Begg, C.; T. Merdes, C. S. Byington, and K. P. Maynard, Mechanical System Modeling for Failure Diagnosis and Prognosis, Maintenance and Reliability Conference (MARCON 99), Gatlinburg, Tennessee, May 10-12, 1999.

Dynamics Modeling for Mechanical Fault Diagnostics and Prognostics

Colin D. Begg, Terri Merdes, Carl Byington, and Ken Maynard

The Pennsylvania State University, Applied Research Laboratory Condition-Based Maintenance Department

University Park, Pennsylvania 16804

ABSTRACT

While tremendous improvements have been made in the performance of modern engineered systems due to increased design cycle accuracy and testing capabilities, traditional time/use maintenance practices have not changed much. While wear longevity of many subsystem components has increased with a beneficial decrease in weight and size the margins of safety have also decreased because of greater accuracy in design analysis and improved testing techniques. In an effort to increase efficiency in use of high performance and heavy-duty systems, especially in power generation and transmission subsystems, Condition-Based Maintenance (CBM) has emerged as an improvement over more costly time/use maintenance practices. CBM is being enabled by the same technological (testing, modeling, analysis) improvements that have spawned increased system performance.

As part of a combined experimental-theoretical analysis investigation effort related to CBM diagnostics and prognostics, an experimental gearbox failure test bed was constructed. The primary interest is the study of mechanical fault evolution in damaged rotating components that involve mechanical power transmission. As part of that same research effort a dynamics model of the system is being developed for response simulations and study of in situ mechanical dynamic fault models. Simulations of system vibratory responses will allow physical insights to be gained in vibratory measurement sensor placement and specification, dynamic system response to a fault, and fault detection signal processing algorithms. In this paper, the dynamics modeling of the gearbox drive rotor/bearing-foundation system using the Finite Element method is outlined and it’s relevance to diagnostics and prognostics is highlighted.

INTRODUCTION

Condition-Based Maintenance

CBM has been driven by the demand to increase system efficiency through elimination of unnecessary maintenance in a system. This approach to maintenance relies on monitoring the condition of a system in order to detect anomalies and on the ability to diagnose the health of critical components. An ultimate goal is to develop a prognosis of a faulted component’s Remaining Useful Life (RUL) and an associated functional impact on the system so that appropriate maintenance can be scheduled. The maturation of technologies in the areas of: measurement sensors, signal processing theory, digital processing hardware, dynamic system simulation, multi-sensor data analysis, and approximate reasoning have made CBM possible.

A typical monitoring system will process continuous time signals containing vibration and oil debris information. The detection phase involves a comparison to historical and nominal values for a statistically significant change. During the diagnostics process, specific fault recognition measures (figures of merit) are typically compared to threshold limits. Additional processing may determine a signature pattern in one, or multiple, fault measure(s). Automated reasoning is used to identify the fault type (cracked shaft or gear tooth, bearing spall), location, affected component, and severity of the fault. Prognosis builds upon the diagnostic assessment with a tracked parameter that is related to damage and a

future damage state prediction. These diagnostic and prognostic analyses can be based on either extensive statistical experimental data with an associated empirical model of the particular system, or from an estimate made using predictions from a detailed systems dynamics model, or from a combination of both.

MDTB and Transitional Failures

The Mechanical Diagnostics Test Bed (MDTB) 1 was built as an experimental research station for the study of fault evolution2 in mechanical gearbox power transmission components. It consists of a motor, gearbox, and generator on a steel platform. Gearboxes are instrumented with accelerometers, thermocouples, acoustic emission sensors, and oil debris sensors, and tests are run at various load profiles while logging measurement signals for later analysis. The test gearbox is mounted on a pedestal structure and is driven by a 30 HP variable speed AC motor through a torque cell shaft via gear couplings. A torsion load is supplied to the gearbox by a 75 HP AC (absorption) motor connected through an output torque cell, in the same manner as the input. The MDTB has the capability of testing single and double reduction industrial gearboxes with ratios from about 1.2:1 to 6:1 and with ratings that can range from 5 to 20 HP. Duty cycle profiles can be prescribed for any speed and load. Drive line speeds for tests to date have been fixed at 1750 RPM with variable load profiles that step up to maximum values of 2 to 5 times the rated torque of the test gearbox. The MDTB is shown in Figure 1.

