Fred K. Choy

Detection of cracks in beam structures using measurements of natural frequencies

Abstract A method based on measurements of natural frequencies of structures has been developed for the detection of crack location and quantification of damage magnitude in a uniform beam under simply supported or cantilever boundary conditions. The method adopts rotational massless springs in the beam element as a mechanical model to represent the local flexibility introduced by a crack. For a given natural frequency and a damage location, the characteristic equation can be solved to provide numerical value of the stiffness of the rotational spring. The intersection points of the values of the normalized crack stiffness K at various natural frequencies ω i along the axial direction of the beam represent the possible locations of the crack. Furthermore, the numerical value K has been shown to be directly related to the damage magnitude as Δ I⧸I , where Δ I is the reduction of section modulus and I is the original undamaged section modulus. Two numerical case studies are given to demonstrate the validity of the method.

Analysis of the effects of surface pitting and wear on the vibration of a gear transmission system

Abstract A comprehensive procedure to simulate and analyse the vibrations in a gear transmission system with surface pitting, wear, and partial tooth fracture of the gear teeth is presented. An analytical model was developed where the effects of surface pitting and wear of the gear tooth were simulated by phase and magnitude changes in the gear mesh stiffness. Changes in the gear mesh stiffness were incorporated into each gear-shaft model during the global dynamic simulation of the system. The overall dynamics of the system were evaluated by solving for the transient dynamics of each shaft system simultaneously with the vibration of the gearbox structure. In order to reduce the number of degrees-of-freedom in the system, a modal synthesis procedure was used in the global transient dynamic analysis of the overall transmission ststem. An FFT procedure was used to transform the averaged time signal into the frequency domain for signature analysis. In addition, the Wigner-Ville distribution was also introduced to examine the gear vibration in the joint time-frequency domain for vibration pattern recognition. Experimental results obtained from a gear fatigue test rig at NASA Lewis Research Center were used to evaluate the analytical model.

Vibration Signature Analysis of a Faulted Gear Transmission System

Abstract : A comprehensive procedure in predicting faults in gear transmission systems under normal operating conditions is presented. Experimental data was obtained from a spiral bevel gear fatigue test rig at NASA Lewis Research Center. Time synchronous averaged vibration data was recorded throughout the test as the fault progressed from a small single pit to severe pitting over several teeth, and finally tooth fracture. A numerical procedure based on the Winger-Ville distribution was used to examine the time averaged vibration data. Results from the Wigner-Ville procedure are compared to results from a variety of signal analysis techniques which include time domain analysis methods and frequency analysis methods. Using photographs of the gear tooth at various stages of damage, the limitations and accuracy of the various techniques are compared and discussed. Conclusions are drawn from the comparison of the different approaches as well as the applicability of the Wigner-Ville method in predicting gear faults.

A bulk flow model of a brush seal system

Fibers can be readily fabricated into a variety of seal configurations that are compliant and responsive to high speed or lightly loaded systems. A linear, circular, or contoured brush seal system is a contact seal consisting of the bristle pattern and hardened interface. When compared to a labyrinth seal, the brush seal system is superior and features low leakage, dynamic stability, and permits compliant structures. But in turn, the system usually requires a hardened smooth interface and permits only limited pressure drops. Wear life and wear debris for operations with static or dynamic excitation are largely undetermined. A seal system involves control of fluid within specific boundaries. The brush and rub ring (or rub surface) form a seal system. Design similitudes, a bulk flow model, and rub ring (interface) coatings are discussed. The bulk flow model calculations are based on flows in porous media and filters. The coatings work is based on experience and expanded to include current practice.

Simulation and Control of an Active Tilting-Pad Journal Bearing

This study developed an active tilting-pad journal bearing with a feedback control system to regulate the orbit of a rotating shaft. The control is implemented by means of linear actuators installed behind the pivot of each pad, which allow the radial motion of the pads in real time. The control design uses the linear feedback of the state variables of the bearing-rotor system, with the feedback gains determined by the optimization of a quadratic performance index. The optimization is based on a linear spring-mass model that incorporates the direct stiffness and damping elements associated with each of the bearing pads. This linear model is found by the simulation of the system under small perturbations using a nonlinear Reynolds equation model. The nonlinear model is capable of simulating the radial motions of the pads by the actuators and is used to verify the effectiveness of the feedback control. It is shown that certain design parameters in the quadratic performance index may be used to determine both the stiffness and the damping of the closed-loop bearing system and that the shaft orbit can be thereby suitably regulated.

