Showing papers in "Journal of Vibration and Acoustics in 2001"

Wavelet Analysis and Envelope Detection For Rolling Element Bearing Fault Diagnosis—Their Effectiveness and Flexibilities

Abstract: The components which often fail in a rolling element bearing are the outer-race, the inner-race, the rollers, and the cage. Such failures generate a series of impact vibrations in short time intervals, which occur at Bearing Characteristic Frequencies (BCF). Since BCF contain very little energy, and are usually overwhelmed by noise and higher levels of macro-structural vibrations, they are difficult to find in their frequency spectra when using the common technique of Fast Fourier Transforms (FFT). Therefore, Envelope Detection (ED) is always used with FFT to identify faults occurring at the BCF. However, the computation of ED is complicated, and requires expensive equipment and experienced operators to process. This, coupled with the incapacity of FFT to detect nonstationary signals, makes wavelet analysis a popular alternative for machine fault diagnosis. Wavelet analysis provides multi-resolution in time-frequency distribution for easier detection of abnormal vibration signals. From the results of extensive experiments performed in a series of motor-pump driven systems, the methods of wavelet analysis and FFT with ED are proven to be efficient in detecting some types of bearing faults. Since wavelet analysis can detect both periodic and nonperiodic signals, it allows the machine operator to more easily detect the remaining types of bearing faults which are impossible by the method of FFT with ED. Hence, wavelet analysis is a better fault diagnostic tool for the practice in maintenance.

Inducing Passive Nonlinear Energy Sinks in Vibrating Systems

Abstract: We study the inducement of passive nonlinear sinks in linear vibrating systems. These are substructures that absorb vibrational energy in a one-way, irreversible fashion. The systems considered are composed of strongly coupled, grounded damped linear oscillators with a strongly nonlinear attachment at the end. Applying a complex averaging technique we derive a set of modulation equations that is directly amenable to physical interpretation, and provides insight into the energy pumping phenomenon. For the case of a two DOF system we show that nonlinear energy pumping occurs when a certain frequency of envelope modulation crosses through zero; then the dynamics of the envelope modulation of the motion resemble the dynamics of a forced rigid body. For the case of an impulsively loaded multi-DOF chain with a nonlinear attachment at the end, we show that after some initial transients the response of the nonlinear attachment sets to a motion dominated by a fast frequency identical to the lower bound of the propagation zone of the linear chain. This feature reduces the study of energy pumping in the chain to a two DOF equivalent problem. The applications of the energy pumping phenomenon to practical engineering problems are discussed.

Active Control of Periodic Structures

Abstract: Conventional passive periodic structures exhibit unique dynamic characteristics that make them act as mechanical filters for wave propagation. As a result, waves can propagate along the periodic structures only within specific frequency bands called the Pass Bands and wave propagation is completely blocked within other frequency bands called the Stop Bands. In this paper, the emphasis is placed on providing the passive structures with active control capabilities in order to tune the spectral width and location of the pass and stop bands in response to the structural vibration. Apart from their unique filtering characteristics, the ability of periodic structures to transmit waves, from one location to another, within the pass bands can be greatly reduced when the ideal periodicity is disrupted resulting in the well-known phenomenon of Localization. In the case of passive structures, the aperiodicity (or the disorder) can result from unintentional material, geometric and manufacturing variability. However, in the case of active periodic structures the aperiodicity is intentionally introduced by proper tuning of the controllers of the individual substructure or cell. The theory governing the operation of this class of Active Periodic structures is introduced and numerical examples are presented to illustrate their tunable filtering and localization characteristics. The examples considered include periodic/aperiodic spring-mass systems controlled by piezoelectric actuators. The presented results emphasize the unique potential of the active periodic structures in controlling the wave propagation both in the spectral and spatial domains in an attempt to stop/confine the propagation of undesirable disturbances.

Feedback stability limits for active isolation systems with reactive and inertial actuators

Abstract: Some of the compromises inherent in using a passive system to isolate delicate equipment from base vibration can be avoided using fully active skyhook damping. Ideally, a secondary force, which is made proportional to the absolute equipment velocity by a feedback controller, acts only on the equipment and so the response of the system under control, between the secondary force input and the collocated velocity output, i.e., the plant response, is proportional to the driving point mobility of the mounted equipment. The frequency response of the plant is guaranteed to have a positive real part under these ideal conditions, and so the feedback system is unconditionally stable for any positive real feedback gain. In practice, the actuator generating the secondary force must either react off the base structure or an inertial mass. In both of these cases the plant response is no longer guaranteed to be positive real and so the control system may become unstable at high gains. Expressions for the overall plant responses are derived for both of these arrangements, in terms of the dynamic response of the individual parts of the isolation system. When using a soft mount, the stability of the reactive system is found to be surprisingly tolerant of the additional contributions to the plant response from the reactive force. In order for the inertial system to be stable with a high feedback gain, however, the natural frequency of the actuator must be well below the natural frequency of the equipment on the mounts. Experimentally measured plant responses are compared with those predicted from theory for both types of actuator and the performance of practically implemented feedback controllers is discussed.

The Effect of Tooth Wear on the Vibration Spectrum of a Spur Gear Pair

Abstract: In this paper, the effect of tooth wear on the vibration spectrum variation of a rotating spur gear pair is studied. In order to approximate the dynamic characteristics of an engaging spur gear pair, the load sharing alternation, position dependent mesh stiffness, damping factor and friction coefficient are considered in the mathematical model. The wear prediction model proposed by Flodin et al. is used to simulate the tooth profile wear process. The variation of the vibration spectra introduced from the interaction between the sliding wear and the dynamic load is simulated and analyzed. Numerical results indicate that the dynamic load histogram of an engaging spur gear pair may change greatly with the tooth wear. This finding implies that the variation of the gear vibration spectrum might be used to monitor the tooth wear of an engaging spur gear pair.

Coupled Helmholtz Resonators for Acoustic Attenuation

Abstract: Helmholtz resonators are used in a variety of applications to reduce the transmission of unwanted sound. This work demonstrates that mechanically coupled resonators can be used to design a particular transmission loss response, provide a wider bandwidth of attenuation, and adapt the transmission loss characteristics of a structure to attenuate disturbances of varying frequency. An analytical model is developed for a single, coupled resonator system mounted on a one-dimensional duct. Experiments are conducted on a similar system that uses a thin membrane to couple the resonator volumes. A simplistic model of the membrane is presented to estimate equivalent piston properties from measured physical properties. Experiments confirm that the coupled resonator system behaves as predicted by the model simulations, and that the transmission loss can be shaped by adjusting the mass or stiffness of the coupling member. The experimental results also illustrate the structural-acoustic coupling effects between the resonators and the membrane, and indicate that a more inclusive model of the membrane and acoustic dynamics is required in order to accurately predict the resonator transmission loss.

An Active Microvibration Isolation System for Hi-tech Manufacturing Facilities

Abstract: This paper presents an active microvibration isolation system using voice-coil linear motors, and pneumatic and piezoelectric actuators. This system is designed to reduce microvibration of the six degrees-of-freedom associated with the rigid body modes of the vibration isolation table by feeding back the pseudo absolute displacement and velocity of the table. To improve vibration isolation performance, a feed-forward control link is added to the sway components in each dimension. This system can also control bending modes of the table in the frequency range up to 200 Hz by employing a proposed Virtual Tuned-Mass Damper control strategy, which is a type of the pole assignment method. In this approach, the pole locations are chosen by a genetic algorithm. For ambient microvibration of the floor around 0.5 cm/s 2 and for small earthquakes of around 8 cm/s 2 a reduction by a factor of 100 was achieved in the acceleration of the vibration isolation table. Moreover, the vibration of the isolation table was decreased over the entire frequency range. This system also showed good vibration control performance when an impact excitation was applied directly to the table; vibration was damped out within about 0.1 sec. Additionally, the resonance amplitudes around the bending modes of the table were reduced from 1/5 to 1/15 by the Virtual Tuned-Mass Damper method.

