Experiments and interpretation of propeller vibratory hull pressures on an elastic structure of a shipmodel, Presented at: The Conference on Advances in Propeller Research and Design, Gdansk, Poland, 1981, Published in: International Shipbuilding Progress

EXPERIMENTS AND INTERPRETATION OF PROPELLER VIBRATORY HULL PRESSURES

ON AN ELASTIC STRUCTURE OF A SHIPMODEL ) by

R. Wereldsma **)

Summary

In this paper an outline is given of the fundamentals of measurements on hydroelastic structures. In particular the difficulties as encountered in hull pressure measurements ona shipmodel are reported. An estimate is made of the errors that may occur in the model measurement of propeller excited vibratory hull pressures and a method is given to correct the measured quantities influenced by the elastic response of the hull of the model by means of a dynamic calibration.

i . Introduction

For many years measurements take pince on vibra-tory phenomena generated by the propeller in opera-tion behind a ship. Investigaopera-tions in this field have

been started because fast and high powered ships, suf-fered from time to time from serious vibrations caused

by the propeller. A difficult hydroelastic problem was

introduced in the propeller research of ships.

Nowadays standards and norms, designed by the International Standardisation Organisation (I.S.O.),

are issued, indicating the maximum vibration level for acceptable habitability and comfort. 'It may be

expect-ed that in the near future these maximum vibration levels will be contracted by the shipowner and ship-builder for acceptance of the ships, which means that the shipbuilder needs to know beforehand, preferably in the design stage, what vibratiön level' will be

en-countered when the ship is in full operation.

Facing this situation it is the author's opinion that

strong efforts 'have to be paid to work on a reliable vibration prediction method. Various initiatives have

already been taken e.g.:

- Statistical analysis of many ships treating the phys-ical phenomena in a global way [1], [2], [3]. - Theoretical developments' for the analysis of

pro-peller performance, cavitation and pressure

radia-tion 14], [5], [6].

- Model and full size experiments on pressure

fluc-tuations and structural response.

- Finite Element Procedures for the dynamic, ana-lysis of complex structures operating in water.

All these valuable efforts may improve the insight of researchers and ship designers into the vibration phenomena, but a straight forward rational analysi

of the vibratory operation of the ship, covering the

propeller excitation, the elastic response of the

struc-ture and the final evaluation of the expected vibrations C)_{PaperpresentedattheConfexence on Advances in Propeller Research} and'Design,,Gdansk, Fèbruary 11-13. 1981.

*5)_{Department of Shipbuilding 'and Shipping, Deift University of}

Tech-nology, The Netherlands.

against the acceptable levels is still in a stage of

de-velopment and a reliable analysis for a ship to be built

is still not available [7], [81. It is necessary for the future to work on this problem, and to have an inte-gration of the hydrodynamic and the mechanical re-search in order to have a successful solution of these

hydroelastic problems.

In this paper the attention will be focussed on the experimental approach for the determination of the vibratory propeller hull pressures and forces, being a

problem of hydroelastic nature, ie. serious inter-actions may be expected from the vibrations of the

body on which the measurements take place..

2. Fundamentals of dynamic measurements on hydro-elastic systems

2.1. Propellershafi force measurement

In order to illustrate the essentials of the problems

involved, the measurements of the vibratory

propeller-shaft forces' will be taken as an example. The system is presented in simplified form in Figure 1. For

har-monic oscillations holds:

_w2Mxc.Ax0+ic.x0+Sx0 =F1

0o

F1 Input

'0

X0 output propeller on elastic support 'M= mechanical Mass of the propetu

46= added mass of propeller 3= damping of the propelLer

S stiffness of propeller support

Figure 1. SimplifIed block diagram of a propeller on an elastic support for the dynamic.propeller force measurements.

p-international

Sh ipbui idi

n g

Progress

Vol.28-July 1981 - No. 323 ISSN 0020- 868X MARINE TECHNOLOGY MONTHLY

devoted to theoretical and practical shipbuilding, marine-engine building and allied subjects; viz, ship hydrodynamics, advanced techniques in shipping and ship design, strength and hull vibration, offshore and mooring problems, ship manoeuvrabiity and control unconventional ship types, marine engineering, smaif

craft and dredgers, cargo handling.

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Editors International Shipbuilding Prögress Postbox 199, 2600 AD Deift, The Netherlañds No part of the published papers may be reproduced in any form by print, phótoprint, microfilm or any other means without written permission from the publisher;

A. ANDREONI, Eng. Instituto de Pes-quisas Technológicas, Naval Engineering Section, Sao, Paulo, Brasil.

Dott.lng. G. BRIZZOLARA. Admini-stratore Ing. G. Brizzolara &C., Genova; Consulting Naval Architect, Italy. Prof. 1$. CALDWELL. Professor, De-partment of Naval Architecture and Shipbuilding, The University of New-castleupon Tyne, Great Britain. Prof Dung. EMILIO CASTAGNETO. Head of the Department of Naval Ar-chitecture, University of Naples, Italy. Profi)r Ing. JERZY W. DOERFFER, B.Sc. Technical University, Gdánsk, Poland.

