REPORT No. 116M
December 1968NEDERLANDS SCHEEPSSTUDIECENTRUM TNO
NETHERLANDS SHIP RESEARCH CENTRE TNOENGINEERING DEPARTMENT LEEGHWATERSTRAAT 5, DELFT
TORSIONAL-AXIAL VIBRATIONS OF A SHIP'S
PROPULSION SYSTEM
(TORSIE-AXIAAL TRILLINGEN IN EEN SCHEEPSVOORTSTUWINGSSYSTEEM)
.PART I
(DEEL I)
COMPARATIVE INVESTIGATION OF CALCULATED AND MEASURED
TORSIONAL-AXIAL VIBRATIONS IN THE SHAFTING OF A DRY CARGO MOTORSHIP
(VERGELUKEND ONDERZOEK VAN BEREKENDE EN GEMETEN TORSIE=AXIAAL TRILLINGEN IN DE ASLEIDING VAN EEN DROGE .LADING MOTORSCHIP)
by
Drs C. A. M. VAN DER LINDEN
Mathematician,: WerkspoorAmsterdam N.V.
Jr H. H. 'T HART
Research manager, Institute for Mechanical Constructions TNO
r
and
Jr E. R. DOLFIN
Research scientis4 Netherlands Ship Model Basin
'LED
RESEARCH COMMIT'TEE
Jr. C. DRAYER Ir. N. DUKSHOORN
Drs. C. A. M. VAN DER LINDEN
Prof. Dr. Ir. J. D. VAN MANEN
Dr. Ir. R. WERELDSMA
Jr. A. DE MOOY (ex officio)
VOORVVOORD
De snelle ontwildceling van de langzaamlopende scheepshoofd-Motor naar eenheden met groot vermogen en de tendens naar de
toepassing van korte asleidingen in modeme schepen, hebben
geleid tot een trillingsgedrag van het .assysteem dat aanmerkelijk
ingewikkelder is dan bij motorinstallaties in een betrekkelijk
recent verleden.
Deze coMplicatie is voomamelijk het gevolg van het optreden van al of niet gekoppelde torsie- en axiale trillingen van het as-systeem bij toerentallen in het draaigebied van de motor.
Teneinde Ontoelaatbare extra mechanische belastingen van het assysteem, die als gevialg hiervan kunnen optreden, te voorkomen, moeten in het ontwerpstadium doelmatige maatregelen worden genomen. In verband hiermede is het noodzakelijk een betrouw-bare voorspelling van het trillingsgedrag te kunnen doen.
Na uitvoerig theoretisch- en experimenteel modelonderzoek, werd een rekenmethode ontwikkeld, die, rekening houdend met de koppelingseffecten van de krukas, tot de voorspelling van de eigerifrequenties van het assysteem leidt.
Deie methode werd beschreven_in rapport no. 39 M
shaft coupled free torsional-axial vibrations of a ship's propul-sion system". [1]
De resultaten van het modelonderzoek van de
koppelings-effecten van deschroef werden gepubliceerd in rapport no 70 M:
Experiments on vibrating propeller models ". [2]
Ter verificatie van de berekeningsmethode en ter bepaling
van nog niet met voldoende nauwkeurigheid bekende parameters van het stuwblok en de schroef, die mede bepalend zijn voor het
trillingsgedrag, werd een uitvoerige en nauwkeurige
meting uitgevoerd aan de asleiding van het motorschip Koude-kerk" van de Vereenigde Nederlandsche Scheepvaart
In dit rapport wordt een samenvatting gegeven van de
be-rekeningsprocedure, de toegepaste meettechniek, de gebruikte
methode voor de bewerking van de meetsignalen alsmede de
analyse van de resultaten.
De berekening werd uitgevoerd met twee geschatte stuwblok-stijfheden en uit rapport 70 M geextrapoleerde waarden van de schtoefcoefficienten. Het elastisch gedrag van de lcrukas werd bepaald met behulp van modelonderzoelc dat werd beschreven in rapport 39 M [1].
Uit de resultaten van het beschreven onderzoek is gebleken dat, na correctie van de geschatte groothedeni de berekende
frequenties goed overeenstemmen met de gemeten waarden. Aanvullend onderzoek ter verificatie van de door vergelijking van berekenings- en meetresultaten vastgestelde parameters is gowenst.
NEDERLANDS SCHEEPSSTUDIECENTRUM TNO
PREFACE
The rapid development of low speed marine diesel engines to
highly-powered units, and the tendency towards application of short shaftlines in modern ships, have led to a vibration pattern of the shaft system that is considerably more complicated than that of propulsion systems used in relatively recent years.
At speeds in the running range of the modern engine, torsional
and axial vibrations of the shaft system will either be coupled
or not.
In order to avoid inadmissible extra mechanical loads on the shafts that will be due to vibration, suitable precautions should already be taken in the design stage. In this connection, a reliable
prediction of the vibratory behaviour of the shaft system is
essential.
Extensive theoretical work, combined with experimental
in-vestigations on models, have yielded a method of calculation
which takes into account the coupling effects of the crankshaft.
The natural frequencies of crankshaft coupled torsional-axial
vibrations of the propulsion system can thus be predicted. The method is described in Report No. 39 M: "Crankshaft coupled free torsional-axial vibrations of a ship's propulsion system". [1]
The results of the model experiments concerning
hydro-dynamic propeller coefficients are published in Report No. 70 M: "Experiments on vibrating propeller models". [2]
In order to verify the calculation procedure, and to determine the parameters of thrustblock and propeller, which are not yet known with acceptable accuracy, extensive and accurate vibra-tion measurements were carried out on the shafting of the rn.s. "Koudekerk" of the United Netherlands Shipping Company.
This report deals with the method of calculation, the measuring
technique applied and the Processing of signals; it moreover
analyses and discusses the results of this processing.
Calculations were carried out for two estimated thru.stblock stiffnesses and propeller dynamic coefficients derived from values presented in Report No. 70 M. The characteristics of the
crank-shaft were determined by model measurements described in Report No. 39 M.
The results of the work now under report show a good agree-ment between calculated and measured natural frequencies, after correction of the estimated values of unknown parameters.
Further experimental investigation is required to verify the
results obtained.
CONTENTS page Summary! . . .
...
. . 5 1 Introduction 5 2 Data 6 2.1 Main engine . 6 2.2 Shafting 6 2.3 ProPeller 63 Calculation of natural frequencies and modes of vibration .
...
. 63.1 Method used 6 3.2 Values of quantities 8 3.3 Discretion of system 8 3.4 Results-- 9 4 Measurements 10 4.1 Introductiqn 10 4.2 Method used . .
..
. ....
. .. - ... .
10 5 Signal processing 126 Analysis and discussion of the processed results ....
... .
. . . 146.1
Procedure ... .
. . .... .
..
..
...
. ... 14
6.2 Results 14
7 Comparison of results of calculations and measurements 14
8 Conclusions 14
9 Future work 15
10 Acknowledgement . 15
TORSIONAL-AXIAL VIBRATIONS OF A SHIP'S PROPULSION SYSTEM
PART ICOMPARATIVE INVESTIGATION OF CALCULATED AND MEASURED TORSIONAL-AXIAL VIBRATIONS IN THE SHAFTING OF A DRY CARGO MOTORSHIP
by
Drs. C. A. M. VAN DER LINDEN Ir. H. H. 't HART
and
Ir. E. R. DOLFIN
Summary
This report deals with an extensive investigation into the vibratory behaviour of the propulsion system of the rnotorship "Koudekerk' of the United Netherlands Shipping Company.
It describes the procedure of calculation, the measuring technique applied and the processing of signals; it also analyzes and inter-prets the results of this processing.
The results of calculation and those of measurements are compared, while estimated values of unknown parameters are corrected.
1 Introduction
Practical experience has shown that the increasing main engine outputs required for the propulsion of modern motorships, attented with the decreasing number of cylinders of low speed directly coupled engines, as well as the tendency towards application of
short length shafting between the engine and the pro-peller, may result in the occurrence of complicated vibration phenomena in the shafting system.
The dynamic properties of shafting, the elastic be-haviour of bearings and the vibratory components of engine and propeller forces may cause inadmissible torsional and axial vibrations to occur at speeds in the manoeuvring range of the engine.
Due to the heavy weights of reciprocating parts of
large bore engines, the consequences of the depen-dence of the moment of inertia of these parts, relative to the crankshaft centre line, on the rotation angle, as
described by Draminsky, are becoming more
im-portant.
Report No. 39 M: "Crankshaft coupled free
tor-sional-axial vibrations of a ship's propulsion system" [1], describes the results of theoretical and of experi-mental model work on crankshaft coupled free tor-sional-axial vibrations. In the said report, a method is
developed to predict the natural frequencies and modes
of these coupled vibrations in the design stage. Other authors also developed calculation methods
for the natural frequencies of axial vibrations. The
calculation procedure of these natural frequencies is practically analogous to the classical calculation of torsional vibration frequencies, except for an
impor-tant difference due to the relationship of the axial
stiffness of a crank and the angle between one crank and other, especially the adjacent, cranks.
The vibratory behaviour of the propeller was
des-cribed in Report No. 70 M: "Experiments on vibrating
propeller models"; it deals with the results of experi-mental investigations on a series of propeller models With systematic variation of the propeller parameters
[2].
In order to verify the results of the previous work, and to obtain more accurate data of the axial stiffness of the thrustblock and the propeller-entrained water, extensive calculations and accurate torsional-axial vibration measurements were carried out during a normal voyage on the propulsion system of a dry cargo
motorship, consisting of a two stroke cycle low speed
diesel engine directly coupled to the shafting. Calcula-tions of the natural frequencies of the coupled tor-sional-axial vibrations were carried out with estimated
values of the unknown parameters.
The signals obtained from the measuring
instru-ments were processed by periodic sampling in order
to eliminate random components effected by ship
motions, slip rings and the instruments themselves.
The signals so processed were analyzed, and the resulting natural frequencies measured were compared
with the values calculated.
After correction of the estimated values that had been used in these calculations, a good agreement was
established between the results of measurements and
theory.
-2 Data
The propulsion system under consideration consisted
of a uniflow scavenged two stroke cycle turbo-charged
diesel engine directly coupled to the shafting, driving a four-bladed fixed pitch propeller.
2.1 Main engine
Builder: Stork N.V., Hengelo (Holland) Number of cylinders: 6 Output: 13,000 SHP Speed: 114 r.p.m. Bore: 850 mm Stroke: 1700 mm Firing order: 1, 6, 2, 4, 3, 5.
