𝐵𝐵𝐵
𝜎𝜎𝑠𝑠𝑠𝑠 = 𝐶𝐶1 100∙𝑐𝑐𝑡𝑡
2

where:
constant 𝐶𝐶1 is the[MPa][Equation 41]

𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠.
𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 𝑤𝑤𝑤𝑤𝑤𝑤ℎ 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒

If the actual value is not available, 𝐶𝐶1 should be taken as 1.6.
- 𝑀𝑀𝐵𝐵𝐵𝐵 = (0.75 − 𝑟𝑟/𝑅𝑅) ∙ 𝑅𝑅 ∙ 𝐹𝐹, for relative radius r/R < 0.5- 𝐹𝐹 is the maximum of 𝐹𝐹𝑏𝑏 and 𝐹𝐹𝑓𝑓 , whichever is greater.

6.3.2

Acceptability criterion for static loads

The following criterion for calculated blade stresses shall be fulfilled:
𝜎𝜎𝑟𝑟𝑟𝑟𝑟𝑟 2
𝜎𝜎𝑠𝑠𝑠𝑠[-]≥ 1.3[Equation 42]

where:
𝜎𝜎𝑠𝑠𝑠𝑠 calculated stress for the design loads. If FE analysis is used in estimating the stresses,
von Mises stresses shall be used.

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(cont)

6.3.3 Fatigue design of propeller blade
6.3.3.1 General
For materials with a two slope S-N curve (Figure 5) the fatigue calculations defined in thischapter are not required if the following criterion is fulfilled.
𝜎𝜎𝑒𝑒𝑒𝑒𝑒𝑒 ≥ 𝐵𝐵1 ∙ 𝜎𝜎𝑟𝑟𝑟𝑟𝑟𝑟 2 𝐵𝐵2 ∙ 𝑙𝑙𝑙𝑙𝑙𝑙(𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 )𝐵𝐵3

[Equation 43]

where:

𝐵𝐵1, 𝐵𝐵2 and 𝐵𝐵3 are coefficients for open and ducted propellers, given in the Table 12 below.
Table 12: Coefficients to check a dispense from fatigue calculation
𝐵𝐵1
𝐵𝐵2
𝐵𝐵2

Open propeller
0.00328
1.00762.101

Ducted propeller
0.00223
1.0071
2.471

Where the above criterion is not fulfilled the fatigue requirements defined below shall beapplied:The fatigue design of the propeller blade is based on an estimated load distribution for theservice life of the ship and the S-N curve for the blade material. An equivalent stress σfat that
produces the same fatigue damage as the expected load distribution shall be calculated
according to Miner’s rule and the acceptability criterion for fatigue should be fulfilled as givenin this section. The equivalent stress is normalised for 100 million cycles.
The blade stresses at various selected load levels for fatigue analysis are to be taken
proportional to the stresses calculated for maximum loads given in section 5.3.
The peak principal stresses 𝜎𝜎𝑓𝑓 and 𝜎𝜎𝑏𝑏 are determined from 𝐹𝐹𝑓𝑓 and 𝐹𝐹𝑏𝑏 using FEA. The peakstress range ∆𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚 and the maximum stress amplitude 𝜎𝜎𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 are determined on the basis ofload cases 1 and 3, 2 and 4.
∆𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚 = 2 ∙ 𝜎𝜎𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 = �(𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑓𝑓 𝑚𝑚𝑚𝑚𝑚𝑚 � + |(𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑏𝑏 𝑚𝑚𝑚𝑚𝑚𝑚 |[Equation 44]

The load spectrum for backward loads is normally expected to have a lower number of cycles
than the load spectrum for forward loads. Taking this into account in a fatigue analysis
introduces complications that are not justified considering all uncertainties involved.
For the calculation of equivalent stress two types of S-N curves are available.

Two slope S-N curve (slopes 4.5 and 10), see Figure 5.
One slope S-N curve (the slope can be chosen), see Figure 6.
The type of the S-N-curve shall be selected to correspond with the material properties of theblade. If the S-N-curve is not known the two slope S-N curve shall be used.

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(cont)Slope 4.5

Stress amplitude

I3

Slope 10σexp

1,E+041,E+061,E+081,E+10Stress amplitude

I3

Slope m=8
Slope m=10

σexp

1,E+04

Number of loads

Figure 5: Two-slope S-N curve
6.3.3.2

1,E+061,E+081,E+10

Number of loads

Figure 6: Constant-slope S-N curve

Equivalent fatigue stress

Note: A more general method of determining the equivalent fatigue stress of propeller blades
is described in 6.5, where the principal stresses are considered according to 5.3 using theMiner’s rule. For a total number of load blocks 𝑛𝑛𝑏𝑏𝑏𝑏 > 100, both methods deliver the same result.
Therefore, they are regarded as equivalent.
The equivalent fatigue stress for 108 cycles which produces the same fatigue damage as theload distribution is:
𝜎𝜎𝑓𝑓𝑓𝑓𝑓𝑓 = 𝜌𝜌 ∙ (𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑚𝑚𝑚𝑚𝑚𝑚[Equation 45](𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑚𝑚𝑚𝑚𝑚𝑚 = 0.5 ∙ �(𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑓𝑓 𝑚𝑚𝑚𝑚𝑚𝑚 − (𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑏𝑏 𝑚𝑚𝑚𝑚𝑚𝑚 �[Equation 46]

where:(𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑚𝑚𝑚𝑚𝑚𝑚 = mean value of the principal stress amplitudes resulting from design forward
and backward blade forces at the location being studied.
(𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑓𝑓 𝑚𝑚𝑚𝑚𝑚𝑚 = principal stress resulting from forward load
(𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑏𝑏 𝑚𝑚𝑚𝑚𝑚𝑚 = principal stress resulting from backward load
In the calculation of (𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑚𝑚𝑚𝑚𝑚𝑚 , case 1 and case 3 or case 2 and case 4 are considered aspairs for (𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑓𝑓 𝑚𝑚𝑚𝑚𝑚𝑚 , and (𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑏𝑏 𝑚𝑚𝑚𝑚𝑚𝑚 calculations. Case 5 is excluded from the fatigue
analysis.
Calculation of parameter 𝜌𝜌 for two-slope S-N curve
The error of the following method to determine the parameter 𝜌𝜌 is sufficiently small, if thenumber of load cycles 𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 is in the range
5·106 ≤ 𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 ≤ 108

