The Kinetic Study Of Gear Transmission System

In the mechanical transmission field,gear transmission is one of the most important transmission forms.The gear transmission system generally has the following characteristics: First,it is subjected to high torsion by the long time and high strength.Some problems such as pitting,wear or cracking may occur in the gear system.Second,due to the complexity of the system,because of the difference in running machines,Traction motor,gear box,etc.are different.Therefore,the structure of the gear system is also complicated.Third,due to the influence of nonlinear factors,It makes the establishment and analysis of the model difficult,which makes the model of the gear transmission system more complicated.Therefore,the indepth dynamics study of the gear system has important theoretical and practical significance.This article starts from the reality,Three models of gear transmission system with clearance are selected.Based on Newton's second law to calculate the differential equation of gear transmission system,and to obtain the dimensionless differential equations of the gear transmission system,The numerical solution of the corresponding gear transmission system is obtained by numerical calculation.The bifurcation diagram,time history diagram,phase diagram and Poincaré section diagram of the gear transmission system are obtained by using MATLAB numerical simulation software to control the parameters.Then,by combining the response maps corresponding to the various systems obtained above,the specific nonlinear dynamic behaviors are studied,study the changes in the motion state of the gear system,The process from periodic motion to quasi-periodic motion to chaos has been analyzed.This paper provides a reference for the reasonable selection of gear transmission system and system parameters.The second chapter establishes a mechanical model of a single-degree-of-freedom gear transmission system.Several sets of parameters were selected to obtain the bifurcation diagram of the system.Through the analysis of the bifurcation diagram combined with the time history diagram,phase diagram and Poincaré section diagram,It can be seen that the single-degree-offreedom gear transmission system will generate multiplication bifurcation,and the path leading to chaos will occur through multiplication bifurcation.In the third chapter,the mechanical model of a double-degree-of-freedom gear transmission system is established.Through the analysis of the image,the motion state of the mechanical model of the double-degree-of-freedom gear transmission system at different dimensionless frequencies is studied.Numerical simulation is carried out by using MATLAB.The corresponding control parameters are selected to obtain the bifurcation diagram of the system,and then various different motion modes of the gear system and different motion modes are obtained.The fourth chapter establishes a mechanical model of a three-degree-of-freedom gear transmission system.Through the mechanical analysis and numerical calculation of the mechanical model system,the existence condition of the periodic solution of the mechanical model of the three-degree-of-freedom gear transmission system is obtained.The boundary conditions of the system motion establish the Poincaré map of the gear system and the corresponding Jocabi matrix.The behavior of bifurcation and chaos in a three-degree-offreedom gap-gear transmission system is analyzed comprehensively.