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Underplatform dampers (UPDs), a type of dry friction damper, are commonly used for vibration reduction of turbine blades. This study investigated the effect of UPDs on the forced torsional vibration response of turbine blades within a multi-blade system. Pre-stressed finite element modal analysis and the harmonic balance method were combined to calculate the forced torsional vibration responses of a system with and without UPDs. The experiments were then carried out on a rotating multi-blade system with and without UPDs, with a focus on the effect of mass stacking on damping performance. The results showed that the installation of underplatform dampers could increase the frequency corresponding to the maximum response of the blade torsional vibration and cause multiple peaks that varied in the vibration response based on the mass of the UPDs. With an appropriate normal force, the underplatform dampers could effectively reduce the blade torsional vibration by 68.9%. However, excessive normal force of UPDs could lead to multiple large vibration peaks, which should be avoided in engineering practice. Additionally, the numerical results for the forced torsional vibration response of the rotating multi-blade system with UPDs were relatively close to the experimental results, indicating that the calculation method could be effectively applied to the nonlinear prediction of forced vibrations of rotating blades with dampers. [ABSTRACT FROM AUTHOR]

Blade tip-timing is one of the most widely used non-contact measurement methods for rotating blade vibration. The classic blade tip-timing method is to identify the vibration parameters of the blade based on the time of blade tip arrival to the tip-timing sensor installed on the casing. Since the vibration measurement of blade tip-timing is a serious under-sampling method, the blade resonance frequency is usually higher than the sampling frequency of the BTT data acquisition system, resulting in a large identification error of blade vibration parameters. In view of the above shortcomings, a blade vibration parameters identification method is proposed based on the mapping matching between the static waveform of the sensor and the dynamic waveform of the blade tip-timing. The modulation effects of different vibration displacements, velocities and vibration amplitudes on the tip-timing waveform of the sensor are analyzed. The vibration displacements and velocities of the blade tip passing through the sensor are obtained by the waveform mapping method, and then the vibration parameters of the blade are identified. The influence of the number of blade tip-timing sensors on the identification accuracy of the blade vibration parameters identification algorithm is observed based on the waveform mapping theory. The identification accuracy of waveform mapping method is compared with other methods. The results show that compared with the under-sampled time of arrival (TOA) data of classic BTT applications, the modulation of the sensor waveform output by blade vibration can provide additional data, and the waveform mapping method can not only reduce the number of sensors but also improve the identification accuracy of blade vibration parameters. The waveform mapping method has higher identification accuracy of blade vibration parameters compared with the waveform method in the reference. [ABSTRACT FROM AUTHOR]

The motion information of blades is a key reflection of the operation state of an entire wind turbine unit. However, the special structure and operation characteristics of rotating blades have become critical obstacles for existing contact vibration monitoring technologies. Digital image correlation performs powerfully in non-contact, full-field measurements, and has increasingly become a popular method for solving the problem of rotating blade monitoring. Aiming at the problem of large-scale rotation matching for blades, this paper proposes a modified speeded-up robust features (SURF)-enhanced digital image correlation algorithm to extract the full-field deformation of blades. Combining an angle compensation (AC) strategy, the AC-SURF algorithm is developed to estimate the rotation angle. Then, an iterative process is presented to calculate the accurate rotation displacement. Subsequently, with reference to the initial state of rotation, the relative strain distribution caused by flaws is determined. Finally, the sensitivity of the strain is validated by comparing the three damage indicators including unbalanced rotational displacement, frequency change, and surface strain field. The performance of the proposed algorithm is verified by laboratory tests of blade damage detection and wind turbine model deformation monitoring. The study demonstrated that the proposed method provides an effective and robust solution for the operation status monitoring and damage detection of wind turbine blades. Furthermore, the strain-based damage detection algorithm is more advantageous in identifying cracks on rotating blades than one based on fluctuated displacement or frequency change. [ABSTRACT FROM AUTHOR]

Underplatform dampers (UPDs), a type of dry friction damper, are commonly used for vibration reduction of turbine blades. This study investigated the effect of UPDs on the forced torsional vibration response of turbine blades within a multi-blade system. Pre-stressed finite element modal analysis and the harmonic balance method were combined to calculate the forced torsional vibration responses of a system with and without UPDs. The experiments were then carried out on a rotating multi-blade system with and without UPDs, with a focus on the effect of mass stacking on damping performance. The results showed that the installation of underplatform dampers could increase the frequency corresponding to the maximum response of the blade torsional vibration and cause multiple peaks that varied in the vibration response based on the mass of the UPDs. With an appropriate normal force, the underplatform dampers could effectively reduce the blade torsional vibration by 68.9%. However, excessive normal force of UPDs could lead to multiple large vibration peaks, which should be avoided in engineering practice. Additionally, the numerical results for the forced torsional vibration response of the rotating multi-blade system with UPDs were relatively close to the experimental results, indicating that the calculation method could be effectively applied to the nonlinear prediction of forced vibrations of rotating blades with dampers.

