Vibration Characteristics of Two-stroke Low Speed

Vibration Characteristics of Two-stroke Low Speed
Vibration Characteristics
of Two-stroke Low Speed Diesel Engines
This paper gives a general introduction
to the vibration characteristics associated with two-stroke, low speed marine
propulsion diesel engines, and ou#ines
measures t h a t can be taken to counteract any adverse influences arising in the
A few years ago, vibrations were encountered in some ships propelled by
engines wtih a low number of cylnders.
These cases led to intensified investigations of the vibration conditions on board
some of these ships, and prompted a
further careful theoretical investigation
into the vibratory excitation sources.
The vibratory conditions relating to the
coupling betwean torsional vibrations of
the propeller and axial vibrations of the
shaft system, engine and huff wi// be
thoroughly dealt with. These appear especialy where shaft system diameters
have been increased considerably in
order to avoid a “barred speed range’:
In the same period, it has bean verified
that constant pressure turbocharging
and uniRow air scavenging are the working principles which ~provide the lowest
specie fuel consumption of two-stroke
low speed diesel engines.
Fig. 2 illustrates the following:
From a vibration point of view, the
above changes have resulted in certain
vibration characten’stics playing a more
domi- nant role than others. However,
the fundamental excitation principles in
the engine remain the same. The enclosed reference list refers to some recently published papers dealing with
these subjects.
2) Excitation:
Forces or moments acting on the
mass-elastic system
The concern about vibrations on board
ships most often stems from a wish to
provide comfortable conditions. However, if not adequately dealt with, vibrations can reach a level which threatens
the safe operation of mechanical and
electronic components and even the
stabilw of major parts of the ship’s steel
Developments in world economy during the last two decades have led to
drastic changes in the traditions of the
shipping and shipbuilding industries.
As a major licenser, MAN B&W Diesel
are obviously interested in having as
many MAN B&W engines as possible
installed with the optimum overall cost
efficiency. With rward to vibrations, this
means that the optimum combination
of vibration countermeasures are to be
implemented on every propulsion unit.
On the technical side, two-stroke, low
speed diesel engines with a low number of cylinders have become very
popular for the propulsion of oceangoing ships, mainly on account of their
low instaI!ation and operating costs.
According to the authors’ experience,
actual contract conditions have in some
cases prevented the necessary countermeasures from being taken or have even
caused unnecessary countermeasures
to be implemented.
Fig. 1 shows how the number of 4 and
Scylinder engines has increased over
the years at the expense of 7 and 8cylinder engines. The same illustration
also indicates how the stroke/bore ratio
and the ratio between mean indicated
pressure and maximum pressure have
developed with the aim of reducing the
specific fuel consumption and reducing
the engine speed, with consequently
increased propeller efficiency.
Before undertaking a detailed examination of the vibration characteristics of
the diesel propulsion plant, it may be
useful to study a simple mass-spring
system in order to recapitulate the terminology used in a discussion of vibrations.
1) Mass-elastic system:
model used to calculate the physical
system comprising masses, spring
and damping elements
3) Mode shape, or vibration modes,
and natural frequency:
A characteristic deflection fom- of the
mass-elastic system and a corresponding characteristic frequency at
which the system can perform sinusoidal vibrations once excited, after
which jt is left to vibrate freely
4) Harmonic excitation:
In the case of a periodic excitation, it
is possible to describe the excitation
as a sum of sine functions with different amplitudes, phase angles and
periods (Fourier analysis). The pertods
of the sine functions will be 1, i/Z.
l/3, i/4 _.. of the period for the basic
excitation. These sine excitation components are also called the lst, 2nd.
3rd, 4th order harmonic excitations
5) Resonance:
The frequency of a harmonic excitation coincides with the natural frequency of the mass-elastic system.
Depending on the damping of the
system, a considerable magnitication of the response will take place
at resonance. Magnifications of 5 to
50 times will not be unusual
6) Main critical resonance is the condition at which the main harmonic
excitation has resonance
Overcritical condition refers to the condition at which the frequency of the
main harmonic excitation is higher than
the natural frequency.
Conversely, undercritical condition
refers to the condition at which the frequency of the main harmonic excitation
is lower than the natural frequency.
Influence of bordstroke ratio
15,000 EIHP 1979-1992
Fig, 1: Developments in the parameters of two stroke low-sped diesel engines
Influence of Pmax ratio
P. excitation of n’th order:
‘4,: N*,“ralfrq”e”cy for system I
Pn =
Qn sin (m3t + ~“1
n’th order excitation amplitude
engine angular velocity
n’th order excitation phase angle
A periodic excitation F can be split into a number
of harmonic orders P,,:
A, (response Of P”. angularfrequency
*vJwept ‘mm 0 - -,
0 -node natural
F=C Q,sin(nwtxm)
,-node natural
(excitation synth+s)
response of n’th order
X, =
A, sin (nti + qr.)
A, =
n’th order response amplitude
V” =
n’th order response phase angle
For linear system n’th order excitation P,, will give
only n’th order response x,
Characteristic frequencv for the mass-elastic svstem
‘ode shape:
Characteristic “deflection form” in which mass-elastic system responds when
excited at a frequency equal to the natural frequency
Where natural frequency coincides with excitation frequency no
Sub- and super-harmonic response
Non-linear response of order dierentulan the
excitation order
These effects areconsidered in standard torsional
vibration calculations
Fig. 2: Explanation of vibration terms
Excitation - General
Excitations generated by the engine
can be divided into two categories:
1) Primary excitations, which are forces
and moments originating from the
combustion pressure and the inertia
forces of the rotating and reciprocating masses. These are characteristics of the engine as such, and
they can be calculated in advance
and be stated as part of the engine
specification, with reference to a certain speed and power
2) Secondary excitations, stemming
from a forced vibratory response in a
sub-structure. The vibration characteristics of sub-structures are almost
independent of the remaining ship
Examples of secondary excitation
sources from sub-structures could be
anything from transverse vibration of
the engine structure to longitudinal vibration of a radar or light mast on top
of the deckhouse. Such sub-structures
of the complete ship might have resonance or be close to resonance conditions, resulting in considerable dynamically magnified reaction forces at their
interface with the rest of the ship.
Secondary excitation sources cannot
be directly quantified for a certain engine type, but must be calculated at
the design stage of the specific propulsion plant.
Primary excitation sources
The primary excitation sources are very
closely connected to the crankshaft/
connecting rod mechanism and the engine process pressure acting through it.
Even though the function of this mechanism is simple, it can be difficult to axplain the origin and distribution of its
associated internal/external forces and
Fig. 3 shows the forces and moments
of a 1 -cylinder engine. As an approximation for calculation purposes, the
S S’and S”:
Cbnnecting rod force acting on crosshead, equal to connecting rod force acting on
crankpin, equal to force on main beating journals
M I M’ M”and Ml”:
Torque on main bearing journals from combustion pressure forces and inertia forces
T and R:
S, S’ and S”can at the crankpin be given as a sum of a radial component Rand a
tangential component T
Resulting forces on engine frame in vertical direction:
C, F I, F “and FJ’
Resulting forces on engine frame in horizontal direction: C and Fi’
Resulting moment on engine frame:
Fig. 3: Resulting forces and moments on the engine frame from one cylinder
mass of fhe connecting rod has been
divided into two and concentrated at
the centre of the crankpin and the
centre of the crosshead, respectively.
This means that only inertia forces acting on two masses, i.e. the reciprocating mass at the centre of the crosshead and an equivalent rotating mass
at the centre of the crankpin, need to
be considered.
The gas force P will, through the connecting rod, act on the crankshaft with
a torque M, causing an equivalent reaction torque on the engine frame G x I = M.
M and G will contain harmonic excitations of all orders. In MAN B&W’s experience, only excitations of the 1 st to
16th order need to be considered.
At a certain uniform speed of the crankshaft, an inertia force F arises from the
accelerations of the reciprocating mass
M,, and a centrifugal force C acts on
the rotating mass M,: The force F will
contain harmonic excitations of the 1st
2nd, 4th, 6th and higher even orders,
however, normally only the 1st and 2nd
order are taken into account. Force C
will only give 1st order excitation.
Rg. 4: Forces and moments of a multi-cylinder engine
engines with certain numbers of cylinders, however, they will be small
and can be ignored.
For a multi-cylinder engine, Fig. 4. the
firing order will determine the vectorial
sum of the forces and moments from
the individual cylinders.
Distinction should be made between:
External forces and moments, and
Internal forces and moments
The H-type guide force moment is a
moment between the stationary engine frame and the rotating/oscillating parts of the engine. From a practical engineering point of view, it
should be applied to the engine frame
as an external moment.
Internal forces and moments:
The external forces and moments will
act as resultants on the engine and
thereby also on the ship through the
foundation and top bracing of the engine. The internal forces and moments
will tend to deflect the engine as such.
It is the responsibility of the engine designer to provide the engine frame with
sufficient stiffness to cope with the internal forces and moments so that deflections and corresponding stresses
can be kept within acceptable limits.
External forces and moments:
If the engine frame could be assumed
to be infinitely stiff, internal moments
and forces would not be able to give
excitations to the ship’s structure. However, it is obvious that an infinitely stiff
engine frame cannot be obtained and,
therefore, it is the relative stiffness between the engine frame and the connected hull structure which has to be
. 1st order moments in vertical and
horizontal direction. These are of
equal size in MAN B&W engines with
standard balancing.
. 2nd order moments in vertical direction. 4th and higher even order external forces and moments will exist on
In MAN B&W’s experience, the internal
forces and moments of 1st and 2nd
order, caused by the inertia forces on
rotating and reciprocating masses, will
not be able to excite vibrations in the
The X-type guide force moment should,
however, be taken into account because of its higher excitation frequencies and because it acts on the engine
in one of its less rigid directions, particularly in the case of engines with a
high number of cylinders.
Secondary excitation soyces
Torsional vibrations
Torsional vibrations of the entire shaft
system are mainly excited by the tangential force T, Fig. 3. Torsional vibration can, as will be demonstrated in
the next paragraphs, excite vibration in
the hull through the coupling phenomena present in the connecting rod
mechanism and in the propeller.
for the so-called sub- and super-harmonic torsional vibrations. But also external forces F” of (n+l)th and (n-1)th
order will appear for the 1 -cylinder engine, see Fig. 3.
Appendices A, B and C give, as examples, the values of these sacondaty
forces and moments for relevant torsional vibration condition of multi-cylinder engines.
Vibration of blade
section due to
axial vibration
Coupling between vibratory torsional
torque and vibratoty thrust due to
added mass.
Total force on propeller blade
from added mass will be perpendicular to the blade, independent of vibration direction
F~I: Force component contributing
to added moment of inertia
(entrained water) used in tarsional vibration calculation
FAA: Force component contributing
to added mass used in axial
Fig. 5: Torsional vibration induced propeller
Torsional vibration induced moments
and forces due to connecting rod
If a harmonic angular velocity is superimposed upon the nonal uniform rotation of the crankthrow, as in the case
of torsional vibrations, this will cause
harmonic forces and moments to occur.
However, due to the connecting rod
mechanism, the reaction forces will not
solely be of the same order as the superimposed torsional vibration, but significant orders of n-2, n-l, n+l and n+2
will also appear.
One of the best known effects of this is
the (n-2)th and (n+2)th orders in the targential force T, which are responsible
Torsional vibration induced propeller
The propeller can be considered as a
“screw”, optimized to transform power
from a uniform rotating torque into a uniform translatofy moving force, pushing
the ship (the propeller thrust).
With this concept in mind, it is not difficult to imagine that if a varying component is superimposed on the mean input rotational speed (or input torque)
due to vibration of propeller and shafting, this variation will also appear in the
propeller thrust. An investigation of such
an effect is given in Ref. (2).
Fig. 5 shows that this coupling effect
can be explained partly as an added
mass effect, which is also in accordance with the theory in Ref. (2).
Propeller excitations due to
non-uniform wake field
Excitations due to the propeller working
in the non-uniform wake field will be
transmitted to the hull either through the
shaft system as forces and moments or
through the water as pressure fluctuations acting on the hull surface,
lhe forces and moments should also
be considered when calculating the torsional, axial, and lateral vibrations of
the shaft system.
The excitation can be reduced by modifying wake field and propeller design,
however, this subject is beyond the
scope of this paper.
Vibration Modes, Their
Excitation and Control
The general excitations listed in the previous section and the vibration modes
on which they act will be discussed
theoretically and illustrated by relevant
examples in this section. Furthermore,
available countermeasures will be discussed.
Torsional vibrations
Hydrodynamic forces on the propeller
due to vibration of propeller and shafiing will also be able to set up pressure
fluctuations on the hull surface above
the propeller, which can give rise to annoying vibrations.
These phenomena have nothing to do
with the non-uniform wake field.
Axial vibrations
Axial vibrations are excited in the crankshaft from the radial force R as well as
the tangential force T, Fig. 3. The beforementioned torsional vibration induced
propeller thrust will also excite axial vibration in the shaft system. Axial vibrations will create a reaction force in the
thrust bearing which can be considered
as an excitation source for the rest of
the ship.
The control of torsional vibrations is of
vital importance for the propulsion
plant because excessive vibration of
this kind can lead to damage or even
fracture of the crankshaft or the propulsion elements, such as intermediate
shafts, propeller shaft, gears and flexible couplings.
This is also the reason why the classification societies, since the early days,
have required calculation and verification by measurements for this kind of
The classification societies prescribe
two limits, T, and T*, for the torsional
stress in the speed range up to 80 per
cent of MCR, see Fig. 6.
At engine speeds where the lower limit
7, is exceeded, it will be necessary to
Solution A
Rg. 6a and 66: Different shaft systems for a 5L7OMC engine
Solution B
introduce a “barred speed range” in
which continuous operation is prohibited. The upper limit me must not be
exceeded. Above 80 per cent speed
only limit 7, is applicable.
lhe following propulsion systems and
their torsional vibration characteristics
will be treated in the following:
1) Engines with 4, 5 and 6 cylinders,
directly coupled to the propeller
2) Engines with more than 6 cylinders,
directly coupled to the propeller
3) Engines directly coupled to the
propeller and with a small power
4) Engines with a large power take-off
and the possibility of disconnecting
the propeller
Engines with 4,5 and 6 cylinders
With the conventional aft end engine installation, the torsional characteristics
of these engines are dominated by a
resonance of the 1 -node torsional vibration mode excited by the harmonic
order equal to the cylinder number (Le.
5th order 1 -node resonance in case of
a 5-cylinder engine, referred to as main
critical resonance).
This resonance will normally occur somewhere in the middle between minimum
and maximum speed of the engine,
mainly depending on the lengths and
diameters of the shaft system (i.e. total
torsional flexibility of shaft system between propeller and engine).
fig. 6~: Different shaft systems for a 5L7OMC engine
The response at resonance will lead to
torsional stresses in the shaft system
which have to be compared to the limits
stipulated by the classification society
in question. The magnitude of the resonance stresses will depend on the excitations and the damping of the system.
Generally, it can be said that the excitation increases with increasing engine
speed. The system damping will depend
on the ratio between moment of inertia
for propeller and engine, the damping
of the propeller, and the presence of
possible torsional vibration dampers.
Figs. 6 and 7 illustrate three possibilities A, B and C, which are relevant for
the “layout” of the shafting system for
a &cylinder engine directly coupled to
the propeller, but which have widely different torsional vibration conditions.
Solution A is characterised by a relatively flexible shaft system. The material
strength has been increased in order to
reduce the diameter of the shafts, theraby making them even more flexible. A
tuning wheel has been mounted on the
front end of the crankshaft to increase
the ratio between engine and propeller
mass moment of inertia, resulting in
higher damping in the system. The resonance will occur below engine MCR
speed (over-critical).
Excitation order
6th /
Solution C
’ 100
Engine speed 5L70MC
The torsional stresses will be below the
F-limit, but above the 1 -limit, with a
oarrea speea range as a consequence.
Solution E is characterised by a relatively stiff shaft system, e.g. due to the
short distance between propeller and
engine or due to implemented stiff
shaft elements such as shrink-fit couplings, oil distribution box to CP-propeller and ice class requirements on shaft
diameters. This has brought the main
critical resonance relatively close to
MCR, and the resonance stresses will
exceed the upper limit 2 prescribed by
the classification society. In this case
there will be four possibilities:
1) Mounting a torsional vibration damper of appropriate size which will reduce stresses to below the 2 limit,
and the plant will have a barred
speed range
2) Mounting a torsional vibration damper of appropriate size which will reduce stresses to below the 1 limit,
and the plant will have no barred
speed range
3) Increasing shaft diameters in order
to move the main critical resonance to above MCR (solution C)
? 7: Engine speed versus excitation frequency. Natural frequencies for 1 -node torsional
vibration modes art? indicated for solutions A, E and C. Optimum positions of natural
frequency of PTO systems indicated by shaded areas
4) QPT (Quick Passage through a
barred speed range Technique) for
CPP-installation, Ref. 12
The procedure can be described as
a. The carrying out of ordinary
torsional vibration calculations in
maximum pitch condition
b. The carrying out of ordinary
torsional vibration calculations in
minimum pitch condition using
rather pessimistic propeller
damping values
c. The establishment of a simulation
model of ship/propeller/shafUng/
engine/governor which, in the
barred speed range during steady
state operation, Fig. 8 (upper
part), gives results coinciding
with the results of the ordinary
torsional vibration calculations
d. The simulation of engine starting
and stopping with rapid passage
through the barred speed range,
Fig. 9 (upper part)
e. The evaluation of stresses in the
barred speed range based on
results of the start and stop test
simulations for rapid passage
through the barred speed range
In order to ensure the rapid passage through the barred speed
range, a so-called “critical speed
unit” should be installed. This
unit operates on the speed setting signal in such a way that
automatic rapid passage through
the barred speed range is obtained when the engine is operated via the bridge manoeuvring system, as well as when
operating from the engine control room
I< Steady state >I
Start of simulation
Toraw t
ki4m I
Enlarged time scale
- 409
- 818
Fig. 9: Comparison between simulated and measured torque in
the intermediate shaft during starting of main engine and passage
through thebarred speed range (minimum propeller pitch). (As an
example, a 5L5OMC engine is used)
Solution C is obtained by increasing the
diameter of shafts until the main critical
resonance is positioned approximately
40-45 per cent above the nominal
speed (undercritical). Due to the large
shaft diameter (large moment of resistance), only moderate torsional stresses
appear even though the varying torsional
torque in the shaft is high.
fig, 8: Simulated steady state torque and measured torque at minimum pitch. (As an example, a 5L5OMC engine is used)
Soletjon C is chosen either as an unavoidable consequence tor a very
short shaft system or because the ship.I.
owner nas speclrlea mar me sn,p musr
not have any barred speed range.
Besides avoiding a barred speed range,
solution C is characterised by a rather
high varying torque in the shaft which,as already explained, will induce a rather
high varying thrust, called torsional vibration induced propeller thrust.
It should be mentioned that under adverse conditions the varying thrust can
reach levels of up to 50% per cent of
the mean thrust, which is far above
what a propeller designer would accept
as an excitation from the non-uniform
wake field.
Of the three alternatives, A will normally
involve the lowest cost. Solutions A, B
or C cannot be directly related to a
specific engine type, only detailed torsional vibration calculation at the design
stage will reveal the optimum solution.
Trends in the choice and feasibility of
the solutions can be summarised as
4-cylinder engines:
Solution A:
less feasible -not very common
Solution B:
feasible -not very common
Solution C:
feasible -very common
5-cylinder engines:
Solution A:
feasible -very common
Solution S:
feasible -not very common
Solution C:
feasible -common
6-cylinder engines:
Solution A:
feasible also without tuning wheel very common
Solution B:
feasible -not very common
Solution C:
not feasible
Engines with 7 or more cylinders
For such engines, the 1 -node main
critical resonance is not normally important, because it will occur close to or below the minimum speed of the engine.
Furthermore, the 7th order or higher
order excitations of the torsional vibration are considerably smaller than the
4th, 5th and 6th order, which means
that barred speed ranges are not normally required.
As a “rule of thumb”, the lowest natural frequency of the PTO/PTI masselastic system should not be higher than
75 per cent of the frequency corresponding to the main engine speed.
This will give low torsional loads in the
PTO system due to the fact that overcritical vibration condition is obtained
for all harmonic excitations from the
main engine at MCR, see Fig. 7.
Engines with large power take-off
However, the Z-node torsional vibration mode (one node in the crankshaft)
begins to be important and needs attention.
Major resonances for this vibration mode
should be avoided close to MCR. Small
torsional vibration dampers might be
Certain types of ships, such as ferries,
cement carriers and shuttle tankers,
have operating conditions that require
high auxiliary power, simultaneously
with propulsive power. This has been
met by controllable pitch propellers
combined with relatively large power
take-offs comprising clutches, elastic
couplings, gears, generators and/or hydraulic power packs.
Engines with small power take-off
It has become very popular to connect
a power take-off (PTO) to the crankshaft or propulsion shaft system. Some
years ago, also exhaust gas driven
power turbines were introduced, delivering their power to the propulsion
shafting power take-in (PTI). A common
feature of both the PTO and the PTI is
that they are connected to a gear system which needs protection from the
relatively high torsional excitation from
the crankshaft.
In the MAN B&W standard designs, the
PTO and PTI are mounted on the fore
end of the crankshaft, as a compact
unit, and the protection is obtained by
installing an elastic coupling between
the propulsion shafting and the abovementioned gear.
Normally, when the PTO/PTI represents
a power of less than 10 per cent of the
main engine power, the vibration modes
of the PTO/PTI system will not influence
the vibration modes of the propulsion
shaft system. This means that the main
propulsion shaft system can be designed and determined regardless of
whether a PTO/PTI is to be installed
later on.
The torsional vibrations of such installations are very complex, and need careful investigation dun’ng the design stage.
The design philosophy with respect to
torsional vibrations in a power take-off is:
The elastic couplings are necessary
to facilitate alignment and to protect
the gears from the high frequency
torsional excitation of the main engine. Such excitation may, in combination with backlash, produce harmful vibration in the gear
The elastic coupling, or couplings,
should be sufficiently flexible to ensure a natural frequency in the PTOsystem of either approx. 1.5 times
the mainengine speed, or below
0.75 times the main engine speed,
see Fig. 7. This will give main critical
resonances in the PTO-system (4th,
5th and 6th order) at very low speed
or even below the minimum speed.
Furthermore, the 1 st and 2nd order
excitation, which becomes dominant
in case of misfiring, will have resonance away from the nominal speed.
Such tuning of the natural frequencies will normally require very elastic
2) Coupling of torsional vibrations of
the crankshaft to responses in the
axial direction (mechanism: twist of
crankshaft will cause axial deflection).
This coupling depends on the geometry of the crankshaft and is found
where pronounced torsional responses exist. For engines with a
relatively low number of cylinders, it
will almost exclusk&y be found in connection with barred speed ranges
Shafting system
Mass-elastic system
For the following reasons, the axial vibration damper is standard for a// cylinder numbers of MC engines:
kg. 10: Mass-elastic system for axial vibration calculations. Axial deflections of O-node and
l-node mode shape
The combination of low natural frequency and high moment of inertia in the
PTO-system will require special facilities in the engine governor if instabilities in the system are to be avoided.
Axial Vibrations
Axial vibrations are longitudinal shafting
vibrations. Fig. IO shows the masselastic system used for axial vibration
calculations and the mode shapes of
the two lowest modes which are of relevance.
MC engines with more than six cylinders will have main critical resonance
with O-node vibration mode below
MCR speed. For 4,5, and 6-cylinder
engines, the main critical resonance
will occur outside the normal speed
range. However, for 5cylinder S-MC
and 6-cylinder K-MC, L-MC, and SMC engines, the main critical 5th and
6th order resonance, respectively, will
be situated very close to MCR speed.
The 1 -node vibration mode is normally
of less importance. Its natural frequency is determined by the mass and stiffness of the entire shafting system. Especially the stiffness of the thrust bearing
and its support is very decisive.
Normally, the natural frequency is so
high that no dynamic amplification of
this mode will occur.
Axial vibrations are excited by:
. Radial and tangential components of
the combustion pressure and mass
forces in the individual cylinders. The
fact that the pmaJPe ratio of modern
engines has increased considerably
(see Fig. 1) means that especially the
radial components of orders higher
than the 4th order have increased
. Propeller excitation of the blade frequency and multiples hereof from the
non-uniform wake field
Excitations caused by responses from
other vibration modes, such es:
1) Torsional vibration induced propeller
thrust, the magnitude of which depends on how the torsional vibrations (see Fig. 6) are situated. This
excitation may initiate heavy varying
forces in the thrust bearing
First and foremost, the axial vibration
amplitudes are to be kept below a
certain level to protect the crankshaft
against too heavy extra stresses
caused by axial vibrations. For this
reason, MC engines with six or more
cylinders are provided with an axial
vibration damper
The second reason for installing an
axial vibration damper is to be able
to control varying forces in the thrust
bearing, which may excite the hull
structure. In order to control these
varying forces, 4 and 5-cylinder engines are also provided with an axial
vibration damper
The axial vibration damper effectively
reduces the varying forces generated
in the crankshaft and acting on the
thrust bearing. The varying forces originating from torsional vibration induced
propeller thrust are, on the other hand,
left practically unaffected by the axial vibration damper.
Fig. 11 shows measurements of the
varying thrust in the intermediate shaft
of a 4L60MCE engine with an active
axial vibration damper. The figure shows
the thrust originating from the 8th order
1 -node torsional resonance and the
4th order flank. With an inactive damper, the magnitude of the varying thrust
is the same.
For plants on which the torsional vibration induced propeller thrust is negligible, it will still, despite the use of an
axial vibration damper, be necessary to
predetermine the varying force in the
thrust bearing. The damper will leave a
varying force in the thrust bearing of a
magnitude corresponding to the static
deflection of the crankshaft caused by
the mass and gas forces. On account
of the evolution in the pmJpe ratio of
modern longstroke engines, especially
the radial components of these forces
have increased, resulting in a considerable static deflection of the crankshaft.
The above shows that the axial vibration and related torsional vibration
problems should be solved at the design stage of the ship through cooperation between the engine builder and
the shipyard. Especially the force in the
thrust bearing should be determined in
each individual case by combining the
forces from the torsional vibration induced propeller thrust, the forces from
axial vibrations of the crankshaft, and
the forces from coupled axial and torsional vibrations in the crankshaft.
4L6OMCE thrust-variation
86.111 dmin
In order to be able to present solutions
to such cases, MAN B&W use a computer program including FEM (Finite
Element Method) based crankshaft
models (Fig. 12) which allows the firing
order, crank throw geometry, and bearing stiffnesses to be represented. It also
allows the model to be excited directly
by the tangential and radial forces actingon the crankpins, Fig. 13.
An example:
When designing the shafting for a 5cylinder engine, a choice can be made
between an overcritical layout, i.e. using
small diameter shafts and, if necessary, a barred speed range, or an undercritical layout, i.e. the use of large diameter shafts and no barred range.
4L60MCE thrust-variation
60-W r/min
The reason for the interest in Scylinder
engines is that many of these installations are apparently designed for undercritical operation without sufficient
allowance being made in the hull structure for excitations from the thrust
bearing originating from axial vibrations
and the vibrations coupled to them.
Fig. 11: Torsional vibration induced propeller thrust measured in the intermediate shaft ofa
4L60MCE engine. Response of 8th order 1 -node torsional resonance and 4th order flank is
Degree of freedom
fig. 12: Half crantihrow FEM-mode/led in
order to cauy out vibration and stress analysis. Complete crankshaft is mode/led from
this half w&throw by the dedicated system HIFINEL-CIWNK
fig. 13: Crankshaft model
To illustrate the issues with, in particular, undercritical operation, it will be
necessary to recapitulate some conclusions relating to torsional vibrations in
the two layouts.
mode and the O-node torsional mode,
the conditions in Fig. 14, centre, are obtained. The torsional amplitude on the
propeller is the difference between the
two contributions. As these are typically of the same magnitude, the resultant
propeller amplitude at MCR is small compared with that of an undercritical layout.
For a shafting design where the main
critical is situated below but rather
close to MCR, and a torsional vibration
damper is used to control the stresslevels (Fig. 6, solution B), the result will
be a relatively high torsional amplitude
at the propeller. This will give a significant contribution to torsional vibration
induced propeller thrust.
In the case of undercritical layout, the
resonance at the main critical order (in
this case 5th order) should be situated
40-45% above MCR. Measuring results on the thrust bearing of a 5L70MC
confirm the calculations of the 5th order
varying thrust. Depending on propeller
and shafting, values of +200 to +400
kN have bean found at MCR.
The FLS-M vibration compensator, Fig.
15, has been successfully applied as a
so-called thrust pulse compensator in
order to reduce the torsional vibration
induced propeller thrust on 5-cylinder
engines that are coupled to largediameter shafting.
The aspects of the undercritical layout
are illustrated in Fig. 14, upper. At MCR,
the 5th order l-node torsional vibration
resonance is situated above MCR. The
5th order O-node torsional vibration
mode, normally referred to as irregularity, can be considered as over-critical. Thus it can be assumed that the
torsional amplitude on the propeller is
a sum of the two contributing torsional
When passing through a resonance,
Fig. 14, lower, the phase of the pertaining amplitude is changed 180 degrees.
Accordingly, when the shaft system layout is overcritical at MCR, relative to
both the 5th order 1 -node torsional
Corresponding values for the 5th order
varying thrust on the thrust bearing,
when having overcritical layout, are
typically 60 to 100 kN.
The thrust pulse compensator counteracts the varying thrust from a position
on a foundation on the tanktop close
to the thrust bearing; Fig. 16, of a
5L60MC engine.
Under-critical running
Propeller: 5th order response of O-node and 1 -node adds at MCR
free end
Over-critical running
Propeller: 5th order response of O-node and 1 -node subtract at MCR
free end
Phase change due to passage of natural frequency
Propeller amplitude (torsion) for 5 cylinder engines
fig. 14: Torsional response for 5cylinder engines shown in order to illustrate torsional
vibration induced propeller thrust
Upper : situation when running under-critical
Centre: situation when running over-critical
Lower : phase change when passing through a resonance
A: AC Servomotor
B: Gear wheels
C: Flyweights
fig. 15: FLS-M Vibration compensator
Fig. 17 outlines the results of vibration
measurements at the wheelhouse level
of the superstructure in the longitudinal
: direction. It is seen that with the opti~ mum phase of the counterweights of
I the thrust pulse compensator, a reduc~ tion of the vibration level with a factor
‘,; of 8-10 is obtained.
External Forces and Moments
The entire ship forms a mass-elastic
system, with natural frequencies and vibration modes. The horizontal and ver~ tical bending modes of the hull girder
and the corresponding natural frequenties can be calculated. Determination
of vibration modes with 4, 5 and more
nodes requires comprehensive calcu:: lating procedures, whereas modes
with 2 and 3 nodes can be calculated
I by more simple procedures.
fig. 17: 5LtiOMC. Measurements at 92 r/mn at the wheelhouse in
longitudinal direction
In order to obtain the correct decision
basis at the engine contract stage, information about these vibration modes
should be available, as this will make it
possible to decide the measures to be
taken to control the responses from
these vibration modes.
Hull girder vibration modes are excited
by forces and moments acting on the
hull girder, Fig. 18. Excitations of hull
girder vibration modes originating from
the engine are external forces and mo-
ments generated by the inertia forces
of unbalanced rotating and reciprocating masses.
For MAN B&W engines, the external
forces can -for all practical purposes be considered to be zero, due to their
small size. Normally, only the external
moments of 1st and 2nd order need to
be considered. However, modest moments of other orders exist; an example
is shown in Appendix A.
1 st order moments act in both the veniCal and horizontal directions. For MAN
B&W engines with standard balancing,
these moments are of identical magnitudes.
For engines with five cylinders or more,
the 1 st order moment is very rarely harnful to the ship. However, with 4.cylinder
engines, precautions need to be considered.
Jewantinodes (translatory deflection):
dear nodes (angular deflection):
Forces excitation, F, gives forced responses
Moment excitation, M, gives forced responses
The 2nd order moment acts only in a
vertical direction Precautions need only
be considered for 4, 5, and 6-cylinder
To judge the size of the external moments, the so-called Power Related
Unbalance (PRU) has been defined,
Fig. 19.
fig. 18: Excitation of the hull girder modes
Characteristics of mode shapes and their excitations
On 4-cylinder engines, the 1 st order
moment is controlled in the following
According to 1st and 2nd order external moments in layout point LI
0 1 st order
- 2nd order
Compensator most likaely
Com!xnsator likelv t
fig. 19: Power related unbalance for the MC engines
Defined to judge the size of the external moments
adjustable counterweights
1 st order moment compensator
Resonance between the vertical moment and the 2-node vertical hull girder mode may often be criiical, whereas the resonance between the horizontal moment and the 2-node horizontal
hull girder mode normally occurs at engine speeds higher than nominal. As
standard, 4-cylinder engines are fitted
with adjustable counterweights. as illustrated in Fig. 26. These counterweights
reduce the vertical moment to an insignificant value (although simultaneously
increasing the horizontal moment); thus,
this resonance of the 2-node vertical
hull girder mode is easily dealt with.
In rare cases, where the 1 st order moments will cause resonance with both
the vertical and the horizontal 2-node
hull girder mode in the normal speed
range of the engine, a 1 st order moment
compensator, as shown in Fig. 21, can
be introduced in the chain tightener
wheel, reducing the horizontal 1 st order
moment to a harmless value. The com17
Standard balancing
Balancing giving
reduced MW
reduced MIH
Fig. 20: Adjustable counterweights for 1st order external moment
pensator comprises two counter-rotating masses, rotating at the same speed
as the engine is running.
Since resonance with both the vertical
and the horizontal hull vibration modes
is rare, the standard engine is not prepared for the fitting of such compensators
Resonance between the 2nd order vertical moment and the 3,4, and 5.node
hull girder vibration modes are possible
in the normal running range of the engine, Fig. 22, upper. In order to control
the resulting vibratory responses, a
second order compensator can be installed on 4, 5, and 6.cylinder engines.
Several solutions, from which the most
cost-efficient one can be chosen, are
Fig. 21: Compensation of 1st order external moment
available to cope with the 2nd order
vertical moment:
a) No compensators, if considered unnecessary on the basis of the natural
frequency, nodal point, and size of
the 2nd order moment
b) A compensator mounted on the aft
end of the engine, driven by the main
chain drive, Fig. 22
c) A compensator mounted on the
fore end, driven from the crankshaft through a separate chain drive
d) An electrically driven compensator,
synchronized to the correct phase
relative to the free moment. This
type of compensator requires an
extra seating to be prepared,
preferably in the steering gear room
where deflections are largest and
the compensator therefore has the
greatest effect
e) Compensators on both the aft and
fore ends of the engine, completely
eliminating the external 2nd order
moments, Fig. 22
Solutions (b), (c) and (d) are force generating compensators, which are ineffective if they are placed in a node of the
actual hull girder mode, but effective if
they are placed away from the node,
i.e. close to an antinode.
If the node of the critical hull girder
mode is situated close to the engine,
solutions (d) and (e) should be considered.
Frequency of engine moment
MZV = 2 x engine speed
cpm Natural frequency vertical hull vibrations
Statistics of tankers and
bulk carriers
in the actual power range
Expected node position
/I !
20,000 40,000 60,000 60.000 dwt
Compensating moment
Compensating force of
elcectttcally driven compensator
Compensating force of
compensator in the main chain
M2V: 2nd order external moment to
be outbalanced
FB = Lg node
As LB node is given with greater relative
uncertainty than Ls node, Fo can be
-determined more precisely than Fe
Lc node
fig. 23: 2nd order moment balancing.
SensWW of force generating compensators
due to the node position
Moment from compensator
fig. 22: Compensation of 2nd order vertical external moment. 3, 4 and 5.node vertical hull
girder mode should be considered
If placed in the steering gear room, the
electrically driven compensator d) has
the advantage -compared to the other
compensators (b) and (c) -that it is not
as sensitive to the positioning of the
node, Fig. 23.
If compensator(s) are omitted, the engine can be delivered with preparation
for the later fitting of compensators. This
preparation must be decided at the contract stage of the engine. Measurements
taken during the sea trial, or later during service with special loadings of the
ship, will show whether compensator(s)
have to be fitted or not.
In addition to these above discussed
external forces and moments, there
are also secondary external forces and
moments,originating from torsional vibrations. An example concerning an
8S60MCE is given in Appendix A. Secondary external forces and moments
originating from torsional vibrations are
mainly of higher order and will be capable of exciting local vibration modes.
These secondary forces and moments,
which have not so far been reported
as a source of vibration, should be considered at the design stage. They will
appear as a result of thorough torsional
vibration calculations.
Engine Structure and
Double Bottom Vibrations
H - mode
X mode
fig. 24: The three major modes of the engine column structure, H, X and L-mode
The vibration modes of the engine
frame are part of more comprehensive
vibration modes in the aft end of the
ship. There are three major modes:
f 0.61 mm
1. H-mode:
Transverse vibration mode with antinode at the engine top level.
In-phase amplitudes from the first
cylinder to the last cylinder, Fig. 24
2. X-mode:
Transverse vibration mode of
engine top where the foremost part
and the aftmost part of the engine
are 180 degrees out of phase,
having node at the centre part of
the engine, Fig. 24
3. L-mode:
Longitudinal vibration mode with
anti-node at the engine top level,
Fig. 24
The natural frequencies of these vibration modes are to a large extent determined by the stiffness of the seating and
the double bottom on which the engine
is installed. Fig. 25 shows the measured mode shape of a longitudinal
double bottom engine column vibration
mode for a 5L80MCE engine. It appears
that the majority of the elastic deformations
. occur in the double bottom. The
natural rrequency 1s tneretore mainly
determined by this structure, as the en-
L - mode
i oooooc
fig. 25: Longitudinal double bottom engine column vibration mode measured on a
5LBOMCE engine. Main critical 5th order has resonance in the running range
gine as such, compared to the double
bottom, has a much greater stiffness.
A similar example could be given for
the H-vibration mode.
H and X-modes are excited by guide
force moments of the H and X-types,
Fig. 4. The primary values of these
guide force moments can be calculated for each engine type on the basis
of its gas and mass forces. This kind of
excitation is inherent in all engines.
Secondary values of the H and X-type
guideforce moments originate from torsional vibrations and will, therefore, be
different for each installation, even for
the same type of engine. Appendix B
shows primary and secondary values
of guide force moments for a 5L70MC
engine with two different shafting layouts. It is seen that the secondary
values are moderate.
We have experienced some cases
where a proper detuning effect was not
obtained, even though the stiffness requirements had been fulfilled: In this connection, it is relevant to bear in mind
the development during the past ffieen
years, see Fig. 1. Today an engine with
a specified output typically has fewer
cylinders and is considerably higher than
previous engine types, i.e. the height/
length ratio is different. To cope with this
development, classification societies
and shipyards should consider revising
their requirements to the double bottom design.
For two reasons, L-vibration modes
have attracted increasing attention:
As an alternative to the traditional friction type of top bracing, Fig. 26, the hydraulically adjustable top bracing has
been designed for use on vessels having large deflections due to heavy sea,
loading/unloading, etc.
This system, shown in Fig. 27, consists
basically of a hydraulic cylinder and two
spherical bearings. Oil is supplied from
the camshaft lubricating oil system, and
a relief valve prevents the build-up of
excessive forces.
This hydraulically adjustable top bracing is intended for one-side mounting,
and will provide a constant force between engine and hull, irrespective of
deflection and, as such, will still act as
a detuner of the double bottom/main
engrne system.
The excitation of the thrust bearing
has increased
The guide force moments of an 6S6OMC
engine for two alternative firing orders
are given in Appendix C. In this case,
values for the guide force moments
originating from the Z-node torsional
mode are noticed.
The L-mode has in many cases
become resonant with the main critical order in the relevant speed range
(example: see Fig. 25). This is the
most important reason and, again, it
is suggested that the requirements
to the double bottom design should
be reconsidered
The system has been commercially applied in a number of newbuildings with
good results.
L-modes are excited by secondary phenomena only, i.e. installation dependent forces. The example in Fig. 25
shows a case where the L-mode shape
is excited mainly by varying forces in
the thrust bearing initiated by torsional
vibration induced propeller thrust.
In certain cases, longitudinal top bracing has been introduced in order to detune critical orders and the natural frequency of the L-mode. By means of
this arrangement, vibrations in the longitudinal direction have been reduced
to a satisfactory level.
It should be noted that the hydraulically
adjustable top bracing does not increase the building width of an engine,
compared to the friction type bracing.
Another source of excitation is varying
forces in the thrust bearing caused by
axial vibrations of the crankshaft.
Where axial vibrations of the crankshaft
are the main source of excitation, the
longitudinal vibration levels can also be
reduced by means of an axial vibration
H and X-vibration modes are traditionally controlled by bracing the engine
top to the hull structure so as to obtain
resonances with the critical orders situated above the relevant speed range,
thus detuning the system. In order to
obtain a sufficient detuning effect, i.e.
to bring certain resonances with critical
orders above the relevant speed range,
stiffness requirements are specified for
the attachment of the bracing to the
engine room structure.
As mentioned earlier, L-mode excitations are of a secondary type. This
means that the excitation level is determined by vibration characteristics of
other vibration modes. L-mode excitations are determined by means of axial
and torsional vibration characteristics,
and these are to be calculated and synthesized at the design stage of the ship
in order that appropriate precautions
can be taken.
Obviously, this system increases the
overall costs and, therefore, it will replace the friction type only when necessary.
Vibration Levels and Their
There are two basic criteria for determining acceptability level of vibrations:
1) The vibration level must not result in
stress levels that may cause fatigue
damage to the engine, or the
connected hull structure
2) Vibration must not result in
annoyance and/or discomfort for
the operating personnel
With a view to fulfilling these criteria,
certain limits to vibration levels can be
prescribed, and it is common practice
to specify different limits in different frequency ranges:
a) Lower frequency range:
displacement limit
b) Intermediate frequency range:
velocity limit
c) Upper frequency range:
acceleration limit
Rg. 26: Friction type top bracing
The displacement limit in the lower frequency range is determined by static
stress level considerations, In the intermediate range, the velocity limit will keep
the kinetic energy constant throughout
the range, resulting in decreasing permissible displacements, The acceleration limit in the upper frequency range
decreases the permissible displacements further so as to control noise
The limits applying to MAN B&W twostroke engines are given as single order
peak amplitudes, X:
S = *xsin([email protected])
The two-stroke low speed diesel engine is designed to cope with rather
high internal varying forces and, consequently, rather high limits are allowed
for vibration levels in its main structure.
Fig. 28 shows the limits which are acceptable for MAN B&W two-stroke engines.
If vibration levels in zone II (see Fig. 28)
have been measured under a certain
condition of the ship, it should be borne
in mind that zone Ill readings, i.e. not
acceptable, might occur under other
conditions, such as:
1: different draught of the vessel
2: different trim of the vessel
3: different distribution of ballast load
4: different engine loading
5: changing sea condition
Fg. 27: Hydraulically adjustable top bracing
Mechanical vibrations of steel structures
are of a complex nature. When the steel
structure comprises a ship and a twostroke low speed diesel, a coagency of
the excitation sources and the natural
frequencies of the structures may lead
to situations of annoying vibration unless due consideration is paid to this
Based on all the experience gathered
up till now, we are confident that the
necessary means for predicting and
counteracting vibration on board ships
with two-stroke diesel engines are
available today.
The fact that, even today, ships are,
from time to time, delivered with unsatisfactory vibration conditions reflects
that the whole procedure from project
to actual ship in service is subject to
compromises which consider other aspects than the vibrational and that predictions of vibrational behaviour, even
when based on advanced computer
programs, are still subject to uncertainties.
Zone I: Acceptable
Zone I(: Vibration will not damage the main engine, however, under adverse
conditions, annoying/harmful vibration responses may appear in the
connected structures
Zone Ill: Not acceptable
In order to utilise the available possibilities, its is recommended that yards,
owners, and engine builders discuss
the vibration aspects at an early stage,
at least before signing the contract, so
as to ensure that the best possible solutions are selected and incorporated in
the project right from the start.
Fig. 28: Vibration limits
1) Prevention and Remedy of Ship
Vibration (Parts 1 and 2)
By Masaki Mano, Yoshio Ochi and
Kaatsuya Fujii, Ishikawajima-Harfma
Heavy Industries, Co., Ltd. Japan
Shipbuilding & Marine Engineering,
Vol. 12, No. 2, 1978
2) Hydrodynamic Reactions to
Propeller Vibrations
By Dr. S. Hylarides and
Dr. W. van Gent
Trans I Mar E (C) Vol. 91
Conference No. 4. Paper C37, 1979
Recommendations Designed to
Limit the Effects of Vibrations On
Board Ships
Bureau Veritas, 1979. Guidance
Note NI 138 A RD3, June 1979
Guidelines for Prevention of
Excessive Ship Vibration
Bv H. Johannessen and K.T. Skaar
SiAME Transactions, Vol. 88,
1980, pp. 319-356
Balancing the First Order External
Moments of MAN B&W Four
Cylinder Low Speed Engines
By H. Lindquist
MAN B&W Diesel A/S, Copenhagen
The Motor Ship, March 1983
Vibration of Long Stroke Type
Marine Diesel Engine
By Koji Kagawa, Kazunobu Fujita
and Tadahiko Hara
Mitsubishi Heavy Industries Ltd.
International Symposium on Ship
Vibrations, Geneva 1984
New Calculation Method on
Complicated Vibratory Behaviour
of A&Part of Shios
By Yasuo Yoshida and
Makoto Maeda
Ishikawajima-Harima Heavy
Industries Co., Ltd., Tokyo, Japan.
International Symposium on Ship
Vibrations, Geneva, 1984
Fore and Aft Vibration of Main
Engine and Ship Vibrations due to
the Torsional Vibration of 5.cylinder
Main Engine
By Shinji Kumazaki
Ishikawajima-Harima Heavy
Industries Co., Ltd., Japan
ICMES Conference, 1984
Exciting Forces of Ship Vibration
Induced by Torsional and
Longitudinal Vibration of the
Shafting System
By K. Fujii and K. Tanida,
Ishikawajima-Harima Heavy
Industries Co., Ltd., Japan
ICMES Conference, 1984
IO) Vibration of Long Stroke Diesel
Engine with a Small Number of
By MitSUN Mizuuchi, Kohei
Matsumoto, Toshimasa Saitoh.
March, 1985
11) Vibration Control in Ships
By VERITEC Marine Technology
Consultants, Veritasveien 1,
N-l 322 H&k, Norway, 1985
12) A theoretical and experimental
investigation of propeller damping
and transient torsional resonance
By L. Bryndum and S.B. Jakobsen,
MAN B&W Diesel A/S
M. Matosevfc, Uljanik Engineering
Company Ltd.
ICMES Conference, 1990, Newcastle
13) Vibration Aspects of Long-Stroke
Diesel Engines
By L. Bryndum, S.B. Jakobsen and
M.C. Jensen
MAN B&W Diesel Xi
2nd International MarineEngineering
Conference 1991 Shanghai, China
14) Axial Vibrations of Crankshafts of
Long-Stroke Diesel Engines, and
the Control of Their Influence on
Crankshaft Strength and Hull
Vibration Conditions
By S.B. Jakobsen and L. Bryndum,
MAN B&W Diesel A/S
T. Fukuda and M. Ohtsu
Mitsui Enaineerina & Shiobuildina
CIMAC 91, Florence Paper 061
15) Coupled Axial and Torsional
Vibration Calculations on Longstroke Diesel Engines
By S.B. Jakobsen
MAN B&W Diesel A/S
The Society of Naval Architects
and Marine Engineers
1991 Annual Meeting, New York,
Paper No. 14
Appendix A
Example: ES60MCE. 102 r/min, 12,000 kW
External Forces and Moments (vertical)
Firing order:
Firing order:
6 ’ 8
Primaly values
given at
102 rlmin
I st order moment:
b348 kNm
Ith order moment:
t75 kNm
Secondary values due to
Torsional Vibration Responses
Excitation (torsional amplitudes):
Primary values
given at
102 r/min
1st order moment:
f174 kNm
11 th order (92 r/min)
zk2.5 nmd
4th order moment:
*300 kNm
Secondary values due to
Torsional Vibration Responses
Excitation (torsional amplitudes):
+I .O mrad
11 th order (92 r/rain)
X2.5 mrad
Cyl. No.
1 2 3 4 5 6 7 6
Secondary values at 92 r/min:
Free forces:
12th order: *198 kN
13th order: +104 kN
*1 .o mra,
Cyl. No.
1 2 3 4 5 6 7 8
Secondary values at 92 rfmin:
Free forces:
12th order: +299 kN
Free moments:
Free moments:
10th order: &986 kNm
Excitation (torsional amplitudes):
12th order (84 rlmin)
fo.5 mrad
Excitation (torsional amplitudes):
12th order (84 rfmin)
GO mrad
fo.5 mrad
10th order: * 92 kNm
f2.0 mrar 1
12 3 4 56 78
Secondary values at 84 r/min:
Free forces:
1 lth order: f101 kN
13th order: +122 kN
Cyl. No.
1 2 3 4 5 8 7 6
Secondary values at 64 r/min:
Free forces:
11 th order: -01 kN
13th order: +245 kN
Free moments:
Free moments:
Cyl. No.
14th order: * 38 kNm
EXCitatiOn (torsional amplitudes):
12th order (78 r/min)
3il85 m?ad
11 th order: f 61 kNm
13th order: + 75 kNm
14th order: f 38 kNm
Excitation (torsional amplitudes):
13th order (78 rlmin)
f0.8 mrad
XMS mrad
f0.8 mm
Secondary values at 78 r/min:
Free forces:
12th order: ? 52 kN
Cyl. No.
12 3 4 56 78
Secondary values at 78 rlmin:
Free forces:
12th order: -08 kN
Free moments:
Free moments:
Cyl. No.
1 2 3 4 5 6 7 8
14th order: f376 kNm
14th order: f 94 kNrr
15th order: f 67 kNrr
Appendix B
Example: 5L70MC, 95 rlmin. 10,400 kW
Guide Force Moments -H-type
Secondary values of guide force mom& (95 rImin):
5th order: 5213 kNm
5th order: f571 kNm
7th order: *I3 kNm
8th order: f 7 kNm
2nd order: f4 kNm
Secondary values of guide force moments (96 rimin):
7th order: +15 kNm
5th order: ti5 kNm
1Mh order: -3 kNm
Secondary values of guide force moments (68 rimin):
10th order: +I74 kNm
Example: SL70MC. 95 rlmin, 10,400 kW
Guide Force Moments
Excitation (torsional amplitudes): 5th order at 95 dmin
k 31 kNm
522 kNm
f137 kNm
f 6kNm
+ 3kNm
k 20 kNm
Cyl. No.
Secondary values of guide force moments (95 rlmin):
7th order: +75 kNm
3rd order: f3S kNm
8th order: *39 kNm
2nd order: k27kNm
Excitation (torsional ampliiudes): 5th order at 95 rimin
Secondaly values of guide force moments (95 r/min):
3rd order: f12 kNm
51h order: f18 kNm
71h order: f25 kNm
2nd order: * 9 kNm
8th order: fl3 kNm
Excitation (torsional amplitudes): 7th order at 96 rimin
m0.7 mrad hkO.35mrad
Secondary values of guide force moments (96 rlmin):
7th order: *35 kNm
Appendix C
Example: 6S60MCE. 102 Urnin. 12.000 kW
Guide Force Moments -H-type
13th order: +222 kNm
11 th order (92 rImin)
1 2 3 4 5 6
1 2
13lh order: H33 kNm
1 Ith order: k 54 kNm
161h order: f 63 kNm
3 4
1 lib order: T? 76 kNm
Example: 8S60MCE, 102 rImin, 12.000 kW
Guide Force Moments -X-type
f181 kNrn
+350 kNm
SO2 kNm
HI 70 kNm
+ 29 kNm
+ 11 kNm
+ 56 kNm
+ 11 kNm
Excitation (torsional amplitude):
1 Itk order (92 rimin)
+2.5 mrad
ti.5 mrad
C y l . N o . 12 3 4 5 6 7 6
Secondary values of guide lorce moments (92 rImin):
6th order: f 63 kNm
91h order: f 45 kNm
lOth order: k 40 kNm
k 9 1 kNm
f 209 kNm
f1401 kNm
f 451 kNm
f 14kNm
5 kNm
+ 28kNm
f 43kNm
Excitation (torsional amplitude):
lZh order (64 r/min)
32.0 mrad
22.0 mrad
1 2 3 4 5 6 7 6
Seandaly values of guide force moments (64 r/m
9th order: f 39 kNm
10th order: f 16 kNm
Excitation (torsional [email protected]:
13th order (76 rfmin)
M.65 mrad
Excitation (torsional amplitudes):
1 Ith order (92 rimin)
fl .O mrad
ti.65 mrad
C y l . N o . 12 3 4 5 6 7 6
Seconday values of guide force moments (76 rImin):
16th order: + 35 kNm
15th order: + 21 kNm
fl .O mrad
Cyl. NO.
12 3 4 5 6 7 8
Seccn* values of guide face moments (92 rImin
9th order: f 34 kNm
10th order: + 35 kNm
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