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Bladed Disks Structural Dynamics

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A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Mechanical Engineering".

Deadline for manuscript submissions: closed (20 December 2021) | Viewed by 25810

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Prof. Dr. Paolo Neri

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Department of Civil and Industrial Engineering, University of Pisa, Pisa, Italy
Interests: structural dynamics; vision systems; additive manufacturing; 3D printing; digital image correlation; modal analysis; full field methods

Prof. Dr. Ciro Santus

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Department of Civil and Industrial Engineering, University of Pisa, Pisa, Italy
Interests: fracture; fatigue; structural dynamics
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Dr. Christian Maria Firrone

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Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10139 Torino, Italy
Interests: bladed disks structural dynamics; nonlinear vibrations of frictionally damped systems; reduction techniques; aeroelasticity

Special Issue Information

Dear Colleagues,

Rotating machines are widely used in industry for several applications, and the main part of these machines is usually a bladed disk. The cyclic load produced by the machine rotation can cause structural vibrations, which induce noise amplification and efficiency loss. Furthermore, high cycle fatigue failures and even fretting at the connection regions may occur. These phenomena represent a relevant economic loss for industry, since the most frequent impeller failure mechanism is represented by severe blade damage due to the vibrations. For these reasons, research on the dynamic characterization of bladed disks is of utmost importance, aiming at improving the design tools and at further optimizing the components. To this extent, Singh’s advanced frequency evaluation (SAFE) diagram is commonly used to find and thus prevent bladed disk resonances. Regardless, however, any degree of cyclic symmetry loss of the bladed wheel, usually referred to as mistuning, significantly increases the complexity of the modal analysis, and the SAFE approach is no longer valid. Therefore, reduced order modeling methods are required, such as the asymptotic mistuning model, or other analytical techniques which were quite recently proposed and developed.

In order to correctly predict and control the vibratory response and the stress-related field, also nonlinear phenomena as aero-elastic coupling, friction damping due to joints and geometrical nonlinearities must be taken into account and appropriate methodologies are sought to include them in the preliminary stage of the design of rotating components.

The aim of this Special Issue on “Bladed Disk Structural Dynamics” is to investigate the latest developments in bladed disks dynamics, showing both modal numerical and analytical methods, especially on the mistuning, and dedicated experimental activity.

Prof. Dr. Paolo Neri
Prof. Dr. Ciro Santus
Prof. Dr. Christian Maria Firrone
Guest Editors

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Keywords

bladed disk resonance
bladed disk monitoring
blade damage detection
SAFE diagram
mistuned bladed disks
reduced order modelling
Joint simulation
Joint identification
Fretting and wear
experimental modal analysis
aeromechanical test
laser Doppler vibrometry
digital image correlation

Published Papers (11 papers)

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Research

15 pages, 13999 KiB

Open AccessArticle

Experimental and Numerical Investigation of Contact Parameters in a Dovetail Type of Blade Root Joints

by Hadi Dastani, Daniele Botto and Matteo Glorioso

Appl. Sci. 2021, 11(24), 12008; https://0-doi-org.brum.beds.ac.uk/10.3390/app112412008 - 16 Dec 2021

Cited by 4 | Viewed by 2034

Abstract

This paper focuses on the contact characteristics of the blade root joints subjected to the dry friction damping under periodic excitation. The numerical method and experimental procedure are combined to trace the contact behavior in the nonlinear vibration conditions. In experimental procedure, a novel excitation method alongside the accurate measurements is used to determine the frequencies of the blade under different axial loads. In numerical simulations, local behavior of contact areas is investigated using the reduction method as a reliable and fast solver. Subsequently, by using both experimental measurements and numerical outcomes in a developed code, the global stiffness matrix is calculated. This leads to find the normal and tangential stiffness in the contact areas of a dovetail blade root joints. The results indicate that the proposed method can provide an accurate quantitative assessment for investigation the dynamic response of the joints with focusing the contact areas. Full article

(This article belongs to the Special Issue Bladed Disks Structural Dynamics)

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28 pages, 42887 KiB

Open AccessArticle

Study on the Coupled Vibration Characteristics of a Two-Stage Bladed Disk Rotor System

by Yinxin Yu, Xiaolong Jin, Yanming Fu and Tianyu Zhao

Appl. Sci. 2021, 11(18), 8600; https://0-doi-org.brum.beds.ac.uk/10.3390/app11188600 - 16 Sep 2021

Cited by 2 | Viewed by 1800

Abstract

This paper conducts a coupled vibration analysis of a two-stage bladed disk rotor system. According to the finite element method, the bladed disk rotor system is established. The substructure modal synthesis super-element method (SMSM) with a fixed interface and free interface is presented to obtain the vibration behaviors of the rotor system. Then, the free vibration results are compared with the ones calculated by the cyclic symmetry analysis method to validate the analysis in this paper. The results show that the modes of the two-stage bladed disk not only include the modes of the first- and second-stage bladed disk, but also the coupled modes of the two-stage bladed disk. Full article

