Blade Mode Research Articles

Multimodal shunt damping of monolithic bladed drums using multiple digital vibration absorbers

Abstract Based on a digital realization of piezoelectric shunt circuits, this works presents a proof-of-concept damping approach tailored to address the complex dynamics of monolithic bladed drums (BluMs) and attenuate their vibrations. This approach comprises the simultaneous use of multiple digital vibration absorbers (DVAs) together with a mean shunt strategy, taking advantage of the fact that multiple absorbers act simultaneously on the structure and that the blade modes of BluMs appear closely-spaced. In order to target multiple groups of modes, this strategy is incorporated in a multi-staged shunt circuit. The damping concept is numerically and experimentally demonstrated on a BluM with multiple piezoelectric patches, proving its ability to achieve excellent damping performance on multiple groups of modes. This performance is shown to be relatively insensitive to the spatial distribution of the shunted patches. Based on a robustness study, it was also found that the shunts are robust to changes in the host structure which could, e.g., be due to mistuning. Owing their digital nature, DVAs are easily adjustable making them highly attractive in practical applications.

Fluid–acoustic–structure resonance mechanism of a plane cascade via a low-speed wind tunnel test

Acoustic resonance is an important factor that contributes to aeroengine compressor failure. In this study, a plane cascade of compressor blades was designed to reproduce acoustic resonance via a low-speed wind tunnel test. A high-frequency hot-wire, microphone and strain gauge were used to synchronously measure the fluid, acoustic and structural parameters. We analysed the variation in the amplitude and frequency of the multi-field parameters with increasing mean flow velocity and explored the multi-field interaction mechanism that induces the acoustic resonance of the plane cascade. The plane cascade effectively reproduced the acoustic resonance phenomenon. The first-order acoustic-mode frequency of the plane cascade flow duct, second-order torsional vibration mode frequency of the blade and shedding mode frequency of the tip clearance leakage vortex were equal under acoustic resonance. The fluid, acoustic and structural fields showed a strong interaction effect, achieving the maximum blade vibration amplitude and causing fatigue cracks of torsional vibration at the blade root. The frequency lock-in region of the compressor plane cascade was divided into an ‘acoustic–structure’ interaction region, a ‘fluid–acoustic–structure’ interaction region and a first-order acoustic-mode dominant region with increasing mean flow velocity, which demonstrates an interesting phenomenon in which the fluid–acoustic–structure modes compete: acoustic mode > blade vibration mode > vortex shedding mode. The results demonstrate a unique approach to the study of acoustic resonance that provides insight into the acoustic resonance mechanism in a cascade of compressor blades.

Edgewise Structural Damping of a 2.8-MW Land-Based Wind Turbine Rotor Blade

Modern wind turbines push the predictive capabilities of state-of-the-art aero-servo-elastic tools. The existing limitations hide across the numerical tool chain and can result in serious issues, such as missing aeroelastic instabilities during the design phase. Structural damping is an input that is usually hard to estimate, but also has a major impact on the turbine behavior. In this paper, we discuss an experiment that aims to accurately quantify the structural damping characterizing the edgewise modes of modern wind turbine blades. The experiment is carried out on a 2.8-MW land-based wind turbine and features a fast yaw actuation that induces an edgewise motion on one of the three blades. The Covariant-subspace system identification (Cov-SSI) method is then used to post-process the blade root moment to estimate the short-term edgewise structural damping. Despite limitations of the Cov-SSI method, which consistently under-predicts the absolute values of damping, we observe that structural damping decreases across the first three blade edgewise modes, which is different from the stiffness-proportional damping model that assumes that structural damping increases with the modes. This paper argues that a stiffness-proportional damping model, which is implemented in most aeroelastic tools, is therefore not conservative and might hide aeroelastic instabilities that can instead appear in the field.

Vibration characteristics of blade-casing rubbing fault considering rotor–stator coupling

Blade-casing rubbing is a typical fault of aero-engine, but due to the complex structure of the equipment, it is still challenging to diagnose. This paper studies the characteristics of rubbing faults under rotor stator coupling. Firstly, a numerical model, which includes the rotor, bearings, and casing with blades, is constructed. Secondly, simulate the rubbing fault by setting the non-uniform initial gap between the blades and the casing, and the vibration response of the rotor and casing is obtained. Thirdly, combined with the test rig, the vibration characteristics under rubbing fault are verified. Finally, additional theoretical research is conducted on the vibration characteristics of the rotor, casing and blades under different degrees of rubbing fault. Theoretical and experimental results indicate that rubbing faults have different effects on the vibration of the rotor and stator: the rotational frequency amplitude of the rotor decreases while the frequency amplitude of the stator increases. As the fault degree increases, these phenomena become more significant. When rubbing faults occur, the harmonics near the system’s natural frequencies are more affected than the others. Moreover, rubbing faults can also cause the vibration of the rotor to be affected by the blade mode. The conclusions obtained in this paper can provide a reference for diagnosing rubbing faults in aero-engine.

