Simulation of Tip-Timing Measurements of a Cracked Bladed Disk Forced Response

2010 ◽  
Author(s):  
Vsevolod Kharyton ◽  
Jean-Pierre Laine ◽  
Fabrice Thouverez ◽  
Olexiy Kucher
Keyword(s):  
Dynamic Model ◽  
Harmonic Balance Method ◽  
Time History ◽  
Forced Response ◽  
Bladed Disk ◽  
Crack Behavior ◽  
Timing Data ◽  
History Of ◽  
Blade Tip ◽  
Blade Frequency

The study intends to simulate the process of the blade tip amplitude calculation by the tip-timing method. An attention is focused on tip-timing measurements for detection of a cracked blade from the bladed disk forced response. The cracked blade is considered within frameworks of the bladed disk dynamic model that takes into account mistuning presence. Nonlinear formulation of a crack behavior is done with the harmonic balance method in its combination with the contact analysis that allows simulation of crack breathing. In order to make the cracked blade detection process evident, the crack length and location are set in such a way as to produce the cracked blade frequency localization. Reconstruction of the blade tip amplitudes is attained with the arriving time of measured probes of the blade tips. The results are compared with the blade forced response obtained by the bladed disk dynamic model. A possibility is also considered how to reconstruct time-history of the bladed disk forced response with tip-timing data.

Free and Forced Response of an Axially Moving String Transporting a Damped Linear Oscillator

1993 ◽  
Author(s):  
W. D. Zhu ◽  
C. D. Mote
Keyword(s):  
Initial Conditions ◽  
Numerical Algorithms ◽  
Time History ◽  
Coupled System ◽  
Interaction Force ◽  
Forced Response ◽  
Linear Oscillator ◽  
Response Analysis ◽  
History Of ◽  
Axially Moving

Abstract The transverse response of a cable transport system, which is modelled as an ideal, constant tension string travelling at constant speed between two supports with a damped linear oscillator attached to it, is predicted for arbitrary initial conditions, external forces and boundary excitations. The exact formulation of the coupled system reduces to a single integral equation of Volterra type governing the interaction force between the string and the payload oscillator. The time history of the interaction force is discontinuous for non-vanishing damping of the oscillator. These discontinuities occur at the instants when transverse waves propagating along the string interact with the oscillator. The discontinuities are treated using the theory of distributions. Numerical algorithms for computing the integrals involving generalized functions and for solution of the delay-integral-differential equation are developed. Response analysis shows a discontinuous velocity history of the payload attachment point. Special conditions leading to absence of the discontinuities above are given.

Blade Root Joint Modelling and Analysis of Effects of Their Geometry Variability on the Nonlinear Forced Response of Tuned and Mistuned Bladed Disks

2020 ◽  
Author(s):  
Adam Koscso ◽  
E. P. Petrov
Keyword(s):  
Harmonic Balance Method ◽  
Forced Response ◽  
High Fidelity ◽  
Contact Interactions ◽  
Bladed Disks ◽  
Element Mesh ◽  
Disk Model ◽  
Bladed Disk ◽  
Nonlinear Contact ◽  
Manufacturing Tolerances

Abstract One of the major sources of the damping of the forced vibration for bladed disk structures is the micro-slip motion at the contact interfaces of blade-disk joints. In this paper, the modeling strategies of nonlinear contact interactions at blade roots are examined using high-fidelity modelling of bladed disk assemblies and the nonlinear contact interactions at blade-disk contact patches. The analysis is performed in the frequency domain using multiharmonic harmonic balance method and analytically formulated node-to-node contact elements modelling frictional and gap nonlinear interactions. The effect of the number, location and distribution of nonlinear contact elements are analyzed using cyclically symmetric bladed disks. The possibility of using the number of the contact elements noticeably smaller than the total number of nodes in the finite element mesh created at the contact interface for the high-fidelity bladed disk model is demonstrated. The parameters for the modeling of the root damping are analysed for tuned and mistuned bladed disks. The geometric shapes of blade roots and corresponding slots in disks cannot be manufactured perfectly and there is inevitable root joint geometry variability within the manufacturing tolerances. Based on these tolerances, the extreme cases of the geometry variation are defined and the assessment of the possible effects of the root geometry variation on the nonlinear forced response are performed based on a set of these extreme cases.

