bluuebunny/crossref_metadata_2025 huggingface dataset:
A Fractional Calculus Perspective of PID Tuning
Authors: Barbosa Ramiro S. , Machado J. A. Tenreiro , Ferreira Isabel M.
Published: June 2008

This paper gives an interpretation of the classical PID controller tuning based on the fractional calculus theory. The PID parameters are calculated according with the specifications of an elementary system whose open-loop transfer function is a fractional order integrator (FOI). The performances of the two systems are compared and illustrated through the frequency and time responses.
Geometric Interpretation of Discrete Fractional Order Controllers Based on Sampling Time Scaling Property and Experimental Verification of Fractional 1/Sα Systems’ Robustness
Authors: Ma Chengbin , Hori Yoichi
Published: June 2008

This article proposes a geometric interpretation of discrete fractional order controllers based on sampling time scaling property. Due to its clear interpretation, satisfactory accuracy and easy programming, the property could be used as a reliable simulation and realization method for fractional order control systems. The experiments of one-inertia speed control with fractional order integral controllers realized by the proposed sampling time property are also carried out to verify the theoretical robustness of fractional 1/sα systems. The experimental results show the superior robustness performances of fractional 1/sα systems against saturation non-linearity and inertia variation, which highlights the promising aspects of fractional order control.
The CRONE Suspension: Modelling and Stability Analysis
Authors: Moreau Xavier , Altet Olivier , Oustaloup Alain
Published: June 2008

The CRONE suspension, French acronym of “suspension a` Comportement Robuste d’Ordre Non Entier”, results from a traditional suspension system whose spring and damper are replaced by a mechanical and hydropneumatic system defined by a fractional (so-called non-integer) order force-displacement transfer function. Modelling, frequency-domain robust control design methodology and internal stability analysis are presented in this paper.
Fractional Order: Frequential Parametric Identification of the Skin Effect in the Rotor Bar of Squirrel Cage Induction Machine
Authors: Canat Sylvain , Faucher Jean
Published: June 2008

In this article, the authors propose a method of modeling of the skin effect in the rotor bars of asynchronous motors. Two compact transfer functions with a fractional order were selected to represent the admittance of the bar. The compactness of these transfer functions makes it possible to take into account the diffusive phenomenon of the skin effect on a broad frequency band and is characterized by a small quantity of parameters to identify. The authors carried out an identification by the method of the model associated with an iterative procedure of Levenberg-Marquardt.
On the Generalized Navier-Stokes Equations
Authors: El-Shahed Moustafa , Salem Ahmed
Published: June 2008

In this paper, we present a general Inodel of the classical Navier-Stokes equations. With the help of Laplace, Fourier Sine transforms, finite Fourier Sine transforms, and finite Hankel transforms, an exact solutions for three different special cases have been obtained.
Fractional Giona-Roman Equation on Heterogeneous Fractal Structures in External Force Fields and Its Solutions
Authors: Ren Fu-Yao , Liang Jin-Rong , Qiu Wei-Yuan , Xu Yun
Published: June 2008

We introduce a heterogeneous fractional Giona-Roman equation (HFGRE) on heterogeneous fractal structure media describing systems involving external force fields. The HFGRE is shown to obey generalized Einstein relation, and its stationary solution is the Boltzmann distribution. It is proved that the asyrnptotic shape of its solution is a stretched Gaussian and that its solution can be expressed in the form of a function of a dimensionless similarity variable for the case of constant potentials, linear potentials, harmonic potentials, analytic potentials, logarithm potentials and generic potentials.
Chaotic Vibration and Internal Resonance Phenomena in Rotor Systems: Part I — Theoretical Analysis
Authors: Inoue Tsuyoshi , Ishida Yukio
Published: June 2008

Naturally, the gyroscopic moment is small for the many practical rotating machineries. In addition, some mechanical elements of a rotor system make various types of nonlinearity such as clearance in a ball bearing (Yamamoto, 1955)(Yamamoto, 1977), oil film in a journal bearing (Tondl, 1965), geometrical nonlinearity due to the shaft elongation (Shaw, 1988),(Ishida, 1996), etc. In such rotor systems, the natural frequencies of a forward whirling mode pf and a backward whirling mode pb almost satisfy the relation of internal resonance pf : pb = 1 : (−1). And then, the critical speeds of a backward harmonic oscillation and a supercombination oscillation are near from the major critical speed. Similarly, in the vicinity of two times of the major critical speed, the critical speeds of the forward and the backward subharmonic resonances of order 1/2 and the combination resonance are close to each other. Therefore, the internal resonance phenomena may occur at the major critical speed and two times of the major critical speed. However there are few studies on the nonlinear phenomena of the rotor systems due to the influence of internal resonance. In this study, we use a 2DOF rotor model and investigate the dynamic characteristics of nonlinear phenomena, especially the chaotic vibration, due to the internal resonance at the major critical speed and the critical speed of two times of the major critical speed. The following are clarified theoretically: (a) the Hopf bifurcation and consecutive period doubling bifurcations possible route to chaos occur at the major critical speed and at two times of the major critical speed, (b) another chaotic vibration from the combination resonance occur at two times of the major critical speed. The results demonstrate that the chaotic vibration is common nonlinear phenomena in the nonlinear rotor system when the effect of the gyroscopic moment is small.
Chaotic Vibration and Internal Resonance Phenomena in Rotor Systems: Part II — Experimental Analysis
Authors: Inoue Tsuyoshi , Ishida Yukio
Published: June 2008

