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.

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.

A Substructure Based Reduced Order Model for Mistuned Bladed Disks

2009 ◽  
Author(s):  
Andreas Hohl ◽  
Christian Siewert ◽  
Lars Panning ◽  
Jo¨rg Wallaschek
Keyword(s):  
Degrees Of Freedom ◽  
Normal Modes ◽  
Forced Response ◽  
Component Mode Synthesis ◽  
Order Model ◽  
Bladed Disks ◽  
Reduced Order ◽  
Symmetry Approach ◽  
Full Structure ◽  
Value Decomposition

A efficient method for the calculation of the forced response of mistuned bladed disks is introduced. Based on the Component Mode Synthesis techniques the structure is divided into substructures, namely the disk and the blades. The Component Mode Synthesis of the disk is calculated with a fast and accurate cyclic symmetry approach. A recently developed method called Wave Based Substructuring is used to describe the (numerous) coupling degrees of freedom between the disk and the blades. The orthogonal waves are derived with a Singular Value Decomposition or a QR decomposition from the coupling nodes’ normal modes calculated by a modal analysis of the full structure.

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.

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.

A Contact Model for Nonlinear Forced Response Prediction of Turbine Blades: Calculation Techniques and Experimental Comparison

2008 ◽  
Author(s):  
Christian M. Firrone ◽  
Marco Allara ◽  
Muzio M. Gola
Keyword(s):  
Normal Load ◽  
Contact Stiffness ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Forced Response ◽  
Contact Forces ◽  
Contact Model ◽  
Experimental Comparison ◽  
Normal Contact ◽  
Contact Models

Dry friction damping produced by sliding surfaces is commonly used to reduce vibration amplitude of blade arrays in turbo-machinery. The dynamic behavior of turbine components is significantly affected by the forces acting at their contact interfaces. In order to perform accurate dynamic analysis of these components, contact models must be included in the numerical solvers. This paper presents a novel approach to compute the contact stiffness of cylindrical contacts, analytical and based on the continuous contact mechanics. This is done in order to overcome the known difficulties in simultaneously adjusting the values of both tangential and normal contact stiffness experimentally. Monotonic loading curves and hysteresis cycles of contact forces vs. relative displacement are evaluated as a function of the main contact parameters (i.e. the contact geometry, the material properties and the contact normal load). The new contact model is compared with other contact models already presented in literature in order to show advantages and limitations. The contact model is integrated in a numerical solver, based on the Harmonic Balance Method (HBM), for the calculation of the forced response of turbine components with friction contacts, in particular underplatform dampers. Results from the nonlinear numerical simulations are compared with those from validation experiments.

Vibration Control for Integrally Bladed Disks Using Friction Ring Dampers

2007 ◽  
Author(s):  
Denis Laxalde ◽  
Fabrice Thouverez ◽  
Jean-Pierre Lombard
Keyword(s):  
Frequency Domain ◽  
Forced Response ◽  
Reduced Order Model ◽  
Order Model ◽  
Bladed Disks ◽  
Reduced Order ◽  
Design And Optimization ◽  
Beam Elements ◽  
Parametric Studies ◽  
Frequency Domain Approach

A damping strategy for integrally bladed disks (blisks) is discussed in this paper; this involves the use of friction rings located underside the wheel of bladed disks. The forced response of the blisk with friction rings is derived in the frequency domain using a frequency domain approach known as Dynamic Lagrangian Frequency-Time method. The blisk is modeled using a reduced-order model and the rings are modeled using beam elements. The results of some numerical simulations and parametric studies are presented. The range of application of this damping device is discussed. Parametric studies are presented and allow to understand the dissipation phenomena. Finally some design and optimization guidelines are given.

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.