The parameter 𝜌𝜌 relates the maximum ice load to the distribution of ice loads according to theregression formula𝐶𝐶𝜌𝜌 = 𝐶𝐶1 ∙ (𝜎𝜎𝑖𝑖𝑖𝑖𝑖𝑖 )𝑚𝑚𝑚𝑚𝑚𝑚 2 ∙ 𝜎𝜎𝑓𝑓𝑓𝑓 𝐶𝐶2 ∙ 𝑙𝑙𝑙𝑙𝑙𝑙(𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 )𝐶𝐶4

where:[Equation 47]

𝜎𝜎𝑓𝑓𝑓𝑓 = 𝛾𝛾𝜀𝜀1 ∙ 𝛾𝛾𝜀𝜀2 ∙ 𝛾𝛾𝑣𝑣 ∙ 𝛾𝛾𝑚𝑚 ∙ 𝜎𝜎𝑒𝑒𝑒𝑒𝑒𝑒 is the blade material fatigue strength at 108 load cycles, see

6.3.3.3.

The coefficients 𝐶𝐶1 , 𝐶𝐶2 , 𝐶𝐶3 , and 𝐶𝐶4 are given in Table 13
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I3
Table 13 Coefficients to evaluate material fatigue strength

I3(cont)

𝐶𝐶1
𝐶𝐶2
𝐶𝐶3
𝐶𝐶4

Open propeller
0.000747
0.0645-0.0565
2.22

Ducted propeller
0.000534
0.0533-0.04592.584

Calculation of parameter 𝜌𝜌 for constant-slope S-N curve

For materials with a constant-slope S-N curve, see Figure 6, - the factor 𝜌𝜌 shall be calculated
from the following formula:
𝑁𝑁

1
𝑚𝑚

−

1

[Equation 48]

𝜌𝜌 = �𝐺𝐺 𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 � �𝑙𝑙𝑙𝑙(𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 )� 𝑘𝑘
where:

𝑅𝑅

𝑘𝑘 = shape parameter of the Weibull distribution
𝑘𝑘 = 1.0 for ducted propellers and𝑘𝑘 = 0.75 for open propellers

𝑁𝑁𝑅𝑅 = reference number of load cycles (=108)

Values for the parameter 𝐺𝐺 are given in Table 14 below. Linear interpolation may be used to
calculate the value of 𝐺𝐺 for m/k ratios other than those given in the Table 14.
m/k
3
3.5
4
4.5
5

Table 14: Value for the parameter 𝑮𝑮 for different m/k ratios
𝐺𝐺
6
11.6
24
52.3

m/k
5.5
6
6.5
7

𝐺𝐺
287.9
720
1871
5040

m/k
8
8.5
9
9.5

𝐺𝐺
40320
1192923628801.133×106

120

7.5

14034

10

3.623×106

6.3.3.3 Acceptability criterion for fatigue
The equivalent fatigue stress 𝜎𝜎𝑓𝑓𝑓𝑓𝑓𝑓 at all locations on the blade shall fulfil the following
acceptability criterion:
𝜎𝜎𝑓𝑓𝑓𝑓𝜎𝜎𝑓𝑓𝑓𝑓𝑓𝑓[Equation 49]≥ 1.5

where:[Equation 50]

𝜎𝜎𝑓𝑓𝑓𝑓 = 𝛾𝛾𝜀𝜀1 ∙ 𝛾𝛾𝜀𝜀2 ∙ 𝛾𝛾𝑣𝑣 ∙ 𝛾𝛾𝑚𝑚 ∙ 𝜎𝜎𝑒𝑒𝑒𝑒𝑒𝑒
𝛾𝛾𝜀𝜀1
𝛾𝛾𝜀𝜀2
𝛾𝛾𝑣𝑣
𝛾𝛾𝑚𝑚
𝜎𝜎𝑒𝑒𝑒𝑒𝑒𝑒

=
=
=
=
=

reduction factor due to scatter (equal to one standard deviation)
reduction factor for test specimen size effectreduction factor for variable amplitude loading.
reduction factor for mean stress.
mean fatigue strength of the blade material at 108 cycles to failure in seawater

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𝜎𝜎𝑒𝑒𝑒𝑒𝑒𝑒 in Table 15 has been defined from the results of constant amplitude loading fatigue tests
at 107 load cycles and 50% survival probability and has been extended to 108 load cycles.
Fatigue strength values and correction factors other than those given in Table 15 may be
used, provided the values are determined under conditions approved by the classificationsociety.
The S-N curve characteristics are based on two slopes, the first slope 4.5 is from 1000 to 108
load cycles; the second slope 10 is above 108 load cycles.
The maximum allowable stress for one or low number of cycles is limited to 𝜎𝜎𝑟𝑟𝑟𝑟𝑟𝑟2 /𝑆𝑆, with
𝑆𝑆=1.3 for static loads.

The fatigue strength 𝜎𝜎𝑓𝑓𝑓𝑓𝑓𝑓 is the fatigue limit at 100 million load cycles.
The geometrical size factor (𝛾𝛾𝜀𝜀2 ) is:𝑡𝑡
𝛾𝛾𝜀𝜀2 = 1 − 𝑎𝑎 ∙ 𝑙𝑙𝑙𝑙 ��
0.025

where:[Equation 51]“𝑎𝑎” is as given in Table 15 below and “𝑡𝑡” is the maximum blade thickness at the consideredpoint
The mean stress effect (𝛾𝛾𝑚𝑚 ) is
1.4∙𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 0.75
�𝜎𝜎𝑢𝑢𝛾𝛾𝑚𝑚 = 1.0 − �[Equation 52]

The following values should be used for the reduction factors if actual values are notavailable: 𝛾𝛾𝜀𝜀1 = 0.85, 𝛾𝛾𝑣𝑣 = 0.75, and 𝛾𝛾𝑚𝑚 = 0.75.

