Nonlinear Dynamic Analysis Of Bending-torsion Coupled Of Locomotive Gear Transmission System

With the continuous improvement of locomotive and vehicle operating speed,increasing of axle load and the increasing demand for comfort,vehicle dynamics becomes more and more important.As an important part of driving device,locomotive gear transmission system is used to transmit torque of traction motor,which has advantages of high transmission efficiency,reliable operation,stable transmission and long service life.However,because the locomotive has always maintained a high-speed and heavy-load operating state,as a complex elastic transmission system,the gear system will generate vibration under the action of internal and external excitation.Therefore,in order to ensure the safety,stability and reliability of locomotive during operation,it is very important to study the nonlinear dynamics of locomotive gear transmission system.Aiming at the research object of locomotive gear transmission system,a five-degree-of-freedom bending-torsion coupled nonlinear dynamic model of a one-stage gear system is established.The dynamic model of gear systems is solved by 4-5 order adaptive variable step length Runge-Kutta numerical analysis method.The sensitivity parameters such as gear speed,supporting stiffness,supporting damping,backlash in the transmission system are systematically analyzed by the time domain response diagram,phase diagram,Poincaré map,Spectrum diagram,bifurcation diagram,Lyapunov exponent diagram and other nonlinear theory.The results show that,with the change of sensitive parameters,the vibration characteristics of the gear system exhibit one or more movement states such as period-1 motion,period-2 motion,multiple period motion,quasi-periodic motion,chaos,limit cycles,etc.in which the rotational speed and supporting stiffness have great influence on the vibration characteristics of the system,while the influence of the support damping and the backlash are relatively small.When analyzing the meshing stiffness of the driving gear and the driven gear,the Weber energy method in material mechanics is used to calculate it.Then the piecewise function is fitted by determining the minimum absolute residual error,and then a more accurate time-varying meshing stiffness equation is obtained.Through the analysis of backlash and gear speed on the dynamic meshing force,the maximum dynamic meshing force and average dynamic meshing force,it can be seen that to ensure the stability of the gear meshing force,the system must be in a stable period-1 motion,and change backlash on meshing force has little effect.There are many kinds of excitation sources that cause vehicle vibration.In this paper,by analyzing the periodic excitation source that causes the verticalvibration of vehicle,we can see that the vibration of gear increases slightly with the increase of track irregularity amplitude.The change of the creep speed has little effect on the vibration characteristics of the system.Finally,the Floquet theory is applied to analyze the speed,stiffness,damping and backlash of the system.Through the analysis of the system,we can see that there are three forms of period-doubling bifurcation,Hopf bifurcation and saddle structure bifurcation in this model,meanwhile explains the system's movement from period-one motion to period-doubling and steady state to quasi periodic motion process.