On Damping Entire Bladed Disks Through Dampers on Only a Few Blades

2010 ◽  
Vol 132 (9) ◽  
Author(s):  
Javier Avalos ◽  
Marc P. Mignolet
Keyword(s):  
Optimum Design ◽  
Forced Response ◽  
Reduced Order Model ◽  
Order Model ◽  
Bladed Disks ◽  
Single Degree Of Freedom ◽  
Reduced Order ◽  
Bladed Disk ◽  
Single Degree ◽  
Random Mistuning

The focus of this paper is on demonstrating the potential to damp entire bladed disks using dampers on only a fraction of the blades. This problem is first considered without the presence of random mistuning, and it is demonstrated that a few dampers at optimized locations can lead to a significant reduction in the forced response of the entire bladed disk. Unfortunately, this optimum design may not be robust with respect to random mistuning and a notable fraction of the reduction in forced response obtained may disappear because of mistuning. To regain the reduction in forced response but with mistuning present, robustness to mistuning is enhanced by using intentional mistuning in addition to dampers. The intentional mistuning strategy selected here is the A/B pattern mistuning in which the blades all belong to either type A or B. An optimization effort is then performed to obtain the best combination of A/B pattern and damper location to minimize the mistuned forced response of the disk. The addition of intentional mistuning in the system is shown to be very efficient, and the optimum bladed disk design does indeed exhibit a significant reduction in mistuned forced response as compared with the tuned system. These findings were obtained on both single-degree-of-freedom per blade-disk models and a reduced order model of a blisk.

The Influence of Blade Properties on the Forced Response of Mistuned Bladed Disks

2011 ◽  
Author(s):  
Andreas Hohl ◽  
Benedikt Kriegesmann ◽  
Jo¨rg Wallaschek ◽  
Lars Panning
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Degrees Of Freedom ◽  
Vibrational Energy ◽  
Normal Modes ◽  
Element Model ◽  
Forced Response ◽  
Optimization Approach ◽  
Bladed Disks ◽  
Value Decomposition

In turbomachinery applications bladed disks are subjected to high dynamic loads due to fluctuating gas forces. Dynamic excitation can result in high vibration amplitudes which can lead to high cycle fatigue (HCF) failures. Herein, the blades are almost identical but differ due to wear or small manufacturing tolerances. Especially, after regeneration and repair procedures the properties of the blades can differ with a high variance. These deviations of the blade properties can lead to a localization of the vibrational energy in single blades and even higher risk of HCF. A recently developed substructure model with a combination of the Hurty transformation or Component Mode Synthesis (CMS) and the so called Wave Based Substructuring (WBS) is used to obtain a Reduced Order Model (ROM) with a reasonable low number of degrees of freedom. The CMS of the disk can be calculated with one cyclic disk segment of the underlying finite element model. The WBS is used to describe the numerous coupling degrees of freedom between the disk and the blades with a truncated set of waves. The orthogonal waves are derived by a Singular Value Decomposition or a QR decomposition from the coupling nodes normal modes calculated by a cyclic modal analysis of the full structure. The blade eigenvalues of the clamped blade can be mistuned individually under consideration of the variance as well as the correlation between the different eigenvalues of the blades. Monte-Carlo-Simulations are performed to calculate the effect of these parameters on the forced response of a mistuned bladed disk for blade dominated modes. Furthermore, Monte-Carlo-Simulations and a constraint optimization approach is used to calculate the worst and best case blade patterns for specific blade patterns and blade patterns with distributed blade properties.

Reduced Order Modeling and Vibration Analysis of Mistuned Bladed Disk Assemblies With Shrouds

1999 ◽  
Vol 121 (3) ◽  
pp. 515-522 ◽  
Author(s):  
R. Bladh ◽  
M. P. Castanier ◽  
C. Pierre
Keyword(s):  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Modeling Technique ◽  
Computationally Efficient ◽  
Bladed Disks ◽  
Reduced Order ◽  
Synthesis Approach

This paper presents important improvements and extensions to a computationally efficient reduced order modeling technique for the vibration analysis of mistuned bladed disks. In particular, this work shows how the existing modeling technique is readily extended to turbomachinery rotors with shrouded blades. The modeling technique employs a component mode synthesis approach to systematically generate a reduced order model (ROM) using component modes calculated from a finite element model (FEM) of the rotor. Based on the total number of degrees of freedom, the ROM is typically two or three orders of magnitude smaller than the FEM. This makes it feasible to predict the forced response statistics of mistuned bladed disks using Monte Carlo simulations. In this work, particular attention is devoted to the introduction of mistuning into the ROM of a shrouded assembly. Mistuning is modeled by projecting the mistuned natural frequencies of a single, cantilever blade with free shrouds onto the harmonic modes of the shrouded blade assembly. Thus, the necessary mistuning information may be measured by testing individual blades.

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