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.

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.

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.

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).

Non-Linear Dynamics of Steam Turbine Blades With Shroud: Numerical Analysis and Experiments

2012 ◽  
Author(s):  
Stefano Zucca ◽  
Muzio M. Gola ◽  
Francesco Piraccini
Keyword(s):  
Frequency Domain ◽  
Steam Turbine ◽  
Turbine Blades ◽  
Harmonic Balance Method ◽  
Low Pressure ◽  
Forced Response ◽  
Numerical Code ◽  
Accurate Information ◽  
Normal Contact ◽  
Non Linear

The prediction of the aeromechanical behavior of low-pressure blades represents one of the main challenges in the Steam Turbine Industry. The evaluation of forced response and damping is critical for the reliability of new designs and usually requires expensive validation campaigns such as Wheel Box Tests (WBT). A WBT consists of one or more blade rows assembled on a rotor and spun at the desired rotating speed in a vacuum cell, with synchronous excitation provided by various sources. The WBT provides accurate information about the blade modes frequency, the alternating response level, and allows the evaluation of the mechanical damping. Given the large effort in terms of costs and time associated to the experimental activity, the possibility to rely on the output of a numerical code either during the first steps of a new design or to investigate the effect of minor changes to a current design would be extremely beneficial to the development of future products. In order to compute the non-linear forced response of shrouded blades of steam turbines, custom numerical solvers must be developed, since commercial finite element (FE) solvers do not perform this kind of analysis in the frequency domain. In this paper, the forced response of a blade with shrouds of a low pressure steam turbine is computed and numerical results are compared with the experimental Wheel Box Tests performed at GE Oil & Gas. The calculations require a three-step procedure: in the first step, a non-linear static analysis is performed in ANSYS® in order to compute the actual contact area on the shroud surface and the distribution of static normal loads, then a reduced order model of the blade is generated in ANSYS® taking into account the stiffening effect on the blade of the pre-stress due to the centrifugal force, finally the reduced model is imported in a numerical code and the non-linear forced response of the blade is computed. The numerical code solves the balance equations of the system in the frequency domain, by means of the Harmonic Balance Method, imposing cyclic symmetry boundary conditions of the system. An interpolation procedure is implemented in order to manage the non-perfectly matching meshes of the shroud contact surfaces, while the tangential and normal contact stiffness is computed with a numerical model based on the contact mechanics principles. The numerical and the experimental results around some of the critical resonances of the system are compared in order to assess the reliability and accuracy of the numerical tool for its future implementation in the mechanical design practice of the blades.

Nonlinear Vibration Analysis of Turbine Bladed Disks With Mid-Span Dampers

2020 ◽  
Author(s):  
Erhan Ferhatoglu ◽  
Stefano Zucca ◽  
Daniele Botto ◽  
Jury Auciello ◽  
Lorenzo Arcangeli
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Normal Load ◽  
Harmonic Balance Method ◽  
Response Prediction ◽  
Forced Response ◽  
Algebraic Equations ◽  
Friction Contact ◽  
Bladed Disks ◽  
Cyclic Symmetric

Abstract Friction dampers are one of the most common structures used to alleviate excessive vibration amplitudes in turbomachinery applications. There are very well-known types of contact elements exploited efficiently, such as underplatform dampers. However, different design approach is sometimes needed to maximize the effectiveness further. In this paper, computational forced response prediction of bladed disks with a configuration of the secondary structure commonly used by Baker Hughes design, the so-called mid-span dampers, is presented. Mid-span dampers are metal devices positioned at the middle section of the airfoil span and come into contact with the blade by the centrifugal force acting during rotation. Proposed damping mechanism is applied to a realistic steam turbine bladed disk under cyclic symmetric boundary conditions. Friction contact is modeled through a large number of contact nodes between the blade and the damper by using a 2D friction contact element with variable normal load. Harmonic Balance Method and Alternating Frequency/Time approach are utilized to obtain nonlinear algebraic equations in frequency domain and nonlinear forced response is computed by using Newton-Raphson method. The results obtained by numerical simulations show that mid-span dampers are an efficient configuration type of a damping mechanism to be used in the design of the bladed disks for nonlinear vibration analysis.

A Method for the Design of Ring Dampers for Gears in Aeronautical Applications

2010 ◽  
Author(s):  
S. Zucca ◽  
C. M. Firrone ◽  
M. Facchini
Keyword(s):  
Contact Stiffness ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Forced Response ◽  
Design Parameters ◽  
Periodic Force ◽  
Normal Contact ◽  
Gear Teeth ◽  
Force Profile ◽  
Normal Contact Stiffness

In order to reduce resonant vibration of thin walled gears used for aeronautical applications, friction ring dampers may be added to the gear. In order to design the damper geometry, engineers must be able to evaluate its effect on the dynamics of the gear. In this paper a method for the calculation of the forced response of gears with friction ring dampers for aeronautical applications is proposed for the first time. The gear and the damper are modeled by means of FEM and they are coupled by means of contact elements, characterized by tangential and normal contact stiffness. The periodical response of the system is computed in the frequency domain, by means of the harmonic balance method. The harmonic excitation is calculated by means of Fourier analysis of the periodic force profile acting on the gear teeth. The methodology is applied to a case of industrial interest. The effect of the principal design parameters of the ring damper is highlighted.

A Method for the Design of Ring Dampers for Gears in Aeronautical Applications

2012 ◽  
Vol 134 (9) ◽  
Author(s):  
Stefano Zucca ◽  
Christian Maria Firrone ◽  
Marco Facchini
Keyword(s):  
Contact Stiffness ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Forced Response ◽  
Design Parameters ◽  
Periodic Force ◽  
Normal Contact ◽  
Gear Teeth ◽  
Force Profile ◽  
Normal Contact Stiffness

In order to reduce the resonant vibration of thin walled gears used for aeronautical applications, friction ring dampers may be added to the gear. In order to design the damper geometry, engineers must be able to evaluate its effect on the dynamics of the gear. In this paper a method for the calculation of the forced response of gears with friction ring dampers for aeronautical applications is proposed for the first time. The gear and the damper are modeled by means of the finite element method (FEM) and they are coupled by means of contact elements, characterized by tangential and normal contact stiffness. The periodical response of the system is computed in the frequency domain by means of the harmonic balance method. The harmonic excitation is calculated by means of the Fourier analysis of the periodic force profile acting on the gear teeth. The methodology is applied to a case of industrial interest. The effect of the principal design parameters of the ring damper is highlighted.

scholarly journals HARMONIC BALANCE THEORY FOR SCHEME TECHNICAL DESIGN

T-Comm ◽  
2020 ◽  
Vol 14 (11) ◽  
pp. 21-32
Author(s):  
Svetlana F. Gorgadze ◽  
◽  
Anton A. Maximov ◽  
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Projection Methods ◽  
Algebraic Equations ◽  
Electronic Circuits ◽  
Large Signal ◽  
Linear Algebraic Equations ◽  
Methods Of Synthesis ◽  
Signal Mode

The analysis and generalization of the main publications on the methods of synthesis and analysis of non-linear active microwave circuits based on the use of the harmonic balance method are presented. As a result of some classification of mathematical approaches and techniques used in the context of this method, a selection and review of basic algorithms was made, the sequential application of which makes it possible to obtain the final result for a scheme of any complexity. The principles of drawing up the initial system of differential equations for electronic circuits and reducing it to a system of linear algebraic equations are considered. A detailed and, at the same time, simplified interpretation of the approaches involving the use of projection methods and Krylov subspaces is given in order to make them easier to understand. Both the complete and the restart generalized method of minimal residuals are considered, in which the desired solution is obtained in the course of an iterative process, at each stage of which subspaces of lower dimension are constructed. The possibilities of simulators and application packages intended for circuit design of electronic circuits are considered. The problem of matching a power amplifier in large signal mode using the APLAC simulator, which is NI AWR technology for designing high-frequency circuits, is discussed.

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.

Basic Optimization Methodology for the Design of Friction Damping in Blade Shrouds

2013 ◽  
Author(s):  
Michal Hajžman ◽  
Luděk Pešek ◽  
Jan Brůha ◽  
Vladimír Zeman ◽  
Drahomír Rychecký
Keyword(s):  
Vibration Suppression ◽  
Harmonic Balance Method ◽  
Rigid Bodies ◽  
Geometrical Parameters ◽  
Bending Vibration ◽  
Friction Forces ◽  
Normal Contact ◽  
Friction Element ◽  
Experimental Stand ◽  
Optimization Methodology

This paper is focused on the optimization of friction element parameters in blade shrouds for various types of excitation. In order to create and validate a proper modelling methodology an experimental stand and a numerical simulation of blades interaction by means of a friction element placed in the shrouds were prepared. Mathematical models are based on the finite element method combined with rigid bodies. The interaction of the friction element and blades is described by normal contact and tangential friction forces derived for particular geometrical parameters of the studied mechanical system. The models can be analyzed both in frequency domain (by the harmonic balance method) or in time domain (by the numerical integration). The results of the optimization of friction element parameters with respect to the bending vibration suppression are documented in the paper. Another contact modelling approach intended for more complex contact surfaces is based on the decomposition of a contact surface into a set of elementary areas and on the expression of contact and friction forces between these areas. All methodologies are implemented in the MATLAB system and the results for the chosen test cases are compared with the results obtained by a measurement or by the ANSYS software.

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