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Engine dynamics and vibration control
AUTHORS : Hannu Tienhaara, Head of Calculation & Simulation, R&D, Wärtsilä in Finland
Heikki Mikonaho, Strength & Structural Dynamics, R&D, Wärtsilä in Finland
Fig. 1 – A Wärtsilä 8L46 engine with ABB TPL turbocharger.
The increasing demand for lowering
the noise and vibration levels of
engines has forced manufacturers to
make use of advanced analysis and
simulation tools.
In most cases, the practical means to
reduce vibration is simply to detune the
lowest natural frequencies away from the
main dynamic excitation frequencies.
When detuning natural frequencies, the
most effective course is to concentrate on
the heavy structures built on to the engine
and its mounting. A good example is the
turbocharger, because its influence on the
vibration system is very dominating due
to its relatively large mass (Figure 1).
In certain problematic situations, a
tuned mass damper can be used to change
the vibration system dramatically.
As regards reducing vibration on the
Wärtsilä 9L46 engine, a study ended
up with two different solutions: For the
current production engines, a new firing
order was introduced offering a better
distribution of the excitation forces at
certain harmonic orders. This solution
requires the use of a special balancing
device in order to cope with the increased
first order free couples. However, changing
the firing order on a 9-cylinder engine is
not a feasible solution for existing engines
already in the field. For these engines
the tuned mass damper was chosen as
being the most suitable solution.
A tuned mass damper is a device
whereby an additional mass is mounted
with flexible elements on the vibrating
machine. The damper is tuned in
such a way that its own vibration is
producing a counter force against the
main structure’s vibration. Normally a
damper is tuned to dampen a certain
natural frequency, but in the case of a
constant speed engine, it can also be
tuned to a specific excitation frequency.
The two biggest challenges in designing
and tuning this kind of a system are:
1)Handling a wide range of running
speeds and several natural frequencies
and mode shapes.
2)Making a reliable construction
capable of operating for thousands of
running hours without maintenance.
Dynamic system
The relationship between the excitation,
the structural properties, and the response
can be expressed as per the diagram in
Figure 2. The vibration response is a
result of the dynamic properties of the
structure and the excitation force.
A vibration system is normally
presented mathematically by the well-
known general equation of motion:
(1)
where M, C and K are matrices of mass,
damping and stiffness, f(t) is the vector
of applied force (excitation), and x(t) is
the vector of displacement (response)
and its time derivatives, velocity and
acceleration accordingly. The matrices
M, C and K represent the dynamic
characteristics of the structure. Reducing
vibration levels can be achieved by
modifying one or several of these
characteristics, or the excitation vector f(t).
The matrix M is not only the total
mass, but represents also the mass
distribution over the whole structure.
The same applies to the stiffness
matrix K. From the vibration point of
view, it may be very important where
the mass or stiffness is located.
C denotes the damping, which in
practice is not only a uniform number.
In real structures the damping normally
varies depending on the frequency and
mode shape, as well as on the location. In
complex structures like engines, several
different damping types can be found.
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WÄRTSILÄ TECHNICAL JOURNAL 02.2008
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Finally, there is the vector f(t)
representing the force or excitation vector.
Means of modifying the force vector
in order to reduce vibration response
can be, for example, a balancing device
where some additional forces are
included in the system, or changing the
firing order when the forces are applied
in a different order to the system.
Vibration analysis
In the vibration analysis of an engine
or a diesel generating set (genset), the
following parts can be included:
1) Eigenfrequency and mode shape analysis
2) Calculation and analysis of major
excitation forces
3) Dynamic response analysis.
Eigenfrequency analysis
Normally, the first step in making a
structural vibration analysis of a diesel
engine is a calculation of its natural
frequencies and mode shapes.
A typical calculated lowest torsion
mode is shown in Figure 3.
Excitations
The calculation and analysis of excitation
forces are an essential element in vibration
optimization. The major excitations caused
by gas and mass forces, taking into account
the firing sequence of the engine, are
calculated and analyzed. Modern multi-
body dynamics (MBD) simulation tools
offer an accurate and relatively fast way
of calculating the mechanical excitation
forces acting on the engine block.
The excitations of diesel engines are
periodic. For this reason, it is natural
to analyze the excitations as well as
the vibration measurements within
the frequency domain.
