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Using Torsional Vibration Analysis as a Synergistic Method for Crack Detection in Rotating Equipment

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0-7803-8155-6/04/$17.00 © 2004 IEEE

Abstract— A non-intrusive torsional vibration method for monitoring and tracking small changes in crack growth of reactor coolant pump shafts is presented in this paper. This method resolves and tracks characteristic changes in the natural torsional vibration frequencies that are associated with shaft crack propagation. The focus of this effort is to develop and apply the torsional vibration shaft cracking monitoring technique on a Westinghouse 93A reactor coolant pump. While this technique is being applied to reactor coolant pumps it is generally applicable to many types of rotating equipment, including centrifugal charging pumps, condensate and feed water pumps, and may be used to detect and track changes in blade natural frequencies in a gas or steam turbines. A laboratory scale rotor test bed was developed to investigate shaft cracking detection techniques under controlled conditions. The test bed provides a mechanism to evaluate sensing technologies and algorithm development. For accurate knowledge of the crack characteristics (crack depth and front), a sample shaft was seeded with a crack that was propagated using a three-point bending process. Following each crack growth step, the specimen was evaluated using ultrasonic inspection techniques for crack characterization. After inspection, the shaft was inserted in the rotor test bed for analysis and to track changes in shaft torsional vibration features. The torsional vibration measurement method has demonstrated the ability to reliably detect changes in the first natural shaft frequency in the range of 0.1 to 0.2 Hz. This technique shows the potential to enable online structural health diagnostics and ultimately the prevention of shaft or even possibly blade failure due to crack growth. —

TABLE OF CONTENTS 1. INTRODUCTION ....................................................... 1 2. TORSIONAL VIBRATION AS A ROTATING

MACHINERY DIAGNOSTIC TOOL............................ 3 3. TORSIONAL VIBRATION EXPERIMENTS WITH

A (PROGRESSIVELY GROWN FATIGUE) CRACKED SHAFT..................................................... 3

4. TORSIONAL VIBRATION ANALYSIS ........................ 5 5. FEM OF TORSIONAL TEST STAND WITH

CRACKED SHAFTS................................................... 6 6. TORSIONAL VIBRATION MONITORING OF A

REACTOR COOLANT PUMP..................................... 8 7. TURBINE BLADE FAULT DETECTION ..................... 8 8. CONCLUSION........................................................... 9 9. ACKNOWLEDGMENTS ........................................... 10 10. REFERENCES ....................................................... 10 11. BIOGRAPHIES ...................................................... 11 1. INTRODUCTION The importance of shaft crack detection in nuclear power plants is apparent when considering the impact of past failures. For example, Primary Coolant Pumps (PCPs) have experienced shaft cracking and subsequent failure, often with little or no warning from state-of-the-art crack detection systems. The financial loss associated with a forced outage caused by such a shaft failure is substantial. Recently, pre-1974 Westinghouse Reactor Coolant Pumps (RCPs) have come under particular scrutiny, as at least five have experienced significant cracking. A root cause analysis indicated that Model 93A pumps that are operated in counterclockwise Reactor Coolant System (RCS) flow loops are particularly susceptible to developing shaft cracks [1].

