Shaft Vibration Research Articles

Research on Rub-Impact Loads Response of Ship Shafting

Abstract The anti-impact ability of shafting affects stability and security of the ship power transmission directly. Moreover, it also cannot be ignored that the rub-impact loads have influence on the torsion vibration of ship shafting. In order to solve the problem of engineering application of reliability assessment under rub-impact loads, a test rig with rubbing generator is established. By carrying out the integrative analysis, the torsional vibration characteristics, such as vibration amplitude and orbit of axle center under the rub impact load are studied. According to the rub-impact conditions obtained through numerical simulation, the experimental verification is carried out on the test rig with rubbing generator. The results show that it is not obvious the influence of rub-impact loads upon the shafting torsion vibration except in special working conditions, that can be simulated by the rubbing generator. The maximum amplitude of torsional vibration is influenced by the radial rigidity as well as the friction coefficient of rubbing body, and the degree of influence is difference under conditions of continuous rubbing and serious rubbing. By adjusting the rigidity of stern bearing, the influence of rub-impact upon shafting can be weaken, which provides a theoretical reference for the safety evaluation of ship shafting.

Оценка собственных частот крутильных колебаний композиционного нелинейно вязкоупругого вала

Оценка собственных частот крутильных колебаний композиционного нелинейно вязкоупругого вала

Experimental research on the tilting pad bearing under the high temperature of inlet oil

PurposeThe purpose of this study is to analyze the influence of high-temperature inlet oil on the comprehensive performance of tilting-pad bearing.Design/methodology/approachTaking a tilting-pad bearing under high temperature of inlet oil in a natural gas compressor as an example, the experimental system was developed for the tilting-pad bearing applied in a real machine, and the experiment was performed. The bearing lubricating properties under different high temperatures of inlet oil were obtained, including oil film thickness on the pivot, temperature rise and the shaft vibration values at the bearing positions.FindingsThe experimental results showed that the vibration, the oil film thickness on the pivot and the pad temperature were not sensitive to the change in temperature of the inlet oil, but vibrations were observed under the specific speed. At the same speed, when oil temperature changed by 1°C, the bearing temperature rise did not exceed 0.2°C and change in oil film thickness on the pivot was 1 µm. The test results of the actual unit are in good agreement with the experimental results.Originality/valueThe vibration measurement scheme was presented, and an indirect measurement method of fulcrum thickness was proposed. The practicability of the measurement method and the accuracy of test results were verified by the comparison of the test results of the shaft vibration, the bearing pad temperature, the fulcrum oil film thickness and the theoretical calculation results. This study will provide an important reference for designing a tilting-pad bearing with high-temperature inlet oil.

Critical speed of propshaft and effect of forced synchroniztion in transmission of straight-four engine vehicles

The article shows the role of precession of a propshaft in increasing its vibration ativity. An auto inline four-cylinder engine has been shown to trigger a resonance mode of its drive shaft vibrations, i.e. intense flexural vibrations, leading to an emergency situation. This is due to the effect of forced synchronization (frequency capture) when the frequency of the second order unbalanced inertia forces is approaching the critical frequency of drive shaft rotations.

Evaluation of the Continuous Wavelet Transform for Detection of Single-Point Rub in Aeroderivative Gas Turbines with Accelerometers.

A common fault in turbomachinery is rotor–casing rub. Shaft vibration, measured with proximity probes, is the most powerful indicator of rotor–stator rub. However, in machines such as aeroderivative turbines, with increasing industrial relevance in power generation, constructive reasons prevent the use of those sensors, being only acceleration signals at selected casing locations available. This implies several shortcomings in the characterization of the machinery condition, associated with a lower information content about the machine dynamics. In this work, we evaluated the performance of Continuous Wavelet Transform to isolate the accelerometer signal features that characterize rotor–casing rub in an aeroderivative turbine. The evaluation is carried out on a novel rotor model of a rotor–flexible casing system. Due to damped transients and other short-lived features that rub induces in the signals, the Continuous Wavelet Transform proves being more effective than both Fourier and Cepstrum Analysis. This creates the chance for enabling early fault diagnosis of rub before it may cause machine shutdown or damage.

Diagnosis and Treatment of the Shaft Vibration Problem for an Ultra Super-critical 700MW Unit

In this article, there existed a second order unbalance on LP1 shaft of a Super-critical 700MW unit. It can be derived from the mathematical model of flexible and symmetrical shaft vibration characteristics that there are two specific balancing methods, symmetrical for handling odd orders and symmetrical reverse for even orders. The symmetrical reverse balancing method is proved to be effective to solve the second order vibration problems.

Rotating shaft's non-linear response statistics under biaxial random excitation, by path integration

The response of rotating shaft to random excitations is of practical concern for various rotor type engine design applications, with high level of potential external forces of stochastic nature.Authors have studied extreme value statistics of random vibrations of a Jeffcott type rotor, modeled as multidimensional dynamic system with non-linear restoring forces, under biaxial white noise excitation. The latter type of dynamic system is of wide use in stability studies of rotating machinery – from automotive to rocket turbo engine design. In particular, the design of liquid-propellant turbo pump rocket engines may be a potential application area of the studied system, due to the biaxial nature of the mechanical excitation, caused by surrounding liquid turbulent pressure field.In this paper, the extreme statistics of the rotor's non-linear oscillations has been studied by applying an enhanced implementation of the numerical path integration method, benchmarked by a known analytical solution. The obtained response probability distributions can serve as input for a wide range of system reliability issues, for example in extreme response study of turbo-pumps for liquid-propellant rocket engines. Predicting extreme transverse random vibrations of shafts in rotating machinery is of importance for applications with high environmental dynamic loads on Jeffcott type rotor supports.The major advantage of using path integration technique rather than direct Monte Carlo simulation is ability to estimate the probability distribution tail with high accuracy. The latter is of critical importance for extreme value statistics and first passage probability calculations.The main contribution of this paper is a reliable and independent confirmation of the path integration technique as a tool for assessing the dynamics of the kind of stochastic mechanical models considered in this paper. By the latter authors mean application of a unique and nontrivial analytical solution, that yields exact dynamic system response distribution, therefore it provides absolutely reliable reference to be compared to. The potential for providing a good qualitative understanding of the behavior of such systems is therefore available.

An integrated wind turbine failures prognostic approach implementing Kalman smoother with confidence bounds

This paper represents an integrated prognostics method dedicated to the wind turbine high-speed shaft bearing prognosis, which integrates physical degradation models and data driven approaches. In bearing failure prognostics, the excessive shaft vibration eventually leads to the system failure. In this case (crack growth prognostics), the measured data (crack size) is the same as a model prediction from Paris’s law. Indeed, we introduce an integrated prognostic approach based on usage model through Paris’s law and the use of a Kalman smoother to estimate the remaining useful life offering a solution to the inherent phase delay cancellation from Kalman filtering, providing a more accurate and smoother estimate with confidence bounds.The proposed method is validated on a real high-speed shaft bearing wind turbine generator. The used database contains one raw acquisition per day over 50 days of measurement at a high sample rate, 6 s each. The results show that the Kalman smoother is an effective way to improve trending and remaining useful life estimation.

Study on Vibration Characteristics of Fan Shaft of Geared Turbofan Engine With Sudden Imbalance Caused by Blade Off

Based on the requirements of the dynamic design of geared turbofan (GTF) engines, the vibration characteristic of the fan shaft is investigated. The effect of sudden imbalance caused by blade off, the time-varying meshing stiffness, and meshing errors on the vibration characteristics is fully considered in the dynamic model. The improved Euler–Bernoulli beam element considering the effects of shear deformation is employed and a coupled relationship between the gear–shaft–bearing–casing is established. Under windmilling condition with a single blade completely lost, the vibration characteristics of the fan shaft of the turbofan engine with and without a gearbox system are compared. The effect of the gear system on the vibration of the fan shaft under different rotating speeds is examined. The results show that the orbit of the fan shaft center in the turbofan engine with the gearbox system exhibits a multifrequency whirling motion and has a stable limit cycle. Under windmilling condition, the meshing frequency and the modal frequency have multiple intersection points. The critical speed is dense and the peak value of the transient vibration of the GTF engine gearbox shows a wave rise with an increase in speed. The results of this study could provide a reference for the parameter design and optimization of GTF engines.

Lateral vibrations of a microrotating shaft–disk system subjected to an axial load based on the modified strain gradient theory

ABSTRACTIn this article, the lateral vibrational behavior of a microrotating shaft–disk system subjected to an axial load is studied based on the modified strain gradient stress theory to capture size dependency. Hamilton's principle is used to derive governing equations of motion of the micro rotating shaft–disk system by calculating the kinetic and potential energies of the system. Then, the governing partial differential equations have been transformed into a set of infinite ordinary differential equations by using the assumed modes approach. By analytical method, the first two natural frequencies and also the instability rotational speed of the system are determined. Finally, the numerical results of the natural frequencies and also the threshold of instability speed of the system are presented with respect to different values of the system parameters such as the material length scale parameters, the axial load, the rotor length, the rotational speed, and also the location of the thin rigid disk on the microrotating shaft. The results show that the material length scale parameters and also the location of the thin rigid disk are extremely effective on the vibrational behavior characteristics of the system.

Analysis of dynamic parameters of mine fans

The design of the rotor of an axial fan and its main units, namely double leaf blades impeller and the main shaft are discussed. The parameters of a disturbed mine air flow under sudden outbursts are determined and the influence of disturbances on frequencies of axial fan units is assessed. The scope of the assessment embraces the disturbance effect on the blades and on the torsional vibrations of the main shafts. The dependences of the stresses in the elements of the rotor versus the disturbed air flow parameters are derived.

Torsional vibrations of shafts of mechanical systems

The aim of the research is to compare the calculated dependencies for determining the equivalent rigidity of a mechanical system and to come to an agreement on the methods of compiling dynamic models for systems with elastic reducer couplings in applied and classical oscillation theories. As a result of the analysis, it was revealed that most of the damage in the mechanisms and their details is due to the appearance of oscillations due to the dynamic impact of various factors: shock and alternating loads, unbalanced parts of machines, etc. Therefore, the designer at the design stage, and the engineer in the process of operation should provide the possibility of regulating the oscillatory processes both in details and machines by means of creating rational designs, as well as the use of special devices such as vibration dampers, various vibrators with optimal characteristics. A method is proposed for deriving a formula for determining the equivalent stiffness of a double-mass oscillating system of a multistage reducer with elastic reducer links without taking into account the internal losses and inertia of its elements, which gives a result completely coinciding with the result obtained by the classical theory of small mechanical oscillations and allows eliminating formulas for reducing the moments of inertia of the flywheel masses and the stiffness of the shafts.

Damped Vibration Absorbers for Multi-mode Longitudinal Vibration Control of a Hollow Shaft

The present work adopted damped vibration absorbers (DVAs) to attenuate multi-mode longitudinal vibration of the hollow shaft. The dynamic behavior of a shaft is analyzed for the guidance to the initial parameter design of DVAs and the parameters of DVAs are optimized. Subsequently, specific structures of DVAs are designed taking into account the hollow characteristic of the shaft. Furthermore, finite element stimulation of solid modeling has been performed. In this work, with the aid of the transfer matrix method (TMM) in conjunction with the substructure synthesis method (SSM), a dynamic model of the shaft incorporating multiple DVAs is established. The proposed method is developed for the calculation of dynamics character of the coupled system and estimation of absorption effectiveness of DVAs. To demonstrate the validity of theoretical result obtained from the TMM proposed in this paper, a simulation of the shaft vibration by means of the finite element method (FEM) is also carried out. Theoretical and stimulation results both demonstrate that the resonance peaks of the shaft longitudinal vibration are suppressed obviously with the application of those DVAs, which verify the effectiveness of the absorption performance of DVAs.

A Flow Starvation Model for Tilting Pad Journal Bearings and Evaluation of Frequency Response Functions: A Contribution Toward Understanding the Onset of Low Frequency Shaft Motions