• Consider the combined disturbance of rotating speed and rotor displacement. • Build a dynamic model of variable speed rotating blades under parametric and forced excitation. • Propose a method of varying amplitude to determine the typical tuned and detuned solutions. • Reveal the nonlinear interaction between principal and parametric resonances. It is generally acknowledged that the disturbance of rotating speed will cause parametric resonance for blades, and the presence of rotor displacement also can make the blade vibrate transversely. However, the coupled resonance mechanism of blades under the combined action of rotating speed disturbance and rotor displacement is not yet clear. To answer this question, this article investigates the nonlinear coupled resonance behavior of rotating blades in two cases: typical tuned (the frequency ratio of parametric and forced excitations equals 2:1) and frequency ratio detuned. A nonlinear vibration equation for rotating blades is established based on Euler beam theory in conjunction with geometric nonlinearity. The mixing rule and modified Halpin-Tsai model are used to calculate the effective properties of GPLRMF materials. Subsequently, using the method of varying amplitudes (MVA), an approximate analytical solution of the coupled resonance response is derived, the Jacobian matrix is used to determine the stability of non-trivial solutions, and the accuracy of the analytical results is verified with the aid of numerical solutions. Finally, the steady-state response of typical tuned and detuned coupled resonance is analyzed, and the influence mechanism of factors such as excitation amplitude, excitation phase angle and other parameters on coupled resonance is studied in detail. The results indicate that the supercritical coupled resonance curve exhibits double resonance peaks and jumps. Meanwhile, the steady-state response of coupled resonance highly depends on the excitation phase angle. [ABSTRACT FROM AUTHOR]

Dynamic strain of rotating blades is critical in turbomachinery health monitoring and residual life evaluation. Though the blade tip timing (BTT) technique is promising to replace traditional strain gages, the lack of effective strain transformation through BTT hinders the implementation. In this paper, a noncontact dynamic strain reconstruction method of rotating blades is proposed based on the BTT technique and response transmissibility. First, the displacement-to-strain transmissibility (DST) considering rotational speed is derived from the frequency response functions based on blade mode shapes. A quadratic polynomial function of DST with respect to the rotational speed is provided to calibrate DST in blade rotational state. Second, the blade-tip displacement in resonance is obtained by BTT measurement and the Circumferential Fourier Fit processing method. Third, the dynamic strains of critical points on blades are calculated using the DST in conjunction with the tip displacement amplitude. In this paper, to validate the proposed method, acceleration and deceleration experiments, including both BTT and strain gages, are conducted on a spinning rotor rig. Experimental results demonstrate that the reconstructed dynamic strains of different positions on the rotating blades correspond well to the results measured by strain gages. The mean relative error between the reconstructed and measured results is generally within 8%. [ABSTRACT FROM AUTHOR]

In order to solve the problem of difficult blade defect diagnosis caused by severe signal under-sampling in tiptiming technology, a defect diagnosis method for rotating blade based on convolution neural network (CNN) was proposed.In the method, the under-sampled tip timing signal was subject to fast Fourier transform directly to obtain the beat signalof blade at actual vibration frequency. Then, the beat signal was directly used as the input signal of the one-dimensionalCNN model, and by optimizing the network structure and parameters, the sensitive features that can characterize the stateof rotating blades were automatically mined and applied for model training, so as to obtain the applicable diagnosis modelfor defect identification of rotating blades. Finally, the feasibility of the proposed method was verified by the vibration testof rotating blades. The results show that the!![CNN-based defect diagnosis method for rotating blades] could solve the analysisproblem resulted from the under-sampling of blade tip timing signal and the average diagnosis accuracy rate reaches 89%, which provides a new way for defect diagnosis of rotating blades.

Blade tip-timing is one of the most widely used non-contact measurement methods for rotating blade vibration. The classic blade tip-timing method is to identify the vibration parameters of the blade based on the time of blade tip arrival to the tip-timing sensor installed on the casing. Since the vibration measurement of blade tip-timing is a serious under-sampling method, the blade resonance frequency is usually higher than the sampling frequency of the BTT data acquisition system, resulting in a large identification error of blade vibration parameters. In view of the above shortcomings, a blade vibration parameters identification method is proposed based on the mapping matching between the static waveform of the sensor and the dynamic waveform of the blade tip-timing. The modulation effects of different vibration displacements, velocities and vibration amplitudes on the tip-timing waveform of the sensor are analyzed. The vibration displacements and velocities of the blade tip passing through the sensor are obtained by the waveform mapping method, and then the vibration parameters of the blade are identified. The influence of the number of blade tip-timing sensors on the identification accuracy of the blade vibration parameters identification algorithm is observed based on the waveform mapping theory. The identification accuracy of waveform mapping method is compared with other methods. The results show that compared with the under-sampled time of arrival (TOA) data of classic BTT applications, the modulation of the sensor waveform output by blade vibration can provide additional data, and the waveform mapping method can not only reduce the number of sensors but also improve the identification accuracy of blade vibration parameters. The waveform mapping method has higher identification accuracy of blade vibration parameters compared with the waveform method in the reference.

