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AERSP 405/597A Project 6
Vibration Based Airframe Structural Health Monitoring
Justin Long Neal Parsons Rebecca Stavely Thuan Nguyen Anthony Parente Daniel Kraynik Shiang-Ting Yeh Faculty Adviser: Dr. Stephen C. Conlon
[email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]
Fall 2012
(Ref. 3)
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Contents
Chapter 1: Introduction ............................................................................................................ 3
1.1 Motivation ...................................................................................................................... 3
1.2 OH-58 Background ........................................................................................................ 5
1.3 Vibration based Structural Health Monitoring ............................................................... 7
1.4 Reciprocity ..................................................................................................................... 7
1.5 Ground Vibration Testing .............................................................................................. 8
1.6 Signal Processing ........................................................................................................... 8
1.7 Modal Analysis Theory ................................................................................................ 10
1.8 Data Acquisition and Processing for the OH-58 Tail Boom GVT .............................. 12
1.9 High Frequency Methods and Background ................................................................. 13
1.10 Research Objectives ................................................................................................... 15
Chapter 2: Experimental Procedure ....................................................................................... 17
2.1 Test Bed ....................................................................................................................... 17
2.2 Reciprocity and First Bending Mode Tests .................................................................. 17
2.3 Full Modal Tests .......................................................................................................... 19
2.4 Mid-Frequency Impact Testing .................................................................................... 20
2.5 High Frequency Testing ............................................................................................... 21
Chapter 3: Modal and Mid-Frequency Results and Discussion ............................................ 25
3.1 Reciprocity ................................................................................................................... 25
3.2 First Bending Mode Results ......................................................................................... 26
3.3 Full Modal Results ....................................................................................................... 29
3.4 Mid-Frequency Results ................................................................................................ 37
Chapter 4: High Frequency Results and Discussion .............................................................. 42
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4.1 High Frequency Introduction ....................................................................................... 42
4.1 Active-active Testing ................................................................................................... 42
4.2 Passive Testing ............................................................................................................. 53
4.3 Active-Passive Testing ................................................................................................. 56
Chapter 5: Conclusions .......................................................................................................... 62
References .............................................................................................................................. 65
Appendix: Additional Mode Shapes ...................................................................................... 67
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Chapter 1: Introduction
1.1 Motivation
The field of structural health monitoring (SHM) has gained significant interest in recent
years, as the current fleet of aircraft continues to age, and a new generation of aircraft enters
service. Aging metallic airframe structures are consistently at risk of corrosion and fatigue
damage, while a new generation of composite airframes is at risk of delamination and disbands
due to impacts and high cyclic loading. Manufacturing defects can also occur in the fabrication
of both metallic and composite structures. Fatigue damage is most prevalent in rotorcraft
structures, as aircraft such as the OH-58D Kiowa Warrior are being pushed to the limits of their
service lives. As a rotorcraft ages, it is highly susceptible to fatigue damage due to the high
cyclic loading of the rotor systems. Vibration based SHM methods are being developed in order
to detect the presence of damage in these structures, before that damage propagates to a point
where the structure fails. For flight critical structures, the loss of the aircraft is of concern.
In order to understand the requirements of an SHM system it is first necessary to examine
the scale at which damage begins and propagates. In practice, some damage exists to some
degree in all materials, and therefore all structures. Damage occurs when any structural flaw
becomes large enough to affect the performance of the system as a whole (Ref. 1). Vibration
based SHM strives to detect changes in an aircraft structure before the damage becomes great
enough to put the vehicle and its occupants at risk.
A 1984 survey by Campbell and Lahey (Ref. 2) detailed the importance of early damage
detection and recognizing the early onset of damage conditions. The survey highlights the origin
of damage and the number of accidents caused at initiation sites on the airframe. Table 1 shows
the initiation sites for rotary-wing vehicles. As evidenced by the data, loose fasteners and joints
in the airframe are a primary cause of accidents in rotorcraft. In practice, damage conditions
often start with a loose fastener, which causes stress concentrations at the nearby fastener holes.
Under repeated loading, the joint can loosen, causing further stress concentrations along the joint
line. If loading continues, fatigue cracks may propagate and lead to catastrophic failure of the
structure. A vibration based SHM system should have the ability to detect loose joints and
fasteners, before these conditions cause critical damage to the airframe.
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Table 1: Initiation sites for damage in rotary-wing vehicles (Ref. 2). Loose fasteners and joints cause the
vast majority of accidents.
Initiation Site Number of
Accidents %
Bolt, stud or screw 32 26
Fillet, radius or other stress concentration 22 18
Corrosion 19 15
Fastener hole or other hole 12 10
Fretting 10 8
Manufacturing defect or tool mark 9 7
Brinnelling, galling, or wear 7 6
Thread (other than bolt or stud) 4 3
Weld 3 2
Subsurface flaw 3 2
Softened condition or subsurface decarburization 2 1.6
Surface scratch or damage 2 1.6
Total 125
The OH-58 Kiowa Warrior is just one example of an aircraft susceptible to fatigue damage.
Fatigue cracks are known to initiate and propagate near crucial joint locations in the airframe.
Previous studies highlighted damage prone areas and used a tail boom test bed in a free hanging
condition to validate vibration based detection techniques (Ref. 3). Fatigue critical areas include
joints near the tail rotor assembly, connection points to the main fuselage, and hanger bearing
mounts for the tail rotor driveshaft. Figure 1 shows a detailed account of damage and initiation
sites on the OH-58D tail boom. Without an automated method to detect these damaged joints and
fatigue cracks, maintenance personnel depend on visual inspection. When damage is found, the
entire tail boom assembly is dismantled and replaced. However, this approach is costly, and
damage can propagate to dangerous levels before maintenance crews detect the problem. A
vibration based damage detection method has potential to detect airframe damage before it
becomes too severe. For this reason, the methods discussed in this report utilized the OH-58D
tail boom test bed to evaluate a number of vibration based damage detection methods.
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Figure 1. Documented OH-58 tail boom damage locations and classification. Damage is grouped around
several locations, including hanger bearing mounts, fuselage mounting points, and tail rotor assembly areas
(Figure from Ref. 3).
1.2 OH-58 Background
The OH-58 Kiowa Warrior is a scout, or light observation helicopter. It was developed in
1961 when Bell was announced as the winner of the Light Observation Helicopter project. It is a
single-engine, single-rotor, two-bladed helicopter. Since the OH-58 was designed as a scout
helicopter, it is equipped with technology such as advanced surveillance, navigation, and a low
light television laser rangefinder/designator (Ref. 4). The OH-58 first arrived in Vietnam in 1969
where it was of vital importance to the United States’ mission. The earlier models of the OH-58
were used only for reconnaissance while more recent versions are equipped with high-powered
weapons.
In 1988 Bell created an armed variant of the OH-58, known as the OH-58D. The OH-58D is
a highly modified version of the OH-58 A/C. The OH-58D was created in response to a request
by the Army, to fill the need for an armed task force support craft, while maintaining the same
scout capabilities as the earlier version. The OH-58D can perform reconnaissance; security,
command and control, target acquisition/designation, and defensive air combat missions (Ref. 5).
The Bell OH-58D has a highly accurate navigation system which allows it to precisely target
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locations and hand off position data to other attack units. In addition the OH-58D added two
more blades to its main rotor as well as weapons such as HELLFIRE missiles, seven HYDRA 70
rockets, two air-to-air Stinger missiles, and a .50 caliber fixed forward machine gun (Ref. 4).
Figure 2 shows the schematic of the OH-58D Kiowa Warrior and the suppliers of each part.
Reference 6 covers additional details on each component of the aircraft.
Figure 2. OH-58D Kiowa warrior schematic (Figure from Ref. 6). The highlighted tail boom was the
component of interest for this study.
In 1997 the OH-58D received an updated, Rolls-Royce Allison 250-C30R/3 650 engine
equipped with an upgraded hot section to eliminate power drops and improve high-altitude and
high-temperature performance. The update also included a GPS navigation system and laser
warning detector to improve aircraft survivability (Ref. 7).
Today the OH-58D has a highly accurate navigation system, infrared thermal imaging
capability, night vision technology, and a laser guided system for its weaponry. The OH-58D
now has a number of available configurations, making it suitable for most support missions. Its
operation readiness rate is above 85%, which is the highest rate of any rotary wing aircraft in the
army fleet. At the end of 2011 the Kiowa OH-58 fleet had achieved a total of 750,000 combat
hours (Ref. 5).
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The OH-58D has been on the front lines of military engagements for the last decade. Since
the Army has introduced a Wartime Replacement Aircraft Program, Bell Helicopter has begun to
build low cost cabins in an effort to extend the life of the fleet. This update will convert the
existing OH-58A cabins into an OH-58D configuration. To maintain its combat effectiveness,
Bell has begun planning an upgrade to the OH-58D, the OH-58F. The F model will have a nose
mounted sensor, the new Control and Display Subsystem 5 (CDS5), integrated Common Missile
Warning System (CMWS), integrated level II MUM-O (Manned-Unmanned Operations). The F
model will use a Honeywell HFS900 engine. This engine delivers 1,021 horsepower. The F
model will update to a 427 tail rotor and gear box assembly for improved control authority.
Reference 8 contains full details of updated components in the future OH-58 variant.
1.3 Vibration based Structural Health Monitoring
Vibration based techniques are typically classified under two categories, modal techniques
(global vibrations) and ultrasonics (local vibrations and wave propagation). When a structure is
damaged, changes in the modal parameters of the system (natural frequencies, mode shapes and
damping) tend to occur, but this technique is typically only effective for detecting large changes
in the system. Ultrasonics can be useful for detecting small changes in the system, such as those
brought on by loose fasteners and fatigue cracks. This project involved using both techniques
and evaluating their sensitivity to relevant damage on the OH-58D tail boom.
1.4 Reciprocity
A concept associated with linear structures is the frequency response matrix of the system
and the phenomenon known as reciprocity. The frequency response matrix for a linear system is
symmetric due to Maxwell’s Reciprocity Theorem. Given an excitation measurement at point i
and a corresponding response measurement at point j, the same excitation value input at point j
should give the same response value at point i. This is illustrated in Figure 3. A reciprocity test is
conducted by comparing these two reciprocal measurements at various pairs of points and
observing any differences between them. If reciprocal measurements agree, then the structure
can be considered linear, and modal analysis can be used to evaluate vibrational properties of the
system.
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Figure 3. Symmetric Frequency Response Matrix.
1.5 Ground Vibration Testing
The goal of ground vibration testing (GVT) is to characterize a structure’s inherent response
to excitations by identifying all critical mode shapes, modal frequencies, and modal damping.
Ground vibration testing is useful for validating and improving existing analytical vibration
models, and for obtaining data for vibration dynamics analysis. GVT is also a means of
quantifying a structure’s response to excitation so that implications about performance, damage,
and fatigue can be evaluated. Once a baseline ‘healthy’ vibration profile is established,
subsequent test results can be compared to the healthy profile to look for deviations that indicate
some form of damage or change in the structure.
1.6 Signal Processing
The goal of signal processing is to convert an analog signal into a digital format suitable for
storage and further processing. A physical quantity, such as acceleration or temperature, is
measured by a transducer and converted to an electrical signal which is then read by the
acquisition system. In ground vibration testing (GVT) the physical quantity of interest is the
movement of a test structure in response to mechanical excitation by a modal impact hammer or
a shaker unit. The transducers, which typically measure velocity or acceleration, are placed at
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grid points along the structure. The locations and number of the transducers are important for
acquiring the complete response of the structure.
In GVT, the structural response is measured as a function of time. The data acquisition
system (DAQ) records measurements from each transducer at discrete time points at a particular
rate, called the sampling rate. The sampling rate must be set such that the highest vibration
frequency of interest will be adequately resolved. Higher frequencies will be aliased and thus
not correctly measured. These frequencies are discarded by a filter as part of the measurement
setup.
Once the excitation input and response signals are acquired they are converted to the
frequency domain using a Fast Fourier Transform (FFT). Considering the data in the frequency
(spectral) domain is important in GVT because the frequency response of the structure is of most
interest. From the spectral data, one can calculate important mathematical quantities such as the
power-spectra (Equation (1)), cross-spectra (Equation (2)), coherence (Equation (3)), and
frequency response functions (FRFs), as seen in Equation (4). In these expressions, denotes a
mean or average, and ( )* is the complex conjugate of ( ). Note that these quantities are all
approximations. To help reduce random error in the spectral estimates, ensemble averaging is
performed.
[ ( ) ( )]
(1)
[ ( ) ( )]
(2)
| |
(3)
| |
(4)
Of greatest importance in GVT are the FRFs and coherence. The coherence function is
indicative of the linear relation between the input and output signals and is often used as a FRF
quality indicator. The amount of nonlinear behavior exhibited by a test structure can be inferred
from the coherence along with the FRF measurement. Coherence is also a measure of the signal-
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to-noise ratio, so that a high coherence value indicates a high causality between the input signal
and the output signal in a linear system. When the input excitation causes the structure to hit a
resonance, there will be a spike in the magnitude of the structure response, showing a clear
correlation between the driving excitation and the resonance response. However, if the structure
is off-resonance or if there is nonlinearity present, there will be little causality between the input
and the response. Likewise, if the coherence is low, nonlinear behavior may be present. The
FRF magnitude increases and peaks when the structure is on resonance, then decreases as the
response frequency moves away from the resonance frequency.
There are many places in this system where errors can arise. Transducers have specific
operating limitations and sensitivities that affect their ability to detect the response and convert it
to an electrical signal, and the way the transducers are mounted to the structure also affect their
performance. The acquisition system setup and FFT analysis also intrinsically introduce error,
such as aliasing and spectral leakage. Errors in the system can be minimized (but never
completely eliminated) by selecting the appropriate acquisition settings.
1.7 Modal Analysis Theory
Modal analysis produces the following global parameters: resonance frequencies, mode
shapes, damped natural frequencies, and damping loss factors. A series of FRFs are obtained for
a grid of sensors and excitation points, then a curve-fitting search on the eigenvalues of the FRF
matrix is used to find the natural frequencies and mode shapes (Ref. 9)
Fitting algorithms are based on assumptions regarding the structure’s dynamic behavior.
The general assumptions are linearity, reciprocity, and time invariance (Ref. 10). Many
algorithms are available for extracting the desired parameters from the FRF and eigenvalue data.
One common algorithm type is singular value decomposition (SVD), where the FRF matrix is
broken into three separate matrices, as shown in Equation (5). [ ( )] is the left singular matrix,
unitary, related to mode shapes, while [ ( )] is the right singular matrix, unitary, related to
modal participation.
[ ( )] [ ( )] [∑( )] [ ( )]
(5)
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The FRF matrix describes the multiple input/multiple output relationship at each spectral
line at the rth
mode. In order to obtain accurate mode shape estimation the mass and geometry of
the structure and the input/output locations must be included (Ref. 9). The mass matrix is
obtained from another analytical method like Finite Element Analysis. The mass-scaled FRF
matrix (Equation (6)) is used in place of the un-scaled FRF matrix. Here [ ] is the mass
matrix, and [ ] is the reduced mass matrix for the reference points.
( ) [ ]
[ ( )][ ]
(6)
The eigenvalues of [ ( )] [ ( )] are obtained and plotted on a log scale as a function
of frequency. The presence of a mode is indicated by a peak on the plot, and the location of the
peak is the damped natural frequency of the mode. The peaks in Figure 4 below are clearly
distinguishable (Ref. 10).
Figure 4. Eigenvalues vs. Frequency.
Not all peaks indicate modes in this method. Other peaks arise from errors due to noise,
leakage (which distorted the FFT output and made it appear more nonlinear (Ref. 10)),
nonlinearity, and cross-eigenvalue effects (effects from out-of-band modes). The peaks are
determined using an automatic peak detector and sorting algorithm based on preset criteria (Ref.
9). After the “good” modes are picked, mode shape estimations can be made, which can also be
decoupled to find the single mode response function for each mode p, as shown in Equation (7).
In this expression, { ( )} is the unscaled mode shape and { ( )} is the equivalent mode
participation factor.
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( ) { ( )} [ ( )]
{ ( )}
(7)
Another common algorithm is Rational Fraction Polynomials (RFPs). This algorithm
minimizes error from out-of-band mode effects by specifying additional terms to the FRF
denominator or numerator (Ref. 10). The rational fraction form is shown in Equation (8), where
are the numerator polynomials and are the denominator polynomials. In general, adding
additional terms results in greater parameter accuracy.
( )
∑
∑
|
(8)
While this method benefits from the ability to adjust the precision of the curve-fitting, the
way the computation is carried out results in a significant drawback. Modes arising only from
computation and have no physical meaning can end up in the curve-fitting band, which makes it
difficult for the user to determine whether a curve is a real mode or meaningless (Ref. 10).
1.8 Data Acquisition and Processing for the OH-58 Tail Boom GVT
The acquisition and processing of the OH-58D tail boom modal test were performed as
follows (Figure 5): A modal force hammer is used to strike the test structure at a specific point.
The impulse transferred to the structure by the hammer is converted to an electrical signal by a
transducer on its contact surface. The accelerometers on the structure measure the impulse at
their remote locations. The measurements are converted to an electrical signal which is recorded
by the DAQ. The data is processed using a program called Modal Impact. Using an FFT
algorithm, the data is converted and processed to produce power spectra, cross spectrum,
coherence, and FRFs. The FRF matrix is created using the structure/sensor locations geometry.
Reciprocity is then invoked so that points where a force was input become response points. The
matrix can then be used in a modal analysis algorithm to solve for the eigenvalues and obtain the
mode shapes, resonance frequencies, and damping loss factors of the test structure.
13
Figure 5. Acquisition and processing flowchart for the OH-58D tail boom modal testing.
1.9 High Frequency Methods and Background
Nonlinear wave modulation spectroscopy (NWMS) (Ref. 11) is another method for
determining the level of nonlinearity in the elastic response of structures. For airframe structural
healthy monitoring, this methodology may prove more useful than modal analysis. The NWMS
method utilizes excitations at frequencies much higher than those obtained using force hammers
in the modal analysis method. Damage detection depends on observing structural frequencies
corresponding to wavelengths similar in magnitude to the damage length scale. The low
frequency bandwidth of the modal analysis techniques may limit its ability to detect damage in
the tail boom. In the NWMS method, a material sample of interest is excited at two frequencies:
an exercising/forcing low frequency wave and a carrier, or probing, high frequency wave. The
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resulting structural response is obtained at various points. An undamaged structure is assumed to
have a linear elastic response. Therefore, for the healthy linear structure, the two fundamental
frequencies will dominate the structural response. However, a damaged structure is expected to
show non-linear behavior. Therefore, for a damaged nonlinear structure, combinations of the two
frequencies will appear as well. Non-linearity can then be measured by the response of the
harmonics of the two waves and the sideband frequencies. It can be assumed that greater
observable non-linearity is indicative of more structural damage. Therefore, the non-linear wave
modulation spectroscopy (NWMS) method may be used as an effective non-destructive damage
detection technique.
For the OH-58 system, electronic shakers were used for the frequency inputs at the tail rotor
and near the mid-point. The shaker at the tail rotor location was taken to be the
exercising/forcing wave, and the shaker located near the mid-point was taken to be the
carrier/probing wave. Damage was simulated by loosening a hanger bracket located between the
two shakers. The shakers are capable of reliably inputting continuous wave frequencies far above
those given with the force hammer. It will be shown, later, that the low to mid-frequency modal
analyses do not yield significant differences between the healthy and damaged responses. As
such, the non-linear wave modulation spectroscopy tests were generally conducted at much
higher frequencies for the carrier wave. Furthermore, the non-linear wave modulation
spectroscopy method was shown to be critical in detecting damage for the OH-58. In this report,
NWMS studies are referred to as high-frequency tests.
The non-linear response in the high-frequency tests is dependent upon the chosen
frequencies for the carrier and forcing signals, and their respective magnitudes. In general, as the
forcing magnitude increases, the level of non-linearity observed by the damaged structure
increases. However, this phenomenon shows a hysteretic behavior. That is, there is not a linear
relationship between forcing input magnitude and the non-linear response of the damaged
structure. This phenomenon was explored in the OH-58 tail boom test bed.
The high-frequency tests were classified into three different subsets: active-active, active-
passive, and passive testing. For the active-active tests, the forcing signal at the tail rotor and
carrier signal near the mid-point of the tail boom were varied to obtain the optimal non-linear
response for the damaged condition. In active-passive tests, the forcing frequency was set to the
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fundamental tail rotor frequencies and harmonics native to the OH-58. For passive testing, the
mid-point shaker was turned off, and forcing frequency was again set to the tail rotor
fundamental frequencies and harmonics. For each testing subgroup, comparisons between the
healthy and damaged condition response were observed. The active-passive and active-active
tests utilized the NWMS method. Furthermore, each testing subgroup represented varying levels
of hardware implementation for field testing, and, therefore, cost of application. The passive tests
can be easily reproduced on an existing OH-58 without much additional hardware. The active-
passive tests would require the use of some external signal input, and the active-active tests
would require two external signal inputs. Naturally, the cost of implementation of these testing
techniques into real-world application would be a significant concern. Therefore, the
effectiveness of each method was explored. Chapter 4 discusses these results in detail.
1.10 Research Objectives
Vibration based structural health monitoring methods have been developed and used on a
variety of test beds, including both simplified specimens and real airframe structures. The
purpose of this study was to evaluate both traditional modal methods and high frequency
methods for use on the OH-58D Kiowa Warrior. By using an actual OH-58D tail boom structure
and simulating a common form of damage, the goal was to investigate the use of vibration based
techniques and evaluate which of these techniques result in the best damage detection capability.
Some techniques would be more practical than others for real world applications. Therefore,
another goal of this study was to evaluate the practicality of using these techniques on a real
aircraft. Specific testing objectives included the following:
1. Testing for reciprocity to confirm the linear characteristics of the test bed.
2. Preliminary modal testing to extract the first cantilevered modes of the tail boom.
3. Full modal testing using a 500 Hz (low frequency) bandwidth to extract all relevant
modes. FRF’s were studied and compared between healthy and damaged conditions
to evaluate modal methods in damage detection.
4. Mid-frequency impact testing at a bandwidth of 2000 Hz. Again FRF’s were
compared between healthy and damaged conditions.
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5. High frequency testing using a 20000 Hz bandwidth and two shakers at selected
drive frequencies to excite the nonlinear response of the damage. Healthy and
damaged conditions were compared to evaluate detection capability (active).
6. High frequency testing using one shaker to excite only the natural rotor harmonics of
the OH-58D. Again, healthy and damaged conditions were compared (passive).
7. High frequency testing using both a high frequency actuator and rotor harmonics.
Healthy and damaged cases were also evaluated for this mixed approach (active-
passive).
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Chapter 2: Experimental Procedure
2.1 Test Bed
As mentioned previously, the chosen test bed was an OH-58D tail boom. The tail boom was
stripped down to its base structure, with the tail rotor, tail rotor drive train, horizontal and
vertical stabilizers removed. For accurate testing, the weight of missing parts, such as the
horizontal and vertical stabilizers, was simulated to approximately match the correct total mass
and center of gravity. The gearbox mass model was made up of steel and aluminum. Drive shaft
mass models were distributed along the body of the tail boom using hanger bearing brackets. A
bracket was loosened to represent a common type of damage on the structure. Mass was removed
from this bracket in order to simplify testing. A rigid wall mount apparatus with an octagon plate
was manufactured to mount the tail boom on the wall. Accelerometers were placed along the
body of the tail boom, and on vertical and horizontal stabilizers.
2.2 Reciprocity and First Bending Mode Tests
Before the first bending mode test was conducted, a reciprocity test was performed to ensure
accurate FRFs and coherence were achieved from point to point along the structure. Once this
test was completed the first bending mode test was conducted. Two accelerometers were placed
on the upper surface and two accelerometers were placed on the side of the boom. Locations
along the hard points of the tail boom were selected and hit with a soft tipped medium hammer.
Response at each accelerometer location was taken and FRFs between accelerometer pairs were
compared. This preliminary modal test used six modal points in the vertical direction, and six
modal points in horizontal direction, in order to extract the first bending modes. Figure 6 and
Figure 7 show the instrumentation setups for each first bending mode test. Table 2 shows the
data acquisition parameters fed into the Modal Impact acquisition software for the first bending
mode tests.
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Figure 6. First vertical bending mode test setup using accelerometers on the upper surface.
Figure 7. First horizontal bending mode test setup using accelerometers on the horizontal axis.
Table 2: Acquisition parameters for the first bending mode tests.
Parameter Value
Bandwidth 500
Blocksize 131072
Fs (Hz) 1280
T (s) 102.4
df (Hz) 0.009765625
dt (ms) 0.78125
Analog Trigger On
Trigger Channel 1
Slope Rising
Level (%ADC) 1.0
Pretrigger (%Blocksize) 10.0
Window NONE
Averaging Mode RMS
Weighting Linear
Number of Averages 3
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2.3 Full Modal Tests
A full modal test was then conducted. The full impact test was achieved using uni-axial
response accelerometers, which were placed along the tail boom in various locations. At each
accelerometer point, several hammer impacts were averaged to ensure precise data. The response
of the hammer hits were acquired at all of the measurement locations during a time which
allowed for the response to completely damp out. A frequency response function was then
computed between the impact and measurement locations. This was repeated for each uni-axial
accelerometer locations. Figure 8 shows the modal geometry mesh of the tail boom that was used
during the test. Each node point represents a hit point along the tail boom. The geometry was
used to display mode shapes during processing of the modal test. Figure 9 shows the
instrumentation setup for the full modal testing. Seven channels of accelerometers were used in
all, and 104 modal points were used in order to resolve major vibrational modes.
Again the acquisition parameters (Table 3) were loaded into the Modal Impact code, which
performed acquisition and preliminary processing. The test consisted of averaging three hits at
each of the 104 points designated over the tail boom. The Modal Impact program recorded and
averaged the hammer hits, displaying frequency and time trace damping. Once the healthy
condition was fully tested, the damaged condition was tested in the same fashion.
Figure 8. Hit point mesh for the full modal tests. Each node represents one modal point.
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Figure 9: Full modal testing setup. Horizontal accelerometers: 16, 52, 100. Vertical accelerometers: 25,
61, 89, 100. Numbers correspond to modal points on tail boom. 104 modal points were used in all. Damage
was induced by loosening a hangar bearing bracket near the mid-section of the tail boom.
Table 3. Acquisition parameters for the full modal test.
Parameter Value
Bandwidth 500
Blocksize 16384
Fs (Hz) 1280
T (s) 12.8
df (Hz) 0.078125
dt (ms) 0.78125
Analog Trigger On
Trigger Channel 1
Slope Rising
Level (%ADC) 1.0
Pretrigger (%Blocksize) 10.0
Window NONE
Averaging Mode RMS
Weighting Linear
Number of Averages 3
2.4 Mid-Frequency Impact Testing
Impact hammer testing for a mid-frequency range was the next step. Table 4 shows the mid-
frequency testing parameters. This testing also involved adding damage to the structure by again
loosening the hanger bracket on the top of the structure. FRFs were taken over the damage
location, using the accelerometer at point 25. Figure 10 shows the four hit points that were
chosen along the upper surface. Five of the mid-frequency tests were of the healthy configuration
and the other five were of the damaged configuration. Each test consisted of four hit points
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running along the top of the tail boom, which were hit ten times each. As a result of adding
localized damage to the structure, there was an expectation to see changes in the FRFs at higher
frequencies.
Figure 10. Mid-frequency impact testing setup. A vertically oriented accelerometer was used at point 25.
Numbers correspond to modal points on tail boom. Three hit points were chosen in all, corresponding to
modal points 38, 49, and 61.
Table 4. Acquisition parameters for the mid-frequency impact testing.
Parameter Value
Bandwidth 2000
Blocksize 8192
Fs (Hz) 5120
T (s) 1.6
df (Hz) 0.625
dt (ms) 0.1953125
Analog Trigger On
Trigger Channel 1
Slope Rising
Level (%ADC) 1.0
Pretrigger (%Blocksize) 10.0
Window NONE
Averaging Mode RMS
Weighting Linear
Number of Averages 10
2.5 High Frequency Testing
The next step of the project focused on the analysis of the nonlinearities that appear in a
damaged testing configuration. As described in Chapter 1, damage such as fatigue cracks and
loose joints cause a nonlinear wave modulation when two distinct excitations are introduced.
This “clapping” mechanism acts as a nonlinear scatter, with the damage essentially acting as a
secondary source driving at the nonlinear frequencies. An electromagnetic shaker (Wilcoxon F4
shaker) located at the aft end of the tail boom was used to induce a low frequency vibration,
22
while a piezoelectric shaker (Wilcoxon F7 shaker), located near the position of the horizontal
stabilizer, was used to excite a high frequency vibration. Figure 11 shows the positions of the
high frequency actuators on the tail boom test bed. In order to account for the added weight of
the shaker at the tip, equivalent mass, simulating the tail rotor assembly, was removed from the
setup. In addition to actuators, strain sensors and accelerometers were also installed on the tail
boom. 7 strain sensors, distributed along tail boom length, were used to measure dynamic strain.
5 accelerometers were used to acquire an acceleration signal. Figure 12 shows the
instrumentation package installed on the tail boom. Additional components were needed to
complete the test setup, including equipment to monitor voltage and current to the shakers,
National Instruments input and output cards, and a function generator LabView code. Table 5
lists the acquisition parameters loaded into the Modal Impact code. A maximum bandwidth of
20000 Hz was used to resolve higher frequencies, and a Hanning window was applied to the data
in order to resolve an accurate frequency spectrum from the steady-state signals. Using acquired
signals, a nonlinear detection feature was then calculated by analyzing the nonlinear sidebands.
Various aspects of the nonlinear response were studied. These procedures are described in
Chapter 4.
Figure 11: Actuator setup for high frequency testing. The Wilcoxon F4 was mounted underneath the
free end, while the piezoelectric F7 was mounted near the mid-section.
23
Figure 12: Tail boom instrumentation setup. 5 accelerometer channels: 4 in the vertical orientation, 1
mounted in the horizontal orientation (on bulkhead). 7 strain gage channels: 6 mounted in the longitudinal
direction, 1 mounted in the vertical direction (on bulkhead).
Table 5: Acquisition parameters for high frequency testing.
Parameter Value
Bandwidth 20000
Blocksize 65536
Fs (Hz) 51200
T (s) 1.28
df (Hz) 0.78125
dt (ms) 0.01953125
Analog Trigger Off
Trigger Channel 1
Slope Rising
Level (%ADC) 1.0
Pretrigger (%Blocksize) 10.0
Window Hanning
Averaging Mode RMS
Weighting Linear
Number of Averages 10
The first high frequency method was an active-active approach. This involved using both
installed shakers to drive the structure at set frequencies. A number of frequency pairs were
studied to determine the effects of frequency on the nonlinear response. In addition, amplitude
sensitivity and hysteresis studies were carried out to observe the effects of both drive frequency
amplitudes on the nonlinear response and individual sideband amplitudes. From these studies,
24
drive conditions with high nonlinear response were chosen. Healthy measurements were then
taken and compared to the damaged response in order to determine detection sensitivity. Healthy
and damaged conditions were compared by evaluating nonlinear dB. This metric represents the
change in nonlinear magnitude between damaged and healthy conditions. Positive numbers mean
more nonlinear content due to the damage source.
For low frequency amplitude studies using two inputs, the high frequency was held at
constant at 100 V drive amplitude. Low frequency amplitude was increased to a peak value, then
decreased to observe characteristics of the response at various frequencies. The nonlinear
metric, drive frequency harmonic amplitudes, and sideband amplitudes were observed. For high
frequency amplitude studies the low frequency was held constant with drive current. The high
frequency amplitude was increased to a peak value, then decreased to observe response
characteristics.
Further high frequency studies focused on a fully passive and an active-passive approach. For
fully passive studies, the tail boom was driven only at the tail rotor rotation frequency, blade
passage frequency, and first two harmonics of the blade passage frequency. Using only the
natural vibrations of the helicopter with a spinning rotor, nonlinear characteristics were observed
in the spectrum and quantified to evaluate detection capability. For active-passive studies, one
high frequency vibration was input along with the rotor harmonics. In these tests the rotor
harmonics acted as the low modulation frequencies, causing substantial sideband activity around
the driven high frequency. Various aspects of the spectrum were analyzed to determine detection
capability compared to the previous techniques.
25
Chapter 3: Modal and Mid-Frequency Results and Discussion
3.1 Reciprocity
Before conducting modal testing on the tail boom structure, a reciprocity study was
conducted. This study aimed to prove the linear characteristics of the structure in order to
validate the use of the modal analysis techniques. Figure 13 shows the reciprocity test results
between points 100 and 61. The testing produced good correlation between the low frequency
peaks, but showed less similarity between higher frequency peaks. It is assumed that this is due
to nonlinearities in the structure and the compliance of the impact hammer (roll off in drive force
level) used for these tests.
61 100
0 50 100 150 200 250 300 350 400 450 50010
-5
10-4
10-3
10-2
10-1
100
101
Frequency (Hz)
Ma
gn
itu
de
(E
Uo
ut/E
Uin
)
FRF's Between Modal Points 61 and 100
H1,4 : Pts. 100,61 : Units (m/s2)/(N)
H1,5 : Pts. 61,100 : Units (m/s2)/(N)
Figure 13. Reciprocity Setup and FRF Results between Points 61 and 100.
26
Figure 14 shows the reciprocity test results between points 61 and 25. The testing at these
points also produced good correlation between the low frequency peaks and showed less
similarity between higher frequency peaks. At approximately 175 Hz and higher the FRFs begin
to deviate. Again, this could be due to nonlinearities in the structure which are excited at these
higher frequencies. Overall, the reciprocity results agreed well enough at lower frequencies that
full modal testing could be performed with confidence.
Figure 14. Reciprocity Setup and FRF Results between Points 61 and 25.
3.2 First Bending Mode Results
In order to characterize the first bending modes of the tail boom structure, a large acquisition
time was required so that the modes would damp out and spectral leakage could be reduced.
Using a T value of 102.4s, the FRF was sufficiently resolved, and the resonance peak at
0 50 100 150 200 250 300 350 400 450 50010
-4
10-3
10-2
10-1
100
101
Frequency (Hz)
Ma
gn
itu
de
(E
Uo
ut/E
Uin
)
FRF's Between Modal Points 61 and 25
H1,7 : Pts. 61,25 : Units (m/s2)/(N)
H1,4 : Pts. 25,61 : Units (m/s2)/(N)
61
25
27
approximately 2.7 Hz was well defined. The coherence of the system at the resonance frequency
was found to be 0.97, indicating a quality measurement.
Figure 15. Sample FRF and Coherence at T = 102.4s
The vertical and horizontal bending mode tests consisted of hitting each hit point three times
and averaging the data taken at each point. This test was conducted strictly to obtain and analyze
the first vertical and horizontal bending modes. Figure 16 shows the FRF of the horizontal modal
test. The first horizontal bending mode was found to be at 1.8 Hz with a loss factor of 0.00481.
Looking at the figure, the blue line represents the FRF taken at point 2 and the red line represents
the FRF taken at point 5. Since both hit points are towards the center of the tail boom, they both
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510
-4
10-3
10-2
10-1
100
101
Ma
gn
itud
e (
EU
ou
t/EU
in)
Sample FRF: T=102.4s
X: 2.725
Y: 2.736
H1,7 : Pts. 1,3 : Units (m/s2)/(N)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.2
0.4
0.6
0.8
1
Frequency (Hz)
Ma
gn
itud
e
Coherence
X: 2.725
Y: 0.973
C1,7 : Pts. 1,3
28
have visible peaks at roughly 1.8 Hz. However, it should be noted that the peaks are not very
well defined for this case. This could be due to lower coherence at the lower frequency range,
even though a large sample time was used in taking the data. Because of the lower resolution, the
loss factor may be inaccurate at this resonance peak.
Figure 16. First horizontal bending mode drive point accelerance. The drive point accelerance at modal point
2 is shown in blue, while the drive point accelerance at modal point 5 is shown in red.
Similar testing was conducted to find the first vertical bending mode. Figure 17 shows the
drive point accelerance plots taken for the first vertical bending mode test. The first vertical
bending mode was found to be at 2.7 Hz, with a loss factor of 0.0039. In the figure, the blue line
represents the FRF taken at point 3 and the red line represents the FRF taken at point 6. The
drive point accelerance at modal point 6 likely shows minimal changes in magnitude over the
frequency range due to its proximity to the wall mount. The peak in the drive point accelerance
of modal point 3 is well defined due to good coherence of measurements at this frequency. The
first horizontal mode is also visible in this plot, possibly due to a cross-coupling effect in the
measurement, excitation, or both.
29
Figure 17. The first horizontal bending mode drive point accelerance. The drive point accelerance at modal
point 2 is shown in blue, while the drive point accelerance at modal point 5 is shown in red.
3.3 Full Modal Results
To obtain a definitive description of the response of the OH-58 tail boom structure, a
thorough modal analysis was conducted. Accelerometers were distributed along the tail boom
according to the specifications shown in Figure 9, such that good resolution of the main
structural response modes could be expected. Horizontal accelerometers were placed at points
16, 52, and 100 and vertical accelerometers were placed at points 25, 61, and 100. Recall that a
total of 104 modal hit points were used.
Next, data acquisition parameters were chosen such that the low-frequency dominant
response modes were well resolved, with the exception of the first horizontal and vertical
bending modes previously discussed. As in the previous tests, the method of frequency input was
30
through a force hammer with a rubber tip. An acquisition bandwidth of 500 Hz was used with a
blocksize of 16384, giving acquisition times of 12.8 s, frequency resolution of 0.078 Hz and time
resolution of 0.78 ms. Three averages were taken for each modal point, and force was input to all
104 modal points. A summary of the data acquisition parameters was previously shown in Table
3.
Figure 18 shows the drive point accelerance FRFs for the healthy condition at each of the
respective accelerometer modal points: 16, 25, 52, 61, 89, and 100. The plot shows a complex
response signature at each drive point, with peaks representing resonance frequencies.
Additionally, several pertinent tail rotor frequencies are plotted as dashed lines. The tail rotor
fundamental frequency is 39.7 Hz, blade passage frequency is 79.4 Hz, the first harmonic is
158.8 Hz, and the second harmonic is 238.2 Hz. It can be noted that the tail rotor fundamental
frequency, and first and second tail rotor harmonics are each near resonance frequency peaks,
indicating possible fatigue concerns at those given frequencies. Figure 19 shows the main rotor
frequencies with the drive point accelerance response. The main rotor fundamental frequency is
6.6 Hz, blade passage frequency is 26.4 Hz, the first harmonic is 52.8 Hz, and the second
harmonic is 79.2 Hz. The main rotor second harmonic frequency is observed to be near a
frequency response peak, and is also near the tail rotor blade passage frequency. Additionally,
the main rotor first harmonic is found near another resonance peak. Later, the mode shapes
associated with the frequency response peaks near rotor frequencies will be analyzed. Figure 20
shows only the drive point accelerance response up to 100 Hz, for which ten distinct modes are
apparent past the first vertical and horizontal bending modes. Later, these modes will be
classified and modeled experimentally.
A comparison between healthy and damaged conditions for the low-frequency modal
analysis is desired. Negligible differences between the healthy and damaged conditions for the
low-frequency tests are expected because low frequency inputs generally correspond to structural
wavelengths longer than the damage length scale. Figure 21 shows the drive point accelerance at
modal point 16 for both the healthy and damaged conditions. It is apparent that, particularly for
the lower frequencies studied (less than 300 Hz), that there are very little differences between the
responses for the healthy and damaged conditions, as expected. However, slight differences in
response magnitudes corresponding to frequencies greater than 300 Hz between the healthy and
31
damaged conditions emerge. It is noted that, for frequencies up to approximately 400 Hz,
resonance peaks are found at the same frequencies for each condition. Furthermore, low
coherence is observed above 200 Hz, as shown in Figure 22, indicating that these measurements,
and thus comparisons between healthy and damaged conditions, are not necessarily reliable.
Similar comparisons between the healthy and damaged conditions were observed for drive point
accelerance at the other accelerometer modal points (25, 52, 61, 89, 100).
Figure 18. Drive point accelerance frequency response functions (healthy condition). Tail rotor
harmonics are shown as dashed lines throughout the FRF plots.
32
Figure 19. Drive point accelerance frequency response functions (healthy condition). Main rotor
harmonics are shown as dashed lines throughout the FRF plots.
Figure 20. Drive point accelerance frequency response functions (healthy condition), up to 100 Hz.
33
Figure 21. Negligible FRF differences between damaged, healthy condition for low-frequency input at point
16.
Figure 22. Coherence for drive point accelerance at point 16, healthy condition, deteriorates past 300 Hz.
34
Distinct modes were computed using Singular Value Decomposition (SVD), then a sifting
routine was employed to sort out those modes deemed to be of practical interest. That is, false
modes, for which phase shift does not equal 180 degrees, or repeated modes, were not
considered. A Rational Fraction Polynomial (RFP) method was used to model each of the
distinct modes.
Table 6 below details the classification of the main modes discovered, and the RFP
resonance frequencies and loss factors associated with each mode for both the healthy and
damaged conditions. The dominant resonant modes in the studied low frequency range that are
found in the healthy condition are also found in the damaged condition. Recall previously that
the first vertical and horizontal bending modes were determined.
Table 6 shows that modal analysis also uncovers the existence of second and third vertical
and horizontal bending modes. Additionally, torsional and flapping stabilizer modes are found.
Finally, several shell modes are discovered in both the healthy and damaged cases, up to n = 3.
These and other modes of interest are shown in the Appendix. The third bending modes, shown
in Figure 23 and Figure 24, are excited at frequencies near the main rotor first harmonic. The
shell mode associated with the response at 78.3 Hz is another of particular interest, in Figure 25.
This mode shape shows large deflections near the tail rotor itself, or the aft of the tail boom. As
noted previously, the main rotor second harmonic frequency of 79.2 Hz and tail rotor blade
passage frequency of 79.4 Hz are both near this resonance frequency. Previously, it has been
observed that fatigue damage likely occurs in the aft section of the tail boom. It stands to reason,
therefore, that the main rotor first and second harmonics, and tail rotor blade passage frequencies
may be exciting these resonances, and potentially initiating damage.
The RFP loss factors versus resonance frequencies are plotted in Figure 26 below, for both
healthy and damaged conditions. There is excellent agreement between healthy and damaged
conditions for the resonant frequencies associated with each mode. Additionally, there is
excellent agreement between healthy and damaged conditions for loss factors associated with
bending modes, torsional stabilizer modes, and flapping stabilizer modes. However,
discrepancies begin to appear between the healthy and damaged conditions for loss factors
35
associated with shell modes, particularly those at higher frequencies. It is assumed that these
differences are due to the aforementioned poor coherence for the higher frequencies studied.
As expected, for the most part, there are negligible differences between the low-frequency
responses for the healthy and damaged conditions. Response modes, and corresponding
resonance frequencies and RFP loss factors are in excellent agreement for the dominant bending
modes and stabilizer modes. The length scale of the damage is much shorter than the structural
wavelengths induced by the low-frequency hammer excitation. It is expected that differences in
response will arise at frequencies for which wavelengths are on the same order of magnitude, or
less than, the length of damage.
Table 6. RFP resonance frequencies, damping loss factors, and mode classification for healthy and
damaged cases.
Damaged Healthy
RFP Res
Freq (Hz)
RFP Loss
Factor
RFP Res
Freq (Hz)
RFP Loss
Factor
Mode Classification
17.83 0.004 17.81 0.004 2nd Bending Horizontal
22.16 0.004 22.15 0.004 2nd Bending Vertical
32.73 0.006 32.75 0.006 Symmetric Stabilizer Torsional
41.70 0.008 41.73 0.008 Asymmetric Stabilizer Torsional
56.36 0.009 56.36 0.008 3rd Bending Horizontal
60.53 0.017 60.53 0.017 3rd Bending Vertical
78.62 0.035 78.28 0.026 Aft Shell
83.26 0.018 83.23 0.009 Aft Shell (n=2)
86.82 0.016 86.72 0.013 Aft Shell (n=2)
89.75 0.017 89.74 0.014 Aft Shell (n=2)
126.88 0.001 126.91 0.002 Horizontal Stabilizer Flapping
139.57 0.009 140.24 0.007 Vertical Stabilizer Flapping
177.56 0.012 177.09 0.008 Aft Shell (n=3)
183.23 0.007 183.27 0.006 Aft Shell (n=3)
219.08 0.014 219.31 0.014 Aft Shell (n=3)
262.52 0.005 262.17 0.007 Aft Shell (n=3)
316.11 0.012 315.36 0.004 Asymmetric Horizontal Stabilizer
Flapping
36
Figure 23. Third horizontal bending mode (56.4 Hz). This mode is potentially excited by the main rotor
first harmonic, and shows a high strain region near the aft section of the tail boom.
Figure 24. Third vertical bending mode (60.5 Hz). This mode may also be excited by the main rotor first
harmonic, and shows high strain near the tail rotor assembly.
Figure 25. Aft shell (n = 1) mode (78.3 Hz). This mode is potentially excited by both main and tail rotor
harmonic frequencies. Again, this mode shows high strain at the aft tail boom location.
37
Figure 26. Negligible differences are shown between healthy, damaged conditions for RFP loss factors,
particularly at lower frequencies.
3.4 Mid-Frequency Results
Next, a mid-frequency hammer excitation was examined. As shown in Table 4, a bandwidth
of 2000 Hz was used for this testing. Again, a comparison between healthy and damaged
conditions was desired. Five tests were taken for each condition. The upper confidence band was
created by averaging the healthy FRF data for the five tests, then adding two times the standard
deviation between the five tests. The lower confidence band was created using the same method
except two times the standard deviation was subtracted from the five test average. Overall, there
was little deviation between the damaged condition and the healthy confidence bands at point 25.
Figure 27 shows the FRF magnitude at point 25 as well as a sample peak where the damaged
magnitude shows little deviation from the confidence bands.
38
Figure 27. Mid-frequency FRF magnitude at Point 25.
While most of the well-defined peaks showed little deviation, there were some frequencies
where notable deviations were measured. One such peak occurred at about 788 Hz. At this
frequency the damaged magnitude was 1.74 dB higher than the upper confidence band and 1.98
dB higher than the lower band. This peak, as well as the coherence at 788 Hz, is shown in
Figure 28.
Figure 28. Point 25 - FRF magnitude and coherence at 788 Hz.
Similar to point 25, the damaged FRF magnitude at point 38 did not deviate significantly
from the healthy condition confidence bands, at most of the resonance peaks. At several of the
peaks the damaged magnitude fell between the confidence bands, several examples of this are
shown in Figure 29. This indicates an inability of frequencies at this range to excite
nonlinearities due to the damage.
39
Figure 29. Point 38 FRF magnitude.
This point also exhibited a few peaks where the damaged magnitude was notably higher
than the healthy condition. Figure 30 shows one such peak, located at 734 Hz, and the coherence
at that frequency. While the healthy coherence at this frequency is good the coherence for the
damaged condition is not as desirable. This difference in coherence may be due to the damage, or
an inability of the impact hammer to excite a linear response at these frequencies. Overall, the
coherence at point 38 is worse than the coherence at point 25, at higher frequencies. However, at
most of the resonance peaks the coherence is good, especially at lower frequencies. Figure 31
shows an example resonant peak with good coherence.
Figure 30. Point 38 - FRF magnitude and coherence at 734 Hz.
40
Figure 31. Point 38 - FRF magnitude and coherence at 284 Hz.
Points 49 and 61 showed similar results to points 25 and 38. For the most part, the damaged
magnitude does not deviate significantly from the healthy condition in either case. The data at
these points showed good coherence at resonance peaks and dropped significantly at off resonant
conditions.
For all four test points the majority of the resonance peaks for the damaged conditions
showed only minor deviations from the healthy confidence bands. Deviation in FRF magnitude
between the healthy and damaged conditions for each test was limited to less than 3 dB.
Deviations of this level are not considered to be very significant, especially since results proved
difficult to repeat. However, these deviations are greater than those observed in the low
frequency modal methods, suggesting that the mid-frequency method may show a slight
sensitivity to damage. This is likely due to the fact that the wavelengths of the forcing
frequencies applied to the specimen are larger than the physical size of the damage.
In many cases where deviations in healthy and damaged measurements do exist, coherence
at these frequencies is often poor for the damaged condition. This suggests that the damage
introduces additional non-linearity into the system, causing the coherence to drop. Based on
these results, definitive conclusions cannot be drawn regarding the effect of the induced damaged
on the mid-frequency FRF magnitude. This type of mid-frequency testing does not appear to be
an adequate method to detect the type of damage induced. However, further investigation would
be required to determine this conclusively. The drops in coherence at higher frequencies could
be due to compliance in the material used to manufacture the impact hammer tip, as well as the
41
tail boom specimen. Some measurements showed significant force roll-off at higher frequencies
(an extreme case of this is shown in Figure 32), which contributed to the poor coherence over
this range. In order to improve the coherence and repeatability of the experiment, a piezoelectric
actuator could be used to input a white noise signal into the specimen. Using a set voltage for
each white noise input would result in an equal amount of force being input for each excitation.
Using this method, it would likely be easier to observe where FRF’s show changes in the
damaged condition. However, due to time constraints additional mid-frequency testing was not
pursued. Rather, the decision was made to move on to higher frequency methods.
Figure 32. Force hammer autospectrum. The spectrum shows significant force roll-off above
approximately 300 Hz.
0 200 400 600 800 1000 1200 1400 1600 1800 200010
-5
10-4
10-3
10-2
10-1
100
101
102
Frequency (Hz)
Ma
gn
itu
de
(N
2)
Force Hammer Autospectrum
42
Chapter 4: High Frequency Results and Discussion
4.1 High Frequency Introduction
As discussed in Chapter 1, high frequency methods have proven to be very sensitive to small
sources of damage and material flaws in structures. In each high frequency testing method used
in this study, data from individual sensors was analyzed to extract relevant spectral information
pertaining to the damage. In particular, damage detection metrics focused on sidebands
(combinational tones between two driving frequencies) and higher harmonics (multiples of drive
frequencies). Nonlinear Strain (NLS) and Nonlinear Acceleration (NLA) calculations were used
to determine the magnitude of these quantities over the frequency band of interest. Equations (9)
and (10) show the frequency domain formulations for NLA and NLS, respectively. In these
expressions, is the spectral acceleration value, is the spectral dynamic strain value, is the
initial frequency in the integration band, and is the final frequency in the integration band. The
summation represents the fact that many frequency bands can be integrated and summed to
obtain the final nonlinear magnitude. Similarly, in some applications a wide range of the
autospectrum was integrated. The calculation used for the metric depended on the type of testing
being performed.
∑
∫ [
]
(9)
∑
∫ [
]
(10)
4.1 Active-active Testing
In the active-active configuration, two shakers were used simultaneously, as configured in
Figure 12. In the active-active approach, two frequencies are chosen and input into the system.
As discussed in Chapter 2, in a completely linear system the response will have two frequency
components corresponding to the input frequencies. When nonlinearities are introduced into the
system, the response will exhibit combinational tones of the input frequencies, as shown in
Figure 33. These sidebands can be quantified and used to evaluate the damage state of the
43
structure. The active-active study began by choosing appropriate drive conditions based on
previous studies on the OH-58D tail boom (Ref. 13). A high drive frequency of 4700 Hz and a
low drive frequency of 1000 Hz were used initially.
Figure 33. Modulated wave effect due to nonlinearities in the system.
Before comparing healthy and damaged measurements, an amplitude study was conducted
to observe which low frequency drive condition excited the highest nonlinear response in the
damaged condition. By picking a drive condition that excited a high magnitude response, it was
assumed maximum detection sensitivity could be obtained by observing the difference between
damaged and healthy conditions. Note that the active-active damage feature consisted of using
Equations (9) and (10) to integrate over the first three sidebands, individually, on either side of
the high frequency. These magnitudes were then added to yield the total nonlinear strain or
acceleration for each sensor. Sensor stations were assigned as shown in Figure 34, where each
number corresponds to a position along the tail boom. Stations 3 and 4 were the closest stations
in proximity to the damaged hanger bearing bracket.
Amplitude studies focused on the sensor at station 3 (Figure 35), in an attempt to acquire the
strongest damaged response. The high frequency of 4700 Hz was held at a constant 100 V of
drive amplitude using the F7 shaker. The low frequency of 1000 Hz was then increased in 0.1 A
drive current increments using the F4 electromagnetic shaker. At a peak value of 1 A, the low
frequency drive amplitude was then lowered gradually back to 0. The result is the curve shown
in Figure 36. From this plot, a drive amplitude of 0.8 A was chosen as the best low frequency
drive amplitude (-73 dB). It was determined that past 0.7 A, increasing the amplitude further had
only incremental effects on the nonlinear magnitude, so later studies used 0.7 A as a maximum
value in order to prevent stressing the shaker to its highest operating point.
44
Figure 34. Station configuration for sensors along the length of the tail boom. The damage lies between
stations 3 and 4. These stations are used to classify measurements from each sensor in healthy vs. damaged
comparisons. The strain at station 3 was referenced for most amplitude sensitivity measurements performed
in this study.
Figure 35. Close up view of the hanger bearing bracket damage source and the nearest sensor.
Figure 36. Nonlinear strain magnitude vs. shaker amperage for the station 3 sensor, using 4700 Hz (100
V) and 1000 Hz. Note the highest nonlinear magnitude was found using 0.8 A of drive current with the F4.
45
Having determined 0.8 A to be the best drive level for the exercising frequency with all
other conditions unaltered, the bracket was tightened, returning the structure to its healthy state.
4700 Hz (100 V) and 1000 Hz (0.8 A) signals were input and a healthy measurement was taken.
Converting both damaged and healthy data sets to a dB scale and subtracting the nonlinear
magnitude at each station yielded Figure 37, which shows the NLS and NLA dB between
healthy and damaged conditions. The positive numbers indicate positive detection sensitivity at
each station (See Figure 34). The highest change in NLS comes at station 3 with a detection
sensitivity of 5 dB. This is significant since that sensor lies very close to the damage. However,
station 4 is also close to the damage source, and yet this station shows less than 1 dB in detection
sensitivity. NLA measurements show more change than NLS, with station 6 notably showing a 6
dB increase.
Figure 37. A noticeable difference exists between healthy and damaged measurements, using drive
conditions of 4700 Hz (100 V) and 1000 Hz (0.8 A).
In an effort to increase detection sensitivity, a number of frequency pairs were evaluated in a
similar fashion. Lower exercising frequencies of 500 Hz and 200 Hz resulted in strong detection
sensitivity in many cases, as shown in Figure 38 and Figure 39. However, repeated tests showed
wide variation in these measurements. Future studies may focus more on the uncertainty of
46
repeated measurements at these frequencies. Despite this, the use of lower exercising frequencies
could prove useful, as these frequencies are typically in the vicinity of rotor harmonics. Later
sections will discuss the use of rotor harmonics in high frequency NWMS damage detection
techniques.
Figure 38. 4700 Hz (100 V) and 500 Hz (0.5A) drive conditions also show detection capability.
47
Figure 39. 4700 Hz (100 V) and 200 Hz (0.7A) drive conditions also show detection capability.
Further studies investigated the effect of the high frequency probing/carrier wave on damage
detection ability. This frequency was varied to 5700 Hz and 6700 Hz, and similar low frequency
amplitude studies were carried out. Figure 40 shows the low frequency amplitude hysteresis
curve for 6700 Hz (100 V) and 1000 Hz drive conditions. As evidenced by the curve, the peak
NLS value surpasses that of the previous carrier wave, reaching a magnitude of -68 dB,
compared to the -73 dB NLS using the 4700 Hz carrier wave. The highest evaluated drive level
of 0.7 A resulted in the best nonlinear response, and a hysteretic trend was seen when decreasing
the drive amplitude. To investigate this phenomenon further, the individual sideband amplitudes
were resolved for each drive point on the amplitude hysteresis curve. These sidebands are visible
in the frequency spectrum at the maximum NLS drive point, as shown in Figure 41. Note that in
this figure, , , and are the positive sideband frequencies at 7700 Hz, 8700 Hz,
and 9700 Hz, respectively. Similarly, , , and are the negative sideband
frequencies at 5700 Hz, 4700 Hz and 3700 Hz, respectively. The spectrum shows various other
frequency bands which may result from the nonlinearity of the damage. Further investigations
may seek to evaluate the importance of these higher order nonlinear bands.
48
Figure 40. NLS magnitude for the station 3 sensor, using 6700 Hz (100V) and 1000 Hz, showing the best
response using a drive level of 0.7 A.
Figure 41. Autospectrum for the active-active drive condition of 6700 Hz (100 V) and 1000 Hz (0.7 A).
The trend in individual sideband amplitudes is shown in Figure 42 and Figure 43. Van Den
Abeele et al. (Ref. 11) conducted similar studies on damaged material samples, showing that the
first minus and plus sidebands increased linearly with exercising frequency drive amplitude. This
49
trend is attributed to a classical nonlinearity model of the material stiffness. The second plus and
minus sidebands showed a nonlinear trend with increasing drive amplitude, which was attributed
to the nonlinear hysteretic behavior of the material stiffness.
For the tail boom, sideband amplitudes showed more complex behavior. First positive and
negative sidebands did not increase linearly with exercising drive frequency. Furthermore,
second positive and negative sidebands showed significant hysteretic response, especially in the
case of . Since these sidebands are attributed to the existence of hysteresis in the material
response, it makes intuitive sense that these sidebands would exhibit considerable hysteretic
response with the modulation wave drive amplitude. The tail boom damage condition also
showed considerable increase in the third positive and negative sidebands. These sidebands can
most likely be attributed to the greater nonlinearity inherent in a built up airframe structure.
Indeed the complex behavior of sidebands in the tail boom experiments may be attributed to the
overall greater nonlinearity in the test bed. Ideal material samples, used in the cited research,
would understandably exhibit less nonlinear response. Material samples do not contain complex
geometries and joints that act as sources of nonlinearity in more complex structures.
Figure 42. Negative sideband modulation amplitude study. Hysteretic behavior is clearly visible for the
second sideband.
50
Figure 43. Positive sideband modulation amplitude study. In general, sidebands showed complex
behavior with increasing and decreasing modulation frequency amplitude.
In an effort to further increase detection sensitivity, amplitude sensitivity studies were
performed on the high frequency probing wave. In particular, frequencies of 4700 Hz and 6700
Hz were studied using the previously determined effective drive levels for the 1000 Hz
exercising frequency. Probing wave drive voltage was increased from 20 V to 140 V and then
decreased to observe relevant trends in the nonlinear response. Figure 44 shows the NLS trend
for 4700 Hz and Figure 45 shows the NLS trend for 6700 Hz. Over the selected voltage range,
the 4700 Hz probing wave shows approximately a 2 dB change, while the 6700 Hz probing wave
shows an 18 dB change in the NLS response. Using the 6700 Hz probing wave results in a much
higher overall NLS response at 140 V drive amplitude. The NLS response increases to -62 dB, as
opposed to -79 dB for the 4700 Hz probing frequency. Based on this observation, it was
determined that the 6700 Hz wave should be more effective for damage detection studies,
particularly at the drive level of 140 V.
51
Figure 44. High frequency amplitude sensitivity using a 4700 Hz probing wave and 1000 Hz (0.8 A)
modulation wave.
Figure 45. High frequency amplitude sensitivity study using a 6700 Hz probing wave and 1000 Hz (0.7
A) modulation wave. The highest response is seen at 140 V drive level.
52
As in the previous amplitude study, individual negative sideband amplitudes were observed
over the drive voltage range, as shown in Figure 46. The positive sidebands showed a similar
trend. The result of past studies (Ref. 11) showed that the first two positive and negative
sidebands increased approximately linearly with drive level. On the tail boom structure, the
corresponding sideband amplitudes showed a monotonic increase, but not a linear relation with
the drive level. Notably, these sidebands showed no hysteretic trend with the carrier wave
amplitude, since measurements of increasing drive amplitude corresponded well with
measurements at decreasing amplitudes.
Figure 46. Negative sideband probing wave amplitude study. No hysteretic trend is visible in the
response.
Using improved drive conditions of 6700 Hz (140 V) and 1000 Hz (0.7 A), healthy and
damaged measurements were again compared directly. The corresponding change in nonlinear
response is shown for each station in Figure 47. Compared to the original carrier wave (4700 Hz)
measurement, the change in drive conditions caused a slight increase in sensitivity at station 3 (1
dB) and a more significant increase at station 4 (4 dB). Sensors further from the damage location
showed a smaller change in sensitivity.
53
Figure 47. A change in probing wave frequency and amplitude causes a slight increase in sensitivity over
previous drive conditions, specifically those using a 1000 Hz exercising frequency.
While sensitivity was increased near the damage location, a more formal study of frequency
and amplitude effects is necessary to fully optimize the drive conditions. It is possible that by
exercising a wide range of carrier wave and modulation wave drive conditions, better detection
sensitivity may be obtained. Lower modulation frequencies showed promise in initial testing, but
due to time constraints, these were not fully evaluated. It is possible that with further research,
the active-active technique can become more repeatable and more effective for detecting relevant
damage conditions.
4.2 Passive Testing
The active-active high frequency vibration technique provided good sensitivity for detecting
damage in the tail boom structure. However, this technique requires two actuators to be installed
on the airframe. In older aircraft, especially small scout helicopters such as the OH-58, weight is
a critical factor when making any modifications to the airframe. Depending on the size of the
actuators and the system used to power them, integrating new equipment on the aircraft may be
difficult. Sensors are typically lightweight, but a technique that uses existing sensors on the
airframe would be ideal since no extra equipment would be required.
54
Passive testing aimed to evaluate the use of the tail rotor harmonics as forcing frequencies,
using the same sensor arrangement as in the active-active tests. The tail rotor system imparts
powerful vibrations to the airframe at the rotation frequency, blade passage frequency, and
harmonics of the blade passage frequency. Table 7 shows the frequencies representative of the
tail rotor system on the OH-58D, as listed in MIL-STD-810 (Ref. 12). These frequencies were
output using the installed Wilcoxon F4 electromagnetic shaker at a 1 A drive level. It should be
noted that this drive level is likely not indicative of the actual forcing on the aircraft, but
provided a simulated tail rotor vibration for use in this study.
Table 7. OH-58D tail rotor harmonics. For passive techniques, the structure was driven at these
frequencies using a drive level of 1 A.
Classification Frequency (Hz)
Rotation Frequency 39.7
Blade Passage Frequency 79.4
Blade Passage First Harmonic 158.8
Blade Passage Second Harmonic 238.2
Again, damage was simulated by loosening the hangar bearing bracket near the mid-section
of the tail boom. Spectral data was taken for both healthy and damaged conditions using the
acquisition parameters listed in Table 5. A direct comparison of the spectral content (Figure 48)
for both measurements reveals the difference between healthy and damaged conditions. The
damaged condition exhibits prominent higher harmonic content due to the nonlinearities created
by the damage.
A feature (or damage indicator) was created, again using Equations (9) and (10), to capture
the nonlinear content present in the damaged case. Originally the integration bounds were set to
include the entire spectrum, from 0 Hz to 20000 Hz. A change in total RMS amplitude was
calculated from the acquired healthy and damaged measurements. Figure 49 shows this result. It
was decided that a relatively small change occurred because the response was dominated by the
driven rotor harmonics.
55
Figure 48. Passive technique autospectrum at station 3. Comparing the signatures of healthy and damaged
measurements reveals higher harmonic content as a result of the damage.
Figure 49. Broadband integration yielded very little detection sensitivity.
A different damage feature was conceived, ignoring the driven frequencies in the spectrum
of each strain and acceleration signal. The starting integration bound was set 20 Hz higher than
the driven harmonic of 238.2 Hz, and the upper bound was again set at 20000 Hz. This
56
calculation resulted in substantially higher detection sensitivity at all stations, as shown in Figure
50. Notably, NLA at station 2 shows 11 dB of detection strength and NLS detection strength is
between 4 and 6 dB for all stations near the damage location.
Figure 50. Higher harmonic NLS and NLA show considerable detection sensitivity across most stations,
especially near the damage location.
The fully passive technique shows promising detection capability. Given the NLS sensitivity
between stations across the boom structure, this technique may even provide enough information
to localize the damage source. Further studies should investigate how these magnitudes change
when damage is introduced elsewhere in the structure. In addition, accurately simulating the
forcing levels of the tail rotor and main rotor may provide more insight into the effectiveness of
the technique on real airframes
4.3 Active-Passive Testing
The active-active and passive vibration tests were able to display significant nonlinear
response differences between the healthy and damaged conditions. However, the active-active
tests require two additional actuators on the tail boom, creating a costly test in real-world
application. Additionally, the reliability of the passive testing results is unknown. Active-passive
57
tests may provide a compromise between the cost-effectiveness of the passive test and the
reliability of the active-active tests.
In active-passive testing, the tail rotor harmonics were again used as the forcing frequency.
For these tests, the tail rotor harmonics were used with at 1 A drive level. The carrier signal was
set to 6700 Hz at 140 V drive level. This carrier signal was found to maximize the non-linear
response of the damaged structure in the active-active tests.
The differences in NLS and NLA are shown in Figure 51. The frequency range used for
NLS and NLA integration was 4700-6780 Hz and 6720-8700 Hz. This range ensured that the
non-linear components of the response were well-captured, but excluding expected low
frequency components and the carrier frequency of 6700 Hz. Again, recall that stations 1
through 7 are ordered longitudinally along the tail boom, where station 1 is located near the tail
rotor, station 7 is located near the base of the tail boom, and the simulated damage is located
between stations 3 and 4. First, it is noted that there is significantly more NLS and NLA
sensitivity near the damage location, as expected. This indicates that the active-passive technique
is effective in detecting damage. Furthermore, the level of non-linear response appears to be
related to the distance from the damage. Stations 1 and 7, located at the tail rotor and at the base
of the tail boom, respectively, show little non-linear response. It is also noted that both strain and
acceleration measurements are able to detect damage. However, the maximum difference in
nonlinear magnitude is approximately 3.5 dB, a low value that may not be reliably repeated.
However, examination of the frequency response at several stations may lend some insight into
this low value. It is noted that station 3 provided the highest NLS difference between the healthy
and damaged conditions.
The response as recorded from the strain gauge at station 3 is shown in Figure 52 below,
where it is apparent that there is a significant difference between the healthy and damaged
conditions. Further, the differences, particularly for the sidebands further away from the 6700 Hz
carrier signal, indicate that a difference of approximately 3.5 dB does not fully capture the
sensitivity to damage between the two cases. Figure 53 shows the narrow-band strain response at
station 3 near the carrier frequency. It is apparent that the healthy and damaged conditions both
provide a significant response for the first two sidebands and show good agreement with each
other. Further, it is shown that the differences between the healthy and damaged response begin
58
to manifest themselves past the first two sidebands. Recall that the integration for NLS and NLA
presented in Figure 51 was 4700-6680 Hz and 7200-8700 Hz, which would include the first two
sidebands, for which there is agreement between the healthy and damaged conditions. These
sideband responses are much greater in magnitude than the responses for other frequencies
further away from the 6700 Hz carrier signal. Therefore, inclusion of the first two sidebands
tends to hide the major differences that occur in other frequencies. To eliminate these two
sidebands, a different integration range can be used. Figure 54 shows the differences in NLA and
NLS between the healthy and damaged conditions for integration ranges of 4700-6600 Hz and
6800-8700 Hz, thus eliminating consideration of the carrier frequency and its first two sidebands.
For this computation, the difference in NLS at station 3 was found to be over 8 dB. That value is
more than a 100% increase from the previous computation by merely eliminating the first two
sidebands from the integration procedure.
The adaptive nature of selecting integration bounds that elicit clear damaged versus healthy
differences in NLS and NLA is further highlighted by examining the response at station 5. In
Figure 51 and Figure 54, there are negligible differences between the healthy and damaged NLS
and NLA at station 5. However, examination of the frequency response recorded by the strain
sensor in Figure 55 indicates that there are, in fact, differences between the healthy and damaged
condition as well. These differences appear to manifest themselves beyond +/- 400 Hz of the
6700 Hz carrier signal. NLA and NLS determined by integrating from 4700-6200 Hz and 7200-
8700 Hz eliminate those sidebands for which the healthy and damaged conditions agree. The
resulting NLA and NLS difference for this integration range is shown in Figure 56. This
integration range leads to large NLA differences between healthy and damaged conditions at
stations 5, 6, and 7, which had previously been shown to exhibit negligible differences.
However, it is noted that the NLS differences at station 3 and 4 have been lessened, as compared
to the integration that yielded Figure 54.
It is clear that the active-passive excitations produce distinct differences between the healthy
and damaged responses. However, it was demonstrated that the differences are largely dependent
upon the choice of integration range in determining NLA and NLS. The trial and error method of
integration range selection is not viable in field application of an active-passive healthy
59
monitoring study. Therefore, a clear strategy or algorithm for computing NLS and NLA such that
damage can be detected is critical.
Figure 51. Detectable difference in non-linearity between healthy and damaged conditions, integrating
from 4600-6680 Hz and 6720-8600 Hz (active-passive).
Figure 52. Station 3 frequency response indicates significant differences between healthy, damaged
conditions.
1 2 3 4 5 6 7-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5Nonlinear Strain and Acceleration Healthy vs. Damaged dB
Station
Magnitude (
dB
)
NLA ref 1 (m/s2)2
NLS ref 1 (-S)2
4000 5000 6000 7000 8000 9000 1000010
-12
10-10
10-8
10-6
10-4
10-2
Frequency (Hz)
Ma
gn
itu
de
(d
B)
Damaged
Healthy
60
Figure 53. Good agreement between healthy and damaged condition in response of the first two
sidebands, compromising the effectiveness of NLS and NLA calculations. Differences in frequency response
between healthy and damaged condition at station 3 manifest themselves past the second sideband in each
direction.
Figure 54. Changing integration to 4700-6600 Hz and 6800-8700 Hz gives more sensitivity to non-
linearity differences, particularly at station 3 (active-passive).
6500 6550 6600 6650 6700 6750 6800 6850 690010
-12
10-10
10-8
10-6
10-4
10-2
Frequency (Hz)
Ma
gn
itu
de
(d
B)
Damaged
Healthy
1 2 3 4 5 6 70
1
2
3
4
5
6
7
8
9Nonlinear Strain and Acceleration Healthy vs. Damaged dB
Station
Magnitude (
dB
)
NLA ref 1 (m/s2)2
NLS ref 1 (-S)2
61
Figure 55. Station 5 acceleration frequency response shows clear differences between healthy, damaged
conditions at frequencies removed from carrier 6700 Hz. The broadband increase may be due to the damage,
but the quality of this sensor should also be evaluated in future work.
Figure 56. NLA and NLS differences at station 5 appear when using integration range of 4700-6200 Hz
and 7200-8700 Hz (active-passive).
6100 6200 6300 6400 6500 6600 6700 6800 6900 7000 7100 7200 7300
10-8
10-6
10-4
10-2
100
102
Frequency (Hz)
Ma
gn
itu
de
(d
B)
Damaged
Healthy
1 2 3 4 5 6 70
2
4
6
8
10
12
14
16
18
20Nonlinear Strain and Acceleration Healthy vs. Damaged dB
Station
Magnitude (
dB
)
NLA ref 1 (m/s2)2
NLS ref 1 (-S)2
62
Chapter 5: Conclusions
This airframe structural health monitoring study aimed to evaluate and compare a number of
vibration based techniques for detecting damage on an OH-58D Kiowa Warrior tail boom. This
aircraft is crucial to military missions overseas. However, an extended service life and known
fatigue problems have made this aircraft costly to maintain. Crews rely on lengthy visual
inspections to detect fatigue cracks on the tail boom structure, but this results in substantial down
time, and damage can sometimes be overlooked. This study aimed to evaluate traditional modal
methods for damage evaluation, as well as high frequency methods.
Modal testing and analysis yielded the major vibrational modes of the structure. It was
discovered that some resonance frequencies, particularly at 78.3 Hz and 56.4 Hz, are very close
to known main and tail rotor harmonics. In addition, these modes correspond to high strain areas
on the tail boom, especially near the tail rotor where damage tends to initiate and propagate.
These observations lend insight into the reason for the high percentage of fatigue related damage
cases pertaining specifically to the tail boom.
Damage was induced by loosening a hanger bearing bracket near the mid-section of the tail
boom. In comparing healthy and damaged test cases, it was determined that modal methods had
very low sensitivity to the induced damage. FRFs between healthy and damaged cases were
generally in agreement, especially in the bandwidth of 500 Hz. A mid-frequency FRF method
was employed, using a bandwidth of 2000 Hz, but again, results were inconclusive. The higher
bandwidth FRFs showed some variation in resonance peaks and coherence over the bandwidth.
However, it was determined that these results were not repeatable, making the method difficult to
use in application. Later research may evaluate this method further by employing a shaker
instead of a hammer for forcing.
High frequency methods proved most useful for detecting the damage, utilizing a NWMS
approach and analysis of higher harmonics. High frequency testing was broken into three
different studies. The first was an active-active approach, using two drive sources at selected
frequencies and studying combinational tones between the high frequency carrier wave and the
low frequency exercising wave. This approach initially yielded a detection sensitivity of
63
approximately 5 dB at the station 3 strain sensor. A number of frequency pairs were evaluated,
yielding mixed results. Using lower modulation frequencies of 500 Hz and 200 Hz, detection
sensitivity as high as 13 dB was obtained. However, these results were not highly repeatable.
Using a modulation frequency of 1000 Hz, varying amplitude and carrier wave drive conditions
resulted in better detection strength than in initial results. The drive conditions of 6700 Hz (140
V) and 1000 Hz (0.7 A) resulted in NLS sensitivity of 6.5 dB and 4 dB at stations 3 and 4,
respectively. Since the damage source was between these two stations, these results were
encouraging. The active-active approach proved to be an effective method, and further studies
will focus on optimizing drive conditions and spectral analysis in an attempt to gain the highest
detection capability.
The second approach was a passive technique, using only the tail rotor rotation frequency,
blade passage frequency, and first two harmonics of the blade passage frequency. This approach
is promising because in practice it would require very little hardware to be installed on the
structure. A damage feature was conceived to integrate over the nonlinear higher harmonic
content, ignoring the driven frequencies. This approach resulted in NLS detection sensitivity as
high as 6 dB and NLA detection sensitivity as high as 11 dB. In real world applications, it is
unknown how reliable the results will be, and future studies should seek to further evaluate this
approach, possibly even simulating the actual forces of the tail rotor in flight. Main rotor
harmonics can also be investigated for use in passive detection methods.
The final approach used an active-passive technique, inputting the 6700 Hz high frequency
carrier wave and using tail rotor harmonics as exercising frequencies. This approach requires
minimal integration of new hardware on the airframe, and may prove more reliable than the
purely passive technique. It was discovered that by selectively integrating over different ranges
of sideband frequency content, the approach yielded very high detection sensitivity. Furthermore,
this selective range of integration could be considerably different depending on the sensor and its
location on the tail boom. Using these observations, NLS detection sensitivity of 8.5 dB was
gained, and NLA sensitivity was as high as 19 dB. Future studies should seek to further
investigate this adaptive approach when analyzing the response of various sensors on the tail
boom.
64
The low and high frequency techniques performed in this study resulted in the following
observation. In order to detect damage using vibration based techniques, one must use vibrations
with wavelengths on the order of the damage size. Figure 57 is an illustration of this idea,
showing bending wave frequencies and their associated wavelengths in the OH-58 tail boom skin
(0.040 in thick aluminum). It can be expected that low frequency techniques, on the order of 10
Hz to 100 Hz, may have difficulty exciting a response indicative of damage on the order of the
loose hanger bearing bracket.
Figure 57. Illustration of bending wave frequencies and their associated wavelengths in 0.040 in
aluminum. This material is the same as that used in the OH-58 tail boom skin.
High frequency techniques, such as those investigated in this study, use wavelengths on the
order of 1000-10000 Hz. These techniques proved much more useful for detecting the loose
hanger bearing bracket, using wavelengths on the order of the damage size, or even smaller.
These studies suggest that localization of the damage may also be possible, as sensors closest to
the damage often showed the highest nonlinear detection sensitivity. Future studies should
further investigate the use of active-active, passive, and active-passive high frequency techniques
for detecting relevant damage on the OH-58 tail boom. By developing algorithms to not only
detect, but also localize damage sources, these high frequency techniques have the potential to be
integrated in current and future aircraft in the years to come.
65
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66
10. Richardson, M., Formenti, D. “Parameter Estimation from Frequency Response
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67
Appendix: Additional Mode Shapes
Figure A1. Second horizontal bending mode (17.8 Hz).
Figure A2. Second vertical bending mode (22.2 Hz).
Figure A3. Symmetric stabilizer torsional mode (32.7 Hz).
68
Figure A4. Asymmetric stabilizer torsional mode (41.7 Hz).
Figure A5. Horizontal stabilizer flapping mode (126.9 Hz).
Figure A6. Aft shell (n = 2) mode (83.2 Hz).
69
Figure A7. Aft shell (n = 3) mode (219.3Hz).