Mitchell S. Lebold, Kenneth Maynard,

Karl Reichard Applied Research Laboratory

The Pennsylvania State University P.O. Box 30

State College, PA 16801-0030 lebold@psu.edu

Martin Trethewey, Dennis Bieryla

Penn State University 336 Leonhard Building Univ. Park, PA 16802

Clifford Lissenden Penn State University

212 Earth-Eng. Sciences Build. Univ. Park, PA 16802

David Dobbins Electric Power Research Institute

1300 WT Harris Blvd Charlotte, NC 28262

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In late 2000, Tennessee Valley Authority (TVA) Sequoyah Unit 1, RCP 4 experienced severe cracking that resulted in an extended forced outage. The crack detection system on the RCP provided no warning of substantial crack growth. After shutdown, inspection revealed a circumferential crack of 252º, and only one-third of the cross-sectional area remaining. Note that similar pumps are found at the following US plants: Beaver Valley, Prairie Island, Diablo Canyon, Three Mile Island, Farley, and Sequoyah. The unexpected loss of a Steam Generator Feed Pump (SGFP) in a Pressurized Water Reactor (PWR) or a Reactor Feed Pump (RFP) in a Boiling Water Reactor (BWR) often results in a unit trip and subsequent operation at reduced power. For instance, the loss of a SGFP due to turbine shaft cracking occurred at Plant Vogtle (Southern Nuclear) in the mid-90s. The result was a unit trip, and the usual 3-4 days to return to full operation. In addition, the unit operated at reduced power (~70%) for approximately one week to facilitate turbine repair resulting in a substantial monetary loss. In addition, PCPs in BWRs have had shaft-cracking problems. Recently, for instance, Plant Hatch (Southern Nuclear) has replaced several PCPs due to potential shaft cracking problems identified by the vendor. Other pumps that have experience shaft cracking include Condensate Pumps and Centrifugal Charging Pumps (20 shaft failures of current design used in PWRs in the USA). Although the failure of these pumps due to shaft cracking does not generally result in unit trips or reduced power operation, the unexpected failure can create maintenance scheduling problems and increased safety risk. To address the shaft cracking issue, a health monitoring technique based upon the torsional vibration signature is currently being developed and implemented with EPRI sponsorship. This health monitoring system will identify characteristic changes in shaft torsional vibrations as the result of a propagating crack. This method appears to be less sensitive to changes in the pump rotor context (e.g., seals, oil film, and supports) than the existing crack detection systems. The technique has recently been installed and used successfully in hydro plants for maintenance and health monitoring [2]. Based on laboratory and field experience, to date, this approach has the potential to provide a robust measure of the shaft structural integrity. The overall objectives of this multi-year project presented in this paper are twofold:

1. To demonstrate the feasibility of using torsional vibration as a diagnostic method for shaft cracking detection and monitoring in rotating equipment in nuclear power plants;

2. To develop and install a prototype shaft crack detection system for Westinghouse Model 93A reactor coolant pumps.

This paper presents research to date toward meeting these objectives. Thus far, a laboratory subscale rotor test bed has been used for developing this technique. The test bed uses a simple shaft which is fabricated with a seeded fault. The crack is initiated and grown by fatiguing the shaft for a specified number of cycles with a 3-point bend machine. Once grown, the crack is nondestructively characterized. The shaft is installed and operated in the torsional test rig to extract the torsional vibration signature. The fatigue cycling process is repeated until the crack is grown to a critical length or shaft deformation occurs. The torsional vibration signature is used in conjunction with a crack characterization model to examine the sensitivity of the process. Modeling efforts are being conducted in parallel to understand the effects of shaft crack growth on the torsional and lateral vibration. Finite element models of the subscale shaft have been developed to simulate both the static and dynamic response. Attention focuses on the ability of the models to replicate the torsional and flexural vibration features that are found to be sensitive to crack growth. In addition to modeling the test bed and crack front, a model has been developed to extend this principle to an RCP (Westinghouse 93A). This analysis will also examine the effects that shaft crack development and growth will have on the vibration signature. The RCP modeling effort is being performed jointly between Penn State and EDF (Electricité de France) team members. While this paper focuses on applying this technology to detecting and tracking cracks within reactor coolant pumps, this method may also be applied to detect root cracks within turbine blades. Earlier work conducted at the Applied Research Laboratory has shown the feasibility of detecting changes in blade natural frequencies using a simple blade rotor test bed [6], however additional research most be performed to validate this technique on a full-scale turbine.

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2. TORSIONAL VIBRATION AS A ROTATING MACHINERY DIAGNOSTIC TOOL

A system to measure torsional vibration of a rotating shaft is shown in

Figure 1 [3,4]. Signal detection involves three main aspects, shaft encoding, transduction data discretization, and demodulation. The shaft encoding system can use a variety of approaches including a timing gear, optical encoder, or simply using striped tape. Depending on the shaft encoding device, a number of transducers are viable, including infrared reflective intensity fiber optic sensors, proximity probes, and Hall Effect transducers.