Turbo-charging: pulse system
2.2 Shafting
Crank: Fig. 1
Thrustshaft: length: 2282 mm; diameter: 610 mm Intermediate shafts: total length: 45185 mm;
diameter: 484 mm Propeller shaft: length: 9730 mm;
diameter: 640 mm 2.3 Propeller Diameter: 6,000 mm Number of blades: 4 Pitch at 0.7 R: 5,500 dim Fig. 1. Crank. 390 2351 1225 16 80 8b1 r 420
3 Calculation of natural frequencies and modes of vibration
3.1 Method used
The method used for calculating torsional-axial vibra-tions is analogous to the well-known Holzer method
for torsional vibrations. However, due to the
com-plexity of the vibrating system, the calculations were much more laborious and in fact only practicable on
a computer.
Coupling in the crankshaft between axial displace-ment and force on the one side and torsional rotation
and moment on the other, proceeds by bending of crankpin, webs and journals of the cranks and thus
bending moments, shear forces and the corresponding
displacements cannot-be -neglected [I].
For calculating torsional vibrations, a torque and a rotation are to be determined at every point of the
shafting. For torsional-axial vibrations, twelve quanti-ties must be calculated everywhere, namely: three
forces, three moments, three displacements and three
rotations. At both terminals of the system, these
forces and moments have to be equal to zero and, therefore, only six quantities are still unknown.By means of some formulae, which will be given in
this chapter, the values of the twelve quantities in a point of the system are expressed in their values at a
previous point and in the frequency of the system.
Repeating this procedure, one can express the twelve quantities at one terminal in the six unknown
quanti-ties at the other terminal and in the frequency.
Equating the forces and the moments to zero, one
gets for every value of the frequency six homogeneous
linear equations for six unknowns. Then frequencies have to be found for which the determinant of these equations is equal to zero. This can be done by means of a zero-procedure. In this investigation a quadratic interpolation of values of the determinant is applied. The twelve quantities mentioned are calculated at the locations:
before and after every crank; before and after the thrustblock;
before and after the flywheel;
at 19 points in the shaft line; before and after the propeller;
at the terminals.
The co-ordinate system chosen for the twelve quan-tities is related to a system of co-ordinates having its X-axis along the shafting, the positive direction being from crankshaft to propeller.
In every crank, the Z-axis was chosen perpendicular
to the shafting in the plane of the crank. This
necessi-tated a co-ordinate transformation between every two
cranks, but simplified the formulae considerably.
-In the rest of the system, the Z-axis is the same as that of the last crank.
The Y-axis was chosen perpendicular to X-axis and Z-axis; a rotation from Z-axis to X-axis was seen
clock-wise from the Y-direction.
Rotations on an axis and corresponding moments were taken positive, if seen clockwise from the origin in positive direction.
For the forces, moments, displacements and rota-tions the symbols: P, M, u and co were used.
A first index, x, y or z, refers to the corresponding
co-ordinate axis.
A second index, 1 or 2, refers to the location before or after the element (transformation, mass) for which the formula is used.
The calculation of the cranks is based on results of measurements performed at a scale model of a crank.
At one end this model was clamped and at the
other end it was loaded by forces and moments. The
displacements and rotations at the free end were
measured, giving the following six equations:
1
ax = a1iPx+a12My+a13Pz
py = a2113x+a22My+a23Pz in the plane of the crank
U. = a3,Pz+6132My+1233Pz
cox = b11Mx+b12Py+b13Mz perpendicular to the uy = b2iMz+b22Py+b231viz
Wane of the crank. yoz = b3,Mx+b32Py+b33Mz
The influence numbers au and bu are subjected to
rela-tions of Maxwell: au =
bu =b1 and due to the
symmetry of the crank to the relations: a13 = a121/2;
/223 = a221/2; b13 = 0.; b2.3 = b331/2i where 1 is the length of the crank.
Through these influence numbers, the relations
be-tween the twelve quantities before and after each
crank become:
Px2 = Px 1, Py2 Pz2 = Pz1
Mx2 Mxl,
My2 = M1P1l,Mz2 = Mz I +Pyll
rix2 = lixi +011Px1 +al2Myl +(a13-1a12)Pz19y2 = .9y1+a21Px1+ 422My1 ±(a23 la22)Pz1
= Uzi +19y1 + a3 + a32Myi + 0133 /a32)Pzi
Tx2 (Psi ±b11Mx1+(b12+1b13)Pyt+ bl2A1z1
142 = !Aryl hpz, +b2iMzi +(1722+ /b23)Pyi+452,3Mzi 9z2 = 9z1 + b31MX1 +(b32 ±1b33)Py1 +b331Wz1
In these formulae do not appear the mass of the crank and the moment of inertia.
These are lumped in two equal parts which are
placed before and after the crank.
To calculate the axial inertia force, the mass of the
crank alone is taken as a first approximation. To
express the torsional rotation, a part of the moment of inertia of connecting rod, piston rod, and piston are
added to the moment of inertia of the crank, as is
usually done in calculating torsional vibrations. The formulae used for a lumped mass are:
Mx2 = la29x1 Px2 = Pxl +Ma2Ux1
All other quantities remain unchanged. The formulae for the flywheel are the same.
The formulae used for passing a bearing are:
Py2 Py1+kyuyi
Pz2 = Pz 1 + kzUz1
If ky = kz, co-ordinate transformation is not required;
otherwise a previous transformation brings the Y-axis and the Z-axis in coincidence with the main directions of the bearing.
The mass occurring in a cylindrical part of the shafting is not lumped, but supposed to be equally divided over
the length of the part concerned. Here, the influence
number can easily be deduced from the geometry of a
section of the shaft.
