Development of a Closed-Loop Resonant Fatigue Testing
DEVELOPMENT OF A CLOSED-LOOP RESONANT FATIGUE TESTING
METHODOLOGY AND EXPERIMENTAL LIFE TEST OF ALUMINUM ALLOY
A Thesis
Presented to
The Graduate Faculty of The University of Akron
In Partial Fulfillment
of the Requirements for the Degree
Master of Science
A.B.M. Abdullah
December, 2010 DEVELOPMENT OF A CLOSED-LOOP RESONANT FATIGUE TESTING
METHODOLOGY AND EXPERIMENTAL LIFE TEST OF ALUMINUM ALLOY
A.B.M. Abdullah
Thesis
Approved: Accepted:
Advisor Dean of the College Dr. Gun Jin Yun Dr. George K. Haritos
Faculty Reader Dean of the Graduate School Dr. Craig C. Menzemer Dr. George R. Newkome
Department Chair Date Dr. Wieslaw K. Binienda
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ABSTRACT
A vibration-based testing methodology is presented that assesses fatigue behavior of material for metallic structure. To minimize the testing duration, the test setup is designed for a base-excited multiple-specimen arrangement driven in a high- frequency resonant mode, which allows completion of fatigue testing in an accelerated period. A high performance electro-dynamic exciter (shaker) is used to generate harmonic oscillation of cantilever beam specimens, which are clasped on the shaker armature with specially-designed clamp fixtures. The shaker operates in closed-loop control with dynamic specimen response feedback provided by a scanning laser vibrometer. A test coordinator function is developed to synchronize the shaker controller and the laser vibrometer, and to complete the closed-loop scheme: the test coordinator monitors structural health of the test specimens throughout the test period, recognizes change in specimen dynamic behavior due to fatigue crack initiation, terminates test progression, and acquires test data in an orderly manner. Topological design is completed by constructing an analytical model and performing finite element analysis for the specimen and fixture geometry such that peak stress does not occur at the clamping fixture attachment points. Experimental stress evaluation is conducted to verify the specimen stress predictions. A successful application of the experimental methodology is demonstrated by validation tests with aluminum specimens subjected to fully-reversed bending stress. iii
ACKNOWLEDGEMENTS
The author would like to proclaim sincere gratitude to all those who contributed to the success of the research project reported in this study. Specially, the author wishes to express his highest appreciation to Dr. Gun Jin Yun for his excellent guidance, invaluable suggestions, generous encouragement and persistent support throughout this effort. It was a great honor to work with him.
The author also acknowledges the timely cooperation from Dr. Wieslaw K.
Binienda and Dr. Craig C. Menzemer. Sincere appreciation and thanks to Pierre
Wickramarachi for his tireless effort and technical collaboration on operating DP system. Brett M Bell, David McVaney, William A Wenzel and Dale Ertley deserve the fullest appreciation for their prompt help in manufacturing and machining the specimens and fixtures. The author is also thankful to Arend von der Lieth for his expert experimental advice on running PSV. Thanks also to Shen Shang, Soon G. Lee and Kamil Nizamiev for their constructive cooperation in this work. The author gratefully acknowledges and extends warmest thanks to his family and friends for their continuing encouragement.
NASA Glenn Research Center provided funding to complete the work described herein, and the author is grateful for that enduring commitment. The author also appreciates strong support of David L. Krause, P.E. at NASA GRC and Dr.
Sreeramesh Kalluri at Ohio Aerospace Institute. iv
Finally, the author is particularly indebted to his parents, Mrs. Suraiya Khaleque and Mr. Abdul Khaleque, and his sister Sathi, for their understanding and sacrifice throughout the years he is away from them.
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DEDICATED
To my parents to whom I owe everything I have accomplished
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TABLE OF CONTENTS
Page
LIST OF TABLES…………….….……………………...... ……………………….x
LIST OF FIGURES…………………………………………………………………..xi
LIST OF EQUATIONS……………………………………………………………...xv
CHAPTER
I. INTRODUCTION……………………………………………………...... …...... 1
1.1 Research Motivation……...………………………………….……………….1
1.2 Scope of Work...... …………...... …………………………………….………3
II. LITERATURE REVIEW…………………...... …………………………………..4
III. DEVELOPMENT OF TEST METHODOLOGY…………...…………………..11
3.1 Equipment for Closed-loop HCF Testing………...... ……………………..11
3.1.1 Hardware……...... …….………………...... ……………………...11
3.1.1.1 Polytec Scanning Vibrometer...... 11
3.1.1.2 DP SignalStar Vector Vibration Controller System...... 14
3.1.1.3 DP SignalForce Electrodynamic Shaker System…...... 15
3.1.1.4 Others……...... …………...... ……...... …………....16
3.1.2 Software…….……...... …..……….…...... ……………………...…17
3.1.2.1 HCF Test Coordinator…………....…………….………..…17
3.1.2.2 DP SignalStar Vector Software……...... …....……………...20 vii
3.1.2.3 Others...... 21
3.2 Design of Test Specimen and Fixture……....….....……………...... ….....21
3.3 System Configuration and Integration……...... ……………...…..…29
3.4 Procedure for Closed-loop HCF Testing……...... …...... 30
IV. SHAKER EVALUATION AND VALIDATION TEST...…...... …....…....….34
4.1 Outline....…...... …………...…..………………………………………...34
4.2 Shaker Evaluation………...………..………………………………………...34
4.3 Stress Evaluation………....…………………………………………………..37
4.4 Evaluation of Damping……...... ………………………………………….41
4.5 Relationship between Specimen Tip Disp. and Shaking Amp...... 43
4.6 Validation Test...... 44
V. THEORITICAL APPROACH...... …...…………....…...….48
5.1 General...... …...... ………………...48
5.2 Analytical/Numerical Model...... 48
5.3 Finite Element (FE) Model...... ………………...54
5.3.1 Modal Analysis...... ……………………...54
5.3.2 Direct-solution Steady-state Dynamic Analysis …...... 56
VI. EXPERIMENTAL TESTING AND RESULTS...... 63
6.1 General...... 63
6.2 Stress-Displacement Calibration Test...... 63
6.2.1 Test Set-up...... 64
6.2.2 Measured Data...... 66
6.3 Fatigue Testing...... 69
viii
6.3.1 Test Set-up...... 69
6.3.1.1 Data Acquisition Settings in PSV...... 69
6.3.1.2 DP Shaker Controller Settings...... 76
6.3.1.3 HCF Test Coordinator Settings...... 90
6.3.2 Test Matrix Development...... 91
6.3.3 High-cycle Fatigue Test...... 92
6.3.4 Results and Discussion...... 96
VII. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS...... 100
BIBLIOGRAPHY...... 102
APPENDICES...... 105
APPENDIX A Resonant Frequency History during Fatigue Test...... 106
APPENDIX B Microphotograph of Fatigue Cracks in Tested Specimens...... 109
APPENDIX C Code for HCF Test Coordinator...... 112
ix
LIST OF TABLES
Table Page
3.1 Specimen with Lumped Mass at tip……………………………...... …...... 23
3.2 Specimen with hourglass shape at high stress region.…………………...... …24
5.1 Comparison of natural frequencies from Analytical and FE model...... 50
5.2 Modal analysis output from ABAQUS®.……………...... 55
5.3 ABAQUS® output for specimen tip displacement 1.8 mm (0-pk)...... 58
5.4 ABAQUS® output for specimen tip displacement 1.9 mm (0-pk)...... 59
5.5 ABAQUS® output for specimen tip displacement 2.0 mm (0-pk)...... 60
5.6 ABAQUS® output for specimen tip displacement 2.1 mm (0-pk)...... 61
5.7 ABAQUS® output for specimen tip displacement 2.2 mm (0-pk)...... 62
6.1 Magnitude sensitivity set-up for shaking with different tip disp. amplitude.....82
6.2 Acceleration limit set-up for shaking with different tip disp. amplitude...... 85
6.3 Test Matrix...... …91
6.4 Test Results...... …96
6.5 Parameter data for logarithmic regression analysis...... …99
x
LIST OF FIGURES
Figure Page
1.1 Required stress for fatigue failure...... ……………………...... 1
1.2 Endurance limit...... ……………………...... 2
3.1 PSV-400-M2-20 System ...... ….………………………………...... 12
3.2 Schematic layout of signal flow in the Vibrometer ……………...... …13
3.3 DP ABAQUS Chassis and Relay Box...... ………………...... 14
3.4 DP Shaker System...... …………………...... 15
3.5 Facility upgrade for HCF testing……………...... 17
3.6 Final Specimen Geometry for HCF testing...... 27
3.7 Upper Block of Fixture ………...... 28
3.8 Lower Block of Fixture...... 28
3.9 Specimen with Fixture...... 29
3.10 Closed-Loop Test Configuration...... 33
4.1 Dummy mass attached to shaker armature...... 35
4.2 Specimen and fixture for shaker evaluation...... 35
4.3 Performance of shaker with different operating frequency...... 36
4.4 Unstable shaker armature movement...... 37
4.5 Simple tension test of specimen materials...... 38
4.6 Stress-Strain Plot of test results...... 38 xi
4.7 Five Specimens tested for stress evaluation...... 38
4.8 Stress contour from 3D FE analysis...... 39
4.9 Location of Fatigue Crack...... 39
4.10 Natural frequency and specimen length relationship...... 40
4.11 Specimen tip displacement vs natural frequency...... 41
4.12 Specimen max bending strain vs natural frequency...... 42
4.13 Specimen max bending stress vs natural frequency...... 42
4.14 Variation of damping with natural frequency...... 43
4.15 Shaking amplitude vs specimen tip displacement...... 44
4.16 Natural frequencies and phase angles of ten 4.2 inch specimens...... 45
4.17 Amplitude of velocity measured by laser vibrometer...... 46
4.18 Frequency change due to fatigue crack...... 46
4.19 Tracking of phase angle during fatigue testing...... 47
4.20 Fatigue crack in specimen...... 47
5.1 Relative displacement of vibrating specimen...... 48
5.2 Comparison of natural frequencies...... 50
5.3 Operational deflection shape at 1st natural frequency...... 51
5.4 Operational deflection shape at 2nd natural frequency...... 51
5.5 Operational deflection shape at 3rd natural frequency...... 51
5.6 Operational deflection shape at 4th natural frequency...... 52
5.7 Operational deflection shape at 5th natural frequency...... 52
5.8 Steady-state spectral responses...... 53
5.9 Test Specimen...... 56
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6.1 Al6061-T6 specimens and fixtures...... 63
6.2 Strain Gage on Specimen...... 64
6.3 NI LabVIEW® settings for strain measurement...... 65
6.4 NI LabVIEW® settings for strain gage...... 65
6.5 NI LabVIEW® strain measurement...... 66
6.6 NI LabVIEW® strain measurement (close view)...... 67
6.7 Strain-Displacement Relationship...... 68
6.8 Stress-Displacement Relationship...... 68
6.9 PSV System...... 69
6.10 General acquisition settings in PSV...... 70
6.11 Channels acquisition settings in PSV...... 71
6.12 Settings for filters in PSV...... 72
6.13 Settings for cutoff frequencies in PSV...... 72
6.14 Frequency settings in PSV...... 73
6.15 Window settings in PSV...... 74
6.16 Signal Enhancement settings in PSV...... 75
6.17 Vibrometer settings in PSV...... 75
6.18 DP System...... 76
6.19 Test identification parameters in DP Shaker Controller...... 76
6.20 Drive and shaker parameters in DP Shaker Controller...... 77
6.21 DP Shaker parameters...... 78
6.22 Control and limit parameters in DP Shaker Controller...... 79
6.23 Control and limit channel information in DP Shaker Controller...... 80
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6.24 Control range configuration in DP Shaker Controller...... 80
6.25 Control parameters in DP Shaker Controller...... 81
6.26 Reference displacement settings in DP Shaker Controller...... 83
6.27 Reference displacement input in DP Shaker Controller...... 83
6.28 Acceleration limit settings in DP Shaker Controller...... 84
6.29 Acceleration limit input in DP Shaker Controller...... 84
6.30 Frequency range set-up for resonance search and dwell test...... 86
6.31 Dwell parameter settings in DP Shaker Controller...... 87
6.32 Frequency aborts set-up in DP Shaker Controller...... 88
6.33 Amplitude aborts set-up in DP Shaker Controller...... 88
6.34 Resonance search and dwell control parameters...... 89
6.35 Saving dwell data in DP Shaker Controller...... 90
6.36 FRF phase angle from DP sweep sine test...... 93
6.37 FRF magnitude from DP sweep sine test...... 94
6.38 Shaker accln from DP sweep sine test...... 94
6.39 Excitation freq. from DP res. search and dwell test...... 94
6.40 Specimen tip disp. From DP res. search and dwell test...... 95
6.41 Resonant frequency history...... 95
6.42 Experimental S-N Curve for Al6061-T6...... 97
6.43 Microphotograph of fatigue cracks in tested specimens...... 98
6.44 Comparison of test results...... 99
xiv
LIST OF EQUATIONS
Equation Page
4.1 Analytical equation for shaker armature displacement amplitude……...... 35
4.2 Empirical equation for shaking amplitude and tip displacement………...... …44
5.1 Equation for strain energy...... …49
5.2 Equation for kinetic energy...... …49
5.3 Equation of motion for the vibrating test specimen...... …49
5.4 Equation of motion for undamped free vibration of the test specimen...... …50
6.1 Logarithmic regression equation for stress-completed cycles...... …98
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CHAPTER I
INTRODUCTION
1.1 Research Motivation
Fatigue is a process of structural damage of material that occurs under cyclic loading. The required stress level to induce fatigue crack is often below the ultimate tensile stress, or even the yield stress of material (Figure 1.1 a). The greater the applied stress, the shorter the life (Figure 1.1 b).
