DRAFT Azimuthing thruster ice load calculation and ... · 12/12/2014 · Further details for ice load calculation for each scenario are documented in the ice load model and calculation

RESEARCH REPORT DRAFTVTT-R-XXXX-YY

DRAFT Azimuthing thruster ice load calculation and simplified ice contact load formulation Authors: Aki Kinnunen, Juha Kurkela, Pekka Juuti

Confidentiality: Public

RESEARCH REPORT DRAFT VTT-R-YY

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Report’s title

Azimuthing thruster ice load calculation and simplified ice contact load formulation Customer, contact person, address Order reference

Finnish Transport Safety Agency

Jorma Kämäräinen

PO Box 320, FI-00101 Helsinki, Finland

W14-1 AZIRULE2014

Dno TRAFI /737/02.03.01/2014

Project name Project number/Short name

Azirule2014 86099 / Azirule2014 Author(s) Pages

Aki Kinnunen, Juha Kurkela, Pekka Juuti 152/ Keywords Report identification code

Ice load, ice structure interaction, contact, dynamic model,

measurement, ice class rules

VTT-R-

Summary

The approach for the development of Finnish-Swedish ice class rules for azimuthing thruster is to determine ice load scenarios and load cases to be included in the ice class rules. The ice loads will be calculated with sophisticated models and models will be verified with full scale measurement data from ice breaker Fennica. Simplified load formulae will be developed based on advanced ice load models and measurement data. The results will be combined to form the technical draft of Finnish-Swedish Ice Class Rules for azimuthing propulsion units. In this document, the work done up to and including 2014 is documented. The relevant load scenarios and applicable ice load calculation methods are presented, example cases selected and ice loads calculated for these example cases with different methods. It can be concluded that the developed dynamic impact load model gives contact loads that are at a correct range for full scale and correspond well to small scale experiment on sea ice. A parameter study was done with dynamic impact load model and based on the results, a simplified impact load formulation is suggested. The suggested formulation is currently for review only, it is to be validated by industry and other classification societies. The ridge penetration FE-model show a good correlation in thruster total loads with the full scale measurements and a proposal of the simplified load model for ice class rules is presented. The simplification proposal is based on parameter study with FE-model.Simplified formulation is suggested for azimuthing thruster total load when ship is going through ice ridge. This simplification still needs further testing and verification, and is provided for industry and classification societies review.

Confidentiality Public

Espoo 12.12.2014 Written by

Aki Kinnunen Senior Scientist

Reviewed by

Matti Jussila Senior Scientist

Accepted by

Johannes Hyrynen Technology Manager

VTT’s contact address

Distribution (customer and VTT)

TraFi, Jorma Kämäräinen, PDF and three paper copies VTT Archive, PDF and one paper copy

The use of the name of the VTT Technical Research Centre of Finland (VTT) in advertising or publication in part of

this report is only permissible with written authorisation from the VTT Technical Research Centre of Finland.


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Contents

Contents ..................................................................................................................................... 3

1. Introduction ........................................................................................................................... 5

2. Goal ...................................................................................................................................... 6

3. Ice load scenarions ............................................................................................................... 7

3.1 Ice impact ..................................................................................................................... 7 3.2 Ridge penetration ......................................................................................................... 8

4. Impact model : model development and validation experiments ........................................ 9

4.1 Impact model development .......................................................................................... 9

4.1.1 Indentation pressure ........................................................................................ 9

4.1.2 Description of model ...................................................................................... 11 4.2 Impact experiments purpose and principle ................................................................ 12 4.3 Testing limitations ...................................................................................................... 13 4.4 Impact test method..................................................................................................... 13

4.4.1 Test rig design and construction ................................................................... 13

4.4.2 Instrumentation and data acquisition............................................................. 13 4.5 Measurement results ................................................................................................. 15

4.5.1 Impact force transducer dynamic properties ................................................. 15

4.5.2 Ice properties ................................................................................................. 15

4.5.3 Ice compression strength .............................................................................. 16

4.5.4 Performed impact tests .................................................................................. 18 4.6 Impact load calculation and comparison to measurement ........................................ 19

4.6.1 Initial velocity for impact................................................................................. 19

4.6.2 Ice model parameters for impact model ........................................................ 20

4.6.3 Impact measurement and calculation results: 2014 test cases ................... 21

4.6.1 Impact measurement and calculation results: 2013 test cases .................... 24 4.7 Simplified impact load model ..................................................................................... 28 4.8 Simplified load model application for full scale impacts ............................................ 30 4.9 Impact load calculation summary .............................................................................. 31

5. Ship interaction with ice ridge............................................................................................. 32

5.1 Goal ............................................................................................................................ 32 5.2 Method ....................................................................................................................... 32 5.3 Model introduction ...................................................................................................... 32

5.3.1 Ice ridge ......................................................................................................... 32

5.3.2 Ice properties ................................................................................................. 32

5.3.3 Thrusters and hull .......................................................................................... 33 5.4 Parameter variation .................................................................................................... 35 5.5 Calculation .................................................................................................................. 36 5.6 Results ....................................................................................................................... 37

5.6.1 Thruster forces ............................................................................................... 37

5.6.2 Thruster pressure distribution ........................................................................ 38

5.6.3 Proposed formulation for total force .............................................................. 40

5.6.4 Simplified pressure area model ..................................................................... 41 5.7 Simplified ridge load model ........................................................................................ 42


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6. Conclusions ........................................................................................................................ 44

7. Summary............................................................................................................................. 45

References ............................................................................................................................... 46

Appendix A – Simulated force-time history of the thrusters .................................................... 47

Appendix B – Simulated maximum force of the thrusters ....................................................... 81

Appendix C - Force transducer construction ........................................................................... 87

Load calibration of impact force transducer ....................................................................... 89

Appendix D - Modal Analysis of impact force transducer ........................................................ 92

Experimental modal analysis.............................................................................................. 92 Calculated natural frequencies ........................................................................................... 96 Natural frequency comparison ........................................................................................... 98

Appendix E – Impact measurement signals ............................................................................ 99

Impact to solid ice, 100 mm impact head ........................................................................... 99 Impact to ice block, 100 mm impact head........................................................................ 102 Impact to ice block, 150 mm impact head........................................................................ 104 Measurement signals from 2013 tests ............................................................................. 106

Appendix F – Kinetic energy in impact test ........................................................................... 112

Appendix G - Parameter estimation for simplified impact load model .................................. 117

Main parameter : available kinetic energy ....................................................................... 117 Four – predictor model: kinetic energy, contact area, impactor stiffness ........................ 119 Thruster mass effect evaluation ....................................................................................... 119 Three-predictor model: kinetic energy and contact size, coarse parameter space ........ 123 Three-predictor model: kinetic energy and contact size, finer parameter space (the results

for rule proposal) ...................................................................................................... 124

Appendix H – Simulated contact pressure of the thrusters ................................................... 126

Appendix I – Ridge load simplified model versions ............................................................... 138

Total force maximum from time history, propeller area load included ............................. 139 Total force maximum from time history, propeller area load not included ...................... 141 Thruster force high frequency peaks disregarded, propeller area load included ............ 143 Thruster force high frequency peaks disregarded, propeller area load not included ...... 145 Total force, high frequency peaks disregarded, propeller area load included, ridge

consolidated layer thickness included ..................................................................... 147 Summary of model fits ...................................................................................................... 149


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1. Introduction

The Finnish Transport Safety Agency (Trafi) initiated ice class rule development project for azimuthig thrusters in 2010. Finnish-Swedish ice class rules do not have at the moment specific (ice class) rules for azimuthing thrusters. Into the project steering group were invited representatives from classification societies and azimuthing thruster manufacturing industry in order to get the ice class rule development work onto right track right from the start. VTT Technical Reasearch Centre of Finlad is responsible of the actual development work, following the guideline frames set by the steering group. A project kick-off meeting was held in June 2010 in Helsinki, with a very good attendance from the invited classification societies and industry partners. The initiative meeting was followed by participator survey regarding what to study in this project.

The work progress was followed up in steering group meetings, held annually in 2011, 2012, 2013 and 2014.

In this document the research activities and key results achieved during and up to 2014 are presented. Simplified load formulas are suggested for the studied load cases, namely ice block impact to azimuthing thruster and ice ridge interaction with ship and azimuthing thruster.

.


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2. Goal

The ice class rule development is aimed to be harmonized with international ice class rule work. The approach is to determine ice load scenarios and load cases to be included in the ice class rules. The ice loads will be calculated withsophisticated models and models will be verified with measurement data. Simplified load formulae will be developed based on ice load models and measurement data. The results will be combined to form the technical draft of Finnish-Swedish Ice Class Rules for azimuthing propulsion units.

For 2014, goal was to

- Use the previously implemented ship and thruster geometry for ridge penetration FEM modelling and run a parametric study for thruster-ridge interaction loads, including variation of ship size, thruster size, thruster steering angle and ridge geometry, in order to establish idea of simplified thruster load model for ridge penetration case.

- Use available full scale data for validation purposes; measurements from ice breaker Fennica and Botnica were available, Fennica results were considered primary validation data.

- Ice block impact model was to be further developed and validated, improve ice-structure contact force model functionality and, with a controlled test setup, to evaluate the model accuracy in load calculation and dynamic magnification in impact.


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3. Ice load scenarions

The relevant ice load scenarios for ice structure interaction are shortly described here. Further details for ice load calculation for each scenario are documented in the ice load model and calculation chapters.

3.1 Ice impact

The main parameters when an individual ice block impact to the propulsion structure are the affecting ice mass m (kg) and initial relative velocity v (knots) between the ice and structure. Relevant scenarios include at least impact to propeller hub and ’rear end of propulsion unit’. The relevant load calculation models include at least: VTT, ABS and DNV ice load models. Following figure illustrates the load scenario.

Figure 1. Ice impact load scenario


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3.2 Ridge penetration

Ice ridges are common features in ice-covered sea areas. They are formed when sea ice is compressed or sheared under the action of wind and currents. A ridge contains a large number of ice pieces of varying sizes and shapes that are piled arbitrarily. Rubble above the water line is called a sail and the rubble below the water line is called a keel. Between them, close to the waterline, is the re-frozen solid ice zone called a consolidated layer, Figure 2. First-year ridges are often a key consideration from an engineering perspective.

Figure 2. Principal sketch of ice ridge.

The relevant load calculation methods include finite element simulations (FEM) and corresponding ice load predictions according to DNV. Even though the FEM simulation with advanced ice failure model requires very intensive computation and is fairly complicated to use, it gives basic understanding of failure mechanisms of ice and of ice load development during ice-thruster interaction. This approach can then be further utilized for instance to develop a simplified ice pressure distribution model. The worst scenario to introduce the highest loads on the thruster body was assumed, when the thruster was turned sideways before interacting with an ice ridge (see Fig. 3). The other steering angles can be straightforwardly studied by the FEM-analysis.

Figure 3. Ridge penetration load scenario.


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4. Impact model : model development and validation experiments

4.1 Impact model development

The previously used two-mass (thruster and ice) [1] impact model was revised to use three mass system, i.e. model includes ship mass (ms), flexible connection between thruster and ship (k), thruster mass (mt), contact model between ice and thruster(Fc) and ice mass (mi). Principle is shown in Figure 4.

Figure 4. Impact model principle.