In the practical rotating machinery, the gyroscopic moment is often small. In addition, some mechanical elements of a rotor system make various types of nonlinearity. In such rotor systems, the natural frequency of a forward whirling mode pf and that of a backward whirling mode pb almost satisfy the relation of internal resonance pf : pb = 1 : (−1). However there are few studies on the nonlinear phenomena of the rotor systems due to the influence of internal resonance, especially the experimental investigation have not been reported. In this study, we investigate experimentally the dynamical characteristics of nonlinear phenomena due to the internal resonance at the major critical speed and at two times of the major critical speed. The following are clarified experimentally: (a) the amplitude modulated vibration due to Hopf bifurcation from the steady state vibration occur and then the chaotic vibration occur at the major critical speed, (b) the amplitude modulated vibration due to Hopf bifurcation from the steady state subharmonic resonance of order 1/2 occur and then the chaotic vibration occur at two times of the major critical speed, (c) another chaotic vibration from the combination resonance occur at two times of the major critical speed. These experimental results match to the theoretical results (Part I).
Problems of Vibration Near Critical Speeds in Rigid Rotors With Autobalancing Devices
Authors: Ryzhik Boris , Sperling Lutz , Duckstein Henner
Published: June 2008

Automatic balancing devices comprising several balls in circular tracks can efficiently compensate rigid rotor unbalances in the post-critical ranges of rotational speed. However, near critical speeds the vibration level can be comparatively high as a result of non-synchronous ball motions. The paper considers the possibility of parameter optimization and phase control as tools for reducing rotor vibrations near critical speeds.
Dynamic Analysis of an Unsymmetrical Rotor Supported by Oil Film Bearing
Authors: Liu Zhansheng , Huang Senlin , Su Jiexian , Xia Songbo
Published: June 2008

Unsymmetrical rotor is a type of rotor widely used in engineering, which has different characteristic from symmetrical rotor and is less stable especially. With application to finite element method and Newmark-β method, dynamic characteristic of symmetrical rotor and three types of unsymmetrical rotor are investigated. The numerical and experimental results show that, in the same boundary conditions, speeds of oil whirl and whip are decreasing with the increase of stiffness asymmetry, and become less stable.
Test Response of a Turbocharger Supported on Floating Ring Bearings: Part I — Assessment of Subsynchronous Motions
Authors: Holt Chris , San Andre´s Luis , Sahay Sunil , Tang Peter , La Rue Gerry , Gjika Kostandin
Published: June 2008

Measurements of casing acceleration on an automotive turbocharger running to a top speed of 115 krpm and driven by ambient temperature pressurized air are reported. Waterfall acceleration spectra versus rotor speed show the effects of increasing lubricant inlet pressure and temperature on the turbocharger rotordynamic response. A comprehensive analysis of the test data forwards regimes of speed operation with two subsynchronous whirl motions (rotordynamic instabilities). Increasing the lubricant feed pressure delays the onset speed of instability for the most severe subsynchronous motion. However, increasing the lubricant feed pressure also produces larger synchronous displacements. The effect of lubricant feed temperature is minimal on the onset and end speeds of rotordynamic instability. Nevertheless, operation with a cold lubricant exhibits lower amplitudes of motion, synchronous and subsynchronous. The experimental results show the subsynchronous frequencies of motion do not lock (whip) at system natural frequencies but continuously track the rotor speed. No instabilities (subsynchronous whirl) remain for operating speeds above 90 krpm. Bearings greatly influence turbocharger (TC) rotordynamic performance.
Test Response of a Turbocharger Supported on Floating Ring Bearings: Part II — Comparisons to Nonlinear Rotordynamic Predictions
Authors: Holt Chris , San Andre´s Luis , Sahay Sunil , Tang Peter , La Rue Gerry , Gjika Kostandin
Published: June 2008

Linear and nonlinear analysis results for the operation of a small automotive turbocharger supported on floating ring bearings are presented. A comprehensive fluid film bearing model predicting the forced response of floating ring bearings is also described. The linear rotordynamic model predicts well the rotor free-free modes and onset speed of instability using linearized bearing force coefficients. The nonlinear model incorporating instantaneous bearing reaction forces in the numerical integration of the rotor equations of motion predicts the limit cycle amplitudes with two fundamental sub synchronous whirl frequencies. Comparisons of both models to experimental results follow. The predictions evidence two unstable whirl ratios at approximately 1/2 ring speed and 1/2 ring speed plus 1/2 journal speed. The transient nonlinear responses reveal the importance of rotor imbalance in suppressing the subsynchronous instabilities at large rotor speeds as also observed in the experiments.
Response and Stability of a Gas Pocket Damper Seal to Large Rotor Displacements
Authors: Armendariz Ramon Alberto Aguilar , Vance John M.
Published: June 2008

