Blade Natural Frequencies Research Articles

Free transverse vibration of rotating blades in a bladed disk assembly

This paper investigates the natural frequency of free transverse vibration of blades in rotating disks to examine the relationship of natural frequencies, blade stiffness and nodal diameters to study how neighboring blades react upon each other and affect blade natural frequency. With the use of elastic hinge theory and a cantilever beam model subjected to either a transverse concentrated force or a bending moment at the free end, the force-deflection stiffness/moment-rotation stiffness of the beam have been developed. Thereafter, the reaction forces and moments from the neighboring blades have been determined without the need for an exact solution of large deformation of cantilever beams including geometrical nonlinearity effects. With the use of the energy conservation principle and modal theory, the natural frequency of free transverse vibration of blades in rotating disks has been determined for any nodal diameter. A comparison of the analytical and finite element solutions for a bladed disk with uniform aerofoils shows that the analytical method presented in this paper is accurate.

Numerical Model for Collision Damping of Blades’ Tips

In order to obtain the collision damping of blades’ tips characteristics, around a blades for a 300MW steam turbine, the COMBIN40 element of ANSYS was adopted. The collision damping among blades' tips is equivalent to a damping of spring and friction with a gap. Under the conditions of exciting force and rotating blade natural frequency ,the vibration of a harmonic response was analysed, the nonlinear impact damping of blade response characteristics and the vibration damping mechanism of collision was got.

Vibration Diagnosis Featuring Blade-Shaft Coupling Effect of Turbine Rotor Models

As is well known, zero and one nodal diameter (k=0 and k=1) modes of a blade system interact with the shaft system. The former couples with torsional and/or axial shaft vibrations, and the latter with bending shaft vibrations. This paper addresses the latter. With respect to k=1 modes, we discuss, from experimental and theoretical viewpoints, in-plane blades and out-of-plane blades attached radially to a rotating shaft. We found that when we excited the shaft at the rotational speed of Ω=|ωb−ωs| (where ωb is the blade natural frequency, ωs the shaft natural frequency, and Ω is the rotational speed), the exciting frequency ν=ωs induced shaft-blade coupling resonance. In addition, in the case of the in-plane blade system, we encountered an additional resonance attributed to deformation caused by gravity. In the case of the out-of-plane blade system, we experienced two types of abnormal vibrations. One is the additional resonance generated at Ω=ωb/2 due to the unbalanced shaft and the anisotropy of bearing stiffness. The other is a flow-induced, self-excited vibration caused by galloping due to the cross-sectional shape of the blade tip because this instability disappeared in the rotation test inside a vacuum chamber. The two types of abnormal vibrations occurred at the same time, and both led to the entrainment phenomenon, as identified by our own frequency analysis technique.

Experiment and FEM Analysis for Fracture of Fan Blades

The fracture mechanism of fan blades in the subway system is analyzed by using the finite element method (FEM) and some experiments. Firstly, the mechanics performances of blade materials are obtained on the basis of the hydraulic testing machine. Then, the fracture surface of blades is measured with a scanning electron microscope (SEM). In the end, the natural frequencies of rotation blades are estimated by the means of nonlinear FEM program. It is shown from both the experiment and simulation results that the mechanics performance of blade materials is lower than its national standard, which is due to much bigger gaps and some inclusions in the cast fan. When voltage rises, the 79th natural frequency of blades becomes too approaching the rotating speed of fans easily to resonate. The biggest stress location of fan blades caused by centrifugal force, wind load and resonance is consistent in the fracture place, so the design of fan blades should be improved and optimized for preventing fracture.

Correlation of helicopter rotor aeroelastic response with HART‐II wind tunnel test data