(a) (b)
Figure 1.1 Required stress for fatigue failure
Some structural metals such as ferrous alloys and titanium alloys have distinct amplitude of cyclic stress below which there appears to be no number of cycles that will cause failure (Curve A in Figure 1.2). Other metals, for example aluminum and copper, do not exhibit a distinct limit and will eventually fail even for small stress amplitudes.
(Curve B in Figure 1.2).
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Figure 1.2 Endurance limit
Fatigue life is influenced by a variety of factors, such as temperature, surface finish, microstructure, presence of oxidizing or inert chemicals, residual stresses etc., which have made the process essentially stochastic, often showing considerable scatter even in controlled environment, this scatter tends to increase for longer fatigue lives.
Because of scatter in fatigue data, experimental testing of multiple specimens is necessary to predict a safe limit of fatigue cycle. An intelligent system is required as well that can detect the fatigue crack at initial stage and can stop the excitation to control further crack propagation.
The research was contained in the framework of the project Test Methodology
Development for Experimental Structural Assessment of Advanced Stirling Converter
(ASC) Planar Spring Material for Long-term Durability, sponsored by National
Aeronautics and Space Administration (NASA) Glenn Research Center (GRC).
Recently, a high efficiency Advanced Stirling Radioscope Generator (ASRG) is identified by NASA GRC as a promising power source for future long duration
2 scientific missions such as lunar applications, Mars rovers, and deep space missions, all requiring long life radioisotope power systems. ASC planar spring, which provides translational stiffness, is a key component of ASRG. The planar spring life assessment requires testing of the material to evaluate its durability in the high cycle regime.
The objective of this work is to develop a HCF (High-cycle Fatigue) test procedure, geometric designs of test specimens and fixtures, test controls, and instrumentation, to assure that valid experimental data can be obtained. This effort includes confirmation that the test method permits stable operation of an electro- dynamic exciter in closed-loop control.
1.2 Scope of Work
In this effort, a test configuration for multiple specimens was developed and tested with extensive experiments. The test mechanism synchronizes the shaker controller with the scanning vibrometer by employing HCF Test Coordinator.
Substantial change in dynamic responses, such as resonant frequency or other damage sensitive indices, imply stiffness changes associated with fatigue crack initiation and propagation. With the closed-loop control technique, re-tuning the excitation frequency to the shifted resonant frequency of specimen was accomplished, and thus, by tracking the preset phase angle and monitoring the frequency change, a satisfactory control over the fatigue crack propagation was attained.
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CHAPTER II
LITERATURE REVIEW
In recent years, experimental methods for accelerated measurement of high cycle fatigue properties of materials are continuously under development.
The work by George et al. [3] provides a test methodology to determine stresses to produce fatigue failure corresponding to a fixed number of cycles (106 or 107). A forced-vibration based procedure using step-testing method was employed. Both uniaxial and biaxial stress states under fully reversed bending were considered. The cantilever plate specimen mounted to the electrodynamic shaker head was excited near to the frequency of a particular natural mode of vibration. This method used accelerometer for monitoring the shaker input force, and laser vibrometer to measure the velocity of a point on the specimen. While the specimen was in resonance at various shaker power settings, data were taken from strain gage, which was installed on the high-stressed zone of specimen, and laser vibrometer to calibrate strain, therefore, stress, with respect to the corresponding velocity. The fatigue limit stress was then determined based on resonant frequency shift from the shaker driving frequency. This procedure also proposed experimental technique to produce short and long cracks by keeping the shaker driving frequency fixed or re-tuning it to the decreased resonant frequency because of fatigue crack, respectively. However, this method does not have an automated control to stop the shaker and testing when fatigue crack initiates. 4
Wang et al. [4] adopted a method to measure fatigue properties of thin solid films. In this study, piezo actuators were used to generate oscillation at the clamp of the cantilever beam specimen and the displacements of the specimen were monitored by a fiber-optic measurement system. A LabVIEW® computer program was developed to perform automatic frequency scans and control the frequency output of function generator while keeping amplitude output constant. It was also programmed to count the number of cycles applied on the specimens during the fatigue test, and a feedback mechanism was employed to maintain displacement during the test. The authors utilized 10-Hz algorithm that states that a sample fails when a 10 Hz reduction in its resonant frequency is observed as a result of fatigue crack initiation. Maximum stress was obtained by using curve fitting method based on photograph of the vibrating cantilever, which would introduce significant error in stress estimation.
With the development and application of ultrasonic fatigue testing equipments, it has been recognized that ultrasonic fatigue testing methodology is an effective way to investigate fatigue properties of materials in high cycle regime. Based on ultrasonic vibration theory Xue et al. [5] proposed a procedure to assess flexural fatigue strength of materials in cyclic range of 105 to 1010 at a greatly reduced time. Optical sensor capable of measuring the displacement, at a frequency as high as 20 kHz, was used in calibrating the fatigue vibration system, and thus a reasonable displacement-stress field in the bending resonance system was accomplished.
Unlike the traditional use of single-frequency sinusoidal excitation, S.
Vanlanduit, P. Verboven and P. Guillaume [6] used double-sine excitation signal, which consists of a low-frequency part to obtain fatigue damage and a higher frequency
5
part to excite the structure and measure the response. The response of the excitation signal was displacement, which was decomposed into two signals corresponding to the different excitation frequencies. Displacement response was measured with laser vibrometer, and control and processing of the measurements were performed in
MATLAB®. The authors used maximum likelihood estimator technique, which allowed estimating the confidence level to distinguish changes in resonant frequency due to noise and changes due to structural damage.
Based on the feature that presence of damage implies a nonlinear vibration behavior, an experimental setup of fatigue test was demonstrated by Steve Vanlanduit,
Eli Parloo and Patrick Guillaume [7] to detect fatigue crack. This work was focused to develop a method which demands less user interaction without interrupting the fatigue test. Excitation signal was measured with the aid of a force cell and response from the specimen was measured using an accelerometer. Depending on the excitation frequency, resonant frequency drop of 2% to 10% was observed due to fatigue crack, while higher percentage of frequency drop was noticed for lower excitation frequency.
Recent study by Fabricio Tonon Joaquim, Renato Barbieri and Nilson Barbieri
[8] reports the development of a prototype of an equipment for torsional fatigue testing.
Keeping the driving frequency below the first natural frequency of the specimen, the system was designed for testing with constant and variable amplitude loading. A programmable logic controller was programmed to vary the frequency and amplitude of the external torque. Structural damping was estimated by setting the specimen on free oscillation condition, and measuring the torque afterwards. This value of structural damping was used as an input data for FE simulation. During the test, changes of
6
amplitude in frequency response function, which varies with specimen rigidity, was investigated, and reduction of torsional rigidity was used as a parameter for estimating damage in specimen.
An accelerated life testing was performed by Özsoy, Çelik and Kad1oğlu [9], which considered vibration induced multi-axial stress states. For measuring the vibration level along different directions, tri-axial integrated circuit piezoelectric accelerometers were used. However, the vibration tests were carried out axis by axis successively rather than all the axes simultaneously, and the test results were then superimposed. A closed-loop system driven by power spectral density profiles was employed to run the constant amplitude resonance test. To estimate the appropriate test duration avoiding maximum stress level reaching or exceeding the yield limit, a correlation between accelerated test duration and alternating stress was proposed.
Wozney [10] introduced a method for conducting experimental resonant fatigue testing with amplitude-control system. A separate system was employed to insure that the amplitude of vibration of the specimen does not vary more than a specified quantity.
The transducer signal was connected to an amplitude sensitive circuit, which shuts down the whole system if the amplitude varies more than a specified amount from the set value. To detect fatigue failure, amplifier gain was monitored as more power is required to maintain the same amplitude when the specimen fails and its natural frequency decreases. A high-limit switch was set to stop the test at the predefined increase in power-amplifier gain. With electromagnetic drive and control system, a series of techniques was presented for experimental vibration-fatigue studies.
Since one of the major complications associated to fatigue experiment lies in
7
the time-consuming aspect of the testing, Kim et al. [11] designed a multi-specimen fatigue testing apparatus, which can test ten specimens at a time. This stress-controlled flexural fatigue testing tool was specially designed for test with low frequency and low applied stress level. As increasing the test frequency often gives rise to mechanical failure by hysteric heating, a constant temperature water bath was used to circumvent this problem. For this, liquid medium was filled in the constant temperature water bath where the temperature of the liquid was controlled by the thermostat connected to the heater.
Later, Ay et al. [12] proposed an improved apparatus over Kim, with capability to test sixteen specimens simultaneously. Better balance and less vibration on the apparatus were confirmed by using infrared sensors and adjustable support device. To minimize the heat effect on the testing material, the test frequency was kept low. A signal processing software was used to count and record experimental data and parameters during the test. With the developed adjustable support device, different stress ratios can be obtained. The authors ensured that the forces applied in the test apparatus match the real service conditions and thus reliable test results were warranted.
Shen et al. [13] suggested an integrated computational-experimental approach for fatigue life prediction, in which a series of fatigue tests were conducted to investigate the effect of axial and fully reversed bending stress on fatigue limit.
Accelerometer was used to monitor the shaker input force. Velocity signal from laser was calibrated to the corresponding strain in the fatigue region of the plate specimen by running a calibration test with the test specimen instrumented with a strain gage placed in the expected maximum strain region. To validate the experimental observations and
8
further predict the fatigue life, a high-cycle fatigue criterion was proposed based on the amount of energy loss per fatigue cycle.
Rotem [14] examined an accelerated life testing method by monotonically increasing stress amplitude, which shortens the test time and minimizes the number of tests needed for determination of endurance limit. As per the proposed method, three separate tests are needed to complete the fatigue testing, two of them starting above the endurance limit and one starting below it. The first two tests determine the S/N curve parameters while the third test finds the endurance limit. Selection strategies of the right loading rate and starting stress level were discussed. Tests were performed on an electro-hydraulic servo-controlled test system confirming that every test is ended by fatigue failure.
Nieto, Chiccharo and Pintado [15] intended a simplified approximated methodology for fatigue testing. They investigated the variation of first resonance frequency with accumulated damage and presented a correlation between the vibration response of the specimen and the accumulated damage. In this research, piezoelectric accelerometer, which covers a wide frequency range, was used to monitor fatigue damage. A trigger was used to synchronize the acquisition of force and acceleration signals, when both signals were logged in the computer using a data acquisition card from National Instruments. As an effort to simulate real conditions the samples were not fabricated under controlled laboratory conditions but, rather, were produced in an industrial plant to obtain the typical scatter in fatigue data.
Fressinet, Panis and Bordes [16] used hydraulic shaker to explore the gigacycle domain at a frequency near to 875 Hz. A square plate was excited around the fourth
9
mode to obtain the expected dynamic response. To reach the desired stress level at low energy it was chosen to work with a stress concentration area by making notch in the specimen. Strain gauges were glued to the specimens in order to control stress level during the test, and a laser was used to measure the displacement of a point on the sample. By this way, a correlation between the displacements measured by laser with the stress given by gauge was realized.
Kim, Song and Lee [17] developed a fatigue testing system to perform load- controlled fatigue test for ductile thin films. They also developed a displacement gauge to measure the monotonic and cyclic deformation of thin films during the fatigue test over a wide range of frequency. Using an electro-dynamic actuator, fatigue test was performed in a wide range of frequency. Noticing that in case of horizontally mounted test specimen, the gravitational force likes to act as a laterally distributed bending load which might cause bending stresses and flexural displacement in the specimen, the authors mounted the specimens vertically to minimize the effects of the gravitational force on the specimen.
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CHAPTER III
DEVELOPMENT OF TEST METHODOLOGY
3.1 Equipment for Closed-loop HCF Testing
The HCF test configuration comprises an electro-dynamic shaker system to generate sinusoidal excitation, a vibration controller system to operate the shaker, a scanning vibrometer for vibration measurement, HCF Test Coordinator to synchronize the vibration measurement and excitation, and other supplementary tools.
3.1.1 Hardware
The major hardware used in HCF testing were a scanning vibrometer and an electro-dynamic shaker system with controller.