The motions of equation can be derived for the three mass system as follows.

4.1.1 Indentation pressure

The contact area grows when thruster structure penetration into ice goes further. This means that the contact force grows according to equation (1) because contact area grows faster

than indentation pressure p is decreasing. Contact force 𝐹𝑐 is based on indentation pressure and is determined by equation

𝐹𝑐 = 𝐴𝑝0√𝐴0

𝐴,

( 1 )

where 𝐴0 is a reference area and 𝑝0 is a reference pressure. For Baltic Sea ice 1 m2 and 3 MPa can be used. The reference pressure can be set to the uniaxial compression strength of


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ice if it is known. This reference pressure value is the way to control the ice strength parameter in the contact model. Design curve for the indentation pressure and some full scale data points are shown in the Figure 5. Some full scale data points are from m/s Aatos (Huovinen, 1990) and rest of the data is collected from different sources by Bjerkås (2007)

Figure 5. Indentation pressure as a function of contact area.

In the conducted laboratory scale tests on sea ice, a maximum pressure limit for small area contacts is used in the form

𝑝0√𝐴0

𝐴≤ 𝑝𝑙𝑖𝑚

( 2 )

The behavior of this limit is presented in principle in Figure 6. The area relationship exponent has also effect on the load beahviour and values of ½ and 1/3 are also shown.


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Figure 6.Principle of contact pressure limit for small contact areas.

4.1.2 Description of model

The contact is assumed to take place between a hemispherical section of thruster body

(‘head’) or equally hemispherical propeller hub. For this approach the contact area 𝐴 is the current contact area, defined by

𝐴 = 𝜋(𝑟2 − (𝑟 − 𝑢2 − 𝑢1)2), ( 3 )

where 𝑟 is radius of curvature of the thruster housing / propeller hub. During the impact, contact force 𝐹𝑐 and response force 𝐹𝑟 are defined by equations

−𝐹𝑟 = 𝑚𝑠�̈�0 𝐹𝑟 − 𝐹𝑐 = 𝑚𝑡�̈�1 + 𝑐1(�̇�1 − �̇�0) + 𝑘(𝑢1 − 𝑢0)

−𝐹𝑐 = 𝑚𝑖�̈�2 + 𝑐2(𝑢2̇ − 𝑢1̇)

𝐹𝑐 = 𝐴𝑝0√𝐴0

𝐴

( 4 )

where 𝑚𝑠 is mass of a ship, 𝑚𝑡 is mass of the thruster, 𝑚𝑖 is mass of the impacting ice block

and 𝑢0 , 𝑢1 and 𝑢2 are displacements as shown in Figure 4. Response force 𝐹𝑟 is determined with connection stiffnes k and damping c as follows

𝐹𝑟 = 𝑘𝑥1 + 𝑐�̇�1 𝑥1 = 𝑢1 − 𝑢0

𝑥1̇ = 𝑢1̇ − 𝑢0̇

( 5 )

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

Pressure - area relationship type

Aref

/ Acontact

Pconta

ct /

Plim

p1/2

p1/3


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Then, the equations of motion are solved with difference method in direct time domain solution, with the initial conditions for displacement (zero) and velocity v0 for ship and thruster

𝑢0(0) = 0

𝑢1(0) = 0 𝑢2(0) = 0 𝑢0̇(0) = 𝑣0

𝑢1̇(0) = 𝑣0 𝑢2̇(0) = 0

( 6 )

4.2 Impact experiments purpose and principle

The test setup was done to facilitate controlled impacts to ice for impact model validation The principle of test is to use a pendulum mass to impact a controlled impact with steel structure into ice. Principle is shown in Figure 7.

Figure 7. First sketch for impact testing principle.

Measured quantities in the test were ice contact load, acceleration of impact mass and acceleration of ice.

Goal for the test arrangement is to achieve direct information from steel impact to ice, for comparison with calculation model and further development of the model. The test was done in real environment, on sea ice and impact point was submerged, to get all the elements included in test that are acting in real ship application.


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4.3 Testing limitations

The limitations known during the testing are

- limited number of impact repetitions at each test condition, thus statistically these results are limited.

- Acceleration sensors on ice and impactor mass indicate contact velocities and displacements through integration of the measured acceleration signal. This is not completely accurate.

4.4 Impact test method

4.4.1 Test rig design and construction

The impact test rig shown in Figure 8 was designed at VTT, manufactured from rectangular section tubing, parts connected with bolt joints. The same test rig was used on field tests in winter 2013 in Espoo as well.

Pendulum impactor is constructed of center plate and additional mass plates are bolted to both sides of centerplate. The center plate is cut from 50 mm steel plate. It is shaped to make it feasible to use as force transducer for impact. Impact head was mounted with a M12 stud to the center plate of pendulum.

Figure 8. Impact test rig on sea ice.

4.4.2 Instrumentation and data acquisition

Data acquisition was done with imc Cronos PL8 measurement front-end, used together with imcDevices software for time data recording to laptop PC. Further analyses were done with imc FAMOS software (ver 6.1 rev 7).


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Measured quantities were

- acceleration of impact mass ( triaxial acceleration sensor)

- acceleration of ice block ( triaxial acceleration sensor)

- force between impact mass and impact head (strain gauges)

- synchronization signal (led light voltage) to be used for video and measurement signal synchronization.

Acceleration was measured wit PCB 629A10 type triaxial acceleration sensors. The sensor on impacting mass is seen in Figure 9. The sensor was directly bolted to the impact mass. On ice, a bolt was used for transducer attachment on ice surface.

Figure 9. Acceleration sensor mounted on impact mass. Triaxial sensor X-direction is in direction of impact.


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4.5 Measurement results

The measurements took place near Oulu, Finland, on March 10. – 14., 2014. The ice thickness in the test area was about 50 cm.

4.5.1 Impact force transducer dynamic properties

The force transducer dynamic properties (i.e. lowest natural frequency) were measured by means of experimental modal analysis. Natural frequency in impact direction is used in the impact load model as input to determine the connection stiffness. The impact experiments are reported in Appendix D. Measured natural frequencies for the different impact heads are shown in following table.

Table 1. Natural frequencies in measurement

Impact head size Natural frequency Damping

mm Hz %

100 166,5 0,08

150 151,8 0,11

4.5.2 Ice properties

Ice properties were measured during the field tests on Baltic Sea in Oulu. Level ice thickness varied between 47 cm and 50 cm. In Figure 10 is illustrated the typical structure and temperature of the ice (T = -0,05 °C). Air temperature during the test was 0 °C ± 1 °C. The salinity of the melted ice in all samples was 0 ‰.

Figure 10. Typical structure and temperature of the ice (T = -0,05 °C).


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4.5.3 Ice compression strength

In total ten (10) ice cores were drilled from the test location and compressed in vertical crystal direction. The compression velocity was 2,1 mm/s. Dimensions of the tested cores were 105 mm (diameter) and 250 mm (length). In Figure 11 one can see drilling and compressing of an ice core.

Figure 11. Driliing and compressing of an ice core.

Results of ice core compression tests and the average value of all ten tests can be seen in Table 2. In Figure 12 the ice core compression test results are illustrated as a graph. Compressive maximum pressure varies from 2,6 to 5,0 MPa. Average value of all ten tests is 3,7 MPa.

Table 2. Results of ice core compression tests.

Test # Pressure

[Mpa]

1 2,7

2 3,5

3 3,6

4 2,7

5 5,0

6 2,6

7 4,7

8 4,1

9 3,7

10 4,7

Average 3,7


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Figure 12. Uniaxial ice compression tests.

0

1

2

3

4

5

6

0 2 4 6 8 10

Pre

ssu

re [

MP

a]

Test number

Uniaxial ice compression test

Pressure [Mpa]


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4.5.4 Performed impact tests

Tests included impacts to solid ice, and impacts to freely floating ice block of approximately 200 .. 300 kg. The pendulum start height (impact velocity) was kept constant and impact head size was varied.

The height of the pendulum was measured for each impact. The actual measurement was taken between pendulum mass plate mounting bolt andwater surface. The pendulum height with respect to rest position (pendulum submerged) is calculated based on the submerging depth of the measurement point (0.310 m). Tests are listed in Table 3.

The pendulum mass was varied in the tests, and the masses are listed in Table 4.

Table 3.List of impact tests, March 2014.

Nr Date Time Test description Ice

temperature

Mass start

height (1

Mass start height from water

surface Ice block

C m m kg

1 11.3.2014 16:38 Small head, low speed, solid ice -0,05 0,285 -0,025 na

2

16:50 Small head, low speed, solid ice -0,05 0,285 -0,025 na

3

17:02 Small head, low speed, solid ice -0,05 0,285 -0,025 na

4 12.3.2014 9:27 Small head, low speed, solid ice -0,05 0,285 -0,025 na

5 12.3.2014 10:14 Small head, low speed, ice block -0,05 0,285 -0,025 302

6

10:26 Small head, low speed, ice block -0,05 0,285 -0,025 272

7

10:40 Small head, low speed, ice block -0,05 0,285 -0,025 242

8 12.3.2014 11:33 Big head, low speed, ice block -0,05 0,285 -0,025 242

9

11:37 Big head, low speed, ice block -0,05 0,285 -0,025 242

10

11:48 Big head, low speed, ice block -0,05 0,285 -0,025 212

(1 Mass start height is relative to pendulum mass lowest position

Table 4. Pendulum masses in impact tests, March 2014.

Test ID

Base

plate kg

Mass plate

kgPcs

Total

kg

Size

mm

Mass

kg

Mass

plate kgPcs

Total

kg

Pendulum

total kg

1 ..4 42 14,7 10 147 100 2 2 5 12 201

5..7 42 14,7 4 58,8 100 2 2 5 12 112,8

8..10 42 14,7 4 58,8 150 6 2 3 12 112,8

Pendulum total = baseplate + mass plates + impact head + impact head mass plates

Baseplate + mass plates Impact head


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4.6 Impact load calculation and comparison to measurement

4.6.1 Initial velocity for impact

Initial velocity for impact model load calculation is given as “ship speed”. The model limits the impact calculation by observing the kinetic energy of ice block. It is assumed that maximum energy available for ice crushing is the kinetic energy of ice block at the impact velocity.

In addition to initial velocity, the velocity change (= kinetic energy change) during impact is important.

For test case calculations, it was assumed that the pendulum mass (ship) had equal velocity with ice after impact. This leads to estimating the impact initial velocity as being the sum of velocity change magnitudes during impact.

𝑣𝑖𝑚𝑝𝑎𝑐𝑡 = |∆𝑣𝑖𝑐𝑒| + |∆𝑣𝑖𝑚𝑝𝑎𝑐𝑡𝑜𝑟|

( 7 )

This is used because impactor speed decreases and ice block accelerates during impact. For impact to solid ice, the ice velocity after impact is taken to be zero.

Figure 13. Principle of velocity assumption in impact. Impactor speed decreases, ice block increases.

Impact start Impact end

zero velocity

end velocity

impact velocity

Time

Velo

city

vimpactor

vice


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4.6.2 Ice model parameters for impact model

Impact load calculation parameters that gave good correspondence to measurement with 2013 and 2014 tests are listed in table below.

In 2013 experiment, the ice was softer than in 2014 experiments, also by quantitative estimate on test site.

