Vibration Characteristics Of Blades Research Articles

Vibration characteristics of cracked compressor blades with different materials

Aiming at the influence of different material properties on the vibration characteristics of cracked gas turbine compressor blades, the vibration characteristics of cracked compressor blades with three different materials were studied by numerical calculation. The first order bending vibration of a cracked cantilever beam was simplified to a single degree of freedom system. The breathing crack stiffness model was introduced to change the elastic modulus and other parameters of the material. The fourth-order Runge-Kutta method and fast Fourier transform were used to obtain the cantilever beam vibration characteristic diagram, and the relationship between the material properties and the structural vibration was analyzed. The results show that the elastic modulus of the material is proportional to the stiffness, and the stiffness of the material affects the vibration displacement response of the cantilever beam, and the larger the stiffness is, the smaller the vibration displacement is.

Vibration characteristics of axial compressor blade under complex loads

In this study, 3D models of a compressor blade for an aero engine with three different levels of surface accuracy (with 4, 6 and 10 section profiles) were obtained via reverse engineering by fitting point-cloud data. Then, finite element and flow-field models of the blade were established and validated. The vibration characteristics of the blade under typical operating conditions were analyzed by considering the interaction between the aerodynamic load by airflow and the centrifugal load by blade rotating. The results showed that, under complex centrifugal and aerodynamic loads, the three blade models differed significantly in their high-order dynamic frequencies, and the modal frequencies that were dominated by a torsional mode of vibration were sensitive to the aerodynamic load. Hence, considering both the aerodynamic excitation and the centrifugal load increased the accuracy of the numerical computation of the blade vibration characteristics. Moreover, a comparison of the computational results from the three blade models showed that models B6 and B10 differed only insignificantly, and B6 decreased the complexity of the modeling process while satisfying the required computational accuracy. Thus, model B6 is the best option for engineering analysis and computation.

Determination of the response surface by strength and vibration parameters of the steam turbine blade

The work is devoted the definition of the function of limiting the geometric parameters of the steam turbine blade at given external loads. For this, a geometric model of a steam turbine blade was created, consisting of a blade body, a shank, and a shroud. The variable parameters were the angle of rotation of the middle section relative to the center of mass (which varied from 87 degrees to 92 degrees), as well as the length of the blade (varied from 495 mm to 525 mm). At the next stage, a finite element mesh was created. For the constructed model, an ordered finite element mesh was created in the area of the blade. Determined the stress-strain state of the blade during the operating mode. When carrying out the static analysis, an rotation velocity of 50 Hz was used as a load, and at the point of attachment of the disk in the shank, fixed displacement of all directions were used. The equivalent von Mises stresses and displacement in the structure are obtained. The zone of maximum stresses is located at the point where the blade is attached to the shank, but they do not exceed the limits. To determine the vibration characteristics of a steam turbine blade, its modal analysis was carried out taking into account the prestressed state from the action of static loads. The first six eigen modes of a steam turbine blade are obtained under the indicated initial conditions. The eigen frequency corresponding to the first form coincides with the rotational velocity (equal to 49 Hz), and the subsequent ones correspond to the multiplicities, respectively. At the next stage, a series of calculations was carried out to determine the response surface for the given parameters. The response surface for the maximum von Mises stresses and the first 4 modes of natural vibrations are determined. On the basis of the obtained results of studies of oscillations and deformed state of the blades with varying input parameters, it is possible to obtain a constraint for solving the optimization problem.

