Non-Linear Vibrations of Multi-Stage Bladed Disks Systems With Friction Ring Dampers

2007 ◽  
Author(s):  
Denis Laxalde ◽  
Fabrice Thouverez
Keyword(s):  
Harmonic Balance Method ◽  
Forced Response ◽  
Bladed Disks ◽  
Friction Forces ◽  
Friction Dampers ◽  
Multi Stage ◽  
Non Linear ◽  
Time Domains ◽  
Linear Vibrations ◽  
Stage System

In this paper, we study the non-linear dynamics of a multi-stage system of turbomachinery bladed disks with friction dampers. We focus on the quasi-periodic forced response of this system under multi-frequency rotating excitations. The system’s equations of the motion are expressed in the multi-frequency domain using a multi-frequency harmonic balance method in combination a multi-stage cyclic symmetry reduction. A Dynamic Lagrangian formulation in alternating frequency/time domains is also used for the calculation of the contact and friction forces. In applications we consider a system of two HP compressor stages of integrally bladed disks with friction ring dampers.

Design Methods of Friction Damping at Blade-Disk Joints

2009 ◽  
Author(s):  
Jie Hong ◽  
Lulu Chen ◽  
Yanhong Ma ◽  
Xin Yang
Keyword(s):  
Low Frequency ◽  
Harmonic Balance Method ◽  
Large Error ◽  
Forced Response ◽  
Mode Shapes ◽  
Bladed Disks ◽  
Friction Dampers ◽  
Tracking Motion ◽  
Nonlinear Force ◽  
Free Mode

Friction at blade-disk joints is an important source of damping that reduces low frequency resonant amplitudes to acceptable levels in blade-disk assemblies. An effective method is proposed to predict nonlinear forced response of bladed disks taking account of the nonlinear force at blade-disk joints in frequency domain, which syncretizes the excellencies of harmonic balance method, dynamic softness method and tracking motion method. Constrained Mode Shapes are introduced to express the relative motion which occurs at the contact interfaces of blade roots. Compared to using free mode shapes, fewer number of constrained mode shapes is required in order to obtain the accurate resonant response of a system with friction dampers when the contact state is fully stick. It is more efficient to predict the nonlinear forced response of bladed disks taking account of the nonlinear force at blade-disk joints. Based on this method, the effect of Boundary Conditions on the resonant frequencies and forced response levels under different engine rotational speeds is investigated. Large error in the prediction of forced response levels under low engine rotational speed by using traditional methods is found. The effects of preload distribution at blade roots and excitation level are also investigated.

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.

Reduced Order Modeling for Multi-Stage Bladed Disks With Friction Contacts at the Flange Joint

2017 ◽  
Author(s):  
Giuseppe Battiato ◽  
Christian M. Firrone ◽  
Teresa M. Berruti ◽  
Bogdan I. Epureanu
Keyword(s):  
Displacement Field ◽  
Fourier Coefficients ◽  
Normal Modes ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Contact Forces ◽  
Single Stage ◽  
Bladed Disks ◽  
Reduced Order ◽  
Multi Stage

Most aircraft turbojet engines consist of multiple stages coupled by means of bolted flange joints which potentially represent source of nonlinearities due to friction phenomena. Methods aimed at predicting the forced response of multi-stage bladed disks have to take into account such nonlinear behavior and its effect in damping blades vibration. In this paper a novel reduced order model is proposed for studying nonlinear vibration due to contacts in multi-stage bladed disks. The methodology exploits the shape of the single-stage normal modes at the inter-stage boundary being mathematically described by spatial Fourier coefficients. Most of the Fourier coefficients represent the dominant kinematics in terms of the well-known nodal diameters (standard harmonics), while the others, which are detectable at the inter-stage boundary, correspond to new spatial small wavelength phenomena named as extra harmonics. The number of Fourier coefficients describing the displacement field at the inter-stage boundary only depends on the specific engine order excitation acting on the multi-stage system. This reduced set of coefficients allows the reconstruction of the physical relative displacement field at the interface between stages and, under the hypothesis of the Single Harmonic Balance Method, the evaluation of the contact forces by employing the classic Jenkins contact element. The methodology is here applied to a simple multi-stage bladed disk and its performance is tested using as a benchmark the Craig-Bampton reduced order models of each single-stage.

