Theoretical Analysis And Experimental Study On Nonlinear Coupling Vibration Of Rotor Bearing System

With the development of industry,the theoretical analysis of linear vibration cannot meet the need of solving nonlinear vibration problem in engineering practice.There are a lot of nonlinear factors,such as nonlinear oil film force,nonlinear air gap force,nonlinear sealing force and nonlinear damping force.According to the nonlinear stiffness force and nonlinear damping force which are common in the rotor system,introducing characteristic parameters such as linear scale factor,nonlinear scale factor and coupling ratio,a general form of nonlinear force model is constructed.Then,based on the assumption of large perturbation and large deformation,a general form of nonlinear coupling vibration model of a high-speed flexible single-disc rotor system is constructed.Through comparison with traditional models,such as Jeffcott model,Muszynska model,Lund model and Ravikovich model,the different manifestations of the cross stiffness terms and the nonlinear stiffness damping terms for the nonlinearity of the rotor system are analyzed,and the instability conditions such as resonance and whirl of the rotor system are analyzed.Based on the basic principle and method of multi-scale method,the response analytical solutions of the nonlinear coupling vibration model are deduced under free vibration and forced vibration conditions.In the analytical deduction under free vibration condition,the influence of the nonlinear terms on the natural frequency of the rotor system is discussed.In the analytical deduction under forced vibration condition,there are two type models according to the magnitude orders of the damping: the high order damping forced vibration model and the same order damping forced vibration model,and the analytical solutions of the corresponding models are obtained.The physical significance of parameters in the response analytical solutions is analyzed.The mechanism of frequency modulation,amplitude modulation and phase modulation is researched.The influence mechanism of inherent properties such as stiffness and damping on nonlinear vibration response of the rotor system is analyzed.According to the response expressions of the model in this paper,the frequency response equations are deduced,and are compared with the frequency response equation of the traditional linear model.Besides,the general response ratio is deduced,and the significance and the change degree of the general response in corresponding speed are analyzed.According to the analytical expressions of the general response of the nonlinear coupling vibration model,the theoretical analyses are carried out,and are verified through the numerical simulations and the rotor principle experiments.First,the response calculations are given,including the general response,the steady-state response,the transient-state response,the amplitude curve,the phase curve,and the general response raito curve.Then the whole spectrum characteristics of the Fast Fourier Transform and the Short Time Fourier Transform of the rotor system is studied,and the influence of the characteristic parameters such as the transient time scale factor,the stiffness speed ratio and the damping speed ratio on the rotor vibration response process and the global behavior are analyzed,and the variation characteristics of the nonlinear vibration in time domain and frequency domain are further revealed.Through the experiment of nonlinear vibration on working frequency and the experiment of damping's effect on amplitude-frequency characteristics,the difference of frequency response equation between the model in this paper and the traditional linear model are compared and analyzed,and the influence of linear damping and nonlinear damping on the amplitude are verified.As a result,the rationality and validity of the nonlinear coupling vibration model in this paper and its response analytical solutions are further validated,and the research method of nonlinear rotor dynamics is extended.The typical engineering cases of the high speed cooling turboexpander,turbine generator and micro gas turbine are analyzed.The experimental test systems including gas supply system,control system,data acquisition and analysis system,and the corresponding experimental devices are introduced.The DASP software is used to analyze the experimental data,such as time-amplitude-frequency spectrum,shaft orbit,bifurcation and spectrum analysis.The influence of the experimental parameters such as bearing air pressure,bearing air temperature and sealing material on the inherent properties such as stiffness and damping of the rotor system are studied,and the following influence on the nonlinear vibration behavior such as whirl,whip and rubbing of the rotor system are analyzed.Therefore,the rationality and practicability of the nonlinear coupling vibration model and the response analytical solutions are further verified,and the response mechanism and the vibration law of the rotor linear and nonlinear vibration behaviors are deeply elaborated.There are still many nonlinear problems and phenomena in the rotor system,which cannot be analyzed and explained by linear theory,and this is the direction of further research in nonlinear theoretical analysis and engineering application.