Research On Complicated Dynamics And Stability Of Hybrid Powertrain Transmission System

The analysis of dynamics and stability plays a key role in guaranteeing the safe and reliable operation of the powertrain transmission system.The current research status of powertrain transmission system,which is focused on the two major themes:dynamics and stability,is summarized in this thesis.The nonlinear dynamics and stability are analyzed based on the mathematical model of the permanent magnet synchronous motor in electric vehicle.The influence of the linear term and nonlinear term of the half-shaft on the dynamics and stability of the parallel powertrain transmission system in pure electric mode and parallel hybrid mode are studied.Multi-parameter unified approach was proposed in this thesis.All of the parameters of the permanent magnet synchronous motor are unified in two combined parameters.The equilibrium's local stability condition as well as Hopf bifurcation condition and pitchfork bifurcation condition of the permanent magnet synchronous motor have been derived through the Routh-Hurwitz criterion and the bifurcation theory respectively.The local dynamics of the equilibrium vs.the unified parameter are discussed.The pitchfork and sub-Hopf bifurcation points are obtained.The dynamic behaviors of the permanent magnet synchronous motor along with parameters variation were studied and have presented different mechanisms.For the powertrain transmission system in pure electric mode,a dynamic model contains both nonlinear stiffness and nonlinear damping is established by adding nonlinear terms on the traditional linear Drive-shaft model.The torsional vibration behaviors of Drive-shaft model under constant excitation and time varying excitation are studied and the effects of nonlinear parameters on resonance behaviors are analyzed.Fold and Hopf bifurcation conditions of resonance curves are derived.The nonlinear stiffness coefficient can result in the offset of the resonance curve which may lead to coexistence of multiple equilibrium behavior.Hopf bifurcation is influenced by the nonlinear damping coefficient,and can cause instability of resonance response.The parameter region which can keep the stability of the resonance curve is obtained.The response equation of the nonlinear Drive-shaft model under impact is derived.Furthermore,the stability of the impact response of the nonlinear Drive-shaft model is analyzed qualitatively.The study found that compared with the model which only has linear damping,the one which both have linear and negative nonlinear damping are not conducive to the attenuation of shock response of the transmission system,the positive nonlinear damping is conducive to the attenuation of shock response of the powertrain.Compared with the driveline which only has linear stiffness coefficient,the driveline which has both the linear and negative cubic nonlinear stiffness coefficients is propitious to suppress the torsional shock.The ability of the suppression of the torsional shock can also be improved by properly reducing the linear stiffness of the half-shaft.Based on the nonlinear drive-shaft model,the dynamic behaviors of nonlinear relative rotation system which contains square and cubic terms is studied.The strongly nonlinear torsional vibration of relative rotation system with nonlinear stiffness is considered.The torque perturbation is made as control parameter,and the equilibrium's stability of the torsional vibration system is judged by the Routh-Hurwitz criterion.The bifurcation theory is used to analysis the bifurcation behaviors of the equilibrium,and the condition of Fold bifurcation of the equilibrium is derived.The bifurcation set of the equilibrium on the parameter plane is obtained by simulation,and the stability of equilibrium in different parameter regions are studied.The global dynamic behaviors of torsional vibration system are studied by the Poincaré section,and the complicated dynamic behaviors such as periodic one orbit,periodic three orbit and chaotic behavior are obtained.Based on the model of parallel hybrid power transmission system,the corresponding equivalent model is established by Lagrange method.The stability of equilibrium point of the powertrain in parallel mode is deduced,and verified by numerical analysis.The resonance behavior of the transmission system under the excitation of the engine is analyzed,and the influence of two kinds of half shafts on the resonance behavior of the transmission system is analyzed.It is shown that reducing the stiffness of the half shaft is favorable for reducing the peak value ofresonance.The impact of two kinds of half-shafts on the impact behavior of the transmission system is analyzed.It is also shown that the reduction of the stiffness of the half-shaft is beneficial to the shock response of the powertrain.