Today's evaluation and ckeckpoints
As shown in Figure 2 today's evaluation is restricted to the excitation forces and pressures. Model experi-meñts or theoretical analysis enables the determination
of these excitations in an advanced design stage.
Having experience with many ships and their vibratory behaviour it is possible to judge the force- and pres-sure-fluctuations as regular, extreme high or 'low.
Based on experience 'it might be expected that for the ship under consideration the vibratory behaviour will be' similar to that of previous ships, belonging o the same population. Further it can be stated that it is very difficult to determine a single vibration' 'level, because many local systems vibrating with different amplitudes will be encountered aboard ships. It is im-possible to catch the vibration level with 'one simple
figure.
The habitability of the ship, being so important for the acceptance by the owner, 'is determined by the vibratiOns of the local systems such as cabinfloors, control desks, furnitUre etc. that are to be determined in the design stage. These local systems are platform excited by the overall structure of the hull and it is
this overall vibration :th'at needs to be incorporated in the list of checkpoints, i.e. the mass-elastic behaviour of the hull girder needs to be considered. The elastic behaviour of the ship's hull and as a consequence an additional checkpoint of evaluation is the subject of this paper.
Analysis of theelastic hull girder
Ship vibrations can be broken down into three types of areas, i.e. firstly local vibrations of so-called *) Lectûre presented at the University of Galati, Rumania 1980, Publi-cation No. 226a of the Ship Structures Laboíatory, Delft University of
Technology.
**) Dept. of Naval Architecture, Deift University of Technology, The
Netherlands.
wet details, such as hull plating in the vicinity of the propeller, the rudder, the propeller itself, appendages
7 I«4'io mm
W
;
60 5x10'mm s 1000 FREQUENCY 10Hz I i i i i I 'o' 6000 cimin 100 i i' I i i iFigure 1. GuIdelines for the overall evaluation of vibration in
merchant ships, I.S.O. draft proposal No. 6954, revised
Sep-tember 1979.
96
SSL 226a
TODAY'S DIFFICULTIES IN SHIP 'VIBRATION PREDICTION AND A POSSIBLE SOLUTION*
by
R. Wereldsma**
Introduction
High installed power and increased R.P.M. of today's ships are the very cause of an increased vibration excita-tion, an excitation larger than that of regular ships designed some ten years ago. Also the larger dimensions of today's ships result in ari increased vibration amplitude. At this very moment an international evaluation of ship vibrations is being prepared by the I.S.O. and a proposal for international adaptation has been issued recently (Fi-gure 1). In this proposal the acceptable maximum vibration levels are indicated, and for ships to be built this pro-posed norm is already nowadays a basis for the contracts between the shipbuilder and shipowner. Under these conditions it is necessary to have a reliable prediction technique available in order to analyze the expected ship vibration level in the design stage. A state of the art [1] of vibration prediction techniques shows that a reliable method for the vibration analysis is not yet well possible. In the various checkpoints, available for the ship de-signer, to check his design against vibration acceptance, the mass-elastic response of the hull girder is not incor-porated (Figure 2).
Ship bui idi
n g Progress
Vq1.28 - May 1981 No.321 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 manoeuvrability and control unconventional ship types, marine engineering, small
craft and dredgers, cargo handling.
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No part of the published papers may be reproduced in any
form by print, photoprint, microfilm or any other means
without written permission from the publisher.
A. ANDREONI, Eng. Instituto de Pès.
quisas Technológicas, Naval Engineering Section, Sao, Paulo, Brasil.
Dott.tng. G. BRIZZOLARA. Admini-stratore Ing. G. Brizzolara &C., Genova;
Consulting Naval Architect, Italy.
Prof. J.B. CALDWELL. Professor, De.
partment of Naval Architecture and
Shipbuilding, The University of
New-castle upon Tyne, Great Britain.
Prof .Dr.Ing. EMILIO CASTAGNETO.
Head of the Department of Naval
Ar-chitecture, University of Naples, Italy.
Prof.Drjng. JERZY W. DOERFFER,
B.Sc. Technical University, Gdánsk, Poland.