3.1.1.1 Polytec Scanning Vibrometer
Model PSV-400-M2-20, Polytec, Inc (Figure 3.1), a Scanning Laser
Vibrometer (SLV) system.
a) Junction Box PSV-E-400: This is an interface between PSV Laser sensor head, OFV-5000 controller and data management system PC. It has four ICP- compatible analog input channels. One channel was used for an accelerometer attached on the shaker armature. Velocity data from the OFV-5000 controller were entered into one of the analog input channels of the Junction Box. An auxiliary output channel of 11 digital I/O port was used to send high and low TTL signals to DP ABACUS chassis to coordinate with DP shaker system.
b) Controller OFV-5000: This PSV vibrometer controller has standard BNC connectors to send velocity data in analog voltage signals to a control channel of DP
ABACUS chassis and PSV Junction Box. OFV-5000 can measure up to 10 m/sec velocity.
c) Data Management System PSV-W-400: This is a desktop PC for accessing measured data through PSV vibrometer software.
Specimen on Shaker Armature
Figure 3.1 PSV-400-M2-20 System 12
d) Scanning Head PSV-I-400: This is a long-range laser scanning head which is installed on a stable tripod. It is positioned at an optimum stand-off distance, 20 inches from front face of the head to the specimen.
The laser vibrometer uses the principle of interferometry to acquire the characteristics of mechanical vibrations. To make the vibration measurement, the beam of a helium neon laser is pointed at the vibrating object (specimen) and scattered back from it. Velocity and displacement amplitude of a vibrating object generate a frequency or phase modulation of the laser light due to the Doppler Effect. This modulation is recovered in the signal processing unit with the aid of suitable decoders.
Figure 3.2 Schematic layout of signal flow in the Vibrometer 13
3.1.1.2 DP SignalStar Vector Vibration Controller System
a) ABACUS Chassis: It has four standard BNC input channels. One of them was connected to OFV-5000 for acquiring velocity data of the specimens. The second channel was connected to an accelerometer installed on the shaker armature. The accelerometer was also connected to the reference channel of PSV Junction Box.
b) Relay Box ONTRAK ADU 208: Relay I/0 interfaces physically connect
OFV-5000 controller to a desktop PC running SignalStar Vector through USB. It transmits digital TTL signals to coordinate the dwell testing for multiple specimens.
c) Desktop PC and Monitor: This PC runs SignalStar Vector software for vibration control and was connected to DP ABACUS chassis through TCP/IP (Figure
3.3).
Figure 3.3 DP ABACUS Chassis and Relay Box 14
3.1.1.3 DP SignalForce Electrodynamic Shaker System
a) V100/DSA1-1K: This air-cooled Electrodynamic shaker (Figure 3.4) has a maximum sine force capability of 224.8 lbs and max acceleration of 125 g. Armature mass is 1.7 lbs. Its frequency range is from DC to 7000 Hz with resonance frequency
6850 Hz. It was connected to a field supply unit.
b) Power Amplifier SS1000T: The amplifier was connected to a field supply unit for power acquisition and the ABACUS chassis for shaker driving voltage.
Figure 3.4 DP Shaker System
15
c) Field Supply Unit (FSU100): The power supplier unit provides power to amplifier and shaker.
d) Cooling Blower Unit: A flux jet cooling unit was connected to the V100 shaker to lower the temperature during long-term operation.
3.1.1.4 Others
a) 1TB External Hard Drive, Western Digital (WD) Element: It was connected to the PSV data management system to save HCF test data (Frequency Response
Function (FRF) and the number of loading cycle for each scanning point).
b) 3030B Accelerometer, Dytran Instruments, Inc.: The accelerometer was installed on the shaker armature to measure reference signals. Acceleration data were sent to DP ABACUS chassis and reference channel of PSV system.
c) WK-06-062AP-350 Strain Gage, Vishay Micro-measurements, Inc.: Vishay
WK series strain gages are made of fully encapsulated K-alloy with high endurance lead wires. Its maximally measurable strain range is ±1.5%. Resistance of the strain gage is 350±0.3% (Ohms).
d) NI-1520 (Signal Conditioning Unit for Bridge Type Sensors) and NI-1314
(terminal block for strain gages) in NI SCXI-1001 module, and NI PXI-6259 (M Series
DAQ board) in PXI 1042 Chassis, National Instrument, Inc.: NI DAQ system was used in calibration tests for stress evaluation.
e) Panasonic Network Camera BL-C1A: A network camera was installed for remote surveillance.
f) Other Laboratory Facilities: For secure testing environment, a permanent
16 wall was built as shown in Figure 3.5. In addition, electric power lines were upgraded to accommodate larger power consumption of the shaker system.
Figure 3.5 Facility upgrade for HCF testing
3.1.2 Software
A program was developed to coordinate shaker controller and scanning vibrometer system to control the HCF testing.
3.1.2.1 HCF Test Coordinator
For the closed-loop HCF testing, an automated test coordinator was developed.
Typically, the Polytec SLV system measures each scan point during a single pass (pass meaning one complete scan of all specimens). After a pass, it saves all the data in a single file and stops measuring. However, to run the test until fatigue failure and to continuously monitor the health of specimens, it was required to measure each point multiple times throughout the duration of the HCF test. Consequently, it was required to develop a new automation technique, employing the Visual Basic macro engine (Test
Automation Object Library) that comes with the PSV system [20]. Thus it was possible to control and modify the PSV applications programmatically via the built-in macro
17 subsystem and a program was developed to control the PSV system for multiple measurements. The user can now pre-set the intended number of passes, and after completing one pass of all the scan points, the measurement system restarts automatically, and this process continues. To facilitate data analysis, a program was also developed to save pass data separately for each scan point for every measurement cycle.
Macro code was also developed to access the acquisition settings from the program. Time and frequency domain acquisition parameters, such as, sampling frequency, number of samples, etc. were pre-defined within the macro subroutine.
Macro programming was used to synchronize the Polytec PSV system with the
DP SignalStar Vector Shaker Controller by sending digital pulses (TTL) to the digital output port. A DP relay box was used as a communicating device between the two sub- systems. Two different types of digital pulse were generated thru macro code: high level pulse and low level pulse to create start and stop signals, respectively. The required duration of pulse was also set in the macro program.
The closed-loop HCF testing is triggered by a start TTL signal from HCF Test
Coordinator to the DP system. To obtain the natural frequency and the corresponding phase angle sweep sine test is conducted first. After the completion of sweep sine, resonance dwell test is executed to shake the specimen keeping the tip displacement level, and thus the maximum stress level, constant. HCF Test Coordinator catches the max magnitude of FRF, its corresponding frequency, counts the accumulated number of cycles and saves these data to a file.
On the condition that the frequency change is within the predefined limit, the
18
HCF Test Coordinator sends a start TTL signal to the DP system and laser beam moves to next specimen. After measuring all the specimens, the HCF Test Coordinator sends a start signal to the DP system to start the next pass and this process is repeated until one of the specimens fails in fatigue. When the frequency drop exceeds a preset criterion, which is due to specimen stiffness change from fatigue crack initiation, the HCF Test
Coordinator sends a stopping pulse to the DP system to finally stop the excitation.
In frequency measurement mode, the macro was programmed to search the maximum amplitude in the frequency response function (FRF) spectrum.
Subsequently, the corresponding frequency of the maximum spectral amplitude, which is deemed the resonant frequency, was used as a controlling criterion of the closed-loop system. Multiple averaging technique was used in obtaining FRF from PSV, in which it captures the frequency response for each sampling time duration and keep averaging.
Due to fatigue crack initiation, when the frequency drops by a certain value (for example, one Hz) from the previous frequency, the macro code sends a stopping pulse to the DP system and the test is terminated.
The HCF Test Coordinator has resuming capability. To achieve high cycles, it may need to run the test for long duration. Thus, user can anticipate some unwanted interruption of testing at any stage of the experiment. This unsolicited stoppage may happen because of DP software crash, power breakdown or others. In this case, both DP and PSV stores all the test data prior to unexpected stoppage. With this resuming option user can continue the test from that point it stopped. The user need to input the number of cycles completed before power failure and the frequency it captured at the last scan.
PSV starts computing the completed number of cycles by appending it to the cycles
19 completed before the test stopped. It also compares the new frequency it catches with the frequency of the last scan before the system breakdown. Thus it enables the system to detect fatigue failure immediately after the first scan, if the unexpected stoppage occurs right before the fatigue crack initiation in specimen.
3.1.2.2 DP SignalStar Vector Software
Main feature of this software is that it allows feedback controlled resonant fatigue testing. For the closed-loop HCF testing, DataPhysics SignalStar Vector®
(called as DP Vector software in the followings) was used as shaker controller. The resonance search and dwell test option in DP Vector software is designed to perform vibration-based fatigue testing by tracking resonant frequency of a tested specimen. To track resonant frequencies, a sine sweep test needs to be undertaken prior to the dwell test in order to save the frequency response function and phase angle.
Two channels were used: one for the control channel, which is fed continuously by velocity signals from PSV system (OFV-5000), and the other for a measurement channel, where acceleration signals are measured by Dytran accelerometer installed on the shaker armature. Reflective film was used on test specimens to receive high quality velocity signals.
In the resonance search and dwell test window, the phase angle is set to be continuously tracked. This allows changing the shaker driving frequency to the resonant frequency of the specimen. Another important feature in DP shaker system is its capability of controlling the vibration level. Operators can set a targeted displacement, velocity, or acceleration signal level, measured by PSV laser vibrometer.
20
Then the DP software continuously adjusts shaker driving voltages to maintain the preset targeted level.
3.1.2.3 Others a) NI LabVIEW®
National Instrument’s NI LabVIEW® was used for stain measurement in stress- displacement calibration test. b) ABAQUS®
To determine optimum specimen geometry ABAQUS® program was used for finite element analysis of test specimen. c) MATLAB®
By following theoretical approach modal analysis and steady state response analysis of test specimen were conducted using MATLAB® program.
3.2 Design of Test Specimen and Fixture
Motivated by response from 3D FE simulation using modal analysis and direct solution steady-state dynamic analysis in ABAQUS® for different boundary conditions, the test specimen was designed as a cantilever. As per the project requirement the geometric constraints were the thickness of specimen (0.071 inch) and the width where the maximum stress was to be measured (0.2 inch). To avoid possible occurrence of fretting fatigue or highly localized stress concentrations, it was desired to identify a specimen geometry that possesses a mode shape producing the maximum stress away from the clamped edge. Another consideration was to minimize the testing period by
21 designing the mode shape to be of reasonably high natural frequency but within the operating frequency range of shaker.
The original goal was to shake the specimen near its second bending mode’s natural frequency. However, it was found that the DP shaker could not produce necessary armature displacements to achieve high stress at high frequency for reasonably sized specimens. Therefore, the first bending mode’s natural frequency of the specimen was used, which allowed the larger armature amplitudes necessary to reach high stress in the specimens.
A series of FE analyses were performed to optimize specimen geometry. The base part (the gripped zone and area near the fixed end) was widened to reduce the stress level adjacent to the fixed boundary.
To explore the specimen design space, analyses were completed with several specimen configurations, including: added lumped mass at the tip of specimen; hourglass-shape specimens, in which the section was reduced near the peak stress region; hourglass-shape specimens with a wider tip area; specimens with propped- cantilever boundary conditions; specimens with fixed-fixed boundary conditions; and, specimens with sharp notches, in which high stress occurred in a constricted area. Thus all these alternative designs resulted in localized stress concentration near the curvature.
AISI 1095 steel specimens were used for FE simulation to obtain the desired specimen geometry. Typical material property for AISI 1095 steel is -
Mass Density 7,860 kg/m3 Poisson’s Ratio 0.29
Young’s Modulus 205 GPa Yield Strength 525 MPa
22
Table 3.1 Specimen with Lumped Mass at tip Max Stress Location
Total Length : 2.50 inch Total Length : 2.71 inch 1st Mode’s Natural Freq. : 510.82 Hz 1st Mode’s Natural Freq. : 418.38 Hz Est. Shaking Amp. : 77.71 micron (0-pk) Est. Shaking Amp. : 115.84 micron (0-pk) Expected Structural Damping : 3.255% Expected Structural Damping : 3.255% Max Bending Stress : 1766 MPa Max Bending Stress : 1020 MPa Max Displacement : 6.903 mm (0-pk) Max Displacement : 4.861 mm (0-pk)
Total Length : 2.50 inch Total Length : 2.71 inch 2nd Mode’s Natural Freq. : 3607.1 Hz 2nd Mode’s Natural Freq. : 2925.6 Hz Est. Shaking Amp. : 1.56 micron (0-pk) Est. Shaking Amp. : 2.37 micron (0-pk) Expected Structural Damping : 1.530% Expected Structural Damping : 1.530% Max Bending Stress : 106.6 MPa Max Bending Stress : 130.3 MPa Max Displacement : 70.97 micron (0-pk) Max Displacement : 0.1066 mm (0-pk)
23
Table 3.2 Specimen with hourglass shape at high stress region (cont’d..) Max Stress Location (typ.)
