REPORT No 137 M
December 1969NEDERLANDS SCHEEPSSTUDIECENTRUM TNO
NETHERLANDS SHIP RESEARCH CENTRE 'TNOENGINEERING DEPARTMENT LEEGHWATERSTRAAT 5, DELFT
TORSIONAL-AXIAL VIBRATIONS OF A SHIP'S
PROPULSION SYSTEM
PART III
COMPARATIVE INVESTIGATION OF CALCULATED AND MEASURED
TORSIONAL-AXIAL VIBRATIONS IN THE PROPULSION SYSTEM OF A TANKER
(TORSIE-AXIAAL TRILLINGEN IN EEN SCHEEPSVOORTSTUWINGSSYSTEEM)
DEEL III
(VERGELIJKEND ONDERZOEK VAN BEREKENDE EN GEMETEN TORSIE-AXIAAL TRILLINGEN IN HET VOORTSTUWINGSSYSTEEM VAN EEN TANKER)
by
DRS C. A. M. VAN DER LINDEN
Mathematician, Werkspoor-Amsterdam N.V.
RESEARCH COMMITTEE Jr C. DRAYER
Jr N. DUKSHOORN
Drs C. A. M. VAN DER LINDEN Prof DT Jr J. D. VAN MANEN
Dr Ir R. WERELDSMA
Jr A. DE MOOY (ex officio)
VOORWOORD
De tendens naar snellere en grotere schepen, uitgeru.st met een
langzaamlopende hoofdmotor van groot vermogen en de ten-dens naar de toepassing van korte asleidingen, leiden tot een trillingsgedrag van het assysteern dat aanmerkelijk gecompli-ceerder is dan bij motorinstallaties in een betrekkelijk recent
verleden.
Dit is onder andere het gevolg van het optreden van al of niet gekoppelde torsie-axiaal trillingen in het assysteem bij toeren-tallen in het draaigebied van de motor.
Teneinde ontoelaatbare extra mechanische belastingen van het
assysteem, die als gevolg hiervan kunnen optreden, te
voor-komen, dienen in het ontwerpstadiurn doelrnatige maatregelen genomen te kwuten worden. In verbancl hiermede is het nood-zakelijk een betrouwbare voorspelling van het trillingsgedrag te kunnen doen.
Na uitvoerig theoretisch en experimenteel modelonderzoek
werd een rekenmethode ontwikkelcl, die, rekening houdend met de koppelingseffecten van de lcrukas, tot de voorspelling van de
eigenfrequenties van het assysteem leidt. Deze methode werd
beschreven in rapport no. 39 M Crankshaft coupled free
torsional-axial vibrations of ship's propulsion system". De
resultaten van het modelonderzoek inzake de
koppelings-effecten van de schroef werden gepubliceerd in rapport no. 70 M: Experiments on vibrating propeller models".
Ter verificatie van de berekeningsmethode en ter bepaling van
nog niet met voldoende nauwkeurigheid belcende parameters
van het stuwblok en de schroef, die rnede bepalend zijn voor het trillingsgedrag, werden uitvoerige trillingsmetingen uitgevoerd aan de asleidingen van een tweetal motorschepen t.w. het m.s.
Koudekerk" van de Vereenigde Nederlandsche Scheepvaart-maatschappij N.V. en het m.s. Neverita" van Shell Tankers N.V. De resultaten van de eerste meting werden gepubliceerd
in rapport no. 116 M: Comparative investigation of calculated and measured torsional-axial vibrations in the shafting of a dry cargo motorship". Met de meting op het tweede schip werd tevens beoogd een vergelijking van verschillende meetmethoden. Ge-meten werd met elektrische torsiografen, een absolute
trillings-opnemer en met op de as en op bladveren aangebrachte
rek-stroken.
In dit rapport wordt een samenvatting gegeven van de
bereke-ningsprocedure, de toegepaste meettechnieken, de bewerking
van de meetsignalen alsmede van de analyse van de resultaten. Uit de resultaten van het beschreven onderzoek is, na correctie
van de bij de berekening aangenomen stuwblolcstijfheid, een
goede overeenstemming gebleken tussen de gemeten en berekende eigenfrequenties. Bovendien is vastgesteld dat de met verschil-lende meettechnieken verlcregen signalen dezelfde uitkomsten
opleverden. Aanvullend onderzoek ter bepaling van de
inter-actie van het trillingsgedrag met het dynamisch gedrag van de scheepsconstructie is gewenst.
NEDERLANDS SCHEEPSSTUD1ECENTRUM TNO
PREFACE
The tendency towards faster and bigger ships propelled by low-speed diesel engines of high outputs and the application of short shaftlines have ,led to a vibration pattern of the shafting that is
considerably more complicated than that of propulsion plants
used in relatively recent years.
These complications arise when torsional and axial vibrations, either coupled or not, are to be expected in the shafting. In order to avoid inadmissible extra mechanical stresses that are due to the vibratory behaviour, a reliable prediction concerning the vibra-tions that can possibly be expected has to be made in the design stage.
A method of calculating the natural frequencies of the shafting,
taking into account the coupling effects of the crankshaft, is
described in Report no 39 M : "Crankshaft coupled free torsio-nal-axial vibrations of a ship's propulsion system".
The results of the model experiments concerning
hydro-dynamic propeller coefficients are published in Report no. 70 M: "Experiments on vibrating propeller models".
In order to verify the calculation procedure and to determine
the parameters, which are not yet known with acceptable
accuracy, extensive vibration measurements were carried out on
the shaftings of two motorships, viz. m.s. Koudekerk" of the United Netherlands Shipping Company and m.s. Neverita" of
Shell Tankers. The results obtained from m.s. Koudekerk" are published in Report no. 116 M: "Comparative investigation of calculated and measured torsional-axial vibrations in the shafting of a dry cargo motorship". The investigation carried out on the second ship is published in the present report. This investigation
also aimed at a comparison of different measuring techniques
using electrical torsiographs, an absolute vibration recorder and strain gauges attached on plate springs and the shaft.
The report deals with the method of calculation, the measuring techniques applied and the processing of the signals; it moreover analyses and discusses the results.
The results show a fairly good agreement of the calculated
and measured vibratory behaviour of the shafting. It was found that the signals obtained with the different instruments used do not differ significantly. Further investigation to determine the interaction of shaft vibrations and the dynamical behaviour of the ship's structure is required.
Summail 1 Inlroductkin . 2 Data 5 2.1 Main engine.
. ... ,
. . 6 2.2 Shaftihg 6 2.3 Propeller 6 2.4 Cratils 3 Calculation 6 11 Method used . ... ...
... .
. 6 3.2 Values of quantities 6 3.3 Results of calculation 7 4 Measurements-
104.1 Location and properties of measuring devices 10
4.2 Speed i of the engine during measurements . 11
5 §ignal processing.
...
116 Analysis 11
6.1 Theory, 11
6.2 Analysis of results of measurements 12
6.3 Illustration of results 13
6.4 Accuracy of Measuring results 13
6.5 Comparison of measuring devices 16
6.6 Vibration modes 17
6.7 Summary 17
7 Comparison Of ca1cuLadons4md measurements 17
8 Conclusion ' . 17 9 Acknowledgement 18 References . . . 18 page 5 . . .
. ... .