Figure 1. Mechanical Diagnostics Test Bed A focus of efforts within CBM has been on heavy duty and high-performance power transmission systems containing rotary mechanical elements. These elements are driven to failure (mechanical structure discontinuity) through a complex interaction of component material and internal strains induced by the loading.

a. Helical Reduction Gear b. Overhung Pinion Shafting

Figure 2. Examples of Gearbox Component Material Detachment and Structural Dislocation

Reduction gears, overhung geared shafting, and roller element bearings are typically the first components to experience damage due to wear from operational loads. As examples, Figure 2 shows, a) a gearbox helical reduction gear with partially missing and damaged teeth, and b) a totally dislocated overhung pinion shaft, both of which came from gearbox accelerated fault -to-failures that were induced by controlled overloading.

From dynamics and fracture mechanics it is known that accelerated crack nucleation and micro-crack formation in components can occur due to start-ups and shutdowns, transient load swings, higher than expected intermittent loads, or defective component materials. More commonly, normal wear causes configuration changes (loose fit of assembled parts, work hardened surfaces, and reduced structural section areas) that contribute to increased or unexpected dynamic loading conditions. High cycle dynamic and transmission loads cause micro-crack incubation3 and formation at material grain boundaries in stress concentrated regions (especially between hardened surfaces and softer subsurface material interfaces, and at acute changes in component material geometry). The majority of crack growth evolves in a sub-critical propagation process of crack tip blunting, unstable crack formation, and crack elongation. As super-critical loading in the cracked material region is approached, growth accelerates resulting in material dislocation and detachment. Sub-critical crack evolution is highly dependent on a component’s material, geometry, loading conditions, and the particulars of the unique component crack growth cycle.

An opportunity exists to take corrective or compensatory actions during the periods of micro-crack incubation, formation, and sub-critical propagation in the material of a faulted component. Either of two beneficial actions could be taken: a corrective one to perform maintenance to repair or replace the part, or a compensatory one to reduce system operational loads to extend the life of the faulted part. The informed decision exists only if the system operator has the ability to detect that the fault exists, isolate it to the specific component, and assess its severity.

Model-Based Methodologies

The development of model-based prognostic capability for CBM requires a proven methodology to create and validate physical models that capture the dynamic response of the system under normal and faulted conditions. For a majority of systems, operational demands induce a slow (as compared to operational speed of a rotor) evolution in material property and/or component apparent configuration changes. The potential thus exists to track the fault through the filter of the system’s behavior via its dynamic (vibratory) response. Otherwise, no external difference in performance of a system is noticeable until immediately prior to end stage component material dislocation and parent system catastrophic failure occurs.

Current MDTB1 research goals include the development of an accurate nominal syst ems dynamics model that can be used for vibratory response predictions, and the focused study of theoretical dynamic models of cracked gear shafting and teeth, and bearing spall. Analysis using an accurate nominal dynamics model will provide insight into sensor placement and specification, and into the behavior of fault detection signal processing algorithms for different fault conditions. Also, a model characterizing the nominal system is requisite for dynamic fault model simulation. A principal goal is to include crack evolution into fault models. Validation through comparison and correlation between simulated and experimental responses of the system, with a fault that is not evolving and one that is, could also provide model refinement.

SYSTEM TOPOLOGY AND MODELING CONSIDERATIONS

There are still many research activities that need to take place before the gap is bridged between dynamics modeling of lumped parameter structural (finite element model) and in situ micro-mechanics systems in order to provide reliable fault predictions. Experimentally validated theoretical fault models could glean

some practical insights into bridging this gap and the development of reliable dynamic fatigue models.

The topology of the MDTB mechanical structure is presented with the schematic in Figure 3, and system overview in Figure 4. It provides a guide for the construction of the systems dynamic model and emphasizes salient features that need to be considered for inclusion. Decisions and assumptions need to be made about features such as foundation effects on the rotor system, shaft coupling anomalies, level of detail of finite element model (FEM) nodal meshing, and efficient lumped parameter characterizations of component structures that provide sufficient resolution for accurate dynamic simulation (such as roller bearings).

A consideration that differentiates the modeling of the MDTB from more common rotordynamic systems is the fact that the rotor system contains a pair of meshing gears. One of the most powerful and popular tools for modeling a rotordynamic system has been the finite element method (FEM)4. More recently the modeling of geared rotordynamic systems such as gearboxes has become feasible due to developments in modeling theory and computer technology, and in experimental validation techniques.

