Abstract
In the vehicle composite planetary gear transmission system, nonlinear excitations such as time-varying meshing stiffness, backlash and comprehensive error would lead to large vibration and noise, uneven load distribution, unstable operation and other problems. To address these issues, this work focuses on compound planetary gears and develops the bending-torsion coupling nonlinear dynamic model of the system based on the Lagrange equation. There are internal and external multi-source excitations applied to the system. This model is used to study the bending-torsion coupling meshing deformation relationship of each meshing pair along with the translational and torsional directions. The natural frequencies and vibration modal characteristics of the system are extracted from the model, and the influence of rotational inertia and meshing stiffness on the inherent characteristics of the system are studied. The coupling vibration characteristics of the system under operating condition are analyzed in terms of the inherent characteristics and time–frequency characteristics of the system. The simulation results exhibit that the planetary gear system has three modes. The change in natural frequency trajectory has two phenomena: modal transition and trajectory intersection. The main frequencies include engine rotating frequency, meshing frequency and its double frequency, and the rotation frequency and harmonic frequency of the engine have a great influence on the vibration response of the system. Finally, the virtual prototype of the composite planetary system is used to verify the accuracy of the established model from speed, inherent characteristics, meshing force and frequency composition.
Highlights
The planetary gear transmission system has, as its characteristics, a large transmission ratio, stable transmission, strong carrying capacity, high unit volume, mass power density, coaxial input and output and strong impact resistance and power shunt, which is widely used in various industrial fields
Kim et al [5] offered the planetary gear dynamic model, assuming that the position of the contact line is determined by the average angular motion of the gear
Few people have studied the dynamic characteristics of multi-stage planetary gear system under internal and external nonlinear excitation
Summary
The planetary gear transmission system has, as its characteristics, a large transmission ratio, stable transmission, strong carrying capacity, high unit volume, mass power density, coaxial input and output and strong impact resistance and power shunt, which is widely used in various industrial fields. Wang et al [19] studied the time–frequency characteristics of planetary gear systems by establishing a flexible multi-body dynamics model. Zhang et al [24] established the dynamic model of planetary gear systems with sliding bearing and flexible structure, and the influence of different radial sliding bearings on load sharing characteristics was researched. Few people have studied the dynamic characteristics of multi-stage planetary gear system under internal and external nonlinear excitation. In order to study the vibration problem caused by nonlinear excitation in the composite planetary system, this paper establishes the bending-torsion coupling dynamic model of the composite planetary transmission system, considering the external and internal excitations such as engine harmonic excitation, time-varying stiffness, gear time-varying phase, comprehensive error and dynamic backlash. Machines 2022, 10, 31 the nonlinear system are revealed by analyzing the natural frequency, whic stiffness and inertial trajectory, as well as the time–frequency characteristics response
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