Dr. H. EDSTRAND. General-Director of Statens Skeppsprovningsanstalt, Göte-borg, Sweden.
J. GORDON GERMAN. Partner German & Milne, Montreal, Canada.
Ing. ANTONIO GREGOREI1I. 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., U;S.A.
Prof.Dr.Ing. K. ILLIES. Technical Uni-versity, Hannover, University Hamburg,
Germany,.
Prof.Dr. Eng. TAKAO INUI. Faculty of
INTERNATIONAL EDITORIAL COMMITI'EE
Engineering, University of Tokyo,Japan. Prof,Dr.Techn. JAN-ERIK JANSSON.
Professor of Naval Architecture, The Technical University of Finland,
Ota-niemi-Helsinki, Finland.
-Prof.Dr. INGVÄR JUNG. Professor of Thermal Engineering, Institute of Tech-nology, Stockholm, Sweden (retired).
H. DE LEIRJS. Ingénieur Général du
Génie Maritime, 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.
ProfDr.Techn. C.W. PROHASKA, Ship-building Department, Technical Univer-sity of Denmark, Copenhage; Director, Hydro- and Aerodynamics Laboratory,
Lyngby, Denmark.
Prof. CEDRIC RIDGELY-NEVflT.
Pro-fessor of Naval Architecture, Webb
Insti-tute of Naval Architecture, Glen Cove,
New York, U.S.A.
Prof.Eng.Dr. SALVATORE ROSA.Pro-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, Delft University of Tech-nology, The Netherlands.
Prof.Ir. J. GERRJTSMA. Professor, Department of
Shipbuil-ding and Shipping, Delft 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.Ir. G. AERTSSEN. Professor, Department of Naval
Architecture, University of Ghent; President, Centre Belge
de Recherches Navales, Belgium, (retired)
Prof.Ir. H.E. JAEGER. Professor, Department of
Shipbuil-ding and Shipping, Delft University of Technology,
The-Netherlands. (retired)
Prof.Dr.Ir. W.P.A. VAN LAMMEREN. President, Netherlands ShipModel Basin, Wageningen, The Netherlands. (retired)
Prof.Dr..Ing. 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. SCHOENHERR. Consul-ting Naval Architect; Former Technical Director, Hydromechanics Laboratory,
David Taylor Model Basin (present U.S. Naval Ship Research and Develop. ment Center), Washington, DC.; Former Professor of Engineering Mechanics änd Dean, College of Engineering, 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.Dipl.Ing. S. SILOVIC. Professor of Naval Architecture and Superintendant
of the Ship Research Institute,
Univer-sity of Zagreb, Yugoslavia.
Prof.Dr.Ir. W. SOETE Professor of
Strength of Materials, University of Ghent, Laboratory for Strength of
Ma-terials, Ghent, Belgium.
Dr.Ing. LORENZO SPINELLI.
Manag-ing Director, Registro Italiano Navale,
Genova, Italy.
Proî.Dr.Eng. SHIN TAMIYA. Institute of Structural Engineering, University of Tsukuba, Japan.
A. TOWLE, M.Sc., C.Eng., F.I.Mech. E.
Technical Director, Lubrizol Limited,
Criteria for excitation forces and pressures Ship-design Correction
Figure 2. Summary of today's ship vibration evaluation.
etc.; secondly the global Vibrations of the main girder
of the ship (e.g.
2- and 3-noded vibratory vertka1 modes) and thirdly the local vibrations of the, outfit and other details in the dry area of the hull, being of importance for the habitability and acceptance of the ship. The latter mentioned details are excited through platform excitation by the vibratory displacements of the main girder in the range of blade. frequency andits multiples. It is therefore necessary tó break the
analysis down into four steps. They are: Determination of the excitation forces.
Transfer from pressure distiibutions to main struc-ture excitation through the 'wet details'.
Determination of the forced vibration of the main girder, excited by the 'output forcès' of the
wet-details.
Determination of the inboard 'dry details' vibration level generated by platform excitation due to main girder motiöns.