SIMULATION AND OPTIMIZATION MATERIAL OF WIND TURBINE BLADE PROFILES USING CATIA AND ANSYS,

I Wind energy is a fast-growing way to make power from wind, and it's good for the environment. Wind turbines have big blades that catch the wind to make electricity. This project is all about making those blades work better and cost less money. First, we use special computer programs called CATIA and ANSYS to design and test the blades. CATIA helps us design the shape and size of the blades, while ANSYS helps us see how strong they are and how well they catch the wind. We start by making different blade shapes in CATIA, changing things like length, width, and twist. Then we use ANSYS to test them. We look at things like how much stress they can handle, how much they bend, and how well they catch the wind. After testing, we try to make the blades even better. We use special tools in ANSYS and CATIA to find the best combination of blade features. We want blades that are super-efficient at catching wind, strong enough to last a long time, and don't cost too much to make. By varying material to blade profile checking strength and mode shapes for Aluminium, Carbon fibre and E glass epoxy Keywords: wind energy, Turbines, Wind blades, CATIA, ANSYS

A study on coupled edgewise and flapwise vibration modes of wind turbine blade

The coupled flapwise and edgewise vibrations of a horizontal axis wind turbine blade (HAWT) are discussed in this paper. Kinetic and potential energies of the blade are evaluated with consideration of the effects of gravity and aerodynamic forces. Hamilton’s principle is employed to develop the nonlinear coupled modal equations of the blade. The coupling between the first order edgewise and the first two order of flapwise modes is considered. This leads to three equations with nonlinear terms. Multiple-scales perturbation method is employed to solve these equations. Furthermore, the numerical values of structural specifications of National Renewable Energy Laboratory (NREL) 5-MW reference wind turbine blade are used, for example. It is shown that first edgewise and first flapwise vibrations are dominant, while second flapwise mode of vibration is less significant in the case of transient responses. Energy transfer between resonant modes is observed in both internal and combination resonances. The amplitude–frequency curves and phase diagrams during primary and combination resonances are obtained for the steady-state responses. Combination and primary resonances are further examined by considering various factors such as geometric nonlinearity and aerodynamic force.

Vibration characteristics of pre-twisted rotating Ti-SiC composite airfoil blade

In this paper, a pre-twisted blade model is established based on the FSDT (first-order shear deformation theory), where the Ti-SiC fiber reinforced composite and NACA 4-digit airfoil are innovatively proposed. Rayleigh-Ritz method is utilized to deduce the pre-twisted blade natural frequencies and mode shapes where the exponential polynomials satisfying the cantilever boundary conditions are taken as admissible functions. Comparing with the existing literature, the precision of the model and the method is verified. The material properties of Ti-SiC fiber reinforced composites are calculated by the M-T (Mori-Tanaka) method and FE (Finite Element) method to guarantee the reliability of the calculation method. In addition, the parameters affecting blade vibration, such as rotating speed and aspect ratio, are studied in detail. The research findings indicate that the addition of SiC fibers enhances the properties of the composite blade, and then improves the frequency of the rotating blade. Additionally, the pre-twisted angle, rotating speed, aspect ratio and blade shape significantly affect the natural frequency of Ti-SiC composite airfoil blade. The well-established model accurately predicts the dynamic behaviors of the rotating blade, which has certain guiding value for the optimization of blade material and geometric size.

Analysis of Pressure Pulsation and Structural Characteristics of Vertical Shaft Cross-Flow Pumps

In order to study the pressure pulsation characteristics and structural dynamic response characteristics of a vertical shaft cross-flow pump, this study used a computational fluid dynamics (CFD) numerical simulation method to analyze the pressure pulsation characteristics of the inlet passage, impeller, and guide vane positions of the vertical shaft cross-flow pump device. At the same time, this study analyzed the equivalent stress–strain characteristics of the impeller and guide vane of a vertical shaft cross-flow pump based on fluid structure coupling technology and comprehensively analyzed the deformation modes of the impeller blades and guide vanes under dynamic water flow. This research shows that due to the influence of rotor–stator interaction, the amplitude of pressure pulsation at the interface between the impeller and guide vane of the pump device is the largest and that the main frequency distribution at this position is relatively complex. The non-uniformity of stress distribution at the impeller position gradually decreases with an increase in the radial distance. The high stress and strain zones of the impeller and guide vane are concentrated at the root of the blade. This study can provide reference for hydraulic optimization design and stable operation of similar pump devices.