. . . 5TORSIONAL-AXIAL VIBRATIONS OF A SHIP'S PROPULSION SYSTEM
PART IIICOMPARATIVE INVESTIGATION OF CALCULATED AND MEASURED TORSIONAL-AXIAL VIBRATIONS
IN THE PROPULSION SYSTEM OF A TANKER by
Drs C. A. M. VAN DER LINDEN
Summary
This report deals with an extensive investigation into the vibratory behaviour of the propulsion system of the motortanker Neverita' of Shell Tankers N.V.
It describes the procedure of calculatidn, the measuring techniques applied and the processing of signals.
The results of calculation and those of measurements are compared while agteements and differences are, if possible, explained.
1 Introduction
Results of measurements and calculations of the
torsio-nal-axial vibrations of the propulsion system of the motorship "Koudekerk" [5] suggest the possibility of predicting the dynamical behaviour of Rich a system
by means of an experimental determination of the
stiffness quantities of a scale model of a crank, fol-lowed by a computer calculation using the measured
quantities.
However, some uncertainty still remains as some quantities, that do not depend on the properties of a crank but are necessary for the calculation of natural torsional-axial vibrations, are not yet available in the
design stage of the propulsion system. Therefore, experimental data about the natural frequencies of several propulsion systems will be heeded to get some evidence about the magnitude of these quantities.
One of them is the stiffness of the thrustblock. As
the apparent stiffness of the thrustblock entails the stiffness of the whole ship's foundation and, moreover, the value of this stiffness certainly depends on the
frequency, it will take several years before a reliable calculation method by means of a computer can be
established.
Another source of uncertainty is the influence of the system propeller-water on the vibrations.
Ex-perimental and theoretical work by the Netherlands
Ship Model Basin [2], has resulted in establishing approximate values for the coefficients describing
the performance of the propeller and the propeller-entrained water during torsional-axial vibrations.
The objectives for measurements and calculations
on the propulsion system of the motortanker
"Neverita" were:
1. To try to establish the stiffness of the thrustblock by comparing results of measurements of natural
frequencies with values found by calculation. One can expect that it vvill be possible to determine by means of comparison the thrustblock-stiffness of a ship in the design stage, if measured values for
several types and sizes of ships are available. To investigate the possibility of predicting the
forced torsional-axial vibfation modes by means of a calculation.
Measurements of torsional vibrations are usually carried out at one place of the vibrating system,
displacements and stresses at all other places being calculated from the one measured displacement by
means of the forced vibration mode.
A positive result at this point would simplify the
measurement of torsional-axial vibrations sub-stantially.
Besides these more fundamentally oriented
ob-jectives, a practical purpose was to compare the
results of measurements by means of a set of simple
instruments with the results from more complex
instrumentation.
For a brief description of calculations and measure-ments, reference is made to the Introduction of Part I [5] ; the description not only fits the planning and
execution of work for the motorship "Koudekerk"
but also that for the motortanker "Neverita".
To one difference, however, attention should be
drawn. This time, in order to meet the requirements
of the third research objective, several types of measur-ing instruments were used.
2 Data
The propulsion system of the motortanker "Neverita" consisted of a two-stroke cycle turbo-charged diesel engine, directly coupled to the shafting. The propeller had four blades and a fixed pitch.
2.1 Main engine Type: Number of cylinders: Output: Speed: Bore: Stroke: Firing order:
Mean indicated pressure:
2.2 Shafting Thrustshaft Intermediate shaft Propeller shaft 2.3 Propeller Material: Number of blades : Pitch at 0.72 R: Mass: Moment of inertia: 2.4 Cranks
Figure 1 gives the dimensiofis of the crank. Its elastic properties are to be found in Tables 1 and 2.
Fig. 1 Sulzer 9 RD 90 9 18,000 SHP 119 rpm 0.9 m 1.55 m 1-6-7-3-4-9-2-5-8 8.3 x 105 Nm-2 clinial bronze 4 4.344 m 24,600 kg 54,075 kgm2
Table 1. Influence numbers of a cranIc loaded in its plane.
The values of i and j refer to:
1 axial displacement 2 bending rotation 3 bending displacement 2 3 1 1 axial force bending moment 3 bending force
Table 2. Influence numbers for a crank loaded perpendicularly to its plane.
3 Calculation
3.1 Method used
The method used is entirely the same as that used for the m.s. "Koudekerk". So the formulae for the
calcu-lation of natural frequencies are those of Part I [5]. The influence numbers for a crank were derived from scale model measurements as described in [4].
The propeller coefficients were derived by inter-polation, from a report [2] of the Netherlands Ship Model Basin.
A numerical survey of the system is shown in Table 4.
Table 3. Coefficients for the propeller.
1.486 kg 1.376 kgm 2 3 2 1.376 kgm 0.922 kgm2
The location of the several parts of the system is
shown in Figure 2. 1 1 0.436 mN-1 2 0.793 N-1 3 0.665 mN-1 diameter (m) 0.65 0.49 0.60 length (m) 2.01 6.42 6i,21 0 -1.264 N-1 1.507 m-1N-1 0.366 N-1 1.487 inN-1 1.264 N-1 1 1.090 m-1N-1 2 -0.366 N-1 3 0 1 torsional moment 2 'bending force 3 bending moment The values of i and j refer to:
1 torsional rotation 2 bending displacement 3 bending rotation Table 1 Table 2 Table 3 2 x 109 Nin-1 and 101° Nm-1 3.2 Values of quantities
All values are expressed in the kg-m-sec sytem (Giorgi).
Young's modulus: 2.06x 1011 Nin-2
Modulus of rigidity: 0.814 x 1011 Nm-2
Influence numbers of a crank
for displacements in its plane: for displacements perpen-dicular to its plane:
Coefficients for the propeller: Axial stiffness of the thrustblock:
The values of i and j refer to:
1 axial inertia 2 torsional inertia 1 axial motion 2 torsiOnal motion 0.665 InN-1 1.678 N-1 1.769 raN-1 0.793 N-1 1.998 m-1N-1 1.678 N-1
1 2 3 4 5 6 7 8 9 10 11 12 13141516171819 20 212223 24 25 26 27 28 29 30
Table 4. Survey of the system.
F = flywheel, P = propeller, M = any other mass (flanges)
3.3 Results of calculations
Calculations were made for two different values of the
I
III
III
I Iii
thrust shaft intermediate shaft propeller shaft
crank 9 v -C
es_
7 s=
axial stiffness of the thrustblock ; they were repeated
for different values of the coupling factors, c12, in the propeller.
Finally, calculations were made of the forced
vibra-tions for several values of the forced frequency and at various locations of the exciting force or moment.
The results of the calculations of the natural fre-quencies are collected in Table 5.
Just as with motorship "Koudekerk", a clear dis-tinction could be made between vibration modes,
where relatively large torsional rotations were accom-panied by very small axial displacements and other vibration modes that were mainly axial.
In Table 5, and henceforth in this paper, the
vibra-tion modes that are mainly axial (torsional) will be
called axial (torsional) vibration modes.
Variation of the coupling factors causes only very slight changes in the natural frequency numbers.
The ratio between torsional (axial) and axial (tor-sional) displacements in the axial (tor(tor-sional) modes
increased approximately proportionally to the coupling
factor, ci2 = c21.
Table 5._ Calculated natural frequencies.
_ _
thrustblock stiffness
In Tables 6 and 7 some of the results of the forced vibratiod calculations are collected.