Pocket damper seals (PDSs) have been shown to offer an improved rotordynamic performance compared to conventional labyrinth seals, providing large amounts of direct damping and small cross-coupled coefficients. To this date, the rotordynamic characteristics of the PDSs have been determined using linearized models, with validity limited to small displacements of the rotor. The present investigation determines the effect of the nonlinear forces arising from the pocket damper seal on the response and stability of a PDS-rotor system when subjected to large dynamic excitations. It is determined that the nonlinear forces maintain bounded amplitudes of vibration (“limit cycles”) after the rotor passes the threshold speed of instability predicted by the linear theory. It is also found that the critical speed of the PDS-rotor system is well predicted by using both linear and nonlinear models of the seal forces, as both predictions compare well with the experimental measurements.
Ball Bearing Vibration Analysis Including Localized and Distributed Defects
Authors: Sopanen Jussi T. , Mikkola Aki M.
Published: June 2008

This study proposes the dynamic model of a deep groove ball bearing with six degrees of freedom. The model includes descriptions of non-linear Hertzian contact deformation and elastohydrodynamic fluid film. The geometry, material properties and diametral clearance of the bearing are given as the input to the proposed model. The bearing force and torque components are calculated from the relative displacements and velocities between bearing rings. Distributed defects such as the waviness of the inner and outer ring, and localized defects, such as inner and outer ring defects, are taken into consideration in the proposed model. The effect of the diametral clearance of the bearing on the natural frequencies and vibration response of the rotor bearing system is studied. The diametral clearance is found to have a significant effect on the level of vibration as well as on the natural frequencies. Low-order waviness, also known as out-of-roundness, is found to generate vibration at frequencies of the waviness order multiplied by the rotation speed. Localized defects in the inner and outer ring are found to generate vibrations at bearing defect frequencies. The simulation results are in line with the analytical and experimental results available in literature. The proposed ball bearing model could be used in the general multibody or rotor dynamics computer code as an interference element between the rotor and the housing.
Vibration Suppression by an Elastic Impact Damper
Authors: Yasuda Kimihiko , Kamiya Keisuke , Kato Rentaro
Published: June 2008

This paper concerns a new type of impact damper, an elastic impact damper (EID), which is made of an elastic impacting body and a container. First, damping effect of an EID is examined experimentally. Then, based on the observed motion of the impacting body, a mathematical model for the EID is derived. The validity of the model is confirmed by comparing the responses predicted by the model with those observed in the experiment. Based on the model, mechanism of the damping effect of the EID is examined. Finally, effects of the parameters of the EID is studied, and hints for designing an effective EID is presented.
New Hydraulic System Modelling
Authors: Pfeiffer Friedrich , Borchsenius Fredrik , Foerg Martin
Published: June 2008

One of the drawbacks of classical hydraulic system models consists in the fact, that the simulation programs couple the hydraulic components by compressible joints. Since the compressibility of oil is very small, we get stiff differential equations. To avoid these difficulties stiff elastic couplings can be replaced by unilateral constraints. Examples for hydraulic components with unilateral behavior are check valves, cylinders with stop limits and fluid volumes, in which cavitation can occur. The resulting complementarity equations can be solved with a standard Lemke algorithm. Compared to conventional methods, this leads to a significant reduction of computing times.
Nonlinear Normal Modes for Vibratory Systems Under Periodic Excitation
Authors: Jiang Dongying , Pierre Christophe , Shaw Steven W.
Published: June 2008

This paper considers the use of numerically constructed invariant manifolds to determine the response of nonlinear vibratory systems that are subjected to periodic excitation. The approach is an extension of the nonlinear normal mode formulation previously developed by the authors for free oscillations, wherein an auxiliary system that models the excitation is used to augment the equations of motion. In this manner, the excitation is simply treated as an additional system state, yielding a system with an extra degree of freedom, whose response is known. A reduced order model for the forced system is then determined by the usual nonlinear normal mode procedure, and an efficient Galerkin-based solution method is used to numerically construct the attendant invariant manifolds. The technique is illustrated by determining the frequency response for a simple two-degree-off-reedom mass-spring system with cubic nonlinearities, and for a discretized beam model with 12 degrees of freedom. The results show that this method provides very accurate responses over a range of frequencies near resonances.
Nonlinear Dynamics of a System of Coupled Oscillators With Essential Stiffness Nonlinearities
Authors: Vakakis Alexander F. , Rand Richard H.
Published: June 2008

We study the resonant dynamics of a two-degree-of-freedom system composed a linear oscillator weakly coupled to a strongly nonlinear one, with an essential (nonlinearizable) cubic stiffness nonlinearity. For the undamped system this leads to a series of internal resonances, depending on the level of (conserved) total energy of oscillation. We study in detail the 1:1 internal resonance, and show that the undamped system possesses stable and unstable synchronous periodic motions (nonlinear normal modes — NNMs), as well as, asynchronous periodic motions (elliptic orbits — EOs). Furthermore, we show that when damping is introduced certain NNMs produce resonance capture phenomena, where a trajectory of the damped dynamics gets ‘captured’ in the neighborhood of a damped NNM before ‘escaping’ and becoming an oscillation with exponentially decaying amplitude. In turn, these resonance captures may lead to passive nonlinear energy pumping phenomena from the linear to the nonlinear oscillator. Thus, sustained resonance capture appears to provide a dynamical mechanism for passively transferring energy from one part of the system to another, in a one-way, irreversible fashion. Numerical integrations confirm the analytical predictions.
Study on the Method of Modified Random Decrement for Transfer Function
Authors: Zhang Zhenzhong , Zhu Shijian
Published: June 2008

This paper presents a modified random decrement method to obtain the steady-state response of vibration system. The expressions are deduced. Two numerical simulations and verification are given. The efficiencies of the modified method and the conventional process are compared. It is shown that the method is more efficient than the conventional process to diminish the influence of the initial excitation on the transfer function calculation of the vibration system.
Dynamical Systems Approach to Material Damage Diagnosis
Authors: Chelidze David
Published: June 2008

In this paper, a dynamical systems approach to material damage identification is presented. This methodology does not depend on knowledge of the particular damage physics of material fatigue. Instead, it provides experimental means to determine what are practically observable and observed facts of damage accumulation, thus making it possible to develop or experimentally verify appropriate damage evolution laws. The procedure implicitly uses the fact that the system undergoing fatigue damage accumulation possesses time scale separation, where damage accumulation occurs on a much slower time scale than the observable dynamics of a system. Damage tracking is achieved using a two-time-scale modeling strategy based on phase space reconstruction. Fast-time oscillation data is collected and used to estimate a damage tracking function by calculating the short time reference model prediction error. Tracking metrics based on these estimates are used as feature vectors. Damage identification is achieved either by applying proper orthogonal decomposition or optimal tracking methods to these vectors. The method is experimentally validated using an elasto-magnetic system, in which a harmonically forced cantilever beam in a nonlinear magnetic field accumulates fatigue damage. The damage tracking results were virtually identical for both identification schemes. In both cases tracking data showed power-law type monotonic trends. These results were in good agreement with the Paris fatigue crack growth model during the time-period of macroscopic crack growth. In addition, the tracking provides much needed insight into the incipient or early damage accumulation process, where only one scalar damage variable is needed to describe the incipient or early damage accumulation process.
A Model for the Coupled Lift and Drag on a Circular Cylinder
Authors: Nayfeh Ali H. , Owis Farouk , Hajj Muhammad R.
Published: June 2008

The time-varying coupled lift and drag coefficients acting on a circular cylinder are modeled. Data used for the model are obtained by numerically solving the unsteady Reynolds-Averaged Navier Stokes equations over a wide range of Reynolds numbers. Using spectral moments, we determine the frequency components in the lift and drag coefficients and their phase relations. Using a perturbation technique, we obtain approximate solutions of both the van der Pol and Rayleigh equations. By fitting the amplitude and phase relations, we find that the van der Pol equation is the suitable model for the lift. The Rayleigh equation fails to give the correct phase relation. Because the major frequency in the drag component is twice that of the lift, the drag component is modeled as a quadratic function of the lift. Through analysis with higher-order spectral moments, the correct quadratic relation of the lift that yields the drag is determined. The model and results presented here are a first step in the development of a reduced-order model for vortex-induced vibrations, which includes the motions of the cylinder.
Motion and Vibration Control of a Flexible Transportation System
Authors: Takemoto Keisuke , Mori Masato , Watanabe Toru , Seto Kazuto
Published: June 2008

This paper shows a lumped modeling approach and a motion and vibration control method for a transportation system. The modeling approach is made on the premise that motion influences vibration, but that vibration doesn’t influence motion. To obtain well suppressed vibration and a robustness for the system, LQI control is adopted. It is shown that this theory has superior robustness for in motion and vibration control with variations of the parameters [1]. The control effectiveness is demonstrated through simulation experiments. The vibration modes that occur accordingly become flexible might cause a spillover instability problem. Thus, the purpose of the research is to control such vibration and motion using the modeling method presented by Seto, called the “reduced order physical modeling method” [2]. Computer simulation and control experiments are carried out and the effectiveness of the procedures presented is investigated.
Rotor Stability Criteria for Multi-Stage Centrifugal Compressors
Authors: Fulton John W.
Published: June 2008