Table 15: Mean fatigue strength 𝝈𝝈𝒆𝒆𝒆𝒆𝒆𝒆 for different material types at 108 load cycles andstress ratio R = -1 with a survival probability of 50%.
Mean fatigue strength 𝜎𝜎𝑒𝑒𝑒𝑒𝑒𝑒 for different material types at 108 load cycles
Bronze and brass (a=0.10)
Stainless steel (a=0.05)
Mn-Bronze, CU1 (high tensile
84 MPaFerritic (12Cr 1Ni)
144*)
brass)
Mpa
Mn-Ni-Bronze, CU2 (high tensile 84 Mpa
Martensitic (13Cr
156 Mpa
brass)
4Ni/13Cr 6Ni)
Ni-Al-Bronze, CU3
120 Mpa
Martensitic (16Cr 5Ni)
168 Mpa
Mn-Al-Bronze, CU4
113 Mpa
Austenitic (19Cr 10Ni)
132 Mpa
This value may be used, provided a perfect galvanic protection is active. Otherwise
a reduction of about 30 MPa shall be applied.

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I3

I3

(cont)

6.4

Blade bolts, propeller hub and CP mechanism

6.4.1 General
The blade bolts, CP mechanism, propeller boss and the fitting of the propeller to the propeller
shaft shall be designed to withstand the maximum static and fatigue design loads (asapplicable), as defined in 5.3 and 6.3. The safety factor 𝑆𝑆 against yielding due to static loads
and against fatigue shall be greater than 1.5, if not stated otherwise. The safety factor 𝑆𝑆 forloads, resulting from propeller blade failure as defined in 5.4 shall be greater than 1.0 againstyielding.
Provided that calculated stresses duly considering local stress concentrations are less thanyield strength, or maximum of 70% of 𝜎𝜎𝑢𝑢 of respective materials, detailed fatigue analysis is
not required. In all other cases components shall be analysed for cumulative fatigue. An
approach similar to that used for shafting assessment may be applied (6.5).
6.4.2 Blade bolts
Blade bolts shall withstand the following bending moment considered around a tangent onbolt pitch circle, or any other relevant axis for non-circular joints, parallel to considered root
section:[kNm]

𝑀𝑀𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = 𝑆𝑆 ∙ 𝐹𝐹𝑒𝑒𝑒𝑒�0.8𝐷𝐷−𝑟𝑟2

where:

𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 �[Equation 53]

𝑟𝑟𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 = radius to the bolt plane [m]𝑆𝑆= 1.0 safety factor

Blade bolt pre-tension shall be sufficient to avoid separation between mating surfaces whenthe maximum forward and backward ice loads defined in 5.3 (open and ducted propellers
respectively) are applied. For conventional arrangements, the following formula may be
applied:2 𝐹𝐹∙(0.8∙𝐷𝐷−𝑑𝑑)∙𝑆𝑆∙𝛼𝛼
𝜎𝜎0.2 ∙𝑍𝑍𝑏𝑏𝑏𝑏 ∙𝑃𝑃𝑃𝑃𝑃𝑃[mm]

𝑑𝑑𝑏𝑏𝑏𝑏 = 41 ∙ � 𝑒𝑒𝑒𝑒
where:
𝛼𝛼= 1.6 torque guided tightening= 1.3 elongation guided= 1.2 angle guided= 1.1 elongated by other additional meansother factors may be used, if evidence is demonstrated

𝑑𝑑𝑏𝑏𝑏𝑏effective diameter of blade bolt in way of thread [mm]𝑆𝑆

= 1.0 safety factor

𝑍𝑍𝑏𝑏𝑏𝑏[Equation 54]

number of blade bolts

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(cont)

6.4.3 CP mechanism
Separate means, e.g. dowel pins, shall be provided in order to withstand the spindle torqueresulting from blade failure 𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠 (5.4.2) or ice interaction 𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 (5.3.7), whichever is greater.
Other components of the CP mechanism shall not be damaged by the maximum spindle
torques (𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 , 𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠 ). One third of the spindle torque is assumed to be consumed by friction,
if not otherwise documented trough further analysis.
The diameter of fitted pins 𝑑𝑑𝑓𝑓𝑓𝑓 between the blade and blade carrier can be calculated using
the formula:�𝑄𝑄 −𝑄𝑄𝑓𝑓𝑓𝑓 �𝑠𝑠𝑑𝑑𝑓𝑓𝑓𝑓 = 66 ∙ �𝑃𝑃𝑃𝑃𝑃𝑃∙𝑧𝑧

where:𝑄𝑄𝑠𝑠
𝑆𝑆

𝑄𝑄𝑓𝑓𝑓𝑓[mm]

𝑝𝑝𝑝𝑝𝑝𝑝 ∙𝜎𝜎0.2= 𝑚𝑚𝑚𝑚𝑚𝑚(𝑆𝑆 ∙ 𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ; 𝑆𝑆 ∙ 𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠 )[Equation 55][kNm][Equation 56]= 1.3 for 𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠 and= 1.0 for 𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠= friction between connected surfaces = 0.33·𝑄𝑄𝑠𝑠

The classification society may approve alternative 𝑄𝑄𝑓𝑓𝑓𝑓 calculation according to reaction forces
due to 𝐹𝐹𝑒𝑒𝑒𝑒 , or 𝐹𝐹𝑓𝑓 , 𝐹𝐹𝑏𝑏 whichever is relevant, utilising a friction coefficient = 0.15.
The stress in the actuating pin can be estimated by
𝜎𝜎𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 = ��where:
𝐹𝐹 =𝑙𝑙𝑚𝑚ℎ𝑝𝑝𝑝𝑝𝑝𝑝�23𝜋𝜋∙𝑑𝑑𝑝𝑝𝑝𝑝𝑝𝑝
32

�𝐹𝐹∙

2

� + 3 ∙ �𝜋𝜋
4𝐹𝐹∙𝑑𝑑𝑝𝑝𝑝𝑝𝑝𝑝

2

�

2

𝑄𝑄𝑆𝑆 −𝑄𝑄𝑓𝑓𝑓𝑓
𝑙𝑙𝑚𝑚

[MPa]

[Equation 57][kN][Equation 58]

distance pitching centre of blade – axis of pin [m]ℎ𝑝𝑝𝑝𝑝𝑝𝑝 height of actuating pin [mm]𝑑𝑑𝑝𝑝𝑝𝑝𝑝𝑝 diameter of actuating pin [mm]𝑄𝑄𝑓𝑓𝑓𝑓friction torque in blade bearings acting on the blade palm and caused by the reaction
forces due to 𝐹𝐹𝑒𝑒𝑒𝑒 , or 𝐹𝐹𝑓𝑓 , 𝐹𝐹𝑏𝑏 whichever is relevant; taken to one third of spindle torque 𝑄𝑄𝑠𝑠

