Effects of Intentional Large Mistuning to the Performance of B–B Friction Dampers in the Mistuned Bladed Disk Assembly Subjected to Narrow band Random Excitation

In this study, the effects of intentional mistuning on the performance of B–B friction dampers are investigated in an inherently mistuned bladed disk assembly subjected to narrow band random excitation. The intentional large mistuning and inherent small mistuning are modeled by the additional mass and perturbations in the stiffness of the blade, respectively. It was found that the performance of B–B friction dampers improved owing to the intentional mistuning of the correlated excitations. Based on a simple model of an intentionally and inherently mistuned bladed disk assembly, the analytical technique offers an efficient method to evaluate the effects of intentional mistuning and friction dampers.

Equivalent Linearization of Bladed Disk Assemblies With Friction Nonlinearities Under Random Excitation

The present article addresses the vibrational behavior of bladed disk assemblies with nonlinear shroud coupling under random excitation. In order to increase the service life and safety of turbine blades, intense calculations are carried out to predict the vibrational behavior. The use of friction dampers for energy dissipation and suppression of large amplitudes adds a nonlinearity to the mechanical system, which complicates the calculations. Depending on the stage, different types of excitation can occur in a turbine, from stationary to transient, synchronous to asynchronous as well as deterministic to random excitation. Random excitation in combination with the presence of nonlinearities makes the calculation of the vibrational behavior even more complex. So far, this problem has only been dealt with to a limited extent in the literature on turbomachinery. Nevertheless, there are in general different approaches and methods to address this problem most of which are strongly restricted with regard to the number of degrees of freedom. The focus of this paper is the application of an equivalent linearization method to calculate the stochastic response of an academic model of a bladed disk assembly under random excitation. The fundamental idea of the method is to linearize a nonlinear system in such a way that the most suitable equivalent linear system is found taking into account the approximated distribution of the response amplitude. To apply this method to a system with a friction nonlinearity, the linear part of the system is considered in state space and extended with additional nonlinear equations. The nonlinear contact is modelled with a Bouc-Wen formulation to reproduce the hysteretic character of a nonlinearity occurring in the presence of a friction damper. The classical Bouc-Wen formulation is standardized in such a way that the usual parameters can be replaced by physical ones such as the normal force or contact stiffness. The nonlinear force of the friction nonlinearity is linearized regarding the stochastic distribution of the system response. Both the excitation and the response are limited to mean-free, stationary stochastic processes, which means that the stochastic moments do not change over time. However, the spectrum of the excitation is not limited to being constant, as it is the case with Gaussian white noise. The equivalent linearization method could also deal with a narrowband or broadband excitation spectrum. Unlike previous papers on this topic, the calculations are performed on a full bladed disk assembly in which each sector is represented by a reduced order model with several degrees of freedom.

Equivalent Linearization of Bladed Disk Assemblies with Friction Nonlinearities Under Random Excitation

The present article addresses the vibrational behaviour of bladed disk assemblies with nonlinear shroud coupling under random excitation. In order to increase the service life and safety of turbine blades, intense calculations are carried out to predict the vibrational behaviour. The use of friction dampers for energy dissipation and suppression of large amplitudes makes the mechanical system nonlinear, which complicates the calculations. Depending on the stage, different types of excitation can occur in a turbine, from clearly defined deterministic to random excitation. So far, the latter problem has only been dealt with to a limited extent in the literature on turbomachinery. Nevertheless, there are in general different approaches and methods to address this problem most of which are strongly restricted with regard to the number of degrees of freedom. The focus of this paper is the application of an equivalent linearization method to calculate the stochastic response of an academic model of a bladed disk assembly under random excitation. The nonlinear contact is modelled both with an elastic Coulomb-slider and a Bouc-Wen formulation to reproduce the hysteretic character of a friction nonlinearity occurring in the presence of a friction damper. Both the excitation and the response are limited to mean-free, stationary stochastic processes, which means that the stochastic moments, do not change over time. Unlike previous papers on this topic, the calculations are performed on a full bladed disk assembly in which each segment is approximated with several degrees of freedom.

Modeling the Microslip in the Flange Joint and Its Effect on the Dynamics of a Multistage Bladed Disk Assembly

The complex architecture of aircraft engines requires demanding computational efforts when the dynamic coupling of their components has to be predicted. For this reason, numerically efficient reduced-order models (ROM) have been developed with the aim of performing modal analyses and forced response computations on complex multistage assemblies being computationally fast. In this paper, the flange joint connecting two turbine disks of a multistage assembly is studied as a source of nonlinearities due to friction damping occurring at the joint contact interface. An analytic contact model is proposed to calculate the local microslip based on the different deformations that the two flanges in contact take during vibration. The model is first introduced using a simple geometry representing two flanges in contact, and then, it is applied to a reduced finite element model in order to calculate the nonlinear forced response.

Modelling the Microslip in the Flange Joint and its Effect on the Dynamics of a Multi-Stage Bladed Disk Assembly

The complex architecture of aircraft engines requires demanding computational efforts to take into account the dynamic coupling of the many components constituting the whole assembly. For this reason numerically efficient Reduced Order Models (ROM) and techniques have been developed with the aim of reproducing the global dynamics of the system being computationally fast at the same time. In particular, ROMs have been presented to perform the modal analysis and the calculation of the forced response of rotating components like turbine bladed disks multi-stage assembly. In order to study the effect that joints may have in terms of nonlinearities due to friction in complex structures, in this paper the flange joint is studied as a source of damping due to microslip occurring at the contact interface between two turbine disks. An analytical contact model is proposed to calculate the local microslip based on the different deformations that the two flanges take during vibration. The model is first introduced using a simple geometry representing two flanges in contact and then it is applied to a reduced FE model in order to calculate the nonlinear forced response.

Investigation of Alternate Mistuned Turbine Blades Non-Linear Coupled by Underplatform Dampers

Freestanding turbine blades have typically low structural damping and thus require additional friction damping devices, such as underplatform dampers. The friction coupling between neighboring blades reduces response amplitude and increases resonance frequency. Along with forced response excitation large blades, especially of last stage, could be excited by fluid structural interaction (flutter). To prevent such excitation alternate mistuned blade patterns are beneficial disturbing traveling waves in the stage. In this paper the influence of alternate mistuning is investigated with a simplified oscillator chain as well as a bladed disk assembly coupled by frictional contacts. It is pointed out that the performance of friction coupling can be improved by alternate mistuning as long as the engine order of the excitation is below quarter of the number of blades. Alternate mistuning causes a mode coupling between two nodal diameter vibration mode shapes allowing for energy transfer. The in-house developed software code DATAR is enhanced and alternate mistuning can be applied to the blades as well as to the damping elements. For validation the DATAR code was applied to an alternate mistuned last stage blade of a Siemens gas turbine and compared with available field engine measurement.