Vibration Analysis Of Rotating Research Articles

Nonlinear Vibration and Stability Analysis of Flexible Rotor Supported on SFD by IHB Method

In this paper, the nonlinear vibration of a flexible rotor supported on squeeze-film dampers (SFDs) with centering springs is analyzed using the incremental harmonic balance (IHB) method, and bifurcation phenomena appeared in the resonance region are investigated. Complex nonlinear phenomena occur in this system due to the interaction of the fluid-film forces and the unbalance forces of the rotor in the SFD. Systems with these complex nonlinearities cannot be solved using the classical IHB methods. To overcome this problem, the classical IHB method and the alternating frequency/time (AFT) method are combined. The processing of linear matrices is performed in the same way as the classical IHB method, and only the processing of nonlinear force matrix caused by fluid–structure interaction is modified (application of transformation matrix). To prove the validity of the proposed method, the results calculated using the proposed method are compared with the results calculated using the Runge–Kutta method and the results presented in reference. Then, frequency response curves according to changes in bearing parameter [Formula: see text], gravity parameter [Formula: see text], stiffness ratio [Formula: see text], mass ratio [Formula: see text], and unbalance parameter [Formula: see text] are constructed. Stability and bifurcation analyses of the calculated solution are performed using the Floquet theory. The proposed method can be effectively applied to the nonlinear vibration analysis of rotor systems supported on fluid-film bearings.

Nonlinear Vibration Analysis of Rotor considering Cogging and Harmonic Effects

This paper aims to investigate nonlinear vibration characteristics of rotor system considering cogging and harmonic effects. Firstly, relative permeance with eccentric was established and then corrected by correction factor caused by the cogging effect. Based on the new formula of relative permeance, the expression of unbalanced magnetic force was obtained, and the coefficient of cogging effect was defined. Motion equations of rotor system were established, and Runge–Kutta method was used to solve the equations. Results showed that errors between finite and analytical results were smaller considering cogging and harmonic effects. When the harmonics were taken into consideration, the vibration of rotor increases sharply. When the cogging and harmonics were taken into consideration simultaneously, the vibration of rotor decreased instead, which means that stator slots have the effect of reducing vibration in rotor system. Rotor vibration was axis symmetry with static eccentricity rather than central symmetry with no eccentricity, and double, four times, and six times supply frequency always existed in the components of main frequency with eccentric.

Vibration Reliability Analysis of Aeroengine Rotor Based on Intelligent Neural Network Modeling Framework

In order to improve the accuracy and calculation efficiency of aeroengine rotor vibration reliability analysis, a time‐varying rotor vibration reliability analysis method under the aeroengine operating state is proposed. Aiming at the highly nonlinear and strong coupling of factors affecting the reliability of aeroengine rotor vibration, an intelligent neural network modeling framework (short form‐INNMF) is proposed. The proposed method is based on DEA, with QAR information as the analysis data, and four factors including engine working state, fuel/oil working state, aircraft flight state, and external conditions are considered to analyse the rotor vibration reliability. INNMF is based on the artificial neural network (ANN) algorithm through improved particle swarm optimization (PSO) algorithm and Bayesian Regularization (BR) optimization. Through the analysis of the rotor vibration reliability of the B737‐800 aircraft during a flight mission from Beijing to Urumqi, the time‐varying rotor vibration reliability was obtained, which verified the effectiveness and feasibility of the method. The comparison of INNMF, random forest (RF), and ANN shows that INNMF improves analysis accuracy and calculation efficiency. The proposed method and framework can provide useful references for aeroengine rotor vibration analysis, special treatment, maintenance, and design.

Experimental and Comparative Study of Rotor Vibrations of Permanent Magnet Machines with Two Different Fractional Pole/Slot Combinations

This study deals with the noise, vibration, and harshness (NVH) characteristic analysis of permanent magnet synchronous motors (PMSMs) for electrical machines, such as electrically driven tools that are used in industries. An improved NVH design is needed for application to industrial tools. In general, the electromagnetic NVH characteristics of PMSMs are classified into electromagnetic excitation sources, such as total harmonic distortion of EMF, torque pulsation, magnetic pull force, and unbalanced magnetic force (UMF). This study compares the vibration and noise generated by fractional pole/slot combinations. In PMSMs with fractional pole/slot combinations, UMF is an important NVH source. PMSMs generate UMF because of armature reaction fields based on the pole/slot combinations and harmonics of magnetic flux density. UMF was derived using the finite element method, and the rotor vibration analysis was performed using electromagnetic mechanical coupling analysis. The analysis results and the effect of electromagnetic excitation characteristics on the rotor vibration of the PMSMs were compared and analyzed.

