Direct Parametric Analysis of Resonance Regimes for Nonlinear Vibrations of Bladed Disks

2006 ◽  
Vol 129 (3) ◽  
pp. 495-502 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Large Scale ◽  
Contact Stiffness ◽  
Design Parameters ◽  
Bladed Disks ◽  
Disk Model ◽  
Strongly Nonlinear ◽  
Resonance Frequencies ◽  
Interface Parameters ◽  
First Time ◽  
Analytical Expressions

A method has been developed to calculate directly resonance frequencies and resonance amplitudes as functions of design parameters or as a function of excitation levels. The method provides, for the first time, this capability for analysis of strongly nonlinear periodic vibrations of bladed disks and other structures with nonlinear interaction at contact interfaces. A criterion for determination of major, sub-, and superharmonic resonance peaks has been formulated. Analytical expressions have been derived for accurate evaluation of the criterion and for tracing resonance regimes as function of such contact interface parameters as gap and interference values, friction and contact stiffness coefficients, and normal stresses. High accuracy and efficiency of the new method have been demonstrated on numerical examples including a large-scale nonlinear bladed disk model and major types of contact interfaces including friction contact interfaces, gaps, and cubic nonlinearities.

Direct Parametric Analysis of Resonance Regimes for Nonlinear Vibrations of Bladed Discs

2006 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Large Scale ◽  
Contact Stiffness ◽  
Design Parameters ◽  
Strongly Nonlinear ◽  
Resonance Frequencies ◽  
Interface Parameters ◽  
First Time ◽  
Analytical Expressions ◽  
Contact Stiffness Coefficients

A method has been developed to calculate directly resonance frequencies and resonance amplitudes as functions of design parameters or as a function of excitation levels. The method provides, for a first time, this capability for analysis of strongly nonlinear periodic vibrations of bladed discs and other structures with nonlinear interaction at contact interfaces. A criterion for determination of major, sub- and superharmonic resonance peaks has been formulated. Analytical expressions have been derived for accurate evaluation of the criterion and for tracing resonance regimes as function of such contact interface parameters as gap and interference values, friction and contact stiffness coefficients, normal stresses. High accuracy and efficiency of the new method have been demonstrated on numerical examples including large-scale nonlinear bladed disc model and major types of contact interfaces including friction contact interfaces, gaps and cubic nonlinearities.

A Sensitivity-Based Method for Direct Stochastic Analysis of Nonlinear Forced Response for Bladed Disks With Friction Interfaces

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Stochastic Analysis ◽  
Large Scale ◽  
Sampling Procedure ◽  
Forced Response ◽  
Statistical Characteristics ◽  
Program Code ◽  
Bladed Disks ◽  
Response Level ◽  
Strongly Nonlinear ◽  
Interface Parameters

An efficient method is developed to calculate stochastic and uncertainty characteristics of forced response for nonlinear vibrations of bladed disks with friction and gap contact interfaces. Uncertainty ranges, statistical characteristics, and probability density functions for forced response levels are determined directly without any sampling procedure. The method uses approximations of the forced response level based on derived analytically and calculated extremely fast and accurately sensitivity coefficients of forced response with respect to friction contact interface parameters. The method effectiveness allows analysis of strongly nonlinear vibration of bladed disks using realistic large-scale finite element models. The method is implemented in a program code developed at Imperial College and numerical examples of application of the method for stochastic analysis of a realistic blisc with underplatform dampers are provided.

Analysis of Flutter-Induced Limit Cycle Oscillations in Gas-Turbine Structures With Friction, Gap, and Other Nonlinear Contact Interfaces

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Gas Turbine ◽  
Limit Cycle ◽  
Large Scale ◽  
Direct Calculation ◽  
Aerodynamic Characteristics ◽  
Frequency Domain Method ◽  
Nonlinear Contact ◽  
Limit Cycle Flutter ◽  
Interface Parameters ◽  
First Time

A frequency-domain method has been developed to predict and comprehensively analyze the limit-cycle flutter-induced vibrations in bladed disks and other structures with nonlinear contact interfaces. The method allows, for the first time, direct calculation of the limit-cycle amplitudes and frequencies as functions of contact interface parameters and aerodynamic characteristics using realistic large-scale finite element models of structures. The effects of the parameters of nonlinear contact interfaces on limit-cycle amplitudes and frequencies have been explored for major types of nonlinearities occurring in gas-turbine structures. New mechanisms of limiting the flutter-induced vibrations have been revealed and explained.

