Research On Global Dynamics Of Ageared Transmission Systems

In the field of transmission systems,gears have become a widely used transmission device due to their high reliab ility,long life,and high transmission efficiency,and their safety performance and mechanical behavior affect the entire machinery and equipment.It plays a vital role in steel rolling,aerospace,railway transportation,industrial mining and other fields.Therefore,the study of the dynamic characteristics of the gear system has important theoretical and engineering significance.This paper studies the common cylindrical spur gears.Based on the nonlinear dynamical theory,considering factors such as time-varying meshing stiffness,backlash,and overall error in gear transmission systems,we establish nonlinear dynamic model of a single degree of freedom gearing system with clearances.Using the Melnikov method,the bifurcation and chaotic parameter regions of the single-degree-of-freedom gear system are predicted.The system’s phase line diagram 、 Poincaré sectional diagram、 bifurcation diagram、and maximum Lyapunov exponent diagram are obtained by numerical simulation.Based on the principle of cell mapping,the global attraction domain of the system is obtained,and the dynamic characteristics of t he system with the variation of internal error excitation force,excitation frequency and damping ratio are analyzed.The nonlinear dynamic model of a two-degree-of-freedom geared transmission system with clearances is considered.The bifurcation and chaot ic dynamics of the system are analyzed using numerical simulation methods.The global analysis of the model is performed using the cell mapping method to obtain the attractors and basins of attractors.The numerical results show that with the change of exc itation frequency,the system has the phenomenon of chaotic motion,coexistence of multi-periodic solutions and that of periodic solution and chaotic solution.Finally,the phase diagram of the system is compared with the Poincaré section.Under different initial conditions,the system presents different periodic motions or chaotic motions.Using the numerical calculation results of the cell mapping method,a good system response can be achieved by controlling the initial conditions of the system.