Dr. H. EDSTRAND. General-Director of Statens Skeppsprovningsanstalt, Gote-borg, Sweden.

J. GORDON GERMAN. Partner German & Milne, Montreal, Canada.

Ing. ANTONIO GREGOREUI Assis-tant Manager, Fiat Division Mare,Torino General Manager Grandi Motori Trieste,

Fiat-Ansaldo.C.R.D.A., Italy.

Prof. J. HARVEY EVANS. Massachu-setts Institute of Technology, Depart-ment of Naval Architecture and Marine Engineering, Cambridge, U.S.A. Prof.Dr. J.W. HOYT. Mech. Eng., Rut-gers Univ., New Brunswick. N.J., ILS.A. Prof.Dr.Ing. K. ILLIE& Technical Uni-versity, Hannover, University Hamburg, Germany.

Prof.Dr. Eng TÄKAO INUI. Faculty of

INTERNATIONAL EDITORIAL COMM ITFEE Engineering,.University of Tokyo, Japan.

Prof .Dr.Techn. JAN-ERIK JANSSON. Professor of Naval Architecture, The Technical University of Finland, Ota-niemi-Helsinki, Finland.

ProfDr. INGVAR JUNG. Professor of Thermal Engineering, Institute of Tech-nology, Stockholm, Sweden. (retired). H. DE LEIRIS Ingénieur Général du GenieMaritime, Paris, France.

Prof. J.K. LUNDE B;Sc., M.Sc. Chal-mers University of Technology, Sweden. S.T. MATHEWS. Section Head, Ship Section, National Research Council, Ottawa, Canada.

Prof. L. MAZARREDO. Director, The Shipbuilding Research Association of Spain, Madrid, Spain.

Prof. S. MOTORA. Professor, Faculty of Engineering, University of Tokyo, Japan.

Prof.Dr.Techn C.W. PROHASKA, Ship-building Department, Technical Univer-sity of Denmark, Copenhage; Director, Hydro- and Aerodynamics Laboratory, Lyngby, Denmark.

Prof. CEDRIC RIDGELY-NEVI'rF. Pro-fessor of Naval Architecture, Webb Insti-tute of Naval Architecture, Glen Cove, New York, U.S.A.

Prof.Eng.Dr. SALVATORE ROSA.Pto-fessor of Naval Architecture, Escola de Engenharia of Federal University, Rio de Janeiro; Vice-President, Brazilian Society of Naval Architecture and Marine Engi.

EXECUTIVE EDITORS

Prof ir. N. DIJKSHOORN. Extra-ordinary Professor, Depart. ment of Shipbuilding and Shipping, Deift University of Tech-nology, The Netherlands.

Prof.tr. J. GERRITSMA Professor, Department of Shipbuil-ding and Shipping, Deift University of Technology, The 'Netherlands.

Prof.Dr.Ir. J.D. VAN MANEN. President, Netherlands Ship Model Basin, Wageningen, The Netherlands.

Ir. W.SPUYMAN. Organization for 'Industrial Research TNO, Delft, The Netherlands.

HONORARY COMMITTEE

Prof.h. G. AERTSSEN. Professor, Department of Naval Architecture, University of Ghent; President, Centre Belge de Recherches Navales, Belgium, (retired)

Profir. H.E. JAEGER. Professor, Department of Shipbuil-ding and Shipping, Delft University of Technology, The Netheflands (retired)

Prof.Dr.Ir. W.P.A. VAN LAMMEREN. President, Netherlands Shit, Model Basin, Wageningen, The Netherlands. (retired) Prof.Dr.-Iñg. H. VOLKER. Head Department of Naval Archi-tecture and Marine Engineering, Technical University, Vienna Austria. (retired)

neering SOBENA,Brasil.

Prof.Dr. ARTHUR SARSTEN. Institute of Internal Combustion Engines, Norges Tekniske Högskole, Trondheim Norway. Prof. KARL E. SCHOENUERR. Consul-ting Naval Architect; Former Technical Director, Hydromechanics Laboratory, 'David Taylor Model Basin (present U1S. Naval Ship Research and Develop-ment Center), Washington, D.C.; Former Professor of Engineering Mechanics and Dean, College of Engineer ng, University of Notre Dame, Indiana, U.S.A.

Prof.Dr. H. SCHWANECKE. Head, De-partment of Naval Architecture and Marine Engineering, Technical University Vienna, Austria.

Prof.Diplolng. S SILOVIC. Professor of Naval Architecture and Superbi tendant of the Ship Research Institute,

Univer-sity of Zageeb, Yugoslavia.

Prof.Dr.h. W. SOETE. Professor of Strength of Materials, University of Ghent, Laboratory for Strength of Ma-terials, Ghent, Belgium.

Dring1 LORENZO SPINELLI. Manag-ing Director, Registro Italiano Navale, Genova, Italy.