A New Divergence Based on the Belief Bhattacharyya Coefficient with an Application in Risk Evaluation of Aircraft Turbine Rotor Blades

Belief divergence is a significant measure to quantify the discrepancy between evidence, which is beneficial for conflict information management in Dempster–Shafer evidence theory. In this article, three new concepts are given, namely, the belief Bhattacharyya coefficient, adjustment function, and enhancement factor. And based on them, a novel enhanced belief divergence, called EBD, is proposed, which can assess the correlation of subsets and fully reflect the uncertainty of multielement sets. The important properties of the EBD have been studied. In particular, a new EBD-based multisource information fusion method is designed to handle evidence conflict, where the weight of evidence is decided by the EBD between evidence and the information volume of each evidence. Compared with other methods, the proposed method in the applications of target recognition and iris classification can produce more rational and telling outcomes when dealing with conflict information. Finally, an application in risk priority evaluation of the failure modes of rotor blades of an aircraft turbine is provided to validate that the proposed method has the extensive applicability.

Comparative analysis of the dynamic characteristics of all-metal, composite and composite blades with the same profile, taking into account the influence of the connection of elements and aerodynamic loads

The paper presents a comparative analysis of the dynamic properties of the blades of one rotary machine which have the same airfoil shape, but are made of three different materials, namely aluminum alloy, a complex material combining aluminum alloy and steel, and a composite material which is unidirectional fiberglass. In the case of an all-metal blade, its airfoil and root are made of aluminum alloy. In the case of complex blade airfoil material, the root is made of steel which is also a component of the airfoil material. In the case of a composite blade, the root is steel and is connected at the root section to its composite airfoil. The main attention when comparing models of the mechanical behavior of three types of blades is paid to the influence of the connection of complex and composite elements with the root on the dynamic characteristics of the blade as a whole which is achieved by considering the contact interactions of the elements under the action of centrifugal and aerodynamic loads and the subsequent transfer of the prestressed state of the blades to the modal analysis for determination of the dynamic characteristics of samples and their comparison. In order to correctly display the fixation of elements in the fan impeller in the case of an aluminum blade, the sector of cyclic symmetry of the rotor is considered which makes it possible to draw a conclusion about the possibility of further separate consideration of the blade for determination of its dynamic characteristics due to the much greater stiffness of the connection of the blade with the impeller in comparison with stiffness of the blade airfoil, and to generalize this conclusion in the case of a complex blade by considering a steel root with an aluminum profile with rigid clamping of the model on the contact shelves of the root, and in the case of a composite blade by considering an airfoil with rigid clamping in the root section, where the fastening to the steel root of the blade takes place. The results of a comparative analysis of the dynamic behavior of three types of blades with the same airfoil shape are presented in the form of a study of the blade natural frequencies and mode shapes.

Experimental analysis of chatter in grooving with slender blades

This paper reports on experiments that offer new insights on chatter in grooving with slender blades. Experiments reveal two distinct blade modes cause two types of chatter: diametrical chatter that is of the regenerative kind and snaking chatter on the side walls that is of the mode-coupling type. We find that diametrical chatter can be avoided by using damped blades designed for the purpose. However, since no such blades are available to damp snaking chatter, we show that by cutting in the low-speed process damping region snaking chatter too can be avoided.

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.

Fan Flutter Mechanisms Related to Blade Mode Shape and Acoustic Properties

Abstract The blade mode shape and acoustic properties are important factors that affect the aeroelasticity of fan blades. The goal of this paper is to investigate the stall flutter mechanism associated with the first mode and its components. The paper numerically studies the impact of blade modes on fan flutter under different acoustic propagation conditions. The research focus includes unsteady characteristics inside blade passages, variations in pressure waves under different acoustic modes, as well as the effects of blade modes on the least stable phase angle. The results show that the twist-induced pressure leads to destabilization. Compared with the work of other authors, this study discovered that when the twist-induced pressure on the pressure side act on the plunge rather than twist, the instability effect will be greater, while the effect of twist-induced pressure on the suction side is weak. The phase of unsteady pressure in two-dimensional flow regions is linear with frequency, while the amplitude is highly sensitive to acoustic properties. The plunge-induced pressure inside the passage undergoes significant changes when downstream from acoustic cut-off to cut-on. The twist-induced pressure is more sensitive to changes in the acoustic propagation state, with the peak of the aerodynamic damping curve near upstream acoustic resonance being solely related to the twist-induced pressure acting on the suction side. The study also finds that the position of the blade torsion axis, represented by the twist-to-plunge ratio, does not affect the most unstable nodal diameter.