Figure 3. MDTB Hardware, Excitation, and Failure Overview

Gearbox dynamics problems differentiate themselves from other structural dynamic systems by the branching of transmitted power through a gear mesh. Traditionally vibrations due to local deflections at the meshing gear teeth due to contact and root base motion had been ignored. Rotary kinematics of rigid

System

Rotor and BearingSystem

Rotor Case (Fixed)

Foundation

SubSystem ComponentDrive Motor

Load Generator

Input Tach/TorqueTransducer

OutputTach/TorqueTransducer

Shaft(s)Gear(s)

Roller Bearing(s)

Rotor Coupling(s)

Misalignment

Static orEvolving Crack

BearingDynamics

Unbalance

Gearbox

Hardware

ShaftThroughCrack

Gear ToothFracture/

Fragmentation

Bearing Spall/Fret/Seizer

Failure

UnsafeVibration

Gear MeshMechanics

System Excitation/Fault Origin

Case Flexible Mount

TransmissionLoad

Drive Motor Gearbox Load Generator

Torque/Tachometer Cell

Pedestal

Shaft Coupling

•

Gear Mesh

Figure 2. Schematic of Mechanical Diagnostics Test Bed

motion through the mesh was used in dynamics system modeling (R1pitchθ1=smesh=R2pitchθ2). If vibrations induced in the gearbox case and rotary components due to gear meshing is of concern this treatment is inadequate.

Some common practices have been established in dynamic modeling of geared rotor power transmission systems5,6,7,8 with full-face width hub gearing. The base rotor hub is treated as a rigid disk with gear tooth contact, body, and root deflections lumped together to represent a dependent function of both pinion and gear rigid rotational motion. Two approaches have been used to define the dynamic response between gear pairs. One is referred to as transmission error 9, where normal forces at tooth contact are influenced primarily by the differences in topology of tooth profile geometry and the local elasticity of the contacting gear teeth. The second approach is to define the dynamic forces by combination of system dynamic loads to compute effective gear tooth deflection forces and apparent variable stiffness10 due to meshing action geometric orientation. The later more accurately characterizes a system in terms of effective parameters for dynamic system analysis.

For composite structural-rotordynamic modeling some problems rooted in foundational11,12,13 affects that had been observed in experiment and theory have been addressed. However, the nature of rotordynamic structures presents technical problems that require non-standard treatments for finite element modeling. The presence of gyroscopic effects due to high speeds, or even slow speeds in large inertia rotor systems, presents modes associated with flexible rotor shaft whirl. Theoretically whirl modes manifest themselves in complex mode shapes due to gyroscope force coupling. These modes are fairly well understood, but modeling to accurately reflect them in an actual complicated physical system can be difficult. Experimental testing techniques for validation and verification have only recently been developed14. Moreover, the presence of bearing systems linked to foundations along the chain-like structure of a rotor results in non-symmetry in the system mass and stiffness matrices that is difficult to handle with standard finite element processing techniques. A complete rotor system model is assembled from two separately formed finite element models. This allows special analyses and transformations to be performed that enable the two models to be combined into a tractable form for response simulations15,16. One FEM model is usually comprised of the grounded bearing-case-foundation structure, and the other is just of t he rotor system itself.

Other special issues need to be addressed in the construction of a gearbox system model. These have to do with improving accuracy in a general FEM representation of an actual system17,18 used for response predictions, and in the lumped parameter estimates of rotor/bearing 12,19,20,21, gear teeth elements22,23, and shaft coupling misalignment24. A procedure has been developed for composite modeling of gearbox systems for response simulation25.

MDTB SYSTEM AND SUBSYSTEM MODELS

The MDTB system model includes components of a single stage reduction gearbox, support pedestal, and drive line components from the drive motor to load generator. Drive line rotor components from the drive motor to the input shaft of the gearbox, and from the gearbox output shaft to the load generator, are given only torsional degrees-of-freedom in the model during the subsystem correlation phase of the model. The primary area of interest for response simulations is at the external top surfaces of the gearbox case and exposed surfaces of the input/output gearbox shafts. As part of the model development process, (Figure 5) the

ExperimentalModal andDynamicsAnalysis

Finite Elementand LumpedParameter

Characterization

Validation and

Model Updating

NominalLinear System

Model

Figure 4. Structural Dynamics Model Construction Process

gearbox case, pedestal, and complete drive line (torsional modes only) are validated and updated with experimental modal and dynamics analysis data. Experimental natural frequencies and mode shapes of tested gearbox case and pedestal components with free-free boundary (ungrounded) conditions are used to update free-free finite element representations of the same. Experimental dynamic drive line tests, conducted at zero speed, with half and full gearbox rating loads, performed with torsional impulses introduced at the system gear couplings, provided frequency response function (FRF) measurements from which dominant resonant frequencies associated with the torsional modes of vibration could be assessed. Resonant frequencies were used to validate parameters of the model rotary degrees-of-freedom in the drive line FEM. Figure 6 shows the FEMs used for free-free boundary condition testing (minus a bearing through hole in the gearbox housing).

