Nonlinear Behavior And Chaos Control Of Locomotive Gear Transmission System Considering Temperature And Friction Effects

The gearbox is the core component of the locomotive traction system.During the high-speed and heavy-load operation of the locomotive,the internal temperature of the gearbox will directly affect the tooth surface friction and the gear meshing rigidity,which will affect the vibration characteristics of the gear system.Most of the current research on locomotive gear systems ignores the effects of temperature and friction.This paper takes the locomotive gear transmission system as the research object,comprehensively considers the tooth surface contact temperature,tooth surface friction and other factors,and establishes the locomotive gear transmission system dynamic model.Based on the nonlinear analysis theory,the dynamic sensitive parameters are studied,and the several chaotic control methods are proposed for the chaotic motion in the nonlinear motion of the system.First,the relative sliding speed of the two tooth surfaces is calculated according to the gear meshing motion,and the tooth surface friction factor under the condition of elastohydrodynamic lubrication is calculated by combining with the Hertz contact theory calculation.Based on Block flash temperature theory,the change of tooth surface flash temperature is obtained,and then combined with thermal deformation theory to calculate the tooth profile thermal deformation,the stiffness change caused by the deformation is defined as temperature stiffness.The Weber method is used to calculate the meshing stiffness,and after coupling with the temperature stiffness,a cubic fitting curve is used to perform piecewise fitting to obtain a time-varying meshing stiffness expression.It also analyzes the action mechanism and expression of other internal and external excitations such as tooth surface friction excitationA dynamic model of a three-degree-of-freedom locomotive gear transmission system that takes into account the effects of temperature and friction is established.The differential equations are dimensionlessly processed,and the variable step length Runge Kutta numerical method is used to solve them.The use of nonlinear analysis theories such as bifurcation diagrams,time domain response diagrams,frequency spectrum diagrams,Poincaré diagrams,and phase diagrams to study the effects of gear speed and support stiffness on system motion characteristics.The results show that as the speed and support stiffness change,the system will appear a variety of motion characteristics such as periodic,quasi-periodic,limit cycle and chaos that have strong nonlinearity.The influence of temperature and friction factors on the vibration characteristics of the system is analyzed and compared.It is found that the temperature and friction factors will change the system motion amplitude.Finally,for the chaotic motions appearing in the non-linear motion of the gear transmission system,three feedback control methods including linear,square and cubic,and an externally driven method(non-feedback control method)are adopted.By adjusting the control parameters,the system is successfully controlled or suppressed to a stable periodic orbit from chaotic motion in theory.