Prof.Dr.Eng. SHIN TAMIYA. Institute of Structural Engineering, University of Tsukuba, Japan.

A. TOWLE, M.Sc1, C.Eng. F.I.Mech. E. Technical Director, Lubrizol Limited, London, Great Britain.

The measured displacement x0 (or when strain gauges are applied the product S.x0) is only under certain circumstances equal to the quantity of interest

i.e. when the terms other than S.x0 in the equation of

Figure 1 are negligible.

Besides the mechanical mass term there are two terms referring to hydrodynamic effects, i.e. added massi and damping

When - O the first three terms indeed are negligible and the measurement can take place without

consider-ing possible hydrodynamic interactions. For frequen-cies other then zero, an effect of the hydrodynamic

coefficients and , increasing with increasing fre-quency, wil! be present, leading to unacceptable errors

and unknown hydroelastic effects. The key to an

ac-ceptable compromise for dynamic measurements(C* :#

O) is found in the ratio of the frequencies of interest over the natural frequency of the measuring system s/C/M+.J'.When this ratio equals 1/5 or less, an

ac-ceptable compromise may be assumed. The only vari-able in this measurement arrangement that can be chosen freely is the stiffness C that needs to be ashigh as possible, still allowing some flexibility for the strain gauge output.

From this consideration the conclusion can be

drawn that for measurements of propeller fluctuating shaft forces the hydroelastic problem can be avoided by choosing a sufficiently high value for the stiffness C of the supporting spring, still allowing a

measure-ment by its very small flexibility. This allowance

depends on the signal-noise-ratio of the

electronic-mechanic measüring system.

It is questionable whether other problems of this

nature can be solved in a similar way.

2.2 'Wet detail' pressure measurement

Another fundamental problem in propeller

dyna-mics exists, when the radiated pressure field of a cavitating propeller hits the hull surface. For that reason the following key problem is studied.

A rectangular elastic plate is excited by a specially distributed fluctuating pressure that has to be meas-ured. The plate is part of the ships hull and separates the wet and dry area (see Figure 2). The pressure dis-tribution that excites the plate:

P1(x,y,t)=

A sin sm e

ITX . 11)' Iwt (2)

equals a harmonic spatially distributed pressure, having

a X-Y-distribution coinciding with the first general-ised force of the first mode of the plate vibration, so the deflection of the plate as a function of X and Y

may be formulated according the modal analysis as:

W(x,y,t) W

sin!sin1!

eIw( (3)

Figure 2. Elastic plate, simply supported on the edges, excited by a fluctuating pressure distribution:

P(x,y,t) A sin5 sine1(t.

where: W=A

.. 4(b42;2b2+)

w1

For the transfer function - in the centre of the plate we have:

pláte deflection amplitude pressure distribution amplitude

IA (4)

where:

wi)

S=D.

4(b4+ 212b2+14)

4 b4

This is the regular dynamic response of the first mode of the plate.

When the pressure distribution, sensed by the plate, is transferred through the plate edges to the main

structure of the ship a similar dynamic amplification

due to resonance can be expected as for a simple mass-spring system.

For the case water is on one side of the plate it is -necessary to consider also the induced pressure

dis-tributions due to the motions of the plate.

According to [9] the pressure generated by a vibrating plate equals:

p

P2(x,y,t)

11 1

ir.J

+-12 _b2 =p

i.

b d2W(x,y,t) d2W(x;y,t) dt2 (5) dt2

This hydrodynamic pressure is sensed by the

mechan-ical system as an additional mass and will reduce its natural frequency. It has a similar distribution às the

plate dèflection and glso as the original pressure

loading P1 (x,y,t).

For a pressurepick:up_mountedon_anarbitrary place in the plate the system the block diagram of Figure 3 can be drawn and the ratio of the output

154

input pressure

radiated by the propelLer

1-w2

--Figure 3. BlOck diagram for the analysis of a one side wetted plate equipped with a pressure pick-up.

pressure P0 and the input pressure P,, can be

formu-lated as follows;

'

2M 'PO

(6) P,,

1_2M+

The following conclusions can be drawn:

- When the stiffness of the plate is sufficiently high (S - co)_{(natural frequency well above the frequency}

of measurement), the output pressure R0 equals the

input pressure P,, and we have a correct

measure-ment

- When this stiffness condition is not fuilfilled we will approach the condition that (S O):

M

M+..4'

which shows that the measurement can be seriously incorrect. The incorrectness of the measurement will

be reduced when the mechanical mass M is chosen as large as possible, since the hydrodynamic mass f

cannot be 'changed. For full size ship measurements this is an impossibility, for model measurements measures can be taken to approach this condition. For' the higher modes similar conclusions can be

drawn.

When the stiffness S has a value such that resonance 'conditions are pìesent, a wide variation in the input!

output relation is possible and the word

measure-'ment is not applicable any more.