On the large-amplitude vibration of rotating pre-twisted graphene nanocomposite blades in a thermal environment

The large-amplitude free vibration behaviors of rotating pre-twisted functionally graded (FG) nanocomposite multilayered blade reinforced with graphene platelets (GPLs) in a thermal environment is comprehensively investigated in the paper. It is assumed that the GPLs volume fraction varies gradually from layer to layer across the blade thickness direction but remains constant in each individual GPLs-reinforced composite (GPLRC) layer. The modified Halpin-Tsai micromechanical model is exploited to obtain the effective Young’s modulus of each GPLRC layer while Poisson’s ratio, mass density, and thermal expansion coefficient are determined via Voigt’s rule. The nonlinear dynamic model of pre-twisted GPLRC blades at moderate rotational speed in a thermal environment is derived based on the first-order shear deformation theory (FSDT) combined with the improved version of the Novozhilov nonlinear shell theory. The nonlinear vibration characteristics of FG GPLRC blades are obtained by applying the element-free improved moving least-square Ritz (IMLS-Ritz) method in conjunction with a direct iterative scheme. Validation of obtained results is performed in detail and show effectiveness of used numerical approach and fast convergence of obtained results to exact values. The impacts of rotating speed, pre-twisted angle, presetting angle, and aspect ratio on nonlinear to linear frequency ratio of GPLRC blades are studied with emphasis on temperature rise and nano reinforcement parameters. Finally, new insights into dynamics of nanocomposite rotating blades with conclusions are presented in detail.

Экспериментально-расчетное определение механических свойств материала рабочих лопаток ГТД

A schematic description of a stand based on a digital speckle interferometer with a diffuse reference wave is given, which makes it possible to determine the natural frequencies and vibration modes of the blades in real-time. In the frequency range of 100 ... 3000 Hz, an experimental study of the vibration characteristics of a turbine rotor blade of a gas turbine engine was carried out, under free boundary conditions, which were achieved by placing the blade on soft silicone racks. Blade dimensions: height along the trailing edge - 288 mm, a chord in the middle section - 88.5 mm. 7 modes of vibrations have been identified. The technology of creating a solid-state geometric model of a rotor blade based on a faceted body obtained by 3D scanning with an accuracy of 0.01 mm is presented. The finite element method, using the Lagrange variation principle, is used to calculate the values of natural frequencies and vibration modes of a blade based on the developed geometric model. Concerning the frequency range 100 ... 3000 Hz, using the Ansys Workbench software package, a series of calculations of the resonant frequencies of the blade, by the finite element method, in the range of variation of the values of mechanical properties was carried out: Young's modulus E = 200 ... 230 GPa; Poisson's ratio μ = 0.26 ... 0.3. The density of the material: ρ = 7830 kg / m³, determined experimentally, by the method of hydrostatic weighing. The final element used in the calculation is (tetrahedron) SOLID 187; the minimum element size is 0.6 mm. The total number of elements is about 1.5 ∙ 10⁶. Based on the two-dimensional spline interpolation of the calculated data, the dependence of the standard deviation of the calculated and experimental values on the adopted mechanical properties of the material of the rotor blade is built. In the range of values E = 215 ... 217 GPa and μ = 0.295 ... 0.3, the minimum standard deviation of the calculated frequencies from their experimental values is 0.73%. Provided the value of the standard deviation of frequencies is 1%, the range of values of mechanical properties will be: E = 211 ... 220 GPa and μ = 0.26 ... 0.3. It is shown that narrowing the studied range of values of Young's modulus and Poisson's ratio does not significantly affect the results obtained.

Study on the Reduction of the Resonant Stress of Turbine Blades Caused by the Stage Interaction Force (Simultaneous Optimization of Blade Resonant Stress and Amount of Unbalance)

Abstract Although the bladed disks of turbomachinery are nominally designed to be cyclically symmetric (tuned system), the vibration characteristics of individual blades on a disk vary slightly owing to manufacturing tolerances, deviations in material properties, wear during operation, etc. These small variations break the cyclic symmetry and split eigenvalue pairs. Actual bladed disks with small variations are called mistuned systems. The resonant stress on a mistuned bladed disk may become large and cause a blade failure due to high cycle fatigue. Especially for a bladed disk with a free-standing blade structure, it is essential to use a sufficiently large safety factor at the design stage, considering the mistuning effect. Traditionally, blade designers have adopted various countermeasures to reduce the resonant stress at the design stage. Besides the countermeasures adopted in blade design, for a variable speed engine, which cannot avoid resonance, it is thought that a practical optimization method for a mistuned system (bladed disk with a free-standing blade structure) is to sort the blades so that the resonant stress is minimized. In this study, a simultaneous method for optimizing the blade resonant stress and the amount of unbalance causing rotor vibration is proposed. In this method, first, the natural frequencies and weights of all blades on a disk are measured. Then, a mistuned system is assembled and the analysis model is generated. Next, the resonant stress and the amount of unbalance in the mistuned system are analyzed. To reduce the computation time, the reduced-order model known as fundamental mistuning model (FMM) is used to calculate the resonant stress in the mistuned system. The analyses of the resonant stress and the amount of unbalance are carried out repeatedly, sorting the blades on the disk, and the optimal solution is explored using Monte Carlo simulations (MCS) or discrete differential evolution (DDE). As an example, a mistuned bladed disk of an aero-engine was analyzed, and the validity of the proposed method was verified.