This paper will be concerned with some fundamen-tal possibilities to analyze the main girder vibrations and the vibratory reactions of the dry details. The other two steps, i.e. the hydrodynamic excitation and the wet-detail-transfer-functions will not be considered
in this paper..
-a. Analysis of the main girder vibrations
When in the design stage the overall structure of the ship to be built has been determined and ageneral lay-out of the equipment and outfit aboard the ship has been made an overall vibration analysis of the ship
by means of a finite element method can be made. OveraLL and LocaL huit vibrations \(missing
4\
criterion) not acceptable acceptabLe :97This analysis enables us to analyze the first eight to ten natural vibration shapes and frequencies, that will be used for a transformation to natural coordinates [2], [3], being the cornerstones for the analysis of the local-system-vibrations. In Figure 3 the principle of this modal analysis is shown. The spatially distributed propeller generated excitation forces are broken down into harmonic components and transformed to genera-lized forces.
The- descriptión of the problem in natural coordi-natés makes it possible to apply a system analysis, and-for different frequencies and mode shapes the am-plitudes of the various mode shapes can be determined by a relatively simple mass-spring system analysis.
An addition of the vibratory deflections of the var-ious mode shapes determines the overall hull vibration amplitude as. a function of e.g. the longitudinal ship coordinate for single and twice blade-frequency. In this way different hull vibration amplitudes are ob-tained for the afterbody and other locations along the hull.
This amplitude distribution is mainly determined by the mass distribution and the magnitude of the excita-tion force, because the lower modal systems are ex-cited overcritically. A modification in the rigidity of the hull has no meaning, for the case the obtained
amplitudes need to be. lowered. In that case tile mag-nitude of the excitation has to be reduced. It makes sense, to generate a design criterion on these overall hull vibration amplitudes, because these amplitudes are the platform excitations of the local systems, am-plitudes of which are to be compared with the
&PR EPP
Hull oressure
.e...Jftuctuatlons -having singte land doubLe bLade frequency
Natural Coordinates Determination Of generatised Mass and' Stiffness AmpLitudes of the natural vibration shapi excited by the pr op eUer e I-e e X __,1 _I po io 'io -, ,a
ii
li 1' -a Pa I!2 Ia -. P4 14 IA Genera Li s ed FOr-cesb. Analysis- of the local vibrations
The' vibrations of the- local- systems, of utmost importance- for the' habitability of -the ship, are plat-form excited by the main Structure-. The transfer
-func--tions of the local systems are determined by 'the natural frequency w0 and the dimensionless damping (Figure 4). These- two parameters can easily be ob-tained by an impulsive -excitation and a recorder, or, when' applicable, analyzed by a simple approximate calculation-. It is -then possible 'for the very many local systems aboard ship to determine the transfer ratio
1-x BLade freq. 4? 4? I.
--Transfer e e FunctionsH
-1 2x Blade freq. -+ ' +( in Figure 4) for -single and twice blade-frequency.
X
Because very many local syStems can be recognized a statistical analysis: becomes a requisite.
- A mean- value- for the transfer ratio (or
amplifica-tion factor) and a statistical distribuamplifica-tion of this trans-fer ratio can be established (Figure 4').
The mentioned distribution and its mean value determines the- 'quality-' of the- design of the details They are also different for various places iñ the ship, such as: engineroom, bridge, living quarters etc
Addition -Addition
Platform excitation of LocaL systems Figure 3. Overallship vibration&broken down intonatural coordinates.
Local system
vibration Y
(amplitude of the overaL1 vibration
Transfer functions of Local systems
with different natural frequencies
Research on and evaluation of the dynamics of the local systems are necessary for a successful application of the proposed method and ,improviñg these dynamics belongs to good workmanship.
With the overall vibration, amplitudes and the mean
value of the amplification factor of the details the
vibration level of the local systems can be obtained and checked against the ISO-norm. There is a possibility that some local systems may have too large amplitudes (statistical distribution), but for these systems a cure after the trial trip is simple to carry out (local
stiffe-ning).