The American Petroleum Standard 617, 7th edition [1], screens new designs of centrifugal compressors using its Figure 1.2-5, which plots mean gas density versus rotor flexibility ratio. The purpose is to avoid rotor instability from causing unacceptable vibrations, typically whirling of the first-forward bending mode. The API figure is based on a plot by Fulton [2,3] of the same variables showing a number of compressors tested near the threshold of instability, thus forming an empirical basis for a Stability Map. This paper develops a method to derive a threshold line, using a set of typical industrial rotors varying in flexibility and running on tilt pad bearings. Instability requires a tangential force (normal to the bending displacement) to act on the rotor in the direction of whirl. The source of this force is taken to be the (tooth type) labyrinth seals inside the compressor. This tangential force is represented as linear function of whirl/spin scaled by gas density. This function is applied to the set of rotors to produce a threshold line. The derivation thus forms a basis for understanding the Stability Map.
Usage of the Lund Rotordynamic Programs in the Analysis of Centrifugal Compressors
Authors: Memmott Edmund A.
Published: June 2008

This paper is intended to be a history of the usage of the Jorgen Lund rotordynamic programs in the analysis of centrifugal compressors from the perspective of the author’s experience in that industry. Application of the Lund tilt pad bearing, rotor response, and stability programs will be described. They will be seen to be the basis for an industry wide acceptance criterion for the rotor dynamics of centrifugal compressors. They are used in the required audit reports for new compressors, and in trouble shooting investigations on the rotordynamics of centrifugal compressors.
Dynamic Evaluation of a Three Point Mount Baseplate for a Motor Driven, Centrifugal Compressor Package
Authors: Kubany Joseph S. , Tecza Joseph A. , Gustafsson Per
Published: June 2008

Maintaining acceptable alignment can be an issue for rotating machinery on off-shore floating platforms. Distortion arising from motion within the platform can change the alignment of the production machinery if that machinery is mounted rigidly to the platform. One way to eliminate the effects of such distortion is to attach the machinery on its own baseplate, which is connected to the platform using a three point mounting system. Anti-Vibration Mounts (AVMs) are used at each support location, and these devices are effective in isolating the baseplate and its machinery from the surrounding structure. The package discussed in this paper consists of a centrifugal compressor, a gear, and a 6.3 MW (8500 hp) variable speed motor (1000–1890 RPM) mounted on a baseplate. The equipment train has vibratory modes that could not be moved from the operating speed range. Some of these mode shapes show coupled motion between the motor and the baseplate. Test results were compared to the detailed Harmonic Response Finite Element Analysis (FEA) of the coupled structure, which predicts both baseplate resonance and motor rotor response amplitudes. Both analysis and testing demonstrate that these modes do not have a significant effect on package operation.
Reduction of High-Amplitude Cogging Torque Response in a 12,000 Horsepower Synchronous Drive Motor
Authors: Corliss James M. , Pant Siddharth , Hui Kevin , Duddy Larry , Veno Jon
Published: June 2008

A new 12,000 horsepower adjustable speed drive system has recently been installed in the NASA Langley 14- by 22-Foot Subsonic Wind Tunnel. The new system consists of a salient pole synchronous motor powered by a 12-pulse cycloconverter adjustable speed drive. During system commissioning the drive line torsional vibrations were measured with strain gages and a telemetry-based data acquisition system. Torque measurements were taken during transient and steady-state operations at speeds where the drive motor’s pulsating torques matched the drive line’s torsional natural frequency. Measured peak torsional vibrations during steady-state operation were comparable to values predicted by a finite element model forced response analysis. An unexpected oscillating torque occurred during low speed operations where the motor’s cogging torque matched the torsional natural frequency. The oscillating torque was higher than the mean torque at this speed, and the motor’s electrical flux was tailored in this speed range to reduce the response to acceptable levels. A half-power bandwidth analysis of the torsional resonances concluded that the torsional critical damping ratio of the driveline was approximately 0.7%.
Hydrostatic Gas Journal Bearings for Micro-Turbomachinery
Authors: Liu L. X. , Teo C. J. , Epstein A. H. , Spakovszky Z. S.
Published: June 2008

Several years ago an effort was undertaken at MIT to develop high-speed rotating MEMS (Micro Electro-Mechanical Systems) using computer chip fabrication technology. To enable high-power density the micro-turbomachinery must be run at tip speeds of order 500 m/s, comparable to conventional scale turbomachinery. The high rotating speeds (of order 2 million rpm), the relatively low bearing aspect ratios (L/D < 0.1) due to fabrication constraints, and the laminar flow regime in the bearing gap place the micro-bearing designs to an exotic spot in the design space for hydrostatic gas bearings. This paper presents a new analytical model for axially fed gas journal bearings and reports the experimental testing of micro gas bearings to characterize and to investigate their rotordynamic behavior. The analytical model is capable of dealing with all the elements of, (1) micro-devices, (2) dynamic response characteristics of hydrostatic gas bearings, (3) evaluation of stiffness, natural frequency and damping, (4) evaluation of instability boundaries, and (5) evaluation of effects of imbalance and bearing anisotropy. First, a newly developed analytical model for hydrostatic gas journal bearings is introduced. The model consists of two parts, a fluid dynamic model for axially fed gas journal bearings and a rotordynamic model for micro-devices. Next, the model is used to predict the natural frequency, damping ratio and the instability boundary for the test devices. Experiments are conducted using a high-resolution fiber optic sensor to measure rotor speed, and a data reduction scheme is implemented to obtain imbalance-driven whirl response curves. The model predictions are validated against experimental data and show good agreement with the measured natural frequencies and damping ratios. Last, the new model is successfully used to establish bearing operating protocols and guidelines for high-speed operation.
An Optimal Shaft Balance Solution Using Integer Programming
Authors: Bechhoefer Eric , Tayloe Shawn
Published: June 2008

