scholarly journals Friction-induced traveling wave coupling in tuned bladed-disks

2021 ◽  
Author(s):  
Javier González-Monge ◽  
Salvador Rodríguez-Blanco ◽  
Carlos Martel
Keyword(s):  
Traveling Wave ◽  
Oscillation Amplitude ◽  
Time Integration ◽  
Numerical Continuation ◽  
Elastic Response ◽  
Limit Cycle Oscillation ◽  
Final States ◽  
Small Correction ◽  
Microslip Friction ◽  
Cycle Oscillation

AbstractFlutter is a major constraint on modern turbomachines; as the designs move toward more slender, thinner, and loaded blades, they become more prone to experience high cycle fatigue problems. Dry friction, present at the root attachment for cantilever configurations, is one of the main sources of energy dissipation. It saturates the flutter vibration amplitude growth, producing a limit cycle oscillation whose amplitude depends on the balance between the energy injected and dissipated by the system. Both phenomena, flutter and friction, typically produce a small correction of the purely elastic response of the structure. A large number of elastic cycles is required to notice their effect, which appears as a slow modulation of the oscillation amplitude. Furthermore, even longer time scales appear when multiple traveling waves are aerodynamically unstable and exhibit similar growth rates. All these slow scales make the system time integration very stiff and CPU expensive, bringing some doubts about whether the final solutions are properly converged. In order to avoid these uncertainties, a numerical continuation procedure is applied to analyze the solutions that set in, their traveling wave content, their bifurcations and their stability. The system is modeled using an asymptotic reduced order model and the continuation results are validated against direct time integrations. New final states with multiple traveling wave content are found and analyzed. These solutions have not been obtained before for the case of microslip friction at the blade attachment; only solutions consisting of a single traveling wave have been reported in previous works.

A Harmonic Balance Approach for Modeling Three-Dimensional Nonlinear Unsteady Aerodynamics and Aeroelasticity

2002 ◽  
Author(s):  
Jeffrey P. Thomas ◽  
Earl H. Dowell ◽  
Kenneth C. Hall
Keyword(s):  
Limit Cycle ◽  
Harmonic Balance ◽  
Structural Model ◽  
Oscillation Amplitude ◽  
Three Dimensional ◽  
Unsteady Aerodynamics ◽  
Finite Amplitude ◽  
Limit Cycle Oscillation ◽  
Unsteady Aerodynamic ◽  
Cycle Oscillation

Presented is a frequency domain harmonic balance (HB) technique for modeling nonlinear unsteady aerodynamics of three-dimensional transonic inviscid flows about wing configurations. The method can be used to model efficiently nonlinear unsteady aerodynamic forces due to finite amplitude motions of a prescribed unsteady oscillation frequency. When combined with a suitable structural model, aeroelastic (fluid-structure), analyses may be performed at a greatly reduced cost relative to time marching methods to determine the limit cycle oscillations (LCO) that may arise. As a demonstration of the method, nonlinear unsteady aerodynamic response and limit cycle oscillation trends are presented for the AGARD 445.6 wing configuration. Computational results based on the inviscid flow model indicate that the AGARD 445.6 wing configuration exhibits only mildly nonlinear unsteady aerodynamic effects for relatively large amplitude motions. Furthermore, and most likely a consequence of the observed mild nonlinear aerodynamic behavior, the aeroelastic limit cycle oscillation amplitude is predicted to increase rapidly for reduced velocities beyond the flutter boundary. This is consistent with results from other time-domain calculations. Although not a configuration that exhibits strong LCO characteristics, the AGARD 445.6 wing nonetheless serves as an excellent example for demonstrating the HB/LCO solution procedure.

Basin of Attraction and Limit Cycle Oscillation Amplitude of an Ankle-Hip Model of Balance on a Balance Board

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Erik Chumacero-Polanco ◽  
James Yang
Keyword(s):  
Limit Cycle ◽  
Basin Of Attraction ◽  
Oscillation Amplitude ◽  
Feedback Gain ◽  
Limit Cycle Oscillation ◽  
Physical Parameters ◽  
Risk Of Falls ◽  
Cycle Oscillation ◽  
Three Degree Of Freedom ◽  
Balance Board

The study of upright posture (UP) stability is of relevance to estimating risk of falls, especially among people with neuromuscular deficits. Several studies have addressed this problem from a system dynamic approach based on parameter bifurcation analyses, which provide the region of stability (RoS) and the delimiting bifurcation curves (usually Hopf and pitchfork) in some parameter-spaces. In contrast, our goal is to determine the effect of parameter changes on the size of the basin of attraction (BoA) of the UP equilibrium and the amplitude of the limit cycle oscillations (LCOs) emerging from the Hopf bifurcations (HBs). The BoA is an indicator of the ability of the UP to maintain balance without falling, while LCOs may explain the sway motion commonly observed during balancing. In this study, a three degree-of-freedom model for a human balancing on a balance board (BB) was developed. Analysis of the model revealed the BoAs and the amplitude of the LCOs. Results show that physical parameters (time-delays and feedback control gains) have a large impact on the size of the BoA and the amplitude of the LCOs. Particularly, the size of the BoA increases when balancing on a rigid surface and decreases when either proprioceptive or combined visual and vestibular (V&V) feedback gain is too high. With respect to the LCOs, it is shown that they emerge from both the subcritical and supercritical HBs and increase their amplitudes as some parameters vary.