Let If, = polar moment of inertia It torsional resisting moment
G= modulus of rigidity = density
E= Young's modulus
1= moment of inertia with respect to a diameter
q= area
1= length of the part concerned
a = ,Iew24,121G1 13 = GItcrll
T =
ieco2/2/E, y = 4111a= 11E1, b = 1212E1, c = 1313E1,
then the formulae are:
Px2 = uz, ysinT±PxiCOST Py2 = Py, Pz2 = P.1 Mx2 = 9113sina+ Mx, cos
a-My2 = Myi/Pzi
Mz2 = Mz,+1Py,Ux.2 = uxicos T ±PxiSill y
9y2 = (PA
aMylbPz,
Uz2 = u21+19y1+bMylcP2,
(Px2 = cox, cos a +Mx, sincr113
tiy2 = L41-1921-=:-bM2icPy1
Here the inertial forces for motions in the y-direction and in the z-direction are neglected.
Passing the thrustblock, the only quantity that alters is
P. = 1".1 +111.1
where k = axial rigidity of the thrustblock.
Passing the propeller has two effects. Firstly, the propeller acts as a mass and, therefore, the formulae used for a lumped mass had to be applied.
Secondly, hydrodynamic interference of the sur-rounding water causes additional forces and moments
on the system. This phenomenon is described in ref. 2.
The coefficients in the formulae are derived from the same report:
.Px2 Pxl Ci,c04ux,=ri2c02(pxi mx; = mx, - C2 lth2Uxi C22(0201.
To adapt the co-ordinate system to the position of the
crank a co-ordinate transforniation between every two
crank § is necestary. If rotation takes place Over an
angle a the formulae used are:
;
-qx2 = qx1
(1372 = 9y1cosa-q21sincc qz2 = qylsina+qz,cosa
In them, q had to be replaced successively by u; P, M.
3.2 Values of quantities
All values are expressed in the icgrn sec system (Giorgi). Young's modulus 2.06.10" NinT2
Modulus of rigidity
0.814.10" Nm'
Table 1. Influence numbers for a crank aii- 10"
Table 2. Influence numbers for a crank 62,-10"
Table 3. Masses and moments of inertia
Axial rigidity of the thrustblock:
The calculation was performed with two different
thtustblock rigidities, viz.: 2.109 and 1010 Nm-1
3.3 DiscretiOn of system (Fig. 2)
The numerical values are summarized in Table 5, where: S = shafting, B = beating, C = crank, T
=-= thilistblock, F =-= flywheel, P propeller.
Table 5. Numerical values of the system Item Mass(kg) -Moment of inertia (kge) crank 14,530 10,760 flywheel 2,130 3,520 propeller 22,460 ' 33,075 -1---,..,1 2 1.116 kg 0.898 kgin 0.898 Icgin 1.024 kgrn°
Item Length(m) Diameter(m) Rigidity
(Nm-1) Angle Si 0.2 0.665 -B1 1.87- 10° Cl 0 B2 8.52- 10" Cg 240 B3 7.14. 109 Cs 120 .134 2.18-10' S2 1.45 0.665 Bs 2.18-10' Cg 180 Bg 7.38.10° Cg 0 6 B7 7.59i0° C6 300 B6 2.62-10' 53 0.44 0:665 54 1.775 0.610 T S6 1.775 0.610 F S6 3.725 0.484 57 0.8 0.490 58 4.8 0.484 S. 0.8 0.490
X/
1 2 3 1 0.557 inN-1 0.770 N-1 0.635 mN-1 2 0.770 N-1 1.721 rn-1N-1 1:420 N-1 0.635 mN-1 1'.420N' . 1.835 mN-1X
1 0.966 rn-1N-1 -0.409 N-1 0 -0.409 N-1 1.631 InN-1 -1.121 N-1 3 0 -1.121 N-1 1.359 in-1N-1_ _The mutual interference between axial and torsional
movement appeared to be very small. Accordingly, no perceptible torsional movement was expected at the axial frequencies, neither was perceptible axial
movement expected at the torsional frequencies.
As mentioned already, the calculation was made for Graphs of the expected vibration modes are shown two different values of the axial rigidity of the thrust in Figures 3, 4, 5 and 6.
3,4 Results
-2
Fig. 3. Modes of vibration
B12345678 9 10 11 12 13 14 15 16 17 ) "A AA AIVAA engine A- A--shafting A -A
Fig. 2. Location of the sup Ports.
0.15
0.1
0.05 -1
0.1
block. The natural frequencies are summarized in Table 6.
Table 6. Calculated natural frequencies (vpm)
0
-2
Fig. 4. Modes of vibration.
0.05 0.15 -To-C g 0.1 T,, = ..3 :6. 1 0.05 0.1' 9
Item Length Diameter'
510 5.6 0,484 Su 0.8 0.490 512 4.8 0.484 S13 0.8 0.490 S14 5.6 0.484 S13 0.8 0.490 S113 4.0 0.484 5,7 1.6 0.490 510 5.6 0.484 S19 1.6 0.490 520 1.6 0.484 S21 2.26 0.484 522 2.64 - 0.642 S23 5.5 0.640 524 0.6 0.600 P
Item Thrustblock stiffness
2 -10° Nin-1 10/° Nm-i first torsional 171 171
second torsional 1281 1281
first axial 668 864 second axial 941 946
1: axial rigidity, thrust 2: axial rigidity thrust
-block=1010 Nm7-1; block=2-10' Nrn-1; i n=171 vpm. n=171 vpm. .. , 1 -, ,-,
/
, torsional rotation:
, , / , , , 2I
axial displacement____.,.