The forced vibration modes appear to differ con-siderably from each other and from the natural
fre-quency mode.
Especially when torsional vibration is caused by
axial excitation, the values of axial displacements are
much in excess of the corresponding values in the
natural vibration mode.
Figures 3, 4, 5 and 6 give pictures of the calculated vibration modes. In all these graphs the same relative scale is used to facilitate comparison of the different vibration modes. In natural vibration modes of course no absolute scale is possible. In the relative scale, one
radial torsional rotation corresponds to 0.3 m axial displacement.
7
dia-ele- length Meter rigidity mass
moment
loca-of tion inertia in
nient m 10911m-1 angle kg kgm2 Fig. 2
M, S, 131 0.125 0.36 0.65 1.96 1,306 355 1 2 Cl 160° 11,922 7,493 B2 7.85 3 C2 40° 11,992 7,493 B3 7.85 Cs 280° 11,992 7,493 134 7.85 C4 320° 11,992 7,493 B5 1.96 6 S. 0.36 0.65 M2 0.25 2,192 208 7 S. 0.36 0.65 Bo 1.96 8 C5 80° 11,992 7,493 B, C, B. 7.85 200° 7.85 11,992 7,493 9 10 240° 11,992 7,493 B. 7.85 11 Cs 120° 11,992 7,493 Bi. 7.85 12 Cs 0° 11,992 7,493 B11 1.96 13 S, M. 0.36 0.25 0.65 1,605 208 14 S5 0.635 0.65 M4 0.23 3,459 897 15 S. 0.62 0.65 16 F 0.08 3,251 2,428 17 57 0.52 0.65 N45 1,605 208 18 S8 0.25 0.52 19 S, S10 2.072 0.81 0.486 0.49 20 21 S11 0.30 0.486 Si. 0.40 0.49 23 Si. 2.338 0.486 24 S14 0.25 0.52 DA8 0.25 1,605 208 25 Si8 0.299 0.58 26 Si. 1.828 0.603 27 S17
S
2.401.436 0.601 0.603 28 29 S19 0.248 0.59 P 1.067 24,600 54,075 30S shafting; B = bearing, C = drank, T = thrtistblock,
mode 2 x 109b1m-1 101°Nm--1
first torsional 326.1 vpm 326.2 vpm
second torsional 1119.7 vprn 1121.1 vpm
first axial 672.6 vprn 798.8 vpm
second axial 1492.3 vpm 2082.2 vpin
crank
shaft-i I --I I }
crank 1 2 3 4 5 6 7 8
Table 6. Forced torsional-axial vibration modes in the neighbourhood of the first torsional frequency compared with the natural vibration mode. excitation axial cyl 1 axial cyl 9 axial propeller torsional cyl 1 torsional cyl 9 torsional propeller natural mode Thrustblock stiffness
Dimensions: axial displacements m
rotations rad
exciting axial forcesi 10"N exciting torques 10"Nm
Table 7. Forced torsional-axial vibration modes in the neighbourhood of the second torsional frequency compared with the natural vibration mode. excitation axial cyl 1 axial cyl 9 . axial propeller torsional cyl 1 torsional cyl 9 torsional propeller natural mode Thrustblock stiffness ' 10"Nm--1 Dimensions: axial displacements m
rotations rad
exciting axial forces 10"N
exciting torques 1010Nm displacement axial free end axial thrustblock axial -propeller torsional free end torsional thrust block torsional propeller frequency -30.07 ' -1.237 -1.246 -3.331 -1.204 3.125 320 -30.24 -1.227 -1.181 -15.01 -7.886 14.77 325 -30.36 , -1.268 -1.314 4.258 3.120 -4.395 330 -5.917 -1.078 -1.081 -3.740 -1.635 3.862 320 -5.982 -1.057 -0.9895 -18.65 -10.15 18.70 325 -5.987 -1.100 -1.149 5.892 3.870 -5.720 330 -1.246 : -1.062 -4.111 11.65 6.836 -10.83 320 -1.181 -1.141 -4.317 59.21 34.00 -58.16 325 -1.314 -1.015 -3.823 -19.08 -10.71 19.75 330 -3.311 2.995 11.65 -1814 -975.8 1896 320 -15.01 15.21 59.20 -9296 -5250 9337 325 4.258 -4.894 -19.08 +3015 +1781 -2917 330 -2.123 2.097 8.158 -1194 -683.3 1328 320 -10.19 ' 10.51 40.93 -6350 -3630 6455 325 3.085 -3.339 -13.02 2134 1215 -1990 330 3.125 -2.776 -10.83 1896 1111 -1765 320 14.77 -14.93 -58.16 9338 5361 -9174 325 -4.396 5.075 19.75 -2918 -1640 3018 330 1 -1.043 -4.064 639.2 365.1 -636.0 326.2 displacement axial free end axial thrustblock axial propeller torsional free end torsional thrustblock torsional propeller frequency 15.38 L849 2.267 -12.54 9.842 -1.129 1100 9.489 0.5449 -0 1467 -202.2 203.2 -1233 1120 12.71 1.804 2.345 9.270 -12.28 0.1975 1140 7.893 -0.4238 -0.5861 -13.95 14.02 -0.7520 1100 1.725 -2.095 -3.773 -270.8 -275.8 -15.93 1120 7.686 -0.3109 -0.3290 15.52 -15.96 1.011 1140 2.268 -1.233 -5.038 -5.655 -5.594 0.7785 1100 -0.1493 -1.924 -6.389 -109.8 111.8 -5.368 1120 2.435 -1.214 -5.053 6.301 -6.570 1.516 1140 -12.52 -2.960 -5.648 -469.4 479.0 - -28.93 1100 -202.0 -57.15 -109.7 -8996 9167 1120 9.259 3.261 6.292 506.3 -517.3 28.80 1140 10.06 2.770 5.287 452.5 -448.7 27.10 1100 191.4 54.64 104.9 8612 -8764 509.7 1120 -10.78 -3.177 -6.127 -483.2 503.2 -28.19 1140 -1.130 0.09573 0.7785 -28.97 29.79 10.02 1100 -12.33 -3.108 -5.368 -533.8 544.3 -20.29 1120 0.1977 I 0.4749 1.516 29.02 -29.23 12.57 1140 1 0.2790 0.5255 44.61 -45.46 2.643 1121.1
0.04 . g 0.03 g 0.02 I 0.01 0 0.01 0.02 -0.03 0.04
Fig. 3 First torsional vibration mode
0.04 0.03 0.01 0.02 -0.03 -0.04 -10 -10 12 -0.01
Fig. 4 First axial vibration mode
-2 4 -8 12 7* 4 1 2 0 6 0.02 0.01 0.01 0.02 -0.03 0.04 0.05 18 16 14 12 10 8 6 4 2 0 2 torsional rotation S.
.
.. S. S. axial displacement \ \ \ _--___--\ \ \---
thrustblbck r-thrustblock rgidity=gidity= 2.109 Nm'1010 Nm-1
\ \ \ \\ (n=326 vprn) (n=326 vpm) \ \ \ axial \ displacement \ \ \ \ \ \ 1 I I 1 \ I \ I .. T', -torsional --- thrustblock - thrustblock rotation 7
rigidity= 21e Nal-1 (n= 673 vpm)
rigidity=1010 Nm-1 (n= 799 vpm)
/
\ / \/---
/ / / / / \ \ / \ \ torsional \rotation \ \\\
\
\ / 1 / 1 / / / axial displacement / / / / //
/
- - - thrustblock rigidity= 2.1e Nri1-1
rigidity= 10" Nr6-1 i (n=1120 vpm) (n=1121 vpm) -- thrustblock .. S. \ S.