Vehicle Evaluation of the Performance of Magneto Rheological Dampers for Heavy Truck Suspensions

Abstract: This study is intended to complement many existing analytical studies in the area of semiactive suspensions by providing afield evaluation of semiactive magneto rheological (MR) primary suspensions for heavy trucks. A set of four controllable MR dampers are fabricated and used experimentally to test the effectiveness of a semiactive skyhook suspension on a heavy truck. In order to evaluate the performance of the semiactive suspensions, the performance of the truck equipped with the MR dampers is primarily compared with the performance of the truck equipped with the stock passive dampers. The performance of the semiactive system and the original passive system are compared for two different driving conditions. First, the truck is driven over a speed bump at approximately 8-11 kmh (5-7 mph) in order to establish a comparison between the performance of the MR and stock dampers to transient inputs at the wheels. Second, the truck is driven along a stretch of relatively straight and level highway at a constant speed of 100 kmh (62 mph) in order to compare the performance of the two types of dampers in steady state driving conditions. Acceleration data for both driving conditions are analyzed in bath time and frequency domains. The data for the speed bumps indicate that the magneto rheological dampers used (with the skyhook control policy) in this study have a small effect on the vehicle body and wheel dynamics, as compared to the passive stock dampers. The highway driving data shows that magneto rheological dampers and the skyhook control policy are effective in reducing the root mean square (RMS) of the measured acceleration at most measurement points, as compared to the stock dampers.

Dynamic Modeling and Vibration Analysis of the Atomic Force Microscope

Abstract: The objective of this paper is to formulate the equations of motion and to investigate the vibrations of the atomic force microscope (AFM), which is divided into the contact and noncontact types. First, the governing equations of the AFM including both base oscillator and piezoelectric actuator are obtained using Hamilton's principle. In the dynamic analysis, the piezoelectric layer is treated as a sensor to measure the deflection and as an actuator to excite the AFM via an external voltage. The repulsive force and van der Waals (vdW) force are considered in the contact and noncontact types of the AFM, respectively. Some important observations are made from the governing equations and boundary conditions. Finally, numerical results using a finite element method are provided to illustrate the excitation effects of base oscillator and piezoelectric actuator on the dynamic responses.

Modeling and Control of Acoustic Ducts

Abstract: This paper presents closed-form mathematical models for an acoustic duct with general boundary conditions. These infinite-dimensional models are derived using symbolic computations. A new method to obtain finite dimensional approximations of infinite-dimensional models using quartic functions is presented. The theoretical models are compared with the experimental data obtained for the KSU duct. The experimental results of a new robust broadband feedback controller, designed using passivity-based techniques, are presented. The controller design is shown to be robust to the unmodeled dynamics and parametric uncertainty.

Vibration-Based Damage Identification in Structures Exhibiting Axial and Torsional Response

Abstract: A method is derived to detect and localize linear damage in a structure using the measured modal vibration parameters. This method is applicable when the vibration strain energy is stored in the axial or torsional modes, which differentiates it from previously derived strain-energy-based methods. The new method is compared to the previously derived flexibility-change method for comparison. Both methods are verified by application to an analytical eight degree of freedom model. Experimental validation for both methods is also presented by application to an experimental eight degree of freedom spring-mass structure.

A New Cepstral Analysis Procedure of Recovering Excitations for Transient Components of Vibration Signals and Applications to Rotating Machinery Condition Monitoring

Abstract: A new cepstral analysis procedure with the complex cepstrum for recovering excitations causing multiple transient signal components from vibration signals, especially from rotor vibration signals, has been developed. Along with the problem of singularity, a major problem of the cepstrum is that it cannot provide a correct distribution of the excitations. To solve these problems, a signal preprocessing method, whose function is to provide a definition for the distribution of the excitations along the quefrency axis and remove singular points from the transform, has been added to the cepstrum analysis. With this procedure, a correct distribution of the excitations can be obtained. An example of application to the condition monitoring of rotor machinery is also presented.

Effect of Material and Geometry on the Sound and Vibration Transmission across a Sandwich Beam

Abstract: This paper studies sound and vibration transmission across a sandwich beam made of anisotropic materials. In our previous study, we have found that there is a significant increase in the transmission loss for the sandwich beam with anisotropic materials as compared with isotropic ones. This paper presents an extensive numerical study of the effects of damping, thickness of the laminae and density of the material on the sound transmission loss. This work may eventually lead to a new way of designing sandwich structures with high vibration and noise isolation performance.

Shilnikov Chaos and Dynamics of a Self-Sustained Electromechanical Transducer

Abstract: The dynamics of a self-sustained electromechanical transducer is studied. The stability of the critical points is analyzed using the analytic Routh-Hurwitz criterion. Analytic oscillatory solutions are obtained in both the resonant and non-resonant cases. Chaotic behavior is observed using the Shilnikov theorem and from a direct numerical simulation of the equations of motion.

