Research And Simulation Of Dynamic Characteristics Of Bearing Rotor System Under Hamilton System

As the core component,bearing rotor system is widely used in generators,gas turbine,aviation generator and other mechanical equipment.In view of its dynamic characteristics,the most widely used numerical analysis methods are transfer matrix method and finite element method.However,the accuracy of transfer matrix method is low and numerical instability is easy to occur.Finite element method is time-consuming and takes up a lot of memory.Therefore,this dissertation combines the above two algorithms to build an algorithm with both calculation accuracy and running speed,which not only enriches the algorithm theory,but also has important practical significance.Constructing a symplectic numerical algorithm is the key to ensure long-term numerical stability.Therefore,under the background of Hamilton system,this dissertation constructs the symplectic transfer matrix and verifies that the method has high accuracy in the critical speed and mode.The precise integration scheme based on Magnus series is constructed to solve the problem of insufficient precision and limited stability of the stepwise integration method in solving dynamic equations.The main work of this dissertation is as follows:1.The basic format of the classical transfer matrix method is derived.Some important conclusions about Hamilton matrix and symplectic geometry are given.The precise integration method used to solve the dynamic equations of linear structures is introduced,and the precise calculation steps of the matrix exponential are given.2.The finite element method and transfer matrix method are combined to construct the mathematical model of system motion.The transfer symplectic matrix of the rotor under Hamilton system is derived and the calculation formulas of rotor vibration mode,critical speed and dynamic response are given.Numerical experiments verify that the numerical accuracy and numerical stability of the transfer symplectic matrix method are improved compared with the traditional transfer matrix method when calculating the high order critical speed.3.This dissertation improves the precise integration method and constructs the precise integration scheme based on Magnus series.Firstly,the dynamic equation is directed to the Hamilton system to obtain the structure of the equation solution v(t)=e?(t)v0.Then,the specific expression of the Magnus series Q(t)is obtained through detailed derivation and proof,and the iterative coefficient matrix exp(Qn)is obtained by using the Gauss-Legendre quadrature formula to approximate the numerical value of the Magnus series.The precise integral scheme of the iterative coefficient matrix exp(Qn)is given by using the precise calculation of matrix exponent.Finally,through a numerical example,the precise integration method based on Magnus series is verified superior to the Newmark-? method in the algorithm of calculation accuracy,stability,the computational efficiency and other aspects.In this paper,the transfer symplectic matrix method under Hamilton system is applied to the analysis of the dynamic characteristics of the rotor.Compared with the traditional transfer matrix method,the transfer symplectic matrix method proposed in this paper avoids solving the aggregation model of the rotor beam,and simplifies the calculation to some extent and its physical significance is clear.The precise integration method based on Magnus series is used to solve the transient effect of the dynamic equation,which provides an efficient and stable analysis method for the real-time working condition of the rotor system,and provides a theoretical basis for the optimal design of the rotor's working parameters and structure.