Method for Direct Parametric Analysis of Nonlinear Forced Response of Bladed Discs With Friction Contact Interfaces

2004 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Parametric Analysis ◽  
Large Scale ◽  
Normal Load ◽  
Forced Response ◽  
Finite Element Models ◽  
Contact Interface ◽  
Friction Contact ◽  
Interface Parameters ◽  
First Time ◽  
Contact Parameters

An effective method for direct parametric analysis of periodic nonlinear forced response of bladed discs with friction contact interfaces has been developed. The method allows, for the first time, forced response levels to be calculated directly as a function of contact interface parameters such as the friction coefficient, contact surface stiffness (normal and tangential coefficients), clearances, interferences, and the normal stresses at the contact interfaces. The method is based on exact expressions for sensitivities of the multiharmonic interaction forces with respect to variation of all parameters of the friction contact interfaces. These novel expressions are derived in the paper for a friction contact model, accounting for the normal load variation and the possibility of separation-contact transitions. Numerical analysis of effects of the contact parameters on forced response levels has been performed using large-scale finite element models of a practical bladed turbine disc with underplatform dampers and with shroud contacts.

Method for Direct Parametric Analysis of Nonlinear Forced Response of Bladed Disks With Friction Contact Interfaces

2004 ◽  
Vol 126 (4) ◽  
pp. 654-662 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Parametric Analysis ◽  
Large Scale ◽  
Normal Load ◽  
Forced Response ◽  
Finite Element Models ◽  
Contact Interface ◽  
Friction Contact ◽  
Bladed Disks ◽  
Interface Parameters ◽  
Contact Parameters

An effective method for direct parametric analysis of periodic nonlinear forced response of bladed disks with friction contact interfaces has been developed. The method allows, forced response levels to be calculated directly as a function of contact interface parameters such as the friction coefficient, contact surface stiffness (normal and tangential coefficients), clearances, interferences, and the normal stresses at the contact interfaces. The method is based on exact expressions for sensitivities of the multiharmonic interaction forces with respect to variation of all parameters of the friction contact interfaces. These novel expressions are derived in the paper for a friction contact model, accounting for the normal load variation and the possibility of separation-contact transitions. Numerical analysis of effects of the contact parameters on forced response levels has been performed using large-scale finite element models of a practical bladed turbine disk with underplatform dampers and with shroud contacts.

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.

A Sensitivity-Based Method for Direct Stochastic Analysis of Nonlinear Forced Response for Bladed Discs With Friction Interfaces

2007 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Stochastic Analysis ◽  
Large Scale ◽  
Sampling Procedure ◽  
Forced Response ◽  
Statistical Characteristics ◽  
Contact Interface ◽  
Program Code ◽  
Response Level ◽  
Strongly Nonlinear ◽  
Interface Parameters

An efficient method is developed to calculate stochastic and uncertainty characteristics of forced response for nonlinear vibrations of bladed discs with friction and gap contact interfaces. Uncertainty ranges, statistical characteristics and probability density functions for forced response levels are determined directly without any sampling procedure. The method uses approximations of the forced response level based on derived analytically and calculated extremely fast and accurately sensitivity coefficients of forced response with respect to friction contact interface parameters. The method effectiveness allows analysis of strongly nonlinear vibration of bladed discs using realistic large-scale FE element models. The method is implemented in a program code developed at Imperial College and numerical examples of application of the method for stochastic analysis of a realistic blisc with underplatform dampers are provided.

