# Analysis of the Dynamic Characteristics of Coaxial Counter-Rotating Planetary Transmission System
Based on the dynamics model proposed, they investigated the transmission effects of planet gears, the influence of bolt constraints, and gear vibration. [PERSON] et al. [8] presented a three-dimensional load tooth contact analysis (3 DLTCA) model considering changes in the center distance and root crack discontinuity of planet gears, and they calculated the dynamic response under the combined effects of assembly errors and crack discontinuities. [PERSON] et al. [9], based on the translational-rotational dynamic model of planetary gear systems, studied the effects of multiple excitations on the vibration response of various planet gear components. [PERSON] et al. [10] coupled the concentrated mass dynamic submodel of sun gears and planet gears with the reduced-order finite element submodel and used this model to analyze the coupled dynamics of flexible planet gears under high-speed and variable-speed conditions. In the field of multistage compound planet gears and coaxial counter-rotating gears, [PERSON] et al. [11] proposed a dynamic model for the Dual-Planetary Gear System (DPGS) that integrates the dynamic characteristics of the planet bearing rollers and retainers. [PERSON] et al. [12] proposed a two-dimensional steady-state discrete dynamic model for a dual-stage planetary gear set. They obtained the forced vibration response to gear mesh excitations by applying the modal summation technique. [PERSON] et al. [13] investigated the vibration and acoustic characteristics of a power-split hybrid transmission utilizing a compound planetary gear set through numerical processes and refined dynamics modeling. [PERSON] et al. [14] developed a time-varying reduced-order numerical model for a compound reducer, enabling the prediction of its meshing frequencies and harmonics. [PERSON] et al. [15] established a translational-torsional concentrated mass dynamic model for a compound planetary gear set, calculating eccentric load coefficients under the influence of excitations such as tooth wear accumulation and transmission errors. [PERSON] et al. [16] proposed a multinode dynamic model for a marine compound gear transmission system, investigating its modal characteristics and dynamic responses. [PERSON] et al. [17] developed a dynamic model for a two-stage parallel-axis gear system with variable mesh stiffness, revealing the variations in system vibration under the interaction of coaxial gear ratios and meshing phases. [PERSON] et al. [18] employed a concentrated mass method to establish a translational-rotational dynamic model for a planetary gear system, analyzing the natural frequencies and mode characteristics of a coaxial counter-rotating helicopter main gearbox. [PERSON] et al. [19] developed a hybrid planet dynamic load distribution model, employing finite element substructuring techