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This paper presents two models for predicting the frequency response of micro-scale oscillatory probes. These probes are manufactured by attaching a thin fiber to the free end of one tine of a quartz tuning fork oscillator. In these studies, the attached fibers were either 75 μm diameter tungsten or 7 μm diameter carbon with lengths ranging from around 1 to 15 mm. The oscillators used in these studies were commercial 32.7 kHz quartz tuning forks. The first theoretical model considers lateral vibration of two beams serially connected and provides a characteristic equation from which the roots (eigenvalues) are extracted to determine the natural frequencies of the probe. A second, lumped model approximation is used to derive an approximate frequency response function for prediction of tine displacements as a function of a modal force excitation corresponding to the first mode of the tine in the absence of a fiber. These models are used to evaluate the effect of changes in both length and diameter of the attached fibers. Theoretical values of the natural frequencies of different modes show an asymptotic relationship with the length and a linear relationship with the diameter of the attached fiber. Similar results are observed from experiment, one with a tungsten probe having an initial fiber length of 14.11 mm incrementally etched down to 0.83 mm, and another tungsten probe of length 8.16 mm incrementally etched in diameter, in both cases using chronocoulometry to determine incremental volumetric material removal. The lumped model is used to provide a frequency response again reveals poles and zeros that are consistent with experimental measurements. Finite element analysis shows mode shapes similar to experimental microscope observations of the resonating carbon probes. This model provides a means of interpreting measured responses in terms of the relative motion of the tine and attached fibers. Of particular relevance is that, when a “zero” is observed in the response of the tine, one mode of the fiber is matched to the tine frequency and is acting as an absorber. This represents an optimal condition for contact sensing and for transferring energy to the fiber for fluid mixing, touch sensing, and surface modification applications.

Drill string models are of two major types- Conventional and Periodic. Conventional drill string models are widely used due to their simplicity in manufacturing and dynamics analysis. Drill strings are affected mainly by torsional, lateral and axial vibrations. The dispersive or propagative nature of these vibrations can only be analyzed by using periodic drill string models. Drill pipe makes up the majority of the drill string. In reality, at each end of the drill pipe, tubular, larger-diameter portions called the tool joints are located. Since the dimensions of the tool joint are negligible when compared to the drill pipe, conventional drill string models assume drill strings to be uniform structures. The tool joints in drill strings introduce a geometrical periodicity in the structure.A periodic structural component is comprised of a repeating array of cells, which are themselves an assembly of elements. The elements may have differing material properties as well as geometric variations. The periodic structures act as mechanical filters for the wave propagation. A material or geometrical change in the structure causes a disruption to the continuous propagation of vibration waves.There are three types of waves propagating in rotating structures: torsional, flexural (bending) and longitudinal. Of these waves, torsional and longitudinal waves are dispersive while flexural waves are non- dispersive. The proportions of the waves which are dispersed vary according to the Wavenumber. The wavenumber is a property of the wave and depends on the structural, material and geometrical properties of the wave guide. Waveguide is the medium through which a wave travels. The wave number, and hence the dispersion and propagation characteristics of waves can be tuned by varying the material and geometrical periodicity in the drill strings.This paper presents the vibration propagation and attenuation characteristics in conventional and periodic drill string models. The periodic drill string model is developed such that it can be easily scaled to a real drilling rig model. The research also features a laboratory setting which comprises a mini drilling rig and actual drilling samples. These features ensure robustness of the dynamics analyzed for the periodic drill string model.The research findings are analyzed under zero and non- zero borehole drill string interactions. Vibration information is collected from upper and lower parts of the drill string models to compare the propagation and attenuation characteristics. Proximity sensors are used for the data acquisition which is then analyzed using frequency and power spectrum graphs. The time and frequency domain vibration propagation characteristics are investigated for both the conventional and periodic drill string models. Laboratory testing analyzes (1) introduction of stop and pass band regions in frequency spectra by periodic drill string models, and (2) vibration attenuation in torsional and lateral vibration modes. The tests confirm the introduction of stop bands in frequency spectra for the periodic drill strings, while they were absent and had an all pass-band for conventional drill string models.The research opens up a new method of passive control of drilling vibrations- by introducing tool joint designs which could be tuned to efficiently dampen out the harmful vibrations affecting the drilling rigs.

The possible contact between rotor and stator is considered a serious malfunction that may lead to catastrophic failure. Rotor rub is seen as a secondary phenomenon caused by a primary source, i.e. sudden mass unbalance, instabilities generated by aerodynamic and hydrodynamic forces in seals and bearings among others. The contact event gives rise to normal and friction forces exerted on the rotor at impact events. The friction force plays a significant role by transferring some rotational energy of the rotor to lateral motion. A mathematical model has been developed to capture this for a conventional backup annular guide setup. It is reasonable to superpose an impact condition to the rub, where the rotor spin energy can be fully transformed into rotor lateral movements. Using a nonideal drive, i.e. an electric motor without any kind of velocity feedback control, it is even possible to stop the rotor spin under rubbing conditions. All the rotational energy will be transformed in a kind of “self-excited” rotor lateral vibration with repeated impacts against the housing. This paper studies the impact motion of a rotor impacting a conventional backup annular guide for the case of dry and lubricated inner surface of the guide. For the dry surface case, the experimental and numerical analysis shows that the rotational energy is fully transformed into lateral motion and the rotor spin is stopped. Based on this study this paper proposes a new unconventional backup bearing design in order to reduce the rub related severity in friction and center the rotor at impact events. The analysis shows that the rotor at impacts is forced to the center of the backup bearing and the lateral motion is mitigated. As a result of this, the rotor spin is kept constant.

The stability problem of eccentric rotor in high-speed cutting process is the main factor affecting the performance of cutter transmission system. A modal analysis of eccentric rotor for multi-layer leather high-speed cutting machine based on bond graph method is proposed to obtain the complete modal parameters. The lateral vibration mathematical model of the eccentric rotor is build using bond graph theory. The inherent frequency, deformation modal vibration shape, and velocity modal vibration shape of eccentric rotor are obtained through the Matlab numerical calculation. Then the modal test for eccentric rotor is done and the compared results are given. The results show that using the bond graph method solves the problem more easily than Newton's theory, obtains the two type of modal vibration shape, and its relative error is less than 0.4%. The complete modal information is given that provides a theoretical basis to better understanding the dynamic properties of eccentric rotor and provides the basic parameters for dynamic performance optimization and dynamic balancing analysis of cutter transmission system.

The loading, elastic deformation and hydrodynamic film effect at each rolling element–raceway contact of automobile water pump bearing are analyzed. Based on this analysis, the total radial stiffness, angular stiffness and radial damping of the two rolling element rows are modelled. These stiffness and damping are taken into the transfer matrix to evaluate the lateral vibration characteristics of a rotor-automobile water pump bearing system. The natural frequencies, mode shapes and unbalance responses of the system are calculated. The effects of the pulley and fan unbalances on the system response under different spindle speeds are studied. The calculation results show that the unbalance response of the system can be reduced by fixing the pulley and fan with the initial phase difference between their unbalances to be 180°, and by increasing the pulley unbalance appropriately when keeping the fan unbalance constant.

Geared rotor system analysis is a very challenging problem because of the complicated dynamic behaviour of composite rotors. For example, the whirling motion and critical speed of the system has to be found by considering all the rotors in the system as well as interactions between them, which makes the solution process as well as proper interpretation of the solution extremely complicated. Complex variable approach, which is proposed for the analysis of a single rotor system, is very powerful for this purpose. The approach is expanded to the analysis of combined rotor system to apply it to the gear system dynamics. A finite-element model of a geared rotor system on flexible shaft bearings has been developed. The model includes the bearing stiffness and shaft flexibility taken in two mutually perpendicular directions and the stiffness of the gear mesh. It is shown that the lateral vibrations have considerable effect when the natural frequencies of the lateral vibration and torsional vibration are close to each other. The whirling response of the system is studied for strong lateral-torsional coupling, thereby; the nature of the coupling effect is discussed.

Vibration characteristics of a misaligned rotor with asymmetric shaft stiffness are studied. The system consists of two shafts connected by a flexible coupling with parallel misalignment, two rigid disks attached at the middle of each shaft and one of the shafts has asymmetric stiffness. The governing ordinary differential equations are derived using Lagrange dynamics and integrated through numerical methods. The effects of asymmetry, eccentricity and misalignment are studied through the peak-to-peak lateral vibration amplitude at different rotor speed. Simulation results show that the amplitude peaks at the natural frequency associated with unbalance and parallel misalignment, while half the natural frequency associated with the asymmetric shaft stiffness. This study may contribute to enrich understanding of the vibration of a rotor system under the cases of eccentricity, parallel misalignment and asymmetric shaft stiffness.

The hybrid magnetic bearing using permanent magnets and the high-Tc bulk superconductor (HTSC) has been developed. Repulsive force of the permanent magnet is introduced to increase the load weight of the magnetic bearing. Effect of the hybrid system has been shown. In this paper, influence of the hybrid system on the dynamic characteristics of the rotor is studied. The rotational characteristics in the mechanical resonance state are studied, and the equivalent magnetic spring coefficient is estimated from the experimental results of the load weight. The resonance frequency is measured by the rotation experiments. The rotor achieves stable levitation even in the resonance state. In the hybrid system, effect of the pinning force becomes smaller than that of the lateral force generated by the repulsive force between the two permanent magnets at the smaller air gap. Thus influence of the lateral vibration and the gradient angle in the resonance state becomes larger at a smaller air gap. The equivalent magnetic spring coefficient becomes also small, and the resonance frequency becomes small in the hybrid bearing system.

Journal bearings are widely applied in different rotating machineries. These bearings allow for transmission of large loads at mean speed of rotation. These bearings are susceptible to large amplitude lateral vibration due to self-exited instability which is known as oil whirl or synchronous whirl. This oil whirl depends on many parameters such as oil film thickness, viscosity of lubricant, load on bearing, inertia of fluid etc. out of which oil film thickness plays an important role in operation of Journal bearings. As oil film thickness decreases metal to metal contact occurs this further can damage the journal bearing. So during the operation minimum oil film thickness should be maintained which can avoid the metal to metal contact and further increases the life of bearing. This paper presents a theoretical calculation of oil film thickness and experimental verification of same on journal bearing test rig. Different journal speeds and loads are considered for the analysis.

Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending, the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length. Based on Rayleigh’s quotient, an iterative strategy is developed to find the approximated torsional stiffness coefficients, which allows the reconciliation between the theoretical model results and the experimental ones, obtained through impact tests. The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh’s quotient but also on the mode shapes, considering the shape functions defined in branches. Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.