The blade failure spindle torque 𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠 shall not lead to any consequential damage.
Fatigue strength is to be considered for parts transmitting the spindle torque from the blade toa servo system considering the ice spindle torque acting on one blade. The maximum
amplitude 𝑄𝑄𝑠𝑠𝑠𝑠max is defined as:
𝑄𝑄𝑠𝑠𝑠𝑠max =𝑄𝑄𝑠𝑠𝑠𝑠 +𝑄𝑄𝑠𝑠𝑠𝑠

[kNm]

2

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(cont)

where:
𝑄𝑄𝑠𝑠𝑠𝑠

𝑄𝑄𝑠𝑠𝑠𝑠spindle torque due to |𝐹𝐹𝑏𝑏 | [kNm]
spindle torque due to �𝐹𝐹𝑓𝑓 � [kNm]

6.4.4 Servo pressure

The design pressure for the servo system shall be taken as the pressure caused by 𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 or,
𝑄𝑄𝑠𝑠𝑠𝑠𝑠𝑠 when not protected by relief valves on the hydraulic actuator side, reduced by relevant
friction losses in bearings caused by the respective ice loads. The design pressure shall in any
case not be less than relief valve set pressure.
6.5

Propulsion line components

The ultimate load resulting from total blade failure 𝐹𝐹𝑒𝑒𝑒𝑒 as defined in 5.4 shall consist of
combined axial and bending load components, wherever this is significant. The minimum
safety factor against yielding is to be 1.0 for all shaft line components.
The shafts and shafting components, such as bearings, couplings and flanges shall be
designed to withstand the operational propeller/ice interaction loads as given in 5.
The given loads are not intended to be used for shaft alignment calculation.
Cumulative fatigue calculations shall be conducted according to the Miner’s rule. A fatigue
calculation is not necessary, if the maximum stress is below fatigue strength at 108 load
cycles.
The torque and thrust amplitude distribution (spectrum) in the propulsion line is to be taken as(because Weibull exponent 𝑘𝑘 = 1):
𝑙𝑙𝑙𝑙𝑙𝑙(𝑁𝑁)

𝑄𝑄𝐴𝐴 (𝑁𝑁) = 𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 ∙ �1 − 𝑙𝑙𝑙𝑙𝑙𝑙(𝑍𝑍∙𝑁𝑁

𝑖𝑖𝑖𝑖𝑖𝑖 )[Equation 60]

�This is illustrated by the example in the Figure 7.
Figure7: Cumulative torque distribution
Cumulative Torque Distribution
100

Q_A/Q_Amax [%]

I3

80

60

40

20

0

Z⋅ N ice

Number of ice cycles

The number of load cycles in the load spectrum is defined as 𝑍𝑍 ∙ 𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 .

The Weibull exponent should be considered as 𝑘𝑘 = 1.0 for both open and ducted propeller
torque and bending forces. The load distribution is an accumulated load spectrum, and theload spectrum should be divided into a minimum of ten load blocks when using the Miner
summation method.

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(cont)The load spectrum used counts the number of cycles for 100% load to be the number ofcycles above the next step, e.g. 90 % load. This ensures that the calculation is on theconservative side. Consequently, the fewer stress blocks used the more conservative thecalculated safety margin.
Figure 8: Example of ice load distribution (spectrum) for the shafting (𝒌𝒌 = 1)

Ice Load Divi ded into Load Blocks
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

Ice load/max Ice load

I3

1

10

100

3

1 .10

4

1 .10

5

1 .10

6

1 .10

7

1 .10

8

1 .10

Number of cycles

The load spectrum is divided into 𝑛𝑛𝑏𝑏𝑏𝑏 -number of load blocks for the Miner summation method.

The following formula can be used for calculation of the number of cycles for each load block.
𝑛𝑛𝑖𝑖 = 𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖

𝑘𝑘𝑖𝑖
�𝑛𝑛𝑏𝑏𝑏𝑏1−�1−where:− ∑𝑖𝑖𝑖𝑖=1 𝑛𝑛𝑖𝑖−1[Equation 61]

𝑖𝑖 = single load block 𝑖𝑖 and 𝑛𝑛𝑏𝑏𝑏𝑏 is the number of load blocks
6.5.1

Propeller fitting to the shaft

6.5.1.1 Keyless cone mounting
The friction capacity (at 0° C) shall be at least 𝑆𝑆 = 2.0 times the highest peak torque 𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 as
determined in 5.6 without exceeding the permissible hub stresses.
The necessary surface pressure 𝑃𝑃0℃ can be determined as:
2∙𝑆𝑆∙𝑄𝑄

𝑃𝑃0℃ = 𝜋𝜋∙𝜇𝜇∙𝐷𝐷 2𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝∙𝐿𝐿∙103
where:
𝜇𝜇
𝐷𝐷𝑆𝑆
𝐿𝐿

[MPa]

𝑆𝑆

[Equation 62]= 0.15 for steel-steel,= 0.13 for steel-bronze= is the shrinkage diameter at the mid-length of the taper [m]= is the effective length of taper [m]Above friction coefficients may be increased by 0.04 if glycerine is used in wet mounting.

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(cont)

6.5.1.2 Key mounting
Key mounting is not permitted.
6.5.1.3 Flange mounting
The flange thickness is to be at least 25% of the required aft end shaft diameter (IACS UR
M34).
Any additional stress raisers such as recesses for bolt heads shall not interfere with theflange fillet unless the flange thickness is increased correspondingly.
The flange fillet radius is to be at least 10% of the required shaft diameter.
The diameter of shear pins shall be calculated according to the following equation:
2

𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 ∙𝑆𝑆[mm]

𝑑𝑑𝑝𝑝𝑝𝑝𝑝𝑝 = 66 ∙ �𝑃𝑃𝑃𝑃𝑃𝑃∙𝑧𝑧

𝑝𝑝𝑝𝑝𝑝𝑝 ∙𝜎𝜎0.2

where[Equation 63]

