Search Results (3)

So far it is believed that, for every series-parallel planetary gear system (PGS), as a coupled gear, a very harmful phenomenon of power circulation must occur in at least one of its closed circuits. In this paper (Part I) and in the next two (Part II and Part III), it will be shown that it is possible to construct a three-row series-parallel PGS in which this phenomenon can be avoided. For this purpose, in Part I, a detailed analysis of the kinematics and statics of a planetary gear with power circulation inside a closed loop was carried out. The determination of the angular velocities of gears and carriers is carried out using Willis formulas and the graphical-analytical method (for verification), while the torques are determined using free body diagrams. The magnitudes of angular velocities and torques were used to determine the directions of power flows with improved energy balance equations in the reference frame related to the stationary gear body and, additionally, only to verify the energy balance equation in the mobile reference frame related to the carrier ${\mathrm{h}}_{\mathrm{i}}$ ($\mathrm{i}=2,5,8$). The improvement of the methods was based on the use of the original concept of distinguishing active torque from reactive torque, as well as active power from reactive power, which made it very easy to determine the directions of the power flow. The determined paths of the power flow, including the power circulation in the analysed PGS, are presented graphically. Full article

The modeling and simulation of gearboxes is important for analyzing the dynamic characteristics and designing control strategies of transmission systems. Variable-speed gearboxes include compound planetary gear trains and clutches, which complicates dynamic modeling. Here, a procedural bond graph-based modeling method that considers many uncertainties is proposed. The proposed method yields a constant system–structure model. First, bond graph models of the two most common planetary gears were summarized, and were used as sub-models of a compound planetary gear train. Then, the Karnopp friction sub-model of the friction clutch and a relative angular displacement sub-model of the one-way clutch were constructed. Based on the dynamic coupling between the sub-models, the modeling steps of the gearbox, including the compound planetary gear train friction clutch one-way clutch coupling system, are described in detail. Next, the main sources of uncertainties of gearbox were analyzed and the simulation methods were given. Finally, the novel uncertain bond graph model was used to simulate the double planetary gearbox; the transmission ratio before and after the shift was 2.42 and 1.72, compared with the design values of 2.41 and 1.71, respectively; the deviation is within 5.8%; The average rotating speeds of the output shaft fluctuated by 6 and 2.5% respectively, which was within a reasonable range, so the effectiveness of the method is verified. Full article

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. Full article