Bladed Disk Research Articles

Simulation of the Grain Trajectory along Working Bodies of the Pneumatic Mechanical Dehuller

The aim of this study was to determine control parameters of the pneumomechanical peeling machine for grain crops by changing the angular rotational speeds of its main working bodies, a blade disk (rotor) and a deck, to provide optimal dehulling conditions (removing films (outer shells) from the grain. Based on the model representation of the air flow, changes in the magnitude and direction of the grain velocity under the action of the air flow of the opposite direction created by the reversible deck were examined. A mathematical model of grain movement in the working space of a pneumatic mechanical dehuller is presented, which takes into account the real aerodynamics of a rotating air flow, where the dehulling efficiency is determined by the speed and direction of grain flight. The numerical implementation of this model suggests that the value of the grain velocity when hitting the deck is mainly due to the angular rotational speed of the disk and hardly depends on the angular rotational speed of the deck. The direction of the grain velocity during impact is mainly related to the angular rotational speed of the deck and the curvature of the blade at the edge of the disk. This model makes it possible to control the operation of the dehuller, change the angular rotational speeds of the disc and the deck, and affect the direction of impact of the grain against the deck and the magnitude of the impact interaction, thus making it possible to create optimal conditions for dehulling.

Probabilistic modeling of uncertainties in fatigue reliability analysis of turbine bladed disks

Turbine bladed disks normally operate under complex loadings coupling with uncertainties originate from multiple sources, including material variability, load variation and geometrical uncertainty. The influence of these uncertainties on mechanical response of engineering components are critical for their fatigue assessment and reliability evaluation. In this work, a general framework for fatigue reliability analysis is developed by coupling the Latin hypercube sampling with FE analysis to describe the combined effects of multi-source uncertainties. Fatigue reliability analysis of a full-scale bladed disk under multi-source uncertainties was performed as well as sensitivity analysis for fatigue design. In order to describe the manufacturing errors or tolerances, random dimensions are inputted. Comparing the predicted fatigue lifetime distributions with/without geometrical uncertainty, it shows that geometrical uncertainty matters in structural fatigue reliability. Particularly, sensitivity analysis indicates that the geometrical uncertainty exerts more critical influences on the fatigue lifetime and reliability of the turbine bladed disk than others. The sensitivity factors of three typical dimensions emerges the influence of designed sizes and dimensional tolerances on the failure probability, which provides a reference for engineering design.

Vibration Parameters Estimation by Blade Tip-Timing in Mistuned Bladed Disks in Presence of Close Resonances

The present paper is focused on the post processing of the data coming from the Blade Tip-Timing (BTT) sensors in the case where two very close peaks are present in the frequency response of the vibrating system. This type of dynamic response with two very close peaks can occur quite often in bladed disks. It is related to the fact that the bladed disk is not perfectly cyclic symmetric and the so called “mistuning” is present. A method based on the fitting of the BTT sensors data by means of a 2 degrees of freedom (2DOF) dynamic model is proposed. Nonlinear least square optimization technique is employed for identification of the vibration characteristics. A numerical test case based on a lump parameter model of a bladed disk assembly is used to simulate different response curves and the corresponding sensors signals. The Frequency Response Function (FRF) constructed at the resonance region is compared with the traditional Sine fitting results, the resonance frequencies and damping values estimated by the fitting procedure are also reported. Accurate predictions are achieved and the results demonstrate the considerable capacity of the 2DOF method to be used as a standalone or as a complement to the standard Sine fitting method.

Study on the optimal design of mistuned bladed disk

Study on the optimal design of mistuned bladed disk

Flutter analysis of mistuned bladed disks

Flutter analysis of mistuned bladed disks

A novel modal vibration reduction of a disk-blades of a turbine using nonlinear energy sinks on the disk

