Rupeng Zhu

Modeling and Bifurcation Characteristics of Double Stage Planetary Gear Train With Multiple Clearances

This paper proposes a new non-linear transverse-torsional coupled model for double stage planetary gear train, and gear’s geometric eccentricity error, synthetical transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair’s backlashes and sun gear’s bearing clearance are taken into account. The differential governing equations of motion are derived and solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state is investigated systematically and qualitatively, and exhibits diverse bifurcation and chaos characteristics under different bifurcation parameters including meshing frequency, sun-planet backlash and planet-ring backlash. Analysis results showed that the increasing damping could suppress the region of chaotic motion and improve the system’s stability significantly; the route of period-doubling to chaotic motion was observed for both first and second stage’s motion state under the bifurcation parameter of meshing frequency; The routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun-planet backlash; Besides, the increasing damping ratio could split the bifurcation diagram window into different sections and strong coupling effects are generated to second stage’s motion. Several different types of routes to chaos were observed under the bifurcation parameter of planet-ring backlash including period doubling and 3T-periodic channel; Besides, it concluded that planet-ring backlash could generate a strong coupling effect to both stage’s nonlinear behavior.Copyright

Dynamic Characteristics of Double Helical Planetary Gear Train With Tooth Friction

A new nonlinear dynamics model of the double helical planetary gear train with 44 degrees of freedom is developed, and the coupling effects of the sliding friction, time-varying meshing stiffness, gear backlashes, axial stagger as well as gear mesh errors, are taken into consideration. The solution of the differential governing equation of motion is solved by variable step-size Runge-Kutta numerical integration method. The influence of tooth friction on the periodic vibration and nonlinear vibration are investigated. The results show that tooth friction makes the system motion become stable by the effects of the periodic attractor under the specific meshing frequency and leads to the frequency delay for the bifurcation behavior and jump phenomenon in the system.Copyright

Research on Tooth Profile Modification of the Herringbone Planetary Gear Train

A bending-torsional coupled nonlinear dynamic model which contains the modification parameters of herringbone planetary gear train is presented. A formula of modification incentive is analyzed and deduced. The impact of the straight line and parabolic modification parameters on the amplitude of system transmission error is researched. The optimum modification parameters are acquired according to the minimum amplitude of system transmission error. Different amplitudes of the system transmission error, before and after modification, are compared at different rotational speed. The results indicate that the straight line modification parameters on the amplitude of system transmission error are more sensitive. Modification parameters on the amplitude of system transmission error are researched. When the length of the modification is specified, the amplitude of system transmission error is reduced sharply at first, then increased rapidly with the maximum magnitude of the modification increasing; When the maximum magnitude of the modification is specified, the amplitude of system transmission error is increased weakly at first, then decreased sharply, and increased rapidly in the end, with the length of the modification increasing. The modification parameters could form a crescent-shaped zone which can reduce the system transmission error amplitude significantly. The amplitudes of the system transmission error with modification are all reduced at different rotational speed, especially when there is a sympathetic vibration.Copyright

Study on Dynamic Load Sharing Characteristics of Double-Row Planetary Gear Train

The non-linear transverse-torsional coupled model of double-row planetary gear train is established, and planet’s eccentricity error and time-varying meshing stiffness are taken into consideration. The solution of differential governing equation of motion is determined by applying the Fourier series method. The behavior of dynamic load sharing characteristics affected by the system parameters including gear eccentricity error, torsional stiffness of first stage carrier and input rate are investigated. Some theoretical results are summarized as guidelines for further research and design of double-row planetary gear train at last.