E. P. Petrov

Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Disks

An analytical formulation for the vectors of contact forces and the stiffness matrix of the nonlinear friction contact interface is developed for the analysis of multi-harmonic vibrations in the frequency domain. The contact interface elements provided here an exact description of friction and unilateral contact forces at the interacting surfaces, taking into account the influence of the variable normal load on the friction forces, including the extreme cases of separation of the two surfaces. Initial gaps and interferences at the contact nodes, which affect the normal force, as well as the unilateral action of the normal force at the contact surface, are all included in the model. The accurate calculation of the force vector and the tangent stiffness matrix provides a very reliable and fast convergence of the iteration process used in the search for the amplitudes of nonlinear vibrations of bladed disks. Numerical investigations demonstrate excellent performance with respect to speed, accuracy and stability of computation.

Effects of Damping and Varying Contact Area at Blade-Disk Joints in Forced Response Analysis of Bladed Disk Assemblies

An approach is developed to analyze the multiharmonic forced response of large-scale finite element models of bladed disks taking account of the nonlinear forces acting at the contact interfaces of blade roots. Area contact interaction is modeled by area friction contact elements which allow for friction stresses under variable normal load, unilateral contacts, clearances, and interferences. Examples of application of the new approach to the analysis of root damping and forced response levels are given and numerical investigations of effects of contact conditions at root joints and excitation levels are explored for practical bladed disks.

Finite element theory for curved and twisted beams based on exact solutions for three-dimensional solids Part 1: Beam concept and geometrically exact nonlinear formulation

A geometrically exact and completely consistent finite element theory for curved and twisted beams is proposed. It is based on the kinematical hypothesis generally formulated for large deformation and accounts for all kinds of deformation of a three-dimensional solid: translational and rotational displacements of the cross-sections, warping of their plane and distortion of their contours. The principle of virtual work is applied in a straightforward manner to all non-zero six components of the strain and stress tensors. Expressions are given for tangent matrices of elastic, inertia and external forces and specific techniques for discretization and updating are developed for the analysis of beams in inertial and non-inertial frames. Finally, the numerical properties of the finite element models are demonstrated through examples

A new method for dynamic analysis of mistuned bladed disks based on the exact relationship between tuned and mistuned systems

A new method for the dynamic analysis of mistuned bladed disks is presented. The method is based on exact calculation of the response of a mistimed system using response levels for the tuned assembly togeher with a modification matrix constructed from the frequency response function (FRF) matrix of the tamed system and a matrix describing the mistuning. The train advantages of the method are its efficiency and accuracy, which allow the use of large finite element models of practical bladed disk assemblies in parametric studies of mistuning effects on vibration amplitudes. A new method of calculating the FRF matrix of the tuned system using a sector model is also developed so as to improve the efficiency of the method even further, making the proposed method a very attractive tool for mistuning steadies. various numerical aspects of the proposed method are addressed and its accuracy and efficiency are demonstrated using representative test cases

Analysis of the worst mistuning patterns in bladed disk assemblies

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.

Generic Friction Models for Time-Domain Vibration Analysis of Bladed Disks

New efficient models have been developed to describe dynamic friction effects in order to facilitate analysis of the vibration of bladed disks in the time domain. These friction models describe friction forces occurring at contact interfaces under time-varying normal load variations, including cases of separation. The friction models developed allow one to take into account time-varying friction contact parameters, such as friction coefficient and contact stiffness coefficients. Anisotropy and variation of the friction characteristics over the contact surfaces are included in the proposed models. The capabilities of the new friction models are demonstrated. Analysis of the friction forces is performed for different motion trajectories and different time variations of the normal load, and the effects of anisotropy, variation in time of the friction characteristics and normal load variation are discussed. A numerical analysis of transient vibrations of shrouded blades using the new models is presented

Advanced modeling of underplatform friction dampers for analysis of bladed disk vibration

Advanced structural dynamic models for both wedge and split underplatform dampers have been developed. The new damper models take into account inertia forces and the effects of normal load variation on stick-slip transitions at the contact interfaces. The damper models are formulated for the general case of multiharmonic forced response analysis. An approach for using the new damper models in the dynamic analysis of large-scale finite element models of bladed disks is proposed and realized. Numerical investigations of bladed disks are performed to demonstrate the capabilities of the new models and an analysis of the influence of the damper parameters on the forced response of bladed disks is made

Method for Analysis of Nonlinear Multiharmonic Vibrations of Mistuned Bladed Disks With Scatter of Contact Interface Characteristics

An efficient method for analysis of nonlinear vibrations of mistuned bladed disk assemblies has been developed. This development has facilitated the use of large-scale finite element models for realistic bladed disks, used hitherto in analysis of linear vibration, to be extended for the analysis of nonlinear multiharmonic vibration. The new method is based on a technique for the exact condensation of nonlinear finite element models of mistuned bladed disks. The model condensation allows the size of the nonlinear equations to be reduced to the number of degrees of freedom where nonlinear interaction forces are applied. The analysis of nonlinear forced response for simplified and realistic models of mistuned bladed disks has been performed. For a practical high-pressure bladed turbine disk, several types of nonlinear forced response have been considered, including mistuning by (i) scatter of underplatform dampers, (ii) shroud gap scatter and (iii) blade frequency scatter in the presence of nonlinear shroud interactions.

A High-Accuracy Model Reduction for Analysis of Nonlinear Vibrations in Structures With Contact Interfaces

A highly accurate and computationally efficient method is proposed for reduced modeling of jointed structures in the frequency domain analysis of nonlinear steady-state forced response. The method has significant advantages comparing with the popular variety of mode synthesis methods or forced response matrix methods and can be easily implemented in the nonlinear forced response analysis using standard finite element codes. The superior qualities of the new method are demonstrated on a set of major problems of nonlinear forced response analysis of bladed disks with contact interfaces: (i) at blade roots, (ii) between interlock shrouds, and (iii) at underplatform dampers. The numerical properties of the method are thoroughly studied on a number of special test cases.

State-of-the-art dynamic analysis for non-linear gas turbine structures

Abstract An accurate and robust method has been developed for the general multiharmonic analysis of forced periodic vibrations of bladed discs subjected to abrupt changes of elastic and damping properties at contact nodes located on the interfaces of the components. The approach is based on an analytical formulation of friction contact interface elements which provides exact expressions for multiharmonic forces and stiffness matrices of the elements. The analytical formulation overcomes the numerical difficulties associated with searching for a solution of the non-linear equations, which have been inherent so far for the considered systems, and provides a breakthrough in the analysis of the non-linear forced response of bladed discs and other structures with gaps and friction interfaces. An effective reduction method is reported that allows the size of the resolving equations to be decreased to the number of DOFs (degrees of freedom) at the contact surfaces, while preserving completeness and accuracy of the whole large-scale model. Numerical investigations demonstrate the outstanding properties of the proposed approach with respect to computational speed, accuracy and stability of calculations for practical gas-turbine structures.