Vibration Localization Characteristics Of A Nonlinear Mistuned Bladed Disk System

The bladed disk system is a key component of the turbo machine rotor such as in aero engine and steam turbine. Mistuning is defined as differences in blade to blade geometry or material properties, which may be attributed to material tolerances and manufacturing/installation error or in-service degradation and thus is likely to be “small” and inevitable. The forced response of blades is very sensitive to the mistuning of blades. Mistuning restricts the vibratory energy into several blades, causing vibration localization for the bladed disk system. The localization phenomenon can increase the vibratory stress in the resonant region, resulting in the high cyclic fatigue failure and even bring serious blade crack or break. As the response of the nonlinear system becomes more complex, it is necessary to analyze the vibration localization of the nonlinear bladed disk system. Taking the bladed disk system of the aero-engine compressor as the background, the mechanical model is established which contains dry friction and gap. Using a lumped parameter model and finite element model, the vibration localization of the nonlinear mistuned bladed disk system has been studied and the influence of mistuning on the dynamic response of the nonlinear bladed disk system has also been analyzed.The lumped parameter model with two degree of freedom(DOF) in a single sector of the bladed disk system is described firstly, which contains nonlinear parameters such as dry friction and gap. A concrete analysis of friction, coupling force of the system with clearance, aerodynamic force are showed, then the dynamic equations of the nonlinear bladed disk system are obtained. Secondly, the modal localization and vibration response localization of the bladed disk system are presented respectively, while four order Runge-Kutta numerical method is applied to solve the equation and analyze its dynamic characteristics. The result shows that, the natural frequencies of the strong and weak coupling system both appears two frequency bands; the vibration response localization phenomenon of the weak coupling system is more obvious than those of the strong coupling system. Vibration localization also appears in the tuned system with nonlinear factors. By using amplitude magnification factor(AMF), vibration response localization of the linear and nonlinear mistuned bladed disk has been explored, which uncovers the existence of AMF's threshold. And the degree of vibration response localization of the mistuned system reduces because of nonlinear dry friction and gap. The analysis of the nonlinear tuned system turns out that, with different excitation frequencies, nonlinear dynamics behaviors such as one-period motion, multi-period harmonic motion and chaotic motion have been revealed. Besides, as mistuning factor exists, the behavior of the nonlinear mistuned disk system becomes more complex. Finally the modal localization phenomenon in the mistuned bladed disk system is discussed based on the finite element model. The mode shapes under different mistuning strength or under different order of the tuned/mistuned bladed disk system are analyzed. The coupling mode shapes of the leaf disc under higher order vibration are also explored.The result reveals the influence of dry friction and gap on the mistuned bladed disk system, enrichs the fundamental theories of the vibration localization, and provides guiding about optimization design of detuning of the nonlinear bladed disk system which contains dry friction and gap.