Rotor Vibration Analysis of Large-scale Centrifugal Compressor under the Flexible Support

Rotor Vibration Analysis of Large-scale Centrifugal Compressor under the Flexible Support

An identification method of orbit responses rooting in vibration analysis of rotor during touchdowns of active magnetic bearings

Identification of orbit responses can make the active protection operation more easily realize for active magnetic bearings (AMB) in case of touchdowns. This paper presents an identification method of the orbit responses rooting on signal processing of rotor displacements during touchdowns. The recognition method consists of two major steps. Firstly, the combined rub and bouncing is distinguished from the other orbit responses by the mathematical expectation of axis displacements of the rotor. Because when the combined rub and bouncing occurs, the rotor of AMB will not be always close to the touchdown bearings (TDB). Secondly, we recognize the pendulum vibration and the full rub by the Fourier spectrum of displacement in horizontal direction, as the frequency characteristics of the two responses are different. The principle of the whole identification algorithm is illustrated by two sets of signal generated by a dynamic model of the specific rotor-TDB system. The universality of the method is validated by other four sets of signal. Besides, the adaptability of noise is also tested by adding white noises with different strengths, and the result is promising. As the mathematical expectation and Discrete Fourier transform are major calculations of the algorithm, the calculation quantity of the algorithm is low, so it is fast, easily realized and embedded in the AMB controller, which has an important engineering value for the protection of AMBs during touchdowns.

Forced vibration analysis of rotors with an open edge crack based on a continuous vibration theory

In this paper, the forced vibration of a cracked rotor with an open edge crack has been studied by a new continuous model for flexural vibration of cracked rotors proposed in Ebrahimi et al. (J Sound Vib 333:3522–3535, 2014). The cracked rotor behavior under the external excitation of gravity and unbalance forces is presented. Since the governing equation is linear, using the superposition principle the responses of the cracked rotor to the gravity and unbalance forces are calculated separately. Then, the total response is calculated by summing these two responses. Each of these two responses is found by using a modified Galerkin method. The effect of the crack in the presence of the gravity and unbalance forces on the time response, frequency spectrum, frequency response curve and orbit diagram of the rotor is analyzed. Results can be used for the crack identification of rotors.

Failure of a steam turbine rotor due to circumferential crack growth influenced by temperature and steady torsion

Abstract High cycle fatigue as a final mechanism of failure in rotating systems, especially steam turbines, is a serious phenomenon. Incomplete information of its effective parameters could lead into catastrophic failure of the rotor. In high cycle fatigue, one of the most effective factors in crack growth is high temperature. In fact, a high-temperature change alters mechanical characteristics of material including their fracture mechanic. Therefore, the investigation of crack growth of fatigue and crack front development in various steam temperatures requires a careful consideration of the different parts of the rotor along the steam turbine rotor. This study investigated the propagation of a circumferential crack at three points of the turbine rotor in 24,149 and 260 ∘ C under the influence of rotor weight loading. In addition, the study addressed torque as another important parameter in crack growth which is caused by steam pressure in the turbine. Through the obtained results, a crack front shape is achieved which can be used in rotor vibration analysis. Reviewing the related literature indicated that crack growth rate associated with alternative mode I loading in the presence of steady mode III loading is reduced. To investigation this phenomenon, the study considered roughness induced crack closure due to steady torsion and its corresponding equations by analytical method were derived. Finally, the study investigated the influence of roughness on crack growth rate in abovementioned three points of the rotor.

Identification of harmful time harmonic interactions in a high power squirrel-cage traction machine

The paper offers a methodology for the identification the time harmonic interactions with a strong negative impact on the rotor of a high power induction machine. These potentially dangerous pulsating torques may be effectively reduced by carefully setting the machine’s drive control. A novel approach based on a complex finite element model and further post-processing is used. Results obtained from electromagnetic calculations in the form of pulsating torques are used as mechanical loading of a structural dynamic model. This complex model intended for rotor vibration analysis is described in brief in the mechanical part of the paper. The proposed methodology is applied to the machine used as a propulsion unit for multisystem locomotives of 1600kW power.

