Accurate prediction approach of dynamic characteristics for a rotating thin walled annular plate considering the centrifugal stress requirement

Abstract

In allusion to the problem that experimental results of similitude models of a rotating turbine disc predict dynamic characteristics of the prototype, the accurate design method of dynamic similitude models of a rotating thin walled annular plate is investigated by considering the centrifugal stress requirement. The vibration differential equation is employed to deduce geometrically complete scaling laws of dynamic frequency and centrifugal stress. In order to determine accurate distorted scaling laws of dynamic frequency, the sensitivity analysis and determination principle are used. For distorted scaling laws of centrifugal stress, the average approach of candidate distorted scaling laws is proposed, and its mathematical form is simple. Furthermore, the numerical validation indicates that distorted scaling laws can predict dynamic characteristics of the prototype and reflect the strength conditions or even failures of a prototype with good accuracy, and applicable intervals of the distorted scaling law are calculated. Finally, an acceptable procedure of the similitude design method of a rotating thin walled annular plate is provided, which guides to the design of test models considering centrifugal stress requirement.

Influence of Time Delay on Controlling the Non-Linear Oscillations of a Rotating Blade

“…a n = . φ n = 0 into Equation (11). The resulting non-linear algebraic equations system cannot be solved analytically, leading us to adopt the Newton-Raphson numerical technique.…”

“…This subsection involves the steady-state response curves of the blade vibrational amplitudes versus different parameters. These curves are plotted depending on the fixed points of Equation (11). In the following figures, the solid lines refer to stable trajectories, while the dashed lines refer to unstable ones.…”

“…Li et al [10] proposed an accurate analytical technique for studying the forced Mathieu oscillator based on the parameters variation method. Luo et al [11] considered the centrifugal stress to investigate the accurate design prototype's dynamic characteristics of a thin-walled rotating plate. Zhang et al [12] utilized analytical and numerical techniques to study the local bifurcation and stability of a rotating blade accompanied by extremely hot supersonic gas flow.…”