Time Periodic Control of a Bladed Disk Assembly Using Shaft Based Actuation

2001 ◽  
Vol 123 (3) ◽  
pp. 395-398 ◽  
Author(s):  
Gyo¨rgy Sza´sz and ◽  
George T. Flowers
Keyword(s):  
Dynamical System ◽  
Control Strategy ◽  
Thrust Bearing ◽  
Vibration Modes ◽  
Complete Controllability ◽  
Periodic Control ◽  
Bladed Disk ◽  
Bladed Disk Assembly ◽  
Time Periodic

For a tuned or symmetrically mistuned bladed disk assembly, several vibration modes are coupled only to the axial dynamics, which forces controllers to rely on an axial actuator. A control strategy based upon deliberately mistuning in a nonsymmetric manner, which results in a time periodic dynamical system, is developed. The method presented does not require an active thrust bearing for complete controllability of a bladed disk assembly via hub based actuators.

Time Varying Control of a Bladed Disk Assembly Using Shaft Based Actuation

1999 ◽  
Author(s):  
György Szász ◽  
George T. Flowers
Keyword(s):  
High Frequency ◽  
Thrust Bearing ◽  
Vibration Modes ◽  
Thrust Bearings ◽  
Bladed Disk ◽  
Time Period ◽  
Bladed Disk Assembly ◽  
Linearized Model ◽  
Original Domain ◽  
Time Periodic

Abstract A study of bladed-disk vibration control using magnetic bearings is presented. A key issue is a method for achieving practical controllability for such a system. For a tuned or symmetrically mistuned bladed disk assembly, several vibration modes are coupled only to the axial dynamics. Magnetic thrust bearings generally lack sufficient bandwidth to control even moderately high frequency vibration. A simplified model is developed and used to identify controllable vibration modes. A control strategy based upon deliberately mistuning in a non-symmetric manner is developed. The method presented does not require a thrust bearing for complete controllability of a bladed disk assembly via hub based actuators. However, since the linearized model for such a system has time periodic coefficients, an advanced time period controller is required. Controlling time periodic systems is a significant engineering challenge. One innovative approach that seems to be especially promising involves application of the Lyapunov Floquet (LF) transformation to eliminate time periodic terms from the system state matrices. Traditional control design techniques are then applied and the resulting gains transformed back to the original domain. Some simulation results are presented and discussed to illustrate the method.

scholarly journals Improved Reliability of Bladed Disks due to Friction Dampers

1997 ◽  
Author(s):  
Walter Sextro ◽  
Karl Popp ◽  
Ivo Wolter
Keyword(s):  
Dry Friction ◽  
Three Dimensional ◽  
Line Contact ◽  
Two Dimensional ◽  
Centrifugal Forces ◽  
Friction Damper ◽  
Blade Vibration ◽  
Friction Dampers ◽  
Bladed Disk ◽  
Bladed Disk Assembly

Friction dampers are installed underneath the blade platforms to improve the reliability. Because of centrifugal forces the dampers are pressed onto the platforms. Due to dry friction and the relative motion between blades and dampers, energy is dissipated, which results in a reduction of blade vibration amplitudes. The geometry of the contact is in many cases like a Hertzian line contact. A three-dimensional motion of the blades results in a two-dimensional motion of one contact line of the friction dampers in the contact plane. An experiment with one friction damper between two blades is used to verify the two-dimensional contact model including microslip. By optimizing the friction dampers masses, the best damping effects are obtained. Finally, different methods are shown to calculate the envelope of a three-dimensional response of a detuned bladed disk assembly (V84.3-4th-stage turbine blade) with friction dampers.

