Bladed Disk Research Articles

Nonlinear response analysis of aero-engine rotor bearing rub-impact system caused by horizontal yawing maneuver load

Based on the simplified aero-engine rotor system, a new nonlinear response prediction model of rotor bearing rub-impact system is established. Different from the traditional rotor system rub-impact model, based on the detailed characteristics of the blade–disc system, this paper considers the influence of the number of blades and the dynamic to static clearance on the rub-impact force. In addition, the influence of additional load on the established rotor-bearing system due to the change in the flight motion state of the horizontal yawing maneuver is also considered The Newmark-β numerical method is used to solve the system, and the effects of maneuver load and rub-impact stiffness on the nonlinear dynamics of the system are studied The results show that the system produces a kind of sub harmonic resonance rub-impact phenomenon, that is, the system will produce 1/2 sub harmonic resonance under the action of maneuver load near the double critical speed, which will increase the vibration response amplitude of the system. With the increase of maneuver load, the system always has complex nonlinear phenomenon; with the increase of rub-impact stiffness, the system produces a large number of frequency division and frequency multiplication components, which can be used as the characteristic frequency of rub-impact faults.

Harmonic Component Analysis of Mode Shapes for Packeted Bladed Disk

Vibration characteristics of packeted bladed disk is complicated. To study the vibration characteristics of the governing stage bladed disk of 660mw steam turbine, cyclic symmetry method is used to calculate the mode shapes. Fourier transformation of vibration distribution in the tangential and axial direction along the circumferential of the bladed disk is applied to obtain the harmonic components. It is found that the Fourier decomposition of each blade displacement contains not only unique component, but also other components. For integrally shrouded blades, the resonance of the m nodal diameter mode can be obtained only when the corresponding natural frequency satisfies the condition ωn = kn = mn, where n is the rotational speed and m is the harmonic number. For packeted bladed disk, there are additional harmonics that resonance occurs. The harmonic components are related to the nodal diameter number when the number of blades groups and the total number of blades are given. The diagrammatic method is applied to predict the wavenumbers present in modulated eigenfunctions.

Vibration parameters identification of turbomachinery rotor blades under transient condition using Blade Tip-Timing measurements

During run ups and run downs, the rotating blades are subjected to fluctuating forces with time dependent frequencies and the dynamic response of the blades around the resonance crossings deviates from the stationary response. This paper presents a procedure to identify the vibration parameters of rotating blades under this non-stationary condition. An analytically based solution of a single degree of freedom (SDOF) system exposed to a transient harmonic excitation with linear time varying frequency is used for parameters identification. This analytical model is fitted into the Blade Tip-Timing (BTT) data and the vibration parameters are determined by a least square optimization technique. A numerical simulator based on a lumped parameter model of the bladed disk assembly is employed to demonstrate the method performance. Afterwards, the accuracy of the method is proved by testing it on the experimental data acquired by BTT and strain gauges on a rotating bladed disk.

Relative cyclic component mode synthesis: A reduced order modeling approach for mistuned bladed disks with friction interfaces

A new reduced order modeling technique for nonlinear dynamics of mistuned bladed disks with friction interfaces is presented. Although various models have been developed to characterize the dynamics of either mistuned or frictionally damped structures, predicting the vibratory response of mistuned bladed disks with frictional interfaces remains challenging due to the:large size of refined industrial models,nonsmooth friction nonlinearities and amplitude dependent dynamics, andlack of cyclic symmetry properties.The Relative Cyclic Component Mode Synthesis (RCCMS) approach benefits from the application of relative coordinates prior to performing a reduction. Based on the new method, the kinematics of contact surfaces are first described in terms of relative displacements between contact node pairs, afterwards the Craig-Bampton Component Mode Synthesis (CB-CMS) technique is employed to reduce the model size. Implementation of relative coordinates halves the number of nonlinear unknowns in the reduced space and enhances the CB-CMS reduction basis by incorporating system-level stick modeshapes.The proposed approach admits introduction of either blade or sector frequency mistuning into the final reduced order model. In this way, the reduction is performed only once, which makes it favorable for statistical analyses. In addition, the mistuned ROM can be developed with minimal computational effort by using the sector model only.The developed RCCMS-based ROM is demonstrated on a finite element model of a mistuned bladed disk with blade-root friction damping. Numerical simulations reveal the excellent accuracy in predicting the nonlinear forced response.