For a prediction of the vibratory behaviour of the ship in an advanced design stage and still having the possibility to make major changes in the design if re-quired from a vibration point of view a careful plan
-
fling of the design and the building of. the ship is re-quired. Figure 5 shoWs such a planning.X
I,
3. Nülnerical example
Iñ this chapter a rough analysis will be made ofthe vibration level of a ship according to the method out-lined in chapter 2..
For a ship, having a length of 200m and a displace-ment of I 00.000 m3, operating with blade frequency w = 2Oir rad/Sec, the vibration level will be analyzed,
based on estimated excitation forces and transfer
ratios. The propeller excitation level is, based on many model measurements as carried out in the vacuum towing tank of the N.S.M.B. and amounts to 50 ton for blade frequency.
Mass of the ship.: 1.1 o kg.
Blade frequency propeller excitation: 5.l0 N. Blade fre4uency: = 2Oir rad/s.
Ist Mode:
w24l03(s2)
99.
lxBiFr 2 x BL.Fr. 1x8tFr 2xBL.Fr
'Excitation frequency
Probability densities for single
blade frequency and double blade frequency amplification factors
Figure 4. Transfer functions of locaF systems.
X
Platform excitation
C. o u a) L-o u Compari so n' with ISONorm. o u L o L) Determination of PropeLLer excited Forces and -Pressures and Jud g emen t Determination of overaLl vibration Level and J Ud gemen t Correction Estimate of Local vibration le.ve.L To this point aft erbody.-modific at ions possible Improvement of Local systems if necessary Criterion for excitation forces and pressures Statistical analysis of local hullplating Wet details' correction
I.>'
I o W L o o .0 W 4 In -C u' 'I-O L WC'D O
1)1 C O '-i) 'DL Is >i
Figure 5.Planning'of the vibration ,evaiúation. TriaLtri p
Ampi. of the afterbody:
4.10_8. 102 =4.l06 m.
For the sum of the eight to ten modal displacements
at the location of the afterbody will be estimated!: 1.1 O- rn, being the platform excitation for the local systems located at the afterbody.
For the dynamic amplification due to. resonance of the local systems a factor 10 will be assumed for the
mean value.
This means that the average value of the amplitude of the local systems amounts to be:
l0.lO- rn = m or 0.1 mm amplitude. For the mentioned blade frequency this means ap-prOximately 6 mm/sec amplitude of the velocity or 0.4, m/sec acceleration amplitude, which' are regular valués for regular ships. A similar calculation can be made! forothér harmonics of the blade frequency.
4. Final remarks.
a. In this paper the attention is focussed on the main
girder vibration and the dry-detail-transfer-func-tions.
In order to obtain the main girder excitation it is necessary to analyze the 'wet-detail-transfer-func-tions' as well. It is proposed to design a similar ap
L 10-6 Ampi. of the afterbody: m.
Criterion for overall vibration amplitudes Overall Hu(tgirder dynamics
L
Total Ship,.. Structure .ynamicsFigure 6. Proposed steps in the vibration.evaivation. Statistical analysis of
Local systems
"Dry details"
cor r ect ion
4.10_0 rad. acceptable not acceptable W, 'D 0) L. Q- 2nd Mode:
Ampi. P
"i
s'lo
radw2M
4.l0.--. 1012
C
DI
proach for these wet details ashàs been outlined fòr the dry details although an important wet detail such as the propeller arid its shafting may be con-sidered separately because of its vital importance in
the ship design. For the hull plating a statistical
analysis seems to be adequate:
b. One. of themain difficulties in ship vibration pre-diction is the required timing .of .this prepre-diction. in the design stage. With the proposed method, where, through the statistical analysis Of the many details and a separation in overall and local vibrations, the time of analysis may be shortened the mentioned timing problem may be eliminated.
c An extra criterion on overall vibration as indicated in Figure 6, may help the ship designer to overcome
the risks that have to be taken when maximum
vibration limits are contracted.