With the rapid development of the national economy, the mechanical vibration occurring in a high-speed rotary machine may affect or restrict the normal operation of the system and cause immeasurable losses in production and life. In this paper, a self-sensing eddy current damper is proposed and applied to a rotating disk vibration system to realize the active control of vibration. The mechanism and application of self-sensing eddy current damper are mainly studied from the theoretical research and simulation of control algorithm. Based on the theory of eddy current and electromagnetic force generation, the working principle of self-sensing eddy current damper is analyzed based on the theory of double-coil transmission eddy-current detection. The relationship between the vibration displacement and the input and output of the damper is explored. The correctness of the theoretical modeling is verified. The controller based on H∞ method is designed with robust control theory and the controller feedback gain K (s) is analyzed. According to the control structure of the system, simulink simulation model is designed to simulate the rotating disk vibration system with different rotating speed. The vibration displacement responses before and after the control are compared and analyzed. The simulation results show that the designed controller can effectively reduce the lateral vibration of the rotating disk. The verification experiment of self-sensing eddy current damper and the active control experiment of the rotating disk vibration system are carried out. The experimental results are in good agreement with the simulation results.

Tripod constant velocity joints are used in the driveshaft of front wheel drive vehicles. Thrust force generated by this joint causes lateral vibration in these vehicles. To determine the mechanisms inducing the thrust force, a detailed model is constructed based on a multibody dynamics approach. Although the joint is equipped with three rollers and grooves, this model consists of the principal parts for one roller and groove in order to precisely analyze frictional phenomena occurring between the roller and the groove. These principal parts are defined as rigid bodies and are connected by force elements of contact and friction. The appropriateness of this model is verified by comparing computational and experimental results and it is clarified that the principal factors inducing the thrust force are three kinds of sliding friction force at the point of contact between the roller and the groove. This paper also describes the reason why the third rotating order component of the thrust force is induced by one roller and groove.

A three dimensional numerical model has been developed based on a level set algorithm to predict the surface oscillation behavior of a liquid bridge induced by single and multiple vibrations under space environment. By subjecting the liquid bridge to single lateral vibration, the surface resonance characteristics have been predicted numerically. Moreover, the controlling mechanism of the surface oscillation under multiple vibrations is also determined, and the results show the external vibrations at resonance frequency in lateral direction completely control the surface oscillation in horizontal direction.

Welding is required for a connection between two different components in the nuclear fuel of a pressurized water reactor. This work relies on a mechanical experiment and analytic results to investigate the structural integrity of nuclear fuel in a situation where some components are not welded to each other. A series of lateral vibration tests are performed in a test facility, and the test structures are examined in terms of dynamic behavior. In the tests, the displacement signal at every grid structure that sustains fuel rods is measured and processed to identify the dynamic properties. The fluid-elastic stability of the structure is also analyzed to evaluate susceptibility to a cross flow with an assumed conservative cross flow distribution. The test and analysis results confirm that the structural integrity can be maintained even in the absence of some welding connections.

This paper deals with condition monitoring and vibration diagnostics of vertical sulphuric acid pumps running in continuous long term operation mode. The task of experimental testing and theoretical modeling – to increase reliability and efficiency of vertical pumps through elimination of rotor lateral vibration. On the basis of experimental testing results analysis the dynamic model was designed and simulated. The reason of high vibration of the pump rotor is the rotor technological bow and cavitation phenomenon that take place in the pump.

A tripod constant velocity joint is used in the driveshaft of front wheel drive vehicles. Thrust force generated by this joint causes lateral vibration in these vehicles. To analyze the thrust force, a detailed model is constructed based on a multibody dynamics approach. This model includes all principal parts of the joint defined as rigid bodies and all force elements of contact and friction acting among these parts. This model utilizes a new contact modeling method of needle roller bearings for more precise and faster computation. By comparing computational and experimental results, the appropriateness of this model is verified and the principal factors inducing the second and third rotating order components of the thrust force are clarified. This paper also describes the influence of skewed needle rollers on the thrust force and evaluates the contribution of friction forces at each contact region to the thrust force.

In this article, we analyze the sensitivity of lateral, axial, and torsional vibration of a scanning near-field optical microscope (SNOM) probe. An exact solution for the title problem is obtained using the theory of beam and torsional vibrations. Sensitivities are obtained for a wide range of the intervening physical parameters. This paper discusses the relationship between the sensitivity of a SNOM probe and its geometry. The analysis is presented for a probe in three different cases lateral vibration, axial vibration, and torsional vibration, for a fixed-free configuration. To derive the mathematical relation between the probe and sample (by utilizing springs and damping to simulate different environments) through the process of theory analysis for different environments. Thus a universal touchless SNOM probe sensitivity controller is developed for appropriate control and adjustment of the probe sensitivity suitable under different environments. Such controller helps the SNOM probe achieve the nanoscale resolution through proper control and adjustment probe sensitivity in accordance to changes to different environments and reduce the chance of being damaged during the scan, which in the end further advances the sample inspection technique.

In machine systems where a rotor spins within a finite clearance space supported by bearings, contact between the rotor and its surround can result in persistent coupled vibration of the rotor and stator. When the vibration response is driven predominantly by friction forces, rotordynamic stability becomes a serious issue. This paper introduces a theory for model-based verification of dynamic stability in rotor systems with stator contact and rub. Generalized multi-degree-of-freedom linear models of rotor and stator lateral vibration are considered, combined with contact models that account for finite clearance and Coulomb friction. State-space conditions for global stability as well as stability of contact-free synchronous whirl responses are derived using Lyapunov's direct method. This leads to feasibility problems involving matrix inequalities that can be quickly verified using numerical routines for convex optimization. Parametric studies involving flexible rotor models indicate that tight bounds on regions of stability can be obtained. A case study involving a realistic machine model illustrates how design optimization based on the theory might be used to overcome instability problems in real machines.