Vibrational Stresses of Damaged Steam Turbine Blades After Renovation Repair

The last-stage blades of K-1000-60/3000 steam turbines operate in a humid steam environment, which causes erosion damage in the blades and reduction in their residual life. The relevance of this work is related to the need to continue the safe operation of such turbine blades. A number of variants of the finite-element models of individual blades and last-stage blades in the disk-blade systems of the above turbines are considered. Results of the numerical study of the influence of blade part removals in erosion damage zones after renovation repair on the vibration characteristics of individual blades and blades in the disk-blade system are presented. An analysis of the stress-strain state under the conditional load from the steam flow during the forced oscillations of individual blades and blades in the disk-blade system is carried out. The loads are given as evenly distributed and linearly variable on blade surfaces. The dependence of the maximum equivalent vibration stresses on excitation frequency is determined. It is assumed that the physical and mechanical properties of the blade material are preserved (as for the original version) after the renovation repair of blades and processing of their surfaces. There is a significantly greater reduction in the vibration stresses of blades in the disk-blade system than in the stresses of individual blades. Graphs of the dependence of the maximum stresses on excitation frequency both for undamaged individual blades and blades in the disk-blade system after their renovation repair are given. Various variants of blade part removals in areas of blade leading and trailing edges are considered. It is shown that with decreasing chords of blades after renovation repair, frequency regions of increased vibration may appear in lower blade parts. In the lower parts of individual blades and blades in the disk-blade system, the maximum stresses increase in comparison with their values in undamaged blades. With the change in the stress-strain state of rotor blades in comparison with the original version of undamaged blades, the possibility of extending their safe lifetime in case of multi-cycle fatigue is assessed. The safe lifetime of the considered blades with a chord of at least 150 mm after their renovation repair can be extended according to their stresses, if the cyclic symmetry of the disk-blade system is not violated, and the physical and mechanical properties of the material are preserved after the processing of damage removal zones on blade trailing edges.

A quasi-3D dynamic model for free vibration analysis of rotating pre-twisted functionally graded blades

This study provides a quasi-three-dimensional (quasi-3D) dynamic model for rotating pre-twisted functionally graded (FG) blades based on the three-dimensional elasticity shell theory and Carrera unified formulation. The material properties of the pre-twisted FG blades alter continuously in the direction of the thickness. The boundary conditions (clamped-end and free-edge) are realized by utilizing the well-known penalty method. Initial centrifugal stress field due to the high rotating speed is determined by two centrifugal stress solving methods, direct integration of centrifugal forces (DICF) and static analysis under centrifugal forces (SACF). The modified Fourier spectral approach is utilized to construct the displacement variables of the higher-order configurations. Eigenvalue problems are obtained by using the Hamilton's principle on the base of the kinetic, strain, centrifugal potential and boundary potential energy. The results of the theoretical model display a good agreement with the reference data and FEM results. Parametric studies are then performed to assess the applicability of the centrifugal stress solving methods and investigate the effects of the centrifugal shear stress, rotating speed, pre-twisted angle, penalty factors as well as the volume fraction index on the vibration characteristics of the pre-twisted FG blades. It is expected that the quasi-3D solutions for the rotating pre-twisted FG blades will serve as benchmarks in future researches.

