Response Analysis Of A Mechanical Rotating System Excited By Stochastic Noise

The stochastic noise excitation reflects the change of the system under the actual condition.The dynamic characteristics of the governor system are very complex due to the variable working conditions,state switching,parameter time-varying and some non smooth factors.The optimization of the system needs to understand the matching rules of system parameters.Therefore,it is of practical significance to the research of the governor system under the excitation of stochastic noise.Based on the governor models in different states,this paper focuses on the stability and stochastic bifurcation of the system under stochastic noise excitation.The main work is carried out from two aspects:(1)Based on the mechanical centrifugal governor system,the stochastic response of the centrifugal governor system under the excitation of color noise and the bifurcation analysis of the centrifugal governor system in the two parameter plane under the excitation of color noise are studied.(2)Based on PI turbine speed regulation system with hysteresis,the solution and response of Fokker Planck equation of multivariable delay differential equation under white noise excitation are studied.The core parts of this paper are as follows:1.This paper introduces the research background,significance and research status at home and abroad of speed regulation system and stochastic excitation,and expounds the research methods and theories.2.The stability and stochastic bifurcation of centrifugal governor system under uniform colored noise approximation are studied,and the effectiveness of the solution is verified by Monte Carlo numerical simulation.The simulation results show that the influence of noise intensity and correlation time on probability density function is just opposite.In addition,the bifurcation of the centrifugal governor system in the two parameter plane under the deterministic state and the colored noise excitation is discussed respectively.According to the maximum Lyapunov exponent diagram and bifurcation diagram on the two parameter plane,it is found that there are abundant periodic and chaotic motion modes in the deterministic state,under noise excitation,with the change of noise intensity and correlation time,the periodic state will be destroyed,mainly from quasi periodic state to periodic state.It is further found that the change of noise intensity will change the distribution of coexisting attractors,destroy the coexisting attractors and produce chaotic attractors.3.Based on the lag PI turbine governing system,the stochastic response under white noise parametric excitation is studied.Firstly,the approximate probability density solution of the FPK equation of the multivariable delay differential equation is obtained by using the small delay expansion.Secondly,in the sense of each variable,the maximum Lyapunov exponent method is used to judge the stability conditions.Finally,based on the probability density function with only partial variables,the noise intensity D is used as the control parameter to analyze the stochastic bifurcation.It is found that the increase of parameter D changes the peak shape of the probability density function,resulting in P bifurcation.