The finite element software ANSYS 48 was used to generate the models. Drive line elements consisted of rotary beams with torsional degrees of freedom (ANSYS PIPE16 element), and the gearbox housing and pedestal were modeled with shell and beam elements (ANSYS SHELL93 and BEAM4). Gear mesh connectivity was modeled using lumped stiffness elements to depict nominal gear tooth stiffness (ANSYS COMBIN14) and nodal constraint equations (ui=Riθi) representing the translational displacements at the ends of zero free length springs as a function of the angular motion of the gear rotor hub. The full width hubs were taken to be rigid disks.

Experimental dynamic and modal parameters were obtained using a four channel dynamic analyzer, modal impact hammer, the software package STARModal 49, and single and triaxial accelerometers. Some typical experimental system FRFs are shown in Figure 5.

a. Drive Line (Torsional Only) Elements b. Gearbox Case

c. Gearbox Pedestal

Figure 4. Experimentally Validated System Component Finite Element Models

2885

3077

.5

2450

Hz

1232

Hz

(Bas

e &

Cas

e R

ock

abou

t Y)

2737

.5

2485

Hz

1900

Hz

(Bas

e an

d C

ase

Roc

k ab

out Y

)

665

Hz

(Z tr

ans

case

, B

ase

rock

)

101

Hz

(Cas

e/S

uppr

t Roc

k)

3525

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(Cas

e B

reat

hing

)

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0

0 500 1000 1500 2000 2500 3000 3500 4000

Freq (Hz, in 2.5 Hz bands)

Avg

Imag

(H

xy)

(db

re

1 V

/V)

X dir

Y dir

Z dir

Base rocking motion)

Figure 5. Typical FRFs for MDTB Gearbox on Pedestal Base

The system complete nominal finite element model will be assembled using all degrees-of-freedom of the rotor elements in the input and output gearbox shafts, and lumped parameter characterization of the roller element bearings. Disturbances will be considered as harmonic synchronous shaft speeds and N per revolution (N being an integer) periodic forces depending the disturbance anomaly.

DYNAMIC FAULT MODELS

Modeling of rotordynamic system faults has been an active area of research for the last three decades. The bulk of research efforts have been with the study of transversely cracked rotor shafts. Some work has been reported with defects in roller bearings, while very little has been accomplished with parametric modeling of gear tooth fracture.

Few structural dynamic models of dynamic, in situ, gear tooth fracture appear in the literature. However, variable stiffness tooth profiles have been modified for use in dynamic simulation of a root fracture in a gear tooth26. The damaged tooth’s stiffness profile is lessened by some degree (that is assumed proportional to the damage) per damaged gear mesh contact cycle.

An extensive amount of work has been done studying the dynamic response of a rotor with a transverse crack29. The most recent works feature simple rotors used to model a very simple lumped parameteric30 scheme and a simple distributed parameter scheme28,31. A more comprehensive scheme has been developed using finite elements27. Conflicting results were reported for which spectral response frequencies to focus on (1X or 2X rotor speed) in order to identify a system fault. The simplified models used a breathing crack scheme that prescribed bilinear switching (open or closed), and neglected stiffness cross-coupling terms due to variations from the breathing. The more complete FEM method used continuously variable breathing functions, which were a function of the system response. The switching functions were determined by numerical integration of the system's governing equations for steady operating conditions.

In terms of systems dynamic modeling, roller bearing defects32,33,34 appear to be adequately represented by periodic point impulses. A single impulse represents elastic impact on smooth rolling contact surfaces at a point of an asperity. Periodicity of an impulse depends on the location of the point defect, and the number of rolling elements in the bearing.

The nominal lumped parameter (FEM) system model (Model based: inertia-[M], damping-[C], gyroscopic-[G], and stiffness-[K] parameters) will be modified to incorporate system faults for response simulations. Faults will be incorporated into the overall system model through time varying stiffnesses, perturbations in those stiffnesses, and perturbation forces as prescribed by current fault models, see Equation (1).

