Vibration Characteristics Of Blades Research Articles

Review of Vibration Analysis and Structural Optimization Research for Rotating Blades

AbstractBlades are important parts of rotating machinery such as marine gas turbines and wind turbines, which are exposed to harsh environments during mechanical operations, including centrifugal loads, aerodynamic forces, or high temperatures. These demanding working conditions considerably influence the dynamic performance of blades. Therefore, because of the challenges posed by blades in complex working environments, in-depth research and optimization are necessary to ensure that blades can operate safely and efficiently, thus guaranteeing the reliability and performance of mechanical systems. Focusing on the vibration analysis of blades in rotating machinery, this paper conducts a comprehensive literature review on the research advancements in vibration modeling and structural optimization of blades under complex operational conditions. First, the paper outlines the development of several modeling theories for rotating blades, including one-dimensional beam theory, two-dimensional plate–shell theory, and three-dimensional solid theory. Second, the research progress in the vibrational analysis of blades under aerodynamic loads, thermal environments, and crack factors is separately discussed. Finally, the developments in rotating blade structural optimization are presented from material optimization and shape optimization perspectives. The methodology and theory of analyzing and optimizing blade vibration characteristics under multifactorial operating conditions are comprehensively outlined, aiming to assist future researchers in proposing more effective and practical approaches for the vibration analysis and optimization of blades.

Dynamic modeling and verification of rotating compressor blade with crack based on beam element

Aero-engine blades may crack under harsh operating environments. This reduces the reliability of the aero-engine and causes catastrophic accidents. Although dynamic modeling and vibration characteristics of simplified blades with cracks have been analyzed extensively, there are few studies on the actual compressor blade with varying sections and twisted shapes. Based on Timoshenko beam theory, a new modeling approach for the compressor blade is proposed. Next, according to the strain energy release rate and Castingliano theory, the dynamic model of cracked compressor blades is established considering the stiffness nonlinearity induced by the breathing crack. The modeling approach is validated by the measured natural frequencies of an intact blade. Then, the dynamic model of the cracked blade is verified by comparing the modal characteristics and vibration characteristics using ANSYS software. Finally, some results show that the natural frequencies fn1, fn2, and fn4 increase as the pre-twisted angle and stagger angle increase. Due to the breathing effect, some integer frequencies appear in the spectrum including 0fe and 2fe, and the variations in the amplitude of frequencies 0fr and 2fr are monotonic under different aerodynamic amplitudes. The research can provide some help for the modeling of the actual blade and fault diagnosis of cracked blades.

Experimental Study on the Dynamic Stability of Circular Saw Blades during the Processing of Bamboo-Based Fiber Composite Panels

Bamboo-based fiber composite panel is a new type of composite material with excellent performance. When processing bamboo-based fiber composite panels, the dynamic stability of the circular saw blade affects the surface quality of the product and the life of the machinery and equipment. Sawing heat and vibration characteristics can significantly affect the dynamic stability of circular saw blades. Circular saw blade temperature and vibration characteristics are affected by the processing parameters, and the circular saw blade temperature and vibration characteristics are analyzed by changing the processing parameters. Adopting the thermoset coupling model can be used to analyze the change rule of circular saw blade temperature when sawing bamboo-based fiber composite boards, and at the same time to analyze the change rule of circular saw blade temperature, vibration speed, and vibration acceleration through the use of by CCD experiments. The regression equations for circular saw blade temperature, vibration velocity, and vibration acceleration were derived through the use of ANOVA and significance analysis. The thermoset coupling model predictions agree with the experimental results, and the density of the isotherms is progressively thinner as the temperature is conducted from the serrated region to the body of the saw. Finally, the accuracy of the regression equations for circular saw blade temperature, vibration velocity, and vibration acceleration was checked via error analysis. The temperature change regression equation has the highest fitting accuracy, with an average error of only 1.37%; the vibration velocity and vibration acceleration regression equations have poorer fitting accuracy, with an average error of 9.5% and 11.45%, respectively, but all of them have sufficient accuracy to predict the dynamic stability of circular saw blades. The results of the study can provide some guidance for the innovative design of circular saw blades.