𝑧𝑧𝑝𝑝𝑝𝑝𝑝𝑝 = number of shear pins
𝑆𝑆

= 1.3 safety factor

The bolts are to be designed so that the blade failure load 𝐹𝐹𝑒𝑒𝑒𝑒 (5.4) in backward direction
does not cause yielding of the bolts. The following equation should be applied:𝐷𝐷+1�∙𝛼𝛼
𝑃𝑃𝑃𝑃𝑃𝑃𝐹𝐹 ∙�0.8∙

𝑒𝑒𝑒𝑒
𝑑𝑑𝑏𝑏 = 41 ∙ �

where:
𝛼𝛼[mm]

𝜎𝜎0.2 ∙𝑧𝑧𝑏𝑏[Equation 64]= 1.6 torque guided tightening= 1.3 elongation guided= 1.2 angle guided= 1.1 elongated by other additional meansother factors may be used, if evidence is demonstrated

𝑑𝑑𝑏𝑏

𝑧𝑧𝑏𝑏

diameter flange bolt [mm]number of flange bolts

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(cont)

6.5.2

Propeller shaft

The propeller shaft is to be designed to fulfil the following:
6.5.2.1 The blade failure load 𝐹𝐹𝑒𝑒𝑒𝑒 (5.4) applied parallel to the shaft (forward or backwards)
shall not cause yielding. The bending moment need not to be combined with any other loads.
The diameter 𝑑𝑑𝑝𝑝 in way of the aft stern tube bearing shall not be less than:
𝐹𝐹𝑒𝑒𝑒𝑒 ∙𝐷𝐷

𝑑𝑑𝑝𝑝 = 160 ∙ 3
�𝜎𝜎

0.2 ∙�1−

where:
𝑑𝑑𝑝𝑝
𝑑𝑑𝑖𝑖

[mm]

𝑑𝑑𝑖𝑖 4�𝑑𝑑𝑝𝑝 4=

propeller shaft diameter [mm]=propeller shaft inner diameter [mm][Equation 65]

Forward from the aft stern tube bearing the shaft diameter may be reduced based on direct
calculation of the actual bending moment, or by the assumption that the bending moment
caused by 𝐹𝐹𝑒𝑒𝑒𝑒 is linearly reduced to 25% at the next bearing and in front of this linearly tozero at third bearing.

Bending due to maximum blade forces 𝐹𝐹𝑏𝑏 and 𝐹𝐹𝑓𝑓 have been disregarded since the resulting
stress levels are much lower than the stresses caused by the blade failure load.
6.5.2.2 The stresses due to the peak torque 𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 shall have a minimum safety factor of
𝑆𝑆=1.5 against yielding in plain sections and 𝑆𝑆=1.0 in way of stress concentrations in order toavoid bent shafts.
Minimum diameter of:plain shaft:
𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 ∙𝑆𝑆[mm][Equation 66]

𝑄𝑄

[mm]

[Equation 67]

𝑑𝑑𝑝𝑝 = 210 ∙ 3
�𝜎𝜎𝑑𝑑𝑖𝑖 40.2 ∙�1− 𝑑𝑑4 �notched shaft:∙𝑆𝑆∙𝛼𝛼𝑑𝑑𝑝𝑝 = 210 ∙ 3 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝑑𝑑 4𝑡𝑡
�𝜎𝜎 ∙�1− 𝑖𝑖 �
0.2

𝑑𝑑4

where:

𝛼𝛼𝑡𝑡 = local stress concentration factor in torsion.

Notched shaft diameter shall in any case not be less than the required plain shaft diameter.

6.5.2.3 The torque amplitudes (5.6.4) with the corresponding number of load cycles shall be
used in an accumulated fatigue evaluation where the safety factor is 𝑆𝑆𝑓𝑓𝑓𝑓𝑓𝑓 =1.5. If the plant has
high engine excited torsional vibrations (e.g. direct coupled 2-stroke engines), this shall also
be considered.
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6.5.2.4 The fatigue strengths 𝜎𝜎𝐹𝐹 and 𝜏𝜏𝐹𝐹 (3 million cycles) of shaft materials may be assessedon the basis of the material’s yield or 0.2% proof strength as:
𝜎𝜎𝐹𝐹 = 0.436 ∙ 𝜎𝜎0.2 + 77 = 𝜏𝜏𝐹𝐹 ∙ √3

[MPa]

[Equation 68]

This is valid for small polished specimens (no notch) and reversed stresses, see “VDEH 1983
Bericht Nr. ABF11 Berechnung von Wöhlerlinien für Bauteile aus Stahl”.
The high cycle fatigue (HCF) is to be assessed based on the above fatigue strengths, notch
factors (i.e. geometrical stress concentration factors and notch sensitivity), size factors, meanstress influence and the required safety factor of 1.6 at 3 million cycles increasing to 1.8 at 109
cycles.
The low cycle fatigue (LCF) representing 104 cycles is to be based on the smaller value of yieldor 0.7 of tensile strength/√3. The criterion utilises a safety factor of 1.25.
The LCF and HCF as given above represent the upper and lower knees in a stress-cycle
diagram. Since the required safety factors are included in these values, a Miner sum of unity is
acceptable.
6.5.3

Intermediate shafts

The intermediate shafts are to be designed to fulfil 6.5.2.2 to 6.5.2.4.
6.5.4

Shaft connections

6.5.4.1 Shrink fit couplings (keyless)See 6.5.1.1. A safety factor of 𝑆𝑆 = 1.8 shall be applied.

6.5.4.2 Key mounting

Key mounting is not permitted.
6.5.4.3 Flange mounting
The flange thickness is to be at least 20% of the required shaft diameter (IACS UR M34).
Any additional stress raisers such as recesses for bolt heads shall not interfere with theflange fillet unless the flange thickness is increased correspondingly.
The flange fillet radius is to be at least 8% of the shaft diameter (IACS UR M34).
The diameter of ream fitted (light press fit) bolts shall be chosen so that the peak torque istransmitted with a safety factor of 1.9. This accounts for a prestress. Pins shall transmit thepeak torque with a safety factor of 1.5 against yielding ([Equation 63]).
The bolts are to be designed so that the blade failure load (5.4) in backward direction does
not cause yielding.