)()(])()([][][ tFtFytKtKKyGCyM faultfaultfault δδ −=∆+∆++++ &&& (1)

DETECTION AND DIAGNOSTICS

The seed of CBM may be found in signal processing techniques and diagnostic methods. Many frequency and time-frequency domain methods have been developed primarily for vibratory response signals35,41, (Table 1). Typically it is assumed that signals are acquired from one or more advantageously placed vibration sensor(s), typically surface mounted accelerometers. Signals are processed and analyzed for changes about some primary frequency (fractional, one or two times a shaft rotational, and/or gear mesh frequency). Real-time assessment of signature changes in the signal is made as the rotating structural component goes from a healthy to a faulted condition.

CBM utilizes the detection of signature changes in a sensor signal as markers to aid in determination of a system’s state of health. The uniqueness of individual systems, and of individual fault types (cracked gear or shaft, worn bearing), requires both a degree of system dynamics modeling and analysis, and corroborative experimental data in order to properly design and configure a CBM diagnostics system. Advances in measurement technology and analysis, and structural dynamics modeling theory, have enabled more accurate prediction of a system’s response, and measurement of dynamics phenomenon. The MDTB will exploit advances to develop effective diagnostic protocols using the latest figures of merit and automated reasoning schemes.

Diagnostic methods generally focus on the identification of certain types of faults such as gear tooth fracture37,38,39,40,41,42, roller bearing spall/fret asperity43,44,45,46, gear shaft transverse crack47, and a determination of the extent of the fault damage.

FEATURE DESCRIPTIONRMS Root-mean-square of the raw signature

ACH Change in root-mean-square level

FFT Conversion to frequency domain andspectrum analysis

SO1 First shaft order vibration levelamplitude

SO2 Second shaft order vibration levelamplitude

FM0 Zero-order Figure-of-Merit, indicator oflevel of mesh tones in gear average

FM2 Tooth Fracture Figure-of-Merit (fractionof normalized kurtosis)

FM4 Bootstrap Recognition Figure-of-Merit(normalized kurtosis of enhanced signalaverage)

M6A

M6*

Variation of sixth normalized statisticalmoments of enhanced signal average

M8A Variation of eighth normalized statisticalmoments of enhanced average

NA4

NA4*

Quasi-normalized kurtosis of semi-enhanced signal average

NB4

NB4*

Quasi-normalized kurtosis ofbandpassed signal average's envelope.

EK Normalized kurtosis of envelope ofbandpass signal average with dominantharmonics removed.

I.P.

I.F.

Instantaneous phase and frequencystandard deviation of bandpassed signalaverage's envelope.

Table 1. Figures of Merit for Identification/Diagnostics

(copied with permission from reference 36)

For gear tooth faults on the MDTB, some specific signal processing techniques have provided indications of damage well before macroscopic damage of the gear teeth was evident. These include interstitial processing40, where envelope spectral, kurtosis, and other statistical techniques are applied to casing acceleration data that has been pre-processed by bandpass filtering between higher harmonics of gear mesh frequency. Figure 6 shows an example of a run in which interstitial envelope spectral peak values at gear output speed give strong indication of gear damage before that damage is visible via borescopic inspection (three of four accelerometers).

0.00001

0.0001

0.001

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0.1

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3/19/9812:00

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Date/Time

No

rmal

ized

Am

pli

tud

e

Accelerometer 2Accelerometer 3Accelerometer 4Accelerometer 5Start 3X Load

2:00 AM: No visible damage

3:00 AM:One broken tooth, one cracked

8:15 AM: 8 teeth missing

5:00 AM: Two broken teeth

Figure 6. Interstitial Envelope Spectral Peak Value as a Function of Time (Run 14)

IIRAdaptiveThreshold Wavelet

Magnitude

BinaryDetectionSignal

11:30:9.5 11:30:10 12:30:00 12:30:0.5

Undamaged Two teethbroken

Figure 7. Wavelet Magnitude with IIR Adaptive Threshold (Run 5)

Another technique found to provide early warning is the continuous wavelet transform (CWT). Figure 7 shows the CWT coefficients at a particular scale (corresponding to a frequency of 550 Hz, away from shaft and gear mesh harmonics). The left side of the plot shows the coefficients before damage to the gear teeth had occurred, and the right side following damage. Note that an Alpha-Beta tracker was used to generate a robust threshold (shown in the figure) for the coefficient values. The CWT demonstrated diagnostic capabilities on the same order as those associated with the interstitial methods.