Transfer Matrix Method to Vibration Analysis of Rotors with Coupler Offsets

In this paper a general transfer matrix method (TMM) for rotors containing global and local coupler offset was derived. Rotor response due to imbalances and offsets are then studied via the developed method. The studies showed both global and local offsets played as an external excitation that is a combined effect of all the elements behind the offset. Differences between global offset and local offset were compared and the results showed both types basically retain the same mode patterns but different jumps at the offset. The global offset, yet, imposed more significant dynamic effects since all the offsets accumulate thereafter. The whirling orbits in front and behind the offset were illustrated as well. The results, as expected, showed global offset appeared much larger radii especially after offset. The rotor's whirling orientation reversed, as rotation fell within a certain range and this feature was not changed by offsets. The TMM proposed by this study can be well applied to multiple global and local offsets.

Transfer Matrix Method to Vibration Analysis of Rotors with Coupler Offsets

In this paper a general transfer matrix method (TMM) for rotors containing global and local coupler offset was derived. Rotor response due to imbalances and offsets are then studied via the developed method. The studies showed both global and local offsets played as an external excitation that is a combined effect of all the elements behind the offset. Differences between global offset and local offset were compared and the results showed both types basically retain the same mode patterns but different jumps at the offset. The global offset, yet, imposed more significant dynamic effects since all the offsets accumulate thereafter. The whirling orbits in front and behind the offset were illustrated as well. The results, as expected, showed global offset appeared much larger radii especially after offset. The rotor's whirling orientation reversed, as rotation fell within a certain range and this feature was not changed by offsets. The TMM proposed by this study can be well applied to multiple global and local offsets.

Vibration analysis of rotor with a “breathing” crack using three-dimensional model

A procedure for analyzing vibrations in cracked body using three-dimensional model is presented. The process of “breathing” is described by conditions of contact between the crack faces. Some example calculations are provided.

A Systematic Design of Tilting Pad Journal Bearing for a 1.2MW Turboblower

Studies on bearing properties have been carried out to develop a rotor system with improved high-speed stability and high efficiency. However, there have been few presentations on systematic design of a tilting pad journal bearing with analysis of rotor vibration and fluid properties. Therefore, this paper presents a method to systematically design a tilting pad journal bearing, where stability of the rotor system is taken into consideration, using the general-purpose software, ARMD. This paper describes the bearing design process, which meets the conditions of 0.12mm-bearing clearance and metal temperature below 75°C.

Time-frequency representation based on time-varying autoregressive model with applications to non-stationary rotor vibration analysis

A parametric time-frequency representation is presented based on time-varying autoregressive model (TVAR), followed by applications to non-stationary vibration signal processing. The identification of time-varying model coefficients and the determination of model order, are addressed by means of neural networks and genetic algorithms, respectively. Firstly, a simulated signal which mimic the rotor vibration during run-up stages was processed for a comparative study on TVAR and other non-parametric time-frequency representations such as Short Time Fourier Transform, Continuous Wavelet Transform, Empirical Mode Decomposition, Wigner-Ville Distribution and Choi-Williams Distribution, in terms of their resolutions, accuracy, cross term suppression as well as noise resistance. Secondly, TVAR was applied to analyse non-stationary vibration signals collected from a rotor test rig during run-up stages, with an aim to extract fault symptoms under non-stationary operating conditions. Simulation and experimental results demonstrate that TVAR is an effective solution to non-stationary signal analysis and has strong capability in signal time-frequency feature extraction.