On the Analysis of Time-Periodic Nonlinear Hamiltonian Dynamical Systems

1995 ◽  
Author(s):  
Eric A. Butcher ◽  
S. C. Sinha
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Normal Form ◽  
Linear Part ◽  
Normal Form Theory ◽  
Mathieu’S Equation ◽  
Form Theory ◽  
Hamiltonian Dynamical Systems ◽  
Time Invariant ◽  
Time Periodic

Abstract In this paper, some analysis techniques for general time-periodic nonlinear Hamiltonian dynamical systems have been presented. Unlike the traditional perturbation or averaging methods, these techniques are applicable to systems whose Hamiltonians contain ‘strong’ parametric excitation terms. First, the well-known Liapunov-Floquet (L-F) transformation is utilized to convert the time-periodic dynamical system to a form in which the linear pan is time invariant. At this stage two viable alternatives are suggested. In the first approach, the resulting dynamical system is transformed to a Hamiltonian normal form through an application of permutation matrices. It is demonstrated that this approach is simple and straightforward as opposed to the traditional methods where a complicated set of algebraic manipulations are required. Since these operations yield Hamiltonians whose quadratic parts are integrable and time-invariant, further analysis can be carried out by the application of action-angle coordinate transformation and Hamiltonian perturbation theory. In the second approach, the resulting quasilinear time-periodic system (with a time-invariant linear part) is directly analyzed via time-dependent normal form theory. In many instances, the system can be analyzed via time-independent normal form theory or by the method of averaging. Examples of a nonlinear Mathieu’s equation and coupled nonlinear Mathieu’s equations are included and some preliminary results are presented.

The Effect of Non-Uniform Aerodynamic Loading on the Blade Responses

2007 ◽  
Author(s):  
Abdelgadir M. Mahmoud ◽  
Mohd S. Leong
Keyword(s):  
Turbine Blades ◽  
Forced Response ◽  
Flow Section ◽  
Flow Distortion ◽  
Inlet Flow ◽  
Bladed Disk ◽  
Aerodynamic Loading ◽  
Bladed Disk Assembly ◽  
Flow Generator ◽  
Inlet Flow Distortion

Turbine blades are always subjected to severe aerodynamic loading. The aerodynamic loading is uniform and Of harmonic nature. The harmonic nature depends on the rotor speed and number of nozzles (vanes counts). This harmonic loading is the main sources responsible for blade excitation. In some circumstances, the aerodynamic loading is not uniform and varies circumferentially. This paper discussed the effect of the non-uniform aerodynamic loading on the blade vibrational responses. The work involved the experimental study of forced response amplitude of model blades due to inlet flow distortion in the presence of airflow. This controlled inlet flow distortion therefore represents a nearly realistic environment involving rotating blades in the presence of airflow. A test rig was fabricated consisting of a rotating bladed disk assembly, an inlet flow section (where flow could be controlled or distorted in an incremental manner), flow conditioning module and an aerodynamic flow generator (air suction module with an intake fan) for investigations under laboratory conditions. Tests were undertaken for a combination of different air-flow velocities and blade rotational speeds. The experimental results showed that when the blades were subjected to unsteady aerodynamic loading, the responses of the blades increased and new frequencies were excited. The magnitude of the responses and the responses that corresponding to these new excited frequencies increased with the increase in the airflow velocity. Moreover, as the flow velocity increased the number of the newly excited frequency increased.

Nonlinear Modal Analysis and Energy Localization in a Bladed Disk Assembly

2008 ◽  
Author(s):  
F. Georgiades ◽  
M. Peeters ◽  
G. Kerschen ◽  
J. C. Golinval ◽  
M. Ruzzene
Keyword(s):  
Modal Analysis ◽  
Nonlinear Oscillations ◽  
Periodic Structures ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Energy Localization ◽  
Bladed Disk ◽  
Bladed Disk Assembly ◽  
Nonlinear Modal Analysis ◽  
Nonlinear Normal

The objective of this study is to carry out modal analysis of nonlinear periodic structures using nonlinear normal modes (NNMs). The NNMs are computed numerically with a method developed in [18] that is using a combination of two techniques: a shooting procedure and a method for the continuation of periodic motion. The proposed methodology is applied to a simplified model of a perfectly cyclic bladed disk assembly with 30 sectors. The analysis shows that the considered model structure features NNMs characterized by strong energy localization in a few sectors. This feature has no linear counterpart, and its occurrence is associated with the frequency-energy dependence of nonlinear oscillations.