The Dynamics of a Ball-Type Balancer System Equipped with a Pair of Free-Moving Balancing Masses

Abstract: This study is devoted to evaluate the performance of a ball-type balancer system that is installed in high-speed optical disk drives. The ball-type balancer system, composed of a circular runway and free-moving balls inside, is designed for reducing radial vibrations induced by the inherent unbalance of the rotating system. A balancer system equipped with a pair of balls is considered in this study for its capability to reach possible near-elimination of radial vibrations as opposed to the serious sizing problem of a single balancing-ball system. A mathematical model is first established to describe the dynamics of the balls and rotor system. Utilizing the method of multiple scales and assuming the smallness of radial vibrations, the system dynamics on the slow time scale is represented by eight first-order autonomous differential equations, which accommodate the radial vibratory motions and ball behaviors. The steady-state solutions of these slow equations are then solved and their stability analyzed to predict settling ball positions. The residual vibrations are computed to evaluate the performance of the balancer system and then the design guidelines are distilled for engineers to design the balancer system.

Natural Frequencies of Rotating Uniform Beams with Coriolis Effects

Abstract: A Dynamic Finite Element (DFE) for vibrational analysis of rotating assemblages composed of beams is presented in which the complexity of the acceleration, due to the presence of gyroscopic, or Coriolis forces, is taken into consideration. The dynamic trigonometric shape functions of uncoupled bending and axial vibrations of an axially loaded uniform beam element are derived in an exact sense. Then, exploiting the Principle of Virtual Work together with the nodal approximations of variables, based on these dynamic shape functions, leads to a single frequency dependent stiffness matrix which is Hermitian and represents both mass and stiffness properties. A Wittrick-Williams algorithm, based on a Sturm sequence root counting technique, is then used as the solution method. The application of the theory is demonstrated by two illustrative examples of vertical and radial beams where the influence of Coriolis forces on natural frequencies of the clamped-free rotating beams is demonstrated by numerical results.

Active-passive hybrid constrained layer for structural damping augmentation

Abstract: The invention is a method and apparatus for surface damping augmentation. The apparatus of the present invention includes a viscoelastic material, a hybrid constraining layer mechanically connected to the viscoelastic material and having an active material and a passive material, and the active material mechanically connected to the passive material. The method provides for selecting an active constraining material, selecting a passive constraining material, forming a hybrid constraining layer from the active constraining material and the passive constraining material, and mechanically connecting the hybrid constraining layer to a viscoelastic material.

A Flexible Rotor on Flexible Bearing Supports: Stability and Unbalance Response

Abstract: An experimental study of the effects of bearing support flexibility on rotor stability and unbalance response is presented. A flexible rotor supported by fluid film bearings on flexible supports was used with fifteen support configurations. The horizontal support stiffness was varied systematically while the vertical stiffness was kept constant. The support characteristics were determined experimentally by measuring the frequency response functions of the support structure at the bearing locations. These frequency response functions were used to calculate polynomial transfer functions that represented the support structure. Stability predictions were compared with measured stability thresholds. The predicted stability thresholds agree with the experimental data within a confidence bound for the logarithmic decrement of ±0.01. For unbalance response, the second critical speed of the rotor varied from 3690 rpm to 5200 rpm, depending on the support configuration. The predicted first critical speeds agree with the experimental data within -1.7 percent. The predicted second critical speeds agree with the experimental data within 3.4 percent. Predictions for the rotor on rigid supports are included for comparison.

Thermally Induced Vibration of an Internally Heated Beam

Abstract: Virtually all previous research on thermally induced vibrations has investigated vibrations caused by surface heating. This paper describes the first detailed study of a thermally induced vibration caused by internal heating. A mathematical model was developed to predict the thermal-structural behavior of an internally heated beam. The results from the model were verified using experimental data for an internally heated beam undergoing thermally induced vibrations. The model was shown to predict the steady-state temperatures accurately. The model predicted the steady-state displacements adequately, although it predicted the displacement histories with some error. The analysis showed that the natural frequency of the beam was more important than the heating rate in determining if vibrations will occur. Once initiated, the amplitude of the vibration increased until the amplitude was such that the heat removed by convection balanced the internal heating. The steady-state amplitude was not affected by the initial displacement of the beam. The convection heat transfer caused the vibrations and controlled the steady-state amplitude. This study showed that thermally induced vibrations of internally heated beams belong to the class of vibrations called self-sustaining oscillations.