Modal Verification and Strength Analysis of Bladed Rotors of Turbine in Rated Working Conditions

The Top-pressure Recovery Turbine (TRT) uses the blast furnace gas generated in the iron and steel manufacturing process to push the turbine which drives the generator to generate electricity, and the generated electric energy is supplied to in-plant equipment. In this paper, we investigate the aerodynamic force, centrifugal force, and maximum stress on the structure of the TRT rotor in rated working conditions and the positions of occurrence using the Finite Element Method (FEM), as well as discuss the dynamic characteristics of bladed disks during TRT operation through Campbell and SAFE diagrams. To confirm the effectiveness of the finite element models, the mode shapes and natural frequencies in the FEA-based modal analysis of the TRT rotor will be captured and compared with those of the practical structures through the Experimented Modal Analysis (EMA). To verify the agreement between the mode shapes of the finite element analysis and those of the actual structure, the Modal Assurance Criterion (MAC) is introduced here to confirm the reliability of the finite element model. The stress distribution on the structure in the rotation is obtained by centrifugal force analysis. The TRT rotor is driven as the blast furnace top pressure pushes the moving blade; when the rotor rotates, the moving blade bears centrifugal and periodic aerodynamic forces. The stress distribution is investigated on the structure when these forces act simultaneously using aerodynamic analysis. To discuss whether the bladed disks will resonate with the external force under the operating conditions, Campbell and SAFE diagrams are used for evaluation, and the modal parameters obtained from the EMA are used to estimate the strength and durability of the blades. According to the analysis results when the TRT rotor is in working conditions, the fatigue failure may occur at the maximum stress existing on the dovetail slot.

Preliminary Study of Pineapple Pruning Machine for Pineapple Suckers Production

After the pineapple crop is 15 months old, the pineapple will be harvested and pruning process will be done before fertilization work begin. Normally in conventional method, farmers will use a sharp machete or sickle to pruning the leave since pineapple leaves and cob have a high fibers content causing the leaves and cob break easily. The convention method requires a lot of time as well as the need for a large labor force, and the cost of production would also increase in this regard. The objective of the study was to evaluate the performance and effectiveness pruning using a mechanization approach compare to the conventional method in pruning the pineapple crop. In 11th Malaysia plan (RMK-11) a new concept and prototype were developed with 2 blade disc type, powered by gearbox 1:3 ratio and adjustable height for peat soil condition. Using of 38hp of tractor high clearance rubber trek with powered by PTO (Power take off) speed 540 and rpm 1500.The height of the cutter blade can be adjustable according to the height of the crop needed to be pruned. The machine capable working rate is 0.86 ha/hour, speed tractor is 2.03km/hour and the machine efficiency are 92 %. Machined time operation is up to 1.2 hour/ha and operating for 8.4 ha/per-day. As a result, the machine seems have a clean-cut result on pineapple leaves and cob without breaking the pineapple crop.

Experimental Investigation of Bladed Disk Dynamics at Design Speed Under Synchronous Vibration

This work presents an experimental and computational investigation of a rotating bladed disk excited with air jets. The bladed disk is accelerated through critical speeds corresponding to specific engine orders of interest while air jets apply a constant forcing. These conditions induce synchronous vibrations in the blades. The experimental results were used to compute mistuning and damping values of the system, which were used in the computational analyses. This work uses a parametric reduced order model (PROM) that can adjust the system stiffness based on the rotational speed within the reduced space. Component mode mistuning was coupled with the PROM to create a mistuned model capable of capturing the mistuned system dynamics. Computational values for the blade frequency, amplitude, and damping were compared with experimental results to show how the computational model presented in this work can be used to characterize a rotating bladed disk.