APPLICATION TO PROGNOSTICS

The goal in prognostics is determining the RUL of a monitored component. To achieve prognostics, we expect that there will need to be features that are suit able for tracking and prediction. Some research50,51

has indicated that many features used for diagnostics might not be suitable for prediction. Moreover, researchers have postulated that different feature sets and classification rules should be used for diagnostics and prognostics.

Penn State ARL is currently evaluating future state estimation using subspace and non-linear dynamics methods. Optimal linear estimation is an attempt to optimally estimate a state vector using measurements that may be corrupted with noise. This typically involves minimizing the mean square error of the estimation. There are three types of estimation: filtering, smoothing and prediction. Filtering involves the estimation of the state vector at the current time using past measurements. In smoothing, the state vector estimation is made for a prior time using the measurements made up until that point. Prediction is the estimation of the state vector at a future time using the past measur ements. The Kalman and Alpha-Beta-Gamma tracking filters can be used to estimate the feature state vector by performing a one-step-ahead and n-steps-ahead predictions. The estimated position, velocity, and acceleration can be used to estimate the time remaining in an event.51 Nonlinear dynamics methods also hold promise for state space prediction of damage. The methods exploit the time scale separation between fast dynamic variables and a slow drifting parameter that is related to damage. Locally linear tracking models are constructed using data from a reference system sampled on a fast time scale, employing delay coordinate embedding. The short time prediction error of the tracking models is used as the parameter drift observer.52

E x p e r i m e n t

G e a r r u n - t o - f a i l t e s t

( f a t i g u e c r a c k , p i t t i n g )

D e v e l o p m e n t o f s e n s o r

o b s e r v a b l e s

Vi r tua l Sys tem

G e a r f a u l t

M e s h i n g s t i f f n e s s ( F E M )

E q u a t i o n s o f m o t i o n

Gear s ta t ic /dynamic loads

D i a g n o s t i c

A s s e s s m e n t

F a u l t i s o l a t i o n

a n d s e v e r i t y

F a u l t T r a c k i n g

M e t h o d s

P r o b a b i l i s t i c

G e a r F a i l u r e

M o d e l

S t r e s s / S t r a i n A n a l y s i s

a n d F r a c t u r e

M e c h a n i c s C r a c k P r o p

M o d e l ( F E M )

R e m a i n i n g

U s e f u l

L i fe

P r e d i c t i o n a t

E x p e c t e d

L o a d s

Diagnosis Prognosis

Dynamic(vibrat ion)

E x p e c t e d F u t u r e

L o a d s

Figure 8. Elements of Model-Based Machinery Diagnostics and Prognostics

Figure 8 is a notional design of the parts of the diagnostic and prognostic process.52 The dynamic model representing system operation is used to estimate the static and dynamic load of a gear. Damage such as tooth breakage could be evaluated with an FEM-based crack propagation model to predict growth of gear tooth fatigue crack. The crack geometry and tooth stiffness (or stress concentration factor) calculated by the FEM model could be feed back to the virtual gearbox which will, in turn, predict the new vibration and loading. In actual operation, the model-to-actual comparison may be accomplished explicitly using generalized residuals or implicitly using learned association (neural network) methods. Developing this capability will require dedicated research in this area and is a source of significant effort.

SUMMARY

An overview of the MDTB research modeling effort and considerations has been presented in the context of improving diagnosibility for mechanical systems CBM and machinery prognostics. The relevance of a parametric system dynamics model for the transitional gearbox testbed was presented. The focus of the MDTB is to collect transitional data on mechanical component faults as they evolve towards failure and evaluate such model-based diagnostic/prognostic methods. The evaluation is accomplished through the comparison of the system experimentally observed (vibratory) behavior, and the behavior derived from the dynamics model. The dynamic model of the MDTB, based on a finite element development, provides a numerical test bed for studies that may be correlated with experimental data2. Refined fault models using the system dynamics model are planned to allow identification and diagnosis of fault signatures. Developing prognostics will require future work using the system and subsystem models concentrating on multiple fault circumstances as well as advancing capabilities in tracking and prediction.

ACKNOWLEDGMENT

This work was supported by the Multidisciplinary University Research Initiative for Integrated Predictive Diagnostics (Grant Number N00014-95-1-0461) sponsored by the Office of Naval Research. The authors thank Matt Erickson for the initial MDTB modal testing results.

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