437 部分構造合成法を用いた支持構造物と軸との連成軸振動解析の高速化(連成振動,設計,OS-18 ロータダイナミクス,総合テーマ「伝統を,未来へ!」)

437 部分構造合成法を用いた支持構造物と軸との連成軸振動解析の高速化(連成振動,設計,OS-18 ロータダイナミクス,総合テーマ「伝統を,未来へ!」)

Coupled bending-torsional vibration analysis of rotor with rub and crack

Rotor–stator rub and fatigue crack of the shafts are two important rotor faults. They have detrimental effects on health and reliability of the rotating machinery. In this paper, modelling and vibration signature analysis of rotor with rotor–stator rub, transverse fatigue crack and unbalance is attempted. The rotor–stator interaction effects on the response of a rotor are investigated in the presence/absence of a transverse crack. The torsional vibrations are investigated for their sensitivity to rubbing using finite element model that also accounts for cross coupling of stiffness introduced due to crack. Due to the presence of both rotor–stator rub and transverse crack in a horizontal rotor, the system becomes highly nonlinear. The time localised rub excitations and nonlinear stiffness variation due to breathing of the crack influence the rotor response in both lateral and torsional modes and are explored extensively using Hilbert–Huang transform with the objective of unravelling some unique features of these faults that may be useful for fault identification.

A theoretical study of TeOH in its electronic ground state

The ab initio multireference single- and double-excitation configuration interaction (MRD-CI) method has been used to calculate the potential surfaces for the six lowest-lying electronic states of the TeOH molecule. The 2 A″ ground state is predicted to have a bent equilibrium geometry. The first excited state, 2 A′, is calculated to lie 2695 cm −1 above the ground state. The MORBID program package has been used for the rotation–vibration analysis of the electronic ground state, for which the term values of the fundamental levels are calculated as 582 cm −1 for the Te–O stretching mode, 959 cm −1 for the bending mode, and 3655 cm −1 for the O–H stretching mode.

Vibration analysis of rotors for the identification of shaft misalignment Part 1: Theoretical analysis

Shaft misalignment in machinery causes preload forces to be generated in couplings which are then transmitted to the different machine components, thus reducing their lifetime. Shaft misalignment is a major cause of vibration in machines. Based on tests on coupling stiffness, a new coupling finite element stiffness matrix has been deduced. This has been used in the finite element analysis of a two-rotor system connected by a flexible coupling, to calculate the mechanical vibration resulting from mixed angular and parallel shaft misalignments with residual unbalance. The calculated vibration spectra were determined for two flexible couplings: a three-pin Renold coupling and a three-jaw Lovejoy coupling. The results and analysis indicate that the vibration generated by shaft misalignment is caused by the variation in coupling stiffness on rotation, and that the forcing frequencies generated are harmonics of the shaft's speed and directly depend on the frequency of the variation in coupling stiffness. In addition, the amplitudes of the measured vibratory components were found to rely directly upon the frequency response function that is related to the coupling and measurement points.

Vibration analysis of rotors for the identification of shaft misalignment Part 2: Experimental validation

In Part 1 of this paper, a theoretical model to determine the dynamic behaviour of misaligned shaft rotors connected by a flexible coupling was developed. In this Part 2, experimental tests are performed to validate the model and simulation results obtained in Part 1. Vibratory characteristics, such as the frequency spectrum, waveform and phase shifts of the spectral components across the coupling are presented for different magnitudes of misalignment and types of coupling. Traditional vibration analysis rules used in practical predictive maintenance to diagnose shaft misalignment are evaluated. The influence of the frequency response functions on the amplitude of the spectral components and on the phase shifts of the spectral components across a coupling were studied. Finally, some practical conclusions for more reliable shaft misalignment identification using vibration analysis are suggested.

Analysis of whirl speeds for rotor-bearing systems supported on fluid film bearings

There are several numerical approximations for vibration analysis of rotor bearing systems and the most popular approach is the Finite Element Method. In the light of the above it is proposed to undertake a study on the dynamic behaviour of Timoshenko beam supported on hydrodynamic bearings incorporating internal damping using FEM model. Critical speeds are estimated for synchronous whirl at different operating conditions using Campbell diagrams. It is observed in the analysis that in addition to the natural whirl frequencies, for every spin speed another whirling frequency appears in the solution, which is around half the spin speed. In case of fluid film bearings, half whirl is very common phenomenon. In case of dynamic coefficients evaluated using short bearing approximation, it is observed that these additional frequencies are of the same order as that of the synchronous whirling frequencies. The additional frequencies around half the spin speeds are found using only finite bearing dynamic coefficients; this clearly indicates the deficiency in the use of short bearing approximation in similar work.