To achieve effective gripping of large planar and flexible targets while reducing the risk of scratching, a novel cyclonic-type mechanical gripper based on rotating blades is studied. Firstly, the working principle of this cyclonic gripper is analyzed in detail, followed by the structural design of the gripper unit. Using Fluent computational fluid dynamics software, the flow characteristics of the airflow within the cyclonic gripper chamber are analyzed, and the influence of gripper structural parameters on suction force is investigated. Finally, a suction force testing platform for the cyclonic gripper is constructed, and experimental validation of the simulated suction force results is conducted. The research indicate that the proposed cyclonic-type mechanical gripper based on rotating blades can effectively grip targets, while the suction force is closely related to parameters such as blade rotation speed, number, and diameter. • Proposing a cyclonic mechanical gripper based on rotating blades. • Simple structure, no additional air source required. • Suction cups that can be combined into multiple grippers. [ABSTRACT FROM AUTHOR]

• Developing a rotating orthotropic blade model with adjustable stagger angle. • Analytical and numerical solutions for modal analysis and stability inspection. • Recognizing the possibility of internal resonances between different modes. • Finding the possibility of switching instability zones relative to each other. • Obtaining the effect of different parameters on the instability regions. A blade with an adjustable stagger angle is a type of blade that is able to partially rotate around its long axis. In fact, while a hub rotates, simultaneously the angle of the blade root section can change. The objective of this research is to develop and analyze a model of rotating cantilever orthotropic blade with adjustable stagger angle. Using Hamilton's principle, the governing partial differential equations are derived. In this formulation, both the Coriolis effects and centrifugal inertia forces are accounted for. First, the extended Galerkin method is utilized to discretize the equations of motion. Then, the multiple scales method is used to investigate the dynamic stability of the rotating blades analytically. Consequently, the possibility of internal resonances between different modes is studied and recognized. Moreover, the influence of various parameters on the instability regions is evaluated in detail, and the results are discussed. For validating the results, the modal characteristics of the system obtained by two methods of extended Galerkin and extended Kantorovich are compared with each other. Additionally, the fourth-order Runge–Kutta algorithm is employed to more deeply understand the dynamic behaviors of the system in the cases of constant and variable stagger angles and the differences between them as well as to prove the validity of the results of multiple scales method. The time histories, phase space diagrams and frequency spectrums are provided. Furthermore, a detailed investigation is carried out to determine the properties of the response under different conditions of the amplitude of the variable angle. As far as we know, the present study is the first attempt to demonstrate the effects of time-varying stagger angle for this class of problems in the literature. A stable motion in the adjustable stagger angle configuration gives a more complicated response. It can be observed that in this dynamic situation, the results are affected by Coriolis, both in quality and quantity. The findings indicate that with a change in the speed, there is a possibility of switching instability zones relative to each other. It is also found that the maximum width of the instability regions among the combination resonances is related to the second spanwise and first chordwise bending modes. The type of instability qualitatively depends on the amplitude of angle. [ABSTRACT FROM AUTHOR]

Radar signatures contributed by rotating blades of drones usually refer to the kinematical micro-Doppler phenomenon on spectrograms. Here, theoretical analysis indicates that when sampling time is short enough that this signature becomes instant micro-Doppler signatures with scattering characteristics, appearing as “blade flash” in the time domain and rotor blade modulation (RBM) feature in the spectrum. In an anechoic chamber, we track this instant micro-Doppler signature by using a dynamic measurement system composed of a network analyzer and a high-speed camera to collect high-resolution range profile of a consumer drone, DJI Phantom 3 Vision within S-band, X-band, and Ku-band. The experimental results demonstrate that rotating blades do cause signal fluctuation of “blade flash” and register the RBM feature in the spectrum, and the modulation effects are weak within S-band, strong within X-band, and stronger within Ku-band. This instant micro-Doppler with scattering characteristic establishes a mapping between radar signature and the rotation structure component of the drone and enables us to distinguish a drone from other nonblades objects in the air, especially with little radar observation time. [ABSTRACT FROM AUTHOR]

Drone inexpensive and operational flexibility contributed to its exponential increase by civil users, apart from military applications. This resulted in posing threats due to drone misuses, such as smuggling, unlawful imaging and other significant vulnerability that makes its detection necessary. The study demonstrated a theoretical model of extracting the m-Doppler signature due to rotating blades of a quadcopter drone, in forward scattering radar (FSR) geometry. The model was further validated experimentally by using a parabolic dish antenna in the receiver system of the FSR geometry. Before these, some reported efforts made to detect the drone by using different methodologies such as acoustic, video, audio-visual, radio frequency, radar systems and other non-technical approaches like netting were briefly presented. The result of the authors’ investigation revealed that the drone could be detected from the signature generated due to rotating blades based on the blade orientation. This signature can further be used to identify the drone from other flying targets existing within the same surveillance area.

New large-scale laboratory data are presented on a physical model of a spar buoy wind turbine with angular motion of control surfaces implemented (pitch control). The peculiarity of this type of rotating blade represents an essential aspect when studying floating offshore wind structures. Experiments were designed specifically to compare different operational environmental conditions in terms of wave steepness and wind speed. Results discussed here were derived from an analysis of only a part of the whole dataset. Consistent with recent small-scale experiments, data clearly show that the waves contributed to most of the model motions and mooring loads. A significant nonlinear behavior for sway, roll and yaw has been detected, whereas an increase in the wave period makes the wind speed less influential for surge, heave and pitch. In general, as the steepness increases, the oscillations decrease. However, higher wind speed does not mean greater platform motions. Data also indicate a significant role of the blade rotation in the turbine thrust, nacelle dynamic forces and power in six degrees of freedom. Certain pairs of wind speed-wave steepness are particularly unfavorable, since the first harmonic of the rotor (coupled to the first wave harmonic) causes the thrust force to be larger than that in more energetic sea states. The experiments suggest that the inclusion of pitch-controlled, variable-speed blades in physical (and numerical) tests on such types of structures is crucial, highlighting the importance of pitch motion as an important design factor.

