USING MODAL ANALYSIS TO VERIFY A TORSIONAL
MASS ELASTIC MODEL
Steve Seidlitz
Applied Technology Department
Onan Corporation
1400 73rd Avenue North East
Minneapolis, MN 55432
e-mail sseidlit@notesbridge.cummins.com
ABSTRACT. The use of a mass-elastic model is an
integral part of a typical torsional analysis.
Modal
analysis provides an experimental means for verifying
such a mass-elastic model. This paper describes the
torsional modal tests of a 200 kW diesel powered
generator set. The generator's rotational assembly was
hung for its modal test, which simplifies testing, and the
crankshaft was tested in its cylinder block. This paper
describes these two modal tests and the ensuing masselastic model correlation efforts. When the crankshaft
was installed in its cylinder block, a torsional laser was
used to measure the crankshaft's torsional motions.
Typically a mass-elastic model is built by measuring
component inertias and calculating shaft stiffnesses.
Modal analysis provides a means of verifying the
calculated stiffness values.
The example presented here is a 200 kW generator set,
which is powered by an in-line six cylinder diesel engine.
For 60 Hz power generation, this generator set rotates at
1800 rpm.
Generator
A generator's major rotating components are shown
below.
1.1NTRODUCTION
Performing a torsional analysis of a generator set
typically relies upon using that generator set's masselastic model. Direct measurement of operating torques
throughout the shafting system of a diesel engine
powered generator set would be an enormous task. A
more typical approach is to measure the torsional
behaviors of the generator set's shafting system at each
of its free ends, use this information to build a correlated
torsional model, and then use this model to predict the
operating shaft torques throughout the shafting system.
This process depends upon a valid mass-elastic model of
the generator set. A mass-elastic model is series of
infinitely stiff rotational inertias connected by massless
torsional springs. One such model is shown below.
Fan
Hub
The hub, fan, rotor, and exciter are all pressed on to the
rotor shaft. The rotor and exciter are each stacks of 0.61
mm thick steel disks, that the wire is then wrapped
around. This rotating assembly is attached to the engine
via a pack of three 1.22 mm thick disks. The center of
these disks is bolted to the hub and their outer diameter
is bolted to the engine's flywheel.
Cylinders
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The particular rotor assembly tested here is part of a 200
kW generator set. The rotor is 450 mm long. To perform
a torsional modal of this rotating assembly, it is hung
from a soft support system. Care is taken to insure a
torsionally soft connection between this support system
and the rotor assembly in Fig. 1
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Hanging is the preferred approach, since it provides easy
access to the assembly for accelerometer placement,
minimizes damping which maximizes the torsional
motions to be measured, and minimizes test fixturing.
The only disadvantage of hanging is the need for tall
ceilings when testing a large rotational system. Being an
axially symmetric structure, it should be possible for this
hanging system to have a pure torsion mode, that is free
of bending motions. To increase the chances of this
happening and to get reasonably large torsional motions,
which are associated with low resonant frequencies,
inertia is added at the generator's hub. The number of
added 6.35 mm thick disks is varied until a nearly pure
torsion mode is found. Such added inertia also better
simulates the final application; the added disks simulate
the inertia of the engine's flywheel.
The modal model is shown below. At every axial location
along this rotational system, four equally spaced
measurement locations were selected, except at the
added disks, where eight locations were selected. Only
rotational motion was measured at these measurement
locations, except at the ends. Multi-directional data was
taken at the ends, to check for bending motions. Since
one of our interests was determining the torsional
stiffness of the rotor, the rotor's torsional motion was
measured in seven different planes.
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using four or two added disks. Modal data was taken of
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The system was excited by impacting the rotor in a
rotational fashion. Such a test configuration does a good
job of only exciting the torsional mode of interest, as
displayed in the driving point shown below. Also notice
that this mode is very lightly damped.
1506
The next step in this process is to use this modal
information to build a correlated mass-elastic model. The
rotational inertia of each major component was
measured. Calculated stiffness values were used as a
starting point. Then these stiffness values were varied
until resonant frequency and mode shape correlation was
established. Mode shape correlation of the four added
disk system is shown below and the two added disk
system achieved similarly good results.
Resonant frequencies correlated within half of a percent.
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The next issue was how many inertias were needed to
simulate the rotor's motions. If only matching resonant
frequencies, a one inertia model would suffice. However,
as the plot below shows, using only one inertia incorrectly
predicts the mode shape's motion at the exciter end of
the generator. Since we correlate our torsional model
against measured data collected at the exciter end of the
generator, our model needs to accurately simulate the
exciter's torsional motion. Hence, we used three inertias
to simulate this rotor.
Cylinder block installation introduced two measurement
problems, added friction at the bearings and limited
access to the crankshaft. Friction was minimized by
placing ball bearings in the engine's bearings' center oil
groove. These ball bearings were slightly larger in
diameter than the depth of the oil groove and they were
held in place with grease. A torsional laser was used to
measure the system's torsional motions.
Such a
measurement system is not impacted by the geometry of
the test object, so the torsional motion of the pins could
be measured at any pin surface. The only measurement
requirement is that the laser be perpendicular to the
system's rotational axis. To maximize the system's
torsional motion, a shaker was used, whose excitation
was narrow band random about the system's torsional
resonant frequency. This test setup is shown in Fig. 2.
For visual reference, this rotational system is
approximately one meter long.
This
measurement
procedure
produced
clear
measurements, as shown by the transfer function plotted
below. The torsional laser was measuring peak torsional
motions on the order of +/- 0.002 degrees. Such small
motions were confirmed
by comparing
these
measurements against the calculated angular motions
derived from two linear accelerometers mounted on the
outside diameter of the measu,·ed component.
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As with the rotor assembly, 6.35 mm thick disks are
added at the pulley end of the crankshaft to lower the
system's first torsional mode. The flywheel is attached to
the other end of the crankshaft. The other advantage of
adding disks is that assorted attachments can be tried,
until a nearly pure torsion mode is found. A crankshaft is
not axially symmetric, so an additional question was
posed: does hanging a crankshaft properly simulate its
installed conditions?
To answer that question the
crankshaft was tested twice, one hanging and again
installed in a cylinder block.
1507
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As with the rotor assembly, the inertia of each major
component was measured. After the modal test was
completed, the crankshaft was sectioned, so the inertia of
each crankshaft throw could be measured separately.
Stiffness values were calculated. Then the stiffness
values were varied until correlation was established.
Plotted below is the mode shape correlation with the
crankshaft in its cylinder block with three added disks.
Resonant frequency correlation was within half a percent.
All of the rest of the tested systems produced similar
results.
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The hanging crankshaft's resonant frequencies averaged
two percent lower than their equivalent systems as
measured in the cylinder block.
Summary
Modal analysis provides a means for experimentally
verifying a torsional mass-elastic model of a 200 kW
diesel powered generator set.
Due to its axial symmetry, the generator's rotor assembly
can be hung for its modal test. This simplifies testing.
Thick disks are added at the generator's hub end to
minimize bending mode contamination. When building
the generator's mass-elastic model, the rotor should be
modeled as three inertias, if accurate modal motion is
required at both ends of this rotational assembly.
For accurate results, the crankshaft should be modaled in
its cylinder block. Thick disks are added at the nonflywheel end of the crankshaft to minimize bending mode
contamination. In block testing greatly limits access to
the crankshaft, which hinders transducer placement, but
that issue can be eliminated by using a torsional laser to
measure the system's torsional motions.
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Fig. 1 Rotor Assembly Hanging for Modal Test
Fig. 2 Crankshaft in Cylinder Block Modal Test
1509