Analysis on Load Spectrum of Bogie Frame for High-Speed EMU

2014 ◽  
Vol 633-634 ◽  
pp. 1166-1173
Author(s):  
Yu Guang Wang ◽  
Da Fu Zhang
Keyword(s):  
Fatigue Life ◽  
Dynamic Model ◽  
High Speed ◽  
Estimation Method ◽  
Time History ◽  
Load Spectrum ◽  
Safe Operation ◽  
Bogie Frame ◽  
Key Factor ◽  
History Of

The load spectrum, on which there is not a thorough research, is the key factor of the safe operation of EMU. A dynamic model of some high-speed EMU is established and the load time history of main load on frame is obtained through simulation and analysis based on the Beijing-Tianjin route. The load spectrum for main load is calculated by rain-flow counting, the crossing contrast of load spectrum in basic and fault conditions is proceeded as well, the extent of impact of all kinds of fault conditions to bogie main load is analyzed and a brief introduction of estimation method of the frame fatigue life is put forward in this paper.

scholarly journals Determination of Simultaneous Steady-State Movements Using Blade Tip Timing Data

2019 ◽  
Author(s):  
Mohamed Mohamed ◽  
Philip Bonello ◽  
Peter Russhard
Keyword(s):  
Previous Method ◽  
Vibration Measurement ◽  
Single Type ◽  
Bladed Disk ◽  
Shaft System ◽  
Axial Movement ◽  
Timing Data ◽  
Blade Tip ◽  
Uncertainty Level

Abstract Blade tip timing (BTT) includes a number of uncertainties that discourage its use. One of the main ones is the shift in the equilibrium position of the blade tip due to steady (non-oscillatory) bending and/or twisting of the blade, and axial movement of the bladed disk (blisk)-shaft system. This results in a shift in the effective measurement position of the probe relative to the blade chord, resulting in errors in the tip vibration measurement which can translate to a huge error in the corresponding stress estimate, which relies on calibration against finite element (FE) models. Previous experimentally validated research by the authors introduced a method for quantifying steady movement of a single type (axial, lean, or untwist), using BTT data from not more than two probes. In this paper, a development of the previous method is presented that provides a solution for the case of simultaneous types of blade steady movements. Additional probes are used for determining the direction, but these can be placed at any angular positions. The developed method is validated using a BTT simulator of a blisk, and accurate results obtained. The simultaneous axial and lean movements can be accurately determined when the untwist is negligible, and an uncertainty level can be specified when the untwist is not negligible. The untwist itself can be calculated accurately in all cases of simultaneous movements. Guidelines for the use of the method in different scenarios are provided.

scholarly journals Self-adaptive macroslip array for friction force prediction in contact interfaces with non-conforming meshes

2021 ◽  
Author(s):  
Giuseppe Battiato
Keyword(s):  
Harmonic Balance Method ◽  
Forced Response ◽  
Contact Forces ◽  
Friction Forces ◽  
Bladed Disk ◽  
Current State ◽  
Proposed Model ◽  
Conforming Meshes ◽  
Static Misalignment ◽  
Self Adaptive

AbstractThe steady-state nonlinear forced response (NFR) of finite element (FE) models with friction joints is usually computed in the frequency domain through the combination of node-to-node contact elements and the Harmonic Balance Method (HBM). In the current state of the art, rare are the cases where the friction forces are estimated for contact interfaces with non-conforming mesh grids. This need is nowadays taking place due to the improving capability of commercial FE software to manage any kind of boundary condition (i.e., either coupling or contact), without requiring coincident pairs of nodes at the joint interfaces. Such an advantage becomes a drawback when the analysts are requested to investigate the NFR of the assembly by using build-in codes, where the contact forces prediction usually requires node-to-node contact elements whose parameters (i.e., the contact stiffnesses and friction coefficients) can be easily identified by means of experiments. This paper addresses the mentioned limitation, and proposes a novel self-adaptive macroslip array (SAMA) model for the estimation of the nonlinear friction forces on FE contact interfaces with non-conforming meshes. The SAMA model consists on a set of node-to-node contact elements ordered in parallel, whose contact parameters and normal preloads are identified through a step-by-step self-adaptive weighting algorithm that depends on the topology of the meshes in contact. The goodness of the proposed model is assessed on the calculation of the NFR of a bladed disk with shroud contacts, under the hypotheses of cyclic symmetry and HBM. The nonlinear dynamic behavior of the bladed disk is evaluated in two different cases. First, in the case of lack of node-to-node congruence at the contact interface for the structure being in its undeformed configuration, and second, in the case of a relevant static misalignment of the contact interfaces due to the application of large static loads.

scholarly journals Sensitivity and Forced Response Analysis of Anisotropy-Mistuned Bladed Disks With Nonlinear Contact Interfaces

2019 ◽  
Author(s):  
Adam Koscso ◽  
E. P. Petrov
Keyword(s):  
Harmonic Balance Method ◽  
Computational Effort ◽  
Forced Response ◽  
Response Analysis ◽  
Nonlinear Friction ◽  
Material Anisotropy ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Nonlinear Contact ◽  
Blade Model

Abstract A new method has been developed for the analysis of nonlinear forced response of bladed disks mistuned by blade anisotropy scatter and for the forced response sensitivity to blade material anisotropy orientations. The approach allows for the calculation of bladed disks with nonlinear friction contact interfaces using the multi-harmonic balance method. The method uses efficient high-accuracy model reduction method for the minimization of the computational effort while providing required accuracy. The capabilities of the developed methods are validated and demonstrated using a two-blade model. A thorough study of the influence of the material anisotropy mistuning and its sensitivity on the characteristics of the forced response is carried out using finite element modes of anisotropy mistuned realistic bladed disk with nonlinear friction joints of blade roots and shroud contacts. The dependency of the nonlinear forced response on excitation level and contact pressure values has been carried out for anisotropy mistuned bladed disks.