On the Modal Testing of Microstructures: Its Theoretical Approach and Experimental Setup

Abstract: Small and lightweight structures have very high natural frequencies and small elastic displacement compared to ordinary structures. Due to limited excitation bandwidth and relatively large size of pick up devices, conventional modal testing facilities are not feasible for testing MEMS structures. A modal testing system based on the base excitation principle was developed in this research. In the meantime, the associated mathematical model for frequency response functions was derived as well. Testing structures are mounted on a rigid platform that can move essentially with only one translational degree of freedom. An electric discharge pulse strikes the platform to provide a very wide band excitation. Laser Doppler vibrometers are used to pick up both input and output signals. Since these signals are picked up without contacting structures, the structural dynamic characteristics remain intact without any distortion. With this system, modal parameters of a miniature structure can be extracted, and the receptance functions are synthesized successfully.

Modeling Vibratory Drilling Dynamics

Abstract: The dynamic behavior of deep-hole vibratory drilling is analyzed. The mathematical model presented allows the determination of axial tool and workpiece displacements and cutting forces for significant dynamic system behavior such as the engagement and disengagement of the cutting tool into the workpiece material and tool breakthrough. Model parameters include the actual rigidity of the tool and workpiece holders, time-varying chip thickness, time lag for chip formation due to tool rotation and possible disengagement of drill cutting edges from the workpiece due to tool and/or workpiece axial vibrations. The main features of this model are its nonlinearity and inclusion of time lag differential equations, which require numeric solutions. The specific cutting conditions (feed, tool rotational velocity, amplitude and frequency of forced vibrations) necessary to obtain discontinuous chips and reliable removal are determined. Calculated bifurcation diagrams make it possible to derive the relevant domain of user-specified system parameters along with the determination of optimal cutting conditions.

Identification of Moving Loads on an Orthotropic Plate

Abstract: A method is presented to identify indirectly loads moving on an orthotropic plate. The loads are in a group of two forces or four forces. The dynamic behavior of the plate under the action of these moving loads is analyzed. A method to identify these moving forces from the dynamic responses of the plate is developed basing on the modal superposition principle, and Tikhonov regularization procedure is applied to provide bounds to the solution in the time domain. Prior knowledge on the modal properties of the plate and the velocity of loads is required. The errors in the identified individual loads are discussed. The effect of different combinations of measuring locations on the identification is studied. Numerical results show that acceleration responses would give better and acceptable results than strain measurements.

Autonomous Vibration Suppression Using On-Line Pole-Zero Identification

Abstract: An on-line identification and control algorithm is developed based on the properties of collocated sensing and actuation. The feedback control law consists of second-order compensators that achieve equivalent damping in both the filter dynamics and resonant structural dynamics, thus maximizing the damping in the structure and controller. Optimal design of the feedback compensator is obtained using a pole placement algorithm applied to a single, undamped resonant mode. Numerical analysis indicates that multiple modes and structural damping do not appreciably change the damping achieved using the optimal parameters. The pole placement analysis demonstrates that only the pole-zero spacing and DC gain of the collocated transfer function are required to choose the optimal parameters. An on-line identification procedure is developed that sequentially determines the DC gain and pole-zero spacing and automatically designs the feedback compensator. This forms the basis for the autonomous control algorithm. Experimental results on a flexible beam demonstrate that the procedure can accurately identify the pole-zero spacing and automatically design the feedback compensator. A fivefold increase in damping is achieved in the first mode and a twofold increase in damping is achieved in the second mode. Discrepancies between predicted and measured damping are attributed to phase lags due to signal conditioning and low-pass filtering of the sensor signal.

Complex modal analysis of non-self-adjoint hybrid serpentine belt drive systems

Abstract: A linear damped hybrid (continuous/discrete components) model is developed in this paper to characterize the dynamic behavior of serpentine belt drive systems. Both internal material damping and external tensioner arm damping are considered. The complex modal analysis method is developed to perform dynamic analysis of linear non-self-adjoint hybrid serpentine belt-drive systems. The adjoint eigenfunctions are acquired in terms of the mode shapes of an auxiliary hybrid system. The closed-form characteristic equation of eigenvalues and the exact closed-form solution for dynamic response of the non-self-adjoint hybrid model are obtained. Numerical simulations are performed to demonstrate the method of analysis. It is shown that there exists an optimum damping value for each vibration mode at which vibration decays the fastest.

Applications of the Impedance Method on Multiple Piezoelectric Actuators Driven Structures

Abstract: An impedance-based system modeling technique has been developed to determine the output forces of multiple piezoelectric (PZT) patch actuators on an active structure to produce a known vibration response. In the analysis of the dynamic response of a structure driven by multiple PZT patches, the proposed model includes not only the dynamic interactions between the PZT patch and the host structure but also the impedance couplings among PZT patches. Therefore this approach can apply to a structure with multiple PZT actuators. Furthermore, the bending stiffness and the thickness of a PZT patch that are proved to be important as increases of excitation frequency are included in the proposed impedance model. Examples are given to demonstrate how to synthesize a known vibration response and how to suppress vibration response at an arbitrary location on structures using this technique.

Optimal Design of Rotor-Bearing Systems Using Immune-Genetic Algorithm

Abstract: In this paper, the new combined algorithm (Immune-Genetic Algorithm, IGA) is applied to minimize the total weight of the shaft and the resonance response (Q factor), and to yield the critical speeds as far from the operating speed as possible. These factors play very important roles in designing a rotor-bearing system under the dynamic behavior constraints. The shaft diameter, the bearing length and clearance are chosen as the design variables. The results show that the IGA can reduce the weight of the shaft and improve the critical speed and Q factor with dynamic constraints.

Structural Identification of Mir Using Inverse System Dynamics and Mir/Shuttle Docking Data

Abstract: The objective of this work was to investigate the use of inverse system identification techniques on Mir/Shuttle docking data to identify Mir vibrational characteristics for ultimate application to damage detection. A time-domain technique called a Remote Sensing System was proposed as an approach. The method uses inverse structural dynamics to identify vibrational characteristics of a structure. The Remote Sensing System method was demonstrated with a numerical simulation of Mir/Shuttle docking assuming that sensors were collocated with the Mir docking location. The method was then applied to the combined set of docking data from Mir/Shuttle missions STS-81, STS-89, and STS-91. Overall, the results produced by this work appear to indicate that Mir was in an undamaged state, at least with respect to docking excitation, at the time of STS-91. The significance of the contribution of the Remote Sensing System approach is that it is not affected by the nonstationarity and nonlinearity associated with the Mir/Shuttle docking interface, and docking forces at the interface do not have to be measured.

Influence of Axial Thrust Bearing on the Dynamic Behavior of an Elastic Shaft: Coupling Between the Axial Dynamic Behavior and the Bending Vibrations of a Flexible Shaft

Abstract: This paper presents the nonlinear dynamic behavior of a flexible shaft. The shaft is mounted in two journal bearings and the axial load is supported by a hydrodynamic thrust bearing. The coupling between the axial thrust bearing behavior and the bending vibrations of the shaft is studied in particular. The shaft is modeled with typical beam finite elements. The dynamic behaviors of the fluid supports are considered as nonlinear. The dynamic behavior is analyzed using an unsteady time integration procedure. The paper shows the coupling between the axial dynamic behavior and the bending vibrations of the shaft.

Discrete Frequency Models: A New Approach to Temporal Analysis

Abstract: Forced vibration responses of nonlinear systems contain harmonics of the excitation frequency. These harmonics are either directly forced or are subharmonic, superharmonic, or combination resonances. Nonlinear responses of this type have been modeled historically using continuous time, discrete time, and continuous frequency models. A new approach to dynamic systems analysis is introduced here that uses difference equations in the discrete frequency domain to describe the evolution of forced, single degree of freedom, steady state vibration responses in frequency instead of time. A variety of possible applications in nonlinear experimental structural vibrations are also discussed.

A Bounded Region of Disc-Brake Vibration Instability

Abstract: This paper introduces the velocity-dependent friction law with the Stribeck effect in a moving load model for the vibration and squeal of a car disc brake. Simulated numerical results produce a bounded region of instability for the rotating speed of the disc which is compatible with observed squeal phenomenon.