2.3. Pressure measurements effected by overall vibra-tions

Since the forced vibrations of the model or the full

size ship have frequencies coinciding with the excita-,tion frequency no distinction can be made between the

local effects (see 2.2) 'and the pressure effects of the overall vibration. The question is how large is the

ef-fect of the overall vibration on the local pressure.. For

that purpose an 'estimate will be made of this oyerall

local 'verticaL acceLeration a

Figure 4. Circle cylinder having vertical vibrations with a wave-length X and being semi submerged in water.

effect 'by means of an idealised case derived' from

Re-ference [IO], where for a vibrating semi-submerged

circle cylinder the pressure distribution is derived. The case is illustrated' in Figure 4. The pressure distribution

on the point of observation on the surface 'of the

cylinder as water reaction on the vibratory motion equals:

p

.E. z. H('i! B)

(7)

where:

E-X

For a point of observatiön on the bottom midships

(z =)we have:

'w

₂

ií9,) (B)_iJ-B.H()(!!B)

B

H1)(i! B)

(8) or, abbreviated: . a1 .R (9)

The dependence of R is shown in Figure 5.

This' pressure' has to be considered in connection with the pressure measurements in a similar way as is done in paragraph 2.2, but now considering the dy-namics of the entire hull (of the model! or the ship)

10 08 05 04 0.2 o 0 05 10 15 20 25

Figure 5. The value of the reduction coefficient R agáinst

and the mode weighted integrated pressure distribution

exciting the hull girder(of model orship).

The reduction factor R accounts for three-dimen-sional .effects in longitudinal direction. For shorter wavelength X the water pressure P, due to the body

acceleration will be reduced.

Another effect reducing the water pressure is

found in the shape of the cross-section. Reference

[I 0] refers to a circular cross-section but a more realistic section of .a ship in particularin the afterbody results in an additional reduction. as illustrated in [11] and [1.2].

Further the finite length of the ships hull has not been considered in these references and may result j

another .unknown reduction.

For a rough estimate of the effect we are looking for, i.e.. the effect of the model vibration on the

pro-peller-hull-pressure-measurements, it is assumed that

the effects of sectiôn shape and finite length of the

hull can, for the time being, be left out of consider-ation. Generally speaking, itcan be stated that hydro-dynamic interaction can be avoided when the object

on which the pressure measurement takes .place is

suf-ficiently stiff supported, i.e. having a lowest natural

frequency Well above the maximum frequency of

measurement (seé section 2.1) For a ship model this means that all the natural frequencies of the modes (including heave and pitch) must have values, well

above the third blade frequency harmonic. This is

physically impossible and hydroelastic feedback

ef-fects need to be considered.

In order. to have an impression of the dynamic

properties of the hull of the model an impuls-excited vibratory response of a wooden model of 8 m length has been analyzed in its harmonic content. The result

of this experiment is shown in Figure. 6. It.can be con-cluded that the lowest natural frequencies are well below the blade frequency and range from 10-30

c.p.s.

It also can be concluded that in the range of blade

Q

E

's

h m.ion

lowermode higher mode huit frequencIes huit frequencies

L.l

1.5 96 ₁₀1.7 ₂₆₅

th

i 0 10 2Ô 30 40 50 60 70 80 90 100 frequency c.p.s.-TE th O moda B/21B,2I- _/3--flL . 1 e

tçc&

I SIDE VIEW draft B j -_. B

-propeller pressure excItation cross section area of propeller excitation

BOTîOM VIEW

st

I modo

___

-

- nl

Figure 7. Simplified model for overall vibration and pressure analysis.

range of bLade range of frequency for multi pie

mode L blade

mea sur.ements frequency FiguEe 6. Natural frequencies of the hull of a wooden model, determined by a frequency analysis of an impuls.excited tran-sient response.

frequencies and their multiples some resonance pheno-mena may occur, that have to be considered carefully.

3. Rough estimate of hull vibration inducéd pressure

in model experiments

In order to estimate the effects described in par. 2,

a rectangular simplified ship having al ratio.of 5 and a draft equal to B will be analyzed.

The ship will have a constant mass distribution (see Figure 7). Only the effect of the overall vibrations will be investigated.

The propeller excitation is assumed to be constantly

distributed over an area of B/2 x B/2 in the afterbody

as indicated in Figure 7.

1.56

For this model the first three normal modes will be investigated under the condition that these modes are strongly overcritically excited, so that only mass

ef-fects will play a role in the response calculation. Later, considerations will be made for resonance phenomena.

3.1. Zero-mode n0x) = C

Generalized force

r0 =

n0(x) .P(x

Generalized' mass

M0

'Pn(x) m(x) dx

= C2M

Generalized vertical acceleration

r01 PB.

4M

2

B

-

dx = cf B2

measured in units of mode strength C.

In this case the mass' of the ship equals SB3. p, so that the local physical acceleration at the point of observa-tion equals:

PB2

= _{(a,0 =Cn0)}

20B3 p

and the local pressure in the centreline of the ship due to the water reaction equals, according formula (9):

PB2. _B

P=p

_,'

..R

20B3p 2

In this case X = , fOr which holds (according Figure

5)R= 1.

