scholarly journals Non-Linear Modal Analysis for Bladed Disks With Friction Contact Interfaces

2008 ◽  
Author(s):  
Denis Laxalde ◽  
Loi¨c Salles ◽  
Laurent Blanc ◽  
Fabrice Thouverez
Keyword(s):  
Modal Analysis ◽  
Equations Of Motion ◽  
Dynamical Behaviour ◽  
Forced Response ◽  
Fretting Wear ◽  
External Excitation ◽  
Bladed Disk ◽  
Dynamical Simulation ◽  
Modal Damping ◽  
Non Linear

A method for non-linear modal analysis of mechanical systems with contact and friction interfaces is proposed. It is based on a frequency domain formulation of the dynamical system’s equations of motion. The dissipative aspects of these non-linearities result in complex eigensolutions and the modal parameters (natural frequency and modal damping) can be obtained without any assumptions on the external excitation. The generality of this approach makes it possible to address any kind of periodic regimes, in free and forced response. In particular, stability analysis in flutter applications can be performed. Applications for the design of friction ring dampers for blisks and for the dynamical simulation of bladed disk with dovetail attachment are proposed. Finally, we propose a study of dynamical behaviour coupling with the calculation of fretting-wear at the interfaces based on non-linear modal characterization.

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.

An Efficient Response Analysis Method for a Non-Linear/Parameter Changing System Using Sub-Structure Modes

1993 ◽  
Vol 207 (1) ◽  
pp. 41-52
Author(s):  
H K Kim ◽  
Y-S Park
Keyword(s):  
Equations Of Motion ◽  
Forced Response ◽  
Suggested Method ◽  
Response Analysis ◽  
Synthesis Methods ◽  
Lumped Mass ◽  
State Equations ◽  
Mass Model ◽  
Non Linear ◽  
Forced Responses

An efficient state-space method is presented to determine time domain forced responses of a structure using the Lagrange multiplier based sub-structure technique. Compared with the conventional mode synthesis methods, the suggested method can be particularly effective for the forced response analysis of a structure subjected to parameter changes with time, such as a missile launch system, and/or having localized non-linearities, because this method does not need to construct the governing equations of the combined whole structure. Both the loaded interface free-free modes and free interface modes can be employed as the modal bases of each sub-structure. The sub-structure equations of motion are derived using Lagrange multipliers and recurrence discrete-time state equations based upon the concept of the state transition matrix are formulated for transient response analysis. The suggested method is tested with two example structures, a simple lumped mass model with a non-linear joint and an abruptly parameter changing structure. The test results show that the suggested method is very accurate and efficient in calculating forced responses and in comparing it with the direct numerical integration method.

Modal Analysis of Multi Layer Viscoelastic Rotors Considering Higher Order Model

2013 ◽  
Author(s):  
S. Chandraker ◽  
H. Roy ◽  
G. Maurya
Keyword(s):  
Modal Analysis ◽  
Equations Of Motion ◽  
Stability Limit ◽  
Higher Order ◽  
Constitutive Relationship ◽  
Order System ◽  
Order Model ◽  
Rotor Shaft ◽  
Number Of Layers ◽  
Modal Damping

This paper involves the development of mathematical model of multilayered viscoelastic rotor using beam finite element and at the same time studying their modal analysis. The operator based constitutive relationship is used to obtain the equations of motion. The FE formulation contents higher order system where the number of order increases with the number of layers exists in the rotor shaft. Under these conditions, the complex modal behaviour of the rotor-shaft is studied to get an insight of the dynamic characteristics of the system, in terms of Modal Damping Factors, Stability Limit of Spin-speed (SLS), the directional Frequency Response Function (dFRF) as well as the direction of whirl of the shaft in different modes. Many researchers adopted this methodology for obtaining the dynamic behaviour of a second order system. This work is started by motivation of the absentia of work for higher order system.

Powertrain Resilient Mounting Design Analysis

2018 ◽  
Author(s):  
Tigran Parikyan ◽  
Nikola Naranca ◽  
Jochen Neher
Keyword(s):  
Rigid Body ◽  
Modal Analysis ◽  
Frequency Domain ◽  
Static Analysis ◽  
Software Tool ◽  
Software Tools ◽  
Forced Response ◽  
Marine Engine ◽  
Linear Elastic ◽  
Non Linear

For efficient modeling of engine (or powertrain) supported by non-linear elastic mounts, a special methodology has been elaborated. Based on it, software tool has been developed to analyze the motion of rigid body and elastic mounts, which comprises of three modules: • Non-linear static analysis; • Modal analysis (undamped and damped); • Forced response (in frequency domain). Application example of a large V12 marine engine illustrates the suggested workflow. The results are verified against other software tools and validated by measurements.

Investigation of Damping Potential of Strip Damper on a Real Turbine Blade

2016 ◽  
Author(s):  
M. Afzal ◽  
I. Lopez Arteaga ◽  
L. Kari ◽  
V. Kharyton
Keyword(s):  
Boundary Conditions ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Element Model ◽  
Forced Response ◽  
Contact Forces ◽  
Response Analysis ◽  
Bladed Disk ◽  
Different Types

This paper investigates the damping potential of strip dampers on a real turbine bladed disk. A 3D numerical friction contact model is used to compute the contact forces by means of the Alternate Frequency Time domain method. The Jacobian matrix required during the iterative solution is computed in parallel with the contact forces, by a quasi-analytical method. A finite element model of the strip dampers, that allows for an accurate description of their dynamic properties, is included in the steady-state forced response analysis of the bladed disk. Cyclic symmetry boundary conditions and the multiharmonic balance method are applied in the formulation of the equations of motion in the frequency domain. The nonlinear forced response analysis is performed with two different types of boundary conditions on the strip: (a) free-free and (b) elastic, and their influence is analyzed. The effect of the strip mass, thickness and the excitation levels on the forced response curve is investigated in detail.

scholarly journals Non-linear modal analysis of the forced response of structural systems

1996 ◽  
Author(s):  
Nicolas Boivin ◽  
Christophe Pierre ◽  
Steven Shaw
Keyword(s):  
Modal Analysis ◽  
Forced Response ◽  
Structural Systems ◽  
Non Linear

scholarly journals Test-Model Correlation of Dry-Friction Damping Phenomena in Aero-Engines

2008 ◽  
Author(s):  
P. Jean ◽  
C. Gibert ◽  
C. Dupont ◽  
J.-P. Lombard
Keyword(s):  
Dry Friction ◽  
Forced Response ◽  
Test Model ◽  
Friction Damping ◽  
Bladed Disks ◽  
Friction Dampers ◽  
Bladed Disk ◽  
Resonance Frequencies ◽  
Non Linear ◽  
Aero Engines

In order to control the risk of high cycle fatigue of bladed disks, it is important to predict precisely the vibration levels and to design damping solutions to attenuate them. Therefore, Snecma has made some efforts in the last years in order to characterize better the damping in aero-engines. Among the various damping sources, friction damping is particularly difficult to model due to its non-linear behaviour [1]. For that purpose, two methods based on multi-harmonic balance strategy have been especially developed for Snecma, dedicated to the study of the non-linear forced response of bladed disks. The first one enables to model the bladed disk equipped with dry-friction dampers [2], and the second one takes into account intrinsic friction located in disk-blade interface [3]. To validate both models experimentally, a test campaign has been carried out in a vacuum chamber on a rotating bladed disk excited by piezoelectric actuators. The blade shanks have been softened in order to increase friction effects. Experimental results show a regular and reproducible behaviour of the non-linear forced response, over various rotation speed and excitation levels. The contributions of friction dampers and friction in blade attachment have been decoupled thanks to glue applied in the blade root. Both friction phenomena that were observed experimentally at resonance of the blade first bending mode have been reproduced numerically. After updating modeling parameters, an acceptable correlation was found on resonance frequencies, amplitudes and damping levels over the full experimental setup range, which validates these numerical tools for their use in design process.

A Comparative Study on the Dynamic Characteristics of Bladed Disks With Piezoelectric Network and Piezoelectric Shunt Circuit

2016 ◽  
Author(s):  
Jiuzhou Liu ◽  
Lin Li ◽  
Pengcheng Deng ◽  
Chao Li
Keyword(s):  
Modal Analysis ◽  
Dynamic Characteristics ◽  
Energy Analysis ◽  
Vibration Suppression ◽  
Forced Response ◽  
Bladed Disks ◽  
Electromechanical Systems ◽  
Bladed Disk ◽  
Engine Order ◽  
Shunt Circuit

This paper is meant to contribute a further investigation of the dynamic characteristics of the bladed disks with piezo-network and piezo-shunt circuit. The non-engine-order (NEO) excitation is taken into account from a practical point of view, and the mechanisms of vibration suppression of the two electromechanical systems are explained by means of the modal analysis and the energy analysis. First of all, the dynamic equations are derived based on a lumped parameter electromechanical model, and a normalizing process is used to make the analysis results more general. After the modal analysis of the electromechanical systems, the vibration suppression effect is analyzed when the bladed disk is excited by the engine-order (EO) excitation and the NEO excitation respectively. Then, an energy analysis of the electromechanical systems is performed to understand the dynamic behaviors of the systems better. Finally, the effect of reducing the amplitude magnification of the mistuned bladed disk is investigated. The research results turn out that the electrical natural frequencies (induced by electrical elements) of the system with piezo-shunt circuit are dense, while those of the system with piezo-network are not. When the system is excited by an EO excitation, the energy dissipated by resistors in the shunt circuit is slightly more than that in the network. However, the former is much less than the latter when the system is excited by an NEO excitation. A statistical analysis has been performed and proved that both the piezo-shunt circuit and the piezo-network can compensate the amplitude magnification of the forced response induced by mistuning, and the piezo-network has a better performance when the bladed disk is excited by an NEO excitation.