\
\
\
\-. \\
\ \\ -\/
-- torsional/
rotation __.___. _ ,...--\ N.._./\
/
-./
\ \ \ \ \ \ \ \ S. . . S. ... axial ---displacement ,-- - thrustblock rigidity=2.1e
Nm-=10" Nrn-1
(n= 1492 vpm)
(n=2082 vpm)
-thrustblock rigidity
Fig. 5 Second torsional vibration mode Fig. 6 Second axial vibration mode
0.07 12 E 0.06 8 6 4 0.05 4 t 2 0.04 0.03 0 2 0.02 4 6 0.01 8 0 12 E 0.03 0.02 .7, 1 0.01 0 8 70 6 4 2 o 1 -2 4 6 8 10 12 14 16
1830 propeller shaft
1161111=11
2030
750
Fig. 7 Location of measuring devices. The numbers refer to Table 8
4 Measurements
4.1 Location and properties of measuring devices The location of places where measurements of
vibra-tory motions were carried out, is shown in Fig. 7.
Figures 8 and 9 show the apparatus on board the ship. The output of all measuring devices was recorded on magnetic tape. As the Philips tape-recorder
con-tained seven channels, the measuring points were divided in two batches, one containing points 1, 2, 3, 6, 8, 9, 10 the other containing, 3, 4, 5, 6, 7, 9, 10.
Points 9 and 10 had to be included in each batch,
because they serve to get a proper analysis of the measuring signals. The output of points 3 and 6 is
recorded twice, thus allowing some information about the reproducibility of the measurements.
At points 1 and 2, low frequency electrical
torsio-graphs were situated. The natural frequency of the
seismic system amounts to 0.3 Hz. The output goes to L
a switchbox and from there to the magnetic tape.
At point 3, an absolute vibration recorder was
ISMIL\
W'IMMEMigitigll>
used. The natural frequency of this system amounts to0.5 Hz. The output signal is fed into an accessory am- Fig. 8 Measuring devices on the shaft.
plifier and goes from this amplifier by way of the
switch-box to the magnetic tape.
At measuring points 4, 5, 6, 7 and 8, strain gauges
were used. Here the sensitivity of the measuring device
can be adjusted to meet the requirements of the
measurement.The adjustment factor is defined by:
AF =
relative elongation, expressed in 10-6 m/m --Aft&difference of voltage output between both ends of the scale in mV
During the measurements the following values of AF
/
were used: 100, 300, 1000, 3000.
Here the output is fed into a Peekel strain indicator and amplifier and from there goes via the switchbox
to the magnetic tape.
At measuring points 4 and 5, the strain gauges are
attached to plate springs. The axial displacement of the
shaft causes a lateral displacement of the top of the
spring. The bending strain involved is recorded by Fig. 9 Measuring devices on the shaft. engine
INS
the strain gauges. The natural frequency of the spring
at point 4 amounts to 700 sec -1, and at point 5 to
1350 sec -1.
At measuring points 6 and 7, the strain gauges are
attached to the shafting itself, a complete bridge being
fastened in axial direction. The system therefore acts
only- on axial elongations.
At point 8, too, strain gauges are arranged in a complete bridge. Here the bridge is attached to the shaft in an oblique direction, and records only torsional deformations.
Measuring point 9 gives 180 signals at constant time intervals during one revolution. This signal is
necessary to guide the collection of the vibration out-put by the electronic sampling and averaging
appa-ratus.
Measuring point 10, finally, gives a signal to mark a period 0.8 degrees before top-dead-centre of
cylin-der 7.
The output and the sensitivity at the different mea-suring points are shown in Table 8.
Table 8. Output and sensitivity.
AFrelative elongation expressed in 10-6 m/m=
difference of voltage output between both ends of scale
The sensitivity is supplied with a sign, which enables an
im-pression of the vibration mode by comparing the several output data with each other.
4.2 Speeds of the engine daring measurements
The speeds of the engine for which measurements
were taken are collected in Table 9.
Table 9. Enginespeeds for which measurements were taken,
expressed in revolutions per minute.
5 Signal processing
Data of the measurements were handled by the pro-cess described in Part I [5], the input being the
mag-netic tapes containing the results of the measurements,
the output being the results of a complete harmonic analysis of the signals at the measuring points men-tioned in Table 9.
For each ord-dr (harmonic), and for each measuring
point, a computer made graphs of the amplitude and phase against the number of revolutions.
For each measuring point, and each number of revolutions, a table was produced that contains the
amplitudes and phases of each harmonic.
6 Analysis
6.1 Theory
The axial-torsional vibration frequencies of a ship's
propulsion system can be calculated almost exactly by lumping masses and averaging stiffnesses and so replacing the system by a multimass system [1], [5].
The behaviour of the system in thd vicinity of such a frequency can more easily be understood through
approximating the system by a system with two degrees of freedom, one representing the torsional movements
and the other the axial movements.
The differential equations of a system with two
degrees of freedom are:
(-a co2+ b1ico+c1+k)(-a2co2+b2ico+c2+k)-k2
=.
P2(-a1(02+b1ico+c1+ic)+P1k
(-a1co2 + b1ico+c1+k)(-a2w2+b2ico+c2+k)-k2
Generally b, and b2, representing the damping in the system, and k, representing the coupling between the torsional and axial movements, are small.
The torsional and the axial frequencies of the system
are commonly not close to each other.
Now it is possible to derive from formulae (3) and
(4) how, in these circumstances, the system will respond to an exciting force or moment, if the forcing frequency goes from a value below a natural torsional (axial) frequency to a value upwards of it. Here it will be
worked out for a torsional frequency, but all the
derivations and the conclusions remain true if the word11 121.9 101.4 79.2 54.3 118.8 97.3 74.5 51.4 114.1 93.7 69.3 46.3 110.9 90.3 64.2 40.4 106.4 85.6 58.8 34.6 mea- distance
suring output sensitivity of
['Pint proportional to 1 mV corresponds to marks
a, yi + k(y, -y2) = P (1)
a2.i)2+b2 512 + c2 y2 + k(Y2 -yi) = P2e1". (2)
Let index 1 represent the torsional movement and
index 2 the axial movement.
The solution of these equations is:
P1(-a2a)2+62ico+ C2 k)+ P2k 1 torsional velocity -0.049 rad.sec-1
2 tcirsional velocity 0.0161 rad.sec-'
3 axial velocity -2 . 10-5 tn.sec-1
4 axial displacement 6.8.10-9 AF m 5 axial displacement -45.2. 10-s AF m 6 axial force 3.05 AF N 7 axial force 2.00 AF N 8 torsional moment 6.60 AF Nrn 9 rotation of shaft 2° 10 rotation of shaft 360°
"torsional" is replaced by "axial" and index 1 by
index 2. If a torsional frequency is passed, the value
of the real part of the expression: a1o)2 + b1ico+c1+k
will pass from positive to negative, as k is assumed to
be small and a1co2+c1+k becomes zero in the
neighbourhood of a torsional frequency.