A Numerical Steady State and Dynamic Study in a Data Center Using Calibrated Fan Curves for CRACs and Servers

2013 ◽  
Author(s):  
Sami A. Alkharabsheh ◽  
Bahgat Sammakia ◽  
Saurabh Shrivastava ◽  
Michael Ellsworth ◽  
Milnes David ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Data Center ◽  
Power Dissipation ◽  
Time History ◽  
Boussinesq Approximation ◽  
Design Guidelines ◽  
Thermal Mass ◽  
Transient Model ◽  
History Of ◽  
Fan Speed

This study presents the results of a detailed parametric study for a data center that is air cooled using a set of four CRAC units in a cold/hot aisle raised floor configuration. The fans of the CRAC units and the servers are calibrated using their practical characteristics fan curves. A commercial CFD code is utilized for this purpose in which the buoyancy forces are taken into account. The k-epsilon model and the Boussinesq approximation are used to model the turbulent airflow and the buoyancy effect, respectively. A dynamic model is developed to take into account the changes in flow rates and power dissipation in the data center environment. The current dynamic model does not take into account the thermal mass of the CRAC units or the servers. The effect of the CRAC fan speed, instantaneous change in power dissipation, tiles perforation ratio, and servers fan speeds on the total flow rate in the room and the inlet temperatures of the racks are investigated. In the transient model, we investigate the effect of different CRAC failure scenarios on the time history of the temperatures and the flow pattern in the data center. Time constants and safe time are estimated from this study. A fundamental understanding of the effect of different data center entities on the flow and the temperatures is developed. Interesting flow patterns are observed in the case of different CRAC failures that could be used to recommend general design guidelines.

scholarly journals Application of harmonic balance method for solving non-linear equations of motion

2018 ◽  
Vol 182 ◽  
pp. 02024
Author(s):  
Robert Kostek
Keyword(s):  
Harmonic Balance ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Harmonic Balance Method ◽  
Time History ◽  
Balance Method ◽  
Non Linear ◽  
Time Histories ◽  
History Of ◽  
Non Linear Equations

This article presents the advantages and limitations of a harmonic balance method applied for solving non-linear equations of monition. This method provides an opportunity to find stable and unstable periodic solutions, which was demonstrated for a few equations. An error of solution decreases rapidly with increase of number of harmonics for smooth time history of acceleration, which shows convergence; whereas, for discontinuous time histories, this method is not effective.

A Subspace Method for Modal Identification of Bladed Assemblies Using Blade Tip-Timing Data

2007 ◽  
Author(s):  
Bendali Salhi ◽  
Marc Berthillier ◽  
Joseph Lardies ◽  
Philippe Voinis ◽  
Charles Bodel
Keyword(s):  
Natural Frequencies ◽  
Standard Procedure ◽  
Modal Identification ◽  
Subspace Method ◽  
Subspace Analysis ◽  
Bladed Disk ◽  
Fast Fourier Transform Analysis ◽  
Timing Data ◽  
Vibration Responses ◽  
Blade Tip

Unknown excitation forces are applied to bladed disk assemblies, such as turbines blades, leading to forced vibration responses. Non contact measurement of such vibrations using blade tip-timing data has become an industrial standard procedure and current research focuses on analysis methods for interpretation of measured vibrations. Our purpose is to develop a method for identification of the blade’s natural frequencies and damping ratios using blade tip-timing data. The method is based on a subspace analysis. Its performance is compared to the traditional Fast Fourier Transform analysis. A detailed description of these methods and results are presented.

Method for Analysis of Nonlinear Multiharmonic Vibrations of Mistuned Bladed Disks With Scatter of Contact Interface Characteristics

2005 ◽  
Vol 127 (1) ◽  
pp. 128-136 ◽  
Author(s):  
E. P. Petrov ◽  
D. J. Ewins
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Forced Response ◽  
Finite Element Models ◽  
Linear Vibration ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Interface Characteristics ◽  
Blade Frequency

An efficient method for analysis of nonlinear vibrations of mistuned bladed disk assemblies has been developed. This development has facilitated the use of large-scale finite element models for realistic bladed disks, used hitherto in analysis of linear vibration, to be extended for the analysis of nonlinear multiharmonic vibration. The new method is based on a technique for the exact condensation of nonlinear finite element models of mistuned bladed disks. The model condensation allows the size of the nonlinear equations to be reduced to the number of degrees of freedom where nonlinear interaction forces are applied. The analysis of nonlinear forced response for simplified and realistic models of mistuned bladed disks has been performed. For a practical high-pressure bladed turbine disk, several types of nonlinear forced response have been considered, including mistuning by (i) scatter of underplatform dampers, (ii) shroud gap scatter, and (iii) blade frequency scatter in the presence of nonlinear shroud interactions.

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