Table 5. Dynamic impact load model parameters for good fit to experiment

Parameter Unit Value 2013 Value 2014 Notes

σice MPa 3 3,7 Ice uniaxial compression strength

plim MPa 8 10Pressure-area relationship maximum

pressure value for small area contacts

exponent - 1/3 1/3 Pressure-area relationship exponent


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4.6.3 Impact measurement and calculation results: 2014 test cases

The dynamic impact model was used to calculate loads for experiment cases. Following figures show the results with 2014 experiment.

Figure 14. Impact load measurement and calculated impact loads for test cases 2-4, impact to solid ice with 100 mm impact head. Fr curve is calculated response load curve.

0 0.01 0.02 0.03 0.04 0.05-10

0

10

20

30

40

Time (s)

Fo

rce

(kN

)

Ice impact force, impact to solid ice, 100mm impact head

Meas02

Meas03

Meas04

Fr


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Figure 15. Impact load measurement for test cases 5-7 and respective load calculation. 100 mm impact head, Fr curve is calculated response load curve. 3.7MPa, 10 MPa, 1/3

0 0.01 0.02 0.03 0.04 0.05-10

-5

0

5

10

15

20

25

Time (s)

Fo

rce

(kN

)

Ice impact force, impact to block, 100mm impact head

Meas05

Meas06

Meas07

Fcontact

Fresponse


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Figure 16. Impact load measurement for test cases 8-10 and respective load calculation. 150 mm impact head, .Fr curve is calculated response load curve. 3.7 MPa, 10 MPa, 1/3

0 0.01 0.02 0.03 0.04 0.05-10

-5

0

5

10

15

20

25

Time (s)

Fo

rce

(kN

)Ice impact force, impact to block, 150mm impact head

Meas08

Meas09

Meas10

Fcontact

Fresponse


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4.6.1 Impact measurement and calculation results: 2013 test cases

The measured impact loads from 2013 tests and respective calculated loads with dynamic impact model are shown in following figures.

Figure 17. Impact load measurement and calculated impact loads for 2013 experiment test cases 1-3, impact to solid ice with 100 mm impact head. Model:Fc curve is calculated contact load and Model:Fr curve is calculated response load curve.

-0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-5

0

5

10

15

20

25

30

35

40

45Ice impact force

Time [s]

Forc

e [

kN

]

Model: Fc

Model: Fr

Measured 1

Measured 2

Measured 3


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Figure 18. Impact load measurement for 2013 experiment test cases 4-6 and respective load calculation. 100 mm impact head, start height 0.11m above ice level, 400 kg ice block. Model:Fc curve is calculated contact load and Model:Fr curve is calculated response load curve

-0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-5

0

5

10

15

20

25

30

35

40Ice impact force

Time [s]

Forc

e [

kN

]

Model: Fc

Model: Fr

Measured 1

Measured 2

Measured 3


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Figure 19. Impact load measurement for 2013 experiment test cases 7-8 and respective load calculation. 150 mm impact head, start height 1.28m above ice level, 400 kg ice block. Model:Fc curve is calculated contact load and Model:Fr curve is calculated response load curve

-0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-20

-10

0

10

20

30

40

50

60Ice impact force, impact to block, 150 mm impact head

Time [s]

Forc

e [

kN

]

Model: Fc

Model: Fr

Measured 1

Measured 2


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Figure 20. Impact load measurement for 2013 experiment test cases 9-11 and respective load calculation result. 150 mm impact head, start height 0.11 m above ice surface, 300 kg ice block estimated. Model:Fc curve is calculated contact load and Model:Fr curve is calculated response load curve.

-0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-10

-5

0

5

10

15

20

25

30

35

40Ice impact force, impact to block, 150 mm impact head

Time [s]

Forc

e [

kN

]

Model: Fc

Model: Fr

Measured 1

Measured 2

Measured 3


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4.7 Simplified impact load model

The simplified impact load model is assumed to be, in general, function of ice block mass, impact velocity, contact area, thruster flexibility and ice strength.

𝐹𝑖𝑚𝑝𝑎𝑐𝑡 = 𝑓(𝑚𝑖𝑐𝑒 , 𝑣𝑖𝑚𝑝𝑎𝑐𝑡 , 𝐴𝑐𝑜𝑛𝑡𝑎𝑐𝑡 , 𝑓𝑡ℎ𝑟𝑢𝑠𝑡𝑒𝑟, 𝜎𝑖𝑐𝑒)

( 8 )

The simplified model is achieved in following way

1. Developed the dynamic impact contact load model

2. Dynamic impact load model validation with experiments

3. Parametric study with the validated dynamic impact load model

4. Regression fit of simplified formulation to the parametric study results

The formation of the simplified formula was an iterative process, where different forms of formula were tested with least squares fit to the dynamic impact load model parametric study result set.

From testing several forms of simplified models, a good candidate for estimating the impact contact load is

𝐹𝑖𝑚𝑝𝑎𝑐𝑡 = 𝑏2𝑅1/𝑏1(𝑚𝑖𝑐𝑒 ∗ 𝑣𝑖𝑚𝑝𝑎𝑐𝑡2 )

1/𝑏3

( 9 )

The model variables are

R : The impacting steel part radius, in meters

mice : the impacting ice block mass, in kg

vimpact : The impact initial speed, in m/s

The model in (12) was used in MATLAB regression analysis tool, and fitting the model to the parametric study data set achieved with dynamic impact model gives following results:

Nonlinear regression model:

Fc ~ (Radius^(1/b1))*b2*(Mass_ice*Velocity^2)^(1/b3)

Estimated Coefficients:

Estimate SE tStat pValue

b1 2.1174 0.016651 127.17 0

b2 34653 867.65 39.938 3.2622e-265

b3 3.0962 0.017691 175.02 0

Number of observations: 2295, Error degrees of freedom: 2292

Root Mean Squared Error: 2.41e+05

R-Squared: 0.97, Adjusted R-Squared 0.97

F-statistic vs. zero model: 8.65e+04, p-value = 0


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This means that the simplified model would be

𝐹𝑖𝑚𝑝𝑎𝑐𝑡 = 34653𝑅1/2.1174(𝑚𝑖𝑐𝑒 ∗ 𝑣𝑖𝑚𝑝𝑎𝑐𝑡2 )

1/3.0962

( 10 )

The decimals can be rounded off for the ice class rule proposal version of the simplified formula as follows

𝐹𝑖𝑚𝑝𝑎𝑐𝑡 = 34500𝑅1/2(𝑚𝑖𝑐𝑒 ∗ 𝑣𝑖𝑚𝑝𝑎𝑐𝑡2 )

1/3

( 11 )

Testing the simplified formulation results are compared to the dynamic contact load model results in Figure 21. On X-axis is the dynamic load model contact load estimate, and on Y-axis is the corresponding simplified load model result. Blue circles show the model with decimals and the black circles show the results with the proposed ice class rule formulation for impact contact load.

Figure 21. Simplified impact contact load model results (blue circles), the rule proposal formulation impact contact load model results(blac circles) as a function of the dynamic impact contact load model results. Results are calculated with same input values.

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

8

Dynamic contact model maximum load [MN]

Sim

plif

ied m

odel lo

ad e

stim

ate

[M

N]

Three-predictor nonlinear regression model vs dynamic impact model

Simplified model: Fc = b

2R(1/b1)(m

ice v

ship2 )(1/b3)

Rule proposal


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4.8 Simplified impact load model application for full scale

The example application of the impact load model for full scale is presented in Table 6.

The impact contact load is estimated based on ice class dependent parameters and known thruster impacting part radius. The response load at the thruster connection to ship is estimated to be 1,5 times the contact load. The estimate is based on dynamic magnification in impact.

Table 6. Example application of ice impact load estimate with the simplified load formula.


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4.9 Impact load calculation summary

It can be concluded that the developed dynamic impact load calclulation model, with three-mass system including ice-thruster contact model and flexible connection between thruster and ship, is capable of estimating the contact load rather well. The results presented in this document for the small scale experiment support this as well as previous work with full scale data verification [1,2].

The effect of damping during impact contact event is not yet properly modelled in the simplified impact model and is a point for further study. Tailored experiments are preferred way for establishing the proper understanding for damping in this case.

The developed dynamic load calculation model can be used as load calculation tool for estimating the effect of different parameters to impact load, when developing simplified formulation for ice class rule proposal.

With the dynamic impact load model, a parameter study was done. The input values and corresponding dynamic contact load result were used to formulate a simplified impact contact load formula.

The simplified formula includes term for impact kinetic energy, contact area size and constants. The constants were determined by nonlinear regression model fitting. The used regression fit tool was MATLAB nonlinear model fit.

The resulting simplified model was checked by comparing the simplified load formula results with dynamic model results and full scale applications. The simplified load model gives same level of load as the validated dynamic impact contact load model.

The simplified impact load model described here was distributed to the project steering group members for review purposes, and is therefore not final, subject to revision.


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5. Ship interaction with ice ridge

5.1 Goal

The research goal was to clarify the contact pressure distribution of the thruster body and present a simplified calculation method for contact pressure and thruster total force. The results are compared to available full scale data for validation purposes.

5.2 Method

The ship interaction with ice ridge is simulated with a numerical finite element method. FEM-model is created from a ship and different ice ridges. The FEM simulations are validated with full scale measurements performed on ice breaker Fennica in 1994 [2].

5.3 Model introduction

5.3.1 Ice ridge

The three ridge types used in the simulations are callded mild, typical and extreme. Total ridge height was 3.6 m (mild), 5.0 m (typical) and 10.0 m (extreme). Figure 22 shows the dimensions of ridge.

Figure 22. Ice ridges for ship interaction.

5.3.2 Ice properties

The consolidated layer was divided in FE model into three (mild ridge), five (typical) or nine (extreme) layers in the thickness direction. Mechanical properties: elastic modulus, compressive and tensile strength were varied randomly such that each layer consisted of ten different material properties with the same mean and standard deviation as obtained in the material tests.

Concrete Damaged Plasticity –model (CDP) was applied to simulate the failure of the consolidated layer. Mechanical properties of consolidated layer are listed in Table 7, Table 8

and Table 9. Ice density was = 900 kg/m3. Tensile strength was about 8 % from compression strength.


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Table 7. Consolidated layer ice properties, mild ridge.

Depth [m] Eave [GPa] Estdev [GPa] Sc,ave [MPa] Sc,stdev [MPa]

0.100 0.7655 0.2948 3.9092 1.2238 0.300 0.8441 0.2829 4.1934 0.7482 0.500 0.0916 0.0360 1.0498 0.2842

Table 8. Consolidated layer ice properties, typical ridge.


0.100 0.7047 0.311 3.5218 1.3015 0.300 0.9418 0.33 4.9764 1.1171 0.500 0.8441 0.2829 4.1934 0.7482 0.700 0.5322 0.2036 2.7092 0.5307 0.900 0.0881 0.029 1.1032 0.3376

Table 9. Consolidated layer ice properties, extreme ridge.


