Vibration Analysis Of Rotating Research Articles

Vibration Analysis of Rotors Utilizing Implicit Directional Information of Complex Variable Descriptions

A complex variable description of planar motion incorporates directivity as inherent information which is therefore very convenient in vibration analysis of rotors. This paper proposes to use the directional information explicitly when the equation of motion of a rotor is formulated in complex variables. It is shown that the free vibration solution to the equation of motion formulated as such can be defined as the directional natural mode because it describes not only the shape and frequency but also the direction of the free vibration response. The directional frequency response functions (dFRFs) that have been used recently are obtained as the solution to the forced vibration solution to the equation of motion. Symmetric and anti-symmetric motions of a geometrically symmetric rigid rotor are used as examples to explain these concepts and their practical significances. The proposed approach allows clear understanding and definitions of some unique characteristics of rotor vibrations, such as the forward and backward modes, and forward and backward critical speeds, which have been often used in confusing or incorrect ways.

Coupled Vibration Analysis of Rotor and Foundation Using Quasi-Modal Transformation. 2nd Report. Unbalance Response Analysis.

To estimate the vibration of rotating shafts like turbine-generator sets, the rotor vibration analysis must include the vibration characteristics of the foundation. In this paper we propose a method of analyzing the vibration of a coupled rotor-foundation system. Called a quasi-modal technique, it is based on the same concept as the well known modal synthesis method. It provides a reduced model of an actual system using a combination of eigen modes of an inner system restricted at the bearings plus deflection modes created when inputting the load at the boundary points. A rotor system and a foundation system are each reduced separately by this technique, and the reduced models are then coupled at the bearing boundary points. According to this procedure, we developed computer code for performing vibration analysis of an entire system. In our previous paper, we proved the effectiveness of complex eigen value analysis code. In this paper we propose code for the response analysis of rotor inbalance. We show calculation examples for a coupled turbine-generator-foundation system.

Coupled Vibration Analysis of Rotor and Foundation Using Quasi-Modal Transformation. 1st Report. Complex Eigenvalue Analysis.

For estimating the vibration of rotating shafts like turbine-generator sets, the rotor vibration analysis must include the vibration characteristics of the foundation. In this paper we propose a method of analyzing the vibration of a coupled rotor-foundation system. This is a quasi-modal technique based on the same concept as the well-known modal synthesis method. It provides a reduced model of an actual system using a combination of eigen modes of an inner system restricted at the bearings plus deflection modes created when inputting the load at the boundary points. A rotor system and a foundation system are each reduced using this quasi-modal technique, and the reduced models are then coupled at the bearing boundary points. Through this procedure, we developed computer code for the vibration analysis of the whole system. This code was applied to a simple model consisting of a rotor and a foundation system using several parameters. The calculated results of this coupled system proved the effectiveness of this code.

Vibration Analysis of Rotor for Crack Identification

A theoretical and experimental dynamic analysis of a rotor-bearing system with a transversely cracked shaft is presented. To model the system for FEM analysis, a finite element for a cracked cylindrical shaft is developed. The additional flexibility due to the crack is evaluated from the linear fracture mechanics, using a breathing crack model derived in a rigorous way. A simplified opening/closing crack model is proposed to reduce the computational effort. The resulting parametrically excited system is nonlinear, and the equations of motion are solved using Hilbert, Hughes, and Taylor integration method (HHT) implemented in Matlab platform, where the stationary vibration caused by gravity and unbalance is analyzed. The results show that for half the first critical speed, the super-harmonic 2 ×Ω and the typical orbit provide good indices for crack detection in rotating shafts.

Vibration Analysis of Rotors with a Fluid Balancer. 1st Report. Shallow-Water Sloshing Analysis of Liquid in a Whirling Ring.

This research deals with the vibration of rotors containing liquid, such as rotors of washing machines with a fluid balancer, and is intended to predict the occurrence of self-excited vibration and to evaluate some other characteristics of these rotors by analysis. We developed an analytical method using the assumption of shallow-water sloshing to predict the motion of liquid contained in a whirling ring, and made some calculations for various whirling rates. These calculations confirmed the validity of the method, and yielded following results. (a)Not only major resonances, but also secondary resonances peculiar to nonlinear systems occur when multiples of the exciting frequency correspond to natural frequencies of sloshing. (b)There are some isolated waves(or solitons)near resonance points, and the number of solitons changes when whirling rates changes slightly.

Non-Linear Vibration Analysis of Rotor System Using Substructure Synthesis Method. Analysis with Consideration of Non-Linearity of Rotor.

In this paper, a method to solve a complex nonlinear vibration system is proposed by using both component mode synthesis method and perturbation method to save computation cost. That is, the system is divided into some components and these are approximately transformed to modal coordinate system with nonlinearity under the assumption that the modes shape does not change, then equations of every modes are solved by using a perturbation method. These solutions are synthesized to the whole system and the solution for the whole system is obtained for the modal coordinate system. Finally, it is translated to the physical coordinate system. This method is applied to a vibration analysis of nonlinear rotor and bearing-casing system. In order to illustrate the accuracy and computation time of the proposed method, the results obtained are compared with those obtained by the finite element method.

Thermal Vibration Balancing Method for Turbine Generator Rotor. Rotor Vibration Analysis Method due to Thermal Unbalance.

A middle-load thermal power turbine generator frequently exceeds its critical speed, and it must be balanced at the critical speed carefully. Also, it is desirable to thermally balance the generator rotor to reduce the shaft vibration stroke caused by a load change at rated speed. In particular, when the generator capacity exceeds 500MVA, the generator rotor shifts from the secondary mode to the tertiary mode, and the in-phase unbalanced sensitivity increases due to the thermal bending of the shaft and other causes. As a result, thermal balancing is required in addition to conventional mechanical balance. This paper deals with 3 items. The first is the three-dimensional rotor vibration analysis method considered as asymmetry bearing supporting condition and thermal and magnetic unbalanced force. The second is to clarify bearing support condition using the actual rotor vibration response. The last is to explain an agreement between theory and experiment for rotor vibration phenomenon due to an artificial field coil layer short.