PurposeThis paper aims to validate a comprehensive aeroelastic analysis for a helicopter rotor with the higher harmonic control aeroacoustic rotor test (HART‐II) wind tunnel test data.Design/methodology/approachAeroelastic analysis of helicopter rotor with elastic blades based on finite element method in space and time and capable of considering higher harmonic control inputs is carried out. Moderate deflection and coriolis nonlinearities are included in the analysis. The rotor aerodynamics are represented using free wake and unsteady aerodynamic models.FindingsGood correlation between analysis and HART‐II wind tunnel test data is obtained for blade natural frequencies across a range of rotating speeds. The basic physics of the blade mode shapes are also well captured. In particular, the fundamental flap, lag and torsion modes compare very well. The blade response compares well with HART‐II result and other high‐fidelity aeroelastic code predictions for flap and torsion mode. For the lead‐lag response, the present analysis prediction is somewhat better than other aeroelastic analyses.Research limitations/implicationsPredicted blade response trend with higher harmonic pitch control agreed well with the wind tunnel test data, but usually contained a constant offset in the mean values of lead‐lag and elastic torsion response. Improvements in the modeling of the aerodynamic environment around the rotor can help reduce this gap between the experimental and numerical results.Practical implicationsCorrelation of predicted aeroelastic response with wind tunnel test data is a vital step towards validating any helicopter aeroelastic analysis. Such efforts lend confidence in using the numerical analysis to understand the actual physical behavior of the helicopter system. Also, validated numerical analyses can take the place of time‐consuming and expensive wind tunnel tests during the initial stage of the design process.Originality/valueWhile the basic physics appears to be well captured by the aeroelastic analysis, there is need for improvement in the aerodynamic modeling which appears to be the source of the gap between numerical predictions and HART‐II wind tunnel experiments.

Failure analysis of gas turbine generator cooling fan blades

Since the optimum operation of a generator is highly affected by increasing in temperature, a cooling system is used to control the temperature. Employing a fan as a cooling system for the generator at the end sides of its rotor is a practical method [Montazer Ghaem Gas Turbine Power Plant. Gas turbine generator manual, Iran, 2004]. In some cases, fracture of blades causes short circuit between rotor and stator and consequently generator explosion and huge financial loss. Since fracture in cooling fan blades has been occurred five times in our case study, in this research, the emphasis has been placed on failure analysis and preventing methods from the fracture in this generator’s fan blades. Survey and analysis of the above-mentioned problem have been conducted in different ways, which the main titles results are as follows: • All of these failures have been happened after the first operation of gas turbine or at the early after operation 100 h after gas turbine repairs [Alsthom Company. Failure report for gas turbine fan blades, 1997]. • Metallurgical and structural analyses on the failed blades have not shown any microstructure degradation. • Studies on the ruptured surfaces using scanning electron microscope (SEM) have shown that fracture has been happened as a results of high cycle fatigue (hcf). • Calculation of alternative stresses has indicated that this stress is less than fatigue endurance limit of blade material and none of these stresses and forces could result in fracture. • Modal analysis of blade has indicated that the blades natural frequency has been limited too close to the blades operational frequency. It means that making changes in blades installation conditions; blade natural frequency approaches the operational frequency and consequently causes the resonance. Analysis results show that the final fracture of blades is due to fatigue conditions in resonance state and growth of existent tiny probable cracks.

Cracking Mechanism and Retrofit Design of Governing Stage Blades for a Steam Turbine

Cracking of blade dovetails occurred in a governing stage of a 50MW steam turbines twice within 5 months. To find out the failure mechanism and measures to avoid the failure accident, one of the cracked blades has been inspected by the metallography and a scanning electronic microscope. The inspection results show that the cracking of the blade is caused by the high cycle fatigue. When governing stage blades are in operation, the vibration of blades can extend to platform or even to dovetail parts over radial supporting surfaces depending on temperature, centrifugal force and assembly tolerance. The calculated results by FEM show that not only natural frequencies of blades in operating are smaller than that in stationary but also the modal order shifts when the blade runs from stationary to operation states. The effect of mode shift on the failure was investigated. According to the conclusion, the blades have been retrofitted by increasing neck of dovetail to avoid dangerous resonance, and the blades have been operating in healthy condition for two years after the modification. Contrarily, if the phenomenon of mode shift were ignored, it would be difficult to find out the right reason of resonance and ways to retrofit the damaged blades.

Singing Propellers—Solutions and Case Histories

This paper examines the hydroacoustic processes involved with "singing propellers" aboard marine vessels. Methods are presented to determine the potential for a resonant response of a propeller to a vortex shedding excitation—a phenomenon known as "singing." Methods are provided to determine the likely shedding frequency and structural natural frequency for propeller blades. Diagnostics procedures to determine the presence of singing are explored. Measured and theoretical differences between the blade's natural frequency response in air and in-water are explored. Treatments are identified to change the vortex shedding frequency or to de-tune the structure. Case histories are detailed showing the potential magnitude of the problem and effective solutions.