Stress Displacement Stress Displacement
Total Length : 1.2 inch Total Length : 1.2 inch 1st Mode’s Natural Freq. : 5889.2 Hz 1st Mode’s Natural Freq. : 5171.1 Hz Est. Shaking Amp : 0.58 micron (0-pk) Est. Shaking Amp: 0.76 micron (0-pk) Expec. Structural Damping : 3.255% Expec. Structural Damping : 3.255% Max. Bending Stress : 60.78 MPa Max. Bending Stress : 76.7 MPa Max. Disp. : 27.43 micron (0-pk) Max. Disp. : 34.1 micron (0-pk)
Stress Displacement Stress Displacement
Total Length : 1.35 inch Total Length : 1.2 inch 1st Mode’s Natural Freq. : 3859.8 Hz 1st Mode’s Natural Freq. : 3026.1 Hz Est. Shaking Amp. : 1.36 micron (0-pk) Est. Shaking Amp. : 2.21 micron (0-pk) Expec. Structural Damping : 3.255% Expec. Structural Damping : 3.255% Max. Bending Stress : 107.6 MPa Max. Bending Stress : 292.2 MPa Max. Disp. : 63.29 micron (0-pk) Max. Disp. : 99.34 micron (0-pk)
24
Table 3.2 Specimen with hourglass shape at high stress region (cont’d..)
Stress Displacement Stress Displacement
Total Length : 1.2 inch Total Length : 1.2 inch 1st Mode’s Natural Freq. : 3910.2 Hz 1st Mode’s Natural Freq. : 3571.5 Hz Est. Shaking Amp : 1.33 micron (0-pk) Est. Shaking Amp: 1.59 micron (0-pk) Expec. Structural Damping : 3.255% Expec. Structural Damping : 3.255% Max. Bending Stress : 164.7 MPa Max. Bending Stress : 194.1 MPa Max. Disp. : 58.53 micron (0-pk) Max. Disp. : 69.39 micron (0-pk)
Stress Displacement Stress Displacement
Total Length : 1.5 inch Total Length : 2.0 inch 1st Mode’s Natural Freq. : 2622.6 Hz 1st Mode’s Natural Freq. : 733.36 Hz Est. Shaking Amp.: 2.95 micron (0-pk) Est. Shak. Amp: 37.70 micron (0-pk) Expec. Structural Damping : 3.255% Expec. Structural Damping : 3.255% Max. Bending Stress : 184.1 MPa Max. Bending Stress : 1479 MPa Max. Disp. : 0.1362 mm (0-pk) Max. Disp. : 1.753 mm (0-pk)
25
Table 3.2 Specimen with hourglass shape at high stress region
(Compression Face) (Tension Face)
Total Length : 2.71 inch Expec. Structural Damping : 1.53% 2nd Mode’s Natural Freq. : 3106.8 Hz Max. Bending Stress : 28.84 MPa Est. Shaking Amp. : 2.10 micron (0-pk) Max. Disp. : 16.6 micron (0-pk)
(Compression Face) (Tension Face)
Total Length : 2.71 inch Expec. Structural Damping : 1.53% 2nd Mode’s Natural Freq. : 3115.5 Hz Max. Bending Stress : 34.15 MPa Est. Shaking Amp. : 2.09 micron (0-pk) Max. Disp. : 17.69 micron (0-pk)
(Compression Face) (Tension Face)
Total Length : 2.71 inch Expec. Structural Damping : 1.53% 2nd Mode’s Natural Freq. : 3122.9 Hz Max. Bending Stress : 77.61 MPa Est. Shaking Amp. : 2.08 micron (0-pk) Max. Disp. : 17.99 micron (0-pk)
26
Finally, an optimized specimen geometry was obtained; the highest stress occurs at the end of curvature with slight stress concentration.
Max stress location
(DIMS ARE IN INCHES)
Figure 3.6 Final Specimen Geometry for HCF testing Scatter is an inherent characteristic of mechanical properties of structures and materials and this also applies to fatigue properties. The fatigue lives of similar specimens or structures under the same loading can be significantly different. Hence, a fixture block was designed to accommodate ten specimens with facility of testing multiple specimens simultaneously. Simultaneous testing of ten specimens also reduces the total amount of testing time to obtain fatigue data. The design constraint was to keep the fixture weight low, as more weight demands more shaker power to excite the specimens. 27
(DIMS ARE IN INCHES)
Figure 3.7 Upper Block of Fixture
(DIMS ARE IN INCHES)
Figure 3.8 Lower Block of Fixture 28
(DIMS ARE IN INCHES)
Figure 3.9 Specimen with Fixture
3.3 System Configuration and Integration
A closed-loop HCF testing system was developed by connecting two sub- systems, the PSV Scanning Laser Vibrometer and the Data Physics Shaker Controller. 29
In this method, it was required to test multiple specimens in a single run, monitor health of all specimens, and track resonances of the specimens while keeping the stress level
(i.e., displacement level) constant. If substantial change of the resonant frequency of any specimen is detected during the HCF test, it is also required to stop running the test and save the test data. For these specific test requirements, synchronized coordination between the two systems was accomplished by developing a HCF Test Coordinator explained earlier in this study. Figure 3.10 depicts a schematic configuration of the closed-loop HCF testing algorithm in which the two systems are connected and coordinated. As shown in the Figure 3.10, one of the important features of the HCF test coordinator is a coordinated synchronization between the two systems with flexible testing time tracked for each specimen. Particularly, this feature allows controlling the speed of scanning over multiple specimens. Operators have the discretion to preset the dwell test duration assigned to each specimen to assure that any abrupt fatigue failure is captured.
3.4 Procedure for Closed-loop HCF Testing
Descriptive procedure for the developed test methodology is as follows –
Step 1
At the very beginning of a test, a high TTL signal is sent from HCF Test
Coordinator to the DP system to start the shaker and measurements.
Step 2
Pretest is performed first. Pretest should be conducted prior to running any test 30 with DP shaker system. Its purpose is to check S/N (Signal-to-Noise) ratio, closed-loop between control channel (Laser vibrometer) and reference channel (Accelerometer) by checking transfer function.
Step 3
After passing the pretest, sweep sine test is performed to catch the natural frequency and the corresponding phase angle.
Step 4
After the completion of sweep sine, resonance dwell test is executed using the
FRF from sweep sine test. In DP system, resonance dwell test runs for 60 seconds (this can be flexibly set by the user), during this period the maximum stress level in specimen is kept constant by keeping the tip displacement level unchanged. The effective dwell time is taken as 45 seconds. The remaining 15 seconds is used for ramping up the tip displacement to the predefined level. For smooth restarting, the resonance dwell test should end before the PSV system ends scanning the first specimen. This can be accomplished by adjusting the number of averaging to obtain
FRF in PSV system. The shaker is stopped automatically at the end of dwell.
Step 5
HCF Test Coordinator stores max magnitude of FRF and its corresponding frequency (which is close to the excitation frequency determined by the DP system) and counts the accumulated number of cycles. Test data for each specimen are saved in
31 files on an external hard disk. Time and frequency domain data are also stored in DP system.
Step 6
At the end of scanning the first specimen, the laser beam moves to next specimen and the HCF Test Coordinator sends a high TTL signal to the DP system to start the shaker. After scanning all the specimens (i.e., at the end of first pass), second pass starts automatically. In second pass, after measuring the vibration of each specimen, the PSV Test Coordinator computes the frequency drop in the second pass compared to the first pass. If the frequency drop is within the preset limit (e.g., one Hz), the HCF Test Coordinator sends a start TTL signal to the DP system to start scanning the next specimen. Step 2 to Step 5 is repeated in a loop until the preset frequency drop is exceeded.
Step 7
When HCF Test Coordinator finds the frequency drop exceeding the predefined limit, it sends a low TTL to the DP system to finally stop the shaker.
32
VELO Signals: Ordinary Sensing Control Channel PSV Controller Measurement Channel Acceleration Acceleration ABACUS Chassis Digital Output Output Channel
TCP/IP High: Start PSV Macro HCF Test USB Coordinator Relay Box SignalStar Vector® Visual Basic Engine ® (ADU 208) Low: End
Acquisition On
Start Scan i=1 to NPASS
High: Start Pre‐test: Noise Level; a Send Digital High TTL Transmissibility Function; Close‐Loop Check
b Scanning In FFT‐mode Sweep Sine Test: FRF points
c Save Data Start Resonance Dwell scanning d Frequency drop exceeds Resonance Dwell for 45 sec*
the Checks for Frequency the predefined limit all
Save Data within measuring
is
limit Send Digital Low TTL after
change Pass
Low: End Next predefined
the Stop Shaker and
Frequency Terminate Test
Move to next scanning Point and repeat a thru d Save Data
Figure 3.10 Closed-Loop Test Configuration; PSV Macro Coordination of the HCF Testing; Resonance Search and Dwell Control Algorithm in SignalStar Vector.
*Note: This time can be set by operator.
33
CHAPTER IV
SHAKER EVALUATION AND VALIDATION TEST
4.1 Outline
System damping and amplitudes of DP V100 shaker armature are important parameters that determine stress levels in the specimen. AISI 1095 steel specimens of different lengths were used to evaluate the shaker performance, the damping values and maximally attainable stress level in the specimen.
Using the frequency abort option in DP Vector software a validation test was conducted in order to verify that the test can be aborted based on frequency drop when the fatigue failure is detected.
4.2 Shaker Evaluation
One of the major goals in shaker evaluation was to check if it has sufficient power to reach the targeted stress levels in the specimen to achieve fatigue failure in the requisite time frame. The approximate weight of ten specimens and fixture was 0.85 lb.
Before the specimens and fixtures were made, a circular disc dummy mass with comparable weight was manufactured, and armature amplitudes were evaluated by doing test with the equivalent mass. The shaker was operated at different frequencies and the armature displacement amplitudes (½ of the peak-to-peak displacement) were measured using the Polytec laser vibrometer. 34
Figure 4.1 Dummy mass attached to Figure 4.2 Specimen and fixture for shaker armature shaker evaluation
To estimate the maximum attainable shaker armature amplitude for a target excitation frequency, an analytical equation was derived for the armature displacement amplitude based on energy conservation between electrical and mechanical kinetic energy. The small losses due to friction generated heat, inherent damping in the mechanical system, etc. were neglected.
Marm 0.80× A0-pk × Marm + Msp+ fix (Eq. 4.1) Dmax = 0− pk 4×π 2 × f 2
max where D0− pk is maximally attainable shaker armature amplitude; A 0-pk is maximum shaker acceleration; M arm is armature mass; M sp+ fix is mass of specimen and fixtures and f is excitation frequency.
As indicated in equation 4.1, the shaker armature displacement amplitude is dependent on mass of the armature, specimen and fixture, and operating frequency.
Armature amplitudes from the test were compared with values from the analytical equation in a range of 200 Hz to 2100 Hz as shown in Figure 4.3. It was observed that test results were in close agreement with the analytical estimation in this frequency
35 range. The estimated shaking amplitudes were used in subsequent analytical model and
3D finite element (FE) analyses to determine specimen geometry.
Figure 4.3 Performance of shaker with different operating frequency
However, as the operating frequency approaches 6,850 Hz for the V100 shaker, it was observed that the displacement amplitude rapidly increases, diverging from analytical predictions. This is expected since the analytical estimation does not take into account the dynamics of the shaker armature, which the manufacturer states has a first resonance at 6,850 Hz.
Utilization of the shaker resonance phenomenon was considered for the purpose of gaining higher specimen displacement amplitudes for the test specimens, but large displacement amplitudes at the shaker resonance frequency were inherently erratic.
Thus, it is not recommended to operate the shaker at its own resonant frequency.
36
Figure 4.4 Unstable shaker armature movements at an excitation close to shaker resonant frequency (Velocity – Time Plot @ 6455 Hz)
4.3 Stress Evaluation
At first, a series of simple tension tests were conducted to estimate the yield stress level of the test materials. From the stress-strain curves shown in Figure 4.6 yielding stresses of 350 MPa to 450 MPa were experimentally measured for the same batch of material. To ensure that the stress level is high enough to induce fatigue cracking in specimens under the given shaker power, specimens with lengths ranging from 1.675 to 5.475 inch were manufactured. Figure 4.7 shows five specimens out of eight tested specimen lengths. For different specimen lengths maximum strains, tip displacements and shaker armature displacement amplitudes were measured under shaking operation with maximum power.
37
Figure 4.5 Simple tension test of specimen materials
Figure 4.6 Stress-Strain Plot of test results
Figure 4.7 Five Specimens tested for stress evaluation
38
Vishay strain gages (WK-06-062AP-350), the scanning laser vibrometer, and
Dytran accelerometer (3030B) were used to measure strains, tip displacements and armature displacements (by double integrating the accelerations data obtained from accelerometer), respectively. In this test, the manufactured 10-specimen fixture with 10 specimens was installed on the armature.
Figure 4.8 Stress contour from 3D FE analysis
The strain gages were installed at the location of maximum stress predicted by the 3D FE analysis. This location was justified from crack locations of failed specimens. Before running a test, first bending mode natural frequencies of the
Figure 4.9 Location of Fatigue Crack 39 specimens were identified from sweep sine test using the DP Vector software. As shown in Figure 4.10, natural frequency of the first bending mode increases as the length of specimen decreases.
Figure 4.10 Natural frequency and specimen length relationship
Natural frequencies of the first bending mode ranged from 1100 Hz to 82 Hz.