As the imaginary part bico remains positive and
small, this will cause a rapid change of about 1800 in the phase of the expression.
If, according to the assumption, the axial frequency is not close to the torsional frequency, the expression:
a2co2+b2ico+c2+k will not change phase during passage of the torsional frequency. Moreover its value will not alter considerably.
So the phase of the denominator of formulae (3) and (4) will have a change of about 180°, its value becoming
very small, as b, is only a small quantity. In formula (3) the numerator will not alter very much and,
there-fore, the fraction will become relatively large while the phase has a change of = 180°.
This is the common picture of the behaviour of a one-mass system going through a natural frequency.
In formula (4) the coefficient of P1 behaves in the same way. The numerator of the coefficient of P2, however,
has a change in phase of 1800 and a very small value
in the same region.
This coefficient can be reduced to:
1
k
a2c2o +b ico+c2+k
a1co2+111ico+c1+k
(5)
From this formula it is evident that the total phase change will be zero, for as k is small the second part of
the denominator will be only important in the
imme-diate vicinity
of the torsional
frequency, wherea1co2+b1co+c1+k becomes small.
If the value of k2Ib1co, a quotient of two small
values, itself is small only a slight alteration of ampli-tude and phase will occur.
Otherwise a clear maximum and a clear minimum
will appear close together, while the phase will diverge
from its original value and then come back to it. Translating these Mathematical facts into
mechan-ics, we state: if a torsional frequency is passed, the
system behaves like a system with one degree of
free-dom, if the exciting force is torsional. If the excitation is
axial, the forced torsional movements are again like
those of a one-mass system, but the axial response
behaves differently, as a maximum and a minimum
occur and, besides, the appearing phase shift goes
back to zero again.
6.2 Analysis of results of measurements
As presumably each harmonic of an exciting force is a slowly increasing function of speed, it is expected
that the properties of the graphs of amplitude and phase versus speed will only slightly be affected by the
varia-tion of the exciting force with the number of
revolu-tions.
This is in particular true for the lower harmonics,
whereas the higher harmonics, which are generally small, are more probably subject to comparatively
large, rapid, and in a certain sense even random,
variations as the speed increases.
Therefore it could be expected that especially the lower natural frequencies, which can be observed in the lower harmonics, would appear in graphs that are closely related to the simplified theory. In line with this expectation, it was found that many of the graphs
give a picture similar to that of a system with one degree of freedom. The maximum amplitude then coincides with a phase shift of about 180°. Several
graphs show the peculiar picture of a system with two degrees of freedom with a phase shift that is
subse-quently removed.
In the case of motorship "Koudekerk" [5], only a
few graphs were suitable to derive values of the natural frequencies. The measurements of motortanker "Neverita", however, produce many graphs that can be used for this purpose.
Actually, there are about 50 graphs that give a clear maximum of amplitude at 325 vpm, the first torsional
frequency. In about 30 graphs this maximum is ac-companied by a more or less clear phase shift of 180°,
and in about 10 graphs by an up and down variation of phase. This phase variation is very clear in some other graphs, while the amplitude does not vary
per-ceptibly. According to the theory, the phase-ripple
occurs mainly at the axial measuring points.
Its occurrence at the fourth harmonic indicates that
the most important source of axial excitation is the
fourbladed propeller.
A similar behaviour is seen at the second natural
torsional frequency, near 1120 vpm.
A maximum amplitude at this value can be observed in about 100 graphs.
Many graphs also show the proper variations of
phase. These phase shifts are, however, not so clearly
visible as at the first torsional frequency. This could be
expected, as this vibration mode is only caused by the 10th and higher harmonics. The same phenomenon
is even more evident at the third torsional frequency of
about 2450 vpm, where the phase shift is hardly
detectible in only very few cases.
am-plitude of the 24th harmonic at the various measuring points gives sufficient evidence to conclude that this frequency belongs to a torsional mode, and not to an
axial mode.
The first axial frequency is observed at 710 vpm, in
about 60 graphs. In about 20 graphs the maximum amplitude coincides with a phase shift of 180°. In 5 graphs this phase shift takes place without a per-ceptible maximum of the amplitude. In about 10
graphs a ripple in the phase is visible at the maximum amplitude. Generally the phase shift is then slow, ex-tending from 500 vpm up to 900 vpm and sometimes even deformed by the intervention of the phase shift of the second torsional frequency at 1120 vpm. These
phenomena are possibly due to the fact that the exciting
forces of this axial frequency are often torsional and, as they originate from the 7th to the 18th harmonic,
they are small.
It is
also possible that with axial vibration thedamping at the propeller is more important than with torsional vibration. There is some evidence, in some graphs, about a second axial vibration in the vicinity of 1600 vpm. In other graphs a maximum amplitude occurs at 1800 vpm.
At measuring point 1 the fourth and the fifth
har-monics have, at about 400 vpm, a clear maximum
together with a phase shift of 180°. This phenomenon cannot be accounted for.
6.3 Illustration of results
In reality the torsional axial vibration system will be
excited at many places, the exciting forces are variable
in amplitude and phase with the speed, and damping
will occur everywhere in the system. A slight variation of phase of the exciting forces will appear in the higher
harmonics multiplied by the number of the harmonic. Random movements are largely, but not entirely,
eliminated by the sampling process and they will especially influence the weak signals of the higher harmonics.
The influence of vibrations of the foundation of the propulsion system cannot be eliminated.
The influence of the turbulent motion of the water
near the propeller can only approximately be taken into account by linearizing. So it is not possible to
explain all the features of the graphs of the processed results of the measurements by simplified theory, nor
by the theory of the multimass linear system.
Figures 10 to 21 are reproductions of some of these graphs. They are chosen to give an impression of the average output of the processing; they represent both the clarity and the imperfection of the results. In fact,
14 1.2 10 8 6 4 2 0 _ 40 60 80 100 120
Fig. 11 Measuring point 2, 12th harmonic.
neither the very best nor worthless graphs have been
included.
6.4 Accuracy of measuring results
The sampling took place over two periods and each period was analyzed separately. The differences
be-4 3 2 1 1 2 3 .13 60 50 40 30 20 10 0 40 60 80
101
Fig. 10 Measuring point 1, 4th harmonic.
2 1 1 2 3 4
.5
2.6 2.4 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4
0/
0 40 60 80 100 120Fig: 12 Measuring point 3, 4th harmonic.
0
10 9 8 7 6 5 4 3 2 1..
4
.,
1 -=1 2 2 g 1 I-0 I1
2 34
56
tween the output of the fist period and that of the Second period give some indication about the
ac-curacy of the results of the measurements.
Now the differences in amplitude are for the Main
harmonics generally less than 5%; at measuring points
1 and 8 they are mostly less than 2%. For the weaker
40 60
8000 120
Fig. 13 Measuring point 4, 7th harmonic.0
4
2
1
40 60 80 100 1-20 Fig. 15 Measuring pOint 4, 24th harmonic.
C,
harmonics, the percentage is commonly higher, as the
absolute differences are of about the same order of magnitude.
The differences between the phases behave in a
similar way: They are in the main harmonics usually less than 0.1 radial.
40 60 80 100 120
Fig. 14 Measuring point 4, 12th harmonic.
30 25 20 15 10 5 4 2 I 1 5 2 1
50 '40 30 20 10 0 40 60 80 100 120
Fig. 16 Measuring point 5, 3rd harmonic.
