A new non-linear transverse-torsional coupled model was proposed for 2K-H planetary gear train, and gear's geometric eccentricity error, comprehensive transmission error, time-varying meshing stiffness, sun-planet...A new non-linear transverse-torsional coupled model was proposed for 2K-H planetary gear train, and gear's geometric eccentricity error, comprehensive transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair's backlashes and sun gear's bearing clearance were taken into consideration. The solution of differential governing equation of motion was solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state was investigated systematically and qualitatively, and exhibited diverse characteristics of bifurcation and chaos as well as non-linear behavior under different bifurcation parameters including meshing frequency, sun-planet backlash, planet-ring backlash and sun gear's bearing clearance. Analysis results show that the increasing damping could suppress the region of chaotic motion and improve the system's stability significantly. The route of crisis to chaotic motion was observed under the bifurcation parameter of meshing frequency. However, the routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun-planet backlash; besides, several different types of routes to chaos were observed and coexisted under the bifurcation parameter of planet-ring backlash including period doubling, Hopf bifurcation, 3T-periodic channel and crisis. Additionally, planet-ring backlash generated a strong coupling effect to system's non-linear behavior while the sun gear's bearing clearance produced weak coupling effect. Finally, quasi-periodic motion could be found under all above–mentioned bifurcation parameters and closely associated with the 3T-periodic motion.展开更多
Significant propellant mass saving can be obtained with the use of complex multiple intermediate flyby maneuvers for conventional propulsion systems,and trip time also decreases for a portion of the proper solar sail ...Significant propellant mass saving can be obtained with the use of complex multiple intermediate flyby maneuvers for conventional propulsion systems,and trip time also decreases for a portion of the proper solar sail missions.This paper discusses the performance of gravity assist(GA)in the time-optimal control problem of solar sailing with respect to sail lightness number and the energy difference between the initial and final orbit in the rendezvous problem in a two-body model,in which the GA is modeled as a substantial change in the velocity of the sailcraft at the GA time.In addition,this paper presents a method to solve the time-optimal problem of solar sailing with GA in a full ephemeris model,which introduces the third body’s gravity in a dynamic equation.This study builds a set of inner constraints that can describe the GA process accurately.Finally,this study presents an example for evaluating the accuracy and rationality of the two-body model’s simplification of GA by comparison with the full ephemeris model.展开更多
基金Projects(51375226,51305196,51475226) supported by the National Natural Science Foundation of ChinaProjects(NZ2013303,NZ2014201) supported by the Fundamental Research Funds for the Central Universities,China
文摘A new non-linear transverse-torsional coupled model was proposed for 2K-H planetary gear train, and gear's geometric eccentricity error, comprehensive transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair's backlashes and sun gear's bearing clearance were taken into consideration. The solution of differential governing equation of motion was solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state was investigated systematically and qualitatively, and exhibited diverse characteristics of bifurcation and chaos as well as non-linear behavior under different bifurcation parameters including meshing frequency, sun-planet backlash, planet-ring backlash and sun gear's bearing clearance. Analysis results show that the increasing damping could suppress the region of chaotic motion and improve the system's stability significantly. The route of crisis to chaotic motion was observed under the bifurcation parameter of meshing frequency. However, the routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun-planet backlash; besides, several different types of routes to chaos were observed and coexisted under the bifurcation parameter of planet-ring backlash including period doubling, Hopf bifurcation, 3T-periodic channel and crisis. Additionally, planet-ring backlash generated a strong coupling effect to system's non-linear behavior while the sun gear's bearing clearance produced weak coupling effect. Finally, quasi-periodic motion could be found under all above–mentioned bifurcation parameters and closely associated with the 3T-periodic motion.
文摘Significant propellant mass saving can be obtained with the use of complex multiple intermediate flyby maneuvers for conventional propulsion systems,and trip time also decreases for a portion of the proper solar sail missions.This paper discusses the performance of gravity assist(GA)in the time-optimal control problem of solar sailing with respect to sail lightness number and the energy difference between the initial and final orbit in the rendezvous problem in a two-body model,in which the GA is modeled as a substantial change in the velocity of the sailcraft at the GA time.In addition,this paper presents a method to solve the time-optimal problem of solar sailing with GA in a full ephemeris model,which introduces the third body’s gravity in a dynamic equation.This study builds a set of inner constraints that can describe the GA process accurately.Finally,this study presents an example for evaluating the accuracy and rationality of the two-body model’s simplification of GA by comparison with the full ephemeris model.