We obtain: =

J_

P,,,which' is 2.5% of the

excita-tion pressure This pressure, is' due to the vibratory heave motion of the hull and is felt by every point of

the ships bottom' centreline

3.2 Firstmoden1=a.x

It is assumed that the area where the propeller fluctuating pressure is 'located is so small that this

area can be neglected for the lower modes (the dis-.tributed pressure excitation is approximated by a 'point excitation'), so that the calculation of the. generalized force can be simplified. It follows:

+1/2' _B

r1 =

. dx -1/2 2

= a. 2'BP

.

4=apÇ

+1/2 M1 = f

n (x)mx)dx

-1/2 (10) +1/2 cr2pB2 f x2dx

I02pB5

-1/2

r

_i

'i

The physical acceleration at the point of observation equals:

a101 . a

. 2B

Pp lOpB

It is assumed that x in this case equals 2L, so that.R

0.9 (see Figure 5). According formula (9) it follows:

lOpB

..

0.9 orP)P

(.11)

or .the hydrodynamic pressure due to the vibratory.

pitch motion equals 4.5% of the excitation pressure.

3.3.

For the second mode a similar analysis can be made.

With some assumptions aboút the shape of vibration

and X = L for which holds'R 0.7, it follows:

- P, at the point of observation.

This means that the water reaction pressure equals appr. 3% of the excitation pressure.

3. 4. General observations and conclusions

For the analysis of higher order modes various

ef-fects' have to be considered 'when conclusions are to be

drawn. For the higher modes in general the

genera-lized force will reduce, because of the mode shape weighted integration.

The generalized mass will not reduce.so much, .because of the squared mode shape weighted integration.

The shiplength-wavelength ratio will' increase and the

reduction factor R will reduce These effects will reduce the higher mode vibrations and the resulting water reaction pressure For higher modes however, we will approach more and more resonance conditions (see Figure 6), so that from this viewpoint the

result-ing water reaction pressure will increase Only by

means of further thorough. calculations of the model dynamics it is possible to make a precize analysis.

For the purpose of this paper it suffices to make the acceptable assumption that the first ten modes may contribute equally to the water reaction pressure, each with a value equal to appr. 3% of the excitation pres-sure.

The phasing of these individual modal effects is

after-body and a partial cancellation in the remainder of

the hull. Therefore it may be expected that without

adequate measures the pressure fluctuations measured in the afterbody due to propeller operation are serious-ly effected by the vibratory hull reactioñ and may

amount to 30% of the recorded pressure. This resUlt

is not surprising when it is realized that dynamic meas-urements take place under overcriticàl conditions. This unfavourable condition can be avoided when the

nature of the problem allows a sufficiently stiff

sup-port, as is the case when dynamic propeller shaft force measurements -are projected (see par. 2.1).

Unfortunately this is not well possible in the: case of afterbody pressure measurements and more-

sophis-ticated and complex measuring techniques and

calibra-tion procedures are necessary to obtain the interest-¡ng quantity, i.e. the propeller generated excitation

pressure (see par. 4).

The erroneous results of the pressure measurements

may be amplified when pressure fluctuations are meas-ured in an area where the real propeller excitation becomes small as is the case for locations 2 or 3 times the propeller diameter forward, of the propeller.

For that location the decay of the vibratory pressure field of the propeller is strong and only a small

pres-sure fluctuation exists.

Since the water reaction pressure fluctuations simply

depend on the vibratory motion of the hull, and do

not suffer 'from the decaying mechanism of the pres-sure radiation from the cavitating propeller, the key ratio ¡P,, may increase seriously, and experiments on excitation pressures need a careful interpretation and cannot be evaluated without dynamic calibration

(see par. 4). Since these 'far away' excitatiOn pressures

seem to be important E 13], attention to the

thention-ed difficulties is a requirement.

Excitation frequencies, 'being multiples -ol blade frequency, require a separate treatment because when

resonance conditions of the hull are present (being different for different excitation frequencies) the water reaction pressure phenomena will differ fàr

dif-ferent frequencies.

4. Proposed technique for dynamic calibration and -pressure measurements

Measurements corrected by modal decomposed feed

back

tion with forward speed can be carried out in a towing tank.

The -fundamentals of the proposed correction are

giyen in Figure 8 where we can rea'd:

Pp =Po+Pw

P, is the pressure of interest

P0 is the output of the pressure pick-up during the

excitation measurement

-is the reaction of the surrounding water due to

the model vibrations.

-recorded pressure

PP

excitation

pressure _--g

feed back siqnal due to huit vibration

Vib ra t o r

y-displacement

to' be -recorded

Figure 8. Fundamental layout of feedback mechanism.

Knowledge of is essential- for a qualified meas-urement ofF,, and- amounts-to appr. 30% ofF,,.