References
I. Wereldsma, R., 'Ship vibrations, State-of-the-art 1979', Report M 38 issued by the Netherlands Maritime Institute Rotterdam, 1980:,
2.. Hurty, W..C.,, Rubenstein, M.F., 'Dynamics of structures, Prentice-Hall Inc., NeW Jersey, i964
3. Bishop, R.E.D., Price, W.G., 'On the relàtionship betWeen thy modes and wet modes in the theory of ship response Journal of:Soundand VibEation, l976,pp. 157-164.
Introduction
The cycloidal (or vertical axis) propeller is character-ized by a number of blades which project from the
sur-face of a ship hull and which rotate about an axis normal to the hull surface. The cycloidal propeller derives its name from the path of each blade whichisa cycloidal curve.
Cycloidal propellers have been used for propulsion for lang time. Recently theoretical and experimental research work on cycloidal propellers has been carried out in several countries. The theory of them has been investigated by Taniguchi [1-4] in Japan, Isay [5-8] in Germany, Haberman [9,10] and Jamès [li] in the United States, Sparenberg and de Graaf [12-14] in The Netherlands. Experimental work has been con-ducted by Nakonechny [15,16], Ficken and Dickerson [17,18] in the United States, and by van Manen [19] in The Netherlands.
But until now, the theoretical model of cycloidal propellers that can be applied is only Taniguchi's method, which has been mentioned by Haberman [10]. Other methods predict unreasonable values at all advance coefficients [9] and some of them have not yet yielded practicable solutions.
At DTNSRDC (former DTMB) some experiments have been carried out. Haberman and Harley [9] compared their experiment results with the computa-tional procedure proposed by Taniguchi, for evaluating the performance characteristics of cycloidal propellers, and concluded that is was adequate for semi-elliptical blades But they only compared some cases in which the eccentricities were equal or less than 0.6. Later on more tests have been carried out by Nakonechny, Ficken and Dickerson [151 8].
*) Harbin Shipbuilding Enginéering Institute, Harbin, China.
by DM. Zhu*
Abstract
A' tieoretical computational method to evaluate the performance characteristics of cycloidal propellers is pre-sented Starting from Taniguchi's method improvements have been derived to make it applicable for vanous ec centricities in the whOle advance coefficient, region:
First the effect of the curved Orbit of the blades and the blade rotation is taken into account, that influences camber and zero lift angle. Then the effect of low Reynolds number on drag coefficient and the effect of stalling on lift coefficient are analysed and discussed in detail. Some linearizations are given up to improve the
computa-tioñ accuracy. The improved method is described.
Using this improved method to compute the performance of a DTNSRDC model and comparing the results with systematic experiment results (see .DTNSRDC Report 2983), it is shoWn that the agreement between them is quite good for a larger range of advance ratios and eccentricities.
Comparing the results calculated by Taniguchi's method with the results of the experiments, some dif-ferences are found. Specially in the high eccentricity
region this difference is quite large. Taniguchi's method is adequate only for medium advance coeffi-cients (about 0.4 to 0.5).
The author's work is an improvement of Taniguchi's method to obtain a theoretical computational method that is adequate in the whole advance coefficient region for various eccentricities of cycloidal.propellers. It can be seen in detail in Reference [20].
Analysis of Taniguchi's method
Taniguchi's method for calculating the performance of cycloidal propellers is based on the assumption that a quasi-steady state motion exists. The thrust and tor-que of the whole cycloidal propeller are evaluated by integrating the lift and drag exerted on each blade section. For this purpose, first the values of lift and drag coefficients of the blade section must be obtain-ed, then the magnitude and direction of the induced velocity at each blade section must be estimated.
There are three assumptions in Taniguchi's method: only the longitudinal induced velocities due to the trailing vortex system are taken into account, these induced velocities are constant over the length of blade,
the indúced velocity is not a function of the orbital position of the blade.
The value of the induced velocity is obtained from momentum theory and modified on the base of
ex-perimental data.
The blades of the cycloidal propeller rotate with constant angular velocity u about the propeller center O, which advances with constant speed VA (see