, ,, --- . . _1: axial rigidity thrust 2: axial rigidity thrust
block =104 Nin-1; block=2.109 n=864 vpm. Nm-1; n =668 vpm.
1111r11111111111."-,?....---- ---'axial displacement _t_i_--L--._\ torsional rotation .. 2 i ;10
1-2
Fig. 5. Modes of vibration.
4 Measure-ments 4.1 Introduction
Axial and torsional vibrations were measured in three
locations of the shaft. In addition, axial vibrations
were measured close to the thrugtblock in location 3.
(Fig. 7).
4.2 Method used
The vibrations were measured with absolute accelero-meters. Selection of this measuring tool was based mainly on the linear response characteristics in the
very low frequency range ( < 1 cycle per second). Generally speaking, accelerometers produce a
measuring signal that is considerably disturbed by high frequency noise. During the measurements under
report, accelerometers had to be connected to
ampli-I 0.15 0.05 I 0.1 2 0.05 111 fil!!!!!If
Fig. 7. Locations of the vibratory motion measurements on the
propulsion -system. Number indication of
measure-ments.
2
Fig. 6. Modes of vibration.
fiers by meansofslip-rings and thus the said noise was
even worse. Actually, the system of analysis that was
used especially aims at a noise-free signal.
The accelerometers applied had the following specifications:
Make: Statham, strain-gauge type
Type number: A5-2.5=350 respectively A5-5-350 Frequency_ range: < 110 respectively < 190 cps
Full-scale output: + 4 mV/Volt nominal
Range: + 2.5 respectively ±5 g
The axial motions of the shaft were measured with a
single accelerometer mounted on the shaft in axial direction (Figure 8). At the right hand side of the
photo the four silver sliprings can be seen.
The torsional motions were measured with two accelerometers fitted to the shaft, the one diametrically
opposite the other. These meters were mounted
tan-3-axial I 0.15 15_ 72 7. 3 0.05 1 0.1 0.05 0.1 torsional
6 top dead centre indication
l' 1: axial rigidity thrust 2: axial rigidity thrust
block =_ 1010 Nrn-1; block=2-10' Nrnt: n =1281'vpm. n =-1280 vpm. --- rotation
(Ilk
.911 -1: axial rigidity thrust2: axial rigidity thrust
block=1010 Nrn';' block=2,10' Nn,: ' n=946 vpm. n=941 vpm. 1 1 axial displacement
.-- ---, - I ' torsional rotation , , II- I H=r1 ItHriiii.1
1,11i614i 1111 II 1 11116 torsional 10torque fluctuations 4torsional
7axial 11 thrUtt fluctiations 5 axial 2 axial
9 time indication 12 correlation impulse train
gentially in such a way that the sum of the outputs was influenced by neither the gravity nor the ship's motions
in the vertical plane.
The sensitivities of the two accelerometers had been made equal to each other by fitting a voltage
reduction in the output circuit of the most sensitive meter. Each pair of meters was connected to a set of
four slip-rings. Figure 9 shows a tangentially mounted accelerometer.
For measuring the torsional and axial motions of the propulsion system at the free-end of the shaft, a special device shown in Fig. 10 was applied. In the cylinder three accelerometers are mounted : one in
the centre of rotation in axial direction, for measuring
axial motions, and the other two in tangential direction, for measuring torsional motions. Both measuring
systems were connected to the amplifiers by means of
four slip-rings each.
To obtain a proper analysis of the measuring signals,
two reference signals were required ; one indicating each revolution of the shaft and the other indicating the rotational momentaneous position of the propeller shaft. The first of the said reference signals produced one pulse per revolution of the shaft. The second re-ference signal consisted of 214 pulses per revolution of the shaft.
Figure 11 shows the lay-out of one channel of the measuring arrangement.
Fig. 9. Tangentially mounted accelerometer. The measuring bridge of each accelerometer (axial),
---111.5.
or pair of accelerometers (torsional), was suppliedwith 5 Volts DC. Via a resistance balance, and a "measuring-calibrating" switch, the measuring system
Fig. 10. Measuring device at free-end for axial and torsional
motions. Fig. 8. Axially mounted accelerometer.
iaM
12
R balance.
torsional motions only
calibration resistance bridge oscillating switch ' slip-rings R balance calibrating resistance R balance ba an
had been connected to a DC differential amplifier.
The amplification factor was 1000 x at maximum.
The input signals, however, were too weak to obtain a reasonable input level at the recorder. Therefore, a
second amplifier was applied. The signals were re-corded on a tape-recorder.
During calibration, the accelerometer was dis-connected. A special resistance bridge was put in its
place. This calibration resistance gave an out-of-balance voltage of known value. With the aid of a "oscillating switch, a block function was generated with known, amplitude. The said amplitude can be translated in the physical quantity, using the known sensitivity of the accelerometer or pair of
accelero-meters.
5 Signal processing
Vibration measurements on board ships usually in-volve random disturba.ncesthat are due to manoeu-vring and ship motions, slip ring noise and instrument noise.
For regular measurements (e .g. under resonance conditions), when the signal lsyel is relatively high, interpretation,pf direct reCorgfi'possible. When weak
signals have to be analyzed, as in the investigation
_
switch "meatiiiing-calibrating"
' differential
amplifiers
taperecorder
of higher order axial and torsional shaft vibrations
under report, the signal to noise ratio of the records is too low for immediate evaluation.
Fortunately, the conditions of the present investi-gation were favourable for suppression of that noise by means of correlation [5].
