Research On Stability And Bifurcation Of Nonlinear Planetary Gear System

This paper mainly studies the stability and bifurcation of single-stage planetary gear train. Some progress and developments have been made on key issues such as nonlinear dynamics modeling and experimental test, stability about motion state and stability about vibration intensity of the planetary gear train. The stability about motion state in this paper includes the stability of coexisting periodic orbits of the system, local bifurcation characteristics, the global bifurcation characteristics, the global characteristics of coexisting periodic orbits. The stability about the vibration intensity includes stability region, influence rules of some parameters on dynamical load sharing behavior and the meshing contact-impact characteristics of the planetary gear train.A nonlinear lateral–torsional coupled vibration model and a nonlinear torsional vibration model of a planetary gear train are established respectively by taking transmission errors, time varying mesh stiffness and multiple gear backlashes into account. Through experimental tests, the validity of the torsional vibration model is ascertained.Quasi-fixed-point tracing method is used to study the coexisting periodic orbits of the planetary gear train with certain set of parameters and Floquet theories are used to study the stability of the coexisting periodic orbits based on the torsional vibration model. The study results reveal that a nonlinear planetary gear train with a certain set of parameters may have several coexisting periodic orbits, some of them are stable and some of them are unstable.Based on the torsional vibration model, the local bifurcation characteristics about stability of coexisting periodic orbits with rotational speed, power and relative mesh damping coefficient are studied respectively by using CPNF method. The study results reveal that different periodic orbits of the planetary gear train will reciprocal transform in the way of periodic-doubling bifurcation when bifurcation parameters are changing.Based on the torsional vibration model, the global bifurcation characteristics about the stability of different attractors, including periodic attractors and strange attractors, with rotational speed, power and relative mesh damping coefficient changing in a large range are studied respectively by using direct numerical integration method. The study in this chapter reveals the way to chaos of the periodic orbits and finds a lot of strange attractors, such as quasi periodicity and chaos with different shapes.By using Poincaré-like cell-to-cell mapping method, the global characteristics of the planetary gear train are studied based on the torsional vibration model. The study results make certain of all of the coexisting periodic orbits with long-term stability and their domains of attraction, which can make designers of the planetary gear train forecast the motion state of the system and the scope of disturbance that the motion state can bear.A general method of vibration intensity stability region determination for a nonlinear dynamical system is proposed. By using this new method, the vibration intensity stability region of a planetary gear train is calculated based on the lateral–torsional coupled vibration model. The stable regions of rotational speed of sun gear, backlashes and relative damping ratio are calculated respectively.By using direct numerical integration method, the influence rules of some parameters, such as transmission errors, bending stiffness of the sun gear shaft, number of teeth and backlash, on dynamical load sharing behavior of the planetary gear train are studied based on the nonlinear lateral–torsional coupled vibration model. The influence rules of some parameters, such as transmission errors, power and rotational speed of the sun gear, on the meshing contact-impact of the system are studied too.