-In order to gain knowledge of it is necessary to know the acceleration of the vibratory motion x and the transfer factor 1' as indicated in -Figure 8 and' a

separate dynamic calibration procedure 'is required to enable -the determination of 1 This, calibration

proce-dure is outlined in Figure 9 where the model under investigation is subjected to an external mechanical'

fluctuating force having a variable frequency. By

means of tuning, -the hull can be forced in one of -its natural modes. It- is assumed under these conditions

that the other modes will have a negligible acceleration amplitude whièh is reasonable because of the large

am-plification due to resonance. Under those conditions

we have one single mode vibration and the reaction- of

the water can now be' recorded by the pressure

pick-ups. Since the propeller is not- in operation,.this

pres-For the time being it is assumed that damping forces , ' _o

in phase with the speed of vibration are- not of

import-tre.' e' -' '

ance in the first place. Also the effect of the forward . .. _-' p

W

speedofthe_model_ isassumed_to_be_negligible

although an indicative figure is given in [14]. For the

case this- effect has to be taken into account a calibra calibration procedure.

modal acceleration ampLitude to be recorded

-pressure fluctuation to be recorded

158

sure equals P and the ratio _wm

'm (valid for the

mth mode) is an element oLF, we are looking for.

SimultaneOusly with these recordings it is necessary to detennine the mode shapes during the various

resonance conditions, as well as the required number of modes in connection with the dynamic response of the hull. It is necessary to take those modes into account that may be critically excited by the higher

harmonics of the propeller excitation.

Since the propeller excitation is nonsymmetric

it .s also necessary to consider nonsymmetrical modes

such as the combined torsional-horizontal bending modes. The highest mode number of interest (having the highest frequency and shortest distance between

the nodes) determines the number of required

ac-celerometers. It is required to take at least two times

the maximum number of nodes as the minimum

num-ber of accelerometers for the determination and re-solvability of the hull deflection (comparable in the frequency domain to the highest frequency in

samp-ling technique in order to avoid aliasing).

A proper measurement of can now be made by

recording the pressure P0 and the modal accelerations

of the model during the tests. Both quantities need to be harmonically decomposed. The determination

of the modal accelerations requires an additional

measurement with the set of accelerometers as instal-led in the model for the calibration. This is an extra extension of the experimental determination of the propeller generated vibratory excitation pressures P,,

and is more complex when compared with the direct pressure measurement P0 without modal feed-back, not resulting in excitation pressures. The number of accelerometers and their location needs to be exactly

the same as for the calibration. To determine the

strength of the various modes in which the model is forced to vibrate (in non-resonance condition) during

the measurement by the propeller excitation, the mode

shapes, determined during the calibratiOn, are to be used. Having sufflcient pressure pickups installed, in

order to determine the distribution of the hull pressure

fluctuations, this in addition to the series of accelero-meters necessary for the determination of the model vibrations, a well organised computerised instrunien-tation is a necessity. A more detailed lay-out of the fundamentals of multiple frequency, multiple

pres-sure pick-up and multiple mode calibration and meas-urement is given in Figures lO and 11.

5. Final remarks

1. Another method enabling us to arrive at the vibration response corrections P on the directly

measured pressure fluctuations P0 may be based on

driving point impedance and cross impedance

tech-niques. To apply these techniques each individual pressure pick-up needs to be calibrated with an ex-citer on the pick-up itself. Similarly as in the preceding

paragraph the acceleration sensitivity as a function of frequency has to be determined. The complexity of this experimental method will be similar to the modal

method, which is well understandable because this

complexity is bound to that of the physical problem.

The impedance method, however, requires special designed and manufactured instrumentation, while

for the modal approach 'off-the-shelf instruments can

be used.

For the proposed 'modal correction method' it

is necessary to avoid lOcal plate resonance in the

after-body, in order to avoid additional vibratory effects as has been outlined in paragraph 2.2. For that reason it is proposed to have a stiff aluminium casting as

after-body, having sufficient thickness to avoid local

re-sonance at the interesting frequency range, and thus

avoiding 'wet detail' response.

In order to eliminate the extra dynamic loading of the model due to the propeller-, engine- and shaft-forces which may disturb the calibration-measurement rela-tion, it is recommended for the measurement to drive

and support the propeller fully separated from the hull, i.e. to have the propeller driven from an open

waterboat, installed behind the model.

It is meaningless when looking forextrapolation, to

compare the fluctuating pressures measured on a model with those measured on the full size ship. The different hull dynamics, as well for the global vibrations as for the details of the ship and model,

make a comparison impossible. The distributed input

pressure is then converted into hull vibrations and

water reaction pressures. The rigid boundary pressure

distribution may be completely disturbed by these effects and is not comparable with the distribution measured on model scale.

For the purpose of vibration prediction, however, extrapolation to the full size ship is a requirement.

The true propeller excitation (i.e. the hull pressure on an infinitely stiff boundary) is, apart from the regular

scaling problem associated with wake distribution, cavitation etc., extrapolable to full size ships and

serves as an input for the hull structure vibration ana-list.

The full size ship vibration prediction is a problem

that becomes more and more urgent to be solved [15 1.