(This article belongs to the Special Issue Bladed Disks Structural Dynamics)

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27 pages, 14898 KiB

Open AccessArticle

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

by Chang-Sheng Lin, Hung-Tse Chiang, Chuan-Hsing Hsu, Ming-Hsien Lin, Jui-Kai Liu and Chi-Jeng Bai

Appl. Sci. 2021, 11(14), 6306; https://0-doi-org.brum.beds.ac.uk/10.3390/app11146306 - 08 Jul 2021

Cited by 4 | Viewed by 2860

Abstract

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. Full article

(This article belongs to the Special Issue Bladed Disks Structural Dynamics)

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15 pages, 862 KiB

Open AccessArticle

Key Action Mechanisms of Intentional Mistuning

by Jose Joaquin Sánchez-Álvarez and Carlos Martel

Appl. Sci. 2021, 11(12), 5650; https://0-doi-org.brum.beds.ac.uk/10.3390/app11125650 - 18 Jun 2021

Cited by 3 | Viewed by 1376

Abstract

Intentional mistuning is a common procedure to decrease the uncontrolled vibration amplification effects of the (unavoidable) random mistuning, and to reduce the sensitivity to it. The idea is to introduce an intentional mistuning pattern that is small, but much larger than the existing random mistuning. The frequency of adjacent blades is moved apart by the intentional mistuning, reducing the blade-to-blade coupling and, thus, the effect of the random mistuning. In order to clearly show the action mechanisms of intentional mistuning, we focus in this work in a quite simple configuration: forced response of a blade dominated modal family in a mistuned rotor with linear material damping. The problem is analysed using the asymptotic mistuning model methodology. A more reduced order model is derived that allows us to understand the relevant parameters behind the effect of intentional mistuning, and gives a simple expression for the estimation of its beneficial effect. The results from the reduced model are checked against detailed FEM simulations of two mistuned rotors. Full article

(This article belongs to the Special Issue Bladed Disks Structural Dynamics)

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18 pages, 11049 KiB

Open AccessArticle

A Novel Test Rig for the Basic Nonlinear Characterization of Bolted Joints

by Yongfeng Wang, Yanhong Ma, Jie Hong, Giuseppe Battiato and Christian Maria Firrone

Appl. Sci. 2021, 11(12), 5613; https://0-doi-org.brum.beds.ac.uk/10.3390/app11125613 - 17 Jun 2021

Cited by 2 | Viewed by 1666

Abstract

The paper aims at performing a comprehensive experimental study on the peculiar properties of a bolted joint, and investigates the damping induced at different interfaces (between flanges, bolt head/nut and flange, threads) during vibrations. A novel, simplified, single-bolt system joining a two-beam structure is designed and tested. Experimental results under different boundary conditions are presented, and the influence of the harmonic excitation force, as well as the bolt tension, is investigated. The test results show how the contact interface between the clamped flanges plays an important role in terms of frictional damping provided to the system during vibration, while the contact interfaces between the head/nut and flange, and secondarily between the threads, affect the system response at a less, but not negligible, extent. The test setup and test procedure can provide a database to validate single bolt contact models to be included in a more complex structure. Full article

(This article belongs to the Special Issue Bladed Disks Structural Dynamics)

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21 pages, 5296 KiB

Open AccessArticle

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

by Lorenzo Pinelli, Francesco Lori, Michele Marconcini, Roberto Pacciani and Andrea Arnone

Appl. Sci. 2021, 11(12), 5437; https://0-doi-org.brum.beds.ac.uk/10.3390/app11125437 - 11 Jun 2021

Cited by 13 | Viewed by 3464

Abstract

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. Full article

(This article belongs to the Special Issue Bladed Disks Structural Dynamics)

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12 pages, 3426 KiB

Open AccessArticle

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

by Paolo Neri, Alessandro Paoli and Ciro Santus

Appl. Sci. 2021, 11(12), 5430; https://0-doi-org.brum.beds.ac.uk/10.3390/app11125430 - 11 Jun 2021

Cited by 5 | Viewed by 2221

Abstract

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. Full article

(This article belongs to the Special Issue Bladed Disks Structural Dynamics)

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16 pages, 2182 KiB

Open AccessFeature PaperArticle

A Method to Minimize the Effort for Damper–Blade Matching Demonstrated on Two Blade Sizes

by Chiara Gastaldi and Muzio M. Gola

Appl. Sci. 2021, 11(11), 5171; https://0-doi-org.brum.beds.ac.uk/10.3390/app11115171 - 02 Jun 2021