Aeroelastic Stability Assessment of an Industrial Compressor Blade Including Mistuning Effects

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Yaoguang Zhai ◽  
Ronnie Bladh ◽  
Göran Dyverfeldt
Keyword(s):  
Limit Cycle ◽  
Oscillation Amplitude ◽  
Forced Response ◽  
Design Flow ◽  
Limit Cycle Oscillation ◽  
Flow Conditions ◽  
Aeroelastic Stability ◽  
Flexural Mode ◽  
Choked Flow ◽  
Cycle Oscillation

This paper presents a comprehensive investigation into the aeroelastic stability behavior of a transonic front blade in an industrial compressor when operating outside its normal range of service parameters. The evolution of the airfoil’s aeroelastic stability in the first flexural mode is studied as the front blade operation progresses towards choked flow conditions. First, linearized 3D flutter computations representing today’s industry standard are performed. The linearized calculations indicate a significant, shock-driven flutter risk at these off-design flow conditions. To further explore the aeroelastic behavior of the rotor and to find a viable solution toward flutter risk elimination, two parallel investigations are undertaken: (i) flow perturbation nonlinearity effects and potential presence of limit-cycle oscillation, and (ii) effects of blade mistuning and flutter mitigation potential of intentional mistuning, including its impact on forced response behavior. The nonlinear harmonic analyses show that the minimum aerodynamic damping increases rapidly and essentially linearly with blade oscillation amplitude beyond the linear regime. Thus, a state of safe limit-cycle oscillation is predicted for the fully tuned blade. Additionally, it is found that intentional, realizable blade frequency offsets in an alternating pattern efficiently stabilize the blade. Finally, it is verified that alternating mistuning has a beneficial effect versus the inevitable random mistuning also in the forced response.

Aeroelastic Stability Assessment of an Industrial Compressor Blade Including Mistuning Effects

2011 ◽  
Author(s):  
Yaoguang Zhai ◽  
Ronnie Bladh ◽  
Go¨ran Dyverfeldt
Keyword(s):  
Limit Cycle ◽  
Oscillation Amplitude ◽  
Forced Response ◽  
Design Flow ◽  
Limit Cycle Oscillation ◽  
Flow Conditions ◽  
Aeroelastic Stability ◽  
Flexural Mode ◽  
Choked Flow ◽  
Cycle Oscillation

This paper presents a comprehensive investigation into the aeroelastic stability behavior of a transonic front blade in an industrial compressor when operating outside its normal range of service parameters. The evolution of the airfoil’s aeroelastic stability in the first flexural mode is studied as the front blade operation progresses towards choked flow conditions. First, linearized 3D flutter computations representing today’s industry standard are performed. The linearized calculations indicate a significant, shock-driven flutter risk at these off-design flow conditions. To further explore the aeroelastic behavior of the rotor and to find a viable solution toward flutter risk elimination, two parallel investigations are undertaken: (i) flow perturbation nonlinearity effects and potential presence of limit-cycle oscillation; and (ii) effects of blade mistuning and flutter mitigation potential of intentional mistuning, including its impact on forced response behavior. The nonlinear harmonic analyses show that the minimum aerodynamic damping increases rapidly and essentially linearly with blade oscillation amplitude beyond the linear regime. Thus, a state of safe limit-cycle oscillation is predicted for the fully tuned blade. Additionally, it is found that intentional, realizable blade frequency offsets in an alternating pattern efficiently stabilize the blade. Finally, it is verified that alternating mistuning has a beneficial effect versus the inevitable random mistuning also in the forced response.

scholarly journals Identifying limits of linear control design validity in nonlinear systems: a continuation-based approach

2021 ◽  
Author(s):  
D. H. Nguyen ◽  
M. H. Lowenberg ◽  
S. A. Neild
Keyword(s):  
Limit Cycle ◽  
Equations Of Motion ◽  
Numerical Continuation ◽  
Limit Cycle Oscillation ◽  
Nonlinear Frequency ◽  
Multiple Attractors ◽  
Chaotic Motions ◽  
Frequency Responses ◽  
Linear And Nonlinear ◽  
Cycle Oscillation

AbstractIt is well known that a linear-based controller is only valid near the point from which the linearised system is obtained. The question remains as to how far one can move away from that point before the linear and nonlinear responses differ significantly, resulting in the controller failing to achieve the desired performance. In this paper, we propose a method to quantify these differences. By appending a harmonic oscillator to the equations of motion, the frequency responses at different operating points of a nonlinear system can be generated using numerical continuation. In the presence of strong nonlinearities, subtle differences exist between the linear and nonlinear frequency responses, and these variations are also reflected in the step responses. A systematic way of comparing the discrepancies between the linear and the nonlinear frequency responses is presented, which can determine whether the controller performs as predicted by linear-based design. We demonstrate the method on a simple fixed-gain Duffing system and a gain-scheduled reduced-order aircraft model with a manoeuvre-demand controller; the latter presents a case where strong nonlinearities exist in the form of multiple attractors. The analysis is then expanded to include actuator rate saturation, which creates a limit-cycle isola, coexisting multiple solutions (corresponding to the so-called flying qualities cliff), and chaotic motions. The proposed method can infer the influence of these additional attractors even when there is no systematic way to detect them. Finally, when severe rate saturation is present, reducing the controller gains can mitigate—but not eliminate—the risk of limit-cycle oscillation.

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