Various statistical methods, now under development, make use of the model measured hull pressure fluc-tuation. The reliability of these methods depends on the variance as encountered in the analysis. A

signifi-at nsignifi-atural frequency of mode p at optimum, position for maximum mOde response hull dynamics of thé model broken down in modes

a'

11.1 .Pj.L vector of...pressure distribution due to mode *acceleration

)

computerized data evaluation

strength of. mode p ás èxcited

lip

VL

£flU

movable siñgle frequency exciter P accelerometers

n,n i-i

n

n.

n pressure

pick- ups o hull with m modes O> p> m

pressure pick-up number y

n n

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Lacc. ñumber i

dirêiiòiilïss

véctòr of mode -wei.htin. function column matrix.Ae

r r-

ure orrec ion

muLtipLe frequency

output of P acceLérometers

muLtiple frequency out

of n pressure pick-ups

o,

o,

o,

harmonic analysis blade rate f (and multiple) harmonic analysis blade rate f (añd multiple)

of

:1 p single frequency

lêìäetéf.

outout .wèiqhtinqfunctibns.

i

eq. blade rate f from

calibration(fig.1Q)-I V

ri

__ i 1i nl pi J w _-_w .___ lu.-

ni

p w_im w_{nm pm} rre e

ou ut of

--ressuré

-of

p i i rn

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k

Figure lI. Lay-out ofacomputerized propeller generated hull pressure measurement correctéd for hull vibration.

acceleration stren.th of modes -at fre.ueñc f dunn mea sùr èéñt,s correction matrix obtained from calibrätion fi.iO -(Po P)

re ur - - xcit tion for

one fre.uenc f át re

- eickU

,

n. r

ne ssurefluctuation rue co ec e

.r e er

-accelerometers

fl,n r-in n

n

ri

n n n

n pressure

Dick- ups _{huLl with, m modós}

propelLer in operation

cant part of this variance may be caused by the differ-ences encountered in the noncorrected hull pressure

measurements.

For differently manufactured models (plastic, wood,

wax) of the same ship and propeller, the measurement

may suffer from different correction factors not taken into account. It might therefore be worthwhile to re-consider this statistical approach, and take the effect

of the hull vibration induced pressures into account. 5. For the purpose of experimental verification of theoretically analyzed hull pressures [6], results of

which refer to solid boundary pressure fluctuations

due to the propeller P,,, the proposed dynamically

corrected pressure measurements are a requirement, in particular when the accuracy of the method needs

to be investigàted.

Nomenclature

A amplitude of harmonic pressure

distribu-tion

B athwarthship dimension

constant

D plate b:ending stiffness

E coefficient

F

excitation force H Hankel function M mass M0,M1,M2 generalized mass PO output pressure

Pp excitation pressure generated by the

propeller

Pw pressure dúe to vbratory boundary P1,P2 pressure distribution R - reduction coefficient

s

stiffness coefficient h' displacement a acceleration n natural coordinates

t

time X0 displacement X, y, z spatial coordinates hydrodynamic mass hydrodynamic damping

1 ''2"3

generalized force a constant angle X Wavelength p density of water w circular frequency w1 ,w ,w natural frequencies References

i . . Holtrop. J., 'Estimation of propeller induced vibratory hull forces at the. design state of a ship', RINA-symposium on propeller induced ship vibration, London. December 1979, PaperNo. Il.

Holden K.O., 'Excitation forces and forebody vibrations induced by marine propeller blade cavitation', Norwegian Maritime Research, No. 1, 1979.

Fitzsimmons, A., 'Cavitation induced hull pressures: a comparison of analytical results, ship and model measurè-ments', RINA-symposium on propeller induced ship vibra. tian, London December 1979, Paper No. 9.

Kerwin, i.E. and Lee, C.S., 'Prediction of steady and un-steady marine propeller perfonnance by numerical lifting surface theory', SNAME, Vol., 86, 1978.

5 Vorus, W.S.; Breslin, J.P. and Tela, Y.S, 'Calculation and comparison of propeller unsteady pressuré forces onships', SNAME, Ship Vibration Symposium, Arlington, Va. USA.,.October 1978.

Noordzij, L., 'Pressurefield induced by a cavitating propel-ler', International Shipbuilding Progress, Vol. 23, No. 260,

1976.

Wereldsma, R., 'Ship vibration state-of-the,art 1979', Report No. 227 Ship Structures Lab, Delft University of Technology; Publication No. M 38 of the Netherlands Maritime Institute, Rotterdam, June 1980.

Wereldsma, R., 'Heutige Schwierigkeiten der Schiffs-schwingungs-voraussage und mögliche Lösung', Fachaus-schuss Schiffsvibrationen der ST.G. 1979.

Report No. 226 Ship Structures Lab., Deift University of Technology, 1979.

Grim, O., 'Über den Einflùss der mitschwingenden Was-serrnasse auf die Schwingungseigenschaften lokaler

schwiñ-ngsfer Systeme', Schiff und Hafen, 1953.