Fault identification of beams on elastic foundation

Abstract The capability of identifying both location and severity of damages of faulted elements in a structural system is greatly needed under the present demands of constantly maintaining the safety of civil engineering structures. Presented in this paper is a methodology based on vibration theory that can be used for the detection of faults in a beam of either uniform or nonuniform cross section and under a variety of boundary conditions, including simple support, cantilever support, and beam on elastic foundation. Theoretical developments of the methodology are presented first, followed by numerical experiments to demonstrate the feasibility of the method. Numerical experiments include various damage scenarios such as those faults occurring in a beam section as well as in a subgrade foundation. Furthermore, damage scenarios involving both single fault and multiple faults are also presented. The defect of the supporting subgrade foundation can be modeled either as degrading subgrade stiffness or increasing damping values. Numerical experiments demonstrate the feasibility of the developed NDT methodology which warrants the next stage of field study.

Matrix decomposition based feature extraction for murmur classification.

Heart murmurs often indicate heart valvular disorders. However, not all heart murmurs are organic. For example, musical murmurs detected in children are mostly innocent. Because of the challenges of mastering auscultation skills and reducing healthcare expenses, this study aims to discover new features for distinguishing innocent murmurs from organic murmurs, with the ultimate objective of designing an intelligent diagnostic system that could be used at home. Phonocardiographic signals that were recorded in an auscultation training CD were used for analysis. Instead of the discrete wavelet transform that has been used often in previous work, a continuous wavelet transform was applied on the heart sound data. The matrix that was derived from the continuous wavelet transform was then processed via singular value decomposition and QR decomposition, for feature extraction. Shannon entropy and the Gini index were adopted to generate features. To reduce the number of features that were extracted, the feature selection algorithm of sequential forward floating selection (SFFS) was utilized to select the most significant features, with the selection criterion being the maximization of the average accuracy from a 10-fold cross-validation of a classification algorithm called classification and regression trees (CART). An average sensitivity of 94%, a specificity of 83%, and a classification accuracy of 90% were achieved. These favorable results substantiate the effectiveness of the feature extraction methods based on the proposed matrix decomposition method.

Vibration signature and modal analysis of multi-stage gear transmission

Abstract An analysis is presented for multi-stage multi-mesh gear transmission systems which predicts the overall system dynamics and transmissibility to the gear box or the enclosed structure. The modal synthesis approach of the analysis treats the uncoupled lateral/torsional modal characteristics of each stage or component independently. The vibration signature analysis evaluates the global dynamics coupling in the system. The method synthesizes the interaction of each modal component or stage with nonlinear gear mesh dynamics and modal support geometry characteristics. The analysis simulates transient and steady state vibration events due to torque variations, speed changes, rotor imbalances and gear box support motion excitations. A vibration signature analysis scheme examines the overall dynamic characteristics of the system, and the individual modal component responses. The gear box vibration analysis also examines the spectral characteristics of the support system.

Gear Fault Detection with Time-Frequency Based Parameter NP4

The fact that the Wigner-Ville Distribution (WVD) can represent the energy of a gear vibration signal was used for the gear damage detection. A new gear fault detection parameter called NP4 is derived from the joint timefrequency Wigner-Ville Distribution. The novelty of the NP4 parameter is in application of the previously de®ned statistical parameter called kurtosis to the WVD data and its interpretation for gear fault detection. The important distinct feature of the fault detection parameter NP4 from other fault detection parameters, such as ®gures of merit, is that it does not compare a measured gear vibration signal with the ideal one. Thus, the parameter NP4 can work for the fault detection without a long recorded vibration history of the gear. New techniques for enhancing the information content of the WVD of the gear vibration signal and the reliability of the parameter NP4 are also described. The utility of the gear fault detection parameter has been demonstrated using numerous gear vibration experiments. A correlation between the level of the gear tooth damage and the value of the gear fault detection parameter NP4 is demonstrated. The gear fault detection strategy based on the developed parameter NP4 is presented and investigated in the paper.

New Gear-Fault-Detection Parameter by Use of Joint Time-Frequency Distribution

Anewgear-fault-detectionparametercalledNP4 isintroduced.Thisfault-detectionparameterutilizestheproperties of the joint time ‐frequency analysis given by the Wigner ‐Ville distribution (WVD) and kurtosis. With the WVD, the instantaneous power of the gear-vibration signature for one complete rotor revolution can be obtained. The presence of single-gear-tooth damage can be manifested by the existence of an instantaneous power distribution with a peakedness larger than the normal distribution. The normalized kurtosis, a fourth-order statistical parameter calculated for the instantaneous power distribution, provides the gear-fault-detection parameter NP4. The developed fault-detection parameter NP4 is sensitive to gear-tooth damage, especially for damage in a single tooth. The application of this NP4 fault-detection parameter was demonstrated by experimental data obtained from a gear test rig. The results showed that the NP4 parameter, used with the WVD, can provide an accurate fault identie cation of gear-tooth damage. The parameter NP4 would be of help to the practitioners in the e eld of machine health monitoring.