Figure 1 – Torsional vibration measurement

instrumentation using a fiber optic probe The detection of the passing times from the multiple pulse-per-revolution (PPR) shafts encoders is used to measure the torsional vibrations. A number of variations of the basic measurement scheme have been studied previously, including both analog [2] and more recently entirely digital processing methods. Digital methods of measuring torsional vibrations are becoming viable and cost effective alternatives to the analog hardware due to the rapid increases in digital clock speeds and computing power. Vance describes a prototype system called the TIMS (time interval measurement system) [3] in which a digital tachometer circuit is able to record the passing times of each line on the encoding device. The passage times are then converted to angular shaft velocity. Various investigators have addressed a number of issues and proposed enhancements to this approach [7,8,9,10]. The

torsional measurement scheme used in this work is based upon the TIMS approach. The basic technique has been further advanced by work at Penn State to allow for correction of transducer imperfections and the removal of fixed order components. This refined torsional vibration measurement approach is used in the current research effort. Recent applications of the method have shown the effectiveness of using torsional vibration in monitoring simulated turbine shaft-blade coupled torsional vibrations [5,6]. By monitoring blade natural frequencies, it is possible to determine shifts due to root cracking and other mechanisms. Beyond the laboratory investigations, the approach has been used in several field applications including hydro-electric equipment [2] and with a variety of other types of rotating equipment [6]. 3. TORSIONAL VIBRATION EXPERIMENTS WITH A (PROGRESSIVELY GROWN FATIGUE) CRACKED

SHAFT A test was performed on a shaft with a fatigue crack grown sequentially to eight different degrees of depth. The characteristics of the shaft and crack were evaluated in multiple fashions at each growth increment. The torsional vibration signature of the shaft at each cracked state was determined in laboratory tests. The test sequence is intended to correlate the changing torsional vibration signature to the growth of a fatigue crack under controlled laboratory conditions. The test hardware and procedures are described in the following sections. Fatigue Crack Growth - The test specimen shaft material was 0.625 inch diameter ANSI 316 L stainless steel. To initiate the crack, a 0.010 inch deep notch was machined into the midlength of the shaft specimen with the edge of a milling machine tool (per ASTM E399 specifications for fatigue precracks). The specimen was mounted on an MTS 642.10B 3-point bend fixture and cyclic loading was applied with a servohydraulic MTS 810 test stand operated by a MTS 458.20 electronic controller. The fatigue test hardware is shown in Figure 2. Initial tests were performed on several shaft specimens to determine the cyclic loading parameters needed to grow the crack to a specified depth without causing permanent deformation. These parameters were used to accurately control the crack growth process during final evaluations.

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Figure 2 – Shaft specimen in three point bending MTS fatigue machine Crack Characterization - Upon completion of cyclic loading, the fatigue crack was quantified using both a visual inspection and an ultrasonic NDE method. The visual inspection entailed viewing the crack with a telescope and measuring the fatigue crack surface length while the shaft was under a constant lateral load in the 3-point bending fixture. Note, while in an unloaded condition the crack is closed and the crack location or depth is not visible. Two nondestructive evaluation procedures using ultrasonic waves were applied to map the crack front. One method used a conventional ultrasonic inspection technique with longitudinal waves to estimate the uncracked shaft cross section. The second method used a novel wedge transducer which emits both surface and shear waves.

At the completion of the fatigue cycling, a destructive crack evaluation was performed on the shaft specimen. The shaft was sectioned at the crack location and cross-section viewed with a metallograph to help correlate the NDE results with actual crack characteristics. This cross-section is shown in Figure 3. The crack metric (a/D) is expressed as the distance from shaft surface to the extreme location of elliptical crack front along a diametric line as shown in Figure 3.

Figure 3 – Typical shaft section beach marks

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Torsional Rigidity Measurement – After each fatigue cycling increment, a MTS 319 Axial-Torsion test machine was used to measure the torsional rigidity, GJ, relative to the uncracked condition. Two fully reversed cycles of a triangular torque waveform was applied at a rate of 20 lb-in/s. During each cycle, torque and angle of twist was measured. Linear regression was employed to determine torque-angle relationship and torsional rigidity was calculated. This torsional stiffness is needed in finite element model (FEM) for crack characterization and will reveal modal frequency response of the system. Torsional Vibration Test Stand - A test apparatus was constructed to measure the torsional vibration of rotating cracked shafts under controlled laboratory conditions and is shown in Figure 4. The shaft specimen was mounted in Rulon-J non-metallic flanged sleeve bearings and rotated by a variable speed Perske motor. An encoding wheel was fabricated to sense the torsional vibration with an outer diameter of 3.575 inches and 180 teeth with a 0.125 inch tooth depth. An infrared fiber optic intensity reflective transducer was used to sense the wheel tooth passage as shown in Figure 5. The tooth passage times were sensed and recorded with a National Instruments PCI-6602 Timer/Counter Board using an 80MHz clock reference. Future tests will incorporate the use of a 2048 PPR optical encoder.