Innovative applications of parametrically excited structures have been proposed in microelectromechanical sensors and actuators. In parametrically excited systems, the dynamic response is a result of instability of the trivial equilibrium state. The response amplitude is determined by the nonlinearity of the structure as well as the system damping and forcing parameters. Previous studies on parametrically excited cantilever beams have shown that the agreement between the theory and the experiment is very poor. Even qualitative differences have been reported in the beam frequency response curves of the first mode. These discrepancies have led to more sophisticated models including quadratic dampings in the models. However, this treatment has been found unsatisfactory since it would require different nonlinear damping models for different modes. In this paper, we propose that much of the discrepancy can be attributed to the limited power of the shaker. In fact, the shaker dynamic responses are affected by the beam dynamics upon parametric instabilities. We first report qualitative discrepancies between the theoretical predictions and the experiments. We then propose as the explanation for the discrepancy the coupling between the beam lateral vibration and the shaker vibration amplitude. The coupling is more significant in shakers of limited powers. This finding is important in the design of parametrically excited systems for engineering applications.

In the case of ultra-short-pulsed laser heating, two effects become domineering. One is the non-Fourier effect in heat conduction, and the other is the coupling effect between temperature and strain rate. In the present study, a generalized solution for the coupled thermoelastic vibration of a microscale beam resonator induced by pulsed laser heating is developed. The solution takes into account the above two effects. The combined finite sinusoidal Fourier and Laplace transformation method is used to determine the lateral vibration of the beam. The effects of laser pulse energy absorption depth and reference temperature have been studied.

The paper studies analytically the free vibration of a generalised suspension system. The system is composed of a rigid body with the symmetric shape about its centroid and two symmetrically inclined massless strings with infinite axial stiffness. The two hanging points have horizontal and vertical elastic supports. The rigid body is eccentrically acted by horizontal, vertical and rotational springs. A typical application of the model is to represent a section of cable suspended bridges involving the lateral vibration of small amplitude. The governing differential equations with three degrees-of-freedom are derived where the effect of gravitational potential is considered. The static equilibrium position is determined simultaneously. When the elastic constraints are applied at the centroid of the rigid body, the vibration modes of the system can be divided into symmetric and antisymmetric ones which are studied independently. The analytical expressions of natural frequencies for some special cases are also provided. The effects of various parameters, especially the length and inclined angle of the strings, on the natural frequencies of the system are examined. Some useful conclusions are obtained. Simple model demonstration and verification are conducted to verify some findings in the paper.

The aim of this paper is to study the characteristics of torsional vibration of a rotor with unbalance by numerical simulation. It can be concluded that synchronous torsional vibration accompanying with small higher harmonic components are excited, except when the speed of rotation is near, or equal to, half the natural frequency of torsional vibration, the bisynchronous component is much more remarkable than other harmonic components including the degraded synchronous one, and torsional vibration of the shaft can result in lateral vibration with bisynchronous frequency. Especially, when the rotating frequency is near the natural torsional frequency, where torsional vibration is strongest, the bisynchronous vibration becomes rather strong.

This paper investigates the lateral vibration of a spinning disk–shaft system supported by a pair of ball bearings and subjected to a pair of random axial forces at both ends. The axial forces are assumed as the sum of a static force and a random process with a zero mean. Due to the random axial forces, the rotor-bearing system may experience parametric random instability under certain situations. In this work, the finite element method is applied to yield a set of discretized system equations first. The set of discretized system equations is partially uncoupled by the modal analysis procedure suitable for gyroscopic systems. The stochastic averaging method is then adopted to obtain Ito's equations for the response amplitudes of the system. Finally the first- and second-moment stability criteria are utilized to determine the stability boundaries of the system. Numerical results show that the rotor-bearing system is always stable in the sense of the first-moment stability, and the effects of the average axial compressive force and the disk mass, which will lower all frequencies of the system, tend to destabilize the second-moment stability of the system.

This paper presents a novel way to detect fatigue transverse cracks in rotating shafts. The proposed detection methodology exploits both the typical nonlinear breathing phenomenon of the crack and the coupling of bending–torsional vibrations due to the presence of crack for its diagnosis. A transient torsional excitation is applied for a very short duration at specific angular orientation of the rotor and its effect in the lateral vibrations is investigated. Wavelet transforms (WTs) is used in revealing the transient features of the resonant bending vibrations, which are set up for a short duration of time upon transient torsional excitation. Variation of peak absolute value of wavelet coefficient (of the transient lateral vibration response) with angle at which torsional excitation is applied is investigated. The correlation of this variation with the breathing pattern of the crack is studied. The sensitivity of the proposed methodology to the depth of crack is investigated. The detection methodology gives a vibration response signature that closely correlates with and is very specific to the behaviour of the transverse surface crack in a horizontal rotor. The response features are not likely to be exhibited by other common rotor faults under similar excitation conditions making the proposed detection methodology unambiguous. The fact that the rotor is not required to stop and that the detection process is applied for a rotating shaft with only a short period transient external excitation makes the methodology more convenient.