Ensuring the reliability of the steam turbine is fundamental task for its proper operation. Early detection of any failure avoids material and financial losses. A very important task in turbomachinery diagnostics is monitoring of rotating blades vibration, especially in terms of the last stages of low-pressure turbine parts, where, in general, the vibration can reach the important level due the blades length. The commonly used methods are based on stress evaluation using strain gauges or on the non-contact measurement of blade tips – blade tip-timing (BTT) method. Rising demand for low-cost monitoring systems suitable for blade monitoring has led to development of a new approach based on signal processing of standard turbine instrumentation. The symptoms of blade vibration could be also visible in signals from relative shaft vibration (SV) sensors, which are standardly installed in turbine journal bearings. This paper illustrates the principles and possibilities of the approach based on processing of SV signals for monitoring of actual state of rotating blades. Finally, the comparison of parallel measurements using SV and BTT in operation of steam turbine reveals the properties and advantages of both methods. [ABSTRACT FROM AUTHOR]

Drone inexpensive and operational flexibility contributed to its exponential increase by civil users, apart from military applications. This resulted in posing threats due to drone misuses, such as smuggling, unlawful imaging and other significant vulnerability that makes its detection necessary. The study demonstrated a theoretical model of extracting the m-Doppler signature due to rotating blades of a quadcopter drone, in forward scattering radar (FSR) geometry. The model was further validated experimentally by using a parabolic dish antenna in the receiver system of the FSR geometry. Before these, some reported efforts made to detect the drone by using different methodologies such as acoustic, video, audio-visual, radio frequency, radar systems and other non-technical approaches like netting were briefly presented. The result of the authors' investigation revealed that the drone could be detected from the signature generated due to rotating blades based on the blade orientation. This signature can further be used to identify the drone from other flying targets existing within the same surveillance area. [ABSTRACT FROM AUTHOR]

In this paper, the coupled bending–bending–axial–torsional free vibrations of rotating blades are investigated based on the Euler–Bernoulli beam model. The coupled partial differential equations governing flapwise, edgewise, axial and torsional motions are derived by the Hamilton's principle, wherein three types of velocity-dependent terms, namely static centrifugal terms, dynamic centrifugal terms and gyroscopic coupling terms, are focused. The ordinary differential equations are acquired by the Galerkin truncation, and the natural frequencies in all directions and complex mode shapes of the rotating blades are analyzed in detail. It is revealed that the three types of velocity-dependent terms have different effects on the natural frequencies. The natural frequencies are noticeably dependent on the rotating speed and preset angle, except for the axial vibration, which is almost immune to the preset angle. The complex modal motions are displayed by a series of positions of the central line and free-end cross section for different time instants, showing the coupled vibrations among different directions. [ABSTRACT FROM AUTHOR]

In this article, the vibration analysis of rotating moderately thick cantilever orthotropic plate is analytically investigated. Based on the first order shear deformation plate theory, the partial differential equations of motion are derived using Hamilton's principle. The centrifugal inertia forces and Coriolis effects due to the rotation are all considered. The analytical approaches, both extended Kantorovich method and extended Galerkin method, are employed to obtain the solution of the problem. Results obtained by these two methods are compared with those available in the open literature and good agreements are observed. The effects of various parameters, individually or in combination, on the vibrational behaviors are analyzed in detail. From the studies, it is found that in the rotating plates, when the stiffness ratio increases, the crossing/veering phenomenon occurs in the lower mode orders and/or rotation speeds. The results show that for each stiffness ratio, the effect of hub radius ratio is more significant on the out-of-plane mode frequencies than on the in-plane ones. [ABSTRACT FROM AUTHOR]

Nonlinear dynamics and mode aberration of rotating plates and shells are discussed in this work. The mathematical formalism is based on the one-dimensional (1D) Carrera unified formulation (CUF), which enables to express the governing equations and related finite element arrays as independent of the theory approximation order. As a consequence, three-dimensional (3D) solutions accounting for couplings due to geometry, material, and inertia can be included with ease and with low computational costs. Geometric nonlinearities are incorporated in a total Lagrangian scenario and the full Green-Lagrange strains are employed to outline accurately the equilibrium path of structures subjected to inertia, centrifugal forces, and Coriolis effect. A number of representative numerical examples are discussed, including multisection blades and shells with different radii of curvature. Particular attention is focused on the capabilities of the present formulation to deal with nonlinear effects, and comparison with s simpler linearized approach shows evident differences, particularly in the case of deep shells. [ABSTRACT FROM AUTHOR]