This study evaluates the application of nonlinear energy sinks (NESs), mounted on the disk of a real packeted bladed disk, for an indirect passive vibration attenuation of blades. To this end, the finite element analysis is used to extract the natural modes and SAFE diagram. The cyclic symmetry property reduces the size of the system to the degrees of freedom (DOFs) in a sector containing only one packet and a disk slice. In addition, a 2-DOF reduced order model (ROM) is obtained for the two first modes of the bladed disk. The NES with an essential nonlinear stiffness and a linear damping is added to this ROM to suppress the blades vibration. Then, theoretical and numerical analyses are followed by employing the perturbation and Runge-Kutta methods to solve the system motion equations. Finally, the occurrence of Saddle-Node (SN) and Hopf bifurcations and responses like periodic and strongly modulated responses are surveyed. The results demonstrate a good performance of NESs at the second nodal diameter (ND) of the first mode due to a strong coupling between blades and the disk in out-of-plane modes and a poor performance at the second mode due to a weak coupling in in-plane ones.

Effect of Coriolis force on vibration localization characteristics of mistuned bladed disk

Ignoring the effect of centrifugal force and Coriolis force can increase the vibration localization degree of bladed disk system. In order to address the problem of vibration localization of the mistuned bladed disk of an aeroengine, the finite element reduced order models of bladed disk was established by the component mode synthesis method. The mistuning of the blades were simulated using different mistuned modes. By analyzing the mistuned vibration localization characteristics, it was discussed whether to consider the effect of the centrifugal force and Coriolis force on the vibration localization characteristics on the bladed disk. The effect of the Coriolis force on the vibration localization of the mistuned bladed disk under different engine order of excitation was discussed. The results shows that the centrifugal force and Coriolis force strongly influences the vibration characteristics of both the tuned disk and mistuned bladed disk, in the analysis of the vibration localization characteristics of the mistuned bladed disk, the role of the Coriolis force cannot be ignored.

Uncertainty quantification of bladed disc systems using data driven stochastic reduced order models

This study focusses on the development of stochastic reduced order model for probabilistic characterisation of bladed disc systems with random spatial inhomogeneities. High fidelity finite element modelling is used to mathematically model the system. A two step reduction strategy is applied involving reduction in the state space dimension and reduction in the stochastic dimensions. Information of the spatial inhomogeneities are assumed to be available from limited in situ measurements across the spatial extent and are modelled as non-Gaussian random fields. The stochastic version of the finite element matrices are developed using a polynomial chaos based framework, which optimizes the stochastic dimensionality of the problem. The uncertainties in the input propagates through the system into the response, which are also random. Surrogate models for these response quantities are obtained as PCE and are constructed using the method of stochastic collocations. Challenges involved in application of PCE on complex geometrically irregular spatial domains are addressed. The efficacy of the proposed framework is demonstrated through two numerical examples -an academic bladed disc system and an industrial turbine rotor blade.

High-fidelity calculation of modal damping caused by friction at blade roots for single blades and tuned bladed disc assemblies

A method for the analysis of amplitude-dependent modal damping factors is developed for the cases when the energy dissipation is caused by the micro-slip motion at friction contacts of blade root joints. The modal damping at root joints for a lone blade and for tuned bladed disc assemblies is studied. Large three-dimensional finite element models and detailed description of friction contacts by surface-to-surface friction contact elements at contact interfaces of the root joints are used for the calculations. The method allows using available finite element packages and is based on the direct calculation of the energy dissipated at root joints for prescribed levels of vibration amplitudes. The method takes into account the nonlinear dependency of the modal damping factors on the vibration level. The numerical studies of the dependency of modal damping factors on the vibration amplitudes, rotation speed, and contact interface parameters are performed for different families of modes and different nodal diameter numbers.

Comparative Studies of Surrogate Models for Response Analysis of Mistuned Bladed Disks

The forced responses of bladed disks are highly sensitive to inevitable random mistuning. Considerable computational efforts are required for the sampling process to assess the statistical vibration properties of mistuned bladed disks. Therefore, efficient surrogate models are preferred to accelerate the process for probabilistic analysis. In this paper, four surrogate models are utilized to construct the relation between random mistuning and forced response amplitudes, which are polynomial chaos expansion (PCE), response surface method (RSM), artificial neural networks (ANN) and Kriging interpolation, respectively. A bladed disk with 2-degrees-of-freedom (2-DOF) each sector is used to validate the effectiveness of the surrogate models. The effects of number of training samples on the surrogate model accuracy are discussed. The responses results of one blade (single output) and maximum response of all blades (multi-output) indicate that PCE and Kriging interpolation could yield accurate and stable predictions of the statistical characteristics of the forced responses. PCE is recommended for the mistuned response predictions due to its accuracy and efficiency.

