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.

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.

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.

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.

scholarly journals Nonlinear Modal Analysis of Mistuned Periodic Structures Subjected to Dry Friction

2015 ◽  
Vol 138 (7) ◽  
Author(s):  
C. Joannin ◽  
B. Chouvion ◽  
F. Thouverez ◽  
M. Mbaye ◽  
J.-P. Ousty
Keyword(s):  
Dry Friction ◽  
Periodic Structures ◽  
Forced Response ◽  
Wave Excitation ◽  
Free Response ◽  
Friction Forces ◽  
Bladed Disk ◽  
Complex Modes ◽  
Nonlinear Modal Analysis ◽  
The Impact

This paper deals with the dynamics of a cyclic system, representative of a bladed disk subjected to dry friction forces, and exhibits structural mistuning. The nonlinear complex modes are computed by solving the eigenproblem associated to the free response of the whole structure and are then used to better understand the forced response to a traveling wave excitation. Similarly to the underlying linear system, the tuned model possesses pairs of modes that can be linearly combined to form traveling waves, unlike those of the mistuned structure. However, due to the nonlinearity, the modal properties are not constant but vary with the vibration amplitude in both cases. A qualitative analysis is also performed to assess the impact of the mistuning magnitude on the response and suggests that further statistical investigations could be of great interest for the design of bladed-disks, in terms of vibration mitigation and robustness.

scholarly journals Asymptotic Description of Maximum Mistuning Amplification of Bladed Disk Forced Response

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Carlos Martel ◽  
Roque Corral
Keyword(s):  
Upper Bound ◽  
Amplification Factor ◽  
Forced Response ◽  
Spring Model ◽  
Bladed Disk ◽  
Mass Spring Model ◽  
Amplification Process ◽  
Simple Mass ◽  
Response Amplification ◽  
Mass Spring

The problem of determining the maximum forced response vibration amplification that can be produced just by the addition of a small mistuning to a perfectly cyclical bladed disk still remains not completely clear. In this paper we apply a recently introduced perturbation methodology, the asymptotic mistuning model (AMM), to determine which are the key ingredients of this amplification process and to evaluate the maximum mistuning amplification factor that a given modal family with a particular distribution of tuned frequencies can exhibit. A more accurate upper bound for the maximum forced response amplification of a mistuned bladed disk is obtained from this description, and the results of the AMM are validated numerically using a simple mass-spring model.

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.

Sign in / Sign up

Export Citation Format

Share Document