10 9 8 7 6 5 4 3 2 0 40 60 80 100 120
Fig. 18 Measuring point 6, 4th harmonic.
5
3 I
2 1
To this general behaviour, however, there is an
exception. At 110.9 vpm, many sampled signals show
a great difference between some harmonics of the two
periods especially between the 4th and the 9th
har-monics.
Harmonic analysis of the double period shows that
12 11 10 9 8 7 6 5 4 3 0 40 60 80 100 120
Fig. 19 Measuring point 6, 9th harmonic.
3 2 1 0
1
4 5these differences are due to a 6th order signal; i.e.
a vibration that has 13 periods in two revolutions of
the engine. This 6-ith order harmonic is very clear, and
even one of the largest harmonics at measuring points 4 and 5. At points 1, 6 (second programme) and 8 it is still clear but not very large. At some other measuring
15 60 50 40 30 20 10 0 Fig. 17
--2
3 1 01
2
40 60 80 100 120 Measuring point 5, 6th harrnOnic.ect 3 2 1 0
-- 2
- 3
re.
40 60 80 100 120 Fig. 20 Measuring point 7, 9th harmonic.
3---2
--5
--6
-2
points it is small. The frequency is 64 x 110.9 = 721 vpm also very near the first axial vibration.
Accurate research at the other speeds shovvs only hardly distinguishable two-period signals in the
vicin-ity of 710 vpm. How this axial vibration, which
presumably really exists, can be excited in a two-stroke cycle engine, cannot be explained by linear theory.That a 6th order excitation could be modulated by
the half-th order precession of the journals in the
bearings is possible but not likely. The solution can hardly be sought in the properties of the plate springs,
as also the other measuring devices give the signal, be
it then less significant.
Of course, by averaging the harmonics of the two
periods this 64th order is fully eliminated from the
ultimate results.
The reproducibility of the results was tested on the output of measuring points 3, and 6. As these points were included in both programmes, the measurements were here executed twice. At point 6 the correspon-dence was good, the differences in amplitude for the main harmonics being less than 10%. There was also a good correspondence in phase.
At measuring point 3 considerably larger differences
occurred. The amplitudes in the second programme
were always smaller, sometimes even only 50% of the amplitudes of the first programme The correspondence
in phase was much better.
Now the signal of measuring point 3 was so weak that, for three different speeds in the first programme
2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 40 60 80 100 120
Fig. 21 Measuring point 8, 12th harmonic.
4
1
and for six different speeds in the second programme, the results could not be processed. Therefore it can be
assumed that for the other speeds the signal was some-times too weak. to be processed. Anyhow this bad
correspondence can raise no doubt about the value of the quantitative results at the other measuring points.
6.5 Comparison of measuring devices
The torsional natural frequencies could be determined
by all measuring devices.
The first axial natural frequency was found by all axial measuring devices; even, be it only weakly, at measuring point 7, which was situated near the
thrust-block.
At measuring points 1 and 2 only dubious indica-tions about the existence of this frequency could be found and at measuring point 8 none at all.
The plate spring at measuring point 5 gave some-what clearer results than that at point 4, but the main cause of this difference is more likely to be sought in
the more favourable location of point 5 than in the
variance of dimensions of the springs.
In a similar way, the results of measuring point 6
are superior to those of measuring point 7. For
measuring points 5 and 6, which have the same
lo-cation, but different measuring devices, it can hardly be established, which gave better results.
The general conclusion is that each of the axial
satis-factory results, and that no system is clearly superior. The axial measuring devices can easily be used to determine the torsional frequencies, but the axial
fre-quencies are not satisfactorily recorded by the
tor-sional measuring systems.
6.6 Vibration modes
From the natural frequency vibration mode the relative
displacements, velocities, accelerations and forces at every place in the vibrating system can be calculated.
If at a certain speed one of the harmonics of the
measured quantities is close to a natural frequency, its
relative values at the different measuring points can be compared with the corresponding values of the natural frequency vibration mode. This has been done for several harmonics and the results were not encour-aging.
With torsional vibrations, only a qualitative
resem-blance between the torsional quantities of the measured
and those of the calculated modes could be detected.
Between the axial quantities even a qualitative
agree-ment did not exist. The ratios between the axial and the torsional quantities were commonly in the
mea-sured vibration mode many times, in some cases more than one thousand times, greater than in the calculated
mode.
This can be explained from the formulae for the
relative displacements of a two-mass system.
Be co0l2rc the natural frequency and col2ir the fre-quency of the exciting force in a two-mass system,
excited at the Mass with index 2.
Then the formulae for the displacements are:
Y2
a,coo+c,+k
Y
for the natural frequency
Y2
Yi
for the forced frequency
If co = coo and b, = 0 the formulae give the same result.
However, if k is small, the real part of y2/y1 in the
forced mode alters considerably in the immediate vicinity of coo, while even at a moderate value of b, the
contribution of the imaginary part may be important. Therefore the relative values of the axial quantities
in a torsional vibration mode that is axially excited can
be much larger in the forced vibration than they are in the calculated natural vibration mode. To calculate the forced vibration mode it will be necessary to have
sufficient data of the exciting and damping torsional
and axial forces in the motor and in the propeller. With the aid of this calculation it will be possible to predict a forced vibration mode of a multimass system
and thus obtain Some information about the
properties of some components, e.g. the stiffness of the thrustblock in the real system.
6.7 Summary
From the graphs, the following natural frequencies
were found :
first torsional frequency of 325 vpm;
first axial frequency of 710 vpm;
second torsional frequency of 1120 vpm;
second axial frequency possibly between 1600 vpm
and 1800 vpm;
third torsional frequency of 2450 vpm.
7 Comparison of calculations and measurements The measured values of the first torsional frequency of
325 vpm, and those of the second torsional frequency
of 1120 vpm, agree perfectly with the calculated values of Table 5.
The measured value of the first axial frequency of 710 vpm lies between the calculated values of 672.6
vpm and 798.8 vpm for thrustblock stiffnesses of 2. 109/Im -1 and 1010Nm-1 respectively.
Interpolation
between them can
be executed,assuming that the inverse of the square of the
fre-quency will be a linear function of the inverse of the
stiffness of the thrustblock. The interpolated value
appears to be 2.8 x 109Nm-1. The calculated values
of the second axial frequency for the thrustblock stiffness of 2 .109Nm-1 and 1010Nm-1 are 1492.3 vpm and 2082.2 vpm.
By a similar interpolation, a value of 1640 vpm is obtained for the stiffness of 2.8 x 109Nm-1.
As no exact value for the second axial frequency could be derived from the measurements, it can only
be stated that 2.8 x 109Nm-1 is a probable value of the thrustblock stiffness.
8 Conclusion
Comparison between the results obtained from the
several measuring devices has demonstrated that all
the systems used are satisfactory and that none is
superior to the others.
As the exciting forces affect the vibration modes
severely, an exact knowledge of the exciting forces and moments is necessary to predict the true vibration mode.
Especially the values of the axial (torsional) motions
in the neighbourhood of a torsional (axial) vibration mode are, to a great extent, dependent on the excita- .
tion.
This procures also the explanation of the phenome-non that is mentioned but not explained in Part I [5],
Chapter 7, that all the axial measuring devices recorded
the torsional vibrations.
If these vibrations are, at least partly, produced by
axial excitations, the axial displacements can be many times larger than they appear to be in the natural vibra-tion mode.