Cited by 6 | Viewed by 1976

Abstract

A method called PCR (Platform Centered Reduction) is designed to more effectively perform complex iterative and nonlinear calculations required for the dynamic response of turbine blades damped by dry friction contacts between rigid dampers and airfoil-to-neck platform. The key feature of PCR is to represent all nonlinear forces on the blade platform by means of only six degrees of freedom at a point located within the platform volume, regardless of the number of damper–platform contact elements. Despite reducing the effort and computational time by more than one order of magnitude, the method proves to be fully accurate by a check against the corresponding nonlinear Finite Elements (FE) calculation. It is also shown that the limit exciting force, indicating the upper capability to dampen vibrations, can be calculated with a simple linear modal analysis. In order to search for the best blade–damper match, the preferred graph represents relevant bending stresses on the airfoil against excitation forces. A detailed application of the method concerns two significantly different blade sizes, by varying parameters such as neck length and damper centrifugal force. Finally, it is emphasized that a final check by a complete FE analysis is still possible as a purely linear solution fed by sets of contact forces previously determined through the PCR at any desired frequency and excitation. Full article

(This article belongs to the Special Issue Bladed Disks Structural Dynamics)

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19 pages, 6538 KiB

Open AccessArticle

Study on Influence of Multi-Parameter Variation of Bladed Disk System on Vibration Characteristics

by Honggang Pan, Yunshi Wu and Tianyu Zhao

Appl. Sci. 2021, 11(7), 3084; https://0-doi-org.brum.beds.ac.uk/10.3390/app11073084 - 30 Mar 2021

Cited by 4 | Viewed by 1644

Abstract

As the main components of the rotor system of aero-engines and other rotating machinery equipment, the bladed disk system has high requirements on its structure design, safety and stability. Taking the rotor disk system of aero-engines as the research object, modal calculation of the rotor disk system was based on the group theory algorithm, and using the fine sand movement on the experimental disk to express the disk vibration shape. The experimental vibration mode is used to compare with the finite element calculation results to verify the reliability of the finite element analysis. Study on the effect of dissonance parameter changes on the bladed disk system vibration characteristics concluded that the vibration mode trends of the blisk system and the disc are, basically, consistent. As the mass of the blade increases, the modal frequencies of the entire blisk system gradually decrease, and the amplitude slightly increases. When the mass increases at different parts of the blade, the effect on the modal frequencies of the bladed disk system are not obvious. When the bladed disk system vibrates at low frequency, the disc will not vibrate and each blade will vibrate irregularly. The bladed disk should be avoided to work in this working area for a long time, so as not to cause fatigue damage or even fracture of some blades. Full article

(This article belongs to the Special Issue Bladed Disks Structural Dynamics)

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20 pages, 3738 KiB

Open AccessArticle

Self-Tuning Algorithm for Tuneable Clamping Table for Chatter Suppression in Blade Recontouring

by Markel Sanz-Calle, Zoltan Dombovari, Jokin Munoa, Alexander Iglesias and Luis Norberto López de Lacalle

Appl. Sci. 2021, 11(6), 2569; https://0-doi-org.brum.beds.ac.uk/10.3390/app11062569 - 13 Mar 2021

Cited by 6 | Viewed by 1760

Abstract

The production and repair of blades for aerospace engines and energy turbines is a complex process due their inherently low stiffness and damping properties. The final recontouring operation is usually performed by milling operations where regenerative chatter is one of the main productivity limiting factors. With the objective of avoiding specific stiffening fixtures for each blade geometry, this paper proposes a semi-active tuneable clamping table (TCT) based on mode tuning for blade machining. The active mode of the device can be externally controlled by means of a rotary spring and eddy current damping modules. Its in-series architecture allows damping to be introduced to the critical mode of the thin-walled part without any direct contact in the machining area and enables a more universal clamping. Its chatter suppression capabilities are maximized by means of a novel self-tuning algorithm that iteratively optimizes the tuning for the measured chatter frequency. The benefits of the iterative algorithm are validated through semidiscretization and initial value time-domain simulations, showing a clear improvement in blade recontouring stability compared to regular broad-bandwidth tuning methods. Full article

(This article belongs to the Special Issue Bladed Disks Structural Dynamics)

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16 pages, 530 KiB

Open AccessArticle

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

by Saeed Bornassi, Christian Maria Firrone and Teresa Maria Berruti

Appl. Sci. 2020, 10(17), 5930; https://0-doi-org.brum.beds.ac.uk/10.3390/app10175930 - 27 Aug 2020

Cited by 11 | Viewed by 2461

Abstract

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. Full article

(This article belongs to the Special Issue Bladed Disks Structural Dynamics)

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