Flutter Amplitude Saturation by Nonlinear Friction Forces: Reduced Model Validation

2014 ◽  
Author(s):  
Carlos Martel ◽  
Roque Corral ◽  
Rahul Ivaturi
Keyword(s):  
Initial Conditions ◽  
Oscillation Amplitude ◽  
Reduced Model ◽  
Limit Cycle Oscillation ◽  
Nonlinear Friction ◽  
Disk Model ◽  
Friction Forces ◽  
Elastic Oscillation ◽  
Time Modulation ◽  
Bladed Disk

The computation of the final, friction saturated Limit Cycle Oscillation amplitude of an aerodynamically unstable bladeddisk in a realistic configuration is a formidable numerical task. In spite of the large numerical cost and complexity of the simulations, the output of the system is not that complex: it typically consists of an aeroelastically unstable traveling wave (TW), which oscillates at the elastic modal frequency and exhibits a modulation in a much longer time scale. This slow time modulation over the purely elastic oscillation is due to both, the small aerodynamic effects and the small nonlinear friction forces. The correct computation of these two small effects is crucial to determine the final amplitude of the flutter vibration, which basically results from its balance. In this work we apply asymptotic techniques to consistently derive, from a bladed-disk model, a reduced order model that gives only the time evolution on the slow modulation, filtering out the fast elastic oscillation. This reduced model is numerically integrated with very low CPU cost, and we quantitatively compare its results with those from the bladed-disk model. The analysis of the friction saturation of the flutter instability also allows us to conclude: (i) that the final states are always nonlinearly saturated TW, (ii) that, depending on the initial conditions, there are several different nonlinear TWs that can end up being a final state, and (iii) that the possible final TWs are only the more flutter prone ones.

Flutter Amplitude Saturation by Nonlinear Friction Forces: Reduced Model Verification

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
Carlos Martel ◽  
Roque Corral ◽  
Rahul Ivaturi
Keyword(s):  
Oscillation Amplitude ◽  
Computational Cost ◽  
Model Verification ◽  
Reduced Model ◽  
Limit Cycle Oscillation ◽  
Nonlinear Friction ◽  
Disk Model ◽  
Friction Forces ◽  
Elastic Oscillation ◽  
Bladed Disk

The computation of the final, friction saturated limit cycle oscillation amplitude of an aerodynamically unstable bladed-disk in a realistic configuration is a formidable numerical task. In spite of the large numerical cost and complexity of the simulations, the output of the system is not that complex: it typically consists of an aeroelastically unstable traveling wave (TW), which oscillates at the elastic modal frequency and exhibits a modulation in a much longer time scale. This slow time modulation over the purely elastic oscillation is due to both the small aerodynamic effects and the small nonlinear friction forces. The correct computation of these two small effects is crucial to determine the final amplitude of the flutter vibration, which basically results from its balance. In this work, we apply asymptotic techniques to consistently derive, from a bladed-disk model, a reduced order model that gives only the time evolution on the slow modulation, filtering out the fast elastic oscillation. This reduced model is numerically integrated with very low computational cost, and we quantitatively compare its results with those from the bladed-disk model. The analysis of the friction saturation of the flutter instability also allows us to conclude that: (i) the final states are always nonlinearly saturated TW; (ii) depending on the initial conditions, there are several different nonlinear TWs that can end up being a final state; and (iii) the possible final TWs are only the more flutter prone ones.

Flutter Amplitude Saturation by Nonlinear Friction Forces: An Asymptotic Approach

2013 ◽  
Author(s):  
C. Martel ◽  
R. Corral
Keyword(s):  
Traveling Waves ◽  
Large Time ◽  
Asymptotic Model ◽  
Nonlinear Friction ◽  
Friction Forces ◽  
Elastic Oscillation ◽  
Time Dynamics ◽  
Time Modulation ◽  
Bladed Disk ◽  
Linear Friction

The computation of the friction saturated vibratory response of an aerodynamically unstable bladed-disk in a realistic configuration is a formidable numerical task, even for the simplified case of assuming the aerodynamic forces to be linear. The non-linear friction forces effectively couple different traveling waves modes and, in order to properly capture the dynamics of the system, large time simulations are typically required to reach a final, saturated state. Despite of all the above complications, the output of the system (in the friction microslip regime) is not that complex: it typically consists of a superposition of the aeroelastic unstable traveling waves, which oscillate at the elastic modal frequency and exhibit also a modulation in a much longer time scale. This large time modulation over the purely elastic oscillation is due to both, the small aerodynamic effects and the small nonlinear friction forces. The correct computation of these two small effects (small as compared with the elastic forces) is crucial to determine the final amplitude of the flutter vibration, which basically results from its balance. In this work we apply asymptotic techniques to obtain a new simplified model that gives only the slow time dynamics of the amplitudes of the traveling waves, filtering out the fast elastic oscillation. The resulting asymptotic model is very reduced and extremely cheap to simulate, and it has the advantage that it gives precise information about how the nonlinear friction at the fir-tree actually acts in the process of saturation of the vibration amplitude.