Compressed Sensing-Based Order Analysis for Blade Tip Timing Signals Measured at Varying Rotational Speed

Monitoring the vibrations of high-speed rotating blades is significant to the security of turbomachineries. Blade tip timing (BTT) is considered as a promising technique for detecting blade vibrations without contact online. However, extracting blade vibration characteristics accurately from undersampled BTT signals measured at varying rotational speed (VRS) has become a big challenge. The existing two methods for this issue are restricted within the order bandwidth limitation and require prior information and precise sensor installation angles, which is often unpractical. To overcome these difficulties, a compressed sensing-based order analysis (CSOA) method was proposed. Its feasibility comes from the sparsity of BTT vibration signals in the order domain. The mathematical model for the proposed method was built, and the optimizing principles for sensor number and sensor arrangement were given. Simulated and experimental results verified the feasibility and advantages of the proposed method that it could extract order spectrum accurately from BTT vibration signals measured at VRS without the drawbacks in the existing two methods.

Vibration Characteristics of Multi-Stage Blade–Disk–Shaft Integrated Structure with Three-Dimensional Crack

According to the structural parameters of an actual turbofan aeroengine, the dynamics modeling and vibration analysis of multi-stage blade-disk-shaft integrated structure with three-dimensional crack are conducted. Based on the theory of fracture mechanics, the stress intensity factor is considered as a fracture criterion. This paper proposes a three-dimensional (3-d) equivalent notch model which is simpler and more convenient than the traditional crack simulation model. Moreover, its validity is analyzed. Aiming at the harsh working environment of the blades, the penetration crack is considered at the edge and the middle of a blade root, respectively. The influence of the crack on the strength failure of the rotor system is studied. Results show that the appropriate small angle equivalent notch model can be convenient and effective to simulate the fracture cracks, in which 5° is proved to be the best angle. The crack aggravates the vibration of blades obviously. A parametric study is conducted, with a particular focus on the effects of pressure load and centrifugal load on the stress intensity factors and displacement fields.

Dynamic analysis of cracked rotating blade using cracked beam element

In this paper, the dynamic model of a pre-twisted cracked rotating blade is established using self-programed beam element (CBE) and its nonlinear characteristics are analyzed. Firstly, based on the Castigliano’s theorem, the CBE with an open crack model is established. Secondly, a new breathing model of CBE is proposed in terms of the change of the crack contact region. Subsequently, the finite element (FE) model of a pre-twisted cracked rotating blade is established, and then verified by the ANSYS model. Finally, the effects of the crack depth, the crack position, the aerodynamic amplitude and the rotating speed on blade vibration characteristics and crack breathing status are investigated. The results show that the proposed model relative to the ANSYS model is of high efficiency and accuracy, besides, the larger crack depth and higher rotating speed result in a non-breathing crack, while the larger crack position and aerodynamic amplitude result in a breathing crack.

Constant speed tip deflection determination using the instantaneous phase of blade tip timing data

Blade Tip Timing (BTT) is a non-intrusive measurement technique that can be used to estimate the vibration characteristics of rotor blades during turbomachine operation. BTT uses proximity probes mounted into the turbomachine casing to measure the Time-of-Arrival (ToA) of rotor blades at these proximity probes. The ToAs are determined using a triggering criterion on the proximity probe signal. Rotor blade tip displacements are then calculated from these ToAs. It is therefore imperative that the triggering criterion be as accurate as possible. This article proposes a new method to determine the tip displacement of rotor blades from a proximity probe signal. The method first converts the signal into the angular domain and then obtains the tip deflection through manipulation of the instantaneous phase in the signal. Three experimental tests are conducted where existing triggering criteria are compared to the proposed method. It is found that the proposed method is highly accurate in determining the tip deflections for a constant rotor speed.

