Condition Monitoring of Rotor Using Active Magnetic Actuator

2008 ◽  
Author(s):  
Jerzy T. Sawicki ◽  
Michael I. Friswell ◽  
Alex H. Pesch ◽  
Adam Wroblewski
Keyword(s):  
Parametric Excitation ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Normal Operation ◽  
Robust Techniques ◽  
Induced Changes ◽  
Vibration Signatures ◽  
The Given ◽  
Rotor Dynamic ◽  
Cracked Rotor System

It has been widely recognized that the changes in the dynamic response of a rotor could be utilized for general fault detection and monitoring. Current methods rely on the monitoring of synchronous response of the machine during its transient or normal operation. Very little progress has been made in developing robust techniques to detect subtle changes in machine condition caused by rotor cracks. It has been demonstrated that the crack-induced changes in the rotor dynamic behavior produce unique vibration signatures. When the harmonic excitation force is applied to the cracked rotor system, nonlinear resonances occur due to the nonlinear parametric excitation characteristics of the crack. These resonances are the result of the coexistence of a parametric excitation term and different frequencies present in the system, namely critical speed, the synchronous frequency, and excitation frequency from the externally applied perturbation signals. This paper presents the application of this approach on an experimental test rig. The simulation and experimental study for the given rig configuration, along with the application of active magnetic bearings as a force actuator, are presented.

Further Results on Parametric Excitation of a Dynamic System

1965 ◽  
Vol 32 (2) ◽  
pp. 373-377 ◽  
Author(s):  
C. S. Hsu
Keyword(s):  
Dynamic System ◽  
Parametric Excitation ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Excitation Frequency ◽  
Constant Matrix ◽  
System Parameters ◽  
Multiple Degrees Of Freedom ◽  
The Stability ◽  
The Given

A dynamic system having multiple degrees of freedom and being under parametric excitation has been studied in an earlier paper [2]. However, the analysis given there necessitates certain restrictions on the distribution of the natural frequencies of the system. In this paper those restrictions are removed. The analysis presented here shows how to obtain a constant matrix whose eigenvalues determine the stability or instability of a system of ordinary differential equations with periodic coefficients at a given excitation frequency. The constant matrix is expressed entirely in terms of the given system parameters and the excitation frequency.

Nonlinear Dynamics of a Dielectric Elastomer Membrane Under Compressive Loading

2020 ◽  
Author(s):  
Robert L. Lowe ◽  
Christopher G. Cooley
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Response ◽  
Frequency Response ◽  
Compressive Loading ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Dielectric Elastomer ◽  
Large Strains ◽  
Membrane Stretch ◽  
Wide Range

Abstract This paper investigates the nonlinear dynamics of square dielectric elastomer membranes under time-dependent, through-thickness compressive loading. The dielectric elastomer is modeled as an isotropic ideal dielectric, with mechanical stiffening at large strains captured using the Gent hyperelastic constitutive model. The equation of motion for the in-plane membrane stretch is derived using Hamilton’s principle. The static response of the membrane is first investigated, with equilibrium stretches calculated numerically for a wide range of compressive pre-loads and applied voltages. Snap-through instabilities are observed, with the critical snap-through voltage decreasing with increasing compressive pre-load. The dynamic response of the membrane is then investigated under forced harmonic excitation. Frequency response plots characterizing the steady-state vibration reveal primary, subharmonic, and superharmonic resonances. Near these resonances, two stable vibration states are possible, corresponding to upper and lower branches in the frequency response. Significant and practically meaningful differences in the dynamic response are observed when the system vibrates at a fixed frequency about the upper and lower branches, a feature not discussed in previous research.

scholarly journals Research on the Resonance Characteristics of Rock under Harmonic Excitation

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Siqi Li ◽  
Shenglei Tian ◽  
Wei Li ◽  
Tie Yan ◽  
Fuqing Bi
Keyword(s):  
Resonance Frequency ◽  
Natural Frequency ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Theoretical Research ◽  
Transform Method ◽  
Factors Affecting ◽  
Least Action ◽  
Principle Of Least Action ◽  
Resonance Frequencies

In order to study the resonance characteristics of rock under harmonic excitation, two vibration models have been presented to estimate the natural frequency of rock encountered during the drilling. The first one is a developed single-DOF model which considers the properties and dimensions of the rock. The second one is a multi-DOF model based on the principle of least action. Subsequently, the modal characteristics, as well as the influence of excitation frequency, the mechanical properties, and dimensions of the rock on its resonance frequency, are analyzed by using FEM. Finally, the ultrasonic test on artificial sandstones and materials of drill tools are carried out indoor, and the FFT transform method is adopted to obtain their resonance frequencies. Based on the analysis undertaken, it can be concluded that the natural frequency of the rock increases with the change of vibration mode. For the same kind of rock, the resonance frequency is inversely proportional to mass, while for the different kinds of rocks, the mechanical parameters, such as density, elastic modulus, and Poisson’s ratio, determine the resonance frequency of the rock together. Besides, the shape of the rock is also one of the main factors affecting its resonance frequency. At last, the theoretical research results are further verified by ultrasonic tests.