Nonlinear steady-state vibration analysis of rotor by substructure synthesis.

A new nonlinear steady-state calculation by substructure synthesis is presented for large-order rotordynamic systems with a few nonlinear elements, which is considered popular in actual rotating machines. In this paper, linear dynamic and static structural relations are reduced to small degrees of freedom on nonlinear elements such as nonlinear bearings. Using discreet Fourier transform (DFT, also using FFT), and the Newton-Raphson method, harmonic balance for this reduced nonlinear system can be obtained as efficiently as for a simple rotor system. As examples, the effect of a friction damper on a turbine blade model and nonlinear unbalance response of an actual turbine rotor supported by squeeze film dampers without centering springs are discussed.

Vibration analysis of rotors in consideration of the dynamic characteristic of the support structure by the substructure synthesis method. Correction of compliance matrix.

The critical speed and the unbalance response of rotors are calculated in consideration of a compliance which presents a dynamic characteristic of supportstructures of the rotors. The substructure synthesis method is applied on the total system modeled by the compliance matrix, which is experimentally identified at the bearing in the support structure, and the discrete mass rotor system in the method of transfer matrix. It is found that there is a possibility of calculating a false critical speed because experimental errors cause an imperfection in the compliance matrix indentified from experiments has been suggested. It is shown that this method is effective for such analyses as the critical speed and the unbalance response.

Analysis of Rotor Vibration Excited by Seismic Wave

This paper deals with rotor vibration caused by seismic wave, the influence of gyroscopic force on the response and an aseismic design method using a stopper with clearance. An analysis is presented for calculation of the response of a general flexible rotor excited by an arbirtary external force such as seismic wave. Modal techniques and step by step numerical integration are employed. The calculation method is applied to a rotor with a strong gyroscopic force. The computational results of a harmonic excitation indicate that there exist two resonance frequencies corresponding to forward and backward whirl motions. The numerical history response indicates that even non-circular one-directional stopper is sufficient for aseismic design to keep the clearance induced vibration small. A pump rotor is chosen to demonstrate the seismic resonance of a rotor with a weak gyroscopic force. Then the pump rotor dynamics become very similar to structural dynamics. but the clearance induced vibration of pump rotor exhibits a whirl orbit motion which characterizes the rotor dynamics.

Analysis of Rotor Vibration Excited by Seismic Wave

Analysis of Rotor Vibration Excited by Seismic Wave

Rotation–vibration analysis of the B 0+u–a 1g and B 0+u–a′ 0+g electronic systems of I2 by laser-induced-fluorescence Fourier-transform spectroscopy

The spectrum of fluorescence excited by the 514.5 nm line of a multimode Ar+ laser is recorded by a Fourier-transform spectrometer. In the region 7000–7300 cm−1 (1.43 to 1.37 μm), transitions from the B 0+u state are recorded into two states, which had been previously only indirectly observed, as well as into the X 1Σ+ state. Vibrational levels 0–9 for the 0+g and 0–14 for the 1g states are sampled. The principal molecular constants determined are as follows: where all constants are in cm−1 except when noted, with 2σ uncertainties in parentheses.

Rotational and vibrational analysis of the CaF B2Σ+–X2Σ+ system

A rotation–vibration analysis of the CaFB2S+–X2Σ+ system is reported. Excitation spectra of CaF are recorded with a cw, 1 MHz bandwidth, dye laser combined with restricted-bandpass (2 Å) fluorescence detection. The accuracy of line measurements is 0.003 cm−1. Nine bands in the Δν = 0 sequence are analyzed (ν″ = 0–2,8,9, 12–15) and selected lines in four Δν = −1 bands (ν″ = 1–4) are used to obtain band origins needed for the vibrational analysis. The main constants (1σ error in parentheses) for the CaF B2Σ+ state are: Te = 18 841.309(3) cm−1. Be = 0.342604(7) cm−1, ωe = 572.405(36) cm−1, αe = 0.002630(6) cm−1, ωexe = 3.143(13) cm−1, Re = 1.955 Å. The B2Σ+ state is found to be in pure precession with A2Π with l = 1.

The Study of a Gear Coupling : The Non-Linear Vibration Analysis of Rotors which Have One Gear Coupling

The Study of a Gear Coupling : The Non-Linear Vibration Analysis of Rotors which Have One Gear Coupling

Rotation–vibration analysis by finite difference perturbation technique. Application to 1Σ+ state of NH

A numerical perturbation method is presented for the solution of the one-dimensional Schrödinger equation by a finite difference approximation. The method is noniterative and has an accuracy similar to the Numerov–Cooley procedure. Rotation–vibration analysis for various multiconfiguration wavefunctions of the b and d 1Σ+ states of NH has been carried out using the above method followed by least square eigenvalue fitting procedures. The results are in very good agreement with known experimental data. The best calculated values of ωe, ωexe, Be, αe, and Re (with known experimental values in parentheses) are for the b 1Σ+ state ωe=3365.3 (3347.0) cm−1, ωexe =65.8 (70.7) cm−1, Be=16.78 (16.73) cm−1, αe =0.6249 (0.6049) cm−1; Re=1.953(1.956) bohr; for the d 1Σ state ωe=2671.8(2665.0) cm−1, ωexe =89.7(71.0) cm−1, Be=14.611 (14.409) cm−1, αe=0.999(0.634) cm−1, Re=2.093 (2.108) bohr.