Computer Analysis of Bouncing Vibration and Tracking Characteristics of a Point Contact Slider Model Over Random Disk Surfaces

1999 ◽  
Vol 121 (3) ◽  
pp. 587-595 ◽  
Author(s):  
Kyosuke Ono ◽  
Kan Takahashi ◽  
Kohei Iida
Keyword(s):  
Contact Stiffness ◽  
Point Contact ◽  
Disk Surface ◽  
Design Parameters ◽  
Random Surface ◽  
Disk Interface ◽  
Tracking Ability ◽  
Interface Parameters ◽  
Parameter Values ◽  
Contact Slider

This study is a computational analysis of the bouncing vibration of a point contact slider model over computer generated random disk surfaces and the design conditions of slider to disk interface parameters necessary for contact recording. The Gaussian random surface of a disk with various standard deviations and frequency characteristics is generated by using a modified midpoint displacement algorithm. From the calculated results of bouncing vibration of a slider for various parameter values, it was found that the decrease in contact stiffness and increase in slider load can significantly reduce the bouncing vibration as well as the increase in contact damping and the smoothness of the surface. It was also found that the bouncing vibration spectrum of a contact slider over a simulated disk surface agreed closely with the experimental results presented in a previous study by the authors. The maximum and rms values of the spacing and the contact force were examined for various design parameters. The design conditions of the contact pad to the disk interface were discussed in terms of tracking ability and wear durability for slider loads of 0.5 mN and 5 mN.

Analysis of the Worst Mistuning Patterns in Bladed Disk Assemblies

2003 ◽  
Vol 125 (4) ◽  
pp. 623-631 ◽  
Author(s):  
E. P. Petrov ◽  
D. J. Ewins
Keyword(s):  
Finite Element ◽  
Large Scale ◽  
Optimization Problem ◽  
Element Model ◽  
Design Parameters ◽  
Finite Element Models ◽  
Bladed Disks ◽  
Bladed Disk ◽  
The Many

The problem of determining the worst mistuning patterns is formulated and solved as an optimization problem. Maximum resonant amplitudes searched across the many nodes of a large-scale finite element model of a mistuned bladed disk and across all the excitation frequencies in a given range are combined into an objective function. Individual blade mistuning is controlled by varying design parameters, whose variation range is constrained by manufacture tolerances. Detailed realistic finite element models, which have so far only been used for analyzing tuned bladed disks, are used for calculation of the forced resonant response of mistuned assemblies and for determination of its sensitivity coefficients with respect to mistuning variation. Results of the optimum search of mistuning patterns for some practical bladed disks are analyzed and reveal higher worst cases than those found in previous studies.

scholarly journals A Method for Parametric Analysis of Stability Boundaries for Nonlinear Periodic Vibrations of Structures With Contact Interfaces

2018 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Parametric Analysis ◽  
Large Scale ◽  
Contact Stiffness ◽  
Stability Loss ◽  
Forced Response ◽  
Scale Model ◽  
Design Parameters ◽  
Stability Boundaries ◽  
Analysis Of Stability ◽  
The Stability

A method for parametric analysis of the stability loss boundary has been developed for periodic regimes of nonlinear forced vibrations for a first time. The method allows parametric frequency-domain calculations of the stability loss together with the vibration amplitudes and design parameter values corresponding to the stability boundaries. The tracing algorithm is applied to obtain the trajectories of stability loss points as functions of design parameters. The parametric stability loss is formulated for cases when: (i) the design parameters characterise the properties of nonlinear contact interfaces (e.g. gap, contact stiffness, friction coefficient, etc.) and (ii) the design parameters describe linear components of the analysed structure (e.g. parameters of geometric shape, material, natural frequencies, modal damping etc.) and (iii) these parameters describe the excitation loads (e.g. their level, distribution or frequency). An approach allowing the multiparametric analysis of stability boundaries is proposed. The method uses the multiharmonic representation of the periodic forced response and aimed at the analysis of realistic gas-turbine structures comprising thousands and millions degrees of freedom. The method can be used for the effective search of isolated branches of the nonlinear solutions and examples of detection and search of the isolated branches are given: for relatively small and for large-scale finite element models. The efficiency of the method for calculation of the stability boundaries and for the search of isolated branches is demonstrated on simple systems and on a large-scale model of a turbine blade.

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