The second axial frequency could not be determined exactly, as was done in the case of rnotorship
"Koude-kerk", although the processed results of the measure-ments were generally of better quality.
Now this frequency was for motorship
"Koude-kerk" situated at 915 vpm and for motortanker
"Neverita" at about 1700 vprn.
The conclusion is that the 17th and higher
harmon-ics of the axial excitation forces were so small that they had only a hardly perceptible influence on the system. At the measured speeds, the second axial vibration was therefore hardly excited.
Due to the failure to determine the second axial
vibration, only a probable value for the axial
thrust-block stiffness could be determined. As sufficient data
to calculate the forced torsional axial vibrations were not available, no comparison could be made between calculated and measured forced vibration modes. So no values for the propeller coefficients, especially for
the coupling factor, could be derived from the
mea-snrements.
9 Acknowledgement
The Netherlands Ship Research Centre TNO
acknow-ledges the kind co-operation of "Shell Tankers" and
"Netherlands Dry Dock Company", which enabled
the investigation to be carried out.
The measurements were done by the Engineering
Research Department of Werkspoor, Amsterdam,
and averaging and digitalization of the data took place at the Netherlands Ship Model Basin.
The harmonic analysis and the plotting were pro-grammed by the Engineering Research Department
of Werkspoor.
The calculations were done on the ELX8 of the
Mathematical Centre, Amsterdam.
References
VAN DORT, VISSER, 1963. Netherlands Ship Research Centre
TNO, report no. 39 M: Crankshaft coupled free
torsional-axial vibrations of a ship's propulsion system.
WERELDsmA, 1965. Netherlands Ship Research Centre TNO, report no. 70 M: Experiments on vibrating propeller models.
VissER, 1967. Netherlands Ship Research Centre TNO,
report no. 102 M: The axial stiffness of marine diesel engine
crankshafts, part I, Comparison between the results of full scale measurements and those of calculations according to
published formulae.
VAN DER LINDEN, 1967. Netherlands Ship Research Centre TNO, report no. 103 M: The axial stiffness of marine diesel engine crankshafts, part II, Theory and results of scale model
measurements and comparison with published formulae. VAN DER LINDEN, 'T HART and DOLFIN, 1968. Netherlands
Ship Research Centre TNO, report no. 116 M:
Torsional-axial vibrations of a ship's propulsion system, part I, Com-parative investigation of calculated and measured torsional-axial vibrations in the shafting of a dry cargo motorship. VAN GENT and HYLARIDES, 1969. Netherlands Ship Research Centre TNO, report no. 132 M: Torsional-axial vibrations of a ship's propulsion system, part II, Theoretical analysis of the axial stiffness of the shaft support at the thrustblock location.
PUBLICATIONS OF THE NETHERLANDS SHIP RESEARCH CENTRE TNO PUBLISHED AFTER 1963 (LIST OF EARLIER PUBLICATIONS AVAILABLE ON REQUEST)
PRICE PER COPY DFL.
10,-M = engineering department S = shipbuilding department C = corrosion and antifouling department
Reports
57 M Determination of the dynamic properties and propeller excited
vibrations of a special ship stern arrangement. R. Wereldsma,
1964.
58 S Numerical calculation of vertical hull vibrations of ships by
discretizing the vibration system, J. de Vries, 1964.
59 M Controllable pitch propellers, their suitability and economy for large sea-going ships propelled by conventional, directly coupled engines. C. Kapsenberg, 1964.
60 S Natural frequencies of free vertical ship vibrations. C. B. Vreug-denhil, 1964.
61 S The distribution of the hydrodynamic forces on a heaving and
pitching shipmodel in still water. J. Gerritsma and W. I3eukel-man, 1964.
62 C The mode of action of anti-fouling paints: Interaction between anti-fouling paints and sea water. A. M. van Londen, 1964.
63 M Corrosion in exhaust driven turbochargers on marine diesel
engines using heavy fuels. R. W. Stuart Mitchell and V. A. Ogale,
1965.
64 C Barnacle fouling on aged anti-fouling paints; a survey of pertinent literature and some recent observations. P. de Wolf, 1964. 65 S The lateral damping and added mass of a horizontally oscillating
shipmodel. G. van Leeuwen, 1964.
66 S Investigations into the strength of ships' derricks. Part I. F. X.
P. Soejadi, 1965.
67 S Heat-transfer in cargotanlcs of a 50,000 DWT tanker. D. J. van der Heeden and L. L. Mulder, 1965:
68 M Guide to the application of method for calculation of cylinder liner temperatures in diesel engines. H. W. van Tijen, 1965.
69 M Stress measurements on a propeller model for a 42,000 DWT
tanker. R. Wereldsma, 1965.
70 M Experiments on vibrating propeller models. R. Wereldsma, 1965.
71 S Research on bulbous bow ships. Part II. A. Still water
perfor-mance of a 24,000 DWT bullccarrier with a large bulbous bow. W. P. A. van Larnmeren and J. J. Muntjewerf, 1965.
72 S Research on bulbous bow ships. Part II. B. Behaviour of a
24,000 DWT bulkcarrier with a large bulbous bow in a seaway. W. P. A. van Lammeren and F. V. A. Pangalila, 1965.
73 S Stress and strain distribution in a vertically corrugated bulkhead. H. E. Jaeger and P. A. van Katwijk, 1965.
74 S Research on bulbous bow ships. Part I. A. Still water investiga-tions into bulbous bow forms for a fast cargo liner. W. P. A. van Lammeren and R. Wahab, 1965.
75 S Hull vibrations of the cargo-passenger motor ship "Oranje
Nassau", W. van Horssen, 1965.
76 S Research on bulbous bow ships. Part I. B. The behaviour of a fast cargo liner with a conventional and with a bulbous bow in a sea-way. R. Wahab, 1965.
77 M Comparative shipboard measurements of surface temperatures
and surface corrosion in air cooled and water cooled turbine outlet casings of exhaust driven marine diesel engine
turbo-chargers. R. W. Stuart Mitchell and V. A. Ogale, 1965. 78 M Stern tube vibration measurements of a cargo ship with special
afterbody. R. Wereldsma, 1965.
79 C the pre-treatment of ship plates: A comparative investigation
on some pre-treatment methods in use in the shipbuilding
industry. A. M. van Londen, 1965.
80 C The pre-treatment of ship plates: A practical investigation into
the influence of different working procedures in over-coating
zinc rich epoxy-resin based pre-construction primers. A. M. van Londen and W. Mulder, 1965.
81 S The performance of U-tanks as a passive anti-rolling device.
C. Stigter, 1966.
82 S Low-cycle fatigue of steel structures. J. J. W. Nibbering and
J. van Lint, 1966.
83 S Roll damping by free surface tanks. J. J. van den Bosch and
J. H. Vugts, 1966.
84 S Behaviour of a ship in a seaway. J. Gerritsma, 1966.
85 S Brittle fracture of full scale structures damaged by fatigue.
J. J. W. Nibbering, J. van Lint and R.,T. van Leeuwen, 1966. 86 M Theoretical evaluation of heat transfer in dry cargo ship's tanks
using thermal oil as a heat transfer medium. D. J. van der
Heeden, 1966.
87 S Model experiments on sound transmission from engineroom to accommodation in motorships. J. H. Janssen, 1966.
88 S Pitch and heave with fixed and controlled bow fins. J. H. Vugts,
1966.