0.0972 0.6992 0.322 3.48 1.3224 0.2917 0.7655 0.2948 3.9092 1.2238 0.4861 0.9125 0.3242 4.7985 1.1349 0.6806 0.9074 0.3088 4.6729 0.9444 0.8750 0.8441 0.2829 4.1934 0.7482 1.0694 0.7383 0.2711 3.5709 0.6593 1.2639 0.4546 0.1742 2.4157 0.4862 1.4583 0.0916 0.036 1.0498 0.2842 1.6528 0.0857 0.0243 1.1387 0.3731

Cohesion value and friction angle of the ice rubble are d = 6000 N/m2 and β = 35°. Density of

ice rubble is = 642 Kg/m3, elastic modulus is E = 1.1e+08 N/m2. Poisson’s value = 0.3

and friction coefficient in ice-structure contact = 0.15.

5.3.3 Thrusters and hull

Ship hull shape is from Fennica ice breaker. Ship hull length was 116.0 m, width 26.0 m and draught 12.5 m. The mass of the ship varied according to the propeller size (see Table 10).

Also thruster’s shape was same as Fennica, but it was without the nozzle in the simulations. Fennica thruster’s diameter was 2.40 m and length 5.60 m. Propeller diameter was 4.20 m and number of blades was 4. In simulation, thruster size was scaled on the coefficient 0.5, 1.0, 1.5 or 2.0 (simulation cases 2 m, 4 m, 6 m and 8 m propeller size). Shape of the thruster and hull is shown in Figure 23 and thruster size in Figure 24.


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Figure 23. Thruster and hull shape.

Figure 24. Different thruster size, simulation cases 2 m, 4 m, 6 m and 8 m.

Table 10. Total ship mass on the different propeller size.

Propeller size Ship mass

2 m 1.22e+06 kg 4 m 9.76e+06 kg 6 m 3.29e+07 kg 8 m 7.81e+07 kg

Figure 25 introduces the used FEM-model. Middle part of the model was discretized with dense element mesh and the far-end boundary region with sparse mesh. A dense element mesh size was 400 – 500 mm and sparse mesh 1.0 - 2.5 m. Infinity element size in the edge was 20 - 40 m. In vertical direction the element size in the sail was 125 - 200 mm, in the consolidated layer 194 - 200 mm and in the rubble 375 – 400 mm. The model size was 100 x 200 m to 200 x 200 m, dense mesh area 25 - 100 m and sparse mesh area 10 - 35 m. The number of elements in the model was 240000 - 430000.

Numerical simulations were performed by Abaqus/explicit 6.12.1 program. Element types were C3D8R (ice), CIN3D8 (ice infinity), R3D3 and R3D4 (hull, thruster and propeller). The hull, thruster and propeller were assumed fully rigid. Simulation time was 5 - 30 s.

Figure 25. Fem-model.

Infinity elements

Ship moving

Dense

elements Sparse elements

2 m 4 m 6 m 8 m


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5.4 Parameter variation

Simulation variables were:

- ridge type: mild, typical or extreme

- ship initial speed: 5, 8 or 12 knot

- propeller size: 2, 4, 6 or 8 m

- thruster angle: -180° or -90°.

In the model there were two thrusters. One straight ahead to ice, one sideways. In total, there were 24 simulation cases. In addition to the previous, some 180°/180° simulations

were made. Part of the simulation (4 m propeller) was done 2013. The target simulation cases are listed in Table 11.

Table 11. Parameters for FEM model studies.

Ship speed Ridge size Thruster angle Propeller diameter Notes [knot]

[°] [m]

5

Mild 180 / 90 2

Mild 180 / 90 4 Done 2013 Mild 180 / 90 6

Mild 180 / 90 8

Typical 180 / 90 2

Typical 180 / 90 4 Done 2013 Typical 180 / 90 6

Typical 180 / 90 8

Extreme 180 / 90 2

Extreme 180 / 90 4 Done 2013 Extreme 180 / 90 6

Extreme 180 / 90 8

8

Mild 180 / 90 2 Mild 180 / 90 4 Done 2013 mild 180 / 90 6

Typical 180 / 90 2 Typical 180 / 90 4 Done 2013 Typical 180 / 90 6

Extreme 180 / 90 2 Extreme 180 / 90 4 Done 2013 Extreme 180 / 90 6

12 Mild 180 / 90 4 Done 2013

Typical 180 / 90 4 Done 2013 Extreme 180 / 90 4 Done 2013

The energy available for ship penetrating into ice ridge is the kinetic energy of the vessel before ice ridge – ship interaction event. This principle gives possibility to use same ship size for 2014 ridge penetration simulations that was used before. For example, the Fennica simulations (and full scale tests) were done at 5, 8 and 12 knots initial velocity. When ship mass is four times Fennica’s mass, the equal kinetick energies are available at 2.5, 4 and 6 knots. Table 10 shows the ship mass on the different propellers.

For parameter variations, the initial speed is now taken to be as 5 knots, because this seems reasonable speed for merchant vessels, that are of similar size with IB Fennica. For smaller vessels, speed may be higher, for bigger vessels, speed may be lower.


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5.5 Calculation

In simulation the ship was moving towards the ridge (Figure 25). The ship has an initial speed and ship speed slows down when it penetrates to ice ridge due to the resistance force during penetration. This simulation is considered to correspond to ramming into ice ridge. The contact pressures of thrusters are obtained as results of simulations. Result time histories were printed at 0.005 s intervals.

Only the port side (left) thruster is turned, the starboard side (right) thruster remains unchanged. Table 12 introduces used thruster angles and moving direction.

Table 12. Thruster angles and moving direction.

Angles Port side thruster Starboard side thruster

-90° / -180°

In the calculation of the contact pressure the thrusters is divided into several slices. The upper part was divided into three and the lower part into five slices, see Figure 26 for slicing principle. The average contact pressure is calculated for the area of each slice.

The contact pressure is based on the node forces of the FEM-model. The nodes belong to some slice on the basis of the height coordinate.

Average contact pressure for thruster body pi is

𝑝𝑖 =𝐹𝑖

𝐴𝑖 (1)

where Fi is sum of node forces in slice i Ai is surface area (perpendicular, projected area) in slice i.

The ice-structure contact forces acting on propeller area (see Figure 26) are not included in calculation of the average contact pressure for thruster body. The net contact force for propeller is summed separately according to the slice. Propeller loads are used for calculation of the thruster total force.

Figure 26. Division of the thruster into the slice. The slice numbering is below to up.

Mo

vin

g


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5.6 Results

5.6.1 Thruster forces

The total forces of the thrusters were calculated in all cases. Direction of the force is horizontal (moving direction). Simulated results contained some high frequency numerical disturbances which were filtered away with 15 Hz low-pass filter (Butterworth 8th order low pass filter with 15 Hz cut-off frequency).

Table 13 shows maximum simulated force of the thruster included or not propeller force. Appendix A contains simulated force-time history from all the cases. In cases where several simulations of same case have been done, linear average has been calculated from the results.

The total force increases approximately linearly as a function of the speed and ridge thickness (Figure 27 and appendix B). Also, turning the thruster to the transverse position (-

90) increases the force typically 20 – 30 % compared to the longitudinal position (-180) if propeller force is included. Appendix B contains also simulated total forces of the thrusters include short-term peak values.

Table 13. Maximum simulated total forces of the thrusters. Force is ship moving direction. No include short-term peak values.

Ridge Speed Propeller Thruster force [MN] No propeller force

Thruster force [MN] Include propeller force

Angle -180° Angle -90° Angle -180° Angle -90°

Mild

5 knot

2 m 0.4 0.4 0.4 0.5

4 m 0.8 0.7 0.8 1.0

6 m 1.2 1.1 1.2 1.8

8 m 2.1 2.3 2.1 2.7

8 knot

2 m 0.6 0.5 0.6 0.7

4 m 1.3 1.0 1.3 1.4

6 m 2.2 1.7 2.2 2.8

12 knot 4 m 1.9 1.3 1.9 2.0

Typical

5 knot

2 m 0.6 0.4 0.6 0.7

4 m 1.1 1.3 1.2 1.7

6 m 1.9 1.9 2.0 2.6

8 m 3.8 3.8 4.0 4.6

8 knot

2 m 0.7 0.6 0.7 1.0

4 m 1.2 1.5 1.3 2.2

6 m 2.9 2.8 3.0 4.0

12 knot 4 m 2.2 1.8 2.5 3.3

Extreme

5 knot

2 m 0.6 0.6 0.6 1.1

4 m 1.9 1.7 1.9 2.8

6 m 2.8 3.4 3.7 4.8

8 m 6.5 8.1 6.5 8.8

8 knot

2 m 0.9 0.8 0.9 1.3

4 m 2.5 2.3 2.5 3.6

6 m 5.2 5.7 5.6 7.2

12 knot 4 m 3.3 3.5 3.3 5.0


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Figure 27. Effect of the ship initial speed on the thruster force on different ridge types. Values not include propeller force nor short-term peak values.

5.6.2 Thruster pressure distribution

From the simulation results the contact pressures were calculated according to chapter 5.5. Figure 28 is shown typical maximum thruster pressure distributions according to the slice, longitudinal or transverse position of the thruster.

For the longitudinal thruster position (thruster angle -180), the maximum contact pressures are located usually in slice 3 to 7, according cases. Small thrusters (2 m and 4 m) maximum


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pressure is located lower (slice 3 or 4). Large thruster (8 m), maximum pressure is located upper part of the thruster.

When thruster is sideways in ramming situation, (transverse position -90), maximum contact pressure is located in the upper part, in slice 6 or 7. Generally, the contact pressure reduces linearly downwards. Level of the contact pressure is typically 50 % compared to pressure of the longitudinal position.

Figure 28. Maximum contact pressures of the thrusters by slice, effect of thruster size on the pressure distribution. The contact pressure maxima do not appear at the same time in all the slices.

Figure 29 is shown same as previous figure, but dependence on the height. From the figure it is seen, that the different size thrusters pressure distribution in the height direction is not similar. Relation of the thruster (propeller) size and ridge height have an effect a pressure distribution.

Small thruster (2 m) is always inside the ridge and therefore the pressure level is bigger. The lower part of the large thruster can be below the ridge bottom and therefore the pressure level in the lower part is smaller. The same effect can be seen on both longitudinal and transverse thruster.


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Appendix G is shown the contact pressures on the all cases. The contact pressure maxima do not appear at the same time in all the slices.

Figure 29. Maximum contact pressures of the thrusters by height, effect of thruster size on the pressure distribution. The contact pressure maxima do not appear at the same time in all the slices.

5.6.3 Proposed formulation for total force

A formulation for thruster total force is based on the FEM results. The force is assumed to depend on initial speed of the ship, height of the ridge and cross-sectional area of the thruster.

The form of the proposed formulation for total force F [kN] is:

𝐹 = 𝑎 ∙ 𝑣𝑏 ∙ 𝐻𝑐 ∙ 𝐴𝑑

( 12 )

where v is ship speed [m/s] H is ridge thickness [m]

A is cross-sectional area of the thruster [m2] a, b, c and d are constants.


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The nonlinear regression model fit of the formulation to the FE model simulation result set is

𝐹 = 0.032 ∙ 𝑣0.66 ∙ 𝐻0.9 ∙ 𝐴0.74

( 13 )

The correspondence of the simulation results and formula ( 13 ) is seen from Figure 30. The proposed formulation is conservative.

Figure 30. Simulation results and the formula ( 13 ). 8 m propeller size not included.

5.6.4 Simplified pressure area model

A simplified pressure model was also developed from FEM results. According to results the contact pressure distribution is different for longitudinal or transverse thruster position. See Figure 31. The longitudinal position, the typical distribution varies in different cases, type a), b) or c). The transverse position, contact pressure distribution clearly reduces linearly downwards, type d).