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6.5.4.4 Splined shaft connections
Splined shaft connections can be applied where no axial or bending loads occur. A safety factor
of 𝑆𝑆 = 1.5 against allowable contact and shear stress resulting from 𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 shall be applied.
6.5.4.5 Gear transmissions

6.5.4.6 Shafts
Shafts in gear transmissions shall meet the same safety level as intermediate shafts, butwhere relevant, bending stresses and torsional stresses shall be combined (e.g. by von Misesfor static loads). Maximum permissible deflection in order to maintain sufficient tooth contact
pattern shall be considered for the relevant parts of the gear shafts.
6.5.4.7 Gearing
The gearing shall fulfil following three acceptance criteria:- Tooth root stresses- Pitting of flanks- Scuffing
In addition to above 3 criteria subsurface fatigue may need to be considered.
Common for all criteria is the influence of load distribution over the face width. All relevant
parameters are to be considered, such as elastic deflections (of mesh, shafts and gear
bodies), accuracy tolerances, helix modifications, and working positions in bearings(especially for multiple input single output gears).
The load spectrum (see 6.5) may be applied in such a way that the numbers of load cycles
for the output wheel are multiplied by a factor of (number of pinions on the wheel / number ofpropeller blades 𝑍𝑍). For pinions and wheels operating at higher speeds the numbers of load
cycles are found by multiplication with the gear ratios. The peak torque (𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 ) is also to beconsidered during calculations.
Cylindrical gears can be assessed on the basis of the international standard ISO 6336 series(i.e. ISO 6336-1:2019, ISO 6336-2:2019, ISO 6336-3:2019, ISO 6336-4:2019, ISO 63365:2016 and ISO 6336-6:2019), provided that “method B” is used. Standards within theclassification societies can also be applied provided that they are considered equivalent tothe above mentioned ISO 6336.
For Bevel Gears the methods or standards used or acknowledged by the classificationsociety can be applied provided that they are properly calibrated.
Tooth root safety shall be assessed against the peak torque, torque amplitudes (with thepertinent average torque) as well as the ordinary loads (open water free running) by means ofaccumulated fatigue analyses. The resulting factor of safety is to be at least 1.5. (Ref ISO
6336 Pt 1, 3 and 6 and IACS UR M56)
The safety against pitting shall be assessed in the same way as tooth root stresses, but witha minimum resulting safety factor of 1.2. (Ref ISO 6336-1:2019, ISO 6336-2:2019 and ISO
6336-6:2019 as well as IACS UR M56).
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(cont)The scuffing safety (flash temperature method – ref. ISO/TR 13989-1:2000 and ISO/TR
13989-2:2000) based on the peak torque shall be at least 1.2 when the FZG class of the oil isassumed one stage below specification.
The safety against subsurface fatigue of flanks for surface hardened gears (oblique fracturefrom active flank to opposite root) is to be assessed at the discretion of each Classification
Society. (It should be noted that high overloads can initiate subsurface fatigue cracks that
may lead to a premature failure. In lieu of analyses UT inspection intervals may be used.)
6.5.4.8 Bearings
See section 6.5.8.
6.5.4.9 Gear wheel shaft connections
The torque capacity shall be at least 1.8 times the highest peak torque 𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 (at consideredrotational speed) as determined in 6.5 without exceeding the permissible hub stresses of 80%
yield.
6.5.5

Clutches

Clutches shall have a static friction torque of at least 1.3 times the peak torque 𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 anddynamic friction torque 2/3 of the static.
Emergency operation of clutch after failure of e.g. operating pressure shall be made possible
within reasonably short time. If this is arranged by bolts, it shall be on the engine side of the
clutch in order to ensure access to all bolts by turning the engine.
6.5.6

Elastic couplings

There shall be a separation margin of at least 20% between the peak torque and the torquewhere any twist limitation is reached.
[kNm]

𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 < 0.8 ∙ 𝑇𝑇𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘 (𝑁𝑁 = 1)

[Equation 69]

There shall be a separation margin of at least 20% between the maximum response torque
𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 (see Figure 4) and the torque where any mechanical twist limitation and/or thepermissible maximum torque of the elastic coupling, valid for at least a single load cycle(𝑁𝑁=1), is reached.

A sufficient fatigue strength shall be demonstrated at design torque level 𝑄𝑄𝑟𝑟 (𝑁𝑁 = 𝑥𝑥) and𝑄𝑄𝐴𝐴 (𝑁𝑁 = 𝑥𝑥). This may be demonstrated by interpolation in a Weibull torque distribution (similar
to Figure 7):
𝑄𝑄𝑟𝑟 (𝑁𝑁=𝑥𝑥)log (𝑥𝑥)=1−
𝑄𝑄𝑟𝑟 (𝑁𝑁=1)
log (𝑍𝑍∙𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 )[-][Equation 70]

𝑄𝑄𝐴𝐴 (𝑁𝑁=𝑥𝑥)log (𝑥𝑥)=1−
𝑄𝑄𝐴𝐴 (𝑁𝑁=1)
log (𝑍𝑍∙𝑁𝑁𝑖𝑖𝑖𝑖𝑖𝑖 )[-][Equation 71]

respectively

Where 𝑄𝑄𝑟𝑟 (𝑁𝑁=1) corresponds to 𝑄𝑄𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 and 𝑄𝑄𝐴𝐴 (𝑁𝑁=1) to 𝑄𝑄𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 .
𝑄𝑄𝑟𝑟 (𝑁𝑁=5E4)·𝑆𝑆 < 𝑇𝑇𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾 (𝑁𝑁=5E4)
𝑄𝑄𝑟𝑟 (𝑁𝑁=1E6)·𝑆𝑆 < 𝑇𝑇𝐾𝐾𝐾𝐾Page 36 of 44

[kNm]
[kNm]

[Equation 72][Equation 73]
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(cont)𝑄𝑄𝐴𝐴 (𝑁𝑁=5E4)·𝑆𝑆 < ∆𝑇𝑇𝑚𝑚𝑚𝑚𝑚𝑚 (𝑁𝑁=5E4)[kNm][Equation 74]

𝑆𝑆 is the general safety factor for fatigue, equal to 1.5.