Direct lubrication tilting pad journal bearings (TPJBs) require less oil flow, reduce power consumption, and offer cooler pad temperatures for operation at high surface speeds. Although apparently free of hydrodynamic instability, the literature shows that direct lubrication TPJBs exhibit unexpected shaft vibrations with a broadband low frequency range, albeit small in amplitude. Published industrial practice demonstrates the inlet lubrication type, a reduced supply flow rate causing film starvation, and the bearing discharge conditions (evacuated or end sealed) affect the onset, gravity, and persistency of the subsynchronous vibration (SSV) hash motions. The paper presents a physical model to predict the performance of TPJBs with flow conditions ranging from over flooded to extreme starvation. Lubricant starvation occurs first on an unloaded pad, thus producing a (beneficial) reduction in drag power. As the supplied flowrate decreases further, fluid starvation moves toward the loaded pads and affects the film temperature and power loss, increases the journal eccentricity, and modifies the dynamic force coefficients of each tilting pad and thus the whole bearing. For a point mass rotor supported on a TPJB, the analysis produces eigenvalues and frequency response functions (FRFs) from three physical models for lateral rotor displacements: one with frequency reduced (4 × 4) bearing stiffness (K) and damping (C) coefficients and another with constant K–C–M (inertia) coefficients over a frequency range. The third model keeps the degrees of freedom (DOF) (tilting) of each pad and incorporates the full matrices of force coefficients including fluid inertia. Predictions of rotordynamic performance follow for two TPJBs: one bearing with load between pads (LBP) configuration, and the other with a load on a pad (LOP) configuration. For both examples, under increasingly poor lubricant flow conditions, the damping ratio for the rotor-bearing low frequency (SSV) modes decreases, thus producing an increase in the amplitude of the FRFs. For the LOP bearing, a large static load produces a significant asymmetry in the force coefficients; the rotor bearing has a small stiffness and damping for shaft displacements in the direction orthogonal to the load. A reduction in lubricant flow only exacerbates the phenomenon; starvation reaches the loaded pad to eventually cause the onset of low frequency (SSV) instability. The bearing analyzed showed similar behavior in a test bench. The predictions thus show a direct correlation between lubricant flow starvation and the onset of SSV.

Vibration of Shaft System in the Mixed‐Flow Pump Induced by the Rotor‐Stator Interaction under Partial Load Conditions

In order to reveal the relationship between rotor‐stator interaction‐induced unsteady flow and the shaft vibration of the mixed‐flow pump, PIV (particle image velocimetry) and axis orbit experiments were carried out synchronously in a mixed‐flow pump under designed flow rate (1.0Qdes) and the partial load conditions (0.4Qdes and 0.2Qdes). The distribution of the relative velocity and the vorticity in the rotor‐stator interaction region at a certain position of the mixed‐flow pump impeller was captured; the axis orbit diagram and the time‐domain diagram of shaft system were acquired as well. Besides, the waterfall diagrams of the frequency spectrum under different flow rate conditions were compared. The results show that the backflow and the flow separation phenomenon appear in the rotor‐stator interaction flow field under the partial load condition, indicating the flow instability. The medium‐frequency exciting force and high‐frequency exciting force induced by these unstable flows resulting from the rotor‐stator interaction are the main factors to intensify the shaft vibration at the power frequency. The rotor‐stator interaction under partial load condition is the main reason for the deterioration of shaft system vibration. The 2X frequency also affects the axis orbit in a low level, while other frequencies have less influence on the shaft vibration. The research results can provide the reference and theory instruction for revealing the operating characteristic of mixed‐flow pump when it operates under partial load conditions and to reduce or to prevent the deterioration of vibration of shaft system.

Aerodynamic Performance and Vibration Analyses of Small Scale Horizontal Axis Wind Turbine with Various Number of Blades