Aeroelastic Response of Composite Helicopter Rotor with Random Material Properties

This study investigates the effect of uncertainty in composite material properties on the cross-sectional stiffness properties, natural frequencies, and aeroelastic responses of a composite helicopter rotor blade. The elastic moduli and Poisson’s ratio of the composite material are considered as random variables with a coefficient of variation of around 4%, which was taken from published experimental work. An analytical box beam model is used for evaluating blade cross-sectional properties. Aeroelastic analysis based on finite elements in space and time is used to evaluate the helicopter rotor blade response in forward flight. The stochastic cross-sectional and aeroelastic analyses are carried out with Monte Carlo simulations. It is found that the blade cross-sectional stiffness matrix elements show a coefficient of variation of about 6%. The nonrotating rotor blade natural frequencies show a coefficient of variation of around 3%. The impact of material uncertainty on rotating natural frequencies varies from that on nonrotating blade frequencies because of centrifugal stiffening. The propagation of material uncertainty into aeroelastic response causes large deviations, particularly in the higher-harmonic components that are critical for the accurate prediction of helicopter blade loads and vibration. The numerical results clearly show the need to consider randomness of composite material properties in the helicopter aeroelastic analysis.

Stability Analysis of Rotating Blade Vibration due to Torsional Excitation

This paper presents an approximate analysis of the vibration stability of a rotating blade due to shaft torsional vibration excitation. The governing equation adopted in the study is a Hill's type linear second order ordinary differential equation with multiple harmonically variable coefficient terms. The strained parameters method, a perturbation technique, is utilized in developing the stability transition curves in the plane of parameters related to the rotor speed, the torsional vibration excitation frequency and the blade natural frequency. The stable and unstable regions obtained by perturbations are contrasted to those obtained by numerical stability analysis performed using Floquet theory and an excellent match is observed for small torsional vibration amplitudes. Numerical integration of the original equation at selected points in the predicted stable and unstable regions showed that the predicted behavior of the responses is correct, wherein the unstable regions growing blade vibration is exhibited.

B102 流体構造連成振動下におけるタービン翼列周りの流れの可視化

In the present study, the two- and three-dimensional analyses for turbine blades subjected to flow-induced vibration are compared. To consider the time-dependent motions. of blades, an arbitrary Lagrangian-Eulerian formulation is employed. A complete Navier-Stokes solver incorporating a moving mesh and analytic solutions of the motion equations for the. blade translation and rotation are applied. In the flow-induced vibration condition, the drag, lift and moment coefficients exhibited the time history coupled with the same frequency as that of non-coupling fluid forces and the blade natural frequency. The magnitude of blade fluctuation gradually increased with the reduced velocity. Although the small-scale vortices showing the three-dimensional structure were generated, there were no remarkable differences between two- and three-dimensional simulation in the reduced velocity starting flow induced vibration and the amplitude of the blade displacement.

Analytical formulation of the Jacobian matrix for non-linear calculation of the forced response of turbine blade assemblies with wedge friction dampers

A fundamental issue in turbomachinery design is the dynamical stress assessment of turbine blades. In order to reduce stress peaks in the turbine blades at engine orders corresponding to blade natural frequencies, friction dampers are employed. Blade response calculation requires the solution of a set of non-linear equations originated by the introduction of friction damping. Such a set of non-linear equations is solved using the iterative numerical Newton–Raphson method. However, calculation of the Jacobian matrix of the system using classical numerical finite difference schemes makes frequency domain solver prohibitively expensive for structures with many contact points. Large computation time results from the evaluation of partial derivatives of the non-linear equations with respect to the displacements. In this work a methodology to compute efficiently the Jacobian matrix of a dynamic system having wedge dampers is presented. It is exact and completely analytical. The proposed methods have been successfully applied to a real intermediate pressure turbine (IPT) blade under cyclic symmetry boundary conditions with underplatform wedge dampers. Its implementation showed to be very effective, and allowed to achieve relevant time savings without loss of precision.

Modal Controllability and Observability of Bladed Disks and their Dependency on the Angular Velocity

Rotating bladed disks are characterized by time-variant mathematical models presenting vibration coupling among rotor lateral motion and blade flexible motion. Moreover, they present parametric vibration modes and the blade natural frequencies may change depending on the angular velocity due to centrifugal stiffening. Consequently, the degree of controllability and observability of bladed disks also becomes time-varying, dependent on angular velocity, and a difficult task to analyze. In this paper we present a methodology for analyzing the modal controllability and observability of a bladed disk, based on time-variant modal analysis. The method takes into account time-variant parametric vibration mode shapes, and quantitative measures of modal controllability and observability are calculated. Numerical results show that, in order to control blade and shaft vibrations of a tuned bladed disk, by means of active control, blade-based as well as shaft-based sensing and actuation are required to monitor and control all vibration levels. If rotor blades are properly mistuned, the results show that disk as well as blade vibrations are monitorable and controllable by using only shaft-based sensing and actuation. The analysis shows why the mistuned disk becomes theoretically controllable and observable, via the presence of parametric mode shape components. Finally, the results show that the levels of controllability and observability depend significantly on the angular velocity, no matter the number of applied sensors and actuators used or their positioning.

Fully suspended, five-axis, three-magnetic-bearing dynamic spin rig with forced excitation

A significant advancement in the dynamic spin rig (DSR), i.e., the five-axis, three-magnetic-bearing DSR, is used to perform vibration tests of turbomachinery blades and components under rotating and non-rotating conditions in a vacuum. The rig has three magnetic bearings as its critical components: two heteropolar radial active magnetic bearings and a magnetic thrust bearing. The bearing configuration allows full vertical rotor magnetic suspension along with a feedforward control feature, which enables the excitation of various modes of vibration in the bladed disk test articles. The theoretical, mechanical, electrical, and electronic aspects of the rig are discussed. Also presented are the forced-excitation results of a fully levitated, rotating and non-rotating, unbladed rotor and a fully levitated, rotating and non-rotating, bladed rotor in which a pair of blades were arranged 180° apart from each other. These tests include the “bounce” mode excitation of the rotor in which the rotor was excited at the blade natural frequency of 144 Hz. The rotor natural mode frequency of 355 Hz was discerned from the plot of acceleration versus frequency. For non-rotating blades, a blade-tip excitation amplitude of approximately 100 g A−1 was achieved at the first-bending critical (≈144 Hz) and at the first-torsional and second-bending blade modes. A blade-tip displacement of 1.778×10−3m (70 mils) was achieved at the first-bending critical by exciting the blades at a forced-excitation phase angle of 90° relative to the vertical plane containing the blades while simultaneously rotating the shaft at 3000 rpm.

Fully Suspended, Five-axis, Three-magnetic-bearing Dynamic Spin Rig With Forced Excitation

A significant advancement in the dynamic spin rig (DSR), i.e., the five-axis, three-magnetic-bearing DSR, is used to perform vibration tests of turbomachinery blades and components under rotating and non-rotating conditions in a vacuum. The rig has three magnetic bearings as its critical components: two heteropolar radial active magnetic bearings and a magnetic thrust bearing. The bearing configuration allows full vertical rotor magnetic suspension along with a feedforward control feature, which enables the excitation of various modes of vibration in the bladed disk test articles. The theoretical, mechanical, electrical, and electronic aspects of the rig are discussed. Also presented are the forced-excitation results of a fully levitated, rotating and non-rotating, unbladed rotor and a fully levitated, rotating and non-rotating, bladed rotor in which a pair of blades were arranged 180° apart from each other. These tests include the “bounce” mode excitation of the rotor in which the rotor was excited at the blade natural frequency of 144 Hz. The rotor natural mode frequency of 355 Hz was discerned from the plot of acceleration versus frequency. For non-rotating blades, a blade-tip excitation amplitude of approximately 100 g A−1 was achieved at the first-bending critical (≈144 Hz) and at the first-torsional and second-bending blade modes. A blade-tip displacement of 1.778×10−3m (70 mils) was achieved at the first-bending critical by exciting the blades at a forced-excitation phase angle of 90° relative to the vertical plane containing the blades while simultaneously rotating the shaft at 3000 rpm.

Removal of order domain content in rotating equipment signals by double resampling

Fixed frequency content (i.e. component or structural resonances) in spectra obtained from rotating equipment can be masked by the strong sources at harmonics (order) of the shaft running speed. The ratio of the fixed frequency components to the order components can be greater than 60dB making interpretation of resonances in the spectra difficult. Hence the order components are viewed as a corrupting phenomenon. An approach to remove the order components from the spectra, without affecting the remaining frequency domain information is presented in this work. The technique utilises a sequence of data sampling and transformations, between the time, order and frequency domains as follows:(1)Vibration data is sampled using a constant time basis (Δt).(2)The times corresponding to a constant angular basis (Δθ) are determined.(3)The vibration data is interpolated to a constant angular basis (Δθ).(4)The constant angle sampled data is transformed via the FFT to the order domain.(5)The high amplitude order components are now exactly bin centred and can be removed from the spectra.(6)An inverse FFT is applied to return to a constant angular increment sampled (Δθ) array, sans order content.(7)The constant angular increment sampled (Δθ) array is interpolated to an array sampled with constant time basis (Δt).(8)A FFT is applied and then standard spectral estimation procedures used to compute the vibration spectra with the high-level orders removed.The theoretical and implementation details of the double resampling approach are discussed. The approach is applied to experimental torsional vibration data acquired from a laboratory test rig designed to simulate a turbine rotor. The test results show that the method can recover fixed frequency components (i.e. turbine blade natural frequencies) in the presence of order components 50dB higher.

Numerical Simulation of Aerodynamic Damping for Flutter Analysis of Turbomachinery Blade Rows

This paper describes the calculation of aerodynamic damping for prediction of e utter characteristics of turbomachinery bladerows.Theunsteady aerodynamicbladeloadsareobtainedbysolving theNavier ‐Stokesequations on a dynamically deforming, body-e tted grid. Phase-lagged boundary conditions are used to model the nonzero interbladephaseangleoscillations,and theenergy exchangemethod isused to calculatetheaerodynamicdamping. The analysis is applied to calculate e utter of a transonic forward-swept fan cone guration, which showed e utter at part speed conditions in wind-tunnel tests. The analysis successfully identie ed the most critical mode and the e ow characteristics responsible for the observed e utter. The location of shock wave and variation of its strength were found to strongly ine uence the aerodynamic damping, with outboard stations providing the main contribution. The results also demonstrate that changes in blade shape impact the calculated aerodynamic damping, indicating the importance of using an accurate blade operating shape under centrifugal and steady aerodynamic loading. Sensitivity of thecalculated aerodynamic damping to variation in inlet and exit conditions, the computational time steps, and blade natural frequency are also reported.

317 振動数のばらつきを考慮した圧縮機動翼の最適設計法

Recently, in order to improve performance of gas turbine's compressor, the thickness of compressor blade has become thinner. Therefore, for the purpose of increasing reliability, the blade's natural frequencies should be predicted precisely. In the compressor blade design, many natural frequencies must be tuned so as not to resonate with the frequencies of the excitation force under the constrained conditions which come from the requirements of manufacturing and performance. In this paper, an effective auto-tuning technique of the blade's natural frequencies is presented by combining Taguchi method with optimization method under constrained conditions and its application is shown. The new optimal technique in this paper is very useful in such blade design because the blade frequencies are automatically optimized, and at the same time the expected frequency deviations due to manufacturing tolerance are minimized. The calculated results show this method proposed can be applied to robust design of actual compressor blade.

RANDOM VIBRATION OF A ROTATING BLADE WITH EXTERNAL AND INTERNAL DAMPING BY THE FINITE ELEMENT METHOD

The finite element model is employed to investigate the mean-square response of a rotating blade with external and internal damping under stationary or non-stationary random excitation. The blade is considered to be subjected to white-noise and earthquake excitations. The effects of rotational speed, external and internal damping on the mean-square response are studied. It is found that the mean-square response decreases quickly when the external and internal damping increases within some scope. Moreover, the increment of rotational speed will reduce the mean-square response of a rotating blade. It is also found that the mean-square response decreases when the low natural frequency of base decreases. Inversely, the mean-square response increases when the high natural frequency of base (natural frequencies of base are over the first natural frequency of blade) decreases. The reliability of a rotating blade subjected to stationary or non-stationary excitations is also obtained.

Blade and Shaft Crack Detection Using Torsional Vibration Measurements Part 1: Feasibility Studies

The primary goal of the development project was to demonstrate the feasibility of detecting changes in blade natural frequencies (such as those associated with a blade crack) on a turbine using non-contact, non-intrusive measurement methods. The approach was to set up a small experimental apparatus, develop a torsional vibration detection system, and maximize the dynamic range and the signal to noise ratio. The results of the testing and analysis clearly demonstrated the feasibility of using torsional vibration to detect the change in natural frequency of a blade due to a change in stiffness such as those associated with a blade crack.