See illustration in below Figure 9, Figure 10 and Figure 11.
The torque amplitude (or range ∆) shall not lead to fatigue cracking, i.e. exceeding thepermissible vibratory torque. The permissible torque may be determined by interpolation in a
Weibull torque distribution where 𝑇𝑇𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾1 respectively ∆𝑇𝑇𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾 refer to 50000 cycles and 𝑇𝑇𝐾𝐾𝐾𝐾
refer to 106 cycles. See illustration in below Figure 9, Figure 10 and Figure 11.
𝑇𝑇𝐾𝐾𝐾𝐾𝐾𝐾𝐾𝐾1 ≥ 𝑄𝑄𝑟𝑟 𝑎𝑎𝑎𝑎 5 ∙ 104 load cycles

Figure 9[kNm][Equation 75]

Figure 10

Figure 116.5.7 CrankshaftsSpecial considerations apply for plants with large inertia (e.g. flywheel, tuning wheel or PTO)
in the non-driving end front of the engine (opposite to main power take off).
6.5.8 Bearings
The aft stern tube bearing as well as the next shaft line bearing are to withstand 𝐹𝐹𝑒𝑒𝑒𝑒 as given
in 5.4, in such a way that the ship can maintain operational capability. Rolling bearings are tohave an 𝐿𝐿10𝑎𝑎 lifetime of at least 40 000 hours according to ISO 281:2007. Thrust bearings
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(cont)and their housings are to be designed to withstand with a safety factor 𝑆𝑆 = 1.0 the maximum
response thrust 5.5 and the axial force resulting from the blade failure load 𝐹𝐹𝑒𝑒𝑒𝑒 in 5.4. For the
purpose of calculation, except for 𝐹𝐹𝑒𝑒𝑒𝑒 , the shafts are assumed to rotate at rated speed. For
pulling propellers special consideration is to be given to loads from ice interaction on thepropeller hub.
6.5.9 Seals
Seals are to prevent egress of pollutants and be suitable for the operating temperatures.
Contingency plans for preventing the egress of pollutants under failure conditions are to be
documented.
Seals installed are to be suitable for the intended application. The manufacturer is to provide
service experience in similar applications and/or testing results for consideration.
6.6

Azimuthing main propulsors

In addition to the above requirements, special consideration shall be given to those loadingcases which are extraordinary for propulsion units when compared with conventional
propellers. The estimation of load cases shall reflect the way the thrusters are intended tooperate on the specific ship. In this respect, for example, the loads caused by the impacts ofice blocks on the propeller hub of a pulling propeller shall be considered. Furthermore, loads
resulting from the thrusters operating at an oblique angle to the flow shall be considered. The
steering mechanism, the fitting of the unit, and the body of the thruster shall be designed towithstand the loss of a blade without damage. The loss of a blade shall be considered for thepropeller blade orientation which causes the maximum load on the component being studied.
Typically, top-down blade orientation places the maximum bending loads on the thruster
body.
Azimuth thrusters shall also be designed for estimated loads caused by thruster body/ice
interaction. The thruster body shall withstand the loads obtained when the maximum ice
blocks, which are given in section 5.2, strike the thruster body when the ship is at a typical ice
operating speed. In addition, the design situation in which an ice sheet glides along the ship’s
hull and presses against the thruster body should be considered. The thickness of the sheet
should be taken as the thickness of the maximum ice block entering the propeller, as definedin section 5.2.
7

Prime Movers

7.1

Propulsion engines

Engines are to be capable of being started and running the propeller in bollard condition.
Propulsion plants with CP propeller are to be capable being operated even when the CP
system is at full pitch as limited by mechanical stoppers.
7.2

Starting arrangements

The capacity of the air receivers shall be sufficient to provide, without recharging, not lessthan 12 consecutive starts of the propulsion engine, if this has to be reversed for going asternor 6 consecutive starts if the propulsion engine does not have to be reversed for going astern.
If the air receivers serve any other purposes than starting the propulsion engine, they shallhave additional capacity sufficient for these purposes.

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The capacity of the air compressors shall be sufficient for charging the air receivers fromatmospheric to full pressure in one (1) hour, except for a ship with the ice class PC6 to PC1, if
its propulsion engine has to be reversed for going astern, in which case the compressor shallbe able to charge the receivers in half an hour.
7.3

Emergency power units

Provisions shall be made for heating arrangements to ensure ready starting from cold of theemergency power units at an ambient temperature applicable to the Polar Class of the ship.
Emergency power units shall be equipped with starting devices with a stored energy
capability of at least three consecutive starts at the above mentioned temperature. The
source of stored energy shall be protected to preclude critical depletion by the automatic
starting system, unless a second independent mean of starting is provided. A second sourceof energy shall be provided for an additional three starts within 30 min., unless manual
starting can be demonstrated to be effective.
8

Equipment fastening loading accelerations

8.1

GeneralEssential equipment and supports shall be suitable for the accelerations as indicated in thefollowing paragraphs. Accelerations are to be considered as acting independently.
8.2

Longitudinal Impact Accelerations, 𝒂𝒂𝟏𝟏

Maximum longitudinal impact acceleration at any point along the hull girder,
𝑎𝑎1 =
8.3

𝐹𝐹𝐼𝐼𝐼𝐼
𝐻𝐻∙ �1.1 ∙ tan(𝛾𝛾 + 𝜑𝜑) + �7 ∙ ��∆𝐿𝐿

[m/s2][Equation 76]

Vertical acceleration, 𝒂𝒂𝒗𝒗

Combined vertical impact acceleration at any point along the hull girder,𝐹𝐹

𝑎𝑎𝑣𝑣 = 2.5 ∙ � ∆𝐼𝐼𝐼𝐼 � ∙ 𝐹𝐹𝑋𝑋

[m/s2][Equation 77]

𝐹𝐹𝑋𝑋 = 1.3 at FP= 0.2 at midships= 0.4 at AP= 1.3 at AP for vessels conducting ice breaking asternIntermediate values to be interpolated linearly.