Vibration attenuation is necessary in many electro-mechanical systems. In this paper electromagnetic damping is applied on a flexible cantilever beam (FCB) made of ferromagnetic material. The lateral vibration is controlled by employing two electromagnetic poles mounted in the same axis as that of a vibrating cantilever beam. A power amplifier is developed to provide desired current to the electromagnet. Comparison of damping achieved at different electromagnetic forces is presented. The study employs a new method of applying a constant DC power to one of the electromagnets while other is connected to a variable current source. Experimental results are presented that show the effectiveness of the presented approach.

This work deals with the robust asymptotic output tracking control problem of the tip position of a space frame flexible structure, mounted on a rigid revolute servomechanism actuated and controlled with a dc motor. The structure is also affected by undesirable vibrations due to excitation of its first lateral vibration modes and possible variations of the tip mass. The overall flexible structure is modeled by using finite element methods and this is validated via experimental modal analysis techniques. The tip position of the structure is estimated from acceleration and strain gauge measurements. The asymptotic output tracking problem is formulated and solved by means of Passivity-Based and Sliding-Mode Control techniques, applied to the dc motor coupled to the rigid part of the structure, and those undesirable vibrations are simultaneously attenuated by an active vibration control using Positive Position Feedback control schemes implemented on a PZT stack actuator properly located into the mechanical structure. The investigation also addresses the trajectory tracking problem of fast motions, with harmonic excitations close to the first vibration modes of the structure. The overall dynamic performance is evaluated and validated by numerical and experimental results.

A shaft train in power plants is comprised of many journal bearings supporting turbines, generator and exciter. Each single rotor may possess one or more natural frequencies below or close to the rated speed. The entire shaft train often possesses many coupled or uncoupled natural modes close to the rated speed which influence the lateral vibration behavior in the normal operation. Some modes are low damped and some highly damped. It is difficult to judge how sensitively the machine reacts to theses modes and to make an acceptance design criteria for them. ISO 21940-31 makes some recommendation about vibration sensitivity of the damped modes of simple systems with rotors having only one resonant speed over the entire service speed range or widely separated resonance speeds. But it cannot be applied to evaluate a large turbine generator shaft train with many interacting resonances. This paper proposes two methods—sum of unbalance responses and sum of modal magnification factors to analyze the vibration sensitivity of a rotor system with many frequencies in the vicinity of the service speed.

Taking a 1000 MW turbo-generator rotor as an example, the sensitivities to thermal effect in temperature range of 20–570 °C, both for lateral and torsional vibration, are analyzed. In addition, for lateral vibration, the sensitivities of the critical speeds are analyzed by changing bearing stiffness. The results show that increasing bearing-support stiffness leads to natural frequencies increased gradually but not linear. The first order is much more sensitive than the others. When stiffness of bearing is large enough, the natural frequencies almost do not change. For torsional vibration, the sensitivities of natural frequencies are analyzed by changing some mechanical parameters. With changing the stiffness and inertia of the rotor, their influences to the characteristics of the torsional vibration are obtained. The frequency can be modulated by changing the sectional structure of the shafting to avoid torsional vibration resonant. The results are also shown that torsional frequency and mode shape are much more sensitive to mechanical parameter than to thermal effect.

Active Vibration Control has proven to be a good opportunity for attenuation of lateral vibration of rotating shafts in literature. Besides the choice of suitable sensors and actuators, the controller itself has a particularly strong influence on the performance of an Active Vibration Control system since it generates the control signal from sensor signals. There are numerous controller types available for the purpose of active vibration control. These controllers include simple feedback approaches but also more sophisticated model based feedback and feedforward approaches. In this part I of a two-part article three feedback controllers from different fields of research and a feedforward controller are designed for active control of lateral synchronous vibration of a rotor test rig. In particular, PDT1-Control, H∞-Optimal Control, LQG-Control and feedforward control using the FxLMS algorithm are introduced.

Based on the principles of laser Doppler velocimetry, the laser torsional vibrometer (LTV) was developed for non-contact measurement of torsional oscillation of rotating shafts, offering significant advantages over conventional techniques. This paper describes comprehensive theory to account for the sensitivity of the LTV's measurements to shaft motion in all degrees of freedom. The optical geometry of the LTV offers inherent immunity to translational motion of the target shaft, either axial or radial. However, its measurements are sensitive to angular lateral vibration of the shaft. The significance of this sensitivity is compared with the instrument noise floor and typical torsional and lateral vibration levels. Optimum alignments of the instrument are then specified to ensure effective immunity to all lateral motion in typical applications. To overcome this problem more reliably, a new technique is proposed permitting unambiguous measurement of pure torsional vibration in situations where use of a single LTV demonstrates unacceptable sensitivity to angular lateral vibrations. Practical application of this technology is demonstrated with torsional vibration measurements from a diesel engine crankshaft. Simultaneously, previously unattained measurements of shaft bending vibration measurements are made. The first bending mode of the crankshaft was identified and its vibration amplitude and damping estimated. This application of laser vibrometry for non-contact measurements of shaft vibration represents a further step forward in the use of this technology for machinery diagnostics.

The mechanism of phase modulation method for reducing the vibration amplitude of vibrating systems accelerating or decelerating through its resonance is presented. The method is theoretically used to rotor and one degree of freedom oscillator models with numerical simulation; numerical results show that the maximum amplitude can be reduced by about 15–20% with phase modulation in comparison with the constantly accelerating case. Possible implementation of the method was introduced. Experiments with a cantilever sheet subjected pulses excitation were conducted to confirm the method; experimental results show that the lateral vibration amplitude of the cantilever at the passage of its first resonance can be reduced about 18% with phase modulation method.