The specimen length in Figure 4.10 is measured from clamped edge to free end excluding the gripped zone. After identifying the natural frequencies, the DP shaker system was operated to its maximum power level with excitation frequency tuned to the identified natural frequencies. Shaker driving voltage signals were generated from an external function generator (Agilent Function Generator 33250A). In the test, the two longest specimens (4.475 inch and 4.075 inch) failed within less than one minute since the stress levels were very high (749 MPa and 646 MPa, respectively). Thus, the tip displacement and armature displacement amplitude data could not be measured.
40
As shown in Figure 4.11, the measured tip displacement amplitude gradually decreases as the natural frequency increases.
Figure 4.11 Specimen tip displacement vs natural frequency
Figure 4.13 shows correlations between natural frequencies and stress levels. It can be noted that stresses (749 MPa and 646 MPa corresponding to failed specimens) at the lower frequencies are overestimated since the assumption of linear elastic behavior was not valid due to observed plastic deformation.
4.4 Evaluation of Damping
Damping has significant effects on the stress level. From the experimental results damping was found to be dependent on tip displacement amplitudes of the test specimen.
41
Figure 4.12 Specimen max bending strain vs natural frequency
Figure 4.13 Specimen max bending stress vs natural frequency
It was observed that damping gradually increases as the specimen tip amplitude increases. The source of damping could be a mixture of clamped edge, inherent material damping, hysteretic damping in case of plastic deformations, air damping, etc.
42
In 3D FE analyses, damping was modeled as structural damping; analyses were performed with varying values of damping so that the resulting maximum stresses match the stresses obtained experimentally. In this way, damping was estimated for the various stress levels, these results are preliminary because high experimental strain values indicated that yielding of at least some of the specimens occurred.
Figure 4.14 Variation of damping with natural frequency
Figure 4.14 indicates the structural damping values used in 3D FE analyses to match the FEA stresses with the experimental results. As expected, the damping significantly increases as the natural frequency decreases. This could be due to air damping due to large tip amplitudes, to a lesser extent from hysteretic damping due to material yielding, or some other effects.
4.5 Relationship between Specimen Tip Disp. And Shaking Amp
Tests were performed by varying the specimen tip displacement level, and the
43 corresponding shaker armature amplitudes were recorded. Based on the experimental results, a linear regression equation for the test specimen geometry was approximated as
Shaking Amplitude = Tip Displacement ൈ 0.0097 – 6ൈ10-5 (Eq. 4.2)
Figure 4.15 Shaking amplitude vs specimen tip displacement
4.6 Validation Test
Based on frequency drop, a validation test was conducted using the resonance dwell option in DP Vector software to abort the operating shaker when fatigue failure is detected. In the DP Vector software, the abort frequency upper and lower bounds were set to within ±10% of resonance frequency. It is noted that this frequency abort option in DP was turned off during the fatigue test by HCF Test Coordinator, instead, the abort criteria was set in the macro code.
44
Figure 4.16 Natural frequencies and phase angles of ten 4.2 inch specimens
The stress analysis indicates that the 4.2 inch long specimens can generate up to
550 MPa stress with a 5.2 mm (0-pk) tip amplitude under maximum shaker power operation. The specimen has the first bending mode natural frequency of nearly 190 Hz.
The first bending mode natural frequencies and phase angles for the ten specimens are shown in Figure 4.16. It is noted that the 4.2 inch length is from end to end, with a
3.675 inch length from the to the tip.
45
Indication of fatigue crack existence
Figure 4.17 Amplitude of velocity measured by laser vibrometer
Frequency drop due to fatigue crack
Figure 4.18 Frequency change due to fatigue crack
As planned, single specimen validation test was conducted using the DP Vector controller, but the 550 MPa stress level corresponding to 5.2 mm amplitude was beyond the yield point of the material and quickly failed. To achieve longer fatigue life, the controlled tip displacement amplitude was set to less than 5.0 mm. Figure 4.17 and
Figure 4.18 show the changes in the velocity amplitude and the excitation frequency, measured by the laser vibrometer, during resonance dwell fatigue testing.
Velocity amplitudes began displaying high signal-noise after 100 seconds, which indicated the formation of fatigue cracks in the specimen. The frequency dropped at a higher rate after 140 seconds. This result is consistent with the
46 observation of velocity amplitude drops as shown in Figure 4.17. On the contrary, tracking of phase angle proved to be less discriminatory, as shown in Figure 4.19. The resonance dwell test tracked the phase angle (173 degree) assigned prior to the testing, but changed a little, even during the crack initiation and growth, this is because phase tracking mehod was used in DP resonance dwell algorithm. After automatic termination of the test, the fatigue crack could be visually inspected as shown in Figure 4.20.
Figure 4.19 Tracking of phase angle during Figure 4.20 Fatigue crack in specimen fatigue testing
47
CHAPTER V
THEORITICAL APPROACH
5.1 General
As a part of design process of the specimen, an analytical model is developed to obtain the natural frequencies and determine the location of monitoring point. In addition, the highest stress and its location are ensured by 3D finite element analyses.
5.2 Analytical/Numerical Model
Steady-state response analysis of the test specimen was conducted as a part of design steps. An equation of motion was obtained by using the extended Hamilton's principle with Lagrange equation. The spatial deflection was approximated by the Ritz method. Figure 5.1 illustrates the specimen geometry with boundary condition and response variables. The physical coordinate (X) starts from the left end, that is, the clamped edge.
Figure 5.1 Relative displacement of vibrating specimen 48
To have non-dimensional parameters, the parameters have been normalized as follows
ξ U (t) W (ξ,t) U (X ,t) X = , u (t) = G , w(ξ,t) = , u (ξ,t) = T L G L L T L where X is the physical coordinate; ξ is the variable in isoparametric coordinate; L is the length of the beam and t is the time. Then the strain energy (S) and kinetic energy
(T) are computed as follows
2 2 L 1 ⎛ ∂ 2W (X ,t) ⎞ E 1 ⎛ ∂ 2 w(ξ,t) ⎞ Strain energy (S) = EI(X )⎜ ⎟ dX = I(ξ)⎜ ⎟ dξ (Eq. 5.1) ∫ 2 ⎜ ∂X 2 ⎟ 2L ∫ ⎜ ∂ξ 2 ⎟ 0 ⎝ ⎠ 0 ⎝ ⎠
2 2 L 3 1 1 ⎛ ∂U T (X ,t) ⎞ L ⎛ ∂u T (ξ,t) ⎞ Kinetic energy (T) = m(X )⎜ ⎟ dX = m(ξ )⎜ ⎟ dξ ∫ 2 ⎜ ∂t ⎟ 2 ∫ ⎜ ∂t ⎟ 0 ⎝ ⎠ 0 ⎝ ⎠ 2 3 1 L ⎛ ∂[w(ξ,t) + u G (t)]⎞ = m(ξ )⎜ ⎟ dξ (Eq. 5.2) 2 ∫ ⎜ ∂t ⎟ 0 ⎝ ⎠ where I is the moment of inertia; E is Young’s modulus; and m is mass per unit length.
iΩt Under harmonic base excitation, uG (t) = uGe , where Ω is excitation frequency in rad/sec, the transverse displacement field can be approximated as
P w(ξ,t) = a (t)ξ n , where a (t) = a eiΩt and a is the complex variable that ∑n=0 n n n n holds information about phase angles. P is the max order of polynomial functions.
Applying Lagrange’s equation as follows, the equation of motion is obtained (Eq. 5.3).
d ⎛ ∂T ⎞ ∂T ∂S ⎜ ⎟ − + = 0 , where k = 0, 1, 2,...., N dt ⎝ ∂a&k ⎠ ∂ak ∂ak
1 1 1 ⎡ 3 2 T ⎤ ⎡ E T ⎤ ⎡ E T ⎤ ⎢− L Ω m(ξ )N Ndξ ⎥{}an + ⎢iγ I(ξ )Nξξ Nξξ dξ ⎥{}an + ⎢ I(ξ )Nξξ Nξξ dξ ⎥{}an ∫ L ∫ L ∫ ⎣ 0 ⎦ ⎣ 0 ⎦ ⎣ 0 ⎦ 1 = L3Ω2u m(ξ)N T dξ (Eq. 5.3) G ∫ 0 49
where is the structural damping factor. Approximating the displacement field by 11th
degree polynomial and enforcing boundary conditions ( w(0,t) = 0 annd w'(0,t) = 0),
the shape function becomes
N = [ξ11 ξ 10 ξ 9 ξ 8 ξ 7 ξ 6 ξ 5 ξ 4 ξ 3 ξ 2] where 0 ≤ ξ ≤ 1.0
Neglecting damping, and for free vibration analysis when the base motion is zero,
⎡ 1 ⎤ ⎡E 1 ⎤ − L3Ω2 m(ξ)N T Ndξ a + I(ξ)N T N dξ a = 0 ⎢ ∫ ⎥{}n ⎢ ∫ ξξ ξξ ⎥{ n } (Eq. 5.4) ⎣ 0 ⎦ ⎣ L 0 ⎦
The natural frequencies and operational deflection shapes extracted from Eq. 5.3~5.4
were in close agreement with the finite element analysis (FEA) results.
Table 5.1 Comparison of natural frequencies from Analytical and FE model Natural Frequency, Hz Mode of Analytical/Numerical FE Model Vibration Difference in % (using MATLAB®) (using ABAQUS®) 1st 757.89 746.63 1.49
2nd 4610.4 4497.1 2.46
3rd 12557 12132 3.38
4th 23909 22862 4.38
5th 38497 36325 5.64
Figure 5.2 Comparison of natural frequencies 50
Operational Deflection Shapes by plotting imaginary part of transverse displacement:
Figure 5.3 Operational deflection shape at 1st natural frequency
Figure 5.4 Operational deflection shape at 2nd natural frequency
Figure 5.5 Operational deflection shape at 3rd natural frequency 51
Figure 5.6 Operational deflection shape at 4th natural frequency
Figure 5.7 Operational deflection shape at 5th natural frequency
By performing frequency sweep, the complex coefficients an were obtained.
Steady-state spectral responses for specimen tip displacement, velocity and acceleration
P P were acquired using the relations w(ξ,t) = a eiΩtξ n , w(ξ,t) = iΩa eiΩtξ n ∑n=0 n & ∑n=0 n
P and w(ξ,t) = − Ω2a eiΩtξ n , respectively (shown in Figure 5.8). && ∑n=0 n
52
(a)
(b)
(c) Figure 5.8 Steady-state spectral responses for (a) displacement, (b) velocity and (c) acceleration measured at the tip of vibrating specimen.
Both in FEA and analytical simulation, specimen base excitation amplitude was 21.28 micron (0-pk) that resulted tip displacement of 2.2 mm (0-pk). Structural damping factor 0.016 was determined by trial and error to match the stress obtained
53 from FEA with the experiments. Based on the simulation results, the natural frequencies and the monitoring point could be obtained by changing the length of the specimen. For identifying detail location of the highest stress, FEA were conducted for finalizing the geometrical design.
5.3 Finite Element (FE) Model
FE simulation was performed to obtain a specimen sizing that optimizes the attainable stress level, which is limited by availability of shaker power, and natural frequency of test specimen, on which the duration of test depends. In addition, the highest stress and its location are ensured from FE stress contour.
5.3.1 Modal Analysis
Modal analysis was performed to extract natural frequency and corresponding mode shape of specimen.
In ABAQUS® the test specimen was modeled as C3D20: A 20-node quadratic brick element. The material property for Al 6061-T6 is -
Mass Density 2,700 kg/m3
Young’s Modulus 68.9 GPa
Poisson’s Ratio 0.33
Yield Strength 276 MPa
Analyses were performed for different specimen lengths; finally, a specimen of
2.5165 inch length was selected, which had the first mode’s natural frequency of 746.63
Hz. 54
Table 5.2 Modal analysis output from ABAQUS®
Bending Mode Mode Shape Natural Frequency, Hz
1 746.63
2 4,497.1
3 12,132
4 22,862
5 36,325
55
(DIMS ARE IN INCHES)
Figure 5.9 Test Specimen
Considering the limitation of shaker power to produce high armature amplitudes at high frequencies, it was decided to excite the specimen at its first mode’s natural frequency as higher modes having higher natural frequencies for which the DP shaker could not generate armature amplitudes high enough to achieve the required stress to induce fatigue failure in specimen within affordable time limit.
5.3.2 Direct-solution Steady-state Dynamic Analysis
To estimate the attainable stress level in specimen direct-solution steady-state dynamic analysis was performed, which was done as a frequency sweep by applying
56 the loading at a series of different frequencies and recording the response.
