Blade Natural Frequencies Research Articles

Static Structural and Modal Analysis of Gas Turbine Blade

Gas turbine is one of the most versatile items of turbo machinery nowadays. It is used in different modes such as power generation, oil and gas, process plants, aviation, domestic and related small industries. This paper is based on the problems concerning blade profile selection, material selection and turbine rotor blade vibration that seriously impact the induced stress-deformation and structural functioning of developmental gas turbine engine. In this paper for generating specific power by rotating blade at specific RPM, blade profile and material has been decided by static structural analysis. Gas turbine rotating blade RPM is decided by Modal Analysis so that the natural frequency of blade should not match with the excitation frequency. For the above blade profile has been modeled in SOLIDWORKS and analysis has been done in ANSYS WORKBENCH 14. Existing NACA6409 profile has been selected as base model and then it is modified by bending it through 72.5° and 145°. Hence these three different blade profiles have been analyzed for three different materials viz. Super Alloy X, Nimonic 80A and Inconel 625 at three different speed viz. 20000, 40000 and 60000RPM. It is found that NACA6409 with 72.5° bent gives best result for all material at all speed. Among all the material Inconel 625 gives best result. Hence Blade of Inconel 625 having 72.5° bent profile is the best combination for all RPM.

Wavelet-based identification of rotor blades in passage-through-resonance tests

Abstract Turbine blades are critical components in turbo engines and their design process usually includes experimental tests in order to validate and/or update numerical models. These tests are generally carried out on full-scale rotors having some blades instrumented with strain gauges and usually involve a run-up or a run-down phase. The quantification of damping in these conditions is rather challenging for several reasons. In this work, we show through numerical simulations that the usual identification procedures lead to a systematic overestimation of damping due both to the finite sweep velocity, as well as to the variation of the blade natural frequencies with the rotation speed. To overcome these problems, an identification procedure based on the continuous wavelet transform is proposed and validated through numerical simulation.

Influences of physical and structural parameters on vibration modes for large-scale rotating wind turbine blades

For large-scale offshore wind turbine blades, ANSYS and UG were respectively used to complete the solid modeling and the calculation of vibration modes, and the influences of the rotating speed on each order vibration mode and their main reasons were analyzed. Furthermore, the effects of material categories, the deviations of physical parameters in the process of material manufacture and structural parameters on the natural frequencies of rotating blades were respectively compared. Numerical results show that the dynamic stiffening effect of rotating blades is obvious, and the stress stiffness and the geometric stiffness play a dominant role on the natural frequencies from the first to the sixth order and from the seventh to the tenth order respectively. The influences of material categories on natural frequencies of the blades are significantly higher than those of physical parameter deviations and chord length changes. The effects of the equal amplitude increase of elasticity modulus or the chord length and the equal amplitude decrease of density on the tenth order frequency for the torsional vibration are less than those of them on the first nine orders' frequencies for the shimmy and flapping vibration, making that the increase amplitude of the blade natural frequencies first increases and then decreases with the increase of the order number. In addition, the results in this work can provide technical references for the optimization design and the further analysis of vibration characteristics of wind turbine blades.

Multi-axis fatigue loading system of wind turbine blade and vibration coupling characteristics

This paper presents a new method which focuses on the multi-axis fatigue loading mode for wind turbine blade and aims to shorten the fatigue loading cycle. The whole test scheme is design for the measurement of fatigue loading system. The two leading sources of fatigue loading system are asymmetric arrangement in the space. In addition, its vibration mathematical model is derived according to the Lagrange equation. The numerical simulation model is developed by means of Matlab Simulink. The vibration coupling characteristics including motor revolution speed, phase and amplitude of wind turbine blade is obtained. Moreover, the trajectory of wind turbine blade is obtained. Finally, a multi-axis fatigue loading platform for small wind turbine blade is built for the proposed study. The on-site test showed that if the revolution speeds of the two loading sources is the same as the natural frequency of wind turbine blade, the revolution speed, the phase angle of motor and the blade trajectory were relative changed smoothly. Thus, the amplitude of blade is state and the largest. Otherwise when the revolution speed of motor is different with the natural frequency of blade, the revolution speeds and phase angle of the two loading sources fluctuated largely. The above conclusion provided the theoretical basis for the subsequent decoupling control algorithm of multi-axis fatigue loading test.

Influence of Icing on the Modal Behavior of Wind Turbine Blades

Wind turbines installed in cold climate sites accumulate ice on their structures. Icing of the rotor blades reduces turbine power output and increases loads, vibrations, noise, and safety risks due to the potential ice throw. Ice accumulation increases the mass distribution of the blade, while changes in the aerofoil shapes affect its aerodynamic behavior. Thus, the structural and aerodynamic changes due to icing affect the modal behavior of wind turbine blades. In this study, aeroelastic equations of the wind turbine blade vibrations are derived to analyze modal behavior of the Tjaereborg 2 MW wind turbine blade with ice. Structural vibrations of the blade are coupled with a Beddoes-Leishman unsteady attached flow aerodynamics model and the resulting aeroelastic equations are analyzed using the finite element method (FEM). A linearly increasing ice mass distribution is considered from the blade root to half-length and thereafter constant ice mass distribution to the blade tip, as defined by Germanischer Lloyd (GL) for the certification of wind turbines. Both structural and aerodynamic properties of the iced blades are evaluated and used to determine their influence on aeroelastic natural frequencies and damping factors. Blade natural frequencies reduce with ice mass and the amount of reduction in frequencies depends on how the ice mass is distributed along the blade length; but the reduction in damping factors depends on the ice shape. The variations in the natural frequencies of the iced blades with wind velocities are negligible; however, the damping factors change with wind velocity and become negative at some wind velocities. This study shows that the aerodynamic changes in the iced blade can cause violent vibrations within the operating wind velocity range of this turbine.

Rotor aeromechanics study using two different blade property data sets

Purpose This paper aims to compare the comprehensive rotorcraft analyses using the two different blade section property data sets for the blade natural frequencies, airloads, elastic deformations, the trimmed rotor pitch control angles and the blade structural loads of a small-scale model rotor in a blade vortex interaction (BVI) phenomenon. Design/methodology/approach The two different blade section property data sets for the first Higher-harmonic control Aeroacoustic Rotor Test (HART-I) are considered for the present rotor aeromechanics analyses. One is the blade property data set using the predicted values which is one of the estimated data sets used for the previous validation works. The other data set uses the measured values for an uninstrumented blade. A comprehensive rotorcraft analysis code, CAMRAD II (comprehensive analytical model of rotorcraft aerodynamics and dynamics II), is used to predict the rotor aeromechanics such as the blade natural frequencies, airloads, elastic deformations, the trimmed rotor pitch control angles and the blade structural loads for the three test cases with and without higher-harmonic control pitch inputs. In CAMRAD II modelling with the two different blade property data sets, the blade is represented as a geometrically nonlinear elastic beam, and the multiple-trailer wake with consolidation model is used to consider more elaborately the BVI effect in low-speed descending flight. The aeromechanics analysis result sets using the two different blade section property data sets are compared with each other as well as are correlated with the wind-tunnel test data. Findings The predicted blade natural frequencies using the two different blade section property data sets at non-rotating condition are quite similar to each other except for the natural frequency in the fourth flap mode. However, the natural frequencies using the predicted blade properties at nominal rotating condition are lower than those with the measured blade properties except for the second lead-lag frequency. The trimmed collective pitch control angle with the predicted blade properties is higher than both the wind-tunnel test data and the result using the measured blade properties in all the three test cases. The two different blade property data sets both give reasonable predictions on the blade section normal forces with BVI in the three test cases, and the two analysis results are reasonably similar to each other. The blade elastic deformations at the tip using the measured blade properties are correlated more closely with the wind-tunnel test data than those using the predicted blade properties in most correlation examples. In addition, the predictions of blade structural loads can be slightly or moderately improved by using the measured blade properties particularly for the oscillatory flap bending moments. Finally, the movement of the sectional centre of gravity location of the uninstrumented blade has a moderate influence on the blade elastic twist at the tip in the baseline case and the oscillatory flap bending moment in the minimum noise case. Practical implications The present comparison study on rotor aeromechanics analyses using the two different blade property data sets will show the influence of blade section properties on rotor aeromechanics analysis. Originality/value This paper is the first attempt to compare the aeromechanics analysis results using the two different blade section property data sets for all three test cases (baseline, minimum noise and minimum vibration) of HART-I in low-speed descending flight.