Grim, O., 'Elastische Querschwingüngen des Schiffskörpers'. Schiffstechnik, Band 7, 1960.

Huse, E., 'Hull vibratiOn, and measurements of propeller induced pressure fluctuations', International Shipbuilding Progress, Vol. 17, March 1970.

Joosen, WP.A. and Sparenberg, JA.,, 'On the longitudinal redúction factor for the added mass of vibrating ships with rectangular cross-section', International Shipbuilding Progress, Vol. 8, April 1961. - -

-Morgan, Wm.B. (chairman), 'Propeller cominittèe report of the 15th l.T.T.C., The Hague 1978', ITTC.Proceedings issued by Netherlands Ship Model Basin, The Netherlands. Grim, O;, 'Hydrodynamische Masse bei lokalen Schwin-gungen, iñsbesondere bei Schwingungen im Bereich des Maschinenraums', Schiff und Hafen, Heft 11, 1975. McFarland, R. and Lindquist, D., 'Vibration from a shi-owner's standpoint', SNAME and SSC Ship Vibration Symposium, Arlington, Va. U.S.A., 1978.

162

SELF-TUNING ADAPTIVE CONTROL OF LARGE SHIPS IN NONSTATIONARY CONDITIONS by

A.W. Brink* and A. Tiano**

Abstract

-This paper describes a simulation study on the self4uning adaptive control o. a supertanker and a nd genera-tion contamership. The simulagenera-tion covers the main operagenera-tional navigagenera-tion sitUagenera-tions, i.e course keeping and

course changing in stationary as well as non-stationary conditions The design of the adaptive autopilOt is obtained by application of an extended self-tuning controller which minimizes a preset cost function, whose form depends

on the operational situation and on the environmental conditions. The way the non-stationary conditions can be

taken into account is discussed. Foreach type of ship a large number of runs were carried out. The results indicate that a self-tuning adaptive autopilot is a feasible and efficient solution for the automatic steering of the ship in all the considered situations.

1. Introduction

The application of automatió control techniques to ship steering has proved to be a powerful tool for

im-proving the efficiency and safety of the ship navigation

process. Many studies and research programs have been carried out in different countries, in particular

oriented in the recent years towards the design of adaptive autopilots which are based on advanced

con-trol techniques, see [I] to [7]. An up-to-date review of the most recent contributions in this field is

con-tained in the proceedings of a symposium, held in

Genoa in June 1980 [8].

Within this context, when experimenting with and

verifying advanced automatic control strategies applied to ship steering, simulation studies are very useful, due to their great flexibility and the time saved in compari-son with sea trials Simulation, in fact, provides an effective way of checking out different autopilots for different types of ships under widely varying opera-tional and weather conditions, before the expensive development of the first prototype takes place and the implementation and testing during full-scale trials at

sea h carried out.

This paper describes a simulation study on the self-tuning adaptive control of a supertanker and a 2nd generation containership in non-stationary conditions,

carried out within the framework of a joint-research program of the Italian Istituto per l'Automazione Na-vale (lAN-CNR) in Genova and the Dutch

TNO-In-stitute for Mechanical Constructions (TNO-IWECO) in Delft.

The prime objective of this joint-research which started in 1977 was to develop different adaptive

con-trol strategies for the ship steering process in the main

operational navigation situations, i.e. course keeping,

course changing and track keeping.

*) TNO-tnstitute for Mechanical Constructions, Delft, The Netherlands. **) Istituto per l'Automazione Navale, Genova, Italy.

During the first phase of the joint-research, carried out in 1 977 at the Delft Manoeuvring Simulator

Cen-ter, a self-tuning minimum variance regulator -was tested in different environmental conditions and its performance was compared with an 'ad hoc' designed

P.I.D. autopilot [41.

The simulation trials carried out for the two ships were limited to course keeping in stationary condi-tions, with the main purpose of verifying the stability and convergence characteristics of the self-tuning adaptive autopilot.

On the basis of the promising results obtained

during the first phase of the joint-research, the

IAN-CNR and TNO-IWECO decided to continue the simula-tion study in 1979 by considering the behaviour of the

two ships also. in non-stationary conditions. At the

same time, it was decided not to consider the PID-autopilot anymore, because of the inherent limita-tions of the PID-strategy.

This paper reports of the present status of the pro-ject. The sectiOns òf the paper are organized as fol-lows:

In section 2, the problem is analyzed and the

ob-jectives of the simulation are formulated. The

simu-lation program set-up in order to meet the objec-tivesis also discussed.

The necessary 'tools' to carry out the simulation, i.e.

the mathematical model of the ship and of the non-stationary environment and the adaptive controller are

discussed in sections 3 and 4, respectively.

A detailed scheme of the simulation runs presented in this paper and the run conditions can be found in section 5, together with the discussion of the results.

A number of figures illustrate the findings. On the basis of the results conclusions are drawn in section 6, while at the same time, those aspects are defined which

require further study in view of the overall objective