Steady-state coupling vibration analysis of shaft–disk–blade system with blade crack

Steady-state coupling vibration analysis of shaft–disk–blade system with blade crack

The effect of cutting fluid in improving the machinability of Inconel 718 using ceramic AS20 tool

Industries demand a vast usage of superalloys in heat resistant and high temperature applications. These include nozzle of rocket fuel engines, throttle valve of turbojet engines, turbine blade discs of aerospace industries, rivets and fittings of chemical and production industries, biomedical applications in super strength resistive steels. These superalloys such as Inconel 718 finds its vast applications in all such industries. To machine such materials a lot of wear and tear occurs at the cutting tool. Hence, cutting fluid helps in reduction of tool wear and improving surface roughness. In this paper, two cutting fluids Koolkut 40 and Hicut 590 have been used in emulsified form during the machining of Inconel 718 with Ceramic cutting tool. Hicut 590 has been seen a better heat resistive cutting fluid in reducing the tool wear and thus improving the life of the tool.

Dissolution of delta phase in Ni-based superalloy during linear friction welding: integrated multiphysics computational process modelling

Linear friction welding (LFW) is an increasingly popular solid-state joining method for challenging applications such as integrated blade disk of aero-engines. However, the influence of friction-generated heat on the material microstructural evolution, material deformation and resultant mechanical performance of the manufactured components is not well understood. A novel integrated multiphysics computational modelling is presented for predicting the component-scale microstructural evolution of IN718 alloy during LFW. A modified time-temperature equivalence formulation was implemented for predicting the evolution of the δ phase, which was coupled with thermomechanical modelling of the LFW process. There is reasonably good agreement between the computational modelling results of this paper and the experimental results from the literature in terms of δ phase volume fraction and weld temperature. The integrated multiphysics computational modelling predicts the influence of process parameters on thermomechanical and microstructural processes of IN718 LFW. By systematically analysing the influence of 10 different LFW process parameter configurations, the friction pressure was identified as the most influential process parameter determining the extent of δ phase dissolution and weld temperature during LFW.

An efficient method for vibration equations with time varying coefficients and nonlinearities

An efficient method for solving vibration equations is the basis of the vibration analysis of a cracked multistage blade–disk–shaft system. However, dynamic equations are usually time varying and nonlinear, and the time required for solving is greatly increased accompanied by an increase in the model order caused by the multistage system and the nonlinearity caused by cracks. In this article, an efficient method for solving the time varying and nonlinear vibration equation is investigated. In the proposed method, the time varying terms are transformed into constant terms, while the local nonlinear matrix of the cracked blade is separated from the assembly stiffness matrix under the constraint of proper orthogonal decomposition (POD) transformation rules. Furthermore, the POD transformations of the constant terms and the linear assembled stiffness matrix can be implemented in the pretreatment steps to achieve a more efficient POD reduction operation. This research provides a method for efficiently performing the comprehensive and rapid analysis of nonlinear vibration characteristics of rotor systems.

Validation of a Modal Work Approach for Forced Response Analysis of Bladed Disks

The paper describes a numerical method based on a modal work approach to evaluate the forced response of bladed disks and its validation against numerical results obtained by a commercial FEM code. Forcing functions caused by rotor–stator interactions are extracted from CFD unsteady solutions properly decomposed in time and space to separate the spinning perturbation acting on the bladed disk in a cyclic environment. The method was firstly applied on a dummy test case with cyclic symmetry where the forcing function distributions were arbitrarily selected: comparisons for resonance and out of resonance conditions revealed an excellent agreement between the two numerical methods. Finally, the validation was extended to a more realistic test case representative of a low-pressure turbine bladed rotor subjected to the wakes of two upstream rows: an IGV with low blade count and a stator row. The results show a good agreement and suggest computing the forced response problem on the finer CFD blade surface grid to achieve a better accuracy. The successful validation of the method, closely linked to the CFD environment, creates the opportunity to include the tool in an integrated multi-objective procedure able to account for aeromechanical aspects.

