TY - GEN
T1 - The Hybrid Dynamic Model of a Single-Stage Planetary Gear Transmission System and Its Nonlinear Vibration Characteristics
AU - Wang, Zhen
AU - Xiang, Chang Le
AU - Liu, Hui
AU - Gao, Jin Ji
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2026.
PY - 2026
Y1 - 2026
N2 - In this paper, the nonlinear dynamic meshing model of the planetary gear with the flexible shaft deformation was derived in detail, and nonlinear dnamic coupling forces between the rigid gear pairs and the flexible shaft were analyzed. Then, the nonlinear hybrid dynamic model of a single-stage planetary gear transmission system was established, and nonlinear lumped-parameter vaiables of the rigid gear and nonlinear distributed-parameter variables of the flexible shaft were taken into account in this model. Nonlinear lumped paramter variables of the rigid gear include the time-varying center distance, the time varying backlash, the dynamic meshing stiffness and the dynamic meshing force, and nonlinear distributed-parameter variables of the flexible shaft include the mass, the stiffness, the elastic force and the gravity. In addition, the distributed-parameter model of the flexible shaft was obtained by using the three-dimensional two-node nonlinear beam element described by the Absolute Node Coordinate Formulation (ANCF), and the lumped-parameter model of the rigid planetary gear was obtained by using the lumped-parameter method of the gear dynamics. Furthermore, the nonlinear hybrid dynamic equation of a single-stage planetary gear transmission system was derived by combining the lumped-parameter model of the rigid planetary gear and the distributed-parameter model of the flexible shaft, and the equation was solved by the generalized - α numerical method. Finally, the complex nonlinear dynamical behaviors and the vibration characteristics of the system were analyzed, and the rigid-flexible coupling dynamic mechanism between the meshing of the rigid gear and the deformation of the flexible shaft was revealed.
AB - In this paper, the nonlinear dynamic meshing model of the planetary gear with the flexible shaft deformation was derived in detail, and nonlinear dnamic coupling forces between the rigid gear pairs and the flexible shaft were analyzed. Then, the nonlinear hybrid dynamic model of a single-stage planetary gear transmission system was established, and nonlinear lumped-parameter vaiables of the rigid gear and nonlinear distributed-parameter variables of the flexible shaft were taken into account in this model. Nonlinear lumped paramter variables of the rigid gear include the time-varying center distance, the time varying backlash, the dynamic meshing stiffness and the dynamic meshing force, and nonlinear distributed-parameter variables of the flexible shaft include the mass, the stiffness, the elastic force and the gravity. In addition, the distributed-parameter model of the flexible shaft was obtained by using the three-dimensional two-node nonlinear beam element described by the Absolute Node Coordinate Formulation (ANCF), and the lumped-parameter model of the rigid planetary gear was obtained by using the lumped-parameter method of the gear dynamics. Furthermore, the nonlinear hybrid dynamic equation of a single-stage planetary gear transmission system was derived by combining the lumped-parameter model of the rigid planetary gear and the distributed-parameter model of the flexible shaft, and the equation was solved by the generalized - α numerical method. Finally, the complex nonlinear dynamical behaviors and the vibration characteristics of the system were analyzed, and the rigid-flexible coupling dynamic mechanism between the meshing of the rigid gear and the deformation of the flexible shaft was revealed.
KW - A single-stage planetary gear transmission system
KW - The flexible shaft
KW - The nonlinear hybrid dynamic model
KW - The rigid gear mesh
KW - Vibration characteristics
UR - https://www.scopus.com/pages/publications/105026959347
U2 - 10.1007/978-981-95-3646-7_34
DO - 10.1007/978-981-95-3646-7_34
M3 - Conference contribution
AN - SCOPUS:105026959347
SN - 9789819536450
T3 - Lecture Notes in Mechanical Engineering
SP - 379
EP - 396
BT - Advances in Mechanical Transmission
A2 - Wang, Shuxin
A2 - Qin, Datong
A2 - Liu, Fei
PB - Springer Science and Business Media Deutschland GmbH
T2 - International Conference on Mechanical Transmission, ICMT 2025
Y2 - 17 April 2025 through 20 April 2025
ER -