Research On Multi-parameter Bifurcation And Global Characteristics Of Gear System

Gear system has the advantages of compact structure,high transmission efficiency and high transmission precision,and it is widely used in mechanical transmission system devices.Nonlinear vibration affects the stability and reliability of gear system.It is of great scientific significance and engineering value to study the mechanism of nonlinear vibration produced by gear system and its influencing factors in order to reduce vibration,reduce noise and improve the service life and reliability of gear system in the process of gear system operation.This paper follows the research route from simple to complex,with single-degree of-freedom gear transmission system,three-degree-of-freedom gear transmission system,gear-rotor system as the research object.Based on nonlinear vibration theory,through the calculation and analysis system of parameter plane characteristic distribution map,bifurcation diagram,Maximum Lyapunov exponent,Floquet multiplication,the multi-parameter bifurcation and global characteristics of gear system are studied by attracting domain,multi-initial phase diagram and multi-initial Poincare mapping diagram,and the contents are as follows:1.By constructing the calculation method of the bifurcation curve in the parameter plane,the bifurcation curve in the parameter plane is obtained,and the stable region and the unstable region of the system in the parameter plane are obtained by calculating the dynamic characteristic distribution diagram in the parametric plane,and the influence of parameter coupling on the dynamic characteristics of the gear system is analyzed by combining the two.2.The Jacobi matrix and Floquet multiplication algorithm of Poincare mapping of gear system are constructed,and the bifurcation types of bifurcation curves are judged by combining single parameter bifurcation graph,maximum Lyapunov index graph(tle graph),phase diagram,Poincare mapping diagram,etc.This paper analyzes the road from the system to chaos,studies the transferred process between different motion types in the parameter plane,and provides a theoretical basis for the dynamic design and parameter optimization of the gear system.3.Calculate the bifurcation diagram,phase diagram and Poincare cross-sectional diagram under the multi-initial value of the gear system,and use the cell mapping algorithm to obtain the evolution process of the attraction domain when the system changes with the parameters.This paper analyzes the evolution mechanism of multi-attraction coexistence and attraction domain,studies the global dynamic characteristics of the system,and provides some theoretical basis for the initial value selection of gear system.