Stereo-DIC Measurements of a Vibrating Bladed Disk: In-Depth Analysis of Full-Field Deformed Shapes

Vibration measurements of turbomachinery components are of utmost importance to characterize the dynamic behavior of rotating machines, thus preventing undesired operating conditions. Local techniques such as strain gauges or laser Doppler vibrometers are usually adopted to collect vibration data. However, these approaches provide single-point and generally 1D measurements. The present work proposes an optical technique, which uses two low-speed cameras, a multimedia projector, and three-dimensional digital image correlation (3D-DIC) to provide full-field measurements of a bladed disk undergoing harmonic response analysis (i.e., pure sinusoidal excitation) in the kHz range. The proposed approach exploits a downsampling strategy to overcome the limitations introduced by low-speed cameras. The developed experimental setup was used to measure the response of a bladed disk subjected to an excitation frequency above 6 kHz, providing a deep insight in the deformed shapes, in terms of amplitude and phase distributions, which could not be feasible with single-point sensors. Results demonstrated the system’s effectiveness in measuring amplitudes of few microns, also evidencing blade mistuning effects. A deeper insight into the deformed shape analysis was provided by considering the phase maps on the entire blisk geometry, and phase variation lines were observed on the blades for high excitation frequency.

Development of a Modal-Based Turbomachine Blade-Disk Attachment Inspection Technique

Turbine blade failures are among the leading causes of steam turbine failure. Failure types typically include cracking, rubbing, blade fouling, and foreign object damage. There is currently a range of non-destructive testing methods used to detect damage at the blade-disk attachment zone, all of which involve disassembling of the blade from the disk for periodic inspection. Evidence indicate that a method to detect damage at the blade-disk attachment zone using a non-contact, non-destructive in-situ off-line modal-based structural health monitoring technique could be useful under some circumstances. Such a technique would have the advantage of eliminating the necessity to disassemble blades during inspection. This would result in significant cost savings. Also, defects associated with the disassembly and reassembly of blades would be avoided. Thus, the aim of this study was to develop a modal-based turbomachinery blade disk attachment inspection technique. Modal parameters were acquired from a robust experimental modal analysis of freely supported low-pressure steam turbine blade-disk segment assemblies. Artificial single-location cracks were intentionally introduced into the turbine blades by cutting a 1 mm thickness notch at three probable damage locations, namely, at the upper pinhole on the leading-edge pressure side, above the root at the base of the aerofoil on the leading-edge and on the trailing-edge. In this work, a finite element analysis of the bladed disk segment assemblies was carried out with and without damage. To validate the reliability of the numerical models, the numerical results were correlated with the measured values, the results of which showed a strong correlation. Finally, a parametric study was conducted in which various healthy and damaged blade-disk cases were systematically investigated. This was done to examine the sensitivity of the blade natural frequency to damage. The artificial damage above the root was found to cause the largest changes in natural frequency. These changes were even more pronounced for assemblies with two blades. Receiver operating characteristic curves were used to assess the discriminatory ability of the results. Each damage case was found to be unique and therefore identifiable from its corresponding healthy case.

Analysis of experimental results of turbomachinery flutter using an asymptotic reduced order model

Flutter of bladed disks is an instability mechanism where the aerodynamic flow pumps energy into the blade vibration. This energy is dissipated through dry friction, normally at the blade-disk attachment, and this balance defines the blade vibration amplitude that sets in. The magnitude of this final vibration amplitude is crucial to correctly estimate the blade fatigue life. In the context of the European project FUTURE, a series of flutter experiments were carried out for a realistic low-pressure turbine with different intentional mistuning patterns. To analyze the results, a simple 3 degrees of freedom per sector mass-spring model is set up with the experimental configuration parameters. This mass-spring system still requires very long integration times due to: (i) the large difference between the fast elastic oscillation time and the slow time associated with the aerodynamic instability, friction, and mistuning, and (ii) the presence of many aerodynamically unstable modes with very similar growth rates. A multiple-scale method is applied to further simplify the mass-spring system. The blade elastic oscillation is filtered out, and the resulting asymptotic reduced order model reduces considerably the integration time required to reach a converged solution. It is found that the final vibration state of the mistuned problem depends on the selected initial conditions, so the model is run for a large number of random initial conditions to explore the possible final states. The asymptotic model gives results that show a good agreement with the experimental measurements, and it also allows to explain the origin of the peaks in the travelling wave content of the final solution found in the experiment for the intentionally mistuned configurations.

Low-speed cameras system for 3D-DIC vibration measurements in the kHz range

The digital image correlation (DIC) was used in this paper to obtain full-field measurements of a target vibrating at a frequency higher than the maximum cameras’ frame rate. The down-sampling technique was implemented to compensate for the cameras’ moderate frame rate, thus getting an accurate displacement acquisition even at 6.5 kHz. Two innovative methods to support the DIC application were introduced. The use of fringe projection (or structured light), initially applied on the sample at rest, reduced the effort and time required for the stereo matching task’s solution and improved this setting’s accuracy and reliability. Additionally, a new time-domain image filtering was proposed and tested to improve the quality of the obtained DIC maps. In combination with the down-sampling, the effect of this filtering technique was tested in this work at (approx.) 2500 and 6500 Hz by measuring the response of a bladed disk to sinusoidal excitation. Evidence of improved results was observed for both frequencies for amplitudes in the range of 10 µm.

Single Nodal Diameter Excitation of Turbine Blades: Experimental and Theoretical Study

Abstract Validating simulation results of vibrating turbine blades relies on measurements of realistic or academic cyclic structures on special test rigs. In real operation the blades are excited mainly by aerodynamic forces. For measurements of blade vibration on special test rigs, the excitation should be well known. It is desirable to use excitation spectra that consist of only a few engine order excitations. Especially for nonlinear systems, unwanted excitation orders can possibly lead to nonlinear effects which may interfere with the measurement. To separate different engine orders, an innovative electromagnetic excitation device was developed at the institution to overcome the aforementioned problems. The excitation force spectrum is controlled by a variable air gap over the circumference between device and blade. Any desired engine order excitation can be realized. Additionally, by varying the devices coil current in a harmonic fashion, frequency sweeps at constant speed can be performed. In this paper an extensive study of the excitation force spectrum of the device is conducted. Therefore, theoretical investigations of the expectable spectrum are given under simultaneous variation of air gap geometry and excitation current. These predictions are then validated by experiments featuring a small, academic bladed disk. The vibrations of the blades are measured. The device promises to create well predictable and controllable excitation force spectra which will improve the validation strategy in particular of non-linear simulation tools for the prediction of turbine blade vibrations.

Data-Driven Modeling Approach for Mistuned Cyclic Structures

A data-driven approach to predict dynamic responses of mistuned cyclic dynamic structures is presented. Nominally cyclic structures such as turbomachinery bladed disks, or blisks, contain deviations from perfect symmetry, called mistuning, which can significantly increase the forced response of the structure subject to periodic excitations. The ability to accurately model the response is crucial for understanding a structure’s dynamics during operation, and thus many reduced-order models have been developed. Data-driven approaches, however, are largely unexplored for predicting physical responses of cyclic structures, and are desirable due to their ability to leverage both computational and experimental data. In this paper, two feed-forward neural networks (FFNNs) are trained using physical responses and parameters from an individual sector of the cyclic structure. The desired physical responses of all sectors are predicted via a cyclic coupling procedure. By only using sector-level data, the number of simulations and/or experiments required to generate training data is substantially reduced, and the approach is not restricted to a specific projection basis unlike previous physics-based methods. A lumped mass model (LMM) of a blisk with stiffness mistuning is used to generate computational surrogate data for training and validation. Both FFNNs achieve high prediction accuracy on both training data and unseen test data. For a test case with an unseen mistuning pattern, this approach shows strong agreement with known actual responses. For this test case, prediction errors in the LMM blade tip amplitudes across all sectors are less than 2%, and the amplification factor error is less than 0.2%.

Structural Strength and Reliability Analysis of Important Parts of Marine Diesel Engine Turbocharger

Supercharging is the main method to improve the output power of marine diesel engines. Nowadays, most marine diesel engines use turbocharging technology, which increases the air pressure and density into the cylinder and the amount of fuel injected correspondingly so as to achieve the purpose of improving the power. In a marine diesel engine, the turbocharger has become an indispensable part. The performance of turbochargers in a harsh working environment of high temperature and high pressure for a long time will directly affect the performance of diesel engine. Based on the market feedback data from manufacturers, the failure modes of compressor impeller, turbine blade, and turbine disk of marine diesel turbocharger are analyzed, and the statistical model of random factors is established. Using DOE design, the structural strength simulation data of 46 compressors and 62 turbines are obtained, and the response surface model is constructed. On this basis, Monte Carlo sampling is carried out to analyze the reliability of the compressor and turbine. The reliability of the compressor is good, while that of the turbine disk is 0.943 and that of the turbine blade is 0.96, which still has the potential of reliability optimization space. Therefore, a multiobjective optimization method based on the NSGA-II genetic algorithm is proposed to obtain the multiobjective optimization scheme data with the reliability and processing cost of turbine disk and blade as the objective function. After optimization, the reliability of turbine disk and blade is 1, the stress value of turbine blade is optimized by 4.7941%, the stress value of turbine disk is optimized by 3.0136%, the machining cost of the turbine blade is reduced by 15.5087%, and the machining cost of turbine disk is reduced by 3.9907%. At the same time, it is verified by simulation, the data based on NSGA-II multiobjective genetic algorithm are more accurate and have practical engineering reference value. The optimized data based on NSGA-II multiobjective genetic algorithm are used to manufacture new turbine samples, and the accelerated test of simulation samples is carried out. The cycle life of the optimized turbine can reach 101,697 cycles and 118,687 cycles, which is 51.75% and 77.11% longer than that of the unoptimized turbine. It can be seen that the optimized turbine can meet the requirements of the reliability index while reducing the manufacturing cost.

Vibration Characteristics of Functionally Graded Porous Nanocomposite Blade-disk-shaft Rotor System Reinforced with Graphene Nanoplatelets

This paper presents a study on the modelling and free vibration analysis of a rotating functionally graded (FG) porous blade-disk-shaft assembly reinforced with graphene nanoplatelets (GPLs) resting on elastic supports. The rotor is made of graphene nanoplatelet (GPL) reinforced porous foam metal matrix. Both uniform and non-uniform distributions of GPLs and pores in the rotating assembly are considered. The effective material properties are thought of as layered change along the directions of blade thickness, disk radius and shaft radius. Moreover, the material values of this functionally graded structure are determined via the open-cell scheme, the Halpin–Tsai model together with the rule of mixtures. According to the finite element (FE) method, the modelling and free vibration analysis of the nanocomposite blade-disk-shaft rotor system is conducted. To verify the present analysis, the experimental method is adopted. The FE results and experimental results have great match with each other. Special attention is paid to the effects of the rotating speed, GPL distribution pattern, GPL weight fraction, length-to-width ratio and length-to-thickness ratio of GPLs, porosity distribution, porosity coefficient and support stiffness. The obtained conclusions can give particularly important suggestions for the design of GPL reinforced porous blade-disk-shaft rotor systems to achieve advanced mechanical performance.