Since the frequencies were known in advance, an effective cross correlation method, based on strobos-copic obseryation crtinldbe applied ,[611 [71.
Using this'inethod of periodic sanipling, the signal
of interest a.- 7-eraged over 4 large number of periods. Because the averaging process was synchronised
witn:the period ici ty of the signal, all non-synchronous
signals (i.e. noise) could be eliminated; the signal to
noise ratio thus improved approximately with the
'square root of the number of periods.
In the original set-up of ref. 5, a
one-point-per-period averaging technique was used. If n points in
one period are needed, and sufficient to define the signal during that period, the process has to be repeated
n times. Due to more sophisticated electronic
instru-ments available at present, these n points in one period
cn-uld be handled simultaneously, thus reducing the processing time by a factor of n.
In the measurement of propeller shaft vibrations, the fundamental frequency of the signal equals one
5 V
d.c.
power
revolution of the shaft. Thus the periodicity of the signal, which is the condition for applying the periodic
sampling technique, was known. In order to mark one period, a top-dead-centre pulse was recorded simul-taneously with the signal. Besides this T.D.C. pulse,
the electronic sampling and averaging apparatus needs
an indication at which points of the period the n
samples have to be taken. So n address pulses
distri-buted regularly over the period were recorded as well.
In the underlying measurements n = 214. The T.D.C. pulse and address pulses were obtained directly from
the propeller shaft, as is described in the previous
section. 114 RPM 110 RPM 411.11.1l. 105 RPM 100 RPM
2
3
5
7 2 1iaxial
axial torsionalFor the torsional shaft vibration measurements, matched pairs of accelerometers were used, in order to
eliminate the modulation of gravity by shaft rotation. The small unbalance of the pair of transducers, still
present, showed a small gravity output. Also the
misalignment of the single axial pick-ups gave this type of disturbance.
Fortunately, the frequency of this effect was low compared with frequencies of interest and, due to the application of accelerometers, the acceleration signal
was favourable.
In order to have the amplitudes of these unwanted
signals as small as possible, no effort has been made to
6
4
13
axial axial axial torsional torsional
lialt,INIMI,
95 RPM
80 RPM
Ak
1 I 7:16,Fig. 12. Correlated signals for one revolution of the shaft.
90 RPM
tti
85 RPM 1
14
integrate the acceleration signals during the final
processing, because velocity or displacement signals
have a worse ratio between the shaft modulation
signals and the signals of interest.
A review of the oscilloscope displays of the
corre-lated signals for one revolution of the shaft is given in Figure 12.
Due to some uncertainties encountered due to weak pulse signals, it sometimes happened that during a
period a few address pulses were not processed in the memory of the sampling and averaging apparatus.
Consequently, a step disturbance occurred between the beginning and the end of that period. This distur-bance introduced higher harmonics into the signal,
making it doubtful whether the highest harmonic
components of interest are true or false. In order to
avoid this difficulty, a simultaneous sampling and
aver-aging over two periods have been performed. With this method of double-period sampling one
"correct" period could be selected from the two
adjacent periods. After this (electronic) averaging process, the noise-free signal was displayed on an oscilloscope and, next, digitized and punched into paper tape. This tape was fed into an electronic digital computer, and so used to determine the harmonic components of the signal.6 Analysis and discussion of the processed results
6.1 Procedure
The results of the sampling and digitizing procedure applied to the signals of the pick-ups (punched tapes)
have been used to start the computation.
These results are the values of the acceleration at
214 equidistant points per period, the values being
averaged over many periods.
Sets of such data were available for 7 measuring
points and at 17 different numbers of revolutions.
Of every set, a harmonic analysis was made by a digital computer. By means of a line printer, a graph
was made for every measuring point as well as for every harmonic of the amplitude and the phase of
the acceleration against the number of revolutions.
Natural frequencies were found from inspection
of these graphs. They appear in the graphs as a
maxi-mum of amplitude and as a change in phase angle.
Moreover, a vibration mode was deduced from the
relative values of the maxima at the several measuring points.
6.2 Results
From the graphs, described in the previmis section the
following natural frequencies Were established:
a. A very clear torsional frequency at 173 vpm. The indicating signal was observed only at torsional measuring points I, 4 and 6.
b. An indistinct axial frequency at about 670 vpm, only observed at axial measuring points 2, 3, 5
and 7.
c. A very clear axial frequency at 915 vpm, observed only at the axial measuring points.
d. A very clear frequency at 1325 vpm. This signal was observed at almost all the measuring points
(1, 3, 4, 5, 6 and 7).
e. A clear torsional frequency at about 1520 vpm, ob-served only at measuring points 4 and 6.
f. A not very clear axial frequency at about 2300
vpmr-it was observable at all the axial measuring points (2, 3, 5, 7).
7 Comparison of results of calculations and
measure-ments
The first-degree torsional frequency, calculated at 171 vpm, appeared at 173 vpm.
The second-degree torsional frequency, calculated at 1281 vpm, appeared at 1325 vpm. According to the calculation, the torsional motion is not accompanied by a perceptible axial motion. The accordance was,
nevertheless, recorded by most axial pick-ups. A
satis-factory explanation of this phenomenon was not (yet)
found.
The third-degree torsional frequency measured at
about 1520 vpm, was calculated at 1930 vpm.
This vibration has a node at the free end of the crank-shaft, since no signal was observed at measuring
point 1.
The first-degree axial frequency was measured at about 670 vpm. The calculation gave, dependent on the thrustblock rigidity, 668 vpm and 864 vpm.