For large-scale offshore wind turbine rotating blades (NREL 5MW), the theoretical model of vibration due to fluid-structure interaction (FSI) is established, and the basic equations for modal analysis are given. Based on ANSYS workbench platform, the blade modal characteristics at different rotating speeds are analyzed, and further research on dynamic stability is carried out. The results indicate that the FSI and the blade rotation have a great influence on modal frequencies, which increase with the rotating speed of the blade under FSI. When the frequency of the periodic wind speed is close to the first-order natural frequency of the blade, both the maximum flapping displacement and the maximum von Mises stress increase with time, and the vibration divergence appears. At the safe tower clearance of 4.50 m, the critical value of the blade maximum von Mises stress shows a linear upward trend with the increase of the elasticity modulus, which provides technical references for optimization design and safe operation of wind turbine blades. [ABSTRACT FROM AUTHOR]

This manuscript is concerned with the free vibration analysis of rotating orthotropic cantilever plates attached with an arbitrary stagger angle to a hub. The general governing equations which include both the centrifugal inertia forces and Coriolis effects are derived using Hamilton’s principle. The results are obtained using extended Kantorovich method and extended Galerkin method which are compared with each other, and available data in the literature and in good agreements are observed. A very detailed study of the influence of varying stiffness ratio, rotation speed, stagger angle, hub radius ratio and aspect ratio on the dynamic characteristics is conducted. These investigations provide complementary results, which leads to improvement in design and appropriate optimization of the material and geometry in this class of problems. The observation of the results shows that the crossing/veering phenomenon is influenced by the stiffness ratio, stagger angle and hub radius ratio. It is found that the centrifugal stiffening rate in the spanwise bending modes is constant, while in the torsion mode is changeable. The plate with the lower stiffness ratio has the higher centrifugal stiffening rate. [ABSTRACT FROM AUTHOR]

Proportional–derivative (PD) controller is applied in this work to study the effects of time delay on its performance for reducing the oscillations of a rotating beam at varying speed. The dual-system vibrational modes are linearly coupled so we have applied the controller to only one mode and the other coupled mode tracks it. The worst resonance cases—verified numerically—in this paper are the primary and the principal parametric resonance cases that should be controlled. The overall nonlinear behavior of the system with and without control is investigated through the remarkable multiple time scales method. Different response curves are involved to investigate controller effect. [ABSTRACT FROM AUTHOR]

This study examined the pool boiling heat transfer of distilled water on a copper heating surface with passive rotating blades installed above the heating surface. The rotating blades were made from copper material, with a diameter of 30 mm, a core of 5 mm, a length of 50 mm, and a blade angle of 90°. The number of blades in this experiment varied between 2, 3, and 4. The study examined the effects of a varying number of blades and the distance between the heating surface and rotating blades (L SB ) on the pool boiling heat transfer coefficient. The experimental results show that, when compared under the same conditions, the rotor with four blades yielded a higher heat transfer coefficient than those with two and three blades. This is because the added blades increased the area that received strike force from the bubbles. As a result, the rotating blades created more disturbance of the working fluid over the heating surface. Furthermore, when compared with the same number of blades, the L SB of 5 mm yielded a higher heat transfer coefficient than the L SB of 15 or 25 mm. This is because the increased L SB provided less chance for the bubbles to strike the rotating blades. Hence, the rotating blades did not create a disturbance of the working fluid over the heating surface. [ABSTRACT FROM AUTHOR]

The paper discusses the structural health monitoring of rotating blades on helicopters (RBH) based on the application of Modal Analysis. The study discussed in this paper includes the experimental validation of state-of-the-art techniques for the on-line measurement of dynamic signals of helicopter rotating units, optimization of the sensor type for rotating unit measurement, analysis of the practical applicability of modal analysis techniques for condition-based monitoring of rotating structures and estimation of the efficiency of the experimental system for the identification of practical damages of blades. The research was conducted using helicopter blade models operating within an experimental test bench. The capabilities of diagnostic technique application to main rotor gears and bearings are also presented. Conclusions are made about the successful analysis of the operational modal analysis technique applicability for the structural health monitoring of a rotating blade, and its effectiveness for damage identification. Two strategies of the RBH repair – with a continuously condition-based monitoring with the proposed technology and one without such monitoring, were discussed. The Markov chain reliability models for each strategy were analyzed and the reliability improvement factor for the proposed monitoring technology in comparison with a traditional one was evaluated. It is shown that the reliability improvement factor is more effective for the proposed method as compared to the traditional one.

• The full-field dynamic strain of rotating blades under multi-mode vibration is reconstructed by BTT and displacement-to-strain transmissibility matrix. • A least-square decoupling model is established to identify multi-mode vibration parameters of rotor blades. • An analytical relationship between the blade-tip displacement and the full-field strain is derived. • The blade strain/stress distribution is visualized via the finite element model. 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. [ABSTRACT FROM AUTHOR]