A mathematical solution for optimal balance weights is presented for single-plane, discrete weight and discrete adjustment point balance. The algorithm uses influence coefficients, either given or derived, and measured synchronous complex vibration data to determine the best adjustment. The solution has a user selected objective: minimum residual vibration or minimum number of adjustments to reach a given vibration. The algorithm is part of Goodrich’s Integrated Mechanical Diagnostics Health Usage Monitoring System (IMD HUMS), currently installed on a number of helicopter platforms.
A Parametric Absorber for Friction-Induced Vibrations
Authors: Ecker Horst
Published: June 2008

This contribution deals with the suppression of friction-induced vibrations of a mechanical system. A two-mass system is considered, with the main mass excited by a friction-generated self-excitation force and a smaller second mass attached to the main mass. The parameter of the connecting stiffness between the main mass and the absorber mass is a harmonic function of time and represents a parametric excitation. The purpose of the second mass is to act as a “parametric absorber” and to cancel vibrations. Critical values for the damping parameters of the conventional system are calculated, where the system operates on the stability limit. Analytical and numerical methods are employed to determine the stability of the parameter-excited system. A study for selected parameters shows within which limits friction-induced vibrations can be suppressed effectively by a parametric absorber.
Order Tracking Filtering Based on Instantaneous Frequency Estimation and Zero-Phase Distortion Digital Filtering
Authors: Qin Shuren , Guo Yu
Published: June 2008

A new method for run-up or coast down vibration signal order tracking filtering of rotating machinery based on instantaneous frequency estimation and zero-phase distortion digital filtering is proposed in this paper. By contrast with traditional methods of order tracking filtering, the features of tacholess, no hardware-based tracking filter required and no frequency shift to original sampling data, etc, make it more attractive. The theorems and algorithms of the method are detailed discussed in this paper. The filtering of overlapped data blocks is used to restrain the edge effect, which caused by digital filtering, is also introduced. An actual test example of a motor’s run-up and coast down vibration is introduced to demonstrate the validity of the method.
Stability Analysis of a Vibrational System Subject to Negative Viscous Damping and Displacement-Dependent Dry Friction Damping
Authors: Ferri Aldo A. , Whiteman Wayne E.
Published: June 2008

A stability analysis is conducted of an autonomous single-degree-of-freedom system damped with negative viscous damping and a displacement-dependent Coulomb friction force. The geometry of the dry friction damping element yields a friction force that grows linearly with the system displacement. The most direct application of this system is in the study of a turbomachinery blade with shroud interfaces designed to achieve this geometry. Recent studies have shown that the damping of systems with this type of displacement-dependent dry friction force resembles linear structural damping and suggests that this arrangement may be an effective means of flutter suppression in these turbine and fan blade applications. For this study, the inclusion of negative viscous damping is used in order to approximate destabilizing aerodynamic forces. An exact analysis is conducted to determine the stability of this autonomous system. Results show that energy losses from the displacement-dependent dry friction damper are large enough to achieve local and even global stability under certain conditions.
Shock Isolation Through Passive Energy Pumping in a System With Piecewise Linear Stiffnesses
Authors: Georgiadis Fotios , Vakakis Alexander F. , McFarland D. Michael , Bergman Lawrence
Published: June 2008

We investigate shock isolation designs based on nonlinear energy pumping caused by piecewise stiffness elements. In particular, we numerically study the shock isolation properties of a primary linear system of two coupled non-conservative oscillators with weakly coupled attachments possessing clearance nonlinearities. Under shock excitation the nonlinear attachments (termed nonlinear energy sinks – NESs) can be designed to absorb a significant portion of the input energy, thus enhancing the shock isolation performance of the primary system. In contrast to the classical linear vibration absorber whose operation is restricted to narrowband frequency ranges, the NESs are capable of efficiently absorbing energies caused by transient broadband disturbances, a feature that facilitates their implementation in practical applications. Moreover, the non-smooth nonlinearities considered in this work are easily implementable since they are realized by means of linear stiffness elements.
Discrete Dynamic Modeling of Shafts With Transverse Cracks Using Bond Graph
Authors: Durali Mohammad , Borhan Hosein
Published: June 2008

Discrete dynamic modeling of rotating Timoshenko shafts deflecting in axial, shear and bending directions is discussed in this article. The method presented here aims for developing an algorithm by which shafts with transverse cracks can easily be modeled and analyzed. To this end, a modular dynamic network is constructed, consisting of a mass, springs and dampers, resembling shaft segments between cracks. The local changes in shaft stiffness as a result of cracks rotating (opening and closing), is entered into the module models as change in springs and dampers properties. The modular model is then repeated to obtain a complete shaft model. Bond Graph method is used in a similar modular manner to extract dynamic equations of shaft motion. The equations have then been solved for shaft lateral displacement and behavior under external loadings. The method presented here enables the users to develop a model of the shaft to simulate the behavior of shafts having cracks, with today’s computational software.
Three Conditions Lyapunov Exponents Should Satisfy
Authors: Lou Jingjun , Zhu Shijian
Published: June 2008