Effective Mistuning Identification Method of Integrated Bladed Discs of Marine Engine Turbochargers

Radial turbine and compressor wheels form essential cornerstones of modern internal combustion engines in terms of economy, efficiency and, in particular, environmental compatibility. As a result of the introduction of exhaust gas turbochargers in the extremely important global market for diesel engines, higher engine efficiencies are possible, which in turn reduce fuel consumption. The associated reduced exhaust emissions can answer questions that results from environmentally relevant aspects of the engine development. In shipping, the international Maritime Organisation (IMO) prescribes the step-by-step reduction of nitrogen oxide and other types of emissions. To reduce these emissions, various systems are being developed, in which turbochargers are an important part. The requirements for the reliability and service life of turbochargers are constantly increasing. Turbocharger blade vibration is one of the most important problems to be solved when designing the rotors. In the case of real rotors, so-called mistuning arises, which is a slight deviation of the properties of the individual blades from the design parameters. The article deals with an effective method of mistuning identification for cases of integrated bladed discs of marine engine turbochargers. Unlike approaches that use costly scanning laser Doppler vibrometers, this method is based on using only a simple laser vibrometer in combination with a computational model of the integrated bladed disc. The added value of this method is, in particular, a significant reduction in the cost of laboratory equipment and a reduction in the time required to obtain the results.

Effects of blade’s interconnection on the modal characteristics of a shaft-disk-blade system

Present work has further developed a packet blade-disk-shaft coupling model based on previous work to interpret the effects of tuned/mistuned lacing wire on the coupled modal properties. In the developed model, the flexible bladed disk system's swing motion inducing by shaft bending is further considered. Corresponding model validation indicates that the improved model is more accurate than our previous model. Present analysis has three parts: in the first part numerical results focus on the effects of varying lacing wire location (XL) and stiffness ratio (KL) on the coupling behavior between subcomponents. As the lacing wire participating in the coupling vibration, the SDB, DB2, and BB mode shift to LSDB, LDB2, and LB mode, while the TDB mode keeps in constant. The frequency values of new coupling modes conspicuously increase, altering the order of occurrence of the dominant modes as well as the patterns of coupling modes. In the second part, a mistuning severity factor has been introduced to represent the lacing wire damage level and its effects on different coupled modes are summarized clearly. Then further analysis points out that the sensitivity of mode frequencies to lacing wire damage depends on a series of factors. The conclusions can provide a reference for the mistuning identification in the shaft-disk-blade packet system. Finally, the effects of rotational speed on the tuned/mistuned shaft-disk-blade packet are compared and depicted in the Campbell diagram.

Study on a 2D field-based multi-objective tool-axis optimization algorithm based on covariant field theory for five-axis tool path generation

In five-axis machining, drastic change of tool axis has negative effects on machining efficiency and quality. Our published work proposed a unified mathematical framework to generate smooth tool-axis field and implemented in 1D domain (Yan et al., J Manuf Syst 48:30–37, 2018). In this paper, we extend the mathematical framework to 2D domain and the framework is an integral functional problem converting diverse machining requirements, such as gouge and collision free, smoothness, into mathematical expressions. A tool-axis vector field (TAVF) defined on the freeform surface is calculated by optimizing the integral functional problem. The surface is discrete into triangular mesh, and the discrete TAVF calculation problem is solved by a numeric 2D finite element method (FEM). Subsequently, the proposed algorithm is implemented to generate field-generated tool path (FGTP). The tool path has been used in machining hub of blade disk (blisk). The blisk is a complex workpiece that impellers should be gouge avoided. Machining experiments indicate that tool path generated by the proposed algorithm can avoid collision and improve smoothness on the whole surface. The freeform surface machining quality is highly improved compared with that machined by region-partitioned tool path (RPTP).

A New Experimental Facility for Characterizing Bladed Disk Dynamics at Design Speed

An experimental facility for structural dynamics programs that uses an above-ground containment tank specifically designed to house bladed disks operating at design speed is described in this work. Key characteristics of the facility are discussed, and the configuration for a blade damping and mistuning study are presented. In particular, the development of an air-jet excitation system that can operate in different configurations to excite synchronous and nonsynchronous vibrations is detailed. Also, the measurement capabilities using a noncontact tip timing system as well as strain gauges are highlighted. Finally, results of data demonstrating the effectiveness of the facility for damping and mistuning studies are discussed.

A novel none once per revolution blade tip timing based blade vibration parameters identification method

The vibration caused blade High Cycle Fatigue (HCF) is seriously affects the safety operation of turbomachinery especially for aero-engine. Thus, it is crucial important to identify the blade vibration parameters and then evaluate the dynamic stress amplitude. Blade Tip Timing (BTT) method is one of the promising method to solve these problems. While, it need a high resolution Once Per Revolution (OPR) signal which is difficult to get for the aero-engine. Here, a Coupled Vibration Analysis (CVA) method for identifying blade vibration parameters by a none OPR BTT is proposed. The method assumes that every real blade has its own vibration performance at a given speed. Whereby, it can take any blade as the reference blade, and the other blades using the reference blade as the OPR for vibration displacement calculating and further parameter identifying. The proposed method is validated by numerical model. Also, experimental studies are carried out on a straight blade and a twisted three dimensional blade test rig as well as a large industrial axial compressor respectively. The results show that the proposed method can accurately identify the blade synchronous vibration parameters and quantitatively evaluate the mistuning in bladed disks, which lays a foundation for the reliability improvement of aero-engine.

Prediction of mistuning effect of bladed disks using eigensensitivity analysis

Vibration modes with repeated eigenvalues often occur in engineering design and analysis practices due to geometrical symmetries of structural systems such as the cyclic symmetry of bladed disk assemblies of turbomachinery. However, the degeneration of eigenvector space and the resulting discontinuities have prevented useful applications of eigensensitivities to vibration analysis of a wide class of problems with repeated modes. To overcome such difficulties, a new concept of a global design variable is developed in which all intended multivariate design modifications are grouped into a single global design variable. Eigensensitivities have then been formulated for repeated eigenvalues from which accurate predictions of vibration characteristics can be made. Further, second order eigenvalue derivatives are also employed to further improve the accuracy of predicted vibration properties. Such newly formulated eigensensitivity analysis has been effectively applied for the first time to the prediction of mistuning effect of bladed disk assemblies. Numerical results from a realistic discrete parameter model of a bladed disk have demonstrated that not only natural frequencies and mode shapes can be predicted very accurately, but also blade vibration responses under engine order excitations. In addition, the proposed eigensensitivty analysis can predict the statistical variations of blade vibrations under random mistuning. Finite element modeling and vibration testing of a practical bladed disk structure have been carried out to demonstrate the practical potential of the proposed method to be possibly integrated into finite element analysis for structural modification predictions, especially for structures with repeated eigenvalues such as bladed disks.

Adaptive control of normal load at the friction interface of bladed disks using giant magnetostrictive material

A novel application of magnetostrictive actuators in underplatform dampers of bladed disks is proposed for adaptive control of the normal load at the friction interface to achieve the desired friction damping in the structure. Friction damping in a bladed disk depends on operating parameters, such as rotational speed, engine excitation order, nodal diameter normal contact load, and contact interface parameters, such as contact stiffness and friction coefficient. The operating parameters have a fixed value, whereas the contact interface parameters vary in an unpredictable way at an operating point. However, the ability to vary some of these parameters such as the normal contact load in a controlled manner is desirable to attain an optimum damping in the bladed disk at different operating conditions. Under the influence of an external magnetic field, magnetostrictive materials develop an internal strain that can be exploited to vary the normal contact load at the friction interface, which makes them a potentially good candidate for this application. A commercially available magnetostrictive alloy, Terfenol-D is considered in this analysis that is capable of providing magnetostrain up to 2 × 10-3 under prestress and a blocked force over 1500 N. A linearized model of the magnetostrictive material, which is accurate enough for a direct current application, is employed to compute the output force of the actuator. A nonlinear finite element contact analysis is performed to compute the normal contact load between the blade platform and the underplatform damper as a result of magnetostrictive actuation. The nonlinear contact analysis is performed for different actuator mounting configurations and the obtained results are discussed. The proposed solution is potentially applicable to adaptively control vibratory stresses in bladed disks and consequently to reduce failure due to high-cycle fatigue. Finally, the practical challenges in employing magnetostrictive actuators in underplatform dampers are discussed.

Development of Working Blades From a Titanium Alloy for the Last Steps of a Low Pressure Cylinder for Powerful Steam Turbines

The main design studies of JSC “Turboatom” are highlighted when creating a working blade made of titanium alloy with an active part length of 1200 mm for the last stages of K-1000-60/3000 turbines. It is noted that complex calculations for blades made of titanium alloy for the last stages of the low-pressure cylinder of powerful steam turbines are an urgent task. A three-dimensional calculation of the strength of these blades was carried out, the stress-strain state and displacements at different values of the natural frequency of the blade were determined. The calculation of the bladed disk of the stage of the low pressure cylinder is performed. The dynamic frequencies of natural vibrations are determined for various rotation frequencies of the turbine rotor. A feature of manufacturing technology that provides for the control assembly on the process disk is indicated. The blades made of titanium alloy manufactured by JSC “Turboatom”, considered in this work, are successfully operated on K-1000-60/3000 turbines of the South Ukrainian and Khmelnitsky nuclear power plants.

Dual-Connected Synchronized Switch Damping for Vibration Control of Bladed Disks in Aero-Engines

An enhanced SSDI (synchronized switch damping on inductor) approach is proposed to suppress the vibration of bladed disks in aero-engines. Different from the authors’ former work (MSSP, 2017; JIMSS, 2018) where a local SSDI circuit is shunted to the piezoelectric materials at each blade sector, in this work two blade sectors are interconnected by a shared SSDI circuit. In this way, the switching action of SSDI is triggered by the relative displacement between two blade sectors. The feasibility of the dual-connected SSDI is numerically examined by a 2-DOF (degree-of-freedom) mechanical system, and further experimentally validated on a single-beam and a double-beam system. Results show that the damping performance increases with the amplitude of relative displacement. This feature is especially favorable for the application of blisks where the blade normally vibrates in different amplitudes and phases. Eventually, we conduct numerical simulation on the forced response of mistuned bladed disk undergoing travelling wave excitation. Results show that the dual-connected configuration can reduce at least half the number of switching shunts while maintain nearly the same performance as the conventional (local) SSDI.

Energy transfer between nodal diameters of cyclic symmetric structures exhibiting polynomial nonlinearities: Cyclic condition and analysis

The recent trend of new design for large slender blades in turboengines facilitates structural large deformation and geometrical nonlinear vibratory effects. The cyclic symmetry properties of such structures, combined with these nonlinearities give rise to specific complex phenomena such as internal resonances or energy localization. Robust and efficient methods have been developed to recover the solutions of such problems but they currently lack proper tools to analyze the results. In this paper, a formula is provided to compute polynomial nonlinear forces directly in the cyclic (spectral) domain of a cyclic symmetric structure. This new approach enables to express the equation of motion directly in the spectral domain, and offers two main advantages. It first provides a reduction of the system by determining a priori which nodal diameters will be coupled and by giving a closed-form expression for a direct evaluation of the cyclic nonlinear force. The proposed approach also facilitates results interpretations. The method is applied to a simplified bladed disk with a cubic nonlinearity that models symmetric large deformation, although the analytical development is valid for any polynomial nonlinearity. A detailed analysis of the different phenomena occurring in the cyclic structure excited along a particular nodal diameter is provided. More precisely, a multiple scales analysis is performed and yields interesting insights of internal resonances between different nodal diameters. This analytical method is completed with several numerical simulations involving the harmonic balance method and bifurcation algorithms. Both of these analyses recover coherent results on the prediction of different internal resonances for traveling or standing wave excitations.