Fatigue test results of the rotating steel blades of the fourth stage of the K-25-0.6 low pressure cylinder Geo steam turbine manufactured in the Kaluga Turbine Plant (hereinafter, KTP) with the ion-plasma coating were presented. Coating formation was carried out at the National Research University (MPEI) on the Gefest vacuum pilot plant by the magnetron sputtering method. Characteristics of the obtained coating were analyzed with the use of the scientific-research equipment of the National Research University (MPEI). Fatigue tests of the rotating blades and determination of the fatigue strength of the material with the ion-plasma coating were carried out on the electrodynamic vibration machines VEDS-400A in the KTP structural laboratory. The following characteristics were obtained after tests: Ti-TiN composition, 10-11 μm thickness, 1200 HV 0.05 microhardness. Fatigue tests showed that destruction, regardless of availability or nonavailability of the coating, took place by cross-section in the root zone both on the leading and trailing edges of the blade, i.e., in the most stressed zones. It was found out that the maximum stresses during tests were revealed in the root section along the trailing edge on the blade pressure side, and the less stresses were on the leading edge. Fatigue strength of the working blades after coating formation increased by 12% minimum. Results of the fatigue tests prove the previously obtained data concerning 10-12% increase of the fatigue strength of the blade steel with the ion-plasma coating and allow claiming that the process of their formation exerts the positive influence on the fatigue characteristics of the blade materials. [ABSTRACT FROM AUTHOR]

The paper discusses the structural health monitoring of rotating blades on helicopters (RBH) based on the application of Modal Analysis. The study discussed in this paper includes the experimental validation of state-of-the-art techniques for the on-line measurement of dynamic signals of helicopter rotating units, optimization of the sensor type for rotating unit measurement, analysis of the practical applicability of modal analysis techniques for condition-based monitoring of rotating structures and estimation of the efficiency of the experimental system for the identification of practical damages of blades. The research was conducted using helicopter blade models operating within an experimental test bench. The capabilities of diagnostic technique application to main rotor gears and bearings are also presented. Conclusions are made about the successful analysis of the operational modal analysis technique applicability for the structural health monitoring of a rotating blade, and its effectiveness for damage identification. Two strategies of the RBH repair – with a continuously condition-based monitoring with the proposed technology and one without such monitoring, were discussed. The Markov chain reliability models for each strategy were analyzed and the reliability improvement factor for the proposed monitoring technology in comparison with a traditional one was evaluated. It is shown that the reliability improvement factor is more effective for the proposed method as compared to the traditional one. [ABSTRACT FROM PUBLISHER]

When the airflow patterns inside a lawn mower deck are understood, the deck can be redesigned to be efficient and have an increased cutting ability. To learn more, a combination of computational and experimental studies was performed to investigate the effects of blade and housing designs on a flow pattern inside a 1.1m wide corotating double-spindle lawn mower deck with side discharge. For the experimental portion of the study, air velocities inside the deck were measured using a laser Doppler velocimetry (LDV) system. A high-speed video camera was used to observe the flow pattern. Furthermore, noise levels were measured using a sound level meter. For the computational fluid dynamics (CFD) work, several arbitrary radial sections of a two-dimensional blade were selected to study flow computations. A three-dimensional, full deck model was also developed for realistic flow analysis. The computational results were then compared with the experimental results.

• The relationship between the natural frequency of the blade and the mistuning coefficient is studied. • An improved blade natural frequency deviation-based mistuning identification method with the application of the blade tip timing (BTT) technology is proposed. • Based on the three simplifying assumptions of the fundamental mistuning model (FMM) method, the fourth condition was added and defined: The mode strain energy proportions of the blade in the isolated modal family can be believed identical. • An improved BTT technique-based dynamic strain prediction method is proposed. • Compared with other methods, numerical analysis and experimental investigations verify the feasibility and reliability of this study. Blade tip timing (BTT) is the most effective technique for vibration monitoring of rotating blades. The research of dynamic characteristics and forced responses of the blisk is crucial to the matters of blade vibration with far-reaching significance. The general mistuning identification techniques require experimental tests and numerical solutions of the whole bladed disk. Since the feature of the BTT technique can identify the modal properties of blades, this paper proposed a blade natural frequency deviation-based mistuning identification method, which achieves the mistuning quantitative evaluation and the model online update of mistuned blisk. Numerical analysis and experimental investigations prove that the improved mistuning identification method can reach accurate and reasonable results, especially in the mode dominated by blade vibration. Furthermore, based on the three assumptions of the fundamental mistuning model (FMM), an additional condition was defined: The mode strain energy proportions of the blade in the isolated modal family can be believed identical. This study revealed the relationship between blade strain and blade vibration, and an improved dynamic strain prediction method for the implementation of non-contact measurement of blade strain was proposed. The numerical analysis shows the prediction error of dynamic strain is less than 3%. Two experimental tests reported that the prediction results of dynamic strain are consistent with the FMM and BTT-based non-contact dynamic stress measurement (FB-NDSM) method, and the maximum error of prediction results is less than 2% about a FB-NDSM method reference, which is acceptable in practical applications. Improved mistuning identification and dynamic strain prediction method with the application of BTT technology are attractive for the dynamic characteristic study and health management of the bladed disk, which significantly promotes the application of BTT technology in blade vibration monitoring of large-scale rotating machinery. [ABSTRACT FROM AUTHOR]

Abstract: The operational modal analysis, OMA, allows estimating the dynamic properties of a structure, natural frequencies, damping ratios, and mode shapes, without measuring the input forces. According to the main hypothesis concerning the input excitation, i.e., stochastic with frequency independent spectra (at least in the frequency band of interest), it is not theoretically possible to apply the OMA procedures in structures characterized by the presence of harmonic components in the excitation loading. In this paper, an approach capable to identify the presence of harmonic excitations, acting together with a broad band stochastic loading, and then to remove their effects in the modal parameter estimate is presented. The approach is based on the joint use of the statistical parameter called “entropy” and the already developed output-only procedure based on the application of the Hilbert transform properties to the output response signals. The capability to improve the OMA procedures is investigated numerically and through whirl tower experimental tests of a rotating blade in which both stochastic and harmonic contributions to the dynamic excitations have been provided by the perturbations arising from the operative conditions. A sensitivity analysis has been also performed to evaluate the effects of the filtered responses, in the time domain, on the statistical characterization, required to distinguish the operational frequencies from the natural ones. [Copyright &y& Elsevier]

A new two-noded, twelve degree of freedom finite element is developed for rotating blades. The shape functions are derived from the exact solutions of the governing static homogenous differential equations for the rotating blades. Such an approach leads to superconvergent elements. These differential equations include out-of-plane bending, in-plane bending, axial deformation, and torsion. The axial and torsion equations yield exact solutions and the flap and lag equations are solved by assuming a constant centrifugal force within the element. Differing from the conventional polynomial shape functions, the new shape functions account for the centrifugal stiffening effect as they depend upon the rotation speed, material properties, and the element position along the length of the blade. The finite element formulation is derived from the energy expressions using the Hamilton's principle. A convergence study for the natural frequencies is performed using the new shape functions and the polynomial shape functions for a coupled and an uncoupled blade. It is observed that the new shape functions lead to much more rapid convergence than the conventional polynomial shape functions for the first few modes at higher rotation speeds, where the effect of centrifugal stiffening is higher. The basis functions can also be used for finite element analysis of rotating rods and beams, and for energy methods. [ABSTRACT FROM AUTHOR]

This paper presents a technique for blade damage detection based on spatial wavelet analysis. The wavelet transform is used to analyze spatially distributed signals (e.g. mode shape) of cracked thick rotating blades. First, a finite element model is applied to the vibration of a thick rotating blade with a single edge crack. The effects of transverse shear deformation and rotatory inertia are taken into account. Then the mode shapes of the cracked rotating blade are analyzed by wavelet transformation. The effects of crack locations and sizes on the wavelet coefficients are studied. It is found that the distributions of the wavelet coefficients can identify the crack position of the rotating blades by showing a peak at the position of the crack. Then the signals are analyzed by wavelet transform. It is found that the distributions of the wavelet coefficients can identify the crack position. Assumed measurement errors are added to nth mode shape for evaluating the effect of measurement errors on the capability of detecting crack position. The moving average method is used to process the data with assumed measurement errors. The crack positions can also be identified when there exist assumed measurement errors. [Copyright &y& Elsevier]

Experimental and computational studies were performed to determine the effects of different blade designs on a flow pattern inside a double-spindle counter rotating mower deck. In the experimental study, two different blade models were tested by measuring air velocities using a forward-scatter LDV system. The velocity measurements were taken at several different azimuth and axial sections inside the deck. The measured velocity distributions clarified the air flow pattern caused by the rotating blades and demonstrated the effects of deck and blade designs. A high-speed video camera and a sound level meter were used for flow visualization and noise level measurement. In the computational works, two-dimensional blade shapes at several arbitrary radial sections have been selected for flow computations around the blade model. For three-dimensional computation applied a non-inertia coordinate system, a flow field around the entire three-dimensional blade shape is used to evaluate flow patterns in order to take radial flow interactions into account. The computational results were compared with the experimental results. [ABSTRACT FROM AUTHOR]

The problem of bending vibration, dynamic response, and actively dynamic control of rotating beams of nonuniform cross section, operating in a temperature field and impacted by a blast, is addressed. The structural model is in the form of a thin-walled beam whose material properties are considered to be temperature dependent. The implemented vibration control methodology is based on the piezoelectric strain actuation. In this context, a system of piezo actuators bonded to the structure surface that are spread over the entire span of the beam and actuated out of phase is considered. As a result, a control bending moment is piezoelectrically induced at the beam tip. In the context of this paper, to control the free and forced vibration, velocity feedback control is implemented. The considered control methodology is also useful toward counteracting the deleterious effects induced by the thermal degradation of material properties of blade structure. Results highlighting the effects of the blade taper on bending natural frequencies, as well as of the temperature and time-dependent external excitation on the open/closed-loop bending dynamic response are presented, and pertinent conclusions are drawn. [ABSTRACT FROM AUTHOR]

This paper addresses the problems of modeling and bending vibration control of tapered rotating blades modeled as nonuniform thin-walled beams and incorporating adaptive capabilities. The blade model incorporates non-classical features such as transverse shear, secondary warping and includes the centrifugal and Coriolis force fields. For the non-adaptive system, an assessment of a number of non-classical features including the taper characteristics is accomplished. The adaptive capabilities are provided by a system of piezoactuators bonded to the structure surface and spread over the entire span of the beam. Based on the converse piezoelectric effect and on the out-of-phase actuation, the piezoactuators produce a localized strain field in response to the applied voltage, and consequently, a change of the dynamic response characteristics is induced. A combined feedback control law relating the piezoelectrically induced transversal bending moment at the beam tip with the kinematical response quantities appropriately selected is used, and the beneficial effects upon the closed-loop dynamic characteristics of the blade are highlighted. [Copyright &y& Elsevier]

One of the difficult tasks in axial flow pump design is the elaborate manner of predicting its correct dimensions. As more test data are accumulated, it depends upon the skill of the designer to discern the effects of these several variables, leading to the optimum hydraulic performance. In an attempt to contribute to saving time spent on determining the basic dimensions for an axial flow pump, a graphical method is proposed to assist in the preliminary determination of these dimensions. [ABSTRACT FROM AUTHOR]

• Dynamic strain measurement of rotating blades is conducted via Blade-Tip Timing. • Blade vibration parameters are identified based on L 1/2 -norm regularization. • Blade dynamic strain is reconstructed based on displacement and transmissibility. • The reconstructed results are compared with the strain gauges' measurements. • Numerical cases and a rotor test validate the strain reconstruction method. Dynamic strain measurement is critical in blade vibration monitoring for evaluating the residual life and health condition of rotating blades. Blade tip time (BTT) is recognized as a promising technique to replace traditional strain gauge measurement. This paper presents a method for dynamic strain reconstruction as well as vibration parameter identification based on BTT via the L 1/2 -norm sparse regularization and response transmissibility. First, a sparse representation model based on the L 1/2 -norm penalty is developed to identify blade vibration frequency and blade-tip displacement. Second, a displacement-to-strain transmissibility (DST) is proposed for strain reconstruction from identified displacement. The mode shapes of the blade are needed to calculate the DST. The proposed method is named L 1/2 -DST, which has a great advantage of achieving non-intrusive strain measurement for rotating blades using BTT. Numerical simulation and spin experiment show that the L 1/2 -DST method enables accurate dynamic strain reconstruction and robustness to noise. [ABSTRACT FROM AUTHOR]

• A unified quasi-3D dynamic model for rotating pre-twisted laminated composite shell panels is first presented. • Initial centrifugal stresses are accurately predicted by a separate quasi-static analysis. • Several typical case studies are presented to show the present model's accuracy and applicability. • Parametric studies are performed on vibrations of pre-twisted laminated composite shell panels. This study presents a unified quasi-three-dimensional (quasi-3D) solution for the free vibration analysis of rotating pre-twisted laminated composite shell panels. Based on the 3D elasticity shell theory, Carrera unified formulation is employed to reduce the complete 3D dynamic model to a hierarchical 2D dynamic model with a capacity for 3D solving accuracy. A separate quasi-static analysis is conducted to precisely acquire the centrifugal stresses that occur in the rotating laminated composite shell panels. The present quasi-3D dynamic model considers the Coriolis forces, rotational softening effect as well as prestress stiffening effect. Several case studies are presented including the rotating pre-twisted plates, pre-twisted cylindrical shell panels and untwisted conical shell panels with different lamination schemes and geometric parameters. In each case study, the vibration characteristics predicted from the present theoretical model are compared with the reported studies and those from the commercial finite element software. It indicates that the quasi-3D dynamic model has good accuracy and is appropriate for different types of rotating laminated composite shell panels. The influences of the rotating speed, pre-twisted angle, fiber orientation and subtended angle on the vibration behaviors of the rotating pre-twisted laminated composite shell panels are studied as well. [ABSTRACT FROM AUTHOR]

New large-scale laboratory data are presented on a physical model of a spar buoy wind turbine with angular motion of control surfaces implemented (pitch control). The peculiarity of this type of rotating blade represents an essential aspect when studying floating offshore wind structures. Experiments were designed specifically to compare different operational environmental conditions in terms of wave steepness and wind speed. Results discussed here were derived from an analysis of only a part of the whole dataset. Consistent with recent small-scale experiments, data clearly show that the waves contributed to most of the model motions and mooring loads. A significant nonlinear behavior for sway, roll and yaw has been detected, whereas an increase in the wave period makes the wind speed less influential for surge, heave and pitch. In general, as the steepness increases, the oscillations decrease. However, higher wind speed does not mean greater platform motions. Data also indicate a significant role of the blade rotation in the turbine thrust, nacelle dynamic forces and power in six degrees of freedom. Certain pairs of wind speed-wave steepness are particularly unfavorable, since the first harmonic of the rotor (coupled to the first wave harmonic) causes the thrust force to be larger than that in more energetic sea states. The experiments suggest that the inclusion of pitch-controlled, variable-speed blades in physical (and numerical) tests on such types of structures is crucial, highlighting the importance of pitch motion as an important design factor. [ABSTRACT FROM AUTHOR]

• A new quasi-3D dynamic model is provided for rotating pre-twisted FG blades. • Higher-order configurations are derived via 3D elasticity shell theory and CUF. • The applicability of two centrifugal stress solving methods, DICF and SACF, is determined. • Parametric studies are performed on vibration of rotating pre-twisted FG 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. [ABSTRACT FROM AUTHOR]