In contrast to the unilateral claim in some papers that a positive Lyapunov exponent means chaos, it was claimed in this paper that this is just one of the three conditions that Lyapunov exponent should satisfy in a dissipative dynamical system when the chaotic motion appears. The other two conditions, any continuous dynamical system without a fixed point has at least one zero exponent, and any dissipative dynamical system has at least one negative exponent and the sum of all of the 1-dimensional Lyapunov exponents id negative, are also discussed. In order to verify the conclusion, a MATLAB scheme was developed for the computation of the 1-dimensional and 3-dimensional Lyapunov exponents of the Duffing system with square and cubic nonlinearity.
Performance of Piecewise Linear Vibration Isolators Under Harmonic Excitation
Authors: He Qiwei , Lou Jingjun , Zhu Shijian
Published: June 2008

Piecewise linear vibration isolators under force excitation are analyzed. Isolators with symmetric restoring forces are considered. The method of numerical simulation is used to obtain the response and force transmissibility. The effects of stiffness ratio and piecewise gap on force transmissibility are reported. The effects of gap on the maximum acceleration of the mass are also discussed here.
Three Fingered Flexible Fixture Design
Authors: Arzanpour Siamak , Mills James K. , Cleghorn William L.
Published: June 2008

Fixturing is an important requirement for many manufacturing and assembly operations. If flexible manufacturing and assembly system are to be truly flexible then the fixturing must also be flexible. A novel grasping strategy and gripper for fixturing in 3-D is presented for robotic assembly. The proposed fixture has three fingers, each equipped with a suction cup, to ease the grasping process and increase attaching flexibility. Using this method, the designed fixture is sufficiently general in order to fully grasp a variety of generic parts. To position suction cups, several linkage-based mechanisms are employed. Pneumatic cylinders and electrical motors are used as actuators to solve the space limitation and weight problem. Software has been developed to calculate the relative positions and angles in the mechanism as required for reconfiguration. A novel localization method is established to compensate for errors related to initial dislocation of the part due to low accuracy part bins from which parts are grasped. Several force and mechanism simulations are provided to verify the function and performance of the fixture.
Distributed-Parameters Base Modeling and Vibration Analysis of Micro-Cantilevers Used in Atomic Force Microscopy
Authors: Jalili Nader , Dadfarnia Mohsen , Dawson Darren M.
Published: June 2008

The atomic force microscope (AFM) system has evolved into a useful tool for direct measurements of intermolecular forces with atomic-resolution characterization that can be employed in a broad spectrum of applications such as electronics, semi-conductors, materials, manufacturing, polymers, biological analysis, and biomaterials. The noncontact AFM offers unique advantages over other contemporary scanning probe techniques such as contact AFM and scanning tunneling microscopy. Current AFM imaging techniques are often based on a lumped-parameters model and ordinary differential equation (ODE) representation of the micro-cantilevers coupled with an ad-hoc method for atomic interaction force estimation (especially in non-contact mode). Since the magnitude of the interaction force lies within the range of nano-Newtons to pica-Newtons, precise estimation of the atomic force is crucial for accurate topographical imaging. In contrast to the previously utilized lumped modeling methods, this paper aims at improving current AFM measurement technique through developing a general distributed-parameters base modeling approach that reveals greater insight into the fundamental characteristics of the microcantilever-sample interaction. For this, the governing equations of motion are derived in the global coordinates via the Hamilton’s Extended Principle. By properly selecting a set of general coordinates, the resulting non-homogenous boundary value problem is then converted to a homogenous one, and hence, analytically solvable. The AFM controller can then be designed based on the original infinite dimensional distributed-parameters system which, in turn, removes some of the disadvantages associated with the truncated-model base controllers such as control spillovers, residual oscillations and increased order of the control. Numerical simulations are provided to support these claims.
Dynamic Modeling and Simulation of Impact in Tether Net/Gripper Systems
Authors: Mankala Kalyan K. , Agrawal Sunil K.
Published: June 2008

The objective of this paper is to study the dynamic modeling and simulation of a tether-net/gripper system during an impact, while it is being deployed or retrieved by a winch on a satellite orbiting around earth. We stick to Tether-Net system but the analysis is applicable to Tether-Gripper systems too. We assume that the net is deployed from the satellite in orbit and the motion is restricted to the orbital plane. This net captures a second satellite and tows it. The motion of a tether-net system can be broken down into the following phases: (i) Phase 1: Net is shot out from the satellite with the tether completely slack, (ii) Phase 2: Net comes to a location where the tether is taut while the drum on the orbiter is locked, (iii) Phase 3: Drum is unlocked and the net moves with the tether, (iv) Phase 4: Net captures a body. The continua (tether) is modeled using mode functions and coordinates. The theory of impulse and momentum can be used to model Phases 1, 2, and 4 of motion of the tether-net system. The dynamics of the motion of the system in phase 3 is characterized by differential and algebraic equations (DAEs). Matlab ODE solvers were used to solve these DAEs.
Modeling and Direction Control of a 2 D.O.F. Heavy Launching Bed on a Moving Car Using a Full Suspension Model
Authors: Durali Mohammad , Afsharzadeh Arash
Published: June 2008

