Research On Non-smooth Characteristics Of Spur Gear System

The gear system is one of the most extensively used for power and motion devices in mechanical equipment,and the noise and vibration problems caused by the gear system cannot be ignored.The paper takes single-degree-of-freedom spur gears system containing backlash as the research object,the n-p-q-r model that containing incentive cycle consists of gear,the tooth surface meshing,tooth back contact and unmeshing movement is established.By means of system bifurcation diagrams,phase diagrams,the Top Lyapunov Exponent,poincare maps and floquet multipliers,the kinetics of local and global stability are studied and the correlation of the system dynamics parameter,It provides a certain theoretical basis for structural design of gear system.The specific research contents are as follows:Firstly,the n-p-q-r model of the single-degree-of-freedom spur gear system containing incentive cycle consists of gear,the tooth surface meshing,tooth back contact and unmeshing movement is established.Secondly,the frequency,torque,time-varying stiffness,comprehensive error and system damping of the system stimulation cycle,tooth surface meshing,tooth contact back and unmeshing of dynamic characteristics of the local and global influence are studied,the parameters of the system dynamic stability section are got,it can provide theoretical basis for gear system dynamic design.Thirdly,in this paper,calculating equation's Floquet multipliers to analyze the stability of the periodic vibration part of the bifurcation characteristic,and the parameters of the gear system in the two-dimensional plane of the saddle node bifurcation and period-doubling bifurcation are determined.Lastly,systems in the parameter plane of the dynamic distribution are computed and double parameter plane system dynamics is got,through the analysis of the plan of these parameters,the parameters of the system is stable state interval can be more intuitive found and the relationship between parameters is summarized.In this paper,some parameters are selected to obtain the bifurcation diagram of the system,the nonlinear dynamic characteristics of the system are analyzed,and the influence of each parameter on the vibration characteristics of the system is analyzed.