On the functional design of the DTU10 MW wind turbine scale model of LIFES50+ project

This paper illustrates the mechatronic design of the wind tunnel scale model of the DTU 10MW reference wind turbine, for the LIFES50+ H2020 European project. This model was designed with the final goal of controlling the angle of attack of each blade by means of miniaturized servomotors, for implementing advanced individual pitch control (IPC) laws on a Floating Offshore Wind Turbine (FOWT) 1/75 scale model. Many design constraints were to be respected: among others, the rotor-nacelle overall mass due to aero-elastic scaling, the limited space of the nacelle, where to put three miniaturized servomotors and the main shaft one, with their own inverters/controllers, the slip rings for electrical rotary contacts, the highest stiffness as possible for the nacelle support and the blade-rotor connections, for ensuring the proper kinematic constraint, considering the first flapwise blade natural frequency, the performance of the servomotors to guarantee the wide frequency band due to frequency scale factors, etc. The design and technical solutions are herein presented and discussed, along with an overview of the building and verification process. Also a discussion about the goals achieved and constraints respected for the rigid wind turbine scale model (LIFES50+ deliverable D.3.1) and the further possible improvements for the IPC-aero-elastic scale model, which is being finalized at the time of this paper.

중형 컨테이너 운반선 축계장치의 선미관 선수베어링 설치 유무에 따른 횡진동 사례 연구

At the initial stage of propulsion shaft design, in line with shaft alignment, an intensified consideration of lateral vibration is needed to verify its operational safety. Recently the alignment problem affecting the lateral vibration has been becoming issues. However, the theoretical method of forced lateral vibration analysis is not cleary established so far and it is about to simply limited among the classification societies and international standards to avoid the blade natural frequency resonance cpm outside of of engine rpm at MCR. On the other hand, longer center distance between each support bearing shows an affirmative result normally in shaft alignment analysis whereas the blade order resonance speed may cause lowering near the limitation in the aspect of lateral vibration. Therefore, it is required careful attention to engineers as described above. As a method to solve the problem, it is mainly considered that remove forward stern tube bearing. In this paper, based on a medium size container ship case, theoretical study was carried out in the context of the forward stern tube bearing. The various effects and functions of forward stern tube bearing are reviewed and evaluated. Then an guidance note to lead the conclusion is proposed.

Fan blade crack diagnosis method study

This article presents a discrete mathematical model for fan blades and theoretically analyses the mathematical relationship between the location and depth of crack and fan blade natural frequency. On the basis of the blade mathematical model, using the theoretical computed natural frequency as the fault feature, this article proposes a fast and efficient fan blade crack fault diagnosis method. Transfer matrix method is used to calculate the first three-order blade natural frequencies under different crack cases and then to build the database in MATLAB. Subsequently, the damaged blade can be detected using changes in natural frequencies by solving the reverse problem. The experimental result shows that this discrete mathematical model can get the exact solution of natural frequency, and the method has certain application value.

Multi-objective design optimization strategies for small-scale vertical-axis wind turbines

Extracting energy from wind has been an interesting and serious topic over the last few decades and a lot of work has been done on the subject. This paper discusses in detail possible approaches to optimization of a somewhat less known type of wind turbines, particularly suitable for small consumers. In order to perform full aerodynamic and structural shape optimization of a small-scale vertical-axis wind turbine, a Double-multiple streamtube model code, known to provide good results in stationary working regimes, was complemented by a finite element analysis and implemented into a multi-objective particle swarm algorithm. For the purpose of shortening the total time needed for aerodynamic computation, the performed numerical simulations were two-dimensional and experimentally measured static airfoil data were used. The used aerodynamic model was validated against the available experimental data of similar wind turbines. The subsequent structural analyses of the composite turbine blades were performed by applying computed maximal aerodynamic forces together with gravitational and inertial loads. By employing various input and output parameters different multi-objective optimization strategies were analyzed and compared and their applicability was demonstrated. Investigated input parameters included: wind turbine rotor diameter, blade length, chord and airfoil, composite shell thickness, laminate lay-up and ply orientations, while optimization goal functions and constraints comprised rated power, cut-in and optimal wind speed, blade mass, tip deflection, failure index and blade natural frequencies. The fidelity and accuracy of proposed methodologies can be increased by employing more complex numerical models which can easily be implemented into the code.

Optimal structural design of compressor stage

Optimal structural design of compressor stage of aviation engine is considered. Structural optimization takes into account the blade shape and disk design. Minimization of mismatching between the blade shape in operating position and predefined aerodynamic blade shape and natural frequency detuning problem are discussed. Disk and joint weight minimization under certain constraints is investigated. Optimization criteria, constraints, parameterization and design models, design parameters are discussed. All results were obtained using finite element analysis program connected with the sequential quadratic programming (SQP) optimization procedure.

풍력터빈의 구조특성 평가에 관한 연구-Part2

This paper presents the structural model verification process of whole wind turbine blade including blade model which proposed in Part1 paper. The National Renewable Energy Laboratory (NREL) Phase VI wind turbine which the wind tunnel and structural test data has publicly available is used for the study. In the Part1 of this paper, the processes of structural model development and verification process of blade only are introduced. The whole wind turbine composed by blade, rotor, nacelle and tower. Even though NREL has reported the measured values, the material properties of blade and machinery parts are not clear but should be tested. Compared with the other parts, the tower which made by steel pipe is rather simple. Since it does not need any considerations. By the help of simple eigen-value analysis, the accuracy of structural stiffness and mass value of whole wind turbine system was verified by comparing with NREL's reported value. NREL has reported the natural frequency of blade, whole turbine, turbine without blade and tower only models. According to the comparative studies, the proposed material and mass properties are within acceptable range, but need to be discussing in future studies, because our material properties of blade does not match with NREL's measured values.

Turbine engine rotor blade fault diagnostics through casing pressure and vibration sensors

In this study, an exact solution is provided for a previously indeterminate equation used for rotor blade fault diagnostics. The method estimates rotor blade natural frequency through turbine engine casing pressure and vibration sensors. The equation requires accurate measurements of low-amplitude sideband signals in the frequency domain. With this in mind, statistical evaluation was also completed with the goal of determining the effect of sampling time and frequency on sideband resolution in the frequency domain.

Modal Analysis of a Turbine Blade Based on Fluid-Thermal-Structural Coupling

The dynamic analysis of a turbine blade is carried out. The pre-stress due to rotation and fluid-thermal-structure coupling effect are considered. At first flow analysis and thermal analysis on the blade and corresponding stator-rotor blade passage are conducted to acquire the flow field and body temperature field of blade. Then stress in the blade is analyzed considering pressure and temperature in a static condition, and the matrix for pre-stress effect and an additional matrix due to the external temperature and pressure loading are obtained. And so the dynamic equation of the blade system including the pre-stress effect and the coupling effect is established. The frequencies and vibration modes of the blade system in six different coupling conditions are obtained by using of ANSYS and CFX. It is found that the fluid-thermal-structural coupling field has a significant influence on the blade natural frequencies. Also, the impact of temperature on frequency is embodied more in the change of material elastic modulus E with temperature than in the thermal stress caused by temperature gradient.

A systematic hub loads model of a horizontal wind turbine

The wind turbine industry has focused offshore on increasing the capacity of a single unit through up-scaling their machines. There is however a lack of systematic studies on how loads vary due to properties of a wind turbine and scaling of wind turbines. The purpose of this paper is to study how applied blade modifications, with similarities such as mass, stiffness and dimensions, influence blade root moments and lifetime damage equivalent loads (DELs) of the rotor blades. In order to produce fatigue load blade root moment trends based on the applied modifications. It was found that a linear trend of lifetime DELs based on the applied modifications of blades, which have effect on the natural frequency of blade of the original or reference model. As the control system was tuned for the specific frequency of the reference model. The linear trend of lifetime DELs was generated as long as the natural frequency of the reference model was preserved. For larger modifications of the wind turbine the controller would need retuning.

Pre-emptive Rotor Blade Damage Identification by Blade Tip Timing Method

The blade tip timing (BTT) method uses the differential arrival timings of the blades at case-mounted sensors to effectively characterize the vibrations of all blades in a rotor. This paper studies the use of the BTT method for pre-emptive prediction of rotor blade damage; through a careful monitoring of blade natural frequencies in conjunction with the blade tip position during an engine test. In the current study, the low pressure turbine stage of a developmental aero engine is instrumented with a combination of eddy current and optical sensors located circumferentially on the casing. This instrumentation effectively captures the engine order resonances of interest for the blade bending mode. During one of the normal engine tests, one of the blades in the LPT stage suddenly showed a drop in natural frequency beyond the allowable scatter and an abrupt change in the blade tip position. As the engine test was continued further, this drop in blade natural frequency and change in blade tip position progressively increased towards blade failure limits. Suspecting a propagating crack in the particular blade, the test was aborted and the engine was withdrawn for detailed inspection. Inspection of the rotor blades confirmed the presence of significant aerofoil crack in the suspect blade.

Time-dependent vibration frequency reliability analysis of blade vibration of compressor wheel of turbocharger for vehicle application

Blade vibration failure is one of the main failure modes of compressor wheel of turbocharger for vehicle application. The existing models for evaluating the reliability of blade vibration of compressor wheel are static, and can not reflect the relationship between the reliability of compressor wheel with blade vibration failure mode and the life parameter. For the blade vibration failure mode of compressor wheel of turbocharger, the reliability evaluation method is studied. Taking a compressor wheel of turbocharger for vehicle application as an example, the blade vibration characteristics and how they change with the operating parameters of turbocharger are analyzed. The failure criterion for blade vibration mode of compressor wheel is built with the Campbell diagram, and taking the effect of the dispersity of blade natural vibration frequency and randomness of turbocharger operating speed into account, time-dependent reliability models of compressor wheel with blade vibration failure mode are derived, which embody the parameters of blade natural vibration frequency, turbocharger operating speed, the blade number of compressor wheel, life index and minimum number of resonance, etc. Finally, the rule governing the reliability and failure rate of compressor wheel and the method for determining the reliable life of compressor with blade vibration is presented. A method is proposed to evaluate the reliability of compressor wheel with blade vibration failure mode time-dependently.

Dynamic Analysis for Wind Turbine Composite Blade

Wind turbine blade model is analyzed based on finite element method. Research and comparison of blade natural frequencies is made in different rotational working conditions taking into account external factors such as the rotational inertia force. Also the relationship between the composite ply angle and natural frequency is analyzed. The result shows that the nature frequency of wind turbine blade is influence greatly by the stress stiffening effect for the blade rotation. And the nature frequency of wind turbine blade can be designed by adjusting the single fiber layer ply angle of blade.

Failure analysis of gas turbine generator cooling fan for 14° and 19° — blades angle of attack

In gas turbine power plants, a fan is used as a cooling system to dissipate generated heat in coils (copper conductors) and generator electric circuits at the end sides of its rotor. In some cases, fracture of blades causes short circuit between rotor and stator and consequently generator explosion and made lot of financial problems. The fracture of cooling fan blades has been occurred five times at the turbine side of the generator in our case of study, just 100 hr after resuming operation after overhaul. Using numerical analysis as well as laboratory investigation — includes visual inspections, metallography and SEM — can help better finding failure problems that cause blade failures. A series of numerical analysis was performed to diagnose the cause of failure possibility. CFD analysis is used to study the airflow distribution in order to observe probable separation phenomenon and pressure forces that they are imposed to fan blades due to operation. A finite element method was utilized to determine the stresses and dynamic characteristics of the fan blade (natural frequencies, stresses and vibrations).

Estimation of turbine blade natural frequencies from casing pressure and vibration measurements

Non-contact measurement of gas turbine rotor blade vibration is a non-trivial task, with no method available which achieves this aim without some significant draw-backs . This paper presents a truly non-contact method to estimate rotor blade natural frequencies from casing vibration measurements at a single engine operating speed. An analytical model is derived to simulate the internal casing pressure in a turbine engine including the effects of blade vibration on this pressure signal. It is shown that the internal pressure inside a turbine contains measureable information about the rotor blade natural frequencies and in-turn the casing vibration response also contains this information. The results presented herein show the residual, pressure and casing vibration, spectrum can be used to determine the rotor blade natural frequencies with validation provided for the analytical model by experimental measurements on a simplified test rig. A simulated blade fault in one of the rotor blades is introduced with successful estimation of the simulated faulty blade natural frequency.