Drive axle half shaft system is simplified to a single-span and double-cantilever rotor system, taking slant crack, bearing and tire sine excitation into consideration, 8-DOF dynamic equations are founded. Based on this model, the cracked half axle rotor system under high-speed drive condition is investigated by numerical simulation. The results indicate that: compared with uncracked half shaft system, cracked half shaft lateral vibration shows second harmonic generation, quadruplicated frequency and their combined frequencies with VC vibration frequency, and their corresponding amplitudes increase with the increase of crack depth. Therefore, slant crack information of axle shaft can be gained from the above three nonlinear factors.

A cable-supported footbridge model with pre-tensioned cables in vertical and horizontal planes is proposed to investigate the vibration characteristics of shallow suspension footbridges under walking dynamic loads in this conceptual study. In this bridge model, the tension forces in the supporting cables can be adjusted by introducing pre-tensions to the reverse-profiled cables, and therefore the natural frequencies can be altered to cover the frequency range of dynamic forces induced by pedestrians. In the numerical analysis, SAP2000 is adopted to study the vibration properties and dynamic response under walking loads. The synchronous response of the bridge structure is stimulated by resonant vibration. The crowd walking loads are modelled as uniform loads acting on the whole bridge deck and they consist of three parts: vertical dynamic force, lateral dynamic force and vertical static force. Numerical results show that for a shallow suspension footbridge the lowest frequencies correspond to lateral and torsional vibration modes which are always combined together and become two types of coupled modes: coupled lateral–torsional modes, as well as coupled torsional–lateral modes. As an example, a bridge model with fundamental frequency of 0·75 Hz in the lateral direction has been studied. It is found that the vibration in the lateral direction is quite different from that in the vertical direction and that damping has significant effect on the vertical vibration but small effect on the lateral one. Moreover, vertical static load has significant effect on the lateral vibration when the bridge structure vibrated in coupled modes.

Novel structure ultrasonic motors which have cross type stator were designed and fabricated. Driving characteristics of the motors were analyzed and measured by changing the materials of the stator. This ultrasonic motor has stator with hollowed cross bar and the stator rotate the rotor using elliptical displacement of the inside tips. This motion is generated by lateral vibration mode of cross bars. This stator was analyzed by finite element analysis depandent on stator`s materials. And the cross type ultrasonic motors were made by analyzed results. The larger displacements were obtained, when the density of material was decreased. But the stress was increased when the stator`s material has large density and Young`s modulus. The fabricated one has high speed and torque in large stress on contact point between rotor and stator. The stress was more effected on speed and torque than the displacement.

A specially designed resonator to avoid the change of the resonance characteristics by thermal influences of the laser beam was fabricated on a silicon on insulator wafer. This resonator design enables one to apply a lateral driving force to generate lateral vibration. The resonator was excited using a laser diode which was driven with sinusoidal current, and the vibration was detected by measuring intensity fluctuation of the He–Ne laser beam reflected on the resonator mass. Four evident resonance frequencies were successfully observed in the range from 100 Hz to 100 kHz.

A method is developed for the control of rotor lateral vibration using multiple frequency components. The control strategy uses a generalized algorithm for the real-time calculation of the amplitude and phase of the vibration components. The complex amplitudes are evaluated successively at the controller sample frequency and can therefore be used for dynamic feedback control. Parallel control of all frequency components is achieved using frequency-matched control signals with amplitude and phase dictated by the control algorithm. The strategy is evaluated experimentally using a flexible rotor system with magnetic bearings. The controller gain matrices are calculated from frequency response identification. The controller sample frequency is the rotational frequency, but the vibration frequencies that are controlled simultaneously include harmonics and subharmonics of the rotational frequency. The controller is shown to be effective in reducing rotor vibration arising from various sources and having a number of discrete frequency components.

Graphene was first discovered in 2004 (Novoselov K S, et al. 2004 Science 306 666), it is a single atomic layer of sp2-bonded carbon atoms arranged in a honeycomb-like lattice. According to its extraordinary electronic, mechanical, thermal and optical properties, one can expect it to have a variety of applications in nanoscale electronics, composite materials, energy storage, and biomedicine fields. Although many experimental and theoretical studies on graphene have been carried, there still exist many obstacles to its applications. A representative example is nanoscale electronics (e.g., field-effect transistors and optoelectronic devices) that requires non-zero band-gap. Therefore, introducing defects into graphene and leading to band-gap opening are key steps for its technique applications.Recently, ion beam irradiation as a defects introducing technique was performed by Lee et al. (2015 Appl. Surf. Sci. 344 52) and Zeng et al. (2016 Carbon 100 16) through 5, 10, and 15 MeV protons and highly charged ions (HCIs) irradiating the graphene separately. Considering the advantages of simplity for preparing samples and feasibility in atmospheric condition of Raman spectroscopy compared with common characterization techniques (high resolution transmission electron microscopy, scanning electron microscopy, atomic force microscopy) for nano-materials, in both studies, Raman spectroscopy is used to obtain the evolution of ID/IG (ID is the peak intensity excited by defects, IG is the peak intensity origining from lateral vibration of carbon atoms) with different energies and fluences, respectively. In this work, considered are the following points:1) the absence of quantitive characterization for defects in the above two studies; 2) the low displacement energy of 25 eV required for a carbon atom to be knocked out (Zhao S J, et al. 2012 Nanotechnology 23 285703); 3) the complex interaction between HCIs and material. The irradiation effects of single layer graphene on silicon substrate are investigated by 750 keV and 1 MeV proton bombarding. This introduces the defects into graphene and thus leads to band-gap opening. By comparing Raman spectra of the samples before and after irradiation, a quantitive characterization about defects in graphene is achieved. Detailed analysis shows that 1) the value of ID/IG increases with the energy loss of incident proton, which is consistent with the result of SRIM simulation; 2) the average distance of defects LD increases with the incident proton energy; 3) the defect density nD decreases with the incident proton energy. These indicate that the damage effect for MeV protons in single layer graphene with substrate is similar to those in three-dimensional materials. The method presented here may facilitate the understanding of the physical mechanism of MeV proton interaction with two-dimensional materials, and provide a potential way of controlling the electronic structure and band-gap.