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.

scholarly journals Modeling of Friction Contact and its Application to the Design of Shroud Contact

1996 ◽  
Author(s):  
Been-Der Yang ◽  
Chia-Hsiang Menq
Keyword(s):  
Friction Force ◽  
Normal Load ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Effective Stiffness ◽  
Force Model ◽  
Friction Forces ◽  
Friction Joint ◽  
Stiffness And Damping

Designers of aircraft engines frequently employ shrouds in turbine design. In this paper, a variable normal load friction force model is proposed to investigate the influence of shroud-like contact kinematics on the forced response of frictionally constrained turbine blades. Analytical criteria are formulated to predict the transitions between slick, slip, and separation of the interface so as to assess the induced friction forces. When considering cyclic loading, the induced friction forces are combined with the variable normal load so as to determine the effective stiffness and damping of the friction joint over a cycle of motion. The harmonic balance method is then used to impose the effective stiffness and damping of the friction joint on the linear structure. The solution procedure for the nonlinear response nf a two-degree-of-freedom oscillator is demonstrated. As an application, this procedure is used to study the coupling effect of two constrained forces, friction force and variable normal load, on the optimization of the shroud contact design.

Characterization of Contact Kinematics and Application to the Design of Wedge Dampers in Turbomachinery Blading: Part 1—Stick-Slip Contact Kinematics

1998 ◽  
Vol 120 (2) ◽  
pp. 410-417 ◽  
Author(s):  
B. D. Yang ◽  
C. H. Menq
Keyword(s):  
Friction Force ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Operating Conditions ◽  
Force Model ◽  
Blade Vibration ◽  
Stick Slip ◽  
Friction Forces ◽  
Contact Kinematics ◽  
Stiffness And Damping

Friction dampers are often used in turbine design to attenuate blade vibration to acceptable levels so as to prolong blades’ service life. A wedge damper, also called a self-centering, blade-to-blade damper, can provide more design flexibility to meet various needs in different operating conditions when compared with conventional platform dampers. However, direct coupling of the two inclined friction interfaces of the wedge damper often leads to very complex contact kinematics. In Part I of this two-part paper, a dual-interface friction force model is proposed to investigate the coupling contact kinematics. The key issue of the model formulation is to derive analytical criteria for the stick-slip transitions that can be used to precisely simulate the complex stick-slip motion and, thus, the induced friction force as well. When considering cyclic loading, the induced periodic friction forces can be obtained to determine the effective stiffness and damping of the interfaces over a cycle of motion. In Part II of this paper, the estimated stiffness and damping are then incorporated with the harmonic balance method to predict the forced response of a blade constrained by wedge dampers.

Forced Response of Interlocked Vane Segments: Numerical Predictions and Experimental Results

2006 ◽  
Author(s):  
Stefano Zucca ◽  
Sergio Filippi ◽  
Fabio Droetti ◽  
Muzio M. Gola
Keyword(s):  
Tangential Force ◽  
Harmonic Balance Method ◽  
Outer Radius ◽  
Forced Response ◽  
Experimental Results ◽  
Numerical Code ◽  
Friction Forces ◽  
Normal Contact ◽  
Numerical Predictions ◽  
Local Compliance

Resonant vibrations affect fatigue life of vane segments. Friction damping is employed to reduce vibration amplitude. When vane segments are assembled, they are twisted so that lower platforms are in contact. The sum of displacements of the two ends of the lower platform after twisting is defined ‘interlocking’. Different ‘interlocking’ values correspond to different values of normal contact force. When interlocked vanes vibrate under external force excitation, energy is dissipated by friction forces at lower platform contacts providing damping to the system. The aim of this paper is the experimental validation of a numerical code for forced response calculation of interlocked vane segments. Since friction forces depend on relative displacements of bodies in contact, the system is nonlinear. System force response is computed by means of Harmonic Balance Method (HBM). Contact model implemented in the code is characterised by tangential and normal stiffness to take into account local compliance of the contact area. Gross slip occurs when the instantaneous ratio of tangential force to normal force is equal to the friction coefficient. Also effect of microslip is taken in account. The experimental set-up used to validate the code is made of a vane segment fixed at the outer radius to an aluminium frame and in contact with two supports at the inner radius. Comparison between the numerical predictions and experimental results is performed for different values of interlocking (i.e. force normal to the contact).