Predicting vibration characteristics of rotating composite blades containing CNT-reinforced composite laminae and damaged fiber-reinforced composite laminae

Existing of cracks within blade structures can cause stiffness degradation and hence changes their vibration characteristics. This study investigates the vibration behaviors of rotating pre-twisted hybrid composite blades containing functionally graded carbon nanotube-reinforced composite (FG-CNTRC) laminae and damaged fiber-reinforced composite (FRC) laminae. The degraded stiffness of the cracked lamina is modeled through the self-consistent model (SCM). The blade is modeled as a shell structure that is formed by twisting a plate around its mean line. With the help of the differential geometry theory, a novel shell model has been derived to describe the kinetics of the blade. The effect of the Coriolis and centrifugal force are both presented in the formulation, which results in a damped-like free vibration system governed by a system of second-order ordinary differential equations (ODEs). Utilizing the state space technique, the system is reformulated to a system of first-order ODEs. The IMLS-Ritz method is then used for discretizing the ODEs. After carefully validating the effectiveness of the presented model through a series of comparison studies, parametric studies including CNT distribution configuration, rotating speed, geometrical parameters on the vibration responses of cross-plied composite blades are systematically examined. The vibration characteristics of angle-plied composite blades are also investigated.

Modeling large amplitude vibration of pretwisted hybrid composite blades containing CNTRC layers and matrix cracked FRC layers

A modeling of the large amplitude free vibration of pretwisted hybrid composite blades is studied by considering the laminated structure which is composed of carbon nanotube reinforced composite (CNTRC) layers and matrix cracked fiber reinforced composite (FRC) layers. Two assumptions are made to facilitate this vibration study of hybrid nanocomposite: (1) CNTs are distributed across the layer thickness uniformly or functionally graded, and (2) the parallel slit matrix cracks disperse in the matrix homogeneously. Based on the theory of differential geometry, a novel shell model for pretwisted hybrid nanocomposites blade is developed. The von Kármán strains are adopted to capture the geometrically nonlinear behaviors of blades. The established governing equations are solved accurately and efficiently via the IMLS-Ritz method. The proposed numerical model is verified by making comparison studies and then the influence of crack density, pretwisted angle, CNT distribution and volume fraction, aspect ratio, width-to-thickness ratio, and ply-angle on the large amplitude vibration characteristics of matrix cracked pretwisted hybrid composite blade are scrutinized systematically. The present study serves as a useful benchmark to researchers who intend do further research in this topic.

Vibration characteristics of matrix cracked pretwisted hybrid composite blades containing CNTRC layers

Stiffness degradation due to matrix cracks is the main initial form of damage in composite laminates. Moreover, the vibration characteristics may change due to the degradation of blade stiffness caused by the introduction of matrix cracks. This paper presents a solution method for studying the static free vibration behaviors of pretwisted hybrid composite blade containing carbon nanotube reinforced composite (CNTRC) layers as well as matrix cracked fiber reinforced composite (FRC) layers. Two types of structure, namely Structure-I and Structure-II, are investigated. The CNTRC layers in Structure-I are considered with carbon nanotubes (CNTs) arranged in uniformly distributions, while Structure-II arranged in functionally graded distributions. The degraded stiffness of cracked layers is modeled via the self-consistent model (SCM) micromechanical framework. A shell model for pretwisted blade is proposed based on the theroy of differential geometry. To consider the effect of the transverse shear deformation and rotary inertia on the vibration behaviors, the first order shear deformation theory (FSDT) is adopted in describing the kinematics of blade. The improved moving least-squares Ritz (IMLS-Ritz) method is engaged to discretize the partial differential equations over the computational domain. Comparison studies indicate that the proposed predictive model can furnish very accurate results for pretwisted blades. Parametric studies on the effect of CNT distribution configuration, matrix crack density, aspect ratio, width-to-thickness ratio, twisted angle, as well as ply-angle on the vibration characteristics are revealed.