Asymptotic Description of Forced Response Vibration Saturation by Friction Forces

2019 ◽  
Author(s):  
Carlos Martel ◽  
Juan A. Martín
Keyword(s):  
Multiple Scales ◽  
Forced Response ◽  
Limit Cycle Oscillation ◽  
Asymptotic Model ◽  
Phase Lag ◽  
Nonlinear Friction ◽  
Friction Forces ◽  
Essential Information ◽  
Bladed Disk ◽  
Mass Spring

Abstract The estimation of the final vibration amplitude of a turbomachinery bladed disk is of extreme practical importance; it is an essential information for the prediction of the level of high cycle fatigue of the blades, and for the subsequent estimation of its operative life span. The forced response vibration is saturated by the nonlinear damping introduced by the friction forces at the interfaces between blade and disk (and/or at the included dampers). The computation of the final amplitude of the limit cycle oscillation requires to solve a quite complicated nonlinear problem. In the case of a tuned bladed disk, this problem can be reduced to a single sector calculation with phase lag boundary conditions. The solution of this one-sector problem requires to consider many harmonics in order to capture the details of the nonlinear time periodic oscillation that sets in. If the small unavoidable differences among blades (mistuning) are also taken into account, then the situation becomes even more complicated because the solution of the mistuned vibration problem requires to consider not only a single sector but the complete bladed disk. The possibility of applying multiple scales techniques to drastically simplify this problem is explored in this paper. The idea is to exploit the fact that all relevant effects present (forcing, nonlinear friction, and mistuning) are, in most practical situations, small effects that develop in a time scale that is much longer than that associated with the natural elastic vibration frequency of the tuned system. A mass-spring model with microslip nonlinear friction is used to represent the forced bladed disk. The multiple scales method is used to asymptotically derive simplified models for both tuned and mistuned configurations. The results of the asymptotic model are compared with those from the mass-spring system, and used to analyze the particular characteristics of the nonlinear friction effects on the final vibration states.

Asymptotic Description of Forced Response Vibration Saturation by Friction Forces

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Carlos Martel ◽  
Juan A. Martín
Keyword(s):  
Multiple Scales ◽  
Forced Response ◽  
Limit Cycle Oscillation ◽  
Asymptotic Model ◽  
Phase Lag ◽  
Nonlinear Friction ◽  
Friction Forces ◽  
Essential Information ◽  
Bladed Disk ◽  
Mass Spring

Abstract The estimation of the final vibration amplitude of a turbomachinery bladed disk is of extreme practical importance; it is an essential information for the prediction of the level of high cycle fatigue of the blades and for the subsequent estimation of its operative life span. The forced response vibration is saturated by the nonlinear damping introduced by the friction forces at the interfaces between blade and disk (and/or at the included dampers). The computation of the final amplitude of the limit cycle oscillation requires to solve a quite complicated nonlinear problem. In the case of a tuned bladed disk, this problem can be reduced to a single sector calculation with phase lag boundary conditions. The solution of this one-sector problem requires to consider many harmonics in order to capture the details of the nonlinear time periodic oscillation that sets in. If the small unavoidable differences among blades (mistuning) are also taken into account, then the situation becomes even more complicated because the solution of the mistuned vibration problem requires to consider not only a single sector but also the complete bladed disk. The possibility of applying multiple scales techniques to drastically simplify this problem is explored in this paper. The idea is to exploit the fact that all relevant effects present (forcing, nonlinear friction, and mistuning) are, in most practical situations, small effects that develop in a time scale that is much longer than that associated with the natural elastic vibration frequency of the tuned system. A mass-spring model with microslip nonlinear friction is used to represent the forced bladed disk. The multiple scales method is used to asymptotically derive simplified models for both tuned and mistuned configurations. The results of the asymptotic model are compared with those from the mass-spring system and used to analyze the particular characteristics of the nonlinear friction effects on the final vibration states.

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks

2004 ◽  
Vol 126 (1) ◽  
pp. 175-183 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Disk Model ◽  
Sector Model ◽  
Bladed Disk ◽  
Symmetry Properties

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disk using a periodic sector model without any loss of accuracy in calculations and modeling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disk forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disk model: (i) using sector finite element matrices and (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disk with shrouds have demonstrated the high efficiency of the method.