Comparative Study on Vibration Characteristics of Biaxial Carbon/Glass Hybrid Wind Turbine Blades

Endeavor to investigate the effect of carbon/glass hybrid ratio on blade flutter vibration characteristics. Based on the theory of strength of materials, the influence of carbon/glass hybrid ratio on the tensile strength of the sample under concentrated load was analyzed experimentally. The 10 KW wind turbine blade model was taken as the research object, and different carbon/glass hybrid ratios (2:6, 4:4, and 6:2) were selected as the blade reinforcement materials. The blade vibration characteristics were analyzed from three aspects: deformation displacement, blade mode, and stress distribution. The results showed that the blade hybrid ratio was between 6:2 and 4:4, and the maximum improvement in tensile performance was achieved. The hybrid ratios of 4:4 and 6:2 significantly improved the deformation resistance of the blades and required a shorter time to reach equilibrium. The blade stress was mainly concentrated at 1/3 of the blade, which was one of the main reasons for the phenomenon of blade waving.

Effects of film cooling holes on vibration characteristics of aeroengine turbine blades

PurposeThe purpose of this paper is to evaluate the effect of film cooling holes on the vibration characteristics of a turbine blade, and provide the design basis for the blade, which may reduce computing costs.Design/methodology/approachModal analysis of the blades with and without film cooling holes is performed to evaluate the effect of film cooling holes on its natural frequency. Harmonic analysis of the blade is performed to calculate the stress concentration factors of film cooling holes for different modes.FindingsThe frequency differences between two blades with and without film cooling holes are insignificant, while the differences of the vibration stress cannot be neglected. For the first three modes of the blades, the stress concentration factor is sensitive to the hole’s shape and position on the blade. With the help of the stress concentration factor defined in this work, the concentration of stresses induced by different film cooling holes can be accurately described when evaluating HCF life of the turbine blade.Originality/valueThe effect of film cooling holes on a turbine blade's natural frequencies was confirmed to be insignificant and the stress concentration factors around the holes are calculated. Therefore, the simplified model of the blade without film cooling holes can be used to evaluate the natural frequencies and vibration stress, which saves a lot of time and cost.

Dynamic Strain Measurement of Rotor Blades in Helicopter Flight Using Fiber Bragg Grating Sensor.

Fiber Bragg grating (FBG) sensor has a lot of advantages over the resistance strain gauge and has been used in many applications. However, there are few applications of rotor blade dynamic measurement in helicopter flight. In this paper, a method for blade dynamic strain measurement using an FBG sensor in a helicopter's real flight is presented. The corresponding measurement system is established and can eliminate the effects of the helicopter's electromagnetic environment on the electrical sensing components in the measurement system with the orthogonal frequency-division multiplexing modulation. The measured dynamic strains on the rotor blades of the helicopter in real flight contain six harmonic frequencies with the vibration characteristics of rotor blades, indicating that the established FBG measurement method and system have practical engineering applications.

Vibration analysis characteristics of a pre-twisted tenon jointed blade with under-platform dampers in a thermal environment

This study proposes a method to study blades with multiple friction interfaces, to reveal the coupling effect of multi-interface blades on nonlinear vibrations. The dynamics of a pre-twisted tenon jointed blade with under-platform dampers in a thermal environment is modeled, considering the combined effects of thermal effects and nonlinear loads. Subsequently, a friction model of the tenon and under-platform dampers contact interface is developed. While studying the coupling effect of multiple friction interface, the effects of natural frequency, temperature, rotational speed and pre-twisted angle on blade vibration characteristics and nonlinear characteristics are analyzed.

