Theoretical and experimental investigations on steady-state responses of rotor-blade systems with varying rotating speeds based on a new nonlinear dynamic model

Abstract

Rotor-blade systems are major units in turbine structures, whose dynamic responses will affect structural safety, energy conversion efficiency, overall durability and service performance. During high-speed rotation, periodic disturbances near resonant regions may lead to a large deflection of flexible blades and an unstable rotation of rotor-blade systems. Due to the coupling effect of rotation and vibration, the distributions of mass/inertia, damping and stiffness are related with varying rotation speed and local deformation in rotor-blade systems, which has not been concerned in conventional harmonic balance methods. In this paper, a modified harmonic balance method is proposed to obtain dynamic responses of rotor-blade systems with a comprehensive model in incremental form, which considers geometric nonlinearity, centrifugal and gyroscopic effects of flexible blades and nonlinear constraints between rotor and multiple blades. Based on Reddy’s high order shear deformation plate theory, dynamic equations for a rotating composite blade with a pre-setting angle is established with consideration of von Kármán type geometrical nonlinearity, varying rotating speeds and equivalent aerodynamic loads. A coupling motion equation for rotor-blade systems is derived out by assembling corresponding elemental equilibrium and joint nonlinear constraints. Steady-state responses are obtained by using a modified harmonic balance method which accounts nonlinearities of mass, damping and stiffness. Numerical and experimental studies for rotor-blade systems are carried out to validate the effectiveness of the proposed model. Results show that a higher rotating speed leads to larger natural frequencies of rotor-blade systems, and a more evidently coupling effect between motion and vibration. Meanwhile, joint constraints, damping effect and load distributions have evident influences on vibration amplitudes and resonant points of system’s steady-state responses.