According to the calculation, an important move-ment of the thrustblock exists. The measuring signal was not clear, and it gave the impression to be subject to a heavy damping, possibly due to the large move-ment of the thrustblock.
The second-degree axial frequency was measured at 915 vpm. Here the thrustblock is situated in a node
of the vibration mode. The calculation gave 941 to 945 vpm.
Third-degree axial vibriaton measured at about 2300 vpm, was calculated at 2330 vpm.
8 Conclusions
An obvious correlation exists between the natural
frequencies measured and the results of calculations. At the first-degree axial vibration, an axial
thrust-block rigidity of 2.109 Nm -1 gives a good result. The difference in the second-degree axial vibration of about
40 vpm has a plausible explanation.
For calculating the mass of a crank, the connecting rod was not taken into account.
However, the connecting rod will partly join in the axial motion of the crank as it is carried along by the oil film in the bearing. Adding to the crank an extra mass of 2000 kg, reduces the calculated value to 915
vpm. An assumed thrustblock rigidity of 2.2. 109 Nm-1 brings the calculated natural frequency of the first
axial vibration mode then down to 670 vpm. Other
frequencies are not perceptibly changed by these assumptions.
9 Future work
The measurements described in this report were the first to be carried out in order to investigate
experi-mentally the dynamic behaviour of a Propulsion system of a merchant ship propelled by a directly
coupled modern marine diesel engine.
A second, similar investigation will be carried out on a motortanker.
---- 10 Acknowledgement
edges the kind co-operation of the United Netherlands Shipping Company, which greatly facilitated the inves-tigation reporfed herein.
References
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PUBLICATIONS OF THE NETHERLANDS SHIP RESEARCH CENTRE TNO
(FORMERLY THE NETHERLANDS RESEARCH CENTRE TNO FOR SHIPBUILDING AND NAVIGATION) PRICE PER COPY DFL. 10.- M engineering department
S = shipbuilding department
C = corrosion and antifouling department
Reports
S The determination of the natural frequencies of ship vibrations 37 M
(Dutch). H. E. Jaeger, 1950.
3 S Practical possibilitiesofconstructional applications of aluminium 38 S alloys to ship construction. H. E. Jaeger, 1951.
4 S Corrugationofbottom shell plating in ships with all-welded or 39 M partially welded bottoms (Dutch). H. E. Jaeger and H. A.
Ver-beck, 1951. 40S
5 S Standard-recommendations for measured mile and endurance
trials of sea-going ships (Dutch). J. W. Bonebakker, W. J. Muller and E. J. Diehl, 1952. 41S
6 S Some tests on stayed and unstayed masts and a comparison of experimental results and calculated stresses (Dutch). A. Verduin 42 S and B. Burghgraef, 1952.
7 M Cylinder wear in marine diesel engines (Dutch). H. Visser, 1952. 43 C
8 M Analysis and testing of lubricating oils (Dutch). R. N. M. A.
Malotaux and J. G. Smit, 1953. 44 S 9 S Stability experiments on models of Dutch and French
standard-ized lifeboats. H. E. Jaeger, J. W. Bonebakker and J. Pereboom, 45 S in collaboration with A. Audig6, 1952.
10 S On collecting ship service performance data and their analysis. 46 C J. W. Bonebakker, 1953.
11 M The use of three-phase current for auxiliary purposes (Dutch).
J. C. G. van Wijk, 1953. 47 C
12 M Noise and noise abatement in marine engine rooms (Dutch).
Technisch-Physische Dienst TNO-TH, 1953.
13 M Investigationofcylinder wear in diesel engines by means of labo- 48-C
ratory machines (Dutch). H. Visser, 1954.
14 M The purification of heavy fuel oil for diesel engines (Dutch).
A. Bremer, 1953. 49 S
15 S Investigations of the stress distribution in corrugated bulkheads with vertical troughs. H. E. Jaeger, B. Burghgraef and I. van der 50 Ham, 1954.
16 M Analysis and testing of lubricating oils II (Dutch). R. N. M. A. 51 M Malotaux and J. B. Zabel, 1956.
17 M The application of new physical methods in the examination of 52 C lubricating oils. R. N. M. A. Malotaux and F. van Zeggeren, 1957. 18 M Considerations on the application of three phase current on board
ships for auxiliary purposes especially with regard to fault pro- 53 S tection, with a survey of winch drives recently applied on board 54 C
of these ships and their influence on the generating capacity
(Dutch). J. C. G. van Wijk, 1957.
19 M Crankcase explosions (Dutch). J. H. Minkhorst, 1957. 55 S 20 S An analysis of the application of aluminium alloys in ships' 56 C
structures. Suggestions about the riveting between steel and
aluminium alloy ships' structures. H. E. Jaeger, 1955. 57 M 21 S On stress calculations in helicoidal shells and propeller blades.
J. W. Cohen, 1955.
22 S Some notes on the calculation of pitching and heaving in longi- 58 S tudinal waves. J. Gerritsma, 1955.
23 S Second series of stability experiments on models of lifeboats. B. 59 M Burghgraef, 1956.
24 M Outside corrosion of and slagformation on tubes in oil-fired
boilers (Dutch). W. J. Taat, 1957. 60 S 25 S Experimental determination of damping, added mass and added
mass moment of inertia of a shipmodel. J. Gerritsma, 1957. 61 S 26 M Noise measurements and noise reduction in ships. G. J. van Os
and B. van Steenbrugge, 1957.