In this paper dynamic modeling and direction control of a launching bed (L.B.) with 2 D.O.F. rotation around vertical and lateral axes, mounted on a vehicle moving on a rough road is investigated. The purpose of direction control is to bring the L.B. from any initial angle to a desired angle with respect to the reference frame and to keep it there. The vehicle model is a full car with bounce, yaw, roll and pitch degrees of freedom. The suspension system of the vehicle is considered to have passive elements and unsprung masses. The stiffness of the tires is also included in the model. To control the position of the launching bed, a servo-hydraulic system comprising of hydro-motors, gearboxes, control servo-valves and a pressure compensated pump is employed. The dynamic equations of vehicle, L.B. and actuating control system are derived using Bond Graph method. The system was then detail designed for a utility vehicle with a heavy launching tower. The performance of the control system was evaluated for rough road conditions using computer simulation.
Effect of Dynamics on Path Planning of Mobile Robots
Authors: Wenzel Bryan , Nataraj C.
Published: June 2008

This paper deals with accurate path planning of two kinds of mobile robots: conventionally steered and differentially steered. In particular, we are concerned with the effect of dynamics. Dynamic models are derived, and numerical and experimental results are presented. The effects of varying mass, velocity and manipulator arms on the mobile robots are presented.
Robust Control in Bending and Torsional Coupled Vibrations of a Flexible Robot Arm
Authors: Takamura Kohei , Yamamoto Kousuke , Kawabe Hiromiti , Dyke Shirley J. , Watanabe Toru , Seto Kazuto
Published: June 2008

This paper address that the vibration control system design for a flexible arm which possesses bending and torsional coupled vibrations. First, an experimental flexible arm is made which has a rotational shaft driven by a servomotor in one end, and an auxiliary mass connected to the other end so that the center of the stiffness of the arm may not exist on the direction of motion of the auxiliary mass which denotes payload. Three degree-of-freedom (DOF) reduced order model is identified according to Seto’s procedure. Based on the obtained model, robust control design procedure utilizing H-infinity control theory is applied. In the controller design procedure, the uncertainty associated with neglecting high frequency modes is represented by unstructured uncertainty. Computer simulations are carried out and it is clarified that the obtained controller achieved a good performance. The effectiveness of presented modeling method and controller design procedure are verified through control experiments.
Hopf Bifurcation in a Disk-Shaped NEMS
Authors: Zalalutdinov Maxim , Parpia Jeevak , Aubin Keith , Craighead Harold , Alan Tuncay , Zehnder Alan , Rand Richard
Published: June 2008

Self-sustained mechanical vibrations of a disc-type microfabricated resonator were experimentally observed when a continuous wave (CW) laser beam was focused on the periphery of the disc (for a 40 μm diameter resonator, natural frequency 0.89MHz, the laser power above a 250 W threshold was required). A theoretical model for self-oscillatory behavior has been developed based on FEM analysis of a stress pattern created within the resonator by the focused laser beam. This model accounts for the fact that the amount of absorbed laser light is modulated due to the motion of the resonator through the optical interferometric pattern. Analytical study reveals the presence of a Hopf-type bifurcation with a critical laser power close to the experimentally observed value. Harmonic balance analysis indicates the existence of a stable limit cycle in the phase plane determining the amplitude of self-oscillations.
A Nonlinear Reduced-Order Model for Electrostatic MEMS
Authors: Abdel-Rahman Eihab M. , Younis Mohammad I. , Nayfeh Ali H.
Published: June 2008

We present an analytical approach and a reduced-order model (macromodel) to investigate the behavior of electrically actuated microbeam-based MEMS. The macromodel provides an effective and accurate design tool for this class of MEMS devices. The macromodel is obtained by discretizing the distributed-parameter system using a Galerkin procedure into a finite-degree-of-freedom system consisting of ordinary-differential equations in time. The macromodel accounts for moderately large deflections, dynamic loads, and the coupling between the mechanical and electrical forces. It accounts for linear and nonlinear elastic restoring forces and the nonlinear electric forces generated by the capacitors. A new technique is developed to represent the electric force in the equations of motion. The new approach allows the use of few linear-undamped mode shapes of a microbeam in its straight position as basis functions in a Galerkin procedure. The macromodel is validated by comparing its results with experimental results and finiteelement solutions available in the literature. Our approach shows attractive features compared to finite-element softwares used in the literature. It is robust over the whole device operation range up to the instability limit of the device (i.e., pull-in). Moreover, it has low computational cost and allows for an easier understanding of the influence of the various design parameters. As a result, it can be of significant benefit to the development of MEMS design software.