4. TORSIONAL VIBRATION ANALYSIS Once encoder data is recorded, tooth passage times are processed with a customized torsional vibration algorithm developed at Penn State. The routine ultimately produces a torsional vibration spectrum. This routine can compensate for unwanted artifacts produced by an encoding device (end-affect inconsistency, differences in individual pulse widths) and remove order content from the signal, thus

improving the signal-to-noise ratio [4].

Figure 5 – Close up photograph of torsional vibration encoding wheel and fiber optic transducer Shaft Testing with Progressively Grown Fatigue Crack – A test sequence was performed that evaluated the shaft torsional vibration signature with a fatigue crack grown progressively in nine different stages. The crack was grown at the midpoint along the shaft. The following test sequence was performed. 1. A new shaft, with a milled crack initiation notch, was

tested in the torsional test rig to establish a baseline signature.

2. The fatigue crack was grown as closely as possible to a specified depth.

3. The crack was nondestructively inspected and the torsional rigidity computed.

4. The shaft was installed and examined in the torsional

Figure 4 – Laboratory-scale torsional test stand

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test rig to determine its natural torsional frequency. The vibration signature was measured over eight to ten complete disassembles and reassembles of the shaft in the torsional test stands. The multiple tests were necessary to statistically establish the system natural frequency due to errors induced by the assembly-disassembly process.

5. Steps 2-4 were repeated for the group of tests.

6. The shaft was destructively sectioned to evaluate the crack front at each fatigue increment. Beach marks in the material show the transition point between fatigue steps.

Test Results – The torsional vibration spectra for four different crack depths is shown in Figure 6. Note that the spectrum is focused around the first natural frequency. The expected reduction in system natural frequency as the crack grows is apparent. Figure 7 shows the shaft system’s torsional natural frequency as a function of the fatigue crack. The results show a gradual decrease in the shaft natural frequency with approximately a 1.5 Hz drop observed for a crack depth of a/D = 60%. The torsional vibration tests with progressively grown fatigue crack show: 1. There is an identifiable natural frequency change which

can be tracked in relation to the seeded fault condition of the shaft.

2. The torsional rigidity (GJ) showed a measurable decrease in relation to the crack growth.

3. A decrease in the first torsional natural frequency was observed as the crack grew in length.

4. Changes in natural frequency as low as 0.1 Hz were identifiable by visual inspection of the spectrum.

Figure 6 – Torsional vibration spectrum from the laboratory test rig with four different fatigue crack depths

Figure 7 – First torsional natural frequencies versus fatigue crack depths

5. FEM OF TORSIONAL TEST STAND WITH CRACKED SHAFTS

The goal of the rotor modeling is to analytically predict the natural frequencies of the system in the presence of a growing crack. For the uncracked case, this was accomplished using a beam model, and extracting natural frequencies in the torsional domain. A torsional spring was introduced to model the crack effects on the shafting system’s natural frequencies. Four methods were used to determine the equivalent spring torsional stiffness. The objective is to determine an approach that accurately estimates the torsional spring stiffness required to replicate the measured natural frequencies shifts as a function of fatigue crack depth.

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Model Geometry and Properties - A finite element model of the experimental rotor system was developed using ANSYS as shown in Figure 8. Beam elements were used for the flexible members and lumped inertial elements for the motor. The model inputs were calculated based on dimensions and properties. The motor properties were based on shaft drawings and rotor weights and dimensions from the manufacturer, augmented by some external measurements. Cracked Shaft Modeling - A torsional spring was integrated into the FEM shaft model at the crack location to evaluate dynamic effects due to crack growth. This is illustrated in Figure 9. The stiffness of the torsional spring model over a range of particular crack depths was calculated using four different methods. Two methods were analytically based, while two methods used the previously acquired experimental results to estimate the stiffness. 1. Localized crack FEM – The crack front is idealized to be straight and assumed to contain no friction between crack faces. The crack is modeled by unconstraining nodes that correspond to a particular crack front. One end of the shaft is completely constrained, while the opposite end is constrained to allow only planar angular deflections. A coupling torque of 1000 lb-in was applied and the corresponding angular deflections computed. The equivalent torsional spring stiffness was then computed. 2. An energy based solution – The torsional spring stiffness is the inverse of the local flexibility induced by a straight open crack. This is computed using the stress intensity factor and Castigliano’s theorem as given by Papadopoulos [11]. 3. Torsional rigidity tests – The equivalent torsional spring needed to produce the angular rotation measured in torsional rigidity tests was computed for each fatigue crack state. The torsional rigidity tests had a relatively high variance; hence the computed spring rates also tend to show a large variation. 4. Torsional vibration test results – The shaft model

shown in Figure 9 was placed in the test stand FEM (Figure 8). The torsional spring constant used to model the crack was adjusted so that the natural frequency coincided with the measured value. This analysis was performed at each fatigue crack increment.

Figure 8 – FEM of laboratory torsional test stand

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Figure 9 – Dynamic modeling of shaft crack with a torsional spring The equivalent torsional spring stiffness computed by the four methods as a function of crack depth is shown in Figure 10. The four methods do not produce consistent results. There is reasonable agreement between the localized FEM and the solution presented by Papadopoulos [11]. There is also some general agreement between the rigidity and dynamic test results. However, the analytical and computational approaches predict a greater flexibility than either experimental method.

The accurate modeling of the crack is important for 1) assessing the method’s applicability to various rotating equipment, and; 2) evaluating the dynamic torsional vibration signature in relation to the shaft’s structural integrity. The modeling of the fatigue crack’s effects on the torsional dynamics remains a topic of investigation and is presently being further analyzed.

6. TORSIONAL VIBRATION MONITORING OF A REACTOR COOLANT PUMP

A prototype torsional vibration package has been developed for tracking shaft cracks on a Westinghouse 93A RCP. An installation on a RCP will allow the capture of torsional vibration signatures and thoroughly examine its features for diagnostic purposes. Lateral vibration signatures will also be acquired and evaluated in conjunction with algorithms developed at Electricité de France for shaft crack monitoring. Depending on the results, data fusion between the lateral and torsional vibration analysis methods may be

implemented. A cutaway view of a 93A-1 pump is shown in Figure 14. A finite element model of the pump has been developed jointly between Penn State and EDF. A torsional line shaft model of a 93A pump is also shown in Figure 14. This work will ultimately be used to examine the effects of crack growth on the pump’s torsional dynamics.

7. TURBINE BLADE FAULT DETECTION Blade crack can be described as the appearance of stress fractures in turbine blades that will eventually cause that blade to fail. The “Christmas tree” cross section, shown in Figure 11 is a location of the turbine blade that is highly prone to experience blade crack failures. In this figure, large cracks can be seen near the root of each tree branch. The initiation and growth of these cracks cause the turbine blade’s stiffness to decrease and this change is reflected in the vibrational natural frequencies of the blade. Blade cracks are generally detected during times of scheduled maintenance when the turbine is shut down. Most detection methods require an increase in the amount of man-hours to correctly perform the procedure, while some even call for extensive disassembly, which could drastically increase the amount of time a system was offline. Extensive disassembly of a turbine can even jeopardize a healthy turbine due to improper assembly errors. By developing a method that can be utilized while the turbine is in operation, online detection of blade crack could be made possible. Doing so would help to eliminate the need for costly preventative maintenance and decrease the amount of downtime experienced, by allowing one to detect blade crack in its earlier stages, well before catastrophic failures could occur.

Figure 11 – Root cracks in the “Christmas tree” area of a turbine blade

Figure 10 – Torsional vibration spectrum from the laboratory test rig with four different fatigue crack depths

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The torsional vibration test stand developed at ARL is shown below. This bladed system contains a single row of stainless steel pins to represent a bladed system and a heavy mass to set the first torsional mode of the shaft. The turbine shaft is suspended by oil impregnated flanged brass bearings, and is driven by a 1/7th hp motor, with a maximum speed of 10,000 rpm, using a DC power supply. At this time of development, a disc wheel and zebra striped tape was used as an encoding mechanism.

Figure 12 – Torsional vibration test stand at ARL For each test, the group of pins was tuned to a specified frequency by adjusting a movable mass in each pin. Throughout the test, one pin would be mistuned in increments by adjusting its movable mass. Figure 13 shows the spectral results after applying the same resampling technique used for shaft crack detection. As the rogue blade is mistuned to simulate a root crack, the natural frequency of that pin will decrease and drop out of the group cluster.

Figure 13 – Torsional Spectrum of Laboratory Rotor with One Detuned Blade

8. CONCLUSION The objective of this work was to demonstrate the feasibility of using torsional vibration as a potential diagnostic method for shaft crack detection and monitoring in nuclear power plant rotating equipment, however this same technique may be used to detect cracks in turbine blades. To this end, a series of experimental and modeling studies have been performed. The major accomplishments of this effort are summarized below: 1. Techniques have been developed to initiate and grow

fatigue cracks in a shaft under a controlled and predictable fashion.

2. Inspection techniques were developed and applied to characterize both the localized crack and its effect on shaft stiffness.

a. An ultrasonic inspection method was developed to quantify the crack front internal to the shaft.

b. Torsional rigidity tests were performed on the shafts to statically measure the effect that a crack has on the shaft shear rigidity (GJ).

3. Fatigue cracks ranging in depth from approximately 20-

65% of a 0.625” diameter stainless steel shaft were created with no significant permanent deformation.

4. A table-top scale test stand was designed and fabricated for torsional vibration testing of the shafts with fatigue cracks.

5. Digital signal processing methods were established to allow identification of the shaft system’s first torsional natural frequency from data acquired from the test stand.

6. A test sequence involving the sequential fatigue crack growth, inspection and torsional vibration evaluation was performed and showed:

a. A measurable decrease in torsional rigidity was correlated with crack growth.

b. A decrease in the first torsional natural frequency was observed as the crack grew.

c. Changes in natural frequency in the range of 0.1 to 0.2 Hz were identifiable by visual inspection of the spectrum.

7. Shaft rigidity results from the localized crack finite

element model were incorporated into the dynamic model to predict natural frequency changes with respect to crack growth.

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The torsional vibration measurement method has demonstrated the ability to reliably detect natural frequency shifts in the range of 0.1 - 0.2 Hz. This frequency shift is within the range of frequency shifts caused by shaft cracks and hence, shows the potential to enable online diagnostics and prevention of shaft failure due to crack growth. Furthermore, natural frequency trending is a rudimentary machinery diagnostic feature. The torsional vibration signature may offer other features that can provide an even more sensitive indicator for early shaft crack detection and monitoring purposes. 9. ACKNOWLEDGMENTS This work was supported by the Electric Power Research Institute (EPRI Contract EP-P9801/C4961). The content of the information does not necessarily reflect the position or policy of the EPRI, and no official endorsement should be inferred. The authors would like to thank Phillip Hitchcock from the Tennessee Valley Authority for his technical assistance in this work. Also would like to thank Pierre Verrier and

Julien Metz from Electricité de France for their assistance and RCP knowledge. 10. REFERENCES [1] InfoGram IG-02-4, RCP Shaft Crack Investigation, Westinghouse Electric Company, December, 2002. [2] Szász, G. and Guindon, E.J., “Using Torsional Vibration Spectra to Monitor Machinery Rotor Integrity,” Proceedings of the ASME 2003 International Joint Power Conference, ASME Paper No. IJPGC2003-40162, Atlanta, GA, USA, June, 2003. [3] Vance, J. M., Rotordyamics of Turbomachinery, John Wiley & Sons, New York, 1988. [4] Maynard, K.P, Trethewey, M.W. and Groover, C.L., “Application of Torsional Vibration Measurement to Shaft Crack Monitoring in Power Plants,” 55th Meeting of the Society for Machinery Failure Prevention Technology, Virginia Beach, VA, USA, 2001.

Figure 14 – Cut away view of Westinghouse 93A-1 Reactor Coolant Pump (Source:

http://www.mhi.co.jp/atom/hq/atome_e/03/08.html) and ANSYS torsional line shaft finite element model of a 93A RCP

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[5] Maynard, K.P. and Trethewey, M.W. “Blade and Shaft Crack Detection Using Torsional Vibration Measurements Part 3: Field Application Demonstrations,” Noise and Vibration Worldwide, Vol 32, pp. 16-23, 2001. [6] Maynard, K.P. and Trethewey, M.W., “On the Feasibility of Blade Crack Detection through Torsional Vibration Measurements,” Noise and Vibration Worldwide, Vol. 31, pp. 15-31, 2000. [7] Wang, P. Davies, P., Starkey, J.M., and Routson, R.L., “A Torsional Vibration Measurement System,” IEEE Transactions of Instrumentation and Measurement, Vol. 41, 1992. [8] Williams, J., “Improved Methods for Digital Measurement of Torsional Vibration,” Society of Automotive Engineers, Paper No. 962204, 1996. [9] Fu, H. and Yan, P., “Digital Measurement Method on Rotating Shaft Torsional Vibration,” ASME Vibration of Rotating Systems, Vol. 60, pp. 271-275, 1993. [10] Wang, P. ,Davies, P., Starkey, J.M., and Routson, R.L., “Torsional Mode Shape Measurements On a Rotating Shaft,” Proceedings of the 10th International Modal Analysis Conference, pp. 676-682, 1992. [11] Papadopoulos, C.A., “ Torsional Vibrations of Rotors with Transverse Surface Cracks,” Computers & Structures, Vol. 51, No. 6, pp. 713-718, 1994. 11. BIOGRAPHIES Mitchell Lebold is an Associate Research Engineer with the Applied Research Laboratory at The Pennsylvania State University with eight years of experience in algorithm development and embedded monitoring systems. He holds an M.S. and B.S. degree in Electrical Engineering from Pennsylvania State University. Mr. Lebold leads several multi-disciplinary research and development projects in the areas of wireless smart sensors, algorithm development, and open standards for condition-based maintenance. He has designed and developed numerous custom test and measurement systems as well as embedded wireless data acquisition systems for machinery health monitoring. His current research involves gear, bearing, and shaft diagnostics and prognostics algorithm development in addition to the development pump, turbine and diesel engine health assessment systems. Mr. Lebold has published over 30 papers in refereed journals, conference publications, and technical reports. Kenneth Maynard has more than 20 years of experience in structural dynamics and machinery vibration diagnostics.

As an Associate Research Engineer at the PSU Applied Research Laboratory, he has lead research in sensor and signal processing applications related to condition-based maintenance. Mr. Maynard began his engineering career at Duke Power Company in Charlotte, NC, where he served as a design engineer. In the 1980s, he was president of SLI Engineering in Charlotte and, later, a consulting engineer with Civil Engineering of Columbia (SC). For eight years, Mr. Maynard served as Senior Engineer for Southern Company Services in Birmingham, AL, prior to joining PSU ARL in 1997. He earned a BSME degree from the University of Florida, a Masters of Engineering in Acoustics from Penn State University, and a Master’s of Divinity degree from Columbia International University. Dr. Karl Reichard has more than 15 years of experience in the development of advanced sensors, measurement systems, and signal processing algorithms. An Assistant Professor of Acoustics at Penn State and Head of the Condition-Based Maintenance Department at the University's Applied Research Laboratory, Dr. Reichard leads advanced research and development efforts in embedded systems, electro-optics, intelligent acoustic and vibration sensors, and signal processing and classification algorithms for active noise and vibration control, manufacturing machinery monitoring, and surveillance systems. Prior to joining Penn State ARL in 1991, he was employed by the U.S. Army Aberdeen Proving Grounds and Virginia Polytechnic Institute and State University, his alma mater. Dr. Reichard has published more than 25 papers in refereed journals, conference publications, and technical reports. Dr. Martin W. Trethewey is a Professor of Mechanical Engineering at Penn State University. He is also affiliated with the interdisciplinary Graduate Program in Acoustics at Penn State where he holds the title of Professor of Acoustics. He has been at Penn State for 21 years. Preceding his academic career he worked at the General Motors Noise and Vibration Laboratory and Union Carbide Corporation. His research has focused on the development and analysis of machine dynamic systems from experimentally acquired data. The effort involves research in experimental technique development, machine vibration, dynamic instrumentation, experimental modal analysis, signal processing, finite element modeling, machine dynamics and noise control. He currently serves as the Assistant Editor for Mechanical Systems and Signal Processing.

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Cliff Lissenden, Ph.D. (University of Virginia, 1993) is an associate professor of Engineering Science and Mechanics at Penn State. In addition to teaching engineering mechanics courses ranging from statics to plasticity theory, he works in the field of solid mechanics; performing experimental and modeling studies of material response in the presence of multiaxial stress states. He is a member of ASM, ASME, ASCE, ASEE, SES, and Sigma Xi. Dennis J. Bieryla is a Graduate Research Assistant at The Pennsylvania State University Applied Research Laboratory. He received his B.S. in Mechanical Engineering with Honors from the Pennsylvania State University in May 2002, and will graduate with an M.S. degree in Mechanical Engineering in May 2004. His current research involves the prediction of shaft cracking in nuclear reactor coolant pumps through torsional vibration analysis. His Masters thesis is titled "Evaluation of Torsional Vibration Signatures for Shaft Cracking Diagnostics." Mr. Bieryla's research interests include machine dynamics and design, signal processing, vibrations, and noise control.