회전 중 블레이드 진동 비접촉 측정기술 기반 저압터빈 블레이드 진동특성 분석

회전 중 블레이드 진동 비접촉 측정기술 기반 저압터빈 블레이드 진동특성 분석

Influence of Fir-Tree Tenon Blade Parameters on Blade Dynamic Characteristics

In this paper, based on the theory of elastic structure analysis, considering the rotational softening and centrifugal stiffening of the blade, the dynamic model of the fir-tree rotating blade and the macroslip hysteresis model of the dry friction on the contact surface of fir-tree tenon are established. Based on elastic mechanics, the pressure distribution model of fir-tree tenon is innovatively established and the relationship between fit clearance and contact pressure has been derived. After the blade is discretized by the finite element method, the dynamic equation of the blade is solved iteratively by the Newmark-β numerical integration method. According to the dynamic equation of the blade, the influence of the change of the tenon angle on the forced response and contact stress of the blade is derived. Finally, some novel conclusions are obtained by analyzing the influence of pressure distribution, tenon angle, friction coefficient, rotational speed, and aerodynamic excitation on blade vibration characteristics. It provides a scheme and relevant basis for the design and development of tenon blades with the most damping effect at different speeds in industrial practice.

Numerical Study on Vibration Response of Compressor Stator Blade Considering Contact Friction of Holding Ring

There are many kinds of assembly structures in heavy-duty gas turbine compressor stator blades which have significant influence on the complex damping vibration characteristics. At present, compressor design is becoming more and more compact, so it is very meaningful to accurately obtain stator blade vibration characteristics of structures with contact damping. Firstly, a fretting slip friction dynamic model was introduced, and then a vibration analysis model of the compressor stator blade with outer ring structure was established based on the slip friction theory. Then, the vibration response of the compressor stator blade was obtained according to various working conditions, and the main factors affecting the vibration characteristics of the stator blade were revealed. Finally, the vibration response of the blade under a particular exciting force condition was simulated. The results show that the damping vibration characteristics of the compressor stator blades were affected by the excitation force and the normal load of the contact surface. The vibration response curve of the stator blade and the equivalent stiffness coefficient of the contact surface were analyzed, and the friction motion of the contact surface changed with the change of the working condition. The model can simulate the nonlinear vibration characteristics of stator blades. This method provides a reference for the vibration safety analysis of compressor stator blades.

Effect of crystal orientation on elastic stresses and vibration characteristics of nickel-based single crystal turbine blade

The impact of crystal orientation on the elastic stress and vibration properties of nickel-based single-crystal turbine blades is complex and can affect their performance. By defining and describing single-crystal blade orientation by Euler angles rotation, this work presents the influence rule of crystal orientation on the elastic stress and dynamic frequency of blade through lotus leaf diagrams. The results shows that the rotations of three Euler angles can affect significantly the distribution of the region where the stress extremum occurs, and the difference between the maximum and minimum of stress is 210.11 MPa. In addition, the degree and mechanism of influence of Euler angles rotations on the several order frequencies are different. From the 1st to 3st order mode, the influence range of the crystal orientation on the dynamic frequency increases gradually, but the frequency ranges of the 3st, 4st and 5st order are roughly the same, and the frequency range of 6st order is the largest variation range. The blade is most likely to generate resonance when the second-order frequency reaches the minimum fmin2. The Euler angle β has a significant influence on the resonance margin, and the larger resonance margin can be obtained easily when the Euler angle β is large enough.

Blade reduced model considering local contact and analyzing blade vibration characteristics

A dynamic model of a tenoned rotating blade considering the pressure distribution characteristics of the contact interface is established and the degree of freedom of the model is reduced by the double coordination free-interface modal synthesis method in this paper. Firstly, the finite element model of the blade is established by ANSYS and the finite element matrix is extracted. Subsequently, multiple contact pairs were established on the contact surface of the tenon to capture the micro-slip characteristics of the contact interface. The normal pressure of the contact pair is obtained by the ANSYS blade-disk contact prediction and load equivalence to take the pressure distribution characteristics into account in the blade dynamics analysis. Then, non-uniform aerodynamic excitation is applied to the blade to simulate the load on the blade under real working conditions. Finally, the double coordination free-interface modal synthesis method is used to reduce the degree of freedom. Due to the coordination condition of the force and displacement of the substructure connection interface, the degree of freedom of the substructure interface is directly reduced. The final reduced degree of freedom is only the sum of the retained modes of the substructure, which greatly improves the computational efficiency. The dynamic equation is solved by the time integration method, and the effects of the tenon angle, rounded corner, and friction coefficient are discussed. The results show that the double coordination free-interface modal synthesis method can greatly reduce the degree of freedom of the tenon-connected blade model under the premise of ensuring accuracy while retaining the local contact characteristics of the contact interface. The structural parameters of the dovetail structure have a great influence on the vibration reduction characteristics of the blade. When designing the tenon structure, it is necessary to pay attention to these parameters.

An approach of micro-slip modeling based on asymmetric contact pressure distribution and its application in nonlinear boundary beam system

A novel micro-slip friction modeling approach based on the Iwan model is presented here. The normal load and tangential stiffness are reassigned reasonably to obtain the tangential force–displacement expression, and the relationship between the asymmetry of contact pressure distribution and the Iwan density function is established. The micro-slip model depends on the distribution of contact pressure, and has the ability to degenerate into a macro-slip model. Based on the model, a simplified non-linear dynamics model of a rotating blade with a dovetail joint is developed, and its effectiveness is verified by comparing it with a relevant reference. The first-order bending vibration of the blade under distributed excitation is analyzed. The results indicate that the pressure distribution of the contact interface has a significant effect on the amplitude–frequency response of the blade and the contact behavior on the joint interface. Compared with the proposed micro-slip model, the single point contact model overestimates the response amplitude. The amplitude–frequency curve obtained by this model is obviously different from the macro-slip model. It is proved that the micro-slip model can more accurately simulate the nonlinear vibration characteristics of tenoned blades, which provides new insights for the study of the vibration characteristics of tenoned blades.

EEMD-based videogrammetry and vibration analysis method for rotating wind power blades

It is difficult to measure the dynamic status because of the far fields working environment of the wind turbine. A method for vibration analysis of wind turbine blades based on videogrammetry is proposed. In order to obtain the space arc-like path coordinates of rotating blades, a videogrammetry experimental platform for rotating wind power blades was constructed. The space arc-like blade measuring points are collected and the error analysis is carried out by fitting the circular arc-like paths. The natural frequency of blade vibration is calculated based on Ensemble Empirical Mode Decomposition (EEMD) and fast Fourier transform (FFT). Evaluate the accuracy of the proposed method through finite element analysis (FEA) and hammering experiment. The results show that the modal & frequency from the presented method are basically consistent with the results of FEA and hammering experiment. It provides a theoretical method and technical means for measuring the dynamic vibration characteristics of blades.

Theoretical and experimental determination of the boundary conditions influence on gas turbine blade vibration charaсteristics

A description of the stand based on a digital speckle interferometer with a diffuse reference wave and separated branches is given, which allows determining the natural frequencies and vibration modes of objects in real time. In the frequency range 100...4000 Hz, an experimental study of the vibration characteristics of a turbine rotor blade of a gas turbine engine was carried out, with rigid fastening of the blade fir tree part, which was achieved by fixing the blade in the lock and then fixing it in the clamping device. In the frequency range from 100 to 4000 Hz, 9 blade vibration modes were identified. The object of the study is the turbine rotor blade of a gas turbine engine with a height along the trailing edge of 288 mm and a chord in the middle section of 88.5 mm. A solid-state geometric model of a rotor blade based on a faceted body obtained from 3D scanning has been created. Concerning the frequency range 100...4000 Hz, using the ANSYS Workbench software package, a series of calculations of the resonant frequencies of the blade by the finite element method was carried out. Many vibration modes have been obtained, and the data obtained from experiments and calculations have been compared. The analysis of the spectrum of the natural vibration frequencies of the blade showed that the root-mean-square value of the deviations between the results obtained is 5.5% for the same modes. To verify the software calculation, the values of the resonance frequencies were recalculated using a three-dimensional model of the blade fixed in the lock. To determine the influence of the boundary conditions for fixing a gas turbine blade on its vibration characteristics, a series of calculations of the resonance frequencies and vibration modes of the blade model with cutting off a part of the blade at different heights was carried out. It is shown that cutting off the fir tree part of the blade root when modeling the boundary conditions of fixing makes it possible to simplify the calculation process by simplifying the geometry of the three-dimensional model of the blade under study, with a minimum loss of calculation accuracy.

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.