Provision of Rational Parameters for the Turning Mode of Small-Sized Parts Made of the 29 NK Alloy and Beryllium Bronze for Subsequent Thermal Pulse Deburring.

The increase in the share of physical and technical processing methods in the arsenal of deburring technologies used in modern production is associated both with the use of difficult-to-machine materials, such as beryllium bronze and the 29 NK alloy, and with the need to solve technological problems for the production of small-sized products with hard-to-reach surfaces. The aim of the study is to improve the processes of blade processing of small-sized parts made of beryllium bronze and the 29 NK alloy to provide rational conditions for thermal pulse deburring. Surface samples were experimentally obtained after turning in different modes on a CITIZEN CINCOM K16E-VII automatic lathe equipped with an Applitec micromechanics tool. The surface quality and burr characteristics were examined using a JEOL JIB-Z4500 electron microscope and a ContourGT-K optical profilometer. The program Statistica 6 allowed processing of the results. The relationship between the parameters of the turning mode and the thickness of the root of the burrs formed on the machined surface, the limitation of which is one of the conditions for the application of the thermal pulse method, was established. The obtained empirical regression dependencies establish a rational range of cutting mode parameters, and the implementation of the formulated recommendations for setting blade modes ensures deburring by the thermal pulse method in compliance with the requirements of drawing under maximum processing performance.

Periodic LQG Wind Turbine Control with Adaptive Load Reduction

A periodic linear quadratic Gaussian (LQG) control law augmented with a reference point adaption to enable adequate rotor speed tracking and sufficient load reductions for a wind turbine is presented. The solution of the periodic LQG control problem is based on solving two periodic Ricatti differential equations in continuous time with a multiple shooting integration technique. For this, the available gridded linear time-variant description of the turbine is converted to a harmonic representation using harmonic Fourier approximation. While the periodic LQG controller provides rotor speed tracking and effective damping of the aeroelastic blade modes, the reference point adaption explicitly reduces the loads resulting from the periodic operation of the turbine rotor at the rotor rotational frequency. The performance of the proposed control system is compared against a baseline controller in realistic wind scenarios using a high fidelity nonlinear simulator. The results show a significant damage equivalent load reduction while maintaining adequate rotor speed tracking.

Tendon-inerter-damper helicopter blade augmentation for improved dynamic performance

A novel helicopter blade concept with an adjustable tendon internally supported by dynamically tuned squeeze film damper guides is proposed to suppress the resonant blade vibrations. A physics-based representation of the tendon guides equivalent to an inerter-damper connected in parallel is further adopted to develop a new integrated blade-tendon-device model. The concept is then studied in terms of its optimal dynamic tuning characteristics and damping augmentation potential. The study is focused on single and multi-modal tuning performance in the context of a variable speed rotor with realistic pre-twisted blades used in modern light weight class helicopters. Initially, the significance of modal veering, non-local modes and eigenvalue merging under control parameter variations which include tendon tension, device damping, inertance and span-wise location is elucidated. Across the two separate two-mode optimal tuning studies, it is shown that the typical nominal levels of 0.5–2.0% of the blade modal damping arising from the structural sources can be significantly increased, for instance to 4.3% in case of the second in-plane blade mode and 13.4% in case of the second out-of-plane blade mode. After performing the conceptual device sizing study under realistic constraints utilising the optimal tuning parameters and an adopted squeeze film damping model, it is shown that the concept can be realised within the existing limits of the blade envelope. The proposed concept is shown to be robust and adaptive in its nature with the ability to introduce highly focused blade damping.

Frequency Lock-In Phenomenon of Vortex Induced Vibration of a Rotating Blade Considering Bending-Torsion Coupling Effect

Abstract A rotating thin blade with bend-torsional coupling subjected to vortex induced vibration (VIV) is considered in this paper. It is necessary to study the motion coupled bending torsion due to the discordant centroid and shear center and the effect of centrifugal force at high-speed. The blade with a single axisymmetric section is regarded as a beam instead of an oscillator. The motion equation coupled bending-torsion of the blade is established by using the Euler–Lagrange equations, and the effect of centrifugal force is also employed. Vortex shedding is described by a nonlinear oscillator satisfying Van Der Pol (VDP) equation. Ritz–Galerkin method is employed to simplify the equations of the blade, and the interaction between the bending and torsion modes of blade and wake modes is discussed. The motion equation is simplified based on the contribution of the blade flutter mode. Furthermore, the single-mode approximation is used to investigate the effects of mass ratio, damping, and coupling coefficient on the locking phenomenon. It is also analyzed that the variation of flutter amplitude and locking region of the rotating blade considering bending-torsion coupling.

Non-contact full-field dynamic strain reconstruction of rotating blades under multi-mode vibration

Dynamic strain measurements of rotating blades have attracted significant attention in the turbomachinery design, testing, and service stages. Measuring the blade full-field strain using traditional strain gauges (SGs) is difficult. Too many SGs may add damping to the measured blades, thereby lowering the peak strain that should have been experienced. The strain level was then underestimated for the blades without SGs. A non-contact displacement measurement technique, called blade tip timing (BTT), is promising for replacing SGs but requires effective displacement-to-strain transformation. The transformation under blade single-mode vibration has been studied in recent years. Although the multi-mode vibration of rotating blades is increasingly common, it is usually ignored. In contrast to single-mode vibration, when the blade is subjected to multi-mode vibration, the peak stress changes in both the temporal and spatial domains. This causes difficulties in predicting the blade stress limit and fatigue life. This study proposes a full-field dynamic strain reconstruction method for rotating blades under multi-mode vibration. Based on the BTT-measured displacement, the proposed method enables the full-field dynamic strain reconstruction of the blade in the time domain. First, the multi-mode displacement response of the rotating blades was measured using the BTT system. Second, a least-squares decoupling model for the multi-mode response was established. The blade tip displacement response was decoupled, and the multi-mode vibration parameters were identified, including the frequency, amplitude, and phase. Third, an analytical transform relationship between the tip displacement and full-field strain was derived based on the blade mode shapes. The blade full-field dynamic strain was reconstructed in the time domain using the decoupled displacement response and a displacement-to-strain transmissibility matrix. Finally, the full-field strain at different instants was visualised using a blade finite element model. The proposed method is validated on a rotor with five blades through both numerical simulations and spinning experiments. The reconstructed strain was compared with the result measured by the SG. The average strain relative errors of the five blades were within 7.1%. The peak stress is predicted, and the critical positions on the blade under multi-mode vibration are marked, which can provide valuable knowledge for blade fatigue life prediction and health monitoring.

Blisk With Small Geometry Mistuning and Blend Repair: As-Measured Finite Element Model and Experimental Verification

Abstract This paper presents an “As-Measured Model” (AMM) of a blended blisk, built upon the measurement of the true geometry of the blisk by the three-dimensional optical scanning technology. This high-fidelity model aims to account for the variances of blade frequencies and mode shapes within the real blisk in the presence of both the blend repair and inherent geometry mistuning due to manufacturing, etc. An improved mesh updating strategy is proposed to adapt a seed blisk finite element model (FEM) to the measured geometry. The resultant AMM is therefore able to accurately represent the measured blade-to-blade geometry variances. The classical blade detuning test (BDT) in combination with a novel “correction” procedure is employed to experimentally evaluate the “blade-alone” frequency mistuning pattern in the real blisk. Experimental verification of the AMM demonstrates that it is able to not only capture the blade-alone frequency and mode shape variations due to both the blend and intrinsic blade geometry variances, but also to reproduce the global dynamics of the blended blisk with acceptable accuracy.

Estimation of dynamic characteristics of a wind turbine blade

Wind energy is considered a clean source of energy that can be used efficiently to produce electricity without any harmful emissions. A wind turbine is an electro-mechanical system that converts the wind's kinetic energy into electricity. A typical wind turbine consists of three components, viz. the rotor (which includes the turbine blades), generator and the supporting structure. The turbine blades are a critical component of any wind turbine. They comprise of numerous airfoil sections with varying chord lengths and twist angles, that are combined together to form a three-dimensional blade surface. When generating electrical power through rotating motion, they are subjected to different loads, such as wind, gravitational, and centrifugal loads. The sheer size of the turbine blade necessitates the use of light and strong materials, and composites are well suited for this. The selection and manufacturing of suitable composite material is critical to blade design as it directly affects the efficiency and power of wind power plants. With blades that are continuously exposed to large wind loads, it is essential to determine the natural frequencies of vibrations at which they occur and understand the consequences. Large amplitude vibrations can induce dynamic stresses and accelerate the fatigue of the blade material leading to blade breakage. Thus, it is of significant importance to analyse the dynamic behaviour of these structures. This study aims to investigate the effect of varying fiber orientation and volume fraction on natural frequencies and vibration modes of the turbine blade.