Nonlinear Dynamics And Numerical Simulation Analysis Of Gear Transmission System

Gear systems are widely used in cranes,gas turbines,wind turbines and other equipment.Studying the nonlinear dynamics of gear system can provide theoretical guidance for designing and manufacturing high quality gears,and for the fault diagnosis and prevention of gear systems.The research on nonlinear dynamics of gear system has always been a hot issue due to the high speed of rotation,complicated system structure,difficult modeling and difficult solution of system dynamics.The main research objects of this paper are single-stage spur gear,single-stage helical gear and multi-stage helical gear.The bending-torsional model of single-stage spur gear,and the bending-torsion-axis-pendulum model of single-stage helical and multi-stage helical gear are established.The fourth-order Runge-Kutta method is used to solve the model.The model mainly considers the nonlinear factors such as time-varying meshing stiffness,meshing error,flank clearance and meshing damping.Time-varying meshing stiffness is difficult to solve in nonlinear dynamics.In this paper,several commonly used methods are introduced:energy method,Ishikawa method,finite element method and theoretical method.The results of four methods are compared and verified.The main contents of the thesis include the following:(1)The bending-torsional model of a single-stage spur gear is established.Three degrees of freedom such as torsion ?z,bending y,and meshing relative displacement are considered.The time-dependent meshing stiffness curve was obtained by energy method,and the approximate expression formula of meshing stiffness was fitted.The meshing comprehensive error was approximated by simple harmonic function.The flank clearance was approximated by the flank clearance function.After dimensionless the model,the fourth-order Runge-Kutta method was used to solve the model.Through the bifurcation diagram and poincare diagram,the influence of shaft support stiffness,high speed shaft speed,damping ratio and high speed shaft input power on system dynamics is discussed.(2)The bending-torsion-axis-pendulum model of a single-stage helical gear is established,taking into account the bending y,torsion ?z,axial z.torsion ?y,a total of 8 degrees of freedom.By using the method in GBT-3480,the approximate Fourier expression formula of the time-varying meshing stiffness of helical gears is obtained.After dimensionless the model,the fourth-order Runge-Kutta method was used to solve the model.Through the bifurcation diagram,poincare diagram,the influence of shaft support stiffness on system dynamics is discussed.(3)The bending-torsion-axis-pendulum model of a two-stage helical gear for crane gearbox is established,with a total of 16 degrees of freedom.By using the method in GBT-3480,the approximate Fourier expression formula of the time-varying meshing stiffness of two pairs of helical gears is respectively obtained.After dimensionless the model,the fourth-order Runge-Kutta method was used to solve the model.Through the bifurcation diagram,poincare diagram,the influence of shaft support stiffness on system dynamics is discussed.