Non-contact vibration monitoring of rotating wind turbines using a semi-autonomous UAV

With the recent demands for more efficient clean renewable energy sources, wind turbines are designed that have large rotor blade diameters. These large-sized wind turbines need to be periodically monitored to prevent catastrophic failures. This paper aims to develop a practice for obtaining the vibration characteristics of wind turbine blades that can be eventually used for structural health monitoring of these structures. This monitoring technique needs to be robust and non-contact to prevent any interference with the operation of the wind turbine. In this work, a digital image correlation (DIC) system installed on a drone is used as a sensing technique to obtain the dynamic characteristics of rotating wind turbine blades. The DIC uses a stereo-camera system to record the deflections of the blades and provides non-contact measurements. The unmanned aerial vehicle (UAV) enables on-site robust measurements. Furthermore, a dynamic stitching technique is used after DIC measurement to obtain vibration characteristics of the entire blade with high accuracy. The proposed health monitoring technique can be used by engineers for remote structural health monitoring of wind turbines during operation in both offshore and inland wind farms.

유동-구조 연성해석 기법을 이용한 플라스틱 축류홴의 블레이드 진동특성 평가

유동-구조 연성해석 기법을 이용한 플라스틱 축류홴의 블레이드 진동특성 평가

Non-linear dynamic analysis of a wind turbine blade

ABSTRACTWind turbine blades’ dynamic behavior must be well investigated during the design process in order to avoid resonance. Modal analysis and nonlinear dynamic analysis of a rotating wind turbine blade are presented in this paper to study the effects of rotation speed on the natural frequencies and displacements. Accordingly, an enhanced finite element formulation based on uncoupled translational and rotational displacements’ kinetic energy was developed. A twisted wind turbine blade was discretized using beam elements with different cross sections; each has six degrees of freedom per node. At rest, the model results were validated using ABAQUS software. Furthermore, the effects of geometrically non-linear phenomena produced by blade displacement on the vibration characteristics of the rotating blade have been discussed. The blade non-linear problem was solved by applying the Newmark method combined with the Newton-Raphson schema. Results show that the blade natural frequencies and displacements increase under angular rotation speed augmentation. This work highlights the significant sensitivity of the blade vibration characteristics to the geometric non-linearity. Accordingly, a modal and a linear analysis are insufficient to precisely estimate the dynamic behavior of a rotating turbine blade.

Investigation of Vibration Characteristics of Titanium Wide-Chord Fan Blade

The vibration characteristics of a wide-chord fan blade affect the safety, reliability, and operability of high-bypass ratio turbofan engines. In this study, the vibration characteristics of a fan blade were investigated using numerical and experimental methods. First, the natural frequencies and mode shapes were obtained and verified. Then, the rotating speed and frequency margins were employed to analyze the stability of the blade. The critical crossings in the Campbell diagram were indicated and evaluated. Next, the strain energy density index and weaklink were used to evaluate the dangerous locations for the high-cycle fatigue characteristics of the blade. Finally, single- and multi-axis random-excitation tests were performed. Results indicated that low-order bending modes were dominant under circumferential- and axial-direction excitations, while the torsional mode response was higher under radial-direction excitation. The weaklinks for different excitation directions exhibited different characteristics. This work presents a comprehensive understanding of the fan-blade vibration and response characteristics.

Influences of wind and rotating speed on the fluid-structure interaction vibration for the offshore wind turbine blade

For the 5MW offshore wind turbine blade, the control and discrete equations of the fluid domain and structural domain were established respectively, and the calculation formulas of blade loads and damping coefficient were given. Furthermore, the blade entity modeling was completed by using UG and ANSYS Workbench. Based on it, the numerical calculation of blade vibration characteristics under different wind and rotating speeds was carried out, and the reliability verification was conducted by the wind tunnel test. The results of calculation indicate that the numerical results of the first principal stresses at the blade surface along the span-wise direction are consistent with the results of wind tunnel test, which verifies the reliability of the theory and numerical models. Both the influences of the bidirectional fluid-structure interaction (BFSI) and the rotation effect on the characteristics of blade vibration should be underlined. The increase of wind or rotating speed results in the nonlinear increase of the maximum span-wise displacement of the blade and of the Mises-stresses. Under different wind or rotating speed, the blade’s maximum displacement occurs at its tip, its maximum Mises-stresses appear at the relative wingspan of 0.55, and the contribution of rotating speed and average wind speed to the displacement or Mises-stress along the span-wise direction is similar.