89 S Estimation of the natural frequencies of a ship's double bottom by means of a sandwich theory. S. Hylarides, 1967.
90 S Computation of pitch and heave motions for arbitrary ship forms. W. E. Smith, 1967.
91 M Corrosion in exhaust driven turbochargers on marine diesel
engines using heavy fuels. R. W. Stuart Mitchell, A. J. M. S. van Montfoort and V. A. Ogale, 1967.
92 M Residual fuel treatment on board ship. Part II. Comparative
cylinder wear measurements on a laboratory diesel engine using filtered or centrifuged residual fuel. A. de Mooy, M. Verwoest and G. G. van der Meulen, 1967.
93 C Cost relations of the treatments of ship hulls and the fuel
con-sumption of ships. H. J. Lageveen-van Kuijk, 1967.
94 C Optimum conditions for blast cleaning of steel plate. J.
Rem-melts, 1967.
95 M Residual fuel treatment on board ship. Part I. The effect of cen-trifuging, filtering and homogenizing on the unsolubles in residual fuel. M. Verwoest and F. J. Colon, 1967.
96 S Analysis of the modified strip theory for the calculation of ship motions and wave bending moments. J. Gerritsma and W. Beu-kelman, 1967.
97 S On the efficacy of two different roll-damping tanks. J. Bootsma and J. J. van den Bosch, 1967.
98 S Equation of motion coefficients for a pitching and heaving des-troyer model. W. E. Smith, 1967.
99 S The manoeuvrability of ships on a straight course. J. P. Hooft,
1967.
100 S Amidships forces and moments on a CB = 0.80 "Series 60"
model in waves from various directions. R. Wahab, 1967. 101 C Optimum conditions for blast cleaning of steel plate. Conclusion.
J. Remmelts, 1967.
102 M The axial stiffness of marine diesel engine crankshafts. Part I. Comparison between the results of full scale measurements and
those of calculations according to published formulae. N. J.
Visser, 1967.
103 M The axial stiffness of marine diesel engine crankshafts Part II. Theory and results of scale model measurements and comparison with published formulae. C. A. M. van der Linden, 1967. 104 M Marine diesel engine exhaust noise. Part I. A mathematical model.
J. H. Janssen, 1967.
105 M Marine diesel engine exhaust noise. Part II. Scale models of
exhaust systems. J. Buiten and J. H. Janssen, 1968.
106 M Marine diesel engine exhaust noise. Part III. Exhaust sound
criteria for bridge wings. J. H. Janssen en J. Buiten, 1967.
107 S Ship vibration analysis by finite element technique. Part I.
General review and application to simple structures, statically loaded. S. Hylarides, 1967.
108 M Marine refrigeration engineering. Part I. Testing of a
decentral-ised refrigerating installation. J. A. Knobbout and R. W. J.
Kouffeld, 1967.
109 S A comparative study on four different passive roll damping tanks. Part I. J. H. Vugts, 1968.
110 S Strain, stress and flexure of two corrugated and one plane
bulk-head subjected to a lateral, distributed load. H. E. Jaeger and
P. A. van Katwijk, 1968.
111 M Experimental evaluation of heat transfer in a dry-cargo ships' tank, using thermal oil as a heat transfer medium. D. J. van der Heeden, 1968.
112 S The hydrodynamic coefficient for swaying, heaving and rolling cylinders in a free surface. J. H. Vugts, 1968.
113 M Marine refrigeration engineering. Part H. Some results of testing a decentralised marine refrigerating unit with R 502. J. A. Knob-bout and C. B. Colenbrander; 1968.
114 S The steering of a ship during the stopping manoeuvre. J. P.
Hooft, 1969.
C. A. M. van der Linden, H. H. 't Hart and E. R. Dolfin, 1968.
117 S A comparative study on four different passive roll damping
tanks. Part II. J. H. Vugts, 1969.
118 M Stem gear arrangement and electric power generation in ships propelled by controllable pitch propellers. C. KaPsenberg, 1968. 119 M Marine diesel engine exhaust noise.; Part IV. Transferdamping
data of 40 modelvariants of a coMpound resonator silencer.
J. Buiten, M. J. A. M. de Regt and W. P. H. Hanen, 1968. 120 C Durability tests with prefabrication primers in use of steel plates.
A. M. van Londen and W. Mulder, 1970.
121 S Proposal for the testing of weld metal from the viewpoint of
brittle fracture initiation. W. P. van den Blink and J. J. W. Nib-bering, 1968.
122 M The corrosion behaviour of cunifer 10 alloys in seawaterpiping-systems on board ship. Part I. W. J. J. Goetzee and F. J. Kievits,
1968.
123 M Marine refrigeration engineering. Part III. Proposal for a specifi-cation of a marine refrigerating unit and test procedures. J. A. Knobbout and R. W. J. Kouffeld, 1968.
124 S the design of UAanks for roll damping of ships. J. D. van den
Bunt, 1969.
125 S A proposal on noise criteria for sea going ships. J. Buiten, 1969. 126 S A proposal for standardized measurements and annoyance rating
of simultaneous noise and vibration in ships. J. H. Janssen, 1969. 127 S The braking of large vessels II. H. E. Jaeger in collaboration with
M. Jourdain, 1969.
128 M Guide for the calculation of heating capacity and heating coils for double bottom fuel oil tanks in dry cargo ships. D. J. van der
Heeden, 1969.
129 M Residual fuel treatment on board ,ship. Part III. A. de MooY, P. J. Brandenburg and G. G. van der Meulen, 1969.
130 M Marine diesel engine exhaust noise. Part V. Investigation of a double resonatorsilencer. J. Buiten, 1969.
131 S Model and full scale motions of a twin-hull vessel. M. F. van
Sluijs, 1969.
132 M Torsional-axial vibrations of a ship's propulsion system. Part II. W. van Gent and S. HYlarides, 1969.
134 M The corrosion behaviour of cunifer-10 alloys in
seawaterpiping-systems on board ship. Part II. P. J. Berg and R. G. de Lange,
1969.
137 M Torsibnal-axial vibrations of a ship's propulsion system. Part III. C. A. M. van der Linden, 1969.
scarcely saponifiable vehicles (Dutch). A. M. van Londen and P. de Wolf,- 1964.
12 C The pre-treatment of ship plates: The treatment of welded joints
prior to painting (Dutch). A. M. van i,onden and W. Mulder,
1965.
13 C Corrosion, ship bottom paints (Dutch). H. C. Ekarna, 1966.
14 S Human reaction to shipboard vibration, a study of existing
literature (Dutch). W. ten Cate, 1966.
15 M Refrigerated containerized transport (Dutch). J. A. Knobbout,
1967.
16 S Measures to prevent sound and vibration annoyance aboard a seagoing passenger and carferry, fitted out with dieselengines (Ditch). J. Buiten, J. H. Janssen, H. F. Steenhoek and L. A. S.
Hageman, 1968.
17 S Guide for the specifiCation, testing and inspection of glass reinforced polyester structures in shipbuilding (Dutch). G.
Hamm, 1968.
18 S An experimental simulator for the Manoeuvring of.surface ships. J. B. van den Brug and W. A. wagenaar, 1969.
19 S The computer programmes system and the NALS language for numerical control for shipbuilding. H. le Grand, 1969:
