Journal of Engineering Science and Technology EURECA 2013 Special Issue August (2014) 96 - 116 © School of Engineering, Taylor’s University
96
EXPERIMENTAL MODAL ANALYSIS (EMA) STUDY ON MULTI-BENT COPPER PHOSPHOROUS SUCTION TUBES
PRASHANTH A/L KAMALANATHAN1, MOHAMMAD
HOSSEINI FOULADI1,*
, YAP KIM HAW2
1School of Engineering, Taylor’s University, Taylor's Lakeside Campus,
No. 1 Jalan Taylor's, 47500, Subang Jaya, Selangor DE, Malaysia 2CAE/FEA, Panasonic Appliances Air-Conditioning R & D Malaysia Sdn Bhd
(PAPARADMY 1), 40300, Shah Alam, Selangor DE, Malaysia
*Corresponding Author: [email protected]
Abstract
Modal Analysis provides valuable information about a structure in terms of its
dynamic properties. In this study, an Experimental Modal Analysis (EMA)
procedure was developed for the testing of two different suction tubes under
“free-free” boundary conditions in order to determine its dynamic properties. The results obtained will then act as a benchmark for the dynamic properties
obtained from the Finite Element (FE) Modal Analysis. Preliminary tests were
conducted on a simple plate structure to validate the developed EMA procedure
based on the comparison of the natural frequencies obtained via EMA against
theoretical natural frequencies. An average percentage error of 5% was
observed deeming the developed procedure reliable for testing on copper tubes. The integrated usage of modal parameter estimation algorithms along with
Mode Indicator Functions (MIFs) are evaluated for dynamic properties
extraction from raw Frequency Response Function (FRF) data and was found to
be a reliable method for dynamic property extraction. The outcomes of this
research will be able to assist air-conditioning manufactures in the design
validation process of new copper tube designs in an efficient and cost effective manner without the need for prototype fabrication.
Keywords: Dynamic properties, Modal parameter estimation, Mode indicator
function, Suction tube, Stability diagram.
1. Introduction
Modal Analysis studies on suction tubes are numbered. One of these studies was
on a pipeline structure similar to that of a suction tube while the other was on a
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suction tube itself. The study done by Loh et al. [1] was on a suction tube that was
attached to the accumulator of the compressor. In this study, the EMA test
procedure was carried out to validate the results obtained from the FE Modal
Analysis. An impact hammer was used to provide the external excitation to the
suction tube and the response of the structure was measured using a single tri-axial
accelerometer. It was found that the results obtained in terms of the natural
frequency of the suction tube compared to the natural frequencies from the EMA
testing procedure has a maximum percentage difference of 8.5% [1]. In the event
where correlation needs to be carried out, the fixed boundary conditions employed
by Loh et al. [1], is not suitable whereas the “free-free” boundary condition which is
used in this study is preferable as it is more reliable [2-3]. The study done by
Haapaniemi et al. [4] was based on a pipeline structure which is almost similar in
shape with a suction tube. EMA was carried out on the pipeline structure using both
an impact hammer and a shaker and it was found that the results obtained from both
testing methods correlated well at lower frequencies. Besides that, it was also
observed that the correlations were better at regions closer to the excitation points.
The author believes that an impact hammer test was more suitable for smaller
structures and in the case where an impact hammer is used to excite a larger
structure, more than one excitation point should be used [4].
The distinguishing factor in this study compared to the previous study is that in
this study, EMA is carried out on a suction tube under “free-free” boundary conditions
as the measurements obtained are very reliable, suitable in cases where correlation is
required and the configuration is easily achieved [2-3]. The suction tube found in the
air-conditioning outdoor unit is attached to the accumulator of the compressor. The
vibrational excitations due to the working conditions of the compressor and the
Nomenclatures
�� Corrected damping
�� Un-corrected damping
��� Natural frequency of a simple plate under “free-free” boundary
conditions
Greek Symbols
��� Lagrange multiplier
ν Poisson’s ratio
� Decay time constant, s
� Natural frequency, Hz
� Un-damped natural frequency, Hz
Abbreviations
CMIF Complex Mode Indicator Function
EMA Experimental Modal Analysis
FFT Fast Fourier Transform
FRF Frequency Response Function
MMIF Multivariate Mode Indicator Function
RFP-Z Rational Fraction Polynomial-Z
SIMO Single Input Multiple Output
SISO Single Input Single Output
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excitations present during the transportation of the outdoor unit itself has led to the
fatigue failure of the suction tube due to resonance. The specified frequency range in
which resonance of the suction tube occurs has been identified to be in the range of 0
Hz to 200 Hz. This frequency range is inclusive of the vibration frequencies due to the
operation of the compressor and also due to the vibration frequency contributed by the
vehicle used in the transportation of the air conditioning outdoor unit.
The objective of the current research is to correlate the dynamic properties of
multi-bent copper phosphorous suction tubes attained via FE Modal analysis
against that obtained from the developed EMA testing procedure. This will
provide a greater confidence factor in the results obtained via FE Modal analysis,
resulting in an efficient and inexpensive design validation process of new copper
tubes. In this study, EMA is used to determine the dynamic properties (natural
frequencies, damping ratio, mode shape) of a 2.0 Hp, and a 2.5 Hp suction tube,
hereafter named as Suction Tube 1 and Suction Tube 2 respectively. Both the
suction tubes are shown in Figs. 1(a) and (b). The dynamic properties of the
structure obtained from EMA are used to validate the results obtained from the FE
Modal Analysis method. The reliability of both the Complex Mode Indicator
Function (CMIF) and the Multivariate Mode Indicator Function (MMIF) will be
evaluated in this study in terms of its capability in determining the dynamic
properties of the suction tube while using the Rational Fraction Polynomial-Z
(RFP-Z) algorithm for the modal parameter estimation process. Prior to EMA
testing on the suction tubes, a preliminary study on a simple plate structure was
carried out to validate the developed EMA testing procedure. Theoretical results
in terms of the natural frequencies of the simple plate are calculated and used as a
validation tool for the natural frequencies obtained from the EMA testing
procedure. A low percentage error gives an indication that the EMA testing
procedure that was developed is reliable and can be used to test the suction tubes.
Fig. 1. The Suction Tubes Used in the Study. (a) 2.0 Hp Suction
Tube (Suction Tube 1) and (b) 2.5 Hp Suction Tube (Suction Tube 2).
2. Research Methodology
The frequency span used for both the suction tubes in this study is 200 Hz with a
frequency resolution of 1 Hz, a record length (T) of 1 s, and a sampling time of 0.002
s. The frequency span used for the simple plate was set to 800 Hz with a frequency
resolution of 1 Hz, a record length (T) of 1 s, and a sampling time of 0.0005 s. To
(a
)
(b
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conduct the EMA testing procedure, the MTC Hammer software and the PULSE
Reflex software by Brüel & Kjær, a Danish based company were used. In terms of the
hardware used in the study, a 12-channel FFT analyser (Model No: 3053-B-120), a
miniature Impact Hammer (Model No: 8204) and seven single-axial accelerometers
(Model No: 4517) by Brüel & Kjær were used to carry out the EMA testing
procedure. The measurement portion of the EMA testing procedure is carried out on
MTC Hammer. Results from the EMA procedure on MTC Hammer is exported to the
PULSE Reflex software for the extraction of the dynamic properties from the
obtained raw empirical data. Here, various Mode Indicator Functions (MIFs) and
modal parameter estimation algorithms are used to extract the dynamic properties of
the structure from the raw data. The PULSE Reflex software is also equipped with the
capability of using a stability diagram to select the stable poles in order to extract the
dynamic properties of the structure. The overall process is described in Fig. 2.
Fig. 2. The Research Flow Process Used in the Study.
To carry out the FE Modal Analysis procedure, the NX Nastran 8.5 Enterprise
solver by Siemens PLM is used. The NX Nastran 8.5 Enterprise solver does not have
a graphical user interface and it only acts as a solver. To overcome this limitation, the
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ANSA software by βETA CAE, a Greek based company is used. The ANSA software
is capable of carrying out high quality and advanced meshing procedures. The ANSA
software is used to carry out the meshing procedure and it is also used to setup the
loadcase for the solving process on the NX Nastran 8.5 Enterprise solver. Since the
NX Nastran 8.5 Enterprise solver does not have a graphical user interface, a platform
is required to observe the mode shapes of the structure. The visualization of the mode
shapes are observed on the µETA software by βETA CAE.
2.1. The finite element (FE) setup
For the FE Modal Analysis in this study, the SOL 103 solver for Normal Modes is
incorporated. The method used in this study for real eigenvalue extraction is the
Lanczos method as it is both reliable and efficient in extracting eigenvalues and
eigenvectors. The eigenvectors are also known as normal modes whereas the
square root of the eigenvalue gives the natural frequency of the structure. In this
study, the ANSA software by βETA CAE is used to set a loadcase parameter
which is required for solving purposes on the NX Nastran 8.5 Enterprise solver.
The Lanczos method uses the EIGRL entry for the loadcase setting.
Shell meshing was used in this study instead of volumetric meshing as it saves
on computational time due to the lower number of elements used and the quality
of the meshing can be easily monitored as compared to a volumetric mesh [5].
The meshing details used in this study for the simple plate and both the suction
tubes are shown in Table 1. Triangular elements were not present in the meshing
and purely quadratic elements were used in the meshing procedure which
indicates the high quality mesh produced. Mapped face meshing was selected for
meshing purposes to produce an even mesh distribution across the surface of the
structure. The mesh used for all three structures can be seen in Figs. 3 to 5.
Table 2 shows the material properties of all three structures used in the study.
Table 1. The Meshing Details of the Different Structures Used in this Study.
Table 2. The Material Properties of the Different Structures used in this Study.
Structure Number of
Elements
Element
Size (m)
Percentage of triangular
elements (%)
Simple Plate 64 000 0.0005 0
Suction Tube
1 (2.0Hp) 142 200 0.0005 0
Suction Tube
2 (2.5Hp) 225 600 0.0005 0
Structure Material
Young’s
Modulus
(E) (GPa)
Mass
Density
(ρ)
(kg/m3)
Poisson’s
Ratio
(ν)
Thickness
(m)
Simple
Plate Steel 212 7850 0.29 0.001
Suction
Tube 1
(2.0 Hp) Copper
Phosphorous 117 8940 0.3
0.0007
Suction
Tube 2
(2.5 Hp)
0.0008
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Fig. 3. Mesh of the Simple Plate Strucure.
Fig. 4. Mesh of Suction Tube 1 (2.0 Hp).
Fig. 5. Mesh of Suction Tube 2 (2.5 Hp).
2.2. The experimental modal analysis (EMA) procedure
In this study, a roving hammer test is carried out on all structures. Another testing
method would be the roving accelerometer test, but the roving hammer test is
preferred in this study. The roving accelerometer test is not preferred in this study as it
leads to mass loading problems which can affect the measurements obtained from
EMA [6]. The roving hammer test is regarded as a Single Input Multiple Output
(SIMO) testing condition where the single input refers to a single excitation point for a
particular measurement whereas the multiple output refers to the usage of multiple
accelerometers to measure the response of the structure. A Single Input Single Output
(SISO) testing condition occurs when a roving hammer test is conducted on a
structure with the usage of only one accelerometer to measure the response of the
structure. The SIMO testing procedure is used in this study. The SIMO roving
hammer test is an example of a multiple reference test [7]. In the case of the roving
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hammer test, the reference is based on the number of accelerometers used whereas in
the case of a roving accelerometer test, the reference is based on the number of
excitation positions. A multiple reference test is beneficial in the sense that it is
capable of producing redundant data in terms FRFs where in the event that one of the
references are not able to capture a particular mode properly, another reference could
capture the mode hence maintaining the quality of the results obtained [7].
In this study, elastic chords were used to replicate the “free-free” boundary
conditions for EMA testing purposes. These elastic chords have to be attached to
the structure in a manner where it does not constrain the mobility of the structure
that is being tested. By constraining the mobility of the structure, the results
obtained from the testing procedure will be flawed and the dynamic properties of
the structure would not be able to be determined accurately. Besides the elastic
chords, the connection wires from the accelerometer to the FFT analyzer can also
act as a constraining device. The connection wires tend to be tangled up and
messy, hence the wires are at times taped to the test rig which is used to suspend
the structure that is being tested. If the accelerometer’s connection wire is taped is
taped to the test rig in which it limits the movement of the structure, the dynamic
properties extracted from the FRFs data will not be accurate.
This study is conducted in an air-conditioned room where the movement of the air
in the room does result in minor displacement of the structure that is being tested. This
is regarded as noise in the measurement. The presence of noise in this case contributes
to the noise in the output as the slight movement of the structure results in the
detection in terms of the response by the accelerometer. To overcome the presence of
noise in the structure, the FRF estimator H1 is used throughout the study.
3. Results and Discussion
3.1. Preliminary investigation on a simple plate
The theoretical natural frequency is computed based on Eq. (1) which was
developed for a testing procedure under “free-free” boundary conditions [8]. The
equation is capable of computing the first six modes of the simple plate; hence the
results from EMA were limited to the first six modes. This process is carried out
to validate the EMA testing procedure that was developed before proceeding to
the testing of the suction tubes. Theoretical validation for the suction tubes are not
available, hence a preliminary study on a simple plate structure is carried out.
��� = �������� � ���
���(����) (1)
where a = length of the plate = 0.2 m, b = width of the plate = 0.08 m
(only used in calculation of the (a/b) ratio), h = height of the plate = 0.001 m,
i = number of half-waves in mode shape along the horizontal axis, j = number of
half-waves in mode shape along the vertical axis, � = mass per unit area of the
plate = 7.85 kg/m2, = Poisson’s ratio of the plate (given value of 0.3),
! = Modulus of elasticity, and � = Lagrange multiplier
This equation is based on the assumption that the Poisson’s ratio of the
material used is equivalent to 0.3. The Lagrange multipliers that are used in the
computation can be seen in Table 3 for a length to width ratio of 2.5. The
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correction of damping for the damping ratio obtained from EMA was carried out
and the decay time constant value τa, used in the response weighting is equal to
0.0291 s. The simple plate can be seen in Fig. 6, whereas the AutoMAC plot is
shown in Table 4. On the other hand, the theoretical and experimental results for
the simple plate are shown in Table 5 whereas the comparison between the results
from FE modal analysis against EMA is shown in Table 6.
Fig. 6. The Placement of the Single-Axial Accelerometers on the Simple Plate.
Table 3. The Values for the Lagrange Multiplier for a Length to
Width Ratio of 2.5 for the First 6 Modes of the Simple Plate [8].
Table 4. The AutoMAC Plot Obtained from the
EMA Testing Procedure on the Simple Plate.
Table 5. The Comparison of the Theoretical and Experimental
Results in Terms of the Natural Frequencies for the Simple Plate.
Mode
Theoretical Experimental
(EMA) Percentage
difference
(%) Natural Frequency
��� (Hz) Natural Frequency
� (Hz)
1 135.41 128.64 -5.00
2 206.80 196.87 -4.80
3 376.31 356.14 -5.36
4 447.27 425.54 -4.86
5 735.22 696.26 -5.30
6 747.11 786.99 5.34
"#
�$% 2 for each mode
1 2 3 4 5 6
2.5 21.64 33.05 60.14 71.48 117.5 119.4
- 128.639 196.873 356.144 425.538 696.264 786.993
128.639 1.000 0.003 0.019 0.015 0.033 0.113
196.873 0.003 1.000 0.006 0.010 0.011 0.014
356.144 0.019 0.006 1.000 0.020 0.026 0.110
425.538 0.015 0.010 0.020 1.000 0.019 0.034
696.264 0.033 0.011 0.026 0.019 1.000 0.207
786.993 0.113 0.014 0.110 0.034 0.207 1.000
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The AutoMAC plot in Table 4, shows off-diagonal values which are
approximately zero except for Mode 5 and Mode 6 where the off-diagonal value
is equivalent to 0.207. This indicates that Mode 5 and Mode 6 have a slight
degree of similarity. This should not be the case as the mode shapes have to be
different from one mode to another. The value of 0.207 on the AutoMAC plot
indicates that the modal parameters were not extracted properly from the stability
diagram. Based on Table 5, the highest frequency difference between the
theoretical natural frequency and the experimental natural frequency is 5.36%.
The percentage difference observed between the natural frequency obtained from
EMA and the theoretical natural frequency is minimal but not negligible. The
anomalies observed in the frequency difference is due to the assumption made in
the equation that the Poisson’s ratio of the material had to be 0.3, whereas the
plate that was tested using EMA had a Poisson’s ratio of 0.29. Other factors could
also contribute to the percentage difference such as the Young’s Modulus of the
simple plate. In most cases, the material under testing does not always have the
same Young’s Modulus used in the theoretical calculations. It is also observed
that the experimental frequency from Mode 1 to Mode 5 is consistently lower
than the theoretical except for Mode 6 which is the complete opposite. The
simulated mode shapes observed in Figs. 7 and 8 are similar in terms of the
deformation for Mode 1 to Mode 5 except for Mode 6.
The irregularities in the dynamic properties of Mode 6 is observed during the
comparison of the natural frequency from EMA and the theoretical natural
frequency and also during the mode shape comparison between the experimental
mode shapes and the simulated mode shapes. Besides that, the corrected damping
values from Table 6 also showed signs of abnormalities for Mode 6 as it does not
follow the decreasing trend of the damping values. This clearly indicates that the
experimental results in terms of the dynamic properties of Mode 6 are flawed. The
rest of the dynamic properties from Mode 1 to Mode 5 showed good comparisons
particularly between the experimental results and the theoretical results.
The poor results obtained for Mode 6 could be due to the fact that only 4
single-axial accelerometers were used to measure the response of the structure. 5
single-axial accelerometers could improve the results for Mode 6, but it might
reduce the natural frequency of the other modes due the effect of mass loading.
Table 6. The Comparison between Experimental Results and
FE Results in Terms of the Natural Frequencies for the Simple Plate.
Mode
Experimental (EMA) Simulation
(FE) Percentage
Difference
(%)
Natural
Frequency
� ('()
Uncorrected
Damping De
(%)
Corrected
Damping
Dc (%)
Natural
Frequency
� ('()
1 128.64 5.389 5.304 134.18 4.31
2 196.87 4.587 4.531 206.37 4.83
3 356.14 2.063 2.032 372.65 4.64
4 425.54 2.162 2.136 442.58 4.00
5 696.26 1.331 1.315 727.52 4.49
6 786.99 4.646 4.632 738.59 -6.15
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Fig. 7. The Comparison of the Experimental Mode Shapes (a) and
Simulated Mode shapes (b) for Mode 1, 2, and 3 for the Simple Plate.
(a) (b)
Mode 1
Mode 3
Mode 2
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Fig. 8. The Comparison of the Experimental Mode Shapes (a) and
Simulated Mode shapes (b) for Mode 4, 5, and 6 for the Simple Plate.
(a) (b)
Mode 4
Mode 6
Mode 5
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Since the natural frequency is inversely proportional to the mass of a structure,
and increase in the mass due to the addition of an extra accelerometer could
reduce the natural frequency of the structure. In this case, a fifth accelerometer
will add to the mass of the structure and decrease the natural frequencies of the
study which will then lead to a further increase in the percentage difference in the
natural frequency between the theoretical results and the experimental results.
This shows that there is a trade-off where one can either obtain a low percentage
error and fewer modes captured or a high percentage error with a higher number
of modes captured.
Overall, the results show that the EMA testing procedure that was developed
is valid and is reliable in determining the dynamic properties of a structure based
on the low percentage of error observed between the theoretical natural
frequencies and the natural frequencies obtained from EMA. The developed EMA
testing procedure is then used to test both the suction tubes used in the study.
3.2. Integrated study on suction tube 1 (2.0 Hp)
The results obtained from the FE modal analysis is validated against the
experimental results in terms of the dynamic properties obtained. The setup of the
experimental procedure is shown in Fig. 9 and 10. Four single-axial accelerometers
with 34 impact positions are used in this study. The decay time constant, τa, used in
this study is equivalent to 0.0772 s which is used in the computation of the
corrected damping value. The proficiency of carrying out the modal parameter
estimation process is based on the AutoMAC plot which is shown in Table 7. The
stability diagram is shown in Fig. 11, where different shaped and coloured poles
represent different dynamic characteristics of the structure. The aim is to select the
red coloured diamond poles which represent a stable pole in terms of all the
dynamic properties of the structure. Table 8 shows the comparison of the natural
frequencies between the FE modal analysis and the EMA testing procedure while
Fig. 12 shows the comparison between the experimental mode shapes and the mode
shapes obtained from the simulation. The AutoMAC plot in Table 7 shows near
zero off-diagonal values which clearly indicates the proper extraction process of the
modal parameters from the empirical data which are the FRF plots. The favorable
results obtained from the AutoMAC plot shows the quality of the modal parameters
extracted from the raw FRF data which validates the experimental procedure on
Suction Tube 1. Three modes are observed in Suction Tube 1 in the frequency span
of 0 Hz to 200 Hz, from both the FE modal analysis and the EMA. The FE modal
analysis is able to compute the natural frequencies of Suction Tube 1 accurately
based on the small percentage difference that is shown in Table 8. The mode shapes
that can be seen in Fig. 12 shows that the mode shapes obtained from the FE modal
analysis are very similar in terms of the deformation compared to the experimental
mode shapes. The suction tube that is highlighted in blue in Fig. 12 indicates the
mode shape whereas the suction tube which is highlighted purple indicates the un-
deformed state of Suction Tube 1. Overall, the results from the EMA testing
procedure are very satisfactory based on the favourable results the AutoMAC plot.
Besides that, the FE modal analysis clearly indicates that it is able to accurately
compute the mode shapes as the deformation of the mode shape clearly resemble
the experimental mode shapes. The FE modal analysis is also reliable in computing
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the natural frequencies of Suction Tube 1 based on the low percentage error
compared to the experimental natural frequencies.
The corrected damping values shows that the third mode at a natural
frequency of 149.71 Hz has the highest possibility of fatigue failure as the
corrected damping percentage of that particular mode is the lowest amongst the
other modes. This conclusion is further strengthened by the high amplitude of the
third CMIF peak that can be seen in the stability diagram in Fig. 11. This
indicates that the third mode of Suction Tube 1 has the highest response compared
to the other modes which results in the highest deformation at the point of
resonance. These arguments indicate that Mode 3 of Suction Tube 1 has the
highest possibility of fatigue failure due to resonance. When Suction Tube 1 is
redesigned to shift its natural frequencies away from the frequency range of 0 Hz
to 200 Hz, more attention should be given to the third mode.
Table 7. The AutoMAC Plot from the EMA Testing of Suction Tube 1.
- 62.844 96.781 149.708
62.844 1.000 0.011 0.108
96.781 0.011 1.000 0.117
149.708 0.108 0.117 1.000
Table 8. The Comparison between Experimental Results
and FE Results in Terms of the Natural Frequencies for Suction Tube 1.
Mode
Experimental (EMA) Simulation
(FE) Percentage
Difference
(%)
Natural
Frequency
� ('()
Uncorrected
Damping De
(%)
Corrected
Damping
Dc (%)
Natural
Frequency
� ('()
1 62.84 3.547 3.481 64.01 1.86
2 96.78 2.398 2.355 95.22 -1.61
3 149.71 1.623 1.595 151.35 1.10
Fig. 9. The Placement of Accelerometers on Suction Tube 1 under
(a) the “free-free” Boundary Condition and (b) on MTC Hammer.
(a) (b)
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Fig. 10. The Impact Locations for Suction Tube 1 on MTC Hammer.
Fig. 11. The Stability Diagram Obtained
from the EMA Testing of Suction Tube 1.
3.3. Integrated study on suction tube 2 (2.5 Hp)
The results obtained in terms of the dynamic properties of Suction Tube 2 form the
FE modal analysis is validated with the results obtained from EMA. This is done by
using 7 single-axial accelerometers to measure the response of the structure and 42
impact locations to provide an excitation force to the structure using a miniature
impact hammer. The setup of the EMA process is shown in Figs. 13 and 14. The
stability diagram is shown in Fig. 15. The AutoMAC plot is used to indicate the
validity of the EMA testing procedure and is shown in Table 9. The comparison of
the simulated mode shapes and the experimental mode shapes are shown in Figs. 16
and 17 whereas the comparison of the natural frequencies between the FE modal
analysis and EMA are shown in Table 10. The decay time constant, τa that is used in
the exponential weighting of the response spectrum is equivalent to 0.043 s which is
required for the computation of the damping correction.
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The AutoMAC plot shown in Table 9 indicates that the modal parameters
were not extracted in the best possible manner. Four non-zero off-diagonal values
were observed in the AutoMAC plot which indicates that the dynamic properties
of Suction Tube 2 are not extracted in the best possible manner. This justifies the
fact that the modal parameter stimation process is not done in the best possible
manner. Six modes are obtained from both the EMA test and the FE modal
analysis procedure in the frequency span of 0 Hz to 200 Hz. The interesting
observation in this study is that although the perentage difference in the natural
frequencies between FE modal analysis and the natural frequencies in the EMA
has a maximum value of only 4.67%, the natural frequencies from the FE modal
analysis underpredicts the natural frequencies except for mode 4. This should not
be the case as the natural frequencies from the EMA procedure should be lower
compared to the natural frequencies computed from the FE modal analysis
approach. This is due to the presence of the extra mass from the accelereometers
and since the natural frequency is inversely proportional to mass, the additional
mass results in a lower natural frequency.
Both the results from the simple plate and Suction Tube 1 show that the FE
modal analysis consistently overpredicts the natural frequencies compared to the
experimental natural frequencies which should be the case. The mode shapes that
are observed are only similar for Mode 1 and Mode 2. The rest of the modes
showed a similar deformation pattern, but the direction of the deformation pattern
is the complete opposite. The irregularities observed in the results obtained from
Suction Tube 2 could be due to the positioning of one of the accelerometers and
the impact positions in terms of its axis. When an EMA testing procedure is
carried out, the geometry alignment of the MTC Hammer software must be
similar to the alignment of the structure under actual testing conditions. In the
case of Suction Tube 2, the alignment is positioned in such a way that one of the
accelerometers that is required to be positioned in the X-axis on the MTC
Hammer software could not be achieved under real testing conditions as the plane
of the suction tube is slanted. The slanted portion of Suction Tube 2 also affected
the impact hammer position as excitation to the structure could not be provided to
the correct axis. Biased errors are observed for Suction Tube 2 due the constrains
in terms of the alignment of the axis of the accelerometer and the axis of the
impact locations at the slanted portion of Suction Tube 2. The poor FRF data
contributed to the poor modal parameter extraction process which is jutified based
on the AutoMAC plot in Table 9.
3.4. Study on the degree of the “Free-Free” boundary condition
Table 11 shows the comparison of the natural frequency of the first bending mode
and the natural frequency of the rigid body mode. Based on the results shown in
Table 11, the simple plate and Suction Tube 1 is considered to have a “free-free”
boundary condition as it falls in the range where the rigid body mode has to be in
the frequency range of 10% to 20% of the first bending mode [9]. Suction Tube 2
on the other hand exceeds the 15% range and it is extremely close to the 20%
limit [9, 10]. This is an indication that Suction Tube 2 is not completely “free-
free’ and has a certain degree of constrain to it. This could also be a contributing
factor to the anomalies in the results obtained for Suction Tube 2.
Experimental Modal Analysis (EMA) Study on Multi-Bent Copper Phosphorous �. 111
Journal of Engineering Science and Technology Special Issue 8/2014
Fig. 12. The Comparison of the Experimental Mode Shapes (a) and
Simulated Mode Shapes (b) for Mode 1, 2, and 3 for Suction Tube 1.
(a) (b)
Mode 1
Mode 2
Mode 3
112 P. Kamalanathan et al.
Journal of Engineering Science and Technology Special Issue 8/2014
Fig. 13. The Placement of Accelerometers on Suction Tube 2 under (a) the
“free-free” Boundary Condition and (b) on MTC Hammer.
Fig. 14. The Impact Locations for Suction Tube 2 on MTC Hammer.
Fig. 15. The Stability Diagram Obtained
from the EMA Testing of Suction Tube 2.
(a) (b)
Experimental Modal Analysis (EMA) Study on Multi-Bent Copper Phosphorous �. 113
Journal of Engineering Science and Technology Special Issue 8/2014
Fig. 16. The Comparison of the Experimental Mode Shapes (a) and
Simulated Mode Shapes (b) for Mode 1, 2, and 3 for Suction Tube 2.
(a) (b)
Mode 1
Mode 2
Mode 3
114 P. Kamalanathan et al.
Journal of Engineering Science and Technology Special Issue 8/2014
Fig. 17. The Comparison of the Experimental Mode Shapes (a) and
Simulated Mode Shapes (b) for Mode 4, 5, and 6 for Suction Tube 2.
(a) (b)
Mode 4
Mode 5
Mode 6
Experimental Modal Analysis (EMA) Study on Multi-Bent Copper Phosphorous �. 115
Journal of Engineering Science and Technology Special Issue 8/2014
Table 9. The AutoMAC Plot from the EMA Testing of Suction Tube 2.
- 38.778 54.017 109.484 144.190 159.870 177.821
38.778 1.000 0.004 0.130 0.008 0.023 0.000
54.017 0.004 1.000 0.004 0.385 0.219 0.200
109.484 0.130 0.004 1.000 0.026 0.321 0.091
144.190 0.008 0.385 0.026 1.000 0.206 0.100
159.870 0.023 0.219 0.321 0.206 1.000 0.176
177.821 0.000 0.200 0.091 0.100 0.176 1.000
Table 10. The Comparison between Experimental Results and FE
Results in Terms of the Natural Frequencies for Suction Tube 2.
Mode
Experimental (EMA) Simulation
(FE) Percentage
Difference
(%)
Natural
Frequency
� ('()
Uncorrected
Damping De
(%)
Corrected
Damping
Dc (%)
Natural
Frequency
� ('()
1 38.78 9.807 9.617 36.97 -4.67
2 54.02 7.327 7.191 51.60 -4.48
3 109.48 3.043 2.976 104.97 -4.12
4 144.19 2.340 2.289 146.56 1.64
5 159.87 2.436 2.390 155.30 -2.86
6 177.22 2.349 2.307 174.35 -1.62
Table 11. The Evaluation of the “free-free” Boundary Condition
Based on the Rigid Body Mode and the First Bending Mode.
Structure
Rigid
Body
Mode (Hz)
First
Bending
Mode (Hz)
Percentage of the Rigid
Body Mode based on the
First Bending Mode (%)
Simple Plate 10.68 128.64 8.3
Suction Tube 1 3.08 62.84 4.9
Suction Tube 2 7.69 38.78 19.8
4. Conclusion
A complete EMA testing procedure was successfully developed for multi-bent
copper phosphorous tubed based on validated results from a preliminary study on a
simple plate structure. The developed EMA procedure was employed onto Suction
Tube 1 and 2 within a frequency span of 0 Hz to 200 Hz. Successful correlations
between FE modal analysis and EMA in terms of natural frequencies and mode
shapes were observed in Suction Tube 1. However, this was not the case in Suction
Tube. It is postulated that the probable cause of a poor correlation based on Suction
Tube 2 could be attributed to a poor positioning of an accelerometer resulting in
biased errors, thus affecting the raw data obtained. Overall, the developed procedure
to extract the dynamic properties of the multi-bent phosphorous deoxidized copper
tube using the CMIF and the RFP-Z modal parameter estimation algorithm was
116 P. Kamalanathan et al.
Journal of Engineering Science and Technology Special Issue 8/2014
capable in determining accurate results except for the biased errors that were
observed in Suction Tube 2.
Acknowledgments
The author would like to thank Mr. Low Lee Leong and Mr. Dimitris Katramados
from βETA CAE Systems for their continuous support and help. The author
would also like to extend his gratitude to the General Manager of PAPARADMY
1, Mr. Cheng Chee Mun for the approval and opportunity to use the software and
equipment available at PAPARADMY1 and to the Deputy Director of
PAPARADMY 1, Mr. Low Seng Chok for the approval of the copper tube
specimens used in the study.
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