27 S Initial metacentric height of small seagoing ships and the in- 62 C accuracy and unreliability of calculated curves of righting levers. J. W. Bonebakker, 1957. 63 M 28 M Influence of piston temperature on piston fouling and pistonring
wear in diesel engines using residual fuels. H. Visser, 1959. 29 M The influence of hysteresis on the value of the modulus of
rigid-ity of steel. A. Hoppe and A. M. Hens, 1959.
30 S An experimental analysis of shipmotions in longitudinal regular waves. J. Gerritsma, 1958.
31 M Model tests concerning damping coefficient and the increase in the moment of inertia due to entrained water of ship's propellers. N. J. Visser, 1960.
32 S The effect of a keel on the rolling characteristics of a ship. J. Gerritsma, 1959.
33 M The application of new physical methods in the examination of lubricating oils (Contin. of report 17 M). R. N. M. A. Malotaux and F. van Zeggeren, 1960.
34 S Acoustical principles in ship design. J. H. Janssen, 1959. 35 S Shipmotions in longitudinal waves. J. Gerritsma, 1960. 36 S Experimental determination of bending moments for three
mod-els of different fullness in regular waves. J. Ch. de Does, 1960. MC 65 S 66 S 67 S 68 M 69 M 70 M 71 S
Propeller excited vibratory forces in the shaft of a single screw tanker. J. D. van Manen and R. Wereldsma, 1960.
Beamknees and other bracketed connections. H. E. Jaeger and J. J. W. Nibbering, 1961.
Crankshaft coupled free torsional-axial vibrations of a ship's
propulsion system. D. van Dort and N. J. Visser, 1963.
On the longitudinal reduction factor for the added mass of
vi-brating ships with rectangular cross-section. W. P. A. Joosen and J. A. Sparenberg, 1961.
Stresses in flat propeller blade models determined by the moire-method. F. K. Ligtenberg, 1962.
Application of modem digital computers in naval-architecture. H. J. Zunderdorp, 1962.
Raft trials and ships' trials with some underwater paint systems. P. de Wolf and A. M. van Londen, 1962.
Some acoustical properties of ships with respect to noise control. Part. I. J. H. Janssen, 1962.
Some acoustical properties of ships with respect to noise control. Part II. J. H. Janssen, 1962.
An investigation into the influence of the method of application
on the behaviour of anti-corrosive paint systems in seawater.
A. M. van Londen, 1962.
Results of an inquiry into the condition of ships' hulls in relation to fouling and corrosion. H. C. Ekama, A. M. van Londen and P. de Wolf, 1962.
Investigations into the use of the wheel-abrator for removing
rust and millscale from shipbuilding steel (Dutch). Interim report. J. Remmelts and L. D. B. van den Burg, 1962.
Distribution of damping and added mass along the length of a shipmodel. J. Gerritsma and W. Beukelman, 1963.
The influence of a bulbous bow on the motions and the propul-sion in longitudinal waves. J. Gerritsma and W. Beukelman,1963. Stress measurements on a propeller blade of a 42,000 ton tanker on full scale. R. Wereldsma, 1964.
Comparative investigations on the surface preparation of ship-building steel by using wheel-abrators and the application ofshop-coats. H. C. Ekama, A. M. van Londen and J. Remmelts, 1963. The braking of large vessels. H. E. Jaeger, 1963.
A study of ship bottom paints in particular pertaining to the
behaviour and action of anti-fouling paints A. M. van Londen,
1963.
Fatigue of ship structures. J. J. W. Nibbering, 1963.
The possibilities of exposure of anti-fouling paints in Curacao, Dutch Lesser Antilles, P. de Wolf and M. Meuter-Schriel, 1963. Determination of the dynamic properties and propeller excited
vibrations of a special ship stem arrangement. R. Wereldsma,
1964.
Numerical calculation of vertical hull vibrations of ships by
discretizing the vibration system. J. de Vries, 1964.
Controllable pitch propellers, their suitability and economy for large sea-going ships propelled by conventional, directly coupled engines. C. Kapsenberg, 1964.
Natural frequencies of free vertical ship vibrations. C. B. Vreug-denhil, 1964.
The distribution of the hydrodynamic forces on a heaving and pitching shipmodel in still water. J. Gerritsma and W. Beukelman, 1964.
The mode of action of anti-fouling paints: Interaction between anti-fouling paints and sea water. A. M. van Londen, 1964.
Corrosion in exhaust driven turbochargers on marine diesel
engines using heavy fuels. R. W. Stuart Michell and V. A. Ogale,
1965.
Barnacle fouling on aged anti-fouling paints; a survey of pertinent literature and some recent observations. P. de Wolf, 1964. The lateral damping and added mass of a horizontally oscillating shipmodel. G. van Leeuwen, 1964.
Investigations into the strenght of ships' derricks. Part I. F. X. P Soejadi, 1965.
Heat-transfer in cargotanks of a 50,000 DWT tanker. D. J. van der Heeden and L. L. Mulder, 1965.
Guide to the application of Method for calculation of cylinder
liner temperatures in diesel engines. H. W. van Tijen, 1965. Stress measurements on a propeller model for a 42,000 DWT
tanker. R. Wereldszna, 1965.
Experiments on vibrating propeller models. R. Wereldsma, 1965.
Research on bulbous bow ships. Part II. A. Still water
perfor-manceofa 24,000 DWT buLkcarrier with a large bulbous bow. W. P. A. van Lammeren and J. J. Muntjewerf, 1965.
