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R. F. Orsagh
M. J. Roemer
Impact Technologies, LLC
125 Tech Park Drive
Rochester, New York 14623
[email protected]
Abstract: Modal testing of bladed-disk assemblies in turbomachines is used to identify
the critical natural frequencies and mode shape information used for avoiding the per-rev
resonant conditions that cause high cycle fatigue (HCF) leading to premature blade and
disk failures. In order to obtain the high quality modal data necessary for accurate modal
identification, experience plays a major role in understanding the strengths and
weaknesses associated with the variety of testing techniques. Application-specific
concerns such as the blade-root disk interface connectivity, tiewire looseness and cover
band design must be understood prior to test. Choices such as pre-test bladed-disk
preparation, modal excitation driving point location, hammer versus shaker force
excitation methods, shaker driving signa l approaches, accelerometer type and location,
and windowing are all important aspects that must be considered when testing specific
bladed-disk configurations. Turbomachinery-specific modal analysis techniques
including extraction of harmonic content and use of interference diagrams for
identification of resonance conditions are also presented. The mentioned concepts are
described in detail with reference to examples, which highlight the importance of the
modal testing techniques implemented for a variety of applications.
Keywords: High cycle fatigue, Modal testing, Resonance, Turbomachinery
Introduction: High cycle fatigue (HCF) plays a significant role in many turbine blade
failures. During operation, periodic fluctuations in the steam force occur at frequencies
corresponding to the operating speed and harmonics and cause the bladed disks to
vibrate. The amplitude of these vibrations depends in part on the proximity of the natural
frequencies of the bladed disk to the forcing frequency. Large amplitude vibration can
occur when the forcing frequency approaches or becomes resonant with a natural
frequency of the bladed disk. Dynamic (alternating) stresses associated with near
resonant or resonant vibration produce HCF damage and can initiate and propagate
cracks very quickly [1].
Steam turbine manufacturers typically design and manufacture bladed disks with
adequate margins between the forcing frequencies and the fundamental natural
frequencies to avoid resonance. However, resonance with the operating speed or
harmonics can occur under normal operating conditions for a variety of reasons including
manufacturing variances, modified shrouding configurations, reverse engineered blades,
routine wear, or any other factor that alters the mass or stiffness of the bladed disk
assembly. To protect bladed disks against HCF damage from high amplitude vibration it
is necessary to ensure that adequate margins exist between the natural frequencies of
bladed disk assemblies and the synchronous forcing frequencies over the entire life of the
bladed disk.
Modal testing can provide valuable information about the dynamic response
characteristics of bladed disks at a relatively low cost. This information typically includes
the natural frequencies and mode shapes of the row at room temperature and in the
absence of centrifugal loading. It is important to note that the dynamic response
characteristics during operation are likely to differ significantly from those measured
under the test conditions due to the effects of thermal changes, fixity differences, stress
stiffening, and spin softening. Thus, modal testing alone can not determine the dynamic
response characteristics of turbine blade rows with sufficient accuracy to predict resonant
conditions during operation. However, a va riety of techniques exist for utilizing modal
test results to mitigate the risk of HCF failures.
While modal testing is a fairly inexpensive and quick process, achieving meaningful
results requires experience. Over the past 10 years, personnel now at Impact
Technologies have developed a variety of turbomachinery specific techniques for
successfully collecting, analyzing, and utilizing modal test data. This paper describes
some of these techniques, and illustrates their use with examples.
Turbomachinery Specific Considerations: Three important considerations influence the
accuracy and effectiveness of modal test data taken from bladed disk assemblies:
connection stiffness within the blade-root interface and blade-tiewire interface,
centrifugal loading effects, and thermal effects. When interpreting modal test results, it is
critical to account for all of these conditions because an error as small as 3% in the
natural frequency calculation can lead to an incorrect resonance diagnosis.
During turbine operatio n, turbine blade engineers rely on the centrifugal force of
thousands of pounds to insure a tight fit at the blade-root interface. Centrifugal force
makes the blade and disk essentially act as an integral structure, with dynamic properties
distinctive from those obtained by testing the separate components. During operation,
centrifugal force can also alter the effective stiffness of the turbine blades. Stress
stiffening, from tensile force on the blades, causes the blade frequencies to rise as the
speed increases. The modulus of elasticity of most turbine blade materials decreases as
their temperature rises. Therefore, a modal test that is conducted at zero speed and room
temperature requires important blade row preparation and analysis to accurately
determine the dynamic characteristics of the blade row during operation.
Problems with blade fixity are best characterized by either a loose blade-root interface
and/or an unsecured floating tiewire. If tested with this type of looseness, the bladed disk
natural frequencies will appear lower than if they were rigidly fixed, and considerable
scatter will exist between natural frequency measurements from different blades or blade
groups as shown in Figure 1. The looseness will also create structural non- linearities, thus
inhibiting the proper distribution of input excitation energy and leading to mode
frequencies that are dependent on vibration amplitude.
A practical method for insuring fixity before performing a modal test is to apply an
adhesive to the blade-root and blade-tiewire interfaces. Depending on the type of root,
tiewire, and amount of looseness prescribed procedures are straightforward and easily
accomplished. Blade rows that have been in service for several years since disassembly
do not typically require any special treatment because deposits that form in the blade
attachment region effectively lock the blade in place by filling the gaps between the blade
and disk. New or recently disassembled blade rows with axial entry roots should be
secured with an adhesive such as LocTite™.
Figure 1
Frequency Response Functions from loose (Left) and tight (Right) structures
Quality Control: Bladed disk assemblies are particularly at risk of resonance problems
following repairs or modifications that could alter the dynamic response characteristics of
the structure. Procedures such as modifying shrouding configurations, or replacing blades
(especially with reverse engineered blades) could create a resonance problem by
changing the amount or distribution of mass or stiffness in the blade row. Gradual
changes such as routine wear from erosion can also change these physical characteristics
and lead to resonance problems.
Modal testing can detect changes in the dynamic response of individual blades or of an
assembled row. Acceptable zero speed natural frequencies for a given blade or row are
not usually available from turbine manufacturers. Turbine designers invest considerable
effort in zero speed modal testing, finite element analysis, and at speed telemetry testing
to ensure frequency margins of at least 5% for the fundamental modes of a bladed disk.
Zero speed natural frequency specifications can be estimated by conducting modal tests
on several blades, or blade groups, in their original condition (as provided by the OEM).
A resonance problem is possible when the zero speed natural frequencies of worn,
modified, or replacement blades deviate from those set by the manufacturer.
Resonance Investigation: A resonance investigation is advised when evidence of HCF is
discovered during a failure investigation or inspection. The most effective and
economical method for identifying potentially resonant conditions in bladed disks utilizes
a combination of modal test results and finite element analysis (FEA) to accurately
predict the dynamic response characteristics of the structure under operating conditions.
While FEA alone can predict the natural frequencies and mode shapes of a blade row
during operation, experience indicates that calibration of such complex models with
modal test results is necessary to accurately predict resonance. Figure 2 shows the
combined testing and modeling approach.
Blade/Disk Geometry, Physical Properties
and Operating Conditions
Individual Blade Test
Individual Blade FE Model
Bladed Disk FE Model
Blade Group Modal Test
Bladed Disk Modal Test
At Speed & Temp. FE Model
Diagnose Resonance Problem
Modified Bladed Disk Modal Test
Modified Bladed Disk FE Model
Figure 2
Block Diagram of Resonance Investigation
A resonance or failure investigation begins with the development of a BladePro [2] finite
element model of the bladed disk under investigation. BladePro utilizes the FEA power
of ANSYS ® to significantly reduce the time required for performing structural analysis of
turbine blades. The program assists the user in all aspects of turbine blade analysis:
model generation, boundary condition application, analysis options, job submission, post
processing, and life assessment.
A three-dimensional finite element model of a single blade is developed using templates
for different components (airfoil, shroud, dovetail, and disk) provided with the BladePro
software. Figure 3 shows part of the model generation process. The single blade model is
eventually condensed into a “superelement,” that is replicated numerous times to fo rm a
full bladed disk assembly model. By changing a few simple input parameters in the
software, the model is exercised under a variety of operating conditions and under the
modal test conditions to determine the dynamic response characteristics of the blade row.
Correlation of the single blade and full bladed disk models with the corresponding modal
test results lends credibility to the model, and supports the calculated dynamic
characteristics during operation.
Figure 3
BladePro model generation
When a blade row resonance condition is identified, the introduction of a small change in
the blade row’s natural frequencies is the most effective way to reduce the dynamic stress
and increase the component fatigue life. Depending on the frequency, a frequenc y margin
of 3% is usually enough to lower the dynamic stresses and ensure that the row remains
detuned regardless of any minor changes that might occur in the future. Although it is
usually more practical to modify a blade row by adding mass, mode frequenc ies can
either be decreased or increased to achieve the necessary frequency margin. Increasing
the bladed disk natural frequencies can be accomplished by stiffening the lower region of
the airfoil, or by removing material from the blade tip or coverband. Decreasing the
natural frequencies is likewise accomplished by removing material from the airfoil base,
or by adding mass to the blade tip or coverband.
The most practical method for altering these natural frequencies to within allowable
limits is by the addition of mass to the blade tip, tiewire, or coverband. This approach has
the following advantages: 1) minimal changes to the airfoil that can significantly affect
aerodynamic operations; 2) adding mass can usually be accomplished without removing
any blades. Common techniques for adding mass to a blade row include brazing stainless
steel sleeves to existing tiewires, brazing aerodynamic masses to the convex side of the
airfoil tip, and increasing weld fillets around the tiewire or coverband regions. Various
modification strategies are first evaluated using the finite element model. The objective is
to introduce small amounts of mass to the model of the blade row that are easy to
implement and result in essentially infinite component life.
Once the test engineer and relevant plant personnel choose a modification strategy, the
detuning weights are temporarily attached to the blade row with an adhesive. Next, a
modal test of the bladed disk is performed to assess the effect of the modification. Once
satisfied with the detuning results, the weights are permanently attached to the blade row.
A final modal test is conducted to verify that the frequency shift produced by the weights
remains within specifications.
Test Procedures: A complete modal test of a bladed disk assembly consists of
measurements to determine the dynamic response characteristics of the entire assembly
and its substructures (blade groups or individual blades). Detailed substructure
measurements are used to identify the fundamental mode families; i.e. tangential, axial,
torsional. The motion associated with the tangential modes is primarily in the
circumferential direction. For the axial modes, the major displacement component is in
the rotor axial direction. The torsional modes of a single blade or blade group exhibit a
twisting motion, where the leading edge is 180° out of phase with respect to the trailing
edge or blade. Measurements of the entire structure’s response are used to identify
amplitude and phase variations in the response of the substructures.
Figure 4
Fundamental mode families. Axial (left), Tangential (center), Twist (right)
The natural frequencies and associated deflection (mode) shapes of substructures are
measured by “meshing” the substructure with a sufficient number of measurement points
to describe the substructure’s deflection. For blade groups, a mesh consisting of three
points per blade (near the platform, mid span, and tip) is sufficient to document the
fundamental mode shapes. Testing all of the substructures is unnecessary since, due to
symmetry, all of the substructures exhibit similar dynamic response characteristics.
While all of the substructures exhibit similar mode shapes at a given natural frequency,
the amplitude and phase (ideally 0 or 180°) varies from substructure to substructure. This
“disk effect” is measured meshing the entire row with measurement points. Typically,
one point per substructure, in a consistent location, is used. Differences in measured
frequencies from substructure to substructure can be anticipated as the normal
consequence of dimensional tolerances, manufacturing defects, material processing and
installation procedures. These standard variances prevent any one blade from being a
“perfect” copy of any other. The result of these minor differences is seen as “scatter” of
natural frequencies about a mean value. Scatter of 5% is normally considered acceptable
among the manufacturing community for low-pressure steam turbine blades. The full row
modal test also documents the scatter associated with differences between substructures.
To excite a bladed disk, a modal hammer and a 75-pound force electromagnetic shaker
have been used successfully. A modal hammer fitted with a piezoelectric force transducer
can be used to excite the structure under investigation with a transient (impact) force.
Hammer excitation generally involves less setup effort than the shaker, but the hammer
requires more effort and skill during data collection. The shaker is connected by a stinger
to a piezoelectric force transducer attached to the driving point on the structure. A
cyanoacrylate or epoxy adhesive works well for bonding the force transducer to the blade
row, so long as the driving point is not on a curved surface such as the leading edge of the
airfoil. For testing unmounted blades, a modal hammer is preferred.
Selection of the driving point location is based largely on the objective to excite as many
of the fundamental modes as possible. So long as the structure is not excited at a node (a
point on the structure that is stationary for a given mode) and the structural response is
linear, for all practical purposes the mode shapes will be independent of the driving point
location. The applied force should act in the rotor axial and disk tangential directions to
unsure coupling with both the axial and tangential modes. A driving point on the platform
or mid span on the airfoil of the leading or trailing blade in a group generally excites the
first and second bending modes in each direction. It is best to avoid flexible areas such as
the trailing edge where significant localized deflection is likely. Access considerations,
especially for shaker excitation, often necessitate selection of a driving point near the
A modal hammer is commonly used in modal analysis to provide a transient excitation of
structures. A piezoelectric force transducer in the hammer tip measures the transient force
applied by the hammer when it strikes an object. A brief impulse of this type in the time
domain corresponds to broad band excitation in the frequency domain, and can therefore
excite many modes simultaneously. Shorter impulses in the time domain, produced by
harder hammer tips, excite a broader range of frequencies. A hard hammer tip such as
steel is usually necessary for testing bladed disk assemblies. The response to at least five
hammer impacts must be averaged to achieve stable results.
An electromagnetic shaker is commonly used in modal analysis to excite of structures
with a user-selected signal. For most steam turbine bladed disks, a 75-pound
electromagnetic shaker can adequately excite the structure. Broad band of forcing signal
such as random (white) noise, burst random, or random multi- sine (a superposition of
bin-centered sinusoids with random phase relationships) are used to simultaneously
excite many modes in the frequency range of interest.
Accelerometers are used to measure the vibratory response of each measurement point on
the structure to the applied excitation. A pair of roving accelerometers oriented in the
axial and tangential directions to the bladed disk (as shown in Figure 5) is moved from
measurement point to measurement point during the data collection process. Wax or a
small magnet holds the accelerometers firmly in place during data collection. Lightweight
accelerometers are used to minimize the effects of mass loading that can reduce the
natural frequencies of the substructure where the accelerometer is attached. Mass loading
is of greater concern when measuring the natural frequencies of unmounted blades
because the total mass of the structure under investigation is much smaller.
Figure 5
Accelerometer Configuration
Excitation and response signals from the test are processed using a multi-channel
dynamic signal analyzer to compute a Frequency Response Function (FRF) for each
measurement point. To prevent errors in the fast Fourier transformation (FFT) that forms
the basis for this calculation, the measured signals must be periodic within the sampling
(data collection) interval. Periodic signals will have an integer number of cycles within
the sampling interval so that the signal begins and ends at the same value, while nonperiodic signals exhibit a discontinuity between the beginning and end of the sampling
interval. Weighting windows are used to control FFT errors by reducing the signal
amplitude to zero at the beginning and end of the sampling interval.
Unfortunately, windowing introduces artificial damping that can mask the structural
damping. Finite element models typically use a nominal structural damping ratio of 0.2%,
but model results can be improved with more accurate damping information from a
modal test. A Hanning window is commonly used when testing with a shaker driven by a
continuous random noise signal. For a hammer test, a user-defined window is used to
suppress the response at the end of the sampling interval. Random multi- sine excitation is
unique in that windowing is not necessary because the structure is driven at discrete bincentered (periodic within the sampling interval) frequencies.
Modal Analysis: Modal test data from a hammer or shaker test is reduced on a personal
computer with modal analysis software [3]. Peaks in the acquired frequency response
functions indicate the blade row natural frequencies. The mode shape and mode damping
ratio associated with each peak or natural frequency is identified by curve fitting one or
more peaks at a time. A polynomial equation for the FRF is fit in a least-squared-error
sense to specified frequency bands of the measurement data. This information is used to
build a table containing normalized mode shape amplitude and phase data for each
measurement point and direction, and at each mode frequency.
Interference Diagram: For a bladed disk structure, the fundamental natural modes of
vibration can be categorized as tangential, axial, or torsional. Associated with each of
these fundamental mode families are a series of “nodal diameter” or “disk effect” modes.
When one of these modes is excited, the amplitude of vibration can vary harmonically
around the disk and the phase relationship between substructures may change as shown in
Figure 6. The number of complete sinusoids around the disk (nodal diameter number) is
used to describe the mode. The nodal diameter number can also be determined by
dividing the number of nodes by two.
Figure 6
Disk effect examples of zero (left), two (center), and four (right) nodal diameters
In a bladed disk structure, for a mode to be strongly excited, the forcing frequency must
match the natural frequency of the row, and the force distribution must match mode
shape. In other words, the number of per-rev excitations must equal the number of nodal
diameters. An interference diagram is a tool used to identify situations in whic h both of
these conditions are met.
Figure 7 shows a typical at speed interference diagram with points representing nodal
diameter modes belonging to one fundamental mode family. The number of nodal
diameters is plotted along the X-axis while the natural frequencies are plotted along the
Y-axis. The diagonal line with slope of 1 per-rev/nodal diameter is the impulse line. A
strong resonant response is guaranteed if the impulse line passes through or close to a
mode point. Note that such a situation satisfies both of the conditions required for a
resonance response of the blade row, namely a frequency match and strong coupling
between the mode shape and applied force.
Interference Diagram
Frequency (Hz)
Mode Family
Nodal Diameter
Figure 7
Interference diagram showing 4 disk effect modes belonging to one family
From the results of a modal test alone, it is only possible to construct a zero speed
interference diagram. The effects of stress stiffening, stage operating temperature, and
changes in operating boundary conditions must be computed with a BladePro finite
element model. This combined approach makes it possible to construct an accurate atspeed interference diagram at a reasonable cost. Purely experimental at-speed
interference diagrams are only obtainable through strain gauge telemetry tests.
Implementation: A brief example from the author’s experience is presented to illustrate
the use of modal testing in resolving a HCF problem. After replacing a row of LP turbine
blades, multiple failures of the new blades occurred over a six- month period. A third
party blade manufacturer provided the replacement blades based on reverse engineering
of the original sample blades from the OEM. Prior to the row replacement and recent
failures, the blade the row had operated without any failures in excess of 30 years. The
rapid nature of the failures during the six- month period suggested that the problem was
due to HCF from a strong resonant condition rather than corrosion, material defects, or
low cycle fatigue.
The objective of the failure investigation was to determine the root cause of the blade row
failures based on modal test data and finite element results. A single blade was analyzed
to determine the geometric dimensions required for developing a finite element model.
Models of the unmounted blade and the complete bladed disk were developed.
The single blade model consisted of two tiewire segments, airfoil, platform, root, and
disk sector. By removing the tiewire and disk segment from the model, the natural
frequencies of the freely, and cantilever supported blade can be calculated. The
unmounted blade was frequency tested under both support configurations and compared
with the corresponding analytical results to verify the accuracy of the single blade model.
The single blade (sector) model was converted to a full row model by repeatedly
replicating the sector to form a “superelement”.
Based on the small differences between the measured and calculated frequencies of the
single blade, it was concluded that the finite element model would be able to reliably
represent the dynamic characteristics of the blade row. Aside from the single blade
model, the more important goal of the investigation was concerned with the bladed disk
natural frequencies under normal operating conditions.
A complete bladed disk modal test was performed on the blade row under investigation.
After reducing the data and incorporating the finite element results an at speed
interference diagram was constructed. Examination of the interference diagram revealed
the possibility of a near resonant condition associated with the 6th nodal diameter mode.
The test engineer, plant personnel, and blade installation specialists considered various
modification strategies to detune the resonant condition. It was decided to add mass at
specific locations along the outer tiewire to lower the bladed disk natural frequencies. In
the original blade row design, the frequency margin for the 6 nodal diameter mode was
only 6 Hz, or 1.7%. A frequency margin of at least 3% is recommended to ensure
resonance free operation. Calculations indicated that a minimum of 200 grams distributed
along the outer tiewire would be required to achieve this frequency margin.
Thirty 9.5 gram masses were temporarily attached to the outer tiewire. The row was
tested again to evaluate the resulting frequency shift in the 6 nodal diameter mode. A
frequency shift of 8 Hz, yielding a frequency margin of 14 Hz or 4.1% of the 6 nodal
diameter frequency was measured. The masses were permanently attached to the tiewire,
and the modal test was repeated as a final verification of the detuned blade row.
Conclusions: Modal testing can provide valuable information about the dynamic
response characteristics of bladed disks at a relatively low cost. This information
typically includes the natural frequencies and mode shapes of the row at room
temperature and in the absence of centrifugal loading. While the dynamic response
characteristics of bladed disks during operation are likely to differ significantly from
those measured under the modal test conditions, these “zero speed” natural frequencies
can serve as a valuable quality control test. The most effective and economical method
for identifying potentially resonant conditions in bladed disks utilizes a combination of
modal test results and finite element analysis (FEA) to accurately predict the dynamic
response characteristics of the structure under operating conditions. This natural
frequency and mode shape information is plotted on an interference diagram that
identifies resonant conditions with the turbine operating speed that are likely to produce a
strong response. When a resonant condition exists, the finite element model is used to
evaluate different blade row modification strategies. Follow-up modal tests are performed
to after any modifications to verify the detuning effects.
[1] Roemer, Hesler, Rieger, “On-Site Modal Testing of Low Pressure Turbine Blade
Rows”, Sound and Vibration, May 1994
[2] BladePro™, Impact Technologies, LLC, 125 Tech Park Drive, Rochester, NY 14623
[3] ME’scope™, Vibrant Technologies, Inc., PO Box 660, Jamestown, CA 95327
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