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

FEM Model maximum load [MN]

Sim

plif

ied m

odel lo

ad e

stim

ate

[M

N]

Simplified rige load model vs FEM results

Simplified model F = 1.1 a Vb Hc Ad

Rule proposal


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Figure 31. Typical contact pressure distributins. Left (a - c) longitudinal pressures and right (d) transverse pressure.

5.7 Simplified ridge load model

The suggested formulation for total force F [kN] is:

𝐹 = 0.032 ∙ 𝑣0.66 ∙ 𝐻0.9 ∙ 𝐴0.74

( 14 )


A is cross-sectional area of the thruster [m2].

The total force F is divided on the projection of the thruster area in the relation of the pressure distribution.

5.8 Simplified ridge load model application for full scale

As an example application, the simplified ridge load model is applied for two vessels. In Table 14 are shown an example values for ice class related input parameters for ridge thickness and ship speed. The azimuthing thruster projection areas are calculated from drawings.

The values for ice class based parameters are provisional in Table 14 and are subject to change when the ice class rules for azimuthing thrusters will be formulated.


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Table 14. Ridge contact load calculation example with simplified ridge load model.


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6. Conclusions

Developed impact load model was capable to give realistic impact load values when compared with impact experiment. Also, full scale measurements indicate impact loads at the level the model estimates [1,2]

The effect of damping during impact contact event is not yet properly modelled in the simplified impact model and is a point for further study. For further studies, the energy dissipation in impact contact is one suggested direction.

The developed dynamic load calculation model can be used as load calculation tool for estimating the effect of different parameters to impact load, when developing simplified formulation for ice class rule proposal. With the dynamic impact load model, a parameter study was done. The input values and corresponding dynamic contact load result were used to formulate a simplified impact contact load formula.

The simplified formula includes relation of impact kinetic energy, contact area size and constants to the contact load. The constants were determined by nonlinear regression model fitting. The used regression fit tool was MATLAB nonlinear model fit.

The resulting simplified model was checked by comparing the simplified load formula results with dynamic model results and full scale applications. The simplified load model gives same level of load as the validated dynamic impact contact load model.

The simplified impact load model described here was distributed to the project steering group members for review purposes, and is therefore not final, subject to revision.

Ridge penetration FE model runs were done , model was verified with full scale measurements. The parameters varied in this study were ship speed, ice ridge size, thruster orientation, propeller diameter ( scaling propulsion unit size and ship mass). The FE simulations of ridge penetration show good correlation with full scale measurements [2].

Based on theFE-simulation parametric study results, a simplified formulation for azimuthing thruster total load is proposed for the load scenario where ship is going through ice ridge.

This simplification still needs further testing and verification, and is provided for industry and classification societies review.


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7. Summary

For developing technical background for azimuthing thruster ice class rules, a research project was initiated in 2010. The need for rule development was stated by Finnish and Swedish maritimie authorities. Funding for the work is covered by Winter navigation research board, a joint research funding instrument between Finnish Transport Safety Agency and Swedish Maritime Administration.

Research project is guided by steering group, where participants from classification societies ( ABS, BV, ClassNK, DNV, GL, Lloyd’s Register, RINA, RMRS) together with azimuthing thruster manufacturers are invited.

The project started with identifying azimuthing thruster ice load scenarios, and finding suitable load calculation methods for such ice-structure interactions. The identified load scenarios include azimuthing thruster interaction with ice ridge and ice block impact to thruster.

Ice load calculation for azimuthing thruster interaction with ice ridge, a finite element method (FEM) model was taken as a research tool. Modeling an ice ridge and ship hull with thrusters with FEM was used to study the interaction process. The simulations run in 2013 gave initial understanding of what the effect of different parameters are to global thruster ice loads. The variable parameters were ship initial speed for ramming into ridge, thruster steering angle, ice ridge size. From these simulations, the global loads for thruster unit are calculated, and were compared to ice breaker Fennica measurement data. Model shows same type of behaviour of loading and same magnitude of loading as in measurement. During 2014, the FEM simulations continued and provided results for different propulsion unit sizes and ship inertia as well.

Based on the parameter studies, a simplified total load formulation for ice ridge interaction with azimuthing thruster is suggested. The simplified model is provisional and subject to change, after it has been revieved by manufacturers and classification societies.

For the ice block impact to azimuthig thruster type load scenario, a dynamic three mass model was considered the simplest possible approach. There a contact between azimuthing thruster housing or propeller hub is assumed, with a hemispherical metal structure indenting into ice block. The contact load for impact was assumed as a pressure-area relationship, and the contact load is increasing as the thruster structure indents deeper into ice.

The impact model validation relies on two sources, full scale data from ice breaker Fennica and small scale tests made on Baltic sea ice. The test setup was a pendulum with hemispherical contact surface, with load measurement, impacting into ice. The impact contact point was submerged. The tests show that the model is capable of estimating the contact load quite well. However, the model is indicating less damping after the impact than is observed in the tests. This question in general is about energy dissipation in impact and ice crushin process and is area of further studies.

Based on the parametric runs of the dynamic impact load model, a simplified impact contact load model was formulated. The simplified model was achieved by nonlinear regression analysis, and is provided as suggestion for ice load calculation. The model was distributed to industry and classification societies for review and may be updated accordingly.


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References

[1] Tikanmäki, M., Heinonen, J., Kinnunen, A., Comparison of ice load models for

azimuthing thruster ice load calculation, VTT-R-10310-10, VTT Technical Research

Centre of Finland, 2010

[2] Kinnunen, A., Tikanmäki, M., Heinonen, J., Kurkela, J., Koskinen, P., Jussila, M., Azimuthing thruster ice load calculation VTT-R-08842-12, VTT Technical Research Centre of Finland, 2012

RESEARCH REPORT VTT-R-XXXX-YY

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Appendix A

Appendix A – Simulated force-time history of the thrusters

Upper picture: total force-time history included propeller force.

Lower picture: total force-time history without propeller force.


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Appendix B

Appendix B – Simulated maximum force of the thrusters

Maximum simulated total forces of the thrusters. Force is ship moving direction. Values include short-term peak values.

Ridge Speed Propeller Thruster force [MN] No propeller force

Thruster force [MN] Include propeller force

Angle -180° Angle -90° Angle -180° Angle -90°

Mild

5 knot

2 m 0.5 0.5 0.5 0.6

4 m 0.9 0.9 0.9 1.1

6 m 1.3 1.2 1.3 1.9

8 m 2.2 2.4 2.2 2.8

8 knot

2 m 0.7 0.5 0.7 0.8

4 m 1.7 1.3 1.7 2.0

6 m 2.4 1.8 2.5 3.0

12 knot 4 m 2.4 1.4 2.3 2.4

Typical

5 knot

2 m 0.7 0.4 0.6 0.9

4 m 1.4 1.9 1.4 2.4

6 m 2.0 1.9 2.2 2.7

8 m 3.9 4.0 4.2 4.9

8 knot

2 m 0.8 0.6 0.8 1.0

4 m 1.7 1.9 1.7 2.4

6 m 3.0 2.9 3.1 4.2

12 knot 4 m 3.4 1.9 3.7 3.6

Extreme

5 knot

2 m 0.7 0.6 0.7 1.2

4 m 1.9 1.7 1.9 3.0

6 m 3.0 3.5 3.9 5.0

8 m 7.0 8.8 6.9 9.5

8 knot

2 m 0.9 0.8 0.9 1.4

4 m 2.8 2.3 2.7 3.7

6 m 5.6 5.9 6.2 7.6

12 knot 4 m 3.4 3.6 3.5 5.3


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Appendix B

Effect of the propeller diameter on the thruster force on different ridge types. Values not include propeller force nor short-term peak values.


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Appendix B

Effect of the ridge thickness on the thruster force on different ship initial speed. Values not include propeller force nor short-term peak values.


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Appendix B

Effect of the ship initial speed on the thruster force on different ridge types. Values include propeller force but not short-term peak values.

Include propeller force




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Appendix B

Effect of the propeller diameter on the thruster force on different ridge types. Values include propeller force but not short-term peak values.





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Appendix B

Effect of the ridge thickness on the thruster force on different ship initial speed. Values include propeller force but not short-term peak values.





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Appendix C

Appendix C - Force transducer construction

The pendulum baseplate is used as a force transducer. The force measurement is done with strain gauges. Principle is to measure the bending caused by impact force. The baseplate is cut from 50 mm S355 steel plate.

The setup is used is half-bridge, 2 active straight strain gauges, one mounted on tension side and the other on compression side of the load measurement plate.

Selecting strain gauge locations was done with FEM model. Several load levels were used for static structure bending analysis in FE model. The stresses were checked on both front and rear faces of impact head mount as a function of location, then location was chosen where both faces have equal symmetric stress for all load levels (front face tension, rear compression, same magnitude). Example load response is seen in Figure 32 and straingauge installation is being prepared as in Figure 33.

Figure 32. FEM model of impact head showing static deformation and stress state for strain gauge positioning

Strain gauges at equal stress

magnitude locations on front and rear

side


88 (151)

Appendix C

Figure 33. Straingauge installation being prepared. Tape marks the measurement location.


89 (151)

Appendix C

Load calibration of impact force transducer

Hydraulic cylinder was used for compressing the impact force transducer, to give calibration load into same direction as the actual impact load. The calibration load was measured with HBM load cell (type C4/100kN) simultaneously with the impact force transducer strain. Calibration arrangement is seen in Figure 34.

Figure 34. Calibration for force transducer.

Measurement equipment in calibration was IMC cronos PL8 sn: 122837, data sampling

interval was set to 500s (sampling frequency 2000 Hz), AAF filter enabled.

Calibration load cell and impact force transducer were balanced to read zero before the measurement. Measurement data is shown in Figure 35. Calibration load vs. transducer strain is shown in Figure 36. A linear load-strain fit is presented in Figure 37.

Measured sensitivity with linear strain-load dependency estimate is -12,54 N / m/m.

Load cell HBM

C4/100kN

Hydraulic cylinder for

loading

Load measurement strain gauges


90 (151)

Appendix C

Figure 35. Measured strain from impact force transducer (blue) and calibration load from load cell (red).

Figure 36. Calibration load as a function of force transducer strain. Data from previous figure as X-Y plot.


91 (151)

Appendix C

Figure 37. Calibration load as a function of measured strain with linear estimate for strain-load sensitivity.

y = -12,541x

-2000

0

2000

4000

6000

8000

10000

12000

14000

16000

-1400 -1200 -1000 -800 -600 -400 -200 0 200

Load

[N

]

Strain[um/m]

Strain um/m

Strain um/m

Linear (Strain um/m)


92 (151)

Appendix D

Appendix D - Modal Analysis of impact force transducer

Experimental modal analysis

The dynamic stiffness of the force transducer is represented with lowest natural frequency in the load calculation model.

Therefore, a simple experimental modal analysis was performed to the force transducer. The transducer was measured with two different size impact heads. The impact heads have different mass, i.e. natural frequency of the mode where the impact nose is bending in direction of impact, should change.

Measurements were done with data physics Quattro measurement fron-end connected to laptop PC running data physics SignalCalc 240 software.

Vibration excitation was given with modal hammer Endevco 2302-5. Vibration response was measured with Brüel&Kjaer triaxial acceleration sensor (type 4506 serial no VTT no #2, serial no 1936622) Acceleration sensor was attached to steel with beeswax. The test setup is shown in Figure 37, Figure 39, Figure 40 and Figure 41.

Figure 38. Modal testing of force transducer with 100mm impact head and five mass plates. Same configuration as in impct tests. Measurement points 5 .. 9 marked.

MP 5

MP 6

MP 7

MP 8

MP 9 X

Z

Y


93 (151)

Appendix D

Figure 39. Measurement points on impact head with 100 mm impact head, five mass plates on impact head.

Figure 40. Modal testing of force transducer with 150mm impact head and three mass plates. Same configuration as in impct tests.

MP 1

MP 2

MP 3

MP 4


94 (151)

Appendix D

Figure 41. Impact excitation to impct head.

Measured FRF:s were analysed with LMS TestLab 13A software. Data was imported with universal files (UFF Dataset 58) for analysis. The geometry model for 100 mm head and 150 mm head is the same, shown in Figure 42. Natural frequencies are listed in Table 15. The important natural mode is the “impact head bending” mode.


95 (151)

Appendix D

Figure 42. Mode shapes for the bending in impact direction. On the left is 100 mm impact head, on the right 150 mm impact head results.

Table 15. Natural frequencies in measurement

Impact head size Natural frequency Damping

mm Hz %

100 166,5 0,08

150 151,8 0,11


96 (151)

Appendix D

Calculated natural frequencies

The impact load transducer ( pendulum base plate ) was modelled with Comsol Multi Physics (COMSOL 4.4.0.195) software. With the steel plate modelled together with the impact head, the natural frequencies were calculated for 100 mm and 150 mm impact head configuration.

Figure 43. FE model of impact force transducer with 150 mm impact head


97 (151)

Appendix D

Figure 44. Natural frequency at 142 Hz, model with 150 mm impact head.

Figure 45. FE model of impact force transducer with 100 mm impact head


98 (151)

Appendix D

Figure 46. Natural frequency at 144 Hz, model with 100 mm impact head.

Natural frequency comparison

Table 16. Natural frequencies in measurement and calculation

Impact head size Natural frequency Damping FEM

mm Hz % Hz

100 166,5 0,08 144

150 151,8 0,11 142


99 (151)

Appendix E

Appendix E – Impact measurement signals

Measurement recordings of impacts 2014.

Impact to solid ice, 100 mm impact head

The measured force, pendulum mass velocity and ice velocity are shown in following figures.

Figure 47.Test 1. Impact to solid ice 100 mm impact head, -0.025m start height from water surface. Force measurement range exceeded, impact results not usable.

Head_100mm_solid_01_segment: force Head_100mm_solid_01_segment: vel_ice_xHead_100mm_solid_01_segment: vel_mass_x

-4

-2

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30kN

-2.0

-1.9

-1.8

-1.7

-1.6

-1.5

-1.4

-1.3

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1m/s

18.92 18.94 18.96 18.98 19.00 19.02 19.04

s


100 (151)

Appendix E

Figure 48. Test 2. Impact to solid ice 100 mm impact head, -0.025m start height from water surface.



-4

-2

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30kN

-2.0

-1.9

-1.8

-1.7

-1.6

-1.5

-1.4

-1.3

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1m/s

120.66 120.68 120.70 120.72 120.74

s


-5

0

5

10

15

20

25

30kN

-2.0

-1.9

-1.8

-1.7

-1.6

-1.5

-1.4

-1.3

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1m/s

52.55 52.57 52.59 52.61 52.63 52.65

s


101 (151)

Appendix E


Figure 51. Impacts 2, 3, and 4 to solid ice, 100 mm impact head, pendulum start height 0.025 m below water surface, force measurements.Data for test #1 not used.


-5

0

5

10

15

20

25

30kN

-2.0

-1.9

-1.8

-1.7

-1.6

-1.5

-1.4

-1.3

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1m/s

54.565 54.585 54.605 54.625 54.645 54.665

s

I02: force I03: force I04: force

-4000

-2000

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

24000

26000

28000

30000N

70 80 90 100 110 120 130 140 150 160 170

ms


102 (151)

Appendix E

Impact to ice block, 100 mm impact head

Figure 52. Test 5. Impact to ice block, 100 mm impact head, start height 0.025m below water surface.


Head_100mm_block_05_segment: force Head_100mm_block_05_segment: vel_ice_xHead_100mm_block_05_segment: vel_mass_x

-5

-3

-1

1

3

5

7

9

11

13

15

17

19

21

23

25kN

-1.5

-1.4

-1.3

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5m/s

93.35 93.37 93.39 93.41 93.43 93.45

s


-5

-3

-1

1

3

5

7

9

11

13

15

17

19

21

23

25kN

-2.0

-1.5

-1.0

-0.5

0.0

0.5m/s

152.34 152.36 152.38 152.40 152.42 152.44

s


103 (151)

Appendix E


Figure 55. Force signal from three impacts to ice block, 100 mm impact head, pendulum start height 0.025m below water surface.


-5

-3

-1

1

3

5

7

9

11

13

15

17

19

21

23

25kN

-2.0

-1.5

-1.0

-0.5

0.0

0.5m/s

94.05 94.07 94.09 94.11 94.13 94.15

s


-4000

-2000

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

24000

N

50 60 70 80 90 100 110 120 130 140 150

ms


104 (151)

Appendix E

Impact to ice block, 150 mm impact head




-5

-3

-1

1

3

5

7

9

11

13

15

17

19

21

23

25kN

-2.0

-1.5

-1.0

-0.5

0.0

0.5m/s

92.00 92.02 92.04 92.06 92.08 92.10

s


-5

-3

-1

1

3

5

7

9

11

13

15

17

19

21

23

25kN

-2.0

-1.5

-1.0

-0.5

0.0

0.5m/s

121.47 121.49 121.51 121.53 121.55 121.57

s


105 (151)

Appendix E


Figure 59. Force signals from tests 8, 9 and 10. Impact to ice block, 150 mm impact head, start height 0.025m below water surface.


-5

-3

-1

1

3

5

7

9

11

13

15

17

19

21

23

25kN

-2.0

-1.5

-1.0

-0.5

0.0

0.5m/s

50.05 50.07 50.09 50.11 50.13 50.15

s


-4000

-2000

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

24000

N

220 230 240 250 260 270 280 290 300 310 320

ms


106 (151)

Appendix E

Measurement signals from 2013 tests

Figure 60. Impact to solid ice. 100 mm head.


Head_100mm_h26cm_solidice_segment: forceHead_100mm_h26cm_solidice_segment: vel_mass_x_pHead_100mm_h26cm_solidice_segment: Work_mass

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34

36

38

40

42

kN

-2.2

-2.0

-1.8

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

m/s

-750

-700

-650

-600

-550

-500

-450

-400

-350

-300

-250

-200

-150

-100

-50

0J

102.26 102.28 102.30 102.32 102.34 102.36

s

y = -694.350 Jx = 102.31414 s

y = -2.2651 m/sx = 102.31444 s

Head_100mm_h26cm_solidice_2segment: forceHead_100mm_h26cm_solidice_2segment: vel_mass_x_pHead_100mm_h26cm_solidice_2segment: Work_mass

-2

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34

36

38

40

42

kN

-2.2

-2.0

-1.8

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

m/s

-750

-700

-650

-600

-550

-500

-450

-400

-350

-300

-250

-200

-150

-100

-50

0J

47.10 47.12 47.14 47.16 47.18 47.20

s

y = -595.736 Jx = 47.14792 s

y = -2.2084 m/sx = 47.14621 s


107 (151)

Appendix E


Figure 63. Impact to block, 100 mm head

Head_100mm_h26cm_solidice_3segment: forceHead_100mm_h26cm_solidice_3segment: vel_mass_x_pHead_100mm_h26cm_solidice_3segment: Work_mass

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34

36

38

40

42

kN

-2.2

-2.0

-1.8

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

m/s

-750

-700

-650

-600

-550

-500

-450

-400

-350

-300

-250

-200

-150

-100

-50

0J

16.16 16.18 16.20 16.22 16.24 16.26

s

y = -666.902 Jx = 16.20975 s

y = -2.2493 m/sx = 16.20807 s

Head_100mm_h11cm_segment: forceHead_100mm_h11cm_segment: vel_ice_x_pHead_100mm_h11cm_segment: vel_mass_x_offset_cHead_100mm_h11cm_segment: Work_mass_ocHead_100mm_h11cm_segment: Work_ice_oc

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34

36

38

kN

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

m/s

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

J

39.32 39.34 39.36 39.38 39.40

s

x = 39.34117 s

y = 399.277 Jx = 39.35657 s

y = 0.3394 m/sx = 39.35808 s

y = 1.9097 m/sx = 39.34107 s

y = 54.121 Jx = 39.35728 s


108 (151)

Appendix E



Head_100mm_h11cm_2_segment: forceHead_100mm_h11cm_2_segment: vel_ice_x_pHead_100mm_h11cm_2_segment: vel_mass_x_offset_cHead_100mm_h11cm_2_segment: Work_mass_ocHead_100mm_h11cm_2_segment: Work_ice_oc

0

2

4

6

8

10

12

14

16

18

20

22

kN

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

m/s

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

J

27.04 27.06 27.08 27.10 27.12 27.14 27.16 27.18 27.20

s

x = 27.09993 s

y = 0.7051 m/sx = 27.11671 s

y = 2.2489 m/sx = 27.10037 s

y = -0.0077 m/sx = 27.10000 s

y = 355.800 Jx = 27.11577 s

y = 84.873 Jx = 27.11652 s

Head_100mm_h11cm_3_segment: forceHead_100mm_h11cm_3_segment: Work_ice_ocHead_100mm_h11cm_3_segment: Work_mass_ocHead_100mm_h11cm_3_segment: vel_mass_x_offset_cHead_100mm_h11cm_3_segment: vel_ice_x_p

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

kN

0

50

100

150

200

250

300

350

400

450

500J

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

m/s

27.94 27.96 27.98 28.00 28.02 28.04 28.06 28.08

s

x = 27.98007 s

y = 490.698 Jx = 28.00108 s

y = 105.805 Jx = 28.00214 s

y = 0.5479 m/sx = 28.00299 s

y = 2.0631 m/sx = 27.97992 s


109 (151)

Appendix E

Figure 66.150 mm impact head, impact to ice block, high speed

Figure 67. 150 mm impact head, impact to ice block, high speed


0

5

10

15

20

25

30

35

40

45

50

55

60

kN

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

m/s

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

kJ

39.42 39.44 39.46 39.48 39.50

s

x = 39.43900 s

y = 2.9150 m/sx = 39.43882 s

y = 0.5265 m/sx = 39.45679 s

y = 0.9743 kJx = 39.45839 s

y = 0.1592 kJx = 39.45861 s


0

5

10

15

20

25

30

35

40

45

50

55

kN

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

m/s

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

kJ

39.78 39.79 39.80 39.81 39.82 39.83 39.84

s

x = 39.79842 s

y = 3.0038 m/sx = 39.79876 s

y = 0.6195 m/sx = 39.81545 s

y = 0.6184 m/sx = 39.828547 s

y = 1.0629 kJx = 39.81560 s

y = 0.1878 kJx = 39.81816 s


110 (151)

Appendix E

Figure 68 Test 9. Impact to ice block 150 mm head and 0.11 m start height.

Figure 69. Test 10. Impact to ice block 150 mm head and 0.11 m start height.


0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

32

34

kN

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

m/s

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

J

32.55 32.56 32.57 32.58 32.59 32.60 32.61 32.62

s

x = 32.57892 s

y = 0.5675 m/sx = 32.59304 s

y = 1.7792 m/sx = 32.57904 s

y = 0.0072 m/sx = 32.58006 s

y = 346.408 Jx = 32.60309 s

y = 80.062 Jx = 32.59393 s


0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

kN

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

m/s

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

J

63.80 63.82 63.84 63.86 63.88

s

x = 63.82428 sy = 1.8963 m/sx = 63.82443 s

y = 0.7201 m/sx = 63.84461 s

y = -9.9088E-4 m/sx = 63.82474 s

y = 409.750 Jx = 63.84351 s

y = 98.274 Jx = 63.84336 s


111 (151)

Appendix E

Figure 70. Test 11. Impact to ice block 150 mm head and 0.11 m start height.


0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

kN

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

m/s

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

kJ

61.38 61.40 61.42 61.44 61.46 61.48 61.50 61.52 61.54 61.56

s

x = 61.44355 s

y = 2.0932 m/sx = 61.44335 s

y = 0.9938 m/sx = 61.45930 s

y = 4.3732E-4 m/sx = 61.44335 s

y = 0.46150 kJx = 61.46427 s

y = 0.15512 kJx = 61.46469 s


112 (151)

Appendix F

Appendix F – Kinetic energy in impact test

Kinetic energy change in impact can be estimated with measured mass velocity and contact force, like

∆𝐸𝑘𝑖𝑛 = ∫ 𝐹𝑐𝑜𝑛𝑡𝑎𝑐𝑡(𝑡) 𝑣𝑚𝑎𝑠𝑠(𝑡)𝑑𝑡 ( 15 )

The velocity is calculated from measured acceleration by integration, and for impact energy estimate, velocity value change during impact is the interesting value. To achieve proper energy integral value, velocity is set to zero at the start of impact. Velocity change during short duration impact is then rather well established.

Figure 71. Measured force, impact mass velocity and calculated impact energy for impact to solid ice with 100mm impact head. Impact # 2.

Head_100mm_solid_02_segment: force Head_100mm_solid_02_segment: vel_mass_x_pHead_100mm_solid_02_segment: Work_mass

-2

0

2

4

6

8

10

12

14

16

18

20

22kN

-1.6

-1.5

-1.4

-1.3

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5m/s

-420

-400

-380

-360

-340

-320

-300

-280

-260

-240

-220

-200

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20J

120.66 120.68 120.70 120.72 120.74 120.76

s

y = -419.522 Jx = 120.72499 s

y = -1.5361 m/sx = 120.71332 s


113 (151)

Appendix F




-3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19kN

-1.6

-1.5

-1.4

-1.3

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5m/s

-340

-320

-300

-280

-260

-240

-220

-200

-180

-160

-140

-120

-100

-80

-60

-40

-20

0

20J

52.54 52.56 52.58 52.60 52.62 52.64 52.66

s

y = -1.5380 m/sx = 52.59478 s

y = -321.021 Jx = 52.59643 s


0

2

4

6

8

10

12

14

16

18

20

22

24

26

28kN

-1.7

-1.6

-1.5

-1.4

-1.3

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5m/s

-500

-450

-400

-350

-300

-250

-200

-150

-100

-50

0J

54.58 54.60 54.62 54.64 54.66

s

y = -1.7247 m/sx = 54.623814 s

y = -445.142 Jx = 54.633192 s


114 (151)

Appendix F

Figure 74. Measured force, impact mass velocity and calculated impact energy for impact to ice block with 100mm impact head. Impact # 5.


Head_100mm_block_05_segment: force Head_100mm_block_05_segment: vel_mass_x_pHead_100mm_block_05_segment: Work_mass

-1

0

1

2

3

4

5

6

7

8

9

10

11

12kN

-1.4

-1.3

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4m/s

-160

-150

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20J

93.34 93.36 93.38 93.40 93.42 93.44 93.46 93.48 93.50

s

y = -1.2031 m/sx = 93.41750 s

y = -157.677 Jx = 93.42253 s


0

1

2

3

4

5

6

7

8

9

10

11

12

kN

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2m/s

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

J

152.30 152.35 152.40 152.45 152.50

s

y = -1.14533 m/sx = 152.38991 s

y = -144.426 Jx = 152.39784 s


115 (151)

Appendix F




-2

0

2

4

6

8

10

12

14

16

18

20

22

24kN

-1.3

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4m/s

-170

-160

-150

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10J

94.02 94.04 94.06 94.08 94.10 94.12 94.14 94.16 94.18

s

y = -1.2212 m/sx = 94.10412 s

y = -160.284 Jx = 94.10677 s


-2

-1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20kN

-1.4

-1.3

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2m/s

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0J

91.98 92.00 92.02 92.04 92.06 92.08 92.10 92.12

s

y = -116.964 Jx = 92.05813 s

y = -1.2214 m/sx = 92.05359 s


116 (151)

Appendix F




-1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21kN

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

m/s

-100

-95

-90

-85

-80

-75

-70

-65

-60

-55

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5J

121.46 121.48 121.50 121.52 121.54 121.56 121.58 121.60

s

y = -1.18072 m/sx = 121.51675 s y = -102.782 J

x = 121.52178 s


-2

-1

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20kN

-1.3

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3m/s

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

J

50.04 50.06 50.08 50.10 50.12 50.14 50.16 50.18 50.20

s

y = -1.2687 m/sx = 50.10709 s

y = -121.165 Jx = 50.11077 s


117 (151)

Appendix G

Appendix G - Parameter estimation for simplified impact load model

Main parameter : available kinetic energy

The estimation of simplified impact load formulation was started with making a hypothesis that the maximum contact load is related to maximum kinetic energy available for the impact.

This assumption is formulated in following way

𝐹𝑖𝑚𝑝𝑎𝑐𝑡 = 𝑓(𝑚𝑖𝑐𝑒 , 𝑣𝑖𝑚𝑝𝑎𝑐𝑡 , 𝐴𝑐𝑜𝑛𝑡𝑎𝑐𝑡, 𝑓𝑡ℎ𝑟𝑢𝑠𝑡𝑒𝑟, 𝜎𝑖𝑐𝑒)

𝐹 = (𝑚𝑖𝑐𝑒 ∗ 𝑣𝑖𝑚𝑝𝑎𝑐𝑡2 )

1/𝐶∗ 𝑓(𝐴𝑐𝑜𝑛𝑡𝑎𝑐𝑡 , 𝑓𝑡ℎ𝑟𝑢𝑠𝑡𝑒𝑟, 𝜎𝑖𝑐𝑒)

( 16 )

For first step analysis, the term dependent on contact area, thruster natural frequency and ice strength is kept constant, with fixed set of parameters.

The parameter space was

𝑚𝑖𝑐𝑒 = 1: 1: 50 [𝑡𝑜𝑛𝑠] f = 14 [Hz]

R = 1,2 [meters] vimpact = 1: 1: 15 [knots]

𝐹 = (𝑚𝑖𝑐𝑒 ∗ 𝑣𝑖𝑚𝑝𝑎𝑐𝑡2 )

1/𝐶∗ 𝑓(𝐴𝑐𝑜𝑛𝑡𝑎𝑐𝑡 , 𝑓𝑡ℎ𝑟𝑢𝑠𝑡𝑒𝑟, 𝜎𝑖𝑐𝑒)

( 17 )

With these parameters, the impact load calculation model gives 750 results for the different set of parameters ice mass and impact velocity.

The results were given as input to MATLAB nonlinear regression analysis tool. The assumed model function was

𝑦 ~𝑏1(𝑥1𝑥2

2)1/𝑏2

( 18 )

where model coefficient b1 refers to effect of contact area, natural frequency and ice strength (being constant for the case) and variable x1 is mass, variable x2 is velocity. The model coefficient b2 is constant. The nonlinear model fitting tool evaluated the result set and gives the model parameters b1 and b2 as output:


y ~ b1*(x1*x2^2)^(1/b2)


Estimate SE tStat pValue b1 40427 316.36 127.79 0 b2 3.0942 0.0055317 559.35 0


118 (151)

Appendix G

Number of observations: 750, Error degrees of freedom: 748 Root Mean Squared Error: 4.47e+04 R-Squared: 0.998, Adjusted R-Squared 0.998 F-statistic vs. zero model: 1.36e+06, p-value = 0

Figure 80. Effect of ice block mass and impact velocity on max contact load at R=1,2 m and f = 14 Hz.

01

23

45

x 104

0

2

4

6

80

1

2

3

4

5

x 106

Ice block mass [kg]

Impact contact load

Impact velocity [m/s]

Conta

ct

load [

N]


119 (151)

Appendix G

Four – predictor model: kinetic energy, contact area, impactor stiffness

The first stage models were reasonably suited for estimating for the effect of ice mass and impact velocity. Then, the impactor radius and natural frequency were added into the model, with assumed model formulation

𝑦 ~𝑅𝑖𝑚𝑝𝑎𝑐𝑡𝑜𝑟

1𝑏1 𝑏2(𝑚𝑖𝑐𝑒𝑣𝑖𝑚𝑝𝑎𝑐𝑡

2 )1

𝑏3(1 −(

𝐹𝑡ℎ𝑟𝑢𝑠𝑡𝑒𝑟10

)

𝑏4)

( 19 )

This model resulted in parameter values Nonlinear regression model: 'Fc ~ (Radius^(1/b1))*b2*(Mass_ice*Velocity^2)^(1/b3)*(1+(Frequency-10)/b4)' Estimated Coefficients: Estimate SE tStat pValue ________ _________ ______ ______ b1 2.1899 0.0034112 641.99 0 b2 35746 171.22 208.77 0 b3 3.1216 0.0034428 906.7 0 b4 126.37 1.9245 65.663 0 Number of observations: 53625, Error degrees of freedom: 53621 Root Mean Squared Error: 2.22e+05 R-Squared: 0.972, Adjusted R-Squared 0.972 F-statistic vs. zero model: 1.78e+06, p-value = 0

Thruster mass effect evaluation

Evaluating the effect of thruster mass was initially done with other parameters fixed. Radius R 1,2 m, ice masses m_ice 6 and 20 tons, velocity 5 knots, thruster natural frequency 11 Hz. With these parameters, the thruster dynamic mass was varied from 10 to 150 tons, 1 ton steps. Resulting thruster mass-contact load curves are below.


120 (151)

Appendix G

Figure 81. Thruster mass effect on contact load, constant radius, velocity, and thruster natural frequency.

This suggests contact load dependency type for thruster mass

𝐹𝑐𝑜𝑛𝑡𝑎𝑐𝑡 ~𝑎 ∗ 𝑚𝑡ℎ𝑟𝑢𝑠𝑡𝑒𝑟

𝑏 + 𝑐

( 20 )

Thruster mass effect on ice contact load X-variable thruster mass ( only varied parameter), R = 1.5, f= 11Hz, M_ice = small 6ton, v = 5 knots Y –variable contact load

0 5 10 15

x 104

0

2

4

6

8

10

12

14

16

18

x 105

Thruster mass effect on contact load

Parameters R: 1.2 m, m

ice: 20 tn, f 11 Hz, speed 5.0 knots

Thruster mass [kg]

Conta

ct

load [

N]

Contact load 6tn

Contact load 20 tn


121 (151)

Appendix G

y = a*x^b + c a = -1.8e-8 b = -0.7752 c = 1.335 e6

Thruster mass effect of “power type” on overall contact load

Testing the five-parameter model of contact load with coarse parameter space %% Parameter test, variable thruster mass, five predictors, coarse mesh

Mthru = [10:50:150].*1000 ; % Thruster mass variation, kg R = [0.5:0.5:1.5]; % Impacting hemisphere radius, meters m_ice = [5:20:60].*1000; % Ice mass, kg f = [6:4:16]; % Impactor natural frequency, Hz v = [1:5:15].*.514; % Impact initial velocity knots -> m/s

Nonlinear model formulation for Fc modelfun = 'Fc ~

(Radius^(1/b1))*b2*(Mass_ice*Velocity^2)^(1/b3)*(1+(Frequency-

10)/b4)*M_thrust^b5';

𝐹𝑐 ~ 𝑅1

𝑏1𝑏2(𝑀𝑖𝑐𝑒𝑣𝑖𝑚𝑝𝑎𝑐𝑡2 )

1𝑏3 (1 +

𝐹𝑡ℎ𝑟𝑢𝑠𝑡𝑒𝑟 − 10

𝑏4) 𝑀𝑡ℎ𝑟𝑢𝑠𝑡𝑒𝑟

𝑏5

( 21 )



b1 2.7192 0.084669 32.116 1.7423e-88

b2 15912 1200.6 13.253 2.1399e-30

b3 3.0208 0.037576 80.39 1.684e-174

b4 85.5 10.617 8.053 3.8726e-14

b5 0.06524 0.0048535 13.442 5.0234e-31

2 4 6 8 10 12 14

x 104

1.2

1.22

1.24

1.26

1.28

1.3

1.32

x 106

Mthruv

Fcm

Fcm vs. Mthru_v

untitled fit 1


122 (151)

Appendix G


123 (151)

Appendix G

Three-predictor model: kinetic energy and contact size, coarse parameter space

The assumed model for contact load with three predictors is

𝐹𝑐 ~ 𝑅1

𝑏1𝑏2(𝑀𝑖𝑐𝑒𝑣𝑖𝑚𝑝𝑎𝑐𝑡2 )

1𝑏3

( 22 )

thus neglecting thruster mass and natural frequency from the evaluation. Giving MATLAB a parameter space to calculate the dynamic contact load maxima

%% Parameter run with three predictors 2014-10-02 % [Fcmax, Frmax]=Impact_load_parametric(R,sigma_,m_ice,m_t,f(5),v,c) R = [0.1:0.6:2.5]; % Radius meters - predictor m_ice = [1:6:50].*1000; % ice mass - predictor f = [11]; % Constant v = [1:2:15].*.514; % velocity knots -> m/s - predictor





b1 1.936 0.042092 45.995 4.3022e-152 b2 31639 2319.9 13.638 2.2161e-34 b3 3.0565 0.050114 60.991 7.1127e-191

Number of observations: 360, Error degrees of freedom: 357 Root Mean Squared Error: 2.81e+05 R-Squared: 0.967, Adjusted R-Squared 0.967 F-statistic vs. zero model: 9.76e+03, p-value = 0

Figure 82. Slice plot for three predictor model, coarse parameter space.


124 (151)

Appendix G

Three-predictor model: kinetic energy and contact size, finer parameter space (the results for rule proposal)

Giving a finer mesh for parameter space :

% Finer parameter space 2014-10-10 R = [0.1:0.3:2.5]; % Radius meters - predictor m_ice = [1:3:50].*1000; % ice mass - predictor f = [11]; % Constant v = [1:1:15].*.514; % velocity knots -> m/s – predictor

Matlab gives the following results:





b1 2.1174 0.016651 127.17 0

b2 34653 867.65 39.938 3.2622e-265

b3 3.0962 0.017691 175.02 0


Root Mean Squared Error: 2.41e+05


F-statistic vs. zero model: 8.65e+04, p-value = 0

Dependendcy over different parameters with these constants is presented in the slice plot below.

Figure 83. Slice plot for three predictor model, finer parameter steps


125 (151)

Appendix G

Figure 84. Dynamic contact load model load estimate and simplified contact load model with three predictors.

Looking at the results from the two fits to three predictor model, a simplified contact load formulation is suggested

𝐹𝑐 ~ 34560𝑅12(𝑀𝑖𝑐𝑒𝑣𝑖𝑚𝑝𝑎𝑐𝑡

2 )13

( 23 )

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

Dynamic contact model maximum load [MN]

Sim

plif

ied m

odel lo

ad e

stim

ate

[M

N]

Three-predictor nonlinear regression model vs dynamic impact model

Simplified model: Fc = b

2R(1/b1)(m

ice v

ship2 )(1/b3)


126 (151)

Appendix H

Appendix H – Simulated contact pressure of the thrusters

Maximum contact pressures of the 2 m thrusters by slice, variation of ridge thickness. Thruster angle -180°. The contact pressure maxima do not appear at the same time in all the

slices.


127 (151)

Appendix H


slices.


128 (151)

Appendix H


slices.


129 (151)

Appendix H


slices.


130 (151)

Appendix H


slices.


131 (151)

Appendix H


slices.


132 (151)

Appendix H

Maximum contact pressures of the 8 m thrusters by slice, variation of ridge thickness. Upper thruster angle -180° and below thruster angle -90°. The contact pressure maxima do not

appear at the same time in all the slices.


133 (151)

Appendix H

Maximum contact pressures of the thrusters by height, effect of thruster size. Thruster angle -180°. The contact pressure maxima do not appear at the same time in total height.


134 (151)

Appendix H



135 (151)

Appendix H



136 (151)

Appendix H



137 (151)

Appendix H

Maximum contact pressures of the thrusters by height, variation of ridge thickness. Upper thruster angle -180° and below thruster angle -90°. The contact pressure maxima do not

appear at the same time in total height.


138 (151)

Appendix I

Appendix I – Ridge load simplified model versions

The ridge penetration FE simulation parameters and results can be handled with diferent approaches:.

1. Total force maximum from time history, propeller area load included

2. Total force maximum from time history, propeller area load not included

3. Total force high frequency peaks disregarded, propeller area load included

4. Total force high frequency peaks disregarded, propeller area load not included

5. Total force, high frequency peaks disregarded, propeller area load included, ridge consolidated layer thickness included

These result tables are processed with MATLAB nonlinear model fitting tool and results presented.


139 (151)

Appendix I

Total force maximum from time history, propeller area load included


Fc ~ b1*(Speed^b2)*(Ridgethickness^b3)*(Thrusterarea^b4)



b1 0.039937 0.0094781 4.2136 0.00012266

b2 0.64089 0.084147 7.6164 1.4432e-09

b3 0.84773 0.055773 15.2 4.0127e-19

b4 0.70713 0.040915 17.283 3.1197e-21


Root Mean Squared Error: 0.5


F-statistic vs. zero model: 520, p-value = 2.02e-36


140 (151)

Appendix I

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10


Sim

plifi

ed m

odel

load

est

imat

e [M

N]


Simplified model F = a Vb H

c A

d


141 (151)

Appendix I

Total force maximum from time history, propeller area load not included





b1 0.03564 0.01573 2.2657 0.028442

b2 0.45638 0.15939 2.8632 0.0064004

b3 0.91489 0.10617 8.6174 5.3317e-11

b4 0.70915 0.075074 9.446 3.7604e-12






142 (151)

Appendix I

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10


Sim

plifi

ed m

odel

load

est

imat

e [M

N]



c A

d


143 (151)

Appendix I

Thruster force high frequency peaks disregarded, propeller area load included





b1 0.031812 0.0061344 5.1858 5.2072e-06

b2 0.62358 0.067966 9.1749 8.8754e-12

b3 0.89304 0.045141 19.783 1.5873e-23

b4 0.73321 0.033166 22.107 1.856e-25






144 (151)

Appendix I

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10


Sim

plifi

ed m

odel

load

est

imat

e [M

N]



c A

d


145 (151)

Appendix I

Thruster force high frequency peaks disregarded, propeller area load not included





b1 0.027373 0.010783 2.5386 0.014744

b2 0.47051 0.14078 3.3421 0.0017042

b3 0.95684 0.094134 10.165 4.0284e-13

b4 0.73755 0.066955 11.016 3.1115e-14






146 (151)

Appendix I

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10


Sim

plifi

ed m

odel

load

est

imat

e [M

N]



c A

d


147 (151)

Appendix I

Total force, high frequency peaks disregarded, propeller area load included, ridge consolidated layer thickness included


Fc ~ b1*(Speed^b2)*(Ridgeconsolidatedlayer^b3)*(Thrusterarea^b4)



b1 0.15532 0.024854 6.2494 1.4501e-07

b2 0.62275 0.064734 9.6201 2.1756e-12

b3 0.94951 0.04719 20.121 8.1031e-24

b4 0.73322 0.031585 23.214 2.5522e-26






148 (151)

Appendix I

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10


Sim

plifi

ed m

odel

load

est

imat

e [M

N]



c

c A

d

Rule proposal


149 (151)

Appendix I

Summary of model fits

The different models give little bit different parameter estimates. Highest R-squared value is for the “no high frequency peaks results with propeller load included”

Max Max, no propeller

No peaks No peaks, no propeller

No peaks, consolidated

layer

Coefficient Estimate Estimate Estimate Estimate Estimate

b1 0,03993692 0,0356404 0,031811777 0,027373168 0.15532

b2 0,64089068 0,45637786 0,623583368 0,470506541 0.62275

b3 0,84773444 0,91489219 0,893039156 0,956836807 0.94951

b4 0,70712869 0,70914765 0,733208257 0,737551186 0.73322

Rsquared 0,93957499 0,82098193 0,96336908 0,8669745 0.967

Model for rule proposal with ridge thickness is

The suggested formulation for total force F [MN] is:

𝐹 = 0.032 ∙ 𝑣0.66 ∙ 𝐻0.9 ∙ 𝐴0.74

( 24 )



The rule proposal model plotted against FE model total max loads together with the best regression fit model in next figure


150 (151)

Appendix I

Figure 85.

Model for rule proposal with ridge consolidated layer thickness is

The suggested formulation for total force F [MN] is:

𝐹 = 0.16 ∙ 𝑣0.6 ∙ 𝐻𝑐𝑜𝑛𝑠𝑜𝑙𝑖𝑑𝑎𝑡𝑒𝑑

0.95 ∙ 𝐴0.74

( 25 )

where v is ship speed [m/s] Hconsolidated is ridge consolidated layer thickness [m]


The rule proposal model plotted against FE model total max loads together with the best regression fit model in next figure

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151 (151)

Appendix I

Figure 86. Thruster total maximum load in ridge contact, simplified formula with ridge consolodated layer parameter.

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Documents

DRAFT Azimuthing thruster ice load calculation and ... · 12/12/2014 · Further details for ice load calculation for each scenario are documented in the ice load model and calculation