Research Of Vibration Characteristics Of Nonlinear Dual-rotor System And Energy Tracks

A dual-rotor system is a core component of the modern advanced equipment such as aero-engines and gas turbines.It has characteristics of high speed,high temperature and large load.Multiple flexible rotors couple with each other.The study of nonlinear dual-rotor systems is of great significance to the structural design,the fault detection and maintenance of aero-engines and gas turbines.Based on structural characteristics of the dual-rotor system,a novel dual-rotor dynamic model with nonlinear spring characteristics of rotors is proposed in this paper.In addition,because analyses of the phase-space will weaken the coupling relationship in the system,a novel analytical method based on the vibration energy space is also proposed to analyze the nonlinear vibration characteristics of the system.According to the lumped mass method,dynamics equations of three typical single-rotor models are obtained.Based on models of rotors,expressions of the potential energy of rotor systems are derived systematically,and the high dimensional nonlinear spring characteristics modelling is revealed firstly through the potential energy with nonlinear variation characteristics.It is found that nonlinear spring characteristics of rotors are inducements of subharmonic resonances and there exists a one-to-one correspondence between nonlinear coefficients of nonlinear spring characteristics and orders of subharmonic resonances.Considering nonlinear spring characteristics of rotors,dynamics equations of the dual-rotor system are obtained based on the Lagrange equation.Combined with results of numerical simulations and mathematical analyses,vibrational responses of the dual-rotor system with linear condition are systematically analyzed.The Campbell diagram of the low pressure rotor shows that the coupling relationship of the high and low pressure rotors causes the coupling critical speed,and the coupling critical speed is consistent with the critical speed of the high pressure rotor.In addition,resonance responses of the dual-rotor system show that the counter rotation between the high and low pressure rotors causes the elliptical axis orbit of the low pressure rotor.Because the coupling relationship of the nonlinear dynamics model of the dual-rotor system is extremely complicated,the genetic algorithm is used to improve the harmonic balance method to obtained theoretical solutions,and the Floquet theory is applied to judge stabilities of theoretical solutions.Theoretical solutions are consistent with numerical simulations,which verifies the correctness of the improved harmonic balance method.With reference to the theory of phase space analyses,this paper elaborates the method of the vibration energy analysis based on the energy space,and proposes some concepts such as the reconstruction of the energy space,the energy-spectrum analysis and energy-phase plane.The study of the energy space shows that energy tracks can well exhibit characteristics of different nonlinear vibrations,and energy tracks by the reconstruction of the energy space are a good proof of theoretical analyses of nonlinear coefficients.Based on nonlinear dynamics equations of the dual-rotor system,the internal resonance phenomena and subharmonic resonances of the dual-rotor system are analyzed for the first time.The internal resonance phenomena in the vicinity of the coupling critical speed of the low pressure rotor are obtained,and it is found that the energy transfer between the high and low pressure rotors causes complex nonlinear vibrations on the high pressure rotor.The complex nonlinear vibrations are similar to internal resonance phenomena on the low pressure rotor.Subharmonic resonances of orders 1/2 and 1/3 are analyzed to obtain the characteristics of subharmonic resonances of the dual-rotor system.Results show that the intense energy exchange between the high and low pressure rotors appears,and independent branching solutions in the solution space appear corresponding to subharmonic resonances of orders 1/2 and 1/3.In addition,the paper studies the vibrational characteristics of the dual-rotor system under strong nonlinear conditions.It is found that the strong nonlinear system has complex nonlinear vibrations,such as beat vibrations,almost periodic motions and chaotic motions,and the transition between the nonlinear vibrations is abrupt.Results of this research will provide a new research direction and a research method for analyzing nonlinear vibration responses of dual-rotor systems,and they will provide a theoretical basis for the vibration analysis and control of rotor systems.