Automotive turbochargers feature a variety of boundary conditions influencing the operating behaviour during run-up procedures. As a novel aspect the influence of the thrust bearing and load on lateral vibration phenomena is investigated in detail for this application. The run-up predictions show that the thrust bearing and load have significant influence on the frequencies as well as on the magnitudes of the vibrations. In particular, the amplitudes of conical vibrational modes are damped. Further, the consideration of the hot gas boundary conditions is identified as decisive in order to predict the bearing parameters and consequently the vibrations precisely.

Synchronous lateral vibration is a frequent cause of machine failure and is probably the most common source of machine noise and vibration. Among the broad ranges of faults that cause synchronous vibration, mass unbalance and bow are the most common faults present in the rotor and hence their detailed understanding is required. In the present study, a rotor model having both mass unbalance and bow is analyzed to find the influence of these faults on the synchronous response. The synchronous response of a rotor is a function of influence coefficients due to mass unbalance and bow. The influence coefficients are analytically derived using transfer matrix method for rotor bearing system having both mass unbalance and bow. The correction unbalance vector required to balance the rotor at its first bending critical speed is computed using these analytically derived influence coefficients and the rotor responses measured at a speed much lower than the first bending critical speed. The balancing method needs a good mathematical model for the rotor system in finding the influence coefficients for mass unbalance and bow. This procedure helps in estimating the correction mass in a single trial run and using a single balancing plane, thus reducing the cycle time for balancing flexible rotors. Experiments are carried out on a test rig to verify the procedure. � 2012 The Author(s).

Considering the underlying reason of tire polygonal wear, a unified mechanical tire model is developed to analyze the different vibration properties between the driving wheel and follower wheel. And the LuGre dynamic friction model is applied to determine the frictional forces between the wheel with a slip angel and the road. Through the stability analysis with Lyapunov theory, it is found that tread self-excited vibration is periodic oscillation caused by Hopf bifurcation. The analysis of the lateral vibration of driving wheel shows that the tread vibration system loses its stability and self-excited vibration occurs when the wheel is rolling at a high speed, is over-loaded, is having a large toe-in angle, or is under a low tire pressure. On this basis, the dynamic behaviors of the driving and follower wheels are distinguished with different slip rates by the numerical simulation. Compared with the dynamic behaviors of the follower wheel under the same condition, the self-excited vibration occurs on the driving wheel with more limited parameter scope, lower oscillation energy, and lower occurrence, which explains why the polygonal wear is less likely to occur on the driving wheel.

The use of magnetic bearings in rotating machinery provides contact-free rotor support, and allows vibration control using both closed-loop and open-loop strategies. One of the simplest and most effective methods to reduce synchronous lateral vibration when using magnetic bearings is through an open-loop adaptive control technique, in which the amplitude and phase of synchronous magnetic control forces are adjusted automatically to minimize the measured vibrations along the rotor. However, transducer malfunction, or faults in the signal-processing channels, may cause the controller to adapt incorrectly, with unwanted and possibly catastrophic effects. It is shown that an extension to the control strategy, which utilizes the variances of the measured system response and identified parameters, enables the faults to be detected and accounted for so that a modified control action can achieve continued and effective control of the synchronous vibration. The approach is extended further to identify changes in external factors, such as unbalance and rotor dynamics. Various faults and perturbations are examined experimentally, and the ability of the controller to detect and compensate for these changes is demonstrated.

A model for the coupled torsional and lateral vibrations of an unbalanced rotor is developed. The equations of motion, obtained using Lagrangian dynamics, showed inertial coupling and nonlinear interaction between the rotor torsional and lateral vibrations. A softening effect of the rotor torsional stiffness has appeared. This effect and some of the nonlinear interaction effects have appeared, for the first time in this model, due to treating the torsional angle as an individual motion. Simulation results showed energetic interaction between the rotor lateral and torsional vibrations. Responses at 1 X and 3 X in the torsional vibration signal and 1 X and 2 X in the lateral vibration signals have appeared.

The misalignment of a gear coupling in a multirotor system is an important problem; it can cause various faults. In the present work the non-linear coupled lateral torsional vibration model of rotor-bearing-gear coupling system is developed based on the engagement conditions of gear couplings. Theoretical analysis shows that the forces and moments acting on gear couplings due to the initial misalignment are from the inertia forces of the sleeve and the internal damping between the meshing teeth, and depend on the misalignment, internal damping, the rotating speed, and the structural parameters of the gear coupling. Numerical analysis of the signature of vibration reveals that the even-integer multiples of the rotating speed of lateral vibration and the odd-integer multiples of the torsional vibration occur in the misaligned system, and the integer multiples of vibration are apparent around the gear coupling.

A comprehensive vibration analysis of a coupled rotor/fuselage system is carried out using detailed 3-D finite element models of the AH-1G airframe from the DAMVIBS program. Predicted vibration results are compared with operational load survey flight test data of the AH-1G helicopter. Modeling of difficult components (secondary structures, doors/panels, etc.) is essential in predicting airframe natural frequencies. Calculated 2/rev vertical vibration levels at the pilot seat show good correlation with the flight test data both in magnitude and phase, but 4/rev vibration levels show fair correlation only in magnitude. Lateral vibration results show more disagreement than vertical vibration results. Refined aerodynamics such as free wake and unsteady aerodynamics have an important role in the prediction of vibration. Main rotor pylon roll mode has a significant contribution (about 26%) on the 2/rev vibration. Accurate prediction of airframe natural frequencies up to about 40 Hz appears essential to predict vibration in airframe.

An analytical model of a wood-cutting circular saw blade is developed for the purpose of understanding the mechanics of a lateral vibration instability known as washboarding. The governing equation developed contains inertial, gyroscopic and stiffness terms based upon the saw plate characteristics with the cutting forces being represented by the product of a time-dependent periodic function and the lateral displacement of the saw tooth. A stability analysis of the system is shown to produce predictions that are consistent with experimental data.

Acomprehensivevibrationanalysisofacoupledrotor/fuselagesystemforatwo-bladedteeteringrotorusinge nite elementmethodsinspaceandtimeisdevelopedthatincorporatesconsistentrotor/fuselagestructural,aerodynamic, and inertial couplings and a modern free-wake model. Coupled nonlinear periodic blade and fuselage equations are transformed to the modal space and solved simultaneously. The elastic line airframe model of the AH-1G helicopter is integrated into the elastic rotor e nite element model. Analytical predictions of rotor control angles, blade loads, hub forces, and vibration are compared with AH-1G operation load survey test data. The blade loads predicted by the present analysis show generally fair agreement with the e ight test data. Calculated 2 and 4 per revolution vertical vibration levels at the pilot seat show fair correlation with the e ight test, but the predicted 2 per revolution lateral vibration level is higher than the measurement, particularly at high advance ratios. Modeling of pylon e exibility is essential in the two-bladed teetering rotor vibration analysis. Ree ned aerodynamics such as free wake and unsteady aerodynamics have an important role in the prediction of vibration. Nomenclature eg = blade center-of-gravity offset from the elastic axis lu = undersling m = blade mass per unit length pfe = temporal fuselage elastic modal displacement vector pfr = temporal fuselage rigid modal displacement vector R = blade radius u;v;w = blade elastic displacements in the axial, lag, and e ap directions x = longitudinal coordinate P x f ; P yf ; P f = fuselage translational velocities

Micromachined silicon sensors employing resonant sensing offer many potential performance benefits over alternative piezoresistive and capacitive techniques. Resonant devices are, however inherently more complicated to design and fabricate. This article provides a brief overview of the principles of resonant sensing and describes a design study involving double-ended tuning-fork (DETF) resonant structures that overcome many practical difficulties due to their dynamically balanced design and mode of operation. The optimum mode is a lateral vibration in the plane of the wafer and this paper also reports a simple method for exciting and detecting lateral vibrations without compromising the degree of dynamic balance of the structure. Test devices have been fabricated in single-crystal silicon.

The optimum mode of double-ended tuning-fork-style resonators is a lateral vibration in the plane of the wafer. Lateral vibrations are typically excited using the comb drive approach, but this requires modification to the resonator structure. This paper reports a simple method for exciting and detecting lateral vibrations without modifying the resonator, thereby enabling the optimum dynamically balanced structure to be used. This approach uses plane electrodes positioned parallel to the resonator's tines to excite the vibrations while the change in resistance along the length of the resonator enables the vibrations to be detected. Test devices have been fabricated in single-crystal silicon using the buried oxide in silicon-on-insulator wafers as a sacrificial layer. The resonators are 340-/spl mu/m long, 3-/spl mu/m thick with tines 2-/spl mu/m wide. The gap between the tines and the electrode is 2 /spl mu/m. Visual inspection in a scanning electron microscope and electrical tests have confirmed the validity of this approach.

An on-line fault detection and isolation technique is proposed for the diagnosis of rotating machinery. The architecture of the system consists of a feature generation module and a fault inference module. Lateral vibration data are used for calculating the system features. Both continuous-time and discrete-time parameter estimation algorithms are employed for generating the features. A neural fuzzy network is exploited for intelligent inference of faults based on the extracted features. The proposed method is implemented on a digital signal processor. Experiments carried out for a rotor kit and a centrifugal fan indicate the potential of the proposed techniques in predictive maintenance.

Superconducting magnetically levitated vehicles have guidance coils that produce vehicle guidance forces using a null flux coil connection. However, the resulting forces do not have sufficient damping forces to suppress lateral vibration of the vehicle. Even though the experimental system has some magnitude of damping, it is still unsatisfactory. Moreover, since the guidance forces are very weak at low speeds, the minimum levitating speed is limited. The paper proposes a guidance method using LSM armature coil currents. When the currents are decomposed into the dq frame variables so that the d-axis is assigned to the field axis, the d-axis component of the currents generates lateral forces. The lateral forces of the vehicle are formulated, and the guidance force coefficient is defined. In addition, the author presents a design formula for a guidance regulator system that employs a dynamic compensator using a feedback signal of lateral displacement. The calculated results show that the guidance regulator system works as intended. © 2001 Scripta Technica, Electr Eng Jpn, 137(2): 44–51, 2001