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

2021 ◽  
Author(s):  
Douksoon Cha
Keyword(s):  
Simple Model ◽  
Efficient Method ◽  
Narrow Band ◽  
Random Excitation ◽  
Additional Mass ◽  
Friction Dampers ◽  
Analytical Technique ◽  
Bladed Disk ◽  
Bladed Disk Assembly

Abstract 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.

Order-Tuned Vibration Absorbers for Cyclic Rotating Flexible Structures

2005 ◽  
Author(s):  
Brian J. Olson ◽  
Steve W. Shaw ◽  
Christophe Pierre
Keyword(s):  
Equations Of Motion ◽  
Flexible Structures ◽  
Closed Form Solution ◽  
Nonlinear Effects ◽  
Form Solution ◽  
Vibration Absorbers ◽  
Bladed Disk ◽  
Tuned Vibration Absorbers ◽  
Engine Order ◽  
Bladed Disk Assembly

This paper investigates the use of order-tuned absorbers to attenuate vibrations of flexible blades in a bladed disk assembly subjected to engine order excitation. The blades are modeled by a cyclic chain of N oscillators, and a single vibration absorber is fitted to each blade. These absorbers exploit the centrifugal field arising from rotation so that they are tuned to a given order of rotation, rather than to a fixed frequency. A standard change of coordinates based on the cyclic symmetry of the system essentially decouples the governing equations of motion, yielding a closed form solution for the steady-state response of the overall system. These results show that optimal reduction of blade vibrations is achieved by tuning the absorbers to the excitation order n, but that the resulting system is highly sensitive to small perturbations. Intentional detuning (meaning that the absorbers are slightly over- or under-tuned relative to n) can be implemented to improve the robustness of the design. It is shown that by slightly undertuning the absorbers there are no system resonances near the excitation order of interest and that the resulting system is robust to mistuning (i.e., small random uncertainties in the system parameters) of the absorbers and/or blades. These results offer a basic understanding of the dynamics of a bladed disk assembly fitted with order-tuned vibration absorbers, and serve as a first step to the investigation of more realistic models, where, for example, imperfections and nonlinear effects are considered, and multi-DOF and general-path absorbers are employed.

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

2020 ◽  
Author(s):  
Alwin Förster ◽  
Lars Panning-von Scheidt ◽  
Jörg Wallaschek
Keyword(s):  
Degrees Of Freedom ◽  
Turbine Blades ◽  
Random Excitation ◽  
Linearization Method ◽  
Equivalent Linearization ◽  
Friction Damper ◽  
Bladed Disk ◽  
Stationary Stochastic Processes ◽  
Bladed Disk Assembly ◽  
Equivalent Linearization Method

Abstract 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.

scholarly journals Full Characterization of Act-and-wait Control for First-order Unstable Lag Processes

2010 ◽  
Vol 16 (7-8) ◽  
pp. 1209-1233 ◽  
Author(s):  
T. Insperger ◽  
P. Wahi ◽  
A. Colombo ◽  
G. Stépán ◽  
M. Di Bernardo ◽  
...  
Keyword(s):  
Time Delay ◽  
Feedback Systems ◽  
Periodic Control ◽  
First Order ◽  
Full Characterization ◽  
The Stability ◽  
And Control ◽  
Time Periodic ◽  
Special Case

Act-and-wait control is a special case of time-periodic control for systems with feedback delay, where the control gains are periodically switched on and off in order to stabilize otherwise unstable systems. The stability of feedback systems in the presence of time delay is a challenging problem. In this paper, we show that the act-and-wait type time-periodic control can always provide deadbeat control for first-order unstable lag processes with any (large but) fixed value of the time delay in the feedback loop. A full characterization of this act-and-wait controller with respect to the system and control parameters is given based on performance and robustness against disturbances.

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