Identification of Structural Parameters in Mistuned Bladed Disks

1997 ◽  
Vol 119 (3) ◽  
pp. 428-438 ◽  
Author(s):  
Marc P. Mignolet ◽  
Chung-Chih Lin
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Structural Model ◽  
Structural Parameters ◽  
Model Parameters ◽  
Disk Model ◽  
Response Data ◽  
State Response ◽  
Bladed Disk ◽  
True Model

The present investigation focused on the estimation of the parameters of a structural model to represent “at best” a set of measurements of the steady state response of a mistuned bladed disk. The applicability of the least squares and maximum likelihood approaches to the identification of the bladed disk model from this data is first investigated. The advantages and drawbacks of these techniques motivate the introduction of a new mixed least squares-maximum likelihood formulation which is shown to recover well the true model parameters from noisy simulated response data.

Vibration Suppression of Mistuned Coupled-Blade-Disk Systems Using Piezoelectric Circuitry Network

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Hongbiao Yu ◽  
K. W. Wang
Keyword(s):  
Piezoelectric Transducer ◽  
Vibration Suppression ◽  
Structural Vibration ◽  
Bladed Disks ◽  
Disk Model ◽  
Bladed Disk ◽  
Engine Order ◽  
Optimal Network ◽  
Random Mistuning ◽  
Engine Components

For bladed-disk assemblies in turbomachinery, the elements are often exposed to aerodynamic loadings, the so-called engine order excitations. It has been reported that such excitations could cause significant structural vibration. The vibration level could become even more excessive when the bladed disk is mistuned, and may cause fatigue damage to the engine components. To effectively suppress vibration in bladed disks, a piezoelectric transducer networking concept has been explored previously by the authors. While promising, the idea was developed based on a simplified bladed-disk model without considering the disk dynamics. To advance the state of the art, this research further extends the investigation with focus on new circuitry designs for a more sophisticated and realistic system model with the consideration of coupled-blade-disk dynamics. A novel multicircuit piezoelectric transducer network is synthesized and analyzed for multiple-harmonic vibration suppression of bladed disks. An optimal network is derived analytically. The performance of the network for bladed disks with random mistuning is examined through Monte Carlo simulation. The effects of variations (mistuning and detuning) in circuit parameters are also studied. A method to improve the system performance and robustness utilizing negative capacitance is discussed. Finally, experiments are carried out to demonstrate the vibration suppression capability of the proposed piezoelectric circuitry network.

scholarly journals Mistuning Effects on the Nonlinear Friction Saturation of Flutter Vibration Amplitude

2020 ◽  
Author(s):  
Carlos Martel ◽  
Salvador Rodríguez
Keyword(s):  
Vibration Amplitude ◽  
Gas Flow ◽  
Travelling Waves ◽  
Computational Cost ◽  
Travelling Wave ◽  
Nonlinear Friction ◽  
Blade Vibration ◽  
Bladed Disk ◽  
Spring System ◽  
Mass Spring

Abstract The blade vibration level of an aerodynamically unstable rotor is a quantity of crucial importance to correctly estimate the blade fatigue life. This amplitude is the result of the balance between the energy pumped into the blades by the gas flow, and the nonlinear dissipation at the blade-disk contact interfaces. In a tuned configuration, the blade displacements can be described as a travelling wave consisting of one fundamental nodal diameter and frequency and its higher harmonics, and the problem can be reduced to the computation of a time periodic solution in just one sector. This simplification is no longer valid for a mistuned bladed disk. The resulting nonlinear vibration of the mistuned system is a combination of several travelling waves with different number of nodal diameters, coupled through mistuning. In this case, the complete bladed disk has to be considered, which requires an extremely high computational cost, and, for this reason, reduced order models (ROM) are required to analyze this situation. In this work, we use a 3 DOF/sector mass-spring system to describe the nonlinear friction saturation of the flutter vibration amplitude of a realistic mistuned bladed disk. The convergence of the solution of the mass-spring system is still quite slow because of the presence of many unstable modes with very similar growth rates. In order to speed-up the simulations a simpler asymptotic ROM is derived from the mass-spring model, which allows for much faster integration times. The simulations of the asymptotic ROM are compared with the measurements obtained in the European project FUTURE, where an aerodynamically unstable LPT rotor was tested with different intentional mistuning patterns.

The Stick Motion of a Harmonically Excited, Friction-Induced Oscillator on a Sinusoidally Traveling Surface

2006 ◽  
Author(s):  
Albert C. J. Luo ◽  
Brandon C. Gegg ◽  
Steve S. Suh
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Dry Friction ◽  
The Other ◽  
Linear Oscillator ◽  
Analytical Prediction ◽  
Nonlinear Friction ◽  
Friction Forces

In this paper, the methodology is presented through investigation of a periodically, forced linear oscillator with dry friction, resting on a traveling surface varying with time. The switching conditions for stick motions in non-smooth dynamical systems are obtained. From defined generic mappings, the corresponding criteria for the stick motions are presented through the force product conditions. The analytical prediction of the onset and vanishing of the stick motions is illustrated. Finally, numerical simulations of stick motions are carried out to verify the analytical prediction. The achieved force criteria can be applied to the other dynamical systems with nonlinear friction forces possessing a CO - discontinuity.

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