The need to generate power from renewable sources to reduce demand for fossil fuels and the damage of their resulting carbon dioxide emissions is now well understood. Wind is among the most popular and fastest growing sources of alternative energy in the world. It is an inexhaustible, indigenous resource, pollution-free, and available almost any time of the day, especially in coastal regions. As a sustainable energy resource, electrical power generation from the wind is increasingly important in national and international energy policy in response to climate change. Experts predict that, with proper development, wind energy can meet up to 20% of US needs. Horizontal Axis Wind Turbines (HAWTs) are the most popular because of their higher efficiency. The aerodynamic characteristics and vibration of small scale HAWT with various numbers of blade designs have been investigated in this numerical study in order to improve its performance. SolidWorks was used for designing Computer Aided Design (CAD) models, and ANSYS software was used to study the dynamic flow around the turbine. Two, three, and five bladed HAWTs of 87 cm rotor diameter were designed. A HAWT tower of 100 cm long and 6 cm diameter was considered during this study while a shaft of 10.02 cm diameter was chosen. A good choice of airfoils and angle of attack is a key in the designing of a blade of rough surface and maintaining the maximum lift to drag ratio. The S818, S825 and S826 airfoils were used from the root to the tip and 4° critical angle of attack was considered. In this paper, a more appropriate numerical models and an improved method have been adopted in comparable with other models and methods in the literature. The wind flow around the whole wind turbine and static behavior of the HAWT rotor was solved using Moving Reference Frame (MRF) solver. The HAWT rotor results were used to initialize the Sliding Mesh Models (SMM) solver and study the dynamic behavior of HAWT rotor. The pressure and velocity contours on different blades surfaces were analyzed and presented in this work. The pressure and velocity contours around the entire turbine models were also analyzed. The power coefficient was calculated using the Tip Speed Ratio (TSR) and the moment coefficient and the results were compared to the theoretical and other research. The results show that the increase of number of blades from two to three increases the efficiency; however, the power coefficient remains relatively the same or sometimes decreases for five bladed turbine models. HAWT rotors and shaft vibrations were analyzed for two different materials using an applied pressure load imported from ANSYS fluent environment. It has proven that a good choice of material is crucial during the design process.

Unbalanced Vibration Identification of Tangential Threshing Cylinder Induced by Rice Threshing Process

Unbalanced vibration of tangential threshing cylinder increased the grain loss, shortened service life of the cylinder, and resulted in structural resonance during the rice threshing process. In this paper, the vibration amplitude and frequency of tangential threshing cylinder shaft were tested, and the vibration state of tangential threshing cylinder was identified. The restricted and working modalities of tangential threshing cylinder were solved by ANSYS software. Then, by comparing the resonance phenomenon between the inherent constraint frequency and the rotation speed frequency, the shaft vibration under the idle condition of tangential threshing cylinder was tested and analyzed. According to the axial vibration and axial trajectory of the cylinder, the inherent properties and characteristics of unbalanced vibration were revealed. Test results showed that when the tangential threshing cylinder was at idling and no‐load state, the amplitude of vibration in the feed direction of straw flow was −0.049~0.060 mm, and the average vibration amplitude was 0.013 mm. As rice flowed along the tangential threshing cylinder, the vibration amplitude slightly increased. The trend and phase of each trajectory were similar, although the amplitude of each trajectory was different. The tangential threshing cylinder axis trajectory was flat oval. Unbalanced vibration was induced by the rice stalks in the concave gap.

Asymptotic method for investigating resonant regimes of nonlinear bending vibrations of elastic shaft

Asymptotic method for investigating resonant regimes of nonlinear bending vibrations of elastic shaft

Elliptical Crack Identification in a Nonrotating Shaft

It is known that fatigue cracks are one of the most important problems of the mechanical components, since their propagation can cause severe loss, both personal and economic. So, it is essential to know deeply the behavior of the cracked element to have tools that allow predicting the breakage before it happens. The shafts are elements that are specially affected by the described problem, because they are subjected to alternative compression and tension stresses. This work presents, firstly, an analytical expression that allows determining the first four natural frequencies of bending vibration of a nonrotating cracked shaft, assumed as an Euler–Bernoulli beam, with circular cross section under pinned‐pinned conditions, taking into account the elliptical shape of the crack. Second, once the direct problem is known, the inverse problem is approached. Genetic Algorithm technique has been used to estimate the crack parameters assuming known the natural frequencies of the cracked shaft.

Experimental Analysis of an Active Vibration Frequency Control in Gearbox

Aiming at the vibrations of the multistage gear transmission system aroused by the gear meshing excitation, a novel active vibration control structure with built‐in piezoelectric actuators (PZT) was established. The active control forces generated by the PZT were transmitted to the shafts through the additional supporting bearings. In addition, an adaptive fuzzy proportion integration differentiation (AFPID) control algorithm was proposed as the primary control algorithm to reduce the transverse vibrations of the gear shaft. According to the control law of PID parameters, a fuzzy inference module was designed to adaptively adjust the PID parameters to obtain the optimal control effect. An experimental platform was set up to verify the control effect of the algorithm. The experiments performed show 10 dB reduction in housing vibrations at certain targeted mesh harmonics over a range of operating speeds.