Research On The Erosion And Bifurcation Of The Safety Basin Of The Spur Gear System

Gear transmission system is a stable,efficient,safe and compact transmission mechanism.It is widely used in automobiles,high-speed railways,spacecrafts,machine tools and other mechanical equipment.When the vibration amplitude of gear meshing exceeds a certain limit,the stability of the system will be destroyed,and the safety performance and service life of mechanical equipment will be affected.In addition,the vibration of gear system will produce a lot of noise,which will do harm to people's physical and mental health.Studying the vibration mechanism of gear transmission system has important practical engineering significance and scientific value,for improving the safety performance and service life,reducing vibration and noise of the mechanical equipment.In this paper,the research of a single-stage spur gear system in an automobile gearbox are carried out.Following the research rules from simple to complex,the safety basin erosion and bifurcation of single-degree-of-freedom gear transmission system,three-degree-of-freedom gear transmission system and gear-rotor transmission system are studied respectively.The main contents of this paper are as follows:Firstly,the torsional vibration model of single-degree-of-freedom gear transmission system is introduced,which takes into account the non-linear factors such as backlash and comprehensive transmission error.Then,according to the dimensionless process of the model and the Hertz formula,the security region of the system is calculated.The process of erosion and bifurcation of the safety basin with different parameters is analyzed by numerical method.The periodicity and safety of the system's movement type in the safety basin are analyzed by the phase diagram and Poincare cross-section diagram.The occurrence of erosion and bifurcation of the safety basin is studied by the multi-initial bifurcation diagram of the system with the parameters changing.Then,the stability of the system motion is analyzed based on the Lyapunov exponent spectrum.Finally,the evolution law of safety basin erosion and bifurcation of single-degree-of-freedom gear transmission system under different parameters is obtained.Secondly,a three-degree-of-freedom gear transmission system model is described,considering the force and displacement of the bearing on the main and follower shaft.Based on the research method of single-degree-of-freedom gear transmission system,the evolution law of safety basin erosion and bifurcation of three-degree-of-freedom system under different parameters is further analyzed.When designing gears,these parameters should be ensured within a reasonable range.The causes of erosion and bifurcation of safety basin are summarized,and the effects of different types of bifurcation on safety basin bifurcation are discussed.Thirdly,the gear-rotor transmission system model is introduced,which abstracts the motor and other components connected to the gear input and output shaft into the rotor.The process of basin erosion and bifurcation of gear-rotor system under different parameters is analyzed,and the evolution law of system safety characteristics is obtained.At the same time,it is found that there are more complex nonlinear dynamic behaviors in the system,including quasi-periodic motion,Hopf bifurcation and so on.The results of this study can provide guidance for the design and selectioin of spur gear system's parameters,and provide theoretical basis for the design of gear system with good stability and low noise.In addition,the research methods of basin erosion and bifurcation in this paper can provide reference for the study of other non-linear systems.