Transient Flutter Stability Analysis of Structural Mistuned Blisk by Energy Growth Method

2021 ◽  
Author(s):  
Luohui Ouyang ◽  
Qingzhen Bi ◽  
Hua Chen ◽  
Hai Shang ◽  
Li-Min Zhu
Keyword(s):  
Stability Analysis ◽  
Finite Time ◽  
Transient Stability ◽  
Maximum Energy ◽  
Dynamic State ◽  
Infinite Time ◽  
Structural Dynamic ◽  
Energy Growth ◽  
Eigenvalue Method ◽  
Growth Method

Abstract Blisks suffer from flutter, a self-sustained vibration caused by aerodynamic coupled forces. This instability could cause serious damage to the blades and the machine. Flutter stability is usually analyzed based on the eigenvalue method in the aspect of the linear structural dynamic system, which transforms a dynamics stability analysis into a point of equilibrium in an infinite time scale. However, in reality, most of the blisk vibrations arise on a finite time horizon. The transient vibration amplification may cause serious damage. This paper proposes a transient flutter stability analysis method in a finite time for structural mistuned blisk based on the energy growth method. Firstly, two common blisk models coupled aerodynamic force with different complexity are built, and are all expressed in the state space representation. A novel energy growth method is then employed to analyze the transient stability and to find the maximum energy growth of the models. The optimal initial condition which leads to the maximum energy growth is obtained. A new flutter stability criterion is developed to consider the transient stability based on the energy growth method and the infinite time stability based on the eigenvalue method. The new transient stability method is verified by two numerical studies. It is found that the structural mistuned blisk model which is traditionally predicted stable still has a transient instability in a finite time due to the non-normal property of the dynamic state matrix.

Non-Normal Dynamic Analysis for Predicting Transient Milling Stability

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Qingzhen Bi ◽  
Xinzhi Wang ◽  
Hua Chen ◽  
Limin Zhu ◽  
Han Ding
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Finite Time ◽  
Time Horizon ◽  
Transient Stability ◽  
Analysis Method ◽  
Linear Dynamics ◽  
Milling Stability ◽  
Energy Growth ◽  
Transient Energy

A transient milling stability analysis method is presented based on linear dynamics. Milling stability is usually analyzed based on asymptotic stability methods, such as the Floquet theory and the Nyquist stability criterion. These theories define stability that can return to equilibrium in an infinite time horizon under any initial condition. However, as a matter of fact, most dynamic processes in milling operations occur on a finite time scale. The transient vibration can be caused by some disturbance in practical milling process. Heavy transient vibrations were observed in existing works, though the machining parameters were selected in the stability zone determined by the asymptotic stability method. The strong transient vibrations will severely decrease the machining surface quality, especially for small workpieces in which the majority of machining process is executed in a short period of time. The analysis method of the transient milling stability is seldom studied, and only some experiments and conjectures can be found. Here the transient milling stability is defined as transient energy growth in a finite time horizon, and the prediction method of transient stability is proposed based on linear dynamics. The eigenvalues and non-normal eigenvectors of the Floquet transition matrix are all used to predict the transient milling stability, while only eigenvalues are employed in the traditional asymptotic stability analysis method. The transient stability is finally analyzed by taking the maximum vibration energy growth and the maximum duration time of transient energy growth in a finite time for optimal selection of processing parameters.

scholarly journals Modelling and Stability Analysis of Articulated Vehicles

2021 ◽  
Vol 11 (8) ◽  
pp. 3663
Author(s):  
Tianlong Lei ◽  
Jixin Wang ◽  
Zongwei Yao
Keyword(s):  
Stability Analysis ◽  
Critical Velocity ◽  
Equations Of State ◽  
Steering System ◽  
Analysis Model ◽  
Nonlinear Dynamic Model ◽  
Equilibrium Equations ◽  
Eigenvalue Method ◽  
Articulated Vehicles ◽  
The Stability

This study constructs a nonlinear dynamic model of articulated vehicles and a model of hydraulic steering system. The equations of state required for nonlinear vehicle dynamics models, stability analysis models, and corresponding eigenvalue analysis are obtained by constructing Newtonian mechanical equilibrium equations. The objective and subjective causes of the snake oscillation and relevant indicators for evaluating snake instability are analysed using several vehicle state parameters. The influencing factors of vehicle stability and specific action mechanism of the corresponding factors are analysed by combining the eigenvalue method with multiple vehicle state parameters. The centre of mass position and hydraulic system have a more substantial influence on the stability of vehicles than the other parameters. Vehicles can be in a complex state of snaking and deviating. Different eigenvalues have varying effects on different forms of instability. The critical velocity of the linear stability analysis model obtained through the eigenvalue method is relatively lower than the critical velocity of the nonlinear model.

scholarly journals Linear Stability Analysis and Validation of a Unified Solution Method for Fluid-Structure-Interaction on Structural Dynamic Problems

2005 ◽  
Author(s):  
C. G. Giannopapa ◽  
G. Papadakis
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Solution Method ◽  
Fluid Structure Interaction ◽  
Analytic Solutions ◽  
Computational Domain ◽  
Structural Dynamic ◽  
Fluid Structure ◽  
Structure Interaction

In the conventional approach for fluid-structure interaction problems, the fluid and solid components are treated separately and information is exchanged across their interface. According to the conventional terminology, the current numerical methods can be grouped in two major categories: Partitioned methods and monolithic methods. Both methods use two separate sets of equations for fluid and solid. A unified solution method has been presented [1], which is different from these methods. The new method treats both fluid and solid as a single continuum, thus the whole computational domain is treated as one entity discretised on a single grid. Its behavior is described by a single set of equations, which are solved fully implicitly. In this paper, 2 time marching and one spatial discretisation scheme, widely used for fluids’ equations, are applied for the solution of the equations for solids. Using linear stability analysis, the accuracy and dissipation characteristics of the resulting difference equations are examined. The aforementioned schemes are applied to a transient structural problem (beam bending) and the results compare favorably with available analytic solutions and are consistent with the conclusions of the stability analysis. A parametric investigation using different meshes, time steps and beam sizes is also presented. For all cases examined the numerical solution was stable and robust and proved to be suitable for the next stage of application to full fluid-structure interaction problems.

Sign in / Sign up

Export Citation Format

Share Document