8.4 Transverse impact acceleration, 𝒂𝒂𝒕𝒕

Combined transverse impact acceleration at any point along hull girder,𝐹𝐹∆𝑎𝑎𝑡𝑡 = 3𝐹𝐹𝑖𝑖 𝑋𝑋[m/s2][Equation 78]

𝐹𝐹𝑋𝑋 = 1.5 at FP= 0.25 at midships
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= 0.5 at AP

I3= 1.5 at AP for vessels conducting ice breaking astern(cont)

Intermediate values to be interpolated linearly.
where:
𝜑𝜑= maximum friction angle between steel and ice, normally taken as 10 [degrees]∆= displacement

𝐻𝐻= distance in meters from the water line to the point being considered [m]𝐹𝐹𝑖𝑖= total force normal to shell plating in the bow area due to oblique ice impact, defined in
UR I2.3.2.1

𝛾𝛾= bow stem angle at waterline [degrees]

𝐿𝐿= length between perpendiculars [m]𝐹𝐹𝐼𝐼𝐼𝐼 = vertical impact force, defined in UR I2.13.2.1

9

Auxiliary Systems

9.1
Machinery shall be protected from the harmful effects of ingestion or accumulation of
ice or snow. Where continuous operation is necessary, means should be provided to purge
the system of accumulated ice or snow.
9.2
Means should be provided to prevent damage to tanks containing liquids due tofreezing.
9.3
Vent pipes, intake and discharge pipes and associated systems shall be designed toprevent blockage due to freezing or ice and snow accumulation.
10

Sea Inlets and Cooling Water Systems

10.1 Cooling water systems for machinery that is essential for the propulsion and safety ofthe vessel, including sea chest inlets, shall be designed for the environmental conditions
applicable to the ice class.
10.2 At least two sea chests are to be arranged as ice boxes (sea chests for water intake insevere ice conditions) for ice class PC1 to PC5 inclusive. The calculated volume for each of
the ice boxes shall be at least 1m3 for every 750 kW of the totally installed power. For PC6
and PC7 there shall be at least one ice box located preferably near centre line.
10.3

Ice boxes are to be designed for an effective separation of ice and venting of air.

10.4 Sea inlet valves are to be secured directly to the ice boxes. The valve shall be a fullbore type.
10.5 Ice boxes and sea bays are to have vent pipes and are to have shut off valvesconnected directly to the shell.
10.6 Means are to be provided to prevent freezing of sea bays, ice boxes, ship side valves
and fittings above the load water line.
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10.7 Efficient means are to be provided to re-circulate cooling seawater to the ice box.
Total sectional area of the circulating pipes is not to be less than the area of the cooling water
discharge pipe.
10.8 Detachable gratings or manholes are to be provided for ice boxes. Manholes are to belocated above the deepest load line. Access is to be provided to the ice box from above.
10.9 Openings in ship sides for ice boxes are to be fitted with gratings, or holes or slots inshell plates. The net area through these openings is to be not less than 5 times the area of
the inlet pipe. The diameter of holes and width of slot in shell plating is to be not less than 20mm. Gratings of the ice boxes are to be provided with a means of clearing. The means ofclearing is to be of a type using low pressure steam. Clearing pipes are to be provided withscrew-down type non return valves.
11

Ballast Tanks

11.1 Efficient means are to be provided to prevent freezing in fore and after peak tanks andwing tanks located above the water line and where otherwise found necessary.
12

Ventilation Systems

12.1 The air intakes for machinery and accommodation ventilation are to be located on
both sides of the ship at locations where manual de-icing is possible. Anti-icing protection of
the air inlets may be accepted as an equivalent solution to location on both sides of the shipand manual de-icing at the Society’s discretion. Notwithstanding the above, multiple air
intakes are to be provided for the emergency generating set and are to be as far apart as
possible.
12.2

The temperature of the inlet air shall be suitable for:-the safe operation of the machinery; and-the thermal comfort in the accommodation.

Accommodation and ventilation air intakes shall be provided with means of heating, if
needed.
13

Steering Systems

13.1 Rudder stops are to be provided. The design ice force on rudder shall be transmitted
to the rudder stops without damage to the steering system.
An ice knife shall in general be fitted to protect the rudder in centre position. The ice knife
shall extend below BWL. Design forces shall be determined according to the I2.15.
13.2

The rudder actuator is to comply with the following requirements 13.2.1 and 13.2.2:

13.2.1 The rudder actuator is to be designed for a holding torque obtained by multiplying theopen water torque resulting from the application of SOLAS Reg. II-1 /29.3.2 (considering
however a maximum speed of 18 knots, by following factors:
Ice
Class
Factor

PC1

PC2

PC3

PC4

PC5

PC6

PC7

5

5

3

3

3

1.5

1.5

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13.2.2 The design pressure for calculations to determine the scantlings of the rudder actuatoris to be at least 1.25 times the maximum working pressure corresponding to the holding
torque defined in 13.2.1 (Derived from SOLAS Reg. II-1 / 29.2.2).
13.3 The rudder actuator is to be protected by torque relief arrangements, assuming thefollowing turning speeds [deg/s] without an undue pressure rise (ref UR M42 for undue
pressure rise):
Table 17: Steering gear turning speeds
Ice ClassTurning
speeds[deg/s]

PC1 and PC2

PC3 to PC5PC6 and PC7

10

7.5

6

If the rudder and actuator design can withstand such rapid loads, this special relief
arrangement is not necessary and a conventional one may be used instead (UR M42).
13.4
Additionally for icebreakers, fast-acting torque relief arrangements are to be fitted inorder to provide effective protection of the rudder actuator in case of the rudder being pushed
rapidly hard over against the stops.
For hydraulically operated steering gear, the fast-acting torque relief arrangement is to be sodesigned that the pressure cannot exceed 115% of the set pressure of the safety valves
when the rudder is being forced to move at the speed indicated in Table 18, also when taking
into account the oil viscosity at the lowest expected ambient temperature in the steering gearcompartment.
For alternative steering systems the fast-acting torque relief arrangement is to demonstrate
an equivalent degree of protection to that required for hydraulically operated arrangements.
The turning speeds to be assumed for each ice class are shown in Table 18 below.
Table 18: Steering gear turning speeds for icebreakers
Ice ClassTurning
speeds[deg/s]

PC1 and PC2

PC3 to PC5PC6 and PC7

40

20

15

The arrangement is to be designed such that steering capacity can be speedily regained.
14

Alternative Design

14.1
As an alternative to UR I3 – a comprehensive design study may be submitted andmay be requested to be validated by an agreed test programme.

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APPENDIXThe following illustrations show the excitation torque for all torsional load cases given in thisUR for different blade numbers (𝑍𝑍). The plots have been made using data for PC7 (𝐻𝐻𝑖𝑖𝑖𝑖𝑖𝑖 = 1.5)

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