The main excitation sources of a medium
speed diesel engine can be categorized as
shown in Figure 4, [1]. The origin of mass
forces is the crank mechanism, which has
both rotating and oscillating components.
On the lowest integer harmonic
orders, the mass forces induce mainly
rigid body motions of the whole engine
structure. However, some bending of the
engine block due to mass forces, is also
visible, especially on long engines. The
gas forces resulting from the cylinder
pressure cause a torque variation at
each cylinder. This torque variation is
transferred to the engine block through
the main bearings and via the lateral force
Fig. 2 – Diagram of the relationship between excitation, structure and response.
Fig. 3 – Typical lowest natural mode shape of torsion of a Wärtsilä 8L46 engine.
Fig. 4 – The main categories of excitation forces.
Excitation
– Frequency, amplitude,
direction, location, etc.
Structural properties
– Natural frequencies, natural
mode shapes, damping
Vibration response
Amplitude, frequency, mode
Excitation type
Excitation
source Oscillating
Appearance
in a multi-
cylinder
engine block
Vibration at the
first harmonic order
Rigid body vibration
and bending
Vibration at lowest
full orders, mainly
orders 1 and 2
Rigid body, bending
and some torsion
- All harmonic orders,
including half orders
- Mainly torsion
based deflections
on the engine
SIMPLE ..................................................... COMPLEX
Main excitations of a 4-stroke engine
Gas forces
Cylinder pressureRotating
(Unbalance)
Mass forces

[MARINE/INDETAIL]
Fig. 5 – Relative comparison of torsional excitations of a 9-cylinder engine
with two firing orders.
Vectorsumoftorsion
Harmonic order
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
1 - 2 - 4 - 6 - 8 - 9 - 7 - 5 - 3
1 - 7 - 4 - 2 - 8 - 6 - 3 - 9 - 5
Fig. 6 – Influence of an added spring-mass-damper system on the resonance
frequencies and response amplitudes of the main structure.
Fig. 7 – The prototype of the tuned mass damper.
of the piston against the cylinder liner.
When analyzing these excitations, it
is necessary to take into account, not
only the excitation strength at different
frequencies, but also the similarity of the
excitation mode and natural mode shapes
within the frequency range in question.
As regards gas-force-induced torsion
excitations, it is relatively easy to quickly
compare different firing orders by
means of a vector summation. Figure
5 shows the difference in torsion
excitations with two different firing
orders on a 9-cylinder engine.
Forced response analysis
When using MBD software to simulate
engine vibrations, the simulation model
itself performs the calculation of the
excitation forces and their application
on the correct locations in the model.
The analysis is done in a time domain,
normally using condensed models of
the structure.
The direct time integration method,
using Finite Element Software, is very time
consuming and often not feasible. Its most
important advantage is that it can take
the structural nonlinearities into account.
A linear analysis in a frequency domain
is fast and sufficiently accurate providing
that the FEM model is presenting the
structural characteristics reliably.
Tuned mass damper
The use of a passive tuned mass damper
is a known method for reducing
vibrations resulting from earthquakes
in high buildings. It has also been used
to eliminate vibration problems on ship
structures, for example, and to solve
different kinds of machinery vibration
problems, but not necessarily so much
for reducing diesel engine vibrations.
The designation “tuned mass damper”
refers to the construction, consisting of a
vibrating mass with a natural frequency,
tuned to the desired frequency. Figure
6 shows the principal effect of a tuned
mass damper. The device is also known
as a vibration absorber in situations
where the damping factor is very small,
such as when just a steel spring is used
without any additional damping.
The blue line shows the vibration
response of the main structure m0 due to
ground movement or applied force. It has
a natural frequency at frequency f0 where
the increased vibration amplitude can
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59indetail
be seen. The red line shows the response
of the same main structure after adding
mass m1 to the system with the spring k1
and damping c1, as shown in the Figure.
When the damper is correctly tuned, it
can reduce vibrations dramatically within
the area of the resonance frequency.
From Figure 6 it can also be seen that
by adding a damper to the system, the
vibration of the main structure outside
the intended damping area increases.
This is one disadvantage of the damper,
which must be taken into account. One
must remember, particularly in the
case of medium speed diesel engines
where the main excitation frequencies
are spread over a wide frequency range,
that at some harmonic orders the
vibration level is increased by the damper.
However, with proper tuning of the mass,
stiffness and damping parameters, it is
possible to reduce this phenomenon.
As it has been clearly shown, the correct
dimensioning of the added mass m1, the
stiffness k1 as well as the damping c1,
is essential in order to achieve the best
possible damper performance. As a rule
of thumb, it can be considered that the
added mass required to achieve a proper
damping effect, is about 5% of the modal
mass of the vibration mode in question.
The spring coefficient k1 and the damping
factor c1 are then chosen so that the
damped natural frequency of the mass m1
will match the frequency to be dampened.
Engine vibration control by
using a tuned mass damper
Contrary to the above theoretical example,
in the case of a real engine, the problem
is somewhat more complicated. Firstly,
finding the correct parameters is not an
easy task when the engine has a wide range
of rotating speeds and several harmonic
orders exciting resonances. Secondly,
finding theoretically the best possible
location and direction for the damper
requires a thorough analysis of the system
using the finite element method. Thirdly,
actual structures usually consist of several
natural mode shapes that contribute to
excessive vibration levels. By choosing a
suitable direction for the damper, it is still
possible to have some influence on more
than one mode shape.
Damper development
The tuned mass damper developed
by Wärtsilä consists of vibrating mass
discs supported by steel springs. Both
are located, together with damping oil,
inside a cylindrical steel frame. All the
damper parameters, mass, stiffness and
damping, can be separately adjusted.
The damping coefficient is changed by
altering the oil flow inside the damper.
The damper is shown in Figure 7.
Vibration simulation and tuning
Comprehensive simulations were carried
out during the development of the mass
damper. The main parts of the engine
model were built in Ideas, and the meshing
was done in Hypermesh. The engine
vibrations with the tuned mass damper
were simulated using Abaqus and Modysol
software.
Modysol is a software package developed
by VTT, the Technical Research Center
of Finland.
The dynamic excitation forces were
calculated using an in-house software called
Dynex.
Optimizing the location of the damper
is essential to minimizing its effective mass.
After several simulations it was noticed
that, in the case of an in-line Wärtsilä
46 engine, the top of the turbocharger
is the most feasible location in order to
minimize the required vibrating mass.
A 9-cylinder four-stroke engine with
a firing order of 1-2-4-6-8-9-7-5-3,
gives high excitation forces for the first
torsion mode at harmonic orders 4.0
and 5.0, as shown in Figure 8. Between
those excitations, the harmonic order
4.5, which corresponds to the firing
frequency, gives a strong rolling excitation.
With the damper mounted so that the
movement of the effective mass is in the
engine transversal direction, it is not very
efficient in damping the vibrations in the
vertical direction. According to vibration
measurements, the vertical vibration is,
however, not very critical in this case.
It is clear, therefore, that there are two
possibilities for tuning the damper: to
concentrate on the 1st
torsion mode at
29 Hz, or on the horizontal bending mode
at 42 Hz. The former option was proven to
be the better one, and was finally chosen.
The same principles are used in the
tuning of the damper for the Wärtsilä 8L46
engine. The most significant excitations are
at the harmonic orders 3.5 and 4.5, as well
as at the order 4.0, which corresponds to
the firing frequency of an 8-cylinder engine.
Fig. 9 – A tuned mass damper mounted
on a turbocharger.
Fig. 8 – The most critical natural frequencies and excitations for
the 1
st
torsion mode on a Wärtsilä 9L46 engine with a firing order
of 1-2-4-6-8-9-7-5-3.
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
Natural frequencies

[MARINE/INDETAIL]
Fig. 10 – Reduction of vibration levels on the turbocharger using the tuned
mass damper. Wärtsilä 9L46 engine.
Overall RMS (2–200 Hz): 80.2 mm/s
RMSVelocity[mm/s]RMSVelocity[mm/s]RMSVelocity[mm/s]
Frequency [Hz]
Frequency [Hz]
Frequency [Hz]
100
90
80
70
60
50
40
30
20
10
0
100
90
80
70
60
50
40
30
20
10
0
100
90
80
70
60
50
40
30
20
10
0
0 20 40 60 80 100
0 20 40 60 80 100
0 20 40 60 80 100
LONGITUDINAL
TRANSVERSAL
VERTICAL
Fig. 11 – Comparison of overall vibration levels on a Wärtsilä 9L46 engine’s
turbocharger and silencer with and without a mass damper.
120
100
80
60
40
20
0
r.m.s.velocity[mm/s]
Without damper
With damper
TCcompressor
L
TCcompressor
T
TCcompressor
V
TC
silencer
L
TC
silencer
T
TC
silencer
V
Field testing and results
In addition to comprehensive simulations
on both the 8-cylinder and 9-cylinder
Wärtsilä 46 engines, the mass damper
has passed full scale field testing on
real engines, as shown in Figure 9.
The field testing was carried out in order
to verify the functionality of the damper
with the optimum tuning parameters,
as well as to assess the performance over
long term operation. The reduction of
the vibration levels on the turbocharger
compressor casing are shown in Figure
10. From these measurements it can be
seen that with the damper well tuned,
the vibration can be reduced at more
than one harmonic order. In this case,
vibrations at all the three major excitation
harmonics are reduced in both transversal
and longitudinal directions. Vibration is
increased only at the harmonic order 4.0
in the vertical direction, but also there the
overall vibration level is slightly reduced.
This can be seen in Figure 11 where L, T
and V denote the longitudinal, transversal
and vertical directions, respectively.
Figure 12 indicates the overall r.m.s.
velocity vibration levels on the same
turbocharger during the engine sweep run.
The running speed was changed from 360
up to 500 rpm with a propeller loading.
Another example, shown in Figures
13 and 14, is taken from the vibration
test results of an 8-cylinder engine.
The figures show the results, with and
without the tuned mass damper, on
the engine’s foot, charge air cooler,
and turbocharger (Figure 14).
At the writing of this article, altogether
15 dampers have been delivered. The
cumulative running hours for these
dampers is 82,000 h. However, some of
these dampers have already accumulated
12,000 running hours without any service
operation.
CONCLUSION
When optimizing the vibration
performance of a medium speed diesel
engine, as many different contributing
aspects as possible should be taken into
account. A thorough vibration analysis
includes the eigenfrequency and mode
shape analysis, the analysis of excitation
forces, and finally, as a combination, the
dynamic forced response simulation
The final result is always a compromise
between many different criteria. For
example, the firing order giving the
60 indetail

61indetail
Without damper
With damper
100
90
80
70
60
50
40
30
20
10
0
20 25 30 35 40 45 50
smallest free forces is most probably not
the best one from the point of view of the
internal bending moment or torsional
vibration. Similarly, the stiffening of the
structure in order to move one natural
frequency away from a critical excitation,
may create another natural frequency
in another excitation frequency area.
When it is not possible to tune
the natural frequencies of the engine
structure properly to avoid vibrations,
and when modifying the excitation
forces is not feasible, a tuned mass
damper can be a good solution.
An accurate prediction of the
performance of a tuned mass damper
requires special simulation tools,
making it possible to include the local
damping within the simulation model.
On the basis of the simulations and
tests described in this article, the best
and most effective location for the tuned
mass damper is on the turbocharger. At
that location the displacement amplitudes
are normally much higher than on other
parts of the engine, which is essential
for the damper to work efﬁciently.
When the damper is properly tuned,
it can reduce vibration levels at more
than one excitation frequency. In the
cases presented here, considerable
vibration reduction was achieved at
three major excitation harmonics.
NOMENCLATURE
C Damping matrix
M Mass matrix
K Stiffness matrix
f(t) Force vector
x(t) Displacement vector
L Longitudinal
T Transversal
V Vertical
c0 Damping of the main structure
mounting
c1 Damping of the damper mass mounting
k0 Stiffness of the main structure
mounting
k1 Stiffness of the damper mass mounting
m0 Mass of the main structure
m1 Added damper mass
r.m.s. Root Mean Square
REFERENCES
[1] TIENHAARA, HANNU, “Guidelines for
engine dynamics and vibration”, Wärtsilä
Marine News, 1/2004
Fig. 12 – Vibration on the turbocharger in the vertical direction.
Wärtsilä 9L46 engine.
Fig. 14 – Vibration results on an 8-cylinder engine’s turbocharger
with and without a damper.
Fig. 13 – Vibration results on an 8-cylinder engine with and without a damper.
30
25
20
15
10
5
0
Engine
foot L
Engine
foot T
Engine
foot V
Charge
air cooler
Charge
air cooler
Charge
air cooler
Without damper
With damper
Without damper
With damper
120
100
80
60
40
20
0
Turbo charger L Turbo charger T Turbo charger V

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