The test conditions were -
Bare Table Maximum Acceleration for GW-V100/DSA1-1k shaker 125 g
Armature Mass for GW-V100/DSA1-1k shaker 1.7 lb
Estimated Mass of Specimen and Fixture 0.76 lb
Excitation Frequency 746.63 Hz
௫ Shaker Armature Amplitude (ܦି) was computed using Eq. 4.1,
M 0.80× A × arm 0-pk M + M Dmax = arm sp+ fix 0− pk 4×π 2 × f 2
ൌ 0.037 mm
Based on Eq. 4.2, Shaking Amplitude = Tip Displacement ൈ 0.0097 - 6ൈ10-5, the maximum attainable specimen tip displacement = 3.82 mm (o-pk)
To have an estimation of damping, an experimental test was performed to measure the stress in specimen. The value of structural damping was retuned in FE analysis so that the resulting maximum stress match the stress obtained experimentally.
Structural damping of 1.6% was used to estimate the stress levels for all the different tip displacements. This estimation was crude since the changes of damping value with change in specimen tip displacements, thus with change in stress levels, were neglected.
57
Table 5.3 ABAQUS® output for specimen tip displacement 1.8 mm (0-pk)
mm
1.8
58
Table 5.4 ABAQUS® output for specimen tip displacement 1.9 mm (0-pk)
mm
1.9
59
Table 5.5 ABAQUS® output for specimen tip displacement 2.0 mm (0-pk)
mm
2.0
60
Table 5.6 ABAQUS® output for specimen tip displacement 2.1 mm (0-pk)
mm
2.1
61
Table 5.7 ABAQUS® output for specimen tip displacement 2.2 mm (0-pk)
mm
2.2
62
CHAPTER VI
EXPERIMENTAL TESTING AND RESULTS
6.1 General
Performance of the fatigue testing system is demonstrated by conducting high- cycle fatigue test of Al 6061-T6 aluminum alloy. Stress-displacement calibration test was performed first for the stress-displacement relation, which was followed by experimental fatigue testing with different stress levels.
Figure 6.1 Al6061-T6 specimens and fixtures
6.2 Stress-Displacement Calibration Test
A calibration test was conducted to obtain the corresponding stress values for the known displacement amplitudes. The calibrated stresses were used to establish an S-
N curve from the fatigue test results.
63
6.2.1 Test Set-up
Vishay strain gages (WK-06-062AP-350) were used to measure strain values in specimens under the first natural mode of vibration. The strain gage was installed as a quarter bridge I on a single side of the specimen to measure dynamic bending stresses as shown in Figure 6.2.
Figure 6.2 Strain Gage on Specimen
Strain gage leads were connected to four hair-like copper wires (two of them are for backup) to minimize any mechanical effects on the specimen vibration andthey were soldered on an adapter to connect to thin wires insulated with an enameled coating. At a distance far from the specimen, shielded sensor cables were connected to
NI-DAQ system.
NI SignalExpress S/W was used for data processing and analysis. The NI S/W automatically performed null offsetting (to remove any DC offset) and shunt calibration. NI-1520 (Signal Conditioning Unit for Bridge type sensor) and NI-1314
(terminal block for strain gages) in NI SCXI-1001 module were connected to NI PXI-
6259 (M Series DAQ board). 64
Figure 6.3 NI LabVIEW® settings for strain measurement
Figure 6.4 NI LabVIEW® settings for strain gage 65
6.2.2 Measured Data
As nearby the natural frequency much less power is needed to achieve the predetermined displacement level, a sweep sine test was performed first to determine the natural frequency of the specimen. With SignalStar Vector S/W, a reference value was entered by setting displacement as a control variable to keep the tip displacement level, and thus the stress level, constant during the dwell test. To run the resonant dwell test, the FRF was obtained by running the sweep sine test earlier.
While running the resonant dwell test in SignalStar Vector, the strain value was captured from NI SignalExpress.
The stress levels with which the specimens were excited were well below the yield point. Thus the stress amplitude was estimated by multiplying the strain value by the Young’s modulus.
Figure 6.5 NI LabVIEW® strain measurement 66
Figure 6.6 NI LabVIEW® strain measurement (close view)
To obtain the stress-displacement calibration curve, tests were performed for the tip displacement levels ranging from 0.5 mm (0-pk) to 2.5 mm (0-pk). Each time the specimen was kept dwelling at a different tip displacement level with DP SignalStar
Vector, and the corresponding strain value was recorded in NI SignalExpress. As the stress levels with which the specimens were excited was well below the yield point, the stress amplitude was estimated by multiplying the strain value by the Young’s modulus.
Thus, the maximum stress in MPa vs. tip displacement (0-pk) in mm relationship was obtained as shown in Figure 6.8.
67
Figure 6.7 Strain-Displacement Relationship
Figure 6.8 Stress-Displacement Relationship
68
6.3 Fatigue Testing
Tests were conducted at different stress levels and the corresponding numbers of cycles before fatigue failure were counted by the HCF Test Coordinator.
Finally, an S-N curve was obtained based on the experimental results.
6.3.1 Test Set-up
Experimental set-up includes data acquisition settings in PSV, DP shaker controller set-up and settings for HCF Test Coordinator.
6.3.1.1 Data Acquisition Settings in PSV
Figure 6.9 PSV System
69
General
Figure 6.10 General acquisition settings in PSV
Measurement Mode - FFT: for frequency domain measurement.
Averaging Type - Peak Hold: Averaging improves the signal-to-noise ratio of spectrum, furthermore, in the case of averaging, a brief drop out of the vibrometer signal in a single spectrum only affects the frequencies around the current sweep frequency, but not the whole frequency range. In the frequency domain averaging, a sequence of time traces is collected. Each time trace has the same number of samples. From each time trace a spectrum is caluculated by the means of an FFT. All spectra have the same number of FFT lines. The averaged spectrum is obtained by averaging all values at each frequency. Peak Hold averaging calculates and displays the respective maximum of the spectra over the set number of spectra.
Number of Spectra - 42: For smooth restarting of the measurement, Sample Time
Number of Spectra in PSV should be greater than the time required for Pre-test + Sine
Sweep + Resonance Dwell in DP.
Remeasure: The scan points with the status Overrange, Invalidated and Not Measured are remeasured at a slightly different position. 70
Channels
Figure 6.11 Channels acquisition settings in PSV
Quantity - Vibrometer - Velocity
Reference - Acceleration
Range - Vibrometer - 10 V: Input range of the data acquisition board for
Vibrometer Channel
Reference - 10V: Input range of the data acquisition board for Reference
Channel
Impedance - Vibrometer - 1 MOhm: Input resistance of the board for Vibrometer
Channel
Reference - 1 MOhm: Input resistance of the board for Reference Channel
Factor - Vibrometer - 1000 mm/s/V: Calibration factor, i.e., the measurement
value which corresponds to an analog input
signal of one volt (measurement range set on
Vibrometer)
Reference – 971.82 m/s2/V: Calibration factor from Accelerometer data
71
Filters
Figure 6.12 Settings for filters in PSV
Under certain circumstances, the signal to be evaluated can be covered by other signals from surroundings. Digital filters are used to suppress these undesired signal portions. High Pass filter with cutoff frequency of 550 Hz (the frequency of interest was around 700 Hz, which was the first natural frequency of the test specimen) was used to allow higher frequencies to pass, and to attenuate lower frequencies.
Figure 6.13 Settings for cutoff frequencies in PSV
72
Frequency
Figure 6.14 Frequency settings in PSV
Parameters for calculating the frequency spectra are set here.
Bandwidth: 2 kHz for the test condition.
From and To: 0 kHz ~1 kHz frequency range was displayed and evaluated.
FFT Lines: The number of FFT lines to be analyzed was set 6400
Sample Frequency = Bandwidth 2.56
= 2 kHz 2.56
= 5.12 kHz
Sample Frequency Nyquiest Frequency 2
. H =
2.56 kHz ~700 Hz, so there should be no aliasing problem
for the frequency range of interest.
Number of FFT Lines Sample Time Bandwidth
= sec 73
3.2 sec
1 Resolution Sample Time
Hz .
0.3125 Hz
Window
Figure 6.15 Window settings in PSV
To minimize the leakage effect Hamming window, which is a combination of Hanning and Rectangular window, was used.
Signal Enhancement
To get an approximately even noise level for all scan points Signal
Enhancement and Speckle Tracking were used during scanning. Without Speckle
Tracking, every scan point is measured at the same position when averaging, so it is possible to always measure a dark speckle. With Speckle Tracking, the position of
74 every scan point is slightly changed on averaging, thus it is quite likely to measure some bright speckles.
Figure 6.16 Signal Enhancement settings in PSV
Vibrometer
The parameters of the controller for data acquisition are set here. Calibration factor for velocity measurement was set 1000 mm/s/V. The respective maximum frequency for the selected measurement range is 1.5 MHz.
Figure 6.17 Vibrometer settings in PSV
75
6.3.1.2 DP Shaker Controller Settings
Test Identification Parameters and Units
Figure 6.18 DP System
Figure 6.19 Test identification parameters in DP Shaker Controller
Run Increment: The Run Increment parameter controls how the run number is incremented and therefore defines the run number at the time the test is started. "Next"
76 increments the run numbers automatically. This increments the run number by one, creates a new Run folder and saves new run data in the new Run folder.
Units: Units are selected to be used for the Displacements, the Velocities and the
Accelerations throughout the dialog boxes and displays. In our test, ‘mm’ for displacement, ‘mm/s’ for velocity and ‘g’ for acceleration were used.
Drive and Shaker Parameters:
Figure 6.20 Drive and shaker parameters in DP Shaker Controller
Max Volts: Max Drive Volts sets the maximum peak voltage allowed from the DAC during a test. It optimizes dynamic range while including a slight buffer for actual drive
Volts during the test. Entering a value far greater than required by the test may cause a loss of dynamic range and affect control. Entering too low a value may cause clipping
77 of the output signal. This parameter also protects the power amplifier by setting the
DAC to match the Amplifier input limit. 2V was found adequate for our testing.
Shaker Maximum Ratings:
Figure 6.21 DP Shaker parameters
Parameters for DP V100 shaker were provided to compare the shaker limits to the calculated test parameters when the test was started.
Channel Parameters:
Transducer Sensitivity (mV/EU): The sensitivity is used to set the gain and maximize the dynamic range of the input channel. Increasing the mV/EU increases the sensitivity of the transducer. The sensitivity parameters in DP for vibrometer and accelerometer should match the acquisition settigns in PSV. In PSV the calibration factor for vibrometer was set 1000 mm/s/V, which matches the DP settings 1 mV/mm/s.
. / Similarly, 10.1 mV/g = V/m/s2 971.28 m/s2/V, which matches the . calibration factor set in PSV for accelerometer.
78
Figure 6.22 Control and limit parameters in DP Shaker Controller
Range: The full-scale input range for velocity signal is 10,000 mm/s, which yields the limit (1 mV/mm/s 10,000 mm/s =) 10 V. Similarly, for acceleration signal, the input range is 99.01 g, which limits the voltage as (10.1mV/g 99.01 g =) 1 V.
79
Figure 6.23 Control and limit channel information in DP Shaker Controller
Figure 6.24 Control range configuration in DP Shaker Controller 80
Figure 6.25 Control parameters in DP Shaker Controller
Control Parameters:
Startup Time: It is the time during which the system initially increases from zero Volts to the full first Run Schedule level as defined as Resonance Search and Dwell. It determines how fast the system ramps up to a new level.
Startup Level: This is the level of the drive from which the test ramp up is started. The test sweep will start whenever the reference level is reached or an active limiting channel is reached during ramp up.
Magnitude Sensitivity: Magnitude Sensitivity defines how quickly the Drive adjusts to changes in the Control signal. This parameter sets the compression rate for the amplitude control loop and determines the amount of damping applied by the digital sine control process to insure control loop stability. A low Magnitude Sensitivity value
81 provides little damping and adjusts rapidly to changes in the Control signal. A higher
Magnitude Sensitivity rate increases the damping which causes a more gradual correction to the Drive Signal. Different values for magnitude sensitivity were used while testing with various tip displacement amplitude.
Table 6.1 Magnitude sensitivity set-up for shaking with different tip disp. amplitude
Tip Displacement Amplitude, 0-pk Magnitude Sensitivity
1.8 mm 30
1.9 mm 30
2.0 mm 25
2.1 mm 25
2.2 mm 25
Reference Displacement:
The displacement amplitude set in profile editor is in pk-pk, which is shown in the reference panel as 0-pk.
82
Figure 6.26 Reference displacement settings in DP Shaker Controller
Figure 6.27 Reference displacement input in DP Shaker Controller
83
Limit Parameter:
Figure 6.28 Acceleration limit settings in DP Shaker Controller
Figure 6.29 Acceleration limit input in DP Shaker Controller 84
The reference channel (the channel that receives acceleration signal) is set up as Limit channel to settle a maximum allowable level to protect the shaker from excessive vibration. Using the Limits Table, user can define limits that affect the channel. If the vibration level reaches the specified limit, an alarm or an abort condition is detected.
Different limits for peak acceleration were used while testing with various tip displacement amplitude.
Table 6.2 Acceleration limit set-up for shaking with different tip disp. amplitude
Tip Displacement Amplitude, 0-pk Acceleration Limit, 0-pk
1.8 mm 11 g
1.9 mm 13 g
2.0 mm 15 g
2.1 mm 18 g
2.2 mm 19 g
85
Run Schedule:
Figure 6.30 Frequency range set-up for resonance search and dwell test
Sweep Frequency Limit: Start Freq defines the starting frequency of the sweep, whereas
End Freq defines the ending frequency of the sweep. To reduce the shaker power requirement, the frequency range should be set close to the resonant frequency of the test specimen.
86
Dwell setup:
Figure 6.31 Dwell parameter settings in DP Shaker Controller
Level: The tip displacement level that should be maintained throughout the dwell test duration is set in Dwell settings.
Duration: This parameter defines the amount of time during which the system dwells on the resonance during the Dwell test.
Frequency Abort: Frequency aborts was set OFF, the abort criteria was controled by
PSV system instead.
Amplitude Abort: Amplitude aborts was set OFF.
87
Figure 6.32 Frequency aborts set-up in DP Shaker Controller
Figure 6.33 Amplitude aborts set-up in DP Shaker Controller
88
Resonance Search and Dwell Control Parameters:
Figure 6.34 Resonance search and dwell control parameters
Frequency Sensitivity: This is a correction value ranging from 0 to 10 specifies how fast the frequency correction to be done during the dwell test, 0 means “no correction”,
1 is the fastest frequency correction and 10 is the slowest frequency correction.
Amplitude Sensitivity: This parameter determines the correction rate of the excitation level during the dwell test. It is a value from 0 to 10 where 0 means “no correction”, 1 is the fastest level correction and 10 is the slowest level correction.
Phase Shift: In our Phase Tracked Dwell test, this parameter fixes the maximum phase shift allowed between the nominal resonance Phase and the control phase measured during the dwell test.
89
Minimum Level: Minimum level under which a control channel generates an abort during the dwell test, this was arbitrarily set as a very low value of 0.0001 mm.
Figure 6.35 Saving dwell data in DP Shaker Controller
With this settings, data, both in time and frequency domain, were saved in separate directory after each run.
6.3.1.3 HCF Test Coordinator Settings
HCF Test Coordinator requires the following user input –
Directory: User needs to create a directory where files containg test data computed by
HCF Test Coordinator, which includes natural frequency, FRF magnitude, number of cycles completed before failure etc., are stored. Separate directory should be specified for each run while resuming from a earlier test.
90
Effective Dwell Time: Effective Dwell Time = Duration of Dwell – Startup Time (or time for ramp up to the dwell level) set in DP. This amount of time may need to be further adjusted based on the time history od displacement level during dwell test.
Parameters for Resuming a Test: To continue a previously stopped test, user need to enter the number of cycles completed before the test was stopped. To check the immediate frequency change, the latest natural frequencies for all the test specimens needs to be provided before resuming the test. These data are retrieved from previously specified directory as the HCF Test Coordinator automatically saves all the data prior to any unsolicitated stoppage of testing.
Fatigue Failure Criterion: User needs to specify the amount of frequency drop from the previous measurement as the controlling criterion to terminate the test.
6.3.2 Test Matrix Development
Based on FE simulation results and stress-displacement calibration test, the following test plan was made to obtain S-N curve for Al6061-T6.
Table 6.3 Test Matrix
Tip Displacement Amplitude, 0-pk (mm) Number of tests
2.2 4
2.1 5
2.0 3
1.9 3
1.8 3
91
6.3.3 High-cycle Fatigue Test
To obtain data points for S-N curve, tests were conducted at different stress level and the corresponding number of completed cycles before failure was counted by the test coordinator. To get statistically significant fatigue data eighteen tests were completed at five different stress levels, where at least three tests were conducted at each stress (listed in Table 6.3). This yields the percent replication,
L PR = 100 1 L is the number of stress levels
ns is sample size = 100 1
72%, which is satisfactory. [19]
In the HCF Test Coordinator a frequency drop of one~two Hz from the previous measurement was set as the controlling criterion to terminate the test. Smooth running of the closed-loop method was observed during the experiment. The HCF Test
Coordinator sent a start command at the end of each pass to start the next pass.
At the end of 9th pass of a test with tip displacement 2.2 mm (0-pk), while completing nearly 2.8x105 fully reversed bending cycles, the HCF Test Coordinator successfully stopped the shaker after detecting the frequency drop (see Figure 6.41 a) caused by fatigue failure, which is evident from the considerable changes in response after the crack initiation as illustrated in Figure 6.36~Figure 6.41. At resonance, the response lagged the input excitation by nearly 178º (almost in phase) before failure, which fell below 128º after fatigue damage (Figure 6.36). Significant drop of FRF magnitude was observed once the failure occurred and FRF became un-symmetric around the resonant frequency, which indicates material non-linearity due to crack
92 development in the test specimen (Figure 6.37). During resonance, shaker acceleration requirement went down noticeably; while it was still high with minor rise and fall once the fatigue crack developed (Figure 6.38). In case of un-cracked specimens, the excitation frequency became stabilized at the end of ramping, and was maintained throughout the rest of resonance dwell duration, whereas rapid decrease in frequency level was observed at the final pass after fatigue failure (Figure 6.39). The shift of resonant frequency is also obvious from Figure 6.36~ Figure 6.39. As shown in Figure
6.40, ramp time is the period while the tip displacement, and thus the stress, gradually rise up to the target level. In cycle counts, the ramping time was excluded, thus the approximate number of completed cycles was computed by multiplying the effective dwell duration by the excitation frequency. At the final pass, the required time for ramping increased, while specimens were vibrated with lower than target stress.
Figure 6.36 FRF phase angle from DP sweep sine test
93
Figure 6.37 FRF magnitude from DP sweep sine test
Figure 6.38 Shaker accln from DP sweep sine test
Figure 6.39 Excitation freq. from DP res. search and dwell test
94
Figure 6.40 Specimen tip disp. from DP res. search and dwell test
(a)
(b) Figure 6.41 Resonant frequency history (a) Gradual frequency fall, (b) Abrupt frequency fall
95
6.3.4 Results and Discussion
The experimental results are listed in Table 6.4. Minor variation of the counted
cycles is noticed among the tests with same stress level. S-N curve obtained from this
experiment is shown in Figure 6.42.
Table 6.4 Test Results d (mm), 0-pk S (MPa) n Test ID N μ COV 1 254475 2 285131 2.2 202.91 4 261151 6.13% 3 252267 4 252731 5 410920 6 382866 2.1 193.26 5 7 412580 399468 4.18% 8 379561 9 411413 10 636553 2.0 186.72 3 11 635977 635039 0.34% 12 632588 13 981703 1.9 173.63 3 14 984009 973701 1.63% 15 955392 16 1495308 1.8 163.98 3 17 1601789 1485304 8.20% 18 1358817 Where d is specimen tip displacement amplitude; S is maximum stress in specimen; n is
number of tests conducted at a stress level; N is completed cycles before failure; μ is the
mean value of completed cycles and COV is its coefficient of variation.
96
Figure 6.42 Experimental S-N curve for Al6061-T6
Before the initiation of fatigue crack in specimen, frequency levels were stable with minor fluctuations (see Figure 6.41). After the crack development, gradual frequency fall was noticed in most of the tests (Figure 6.41 a), whereas, in few tests, frequency suddenly dropped over the set limit (Figure 6.41 b). From microscopic photographs of the tested specimens, relatively wider cracks were observed in case of higher stress and lower cycle tests as shown in Figure 6.43.
97
(high-stress low-cycle test)
(low-stress high-cycle test) Figure 6.43 Microphotograph of fatigue cracks in tested specimens
Experimental S-N curve obtained from this study was compared with literature [13]
(see Figure 6.44). Values of parameter A and B were determined (listed in Table 6.5) from logarithmic regression analysis to use in Equation 6.1.
σ = A − B ln(N) (Eq. 6.1)
98
Table 6.5 Parameter data from logarithmic regression analysis Procedure A B
This study 477.93 22.02
Literature [13] 524.87 27.04
Probable sources of the observed dissimilarity in test results are the differences in excitation frequency (was 1600 Hz in literature compared to nearly 700 Hz in this study), specimen geometry (a rectangular plate with different thickness was used in literature), temperature variation in the testing environment etc.
Figure 6.44 Comparison of test results
99
CHAPTER VII
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
A test procedure and necessary instrumentation is developed and verified to acquire valid experimental data for HCF testing. Required control over the test continuation and termination is attained with the described HCF Test Coordinator, which manages the equipment involved. At various stages of the effort, the shaker was evaluated to check the adequacy of power to reach the targeted stress levels in the test specimens at various excitation frequencies. Several specimen and fixture geometries were tested to obtain a design that optimizes the excitation frequency, and therefore test time and attainable stress levels in the test specimens. Damping evaluation was carried out by matching the FEA results with experimental data for different lengths of specimens. Experimental strain measurement and a calibration test were conducted to obtain stress-displacement relationship.
The multi-specimen closed-loop testing methodology was demonstrated by experimental testing, which confirms the feasibility and applicability of the technique.
It has been shown that this vibration-based method is able to detect the presence of fatigue crack in the test specimen, through observed changes in the resonant frequency, while it is still in the initiation stage. In addition, this method has the advantage of being able to stop the shaker automatically once the presence of fatigue crack is detected, and terminate the test to prohibit any further crack propagation. The 100 development of this technique is an important step in obtaining high cycle bending fatigue data. The next step will be to use this test method to study and control fatigue crack propagation in various metals and composites.
101
BIBLIOGRAPHY
1. A.B.M. Abdullah, G.J. Yun, W.K. Binienda (2010). Development of a Closed- loop High-cycle Resonant Fatigue Testing System. submitted to Experimental Mechanics.
2. G.J. Yun, A.B.M. Abdullah, W.K. Binienda, D.L. Krause, S. Kalluri (2010). Test Methodology Development for Experimental Structural Assessment of Advanced Stirling Convertor Planar Spring Material for Long-Term Durability. submitted to NASA TM.
3. George TJ, Seidt J, Shen MHH, Nicholas T, Cross CJ (2004). Development of a novel vibration-based fatigue testing methodology. International Journal of Fatigue 26 (5): 477-486.
4. Wang YC, Hoechbauer T, Swadener JG, Misra A, Hoagland G, Nastasi M (2006). Mechanical fatigue measurement via a vibrating cantilever beam for self-supported thin solid films. Experimental Mechanics 46 (4): 503-517.
5. Xue HQ, Tao H, Monternbault F, Wang QY, Bathias C (2007). Development of a three-point bending fatigue testing methodology at 20 kHz frequency. International Journal of Fatigue 29 (9-11): 2085-2093.
6. Vanlanduit S, Verboven P, Guillaume P (2003). On-line detection of fatigue cracks using an automatic mode tracking technique. Journal of Sound and Vibration 266 (4): 805-814.
102
7. Vanlanduit S, Parloo E, Guillaume P (2004). An on-line combined linear- nonlinear fatigue crack detection technique. Ndt & E Int. 37 (1): 41-45.
8. Joaquim FT, Barbieri R, Barbieri N (2009). Investigating torsional fatigue with a novel resonant testing fixture. International Journal of Fatigue 31 (8-9): 1271- 1277.
9. Oezsoy S, Celik M, Kadioglu FS (2008). An accelerated life test approach for aerospace structural components. Engineering Failure Analysis 15 (7): 946-957.
10. Wozney GP (1960). Resonant-vibration fatigue testing. SESA annual meeting, Berkeley California.
11. Kim HY, Marrero TR, Yasuda HK, Pringle OA (1999). A simple multi- specimen apparatus for fixed stress fatigue testing. Journal of Biomedical Materials Research 48 (3): 297-300.
12. Ay I, Sakin R, Okoldan G (2008). An improved design of apparatus for multi- specimen bending fatigue and fatigue behaviour for laminated composites. Materials & Design 29 (2): 397-402.
13. Shen MHH, George T, Cross CJ, Calcaterra J (2007). Development of an improved high cycle fatigue criterion. Journal of Engineering for Gas Turbines and Power-Transactions of the Asme 129 (1): 162-169.
14. Rotem A (1981). Accelerated fatigue testing method. International Journal of Fatigue 3 (4): 211-215.
15. Nieto AJ, Chicharro JM, Pintado P (2006). An approximated methodology for fatigue tests and fatigue monitoring of concrete specimens. International Journal of Fatigue 28 (8): 835-842.
103
16. Fressinet M, Panis M, Bordes C (2009). Accelerated fatigue testing on hydraulic shaker. ICAF symposium, Rotterdam.
17. Kim CY, Song JH, Lee DY (2009). Development of a fatigue testing system for thin films. International Journal of Fatigue 31 (4): 736-742.
18. Kocatürk T (2005). Determination of the steady-state response of viscoelastically supported cantilever beam under sinusoidal base excitation. Journal of Sound and Vibration 281 (3-5): 1145-1156.
19. Lee YL, Pan J, Hathaway RB, Barkey ME (2005). Fatigue testing and analysis (theory and practice). Elsevier, Burlington MA, p. 109.
20. Object Model Reference, Visual Basic® Engine, PSV 8.3, Polytec, Inc.
21. Vibrometer Controller User Manual, OFV-5000, Polytec, Inc.
22. Scanning Vibrometer Software Manual, Software 8.2, Polytec, Inc.
23. Scanning Vibrometer Hardware Manual, PSV 400, Polytec, Inc.
24. SignalStar Vibration Controller User Manual, Rev. 09, Data Physics Corp.
25. Data sheet for V100 Shaker, Data Physics Corp.
26. Performance Specification for Series 3030B Accelerometer, Dytran Instruments, Inc.
27. Instruction Manual for Strain Gage Installation, Vishay Micro-measurements.
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APPENDICES
105
APPENDIX A Resonant Frequency History during Fatigue Test
Test 1 Tip Disp Amp 2.2 mm, 0-pk Test 2 Tip Disp Amp 2.2 mm, 0-pkk
Test 3 Tip Disp Amp 2.2 mm, 0-pk Test 4 Tip Disp Amp 2.2 mm, 0-pkk
Test 5 Tip Disp Amp 2.1 mm, 0-pk Test 6 Tip Disp Amp 2.1 mm, 0-pkk
106
Test 7 Tip Disp Amp 2.1 mm, 0-pk Test 8 Tip Disp Amp 2.1 mm, 0-pkk
Test 9 Tip Disp Amp 2.1 mm, 0-pk Test 10 Tip Disp Amp 2.0 mm, 0-pk
Test 11 Tip Disp Amp 2.0 mm, 0-pk Test 12 Tip Disp Amp 2.0 mm, 0-pk
107
Test 13 Tip Disp Amp 1.9 mm, 0-pk Test 14 Tip Disp Amp 1.9 mm, 0-pk
Test 15 Tip Disp Amp 1.9 mm, 0-pk Test 16 Tip Disp Amp 1.8 mm, 0-pk
Test 17 Tip Disp Amp 1.8 mm, 0-pk Test 18 Tip Disp Amp 1.8 mm, 0-pk
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APPENDIX B Microphotograph of Fatigue Cracks in Tested Specimens
Test 1 Tip Disp Amp 2.2 mm, 0-pk Test 2 Tip Disp Amp 2.2 mm, 0-pk
Test 3 Tip Disp Amp 2.2 mm, 0-pk Test 4 Tip Disp Amp 2.2 mm, 0-pk
Test 5 Tip Disp Amp 2.1 mm, 0-pk Test 6 Tip Disp Amp 2.1 mm, 0-pk
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Test 7 Tip Disp Amp 2.1 mm, 0-pk Test 8 Tip Disp Amp 2.1 mm, 0-pk
Test 9 Tip Disp Amp 2.1 mm, 0-pk Test 10 Tip Disp Amp 2.0 mm, 0-pk
Test 11 Tip Disp Amp 2.0 mm, 0-pk Test 12 Tip Disp Amp 2.0 mm, 0-pk
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Test 13 Tip Disp Amp 1.9 mm, 0-pk Test 14 Tip Disp Amp 1.9 mm, 0-pk
Test 15 Tip Disp Amp 1.9 mm, 0-pk Test 16 Tip Disp Amp 1.8 mm, 0-pk
Test 17 Tip Disp Amp 1.8 mm, 0-pk Test 18 Tip Disp Amp 1.8 mm, 0-pk
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APPENDIX C Code for HCF Test Coordinator
'*************************GENERAL DECLARATION*********************
Dim fLagResume As Boolean
Dim fResume(1 To 10) As Double
Dim NResume As Double
Dim PassNum As Integer 'PassNum: pass number (variable)
Dim fName As String
Dim nScanPoint As Integer
Dim nPass As Integer
Dim STime As Double
Dim cumFreq() As Double
Dim p As Integer
Dim MCounter As Integer
Dim fLag2 As Boolean
Dim fLag As Boolean
Dim a() As Double ' this array saves excitation frequency
Dim b() As Double ' this array saves magnitude of FRF at the excitation frequency
Sub Main()
'************************USER INPUT STARTS HERE********************* fName="090710_6" 'file name, new file should be used for each run nScanPoint=10 'nScanPoint: number of scan points or number of specimens nPass=200 'nPass: max number of pass (constant)
STime=45 ' effective dwell time
112 fLagResume=True ' Is it resuming a previous test? TRUE or FALSE
NResume=125860 'Number of Cycles Resume from, for a new test NResume is to be set to 0 fResume(1) = 705.5 'Resume Frequency for sp#1 or Last Frequency if fLagResume =True fResume(2) = 705.7 fResume(3) = 704.8 fResume(4) = 705.9 fResume(5) = 704.7 fResume(6) = 706.1 fResume(7) = 705.2 fResume(8) = 704.6 fResume(9) = 705.3 fResume(10) = 705.5
'**************************USER INPUT ENDS HERE*********************
ReDim a(nPass, nScanPoint) 'Dynamic memory allocation
ReDim b(nPass, nScanPoint)
ReDim cumFreq(nPass*nScanPoint) cumFreq(0)=NResume/STime p=0
MCounter=0
Dim ii As Integer
For ii=1 To nScanPoint Step 1
Open "G:\" & fName & "\Sp_" & Format(ii,"00") & ".txt" For Output As #ii+2 113
Print #ii+2, " (Pass)";" ";"(Sp" & Format(ii,"00") &"-freq [Hz])";" ";"(Sp" & Format(ii,"00") &"-mag [dB])";" ";" (Cycles)"
Close #ii+2
Next ii
fLag2=False ' fLag2 changes to Trus only when one of the specimens fails fLag=False 'fLag changed to True 1) when one of the specimens fails or 2) when MCounter reaches to nScan*nScanPoint
Dim digit As DigitalPort
Set digit = DigitalPorts.Item(ptcDigitalPortOut1) digit.Pulse(True, 100000)' duration in micro sec, sends digital output pulse to start excitation
For PassNum = 1 To nPass Step 1
If fLag=True Then Exit For
Acquisition.ScanFileName = "G:\" & fName & "\Pass_" & PassNum 'This file save data for all specimens at current pass
Acquisition.Scan ptcScanAll
While Acquisition.State <> ptcAcqStateStopped
Wait 1
Wend
Next PassNum
O = "G:\" & fName & "\FFT.txt"
Open O For Output As #2
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Print #2, " (Pass)";" ";"(Sp1-freq [Hz])";" ";"(Sp1-mag [dB])";" ";"(Cycles)";" (Sp2-freq [Hz])";" ";"(Sp2-mag [dB])";" ";"(Cycles)";" (Sp3-freq [Hz])";" ";"(Sp3- mag [dB])";" ";"(Cycles)";" (Sp4-freq [Hz])";" ";"(Sp4-mag [dB])";" ";"(Cycles)";" (Sp5-freq [Hz])";" ";"(Sp5-mag [dB])";" ";"(Cycles)";" (Sp6-freq [Hz])";" ";"(Sp6-mag [dB])";" ";"(Cycles)";" (Sp7-freq [Hz])";" ";"(Sp7-mag [dB])";" ";"(Cycles)";" (Sp8-freq [Hz])";" ";"(Sp8-mag [dB])";" ";"(Cycles)";" (Sp9-freq [Hz])";" ";"(Sp9-mag [dB])";" ";"(Cycles)";" (Sp10-freq [Hz])";" ";"(Sp10-mag [dB])";" ";"(Cycles)"
Close #2
Dim j As Integer
For j = 1 To PassNum-1 Step 1
Open O For Append As #2
Print #2," ";Format(j,"00000000");" ";Format(Round(a(j, 1),2),"00000.00"); " ";Format(Round(b(j, 1),2),"00000.00");" "; Format(cumFreq(j*10- 9)*STime,"000000000000");" ";" ";Format(Round(a(j, 2),2),"00000.00");" ";Format(Round(b(j, 2),2),"00000.00");" ";Format(cumFreq(j*10- 8)*STime,"000000000000");" ";Format(Round(a(j, 3),2),"00000.00");" ";Format(Round(b(j, 3),2),"00000.00");" ";Format(cumFreq(j*10- 7)*STime,"000000000000");" ";Format(Round(a(j, 4),2),"00000.00");" ";Format(Round(b(j, 4),2),"00000.00");" ";Format(cumFreq(j*10- 6)*STime,"000000000000");" ";Format(Round(a(j, 5),2),"00000.00");" ";Format(Round(b(j, 5),2),"00000.00");" ";Format(cumFreq(j*10- 5)*STime,"000000000000");" ";Format(Round(a(j, 6),2),"00000.00");" ";Format(Round(b(j, 6),2),"00000.00");" ";Format(cumFreq(j*10- 4)*STime,"000000000000");" ";Format(Round(a(j, 7),2),"00000.00");" ";Format(Round(b(j, 7),2),"00000.00");" ";Format(cumFreq(j*10- 3)*STime,"000000000000");" ";Format(Round(a(j, 8),2),"00000.00");" ";Format(Round(b(j, 8),2),"00000.00"); _
" ";Format(cumFreq(j*10-2)*STime,"000000000000");" ";Format(Round(a(j, 9),2),"00000.00");" ";Format(Round(b(j, 9),2),"00000.00");" ";Format(cumFreq(j*10-1)*STime,"000000000000");" ";Format(Round(a(j, 10),2),"00000.00");" ";Format(Round(b(j, 10),2),"00000.00");" ";Format(cumFreq(j*10-0)*STime,"000000000000")
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Close #2
Next j
MsgBox "Test Is Completed"
End Sub
Public Sub ScanStateChanged(ScanState As PTCScanState, ScanPoint As Long)
'This subroutine is called when Scan state changes, that is, at the end of each scan
Dim digit As DigitalPort
Set digit = DigitalPorts.Item(ptcDigitalPortOut1)
Dim i As String
Dim x0 As Double ' Frequency value
Dim y0 As Double ' Amplitude value
Dim x00 As Double
Dim y00 As Double
If fLag2=False Then
If ScanState = ptcScanStateEndScanPoint Then i = "G:\" & fName & "\Temp.txt"
Application.ActiveWindow.SaveAs (i,ptcFileFormatText)
Call CalcMax(x0, y0, i) a(PassNum, ScanPoint) = x0 b(PassNum, ScanPoint) = y0
Call CalcMax(x00,y00,i)
116 p=p+1 cumFreq(p)=cumFreq(p-1)+x00
Open"G:\" & fName & "\SP_" & Format(ScanPoint,"00") & ".txt" For Append As #ScanPoint+2
Print #ScanPoint+2," ";Format(PassNum,"00000000");" ";Format(Round(a(PassNum, ScanPoint),2),"00000.00"); " ";Format(Round(b(PassNum, ScanPoint),2),"00000.00");" "; Format(cumFreq(p)*STime,"000000000000")
Close #ScanPoint+2
MCounter=MCounter+1
If MCounter= nScanPoint*nPass Then
Acquisition.Stop fLag=True
Exit Sub
End If
If PassNum=1 Then
If fLagResume=False Then digit.Pulse(True, 100000)' duration in micro sec digit.Pulse(False, 100000)' duration in micro sec digit.Pulse(True, 100000)' duration in micro sec
End If
'*********************CRACK DETECTION CRITERIA*******************
If fLagResume=True And fResume(ScanPoint) - a(PassNum, ScanPoint)<= 1 Then
'Frequency drop limit 117 digit.Pulse(True, 100000)' duration in micro sec digit.Pulse(False, 100000)' duration in micro sec digit.Pulse(True, 100000)' duration in micro sec
End If
If fLagResume=True And fResume(ScanPoint) - a(PassNum, ScanPoint)> 1 Then
Acquisition.Stop fLag=True
MsgBox "Specimen# " & ScanPoint & " Failed @ " & Round(cumFreq(p)*STime) & " Cycles" fLag2=True
Exit Sub
End If
End If
If PassNum>1 Then
If a(PassNum-1, ScanPoint) - a(PassNum, ScanPoint)<= 1 Then digit.Pulse(True, 100000)' duration in micro sec digit.Pulse(False, 100000)' duration in micro sec digit.Pulse(True, 100000)' duration in micro sec
End If
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If a(PassNum-1, ScanPoint) - a(PassNum, ScanPoint)> 1 Then
Acquisition.Stop fLag=True
MsgBox "Specimen# " & ScanPoint & " Failed @ " & Round(cumFreq(p)*STime) & " Cycles" fLag2=True
Exit Sub
End If
End If
End If
End If
End Sub
'********************FINDING RESONANT FREQUENCY******************
Sub CalcMax(ByRef x0 As Double, ByRef y0 As Double, I1 As String)
'This subroutine searches for the max FRF magnitude and its corresponding frequency
Dim x As Double
Dim y As Double i% = 0
Open I1 For Input As #1 x0 = 0 y0 = -10000000 ' a small value
While Not EOF(1)
Line Input #1, l$ i% = i% + 1
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If i% > 5 Then ' Ignore header of AnalyzerMax.txt (first 5 lines) t% = InStr(l$, vbTab) ' Search for 'tab' (delimiter) in the line
If t% <> 0 Then x = CDec(Left$(l$, t% - 1)) y = CDec(Right$(l$, Len(l$) - t%))
If y > y0 Then ' Actual line contains greater y value than any line before y0 = y x0 = x
End If
End If
End If
Wend
Close #1
End Sub
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