Research On Nonlinear Dynamic Analysis And Vibration Control Of Gear Transmission System

Gear is the most common mechanical part in the machinery industry.Gear transmission has many advantages,such as high speed,heavy load and high precision transmission.It is widely used in transmission and rotation devices of metallurgy,electronics,aerospace,chemical industry and other fields.With the development of science and technology and the improvement of mechanical requirements in all fields,the accuracy,speed,load and reliability of mechanical transmission have higher requirements.Due to the error of gear in the process of design,manufacture and assembly,all kinds of nonlinear factors resulting in gear meshing lead to meshing vibration.The meshing motion of a spur gear pair is studied in depth.First of all,the gear nonlinear dynamics with both internal and external excitation is studied.A model has been established including backlash,time-varying stiffness and other factors.The periodic solution is obtained based on the incremental harmonic balance method,and it is verified by four rank changing step length Runge-Kutta method.The influence of internal excitation and external excitation on gear meshing vibration is analyzed respectively,and bifurcation and chaos phenomena caused by external excitation amplitude are analyzed.Based on the knowledge of fractional calculus theory,the nonlinear dynamics of a spur gear pair with a additional viscoelastic materials is studied.A model has been established including backlash,time-varying stiffness,internal and external excitation and other factors.The additional viscoelastic material which can be described by a fractional-order differential term is added to the spoke plate of the gear and dynamic analysis can be obtained.The approximate analytical solution of the model is obtained by the incremental harmonic balance method,and the numerical verification is carried out by the power series method.The meshing vibration of the model is compared with that of the original gear transmission system,and the effect of the internal and external excitation and the fractional-order differential on the gear meshing vibration is analyzed in detail.The integer-order gear model is considered as the control object.Based on the feedback of meshing error change rate,dynamic analysis of spur gear pair under fractional-order PID control is studied.The fractional-order PID control term is added to the dynamic model,and the periodic solution of the model is solved by the incremental harmonic balance method,and the numerical verification is carried out by the power series method.The control effect and performance of fractional-order PID controller and integer-order PID controller is compared.The influence of the fractional-order PID controller parameters on the meshing dynamics of the gear is analyzed in detail.Finally,the meshing motion of a spur gear pair is simulated by ADAMS and MATLAB co-simulation,and the feedback control of integer-order PID controller and fractional-order PID controller is used to verify the effect of the two controllers on the gear mesh vibration control.