Forced Response of Bladed Disks in Cyclic Symmetry With Underplatform Dampers

2006 ◽  
Author(s):  
Stefano Zucca ◽  
Juan Borrajo ◽  
Muzio M. Gola
Keyword(s):  
Contact Stiffness ◽  
Harmonic Balance Method ◽  
Rigid Bodies ◽  
Forced Response ◽  
Numerical Code ◽  
Algebraic Equations ◽  
Bladed Disks ◽  
Disk Model ◽  
Normal Contact ◽  
Linear Algebraic Equations

In this paper a methodology for forced response calculation of bladed disks with underplatform dampers is described. The FE disk model, supposed to be cyclically symmetric, is reduced by means of Component Mode Synthesis and then DOFs lying at interfaces are further reduced by means of interface modes. Underplatform dampers are modeled as rigid bodies translating both in the radial and in the tangential direction of the engine. Contacts between blade platforms and damper are simulated by means of contact elements characterized by both tangential and normal contact stiffness, allowing partial separation of contact surfaces. Differential equilibrium equations are turned in non-linear algebraic equations by means of the Harmonic Balance Method (HBM). The methodology is implemented in a numerical code for forced response calculation of frictionally damped bladed disks. Numerical calculations are performed to evaluate the effectiveness of both the reduced order model and the underplatform model in simulating the dynamic behavior of bladed disks in presence of underplatform dampers.

Explicit Finite Element Models of Friction Dampers in Forced Response Analysis of Bladed Disks

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Finite Element ◽  
Large Scale ◽  
Dynamic Properties ◽  
Forced Response ◽  
Response Analysis ◽  
Contact Interactions ◽  
Contact Interface ◽  
Bladed Disks ◽  
Explicit Finite Element ◽  
Friction Dampers

A generic method for analysis of nonlinear forced response for bladed disks with friction dampers of different designs has been developed. The method uses explicit finite element modeling of dampers, which allows accurate description of flexibility and, for the first time, dynamic properties of dampers of different designs in multiharmonic analysis of bladed disks. Large-scale finite element damper and bladed disk models containing 104−106 degrees of freedom can be used. These models, together with detailed description of contact interactions over contact interface areas, allow for any level of refinement required for modeling of elastic damper bodies and for modeling of friction contact interactions. Numerical studies of realistic bladed disks have been performed with three different types of underplatform dampers: (i) a “cottage-roof” (also called “wedge”) damper, (ii) seal wire damper, and (iii) a strip damper. Effects of contact interface parameters and excitation levels on damping properties of the dampers and forced response are extensively explored.

Reduced Order Modeling for Multistage Bladed Disks With Friction Contacts at the Flange Joint

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Giuseppe Battiato ◽  
Christian M. Firrone ◽  
Teresa M. Berruti ◽  
Bogdan I. Epureanu
Keyword(s):  
Displacement Field ◽  
Fourier Coefficients ◽  
Normal Modes ◽  
Harmonic Balance Method ◽  
Relative Displacement ◽  
Forced Response ◽  
Contact Forces ◽  
Single Stage ◽  
Bladed Disks ◽  
Reduced Order

Most aircraft turbojet engines consist of multiple stages coupled by means of bolted flange joints which potentially represent source of nonlinearities due to friction phenomena. Methods aimed at predicting the forced response of multistage bladed disks have to take into account such nonlinear behavior and its effect in damping blades vibration. In this paper, a novel reduced order model (ROM) is proposed for studying nonlinear vibration due to contacts in multistage bladed disks. The methodology exploits the shape of the single-stage normal modes at the interstage boundary being mathematically described by spatial Fourier coefficients. Most of the Fourier coefficients represent the dominant kinematics in terms of the well-known nodal diameters (standard harmonics), while the others, which are detectable at the interstage boundary, correspond to new spatial small wavelength phenomena named as extra harmonics. The number of Fourier coefficients describing the displacement field at the interstage boundary only depends on the specific engine order (EO) excitation acting on the multistage system. This reduced set of coefficients allows the reconstruction of the physical relative displacement field at the interface between stages and, under the hypothesis of the single harmonic balance method (SHBM), the evaluation of the contact forces by employing the classic Jenkins contact element. The methodology is here applied to a simple multistage bladed disk and its performance is tested using as a benchmark the Craig–Bampton ROMs of each single stage.

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