A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part I: Theoretical Basis

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
O. G. McGee ◽  
C. Fang ◽  
Y. El-Aini
Keyword(s):  
Finite Element ◽  
Predictive Accuracy ◽  
Equations Of Motion ◽  
Response Prediction ◽  
Companion Paper ◽  
Energy Model ◽  
Forced Response ◽  
Bladed Disks ◽  
Reduced Order ◽  
Bladed Disk

In this paper, a reduced order model for the vibrations of bladed disk assemblies was achieved. The system studied was a 3D annulus of shroudless, “custom-tailored,” mistuned blades attached to a flexible disk. Specifically, the annulus was modeled as a spectral-based “meshless” continuum structure utilizing only nodal data to describe the arbitrary volume in which the system's dynamical energy was minimized. An extended Ritz variational procedure was used to minimize this energy, subjected to constraints imposed by an assumed 3D displacement field of mathematically complete, orthonormal “blade-disk” polynomials multiplied by generalized coefficients. The coefficients were determined by constraining the polynomial series to satisfy the extended Ritz stationary equations and essential boundary conditions of the bladed disk. From this, the governing equations of motion were generated into their usual dynamical forms to calculate upper-bounds on the actual free and forced responses of bladed disks. No conventional finite elements and element connectivity or component substructuring data were needed. This paper, Part I, outlines the theoretical foundation of the present model, and through extensive Monte Carlo simulations, establishes the analytical basis, predictive accuracy, and re-analysis efficiency of the present technology in the prediction of 3D maximum response amplitude of mistuned bladed disks having increasing numbers of nodal diameter excitations. Further applications validating the 3D approach against conventional finite element procedures of free and forced response prediction of a mistuned Integrally-Bladed Rotor used in practice is presented in a companion paper, Part II (Fang, McGee, and El-Aini, 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part II: Finite Element Benchmark Comparisons, ASME J. Turbomach., to be published.

Non-Linear Forced Response Analysis of Mistuned Bladed Disk Assemblies

2010 ◽  
Author(s):  
M. Ersin Yu¨mer ◽  
Ender Cig˘erog˘lu ◽  
H. Nevzat O¨zgu¨ven
Keyword(s):  
Degrees Of Freedom ◽  
Linear Equations ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Contact Forces ◽  
Response Analysis ◽  
Disk Model ◽  
Bladed Disk ◽  
Non Linear ◽  
Linear Elements

Forced response analysis of bladed disk assemblies plays a crucial role in rotor blade design, and therefore has been investigated by researchers extensively. However, due to lack of computation power, several studies in the literature utilize either linear mistuned models which are short of capturing nonlinear effects, or non-linear tuned models which do not catch the effects of mistuning. Studying the combined effect of the two, namely non-linearity and mistuning, is relatively recent and generally conducted with methods whose convergence and accuracy depend highly on the number of degrees of freedom related with the non-linear elements. In this paper, a new approach is proposed to predict forced response of frictionally damped mistuned bladed disk assemblies in modal domain. A friction element, which enables normal load variation and separation of the contact interface, is utilized to determine the non-linear contact forces in three-dimensional space, and harmonic balance method is used to obtain a relationship between the non-linear contact forces and the relative motion. As mistuning phenomenon destroys the cyclic symmetry, modeling the whole assembly rather than a sector of it is necessary, which increases the number of non-linear elements required considerably. In the proposed approach, the analysis is carried out in modal domain where the differential equations of motions are converted to a set of non-linear algebraic equations using harmonic balance method and modal superposition technique. Thus, the number of non-linear equations to be solved is proportional to the number of modes retained, rather than the number of degrees of freedom related with the nonlinear elements. Therefore, the proposed approach can be applied to realistic bladed disk models without increasing the number of non-linear equations. Moreover, to accomplish this it is not required to use a reduced order model in the method suggested. Two case studies are presented to illustrate the implementation of the method: a lumped parameter bladed disk model and an academic bladed disk model with shrouds.

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