Noise and Contact in Dynamic AFM Operations

2011 ◽  
Author(s):  
Ishita Chakraborty ◽  
Balakumar Balachandran
Keyword(s):  
White Noise ◽  
Evolution Equations ◽  
Stochastic Dynamics ◽  
Gaussian White Noise ◽  
Excitation Frequency ◽  
Period Doubling ◽  
Harmonic Excitation ◽  
Dynamic Mode ◽  
Grazing Impacts ◽  
Representative System

In this article, the authors study the effects of Gaussian white noise on the dynamics of an atomic force microscope (AFM) cantilever operating in a dynamic mode by using a combination of numerical and analytical efforts. As a representative system, a combination of Si cantilever and HOPG sample is used. The focus of this study is on understanding the stochastic dynamics of a micro-cantilever, when the excitation frequencies are away from the first natural frequency of the system. In the previous efforts of the authors, period-doubling bifurcations close to grazing impacts have been reported for micro-cantilevers when the excitation frequency is in between the first and the second natural frequencies of the system. In the present study, it is observed that the addition of Gaussian white noise along with a harmonic excitation produces a near-grazing contact, when there was previously no contact between the tip and the sample with only the harmonic excitation. Moment evolution equations derived from a Fokker-Planck system are used to obtain numerical results, which support the statement that the addition of noise facilitates contact between the tip and the sample.

scholarly journals Vibration and Stability of 3000-hp, Titanium Chemical Process Blower

2003 ◽  
Vol 9 (3) ◽  
pp. 197-217 ◽  
Author(s):  
Les Gutzwiller ◽  
Mark A. Corbo
Keyword(s):  
Normal Operation ◽  
Oil Film ◽  
Rotor Design ◽  
Tilting Pad ◽  
Shaft Alignment ◽  
Cold Condition ◽  
Metal Disk ◽  
Rotor Dynamic ◽  
Plant Process

This 74-in-diameter blower had an overhung rotor design of titanium construction, operating at 50 pounds per square inch gauge in a critical chemical plant process. The shaft was supported by oil-film bearings and was directdriven by a 3000-hp electric motor through a metal disk type of coupling. The operating speed was 1780 rpm. The blower shaft and motor shaft motion was monitored by Bently Nevada proximity probes and a Model 3100 monitoring system.Although the blowers showed very satisfactory vibration levels during test runs at the manufacturer's plant, the vibration levels in situ had always been higher than was desirable. After several months of monitoring showed ever increasing vibration levels, one of the blowers was shut down in order to diagnose and resolve the problem.Several steps were taken to diagnose the problem: (1) The rotor was removed and the shop balance was checked and corrected. (2) The bearing support movement due to thermal expansion was measured. Then the shafts were misaligned in the cold condition in order to achieve near-perfect shaft alignment during normal operation. (3) The expected shaft vibration at the bearings was determined using lateral rotor dynamics analysis, including critical speed mapping. (4) A heavy sleeve was added to the blower shaft to increase the radial load on the drive-end bearing. (5) The metal disk type of coupling was replaced by a gear coupling. (6) The finite element and impact of the bearing support pedestal were tested to determine the stiffness of the bearing support. (7) The shaft movement was measured during a coast-down. (8)Tilting-pad bearings were evaluated as a possible replacement for the original standard sleeve type of hydrodynamic oil-film bearings.The final solution showed the importance of coupling angular stiffness (often rarely considered in machine design), rotor dynamic analysis, and field alignment.

Use of Mass as a Perturbation Parameter in Vibrations

1967 ◽  
Vol 89 (4) ◽  
pp. 639-644 ◽  
Author(s):  
R. Chicurel ◽  
J. Counts
Keyword(s):  
Perturbation Technique ◽  
Excitation Frequency ◽  
Perturbation Parameter ◽  
Harmonic Excitation ◽  
Power Series Solution ◽  
Continuous Systems ◽  
Linear Vibration ◽  
Denominator Polynomial ◽  
Vibration Problems ◽  
Special Case

Linear vibration problems involving harmonic excitation of discrete and continuous systems are solved by using the classical perturbation technique. The perturbation parameter is proportional to a mass and the square of the excitation frequency. The power series solution for the displacement of some point in the system is converted to the quotient of two polynomials by the use of continued fractions. The eigenvalues (natural frequencies) of the problem are calculated by finding the roots of the denominator polynomial. The situation wherein a quantity which cannot vanish at any frequency can be found is treated as a special case.

Fuzzy Semi-Active Control of Multi-Degree-of-Freedom Structure Using Magnetorheological Elastomers

2017 ◽  
Author(s):  
Nguyen Xuan Bao ◽  
Toshihiko Komatsuzaki ◽  
Yoshio Iwata ◽  
Haruhiko Asanuma
Keyword(s):  
Active Control ◽  
Control Strategy ◽  
Control Strategies ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Effective Control ◽  
Magnetic Flux Density ◽  
Model Parameters ◽  
Structural Vibrations ◽  
Standard Linear Solid

Magnetorheological elastomer (MRE), used in semi-active control, has recently emerged as a smart material that could potentially improve traditional systems in controlling structural vibrations. This study considers two main issues concerning the application of an MRE. The first issue is the modelling and identification of the viscoelastic property, and the second is the formulation of an effective control strategy based on the fuzzy logic system. Firstly, a nonlinear dynamic MRE model was developed to simulate the dynamic behavior of MRE. In this model, the viscoelastic force of the material as an output was calculated from displacement, frequency, and magnetic flux density as inputs. The MRE model consisted of three components including the viscoelasticity of host elastomer, magnetic field-induced property, and interfacial slippage that were modeled by analogy with a standard linear solid model (Zener model), a stiffness variable spring, and a smooth Coulomb friction, respectively. The model parameters were identified by manipulating two sets of data that were measured by changing applied electric current and harmonic excitation frequency. A good agreement was obtained between numerical and experimental results. The proposed model offers a beneficial solution to numerically investigate vibration control strategies. Secondly, a fuzzy semi-active controller was designed for seismic protection of building with an MRE-based isolator. The control strategy was designed to determine the command applied current. The proposed strategy is fully adequate to the nonlinearity of the isolator and works independently with the building structure. The efficiency of the proposed fuzzy semi-active controller was investigated numerically by MATLAB simulations, whose performance was compared with that of passive systems and a system with traditional semi-active controller. Numerical results show that the developed fuzzy semi-active controller not only mitigates the responses of both the base floor and the superstructure, but also has an ability to control structural vibrations adaptively to the different intensity ground motions.

scholarly journals Experimental Study of a Variable Stiffness Seat Suspension Installed With a Compact Rotary MR Damper

2021 ◽  
Vol 8 ◽  
Author(s):  
Shuaishuai Sun ◽  
Jian Yang ◽  
Penghui Wang ◽  
Masami Nakano ◽  
Longjiang Shen ◽  
...  
Keyword(s):  
Ride Comfort ◽  
Excitation Frequency ◽  
Mr Damper ◽  
Variable Stiffness ◽  
Excitation Amplitude ◽  
Harmonic Excitation ◽  
Random Excitation ◽  
Shaking Table ◽  
Seat Suspension ◽  
Vibration Attenuation Performance

Traditional MR seat suspension without stiffness control is not able to avoid the resonance between the excitation and the seat, though it can dampen the vibration energy. To solve this problem, this paper proposed a variable stiffness (VS) magnetorheological (MR) damper to implement an advanced seat suspension. Its natural frequency can be shifted away from the excitation frequency through the variations of stiffness, thereby realizing the non-resonance control. The new seat suspension is designed and prototyped first, and then its dynamic property under different energizing current, excitation amplitude, and excitation frequency was tested using an MTS machine. The testing results verified its stiffness controllability. The vibration attenuation performance of the seat suspension was also evaluated on a vibration shaking table. The vibration reduction performance of the seat suspension was evaluated under two kinds of excitations, i.e., harmonic excitation and random excitation; the experimental results indicate that the new seat suspension outperforms passive seat suspensions regarding their ride comfort.

Periodic Motions in a Single-Degree-of-Freedom System Under Both an Aerodynamic Force and a Harmonic Excitation

2019 ◽  
Author(s):  
Bo Yu ◽  
Albert C. J. Luo
Keyword(s):  
Numerical Simulations ◽  
Analytical Approach ◽  
Aerodynamic Force ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stable Period

Abstract In this paper, a semi-analytical approach was used to predict periodic motions in a single-degree-of-freedom system under both aerodynamic force and harmonic excitation. Using the implicit mappings, the predictions of period-1 motions varying with excitation frequency are obtained. Stability of the period-1 motions are discussed, and the corresponding eigenvalues of period-1 motions are presented. Finally, numerical simulations of stable period-1 motions are illustrated.

Vibration Control Using Parametric Excitation

1999 ◽  
Author(s):  
Phillip H. Nguyen ◽  
Jerry H. Ginsberg
Keyword(s):  
Natural Frequency ◽  
Parametric Excitation ◽  
Excitation Frequency ◽  
Vertical Direction ◽  
Excitation Amplitude ◽  
Forced Response ◽  
Resonant Forcing ◽  
Parametric Frequency ◽  
Selection Of ◽  
Forced Excitation

Abstract A simple pendulum whose pivot executes harmonic motion in the vertical direction is a prototype for systems subjected to parametric excitation. Forced excitation of this system is represented as a harmonically varying torque whose frequency is taken to be arbitrary. The investigation explores whether, for specified values of the natural frequency and the excitation frequency, it is possible to select an amplitude and frequency for the parametric excitation such that the pendulum’s vibratory rotation is reduced. The analysis supplements numerical integration of the equation of motion with a Fourier series analysis suitable to situations where the parametric frequency is a multiple of the forcing frequency. Studies of the behavior for cases of near-resonant forcing and forced excitation far from the natural frequency lead to a general guideline for selecting the parametric excitation amplitude and frequency. The conclusion is that, with judicious selection of the parametric amplitude, a parametric frequency that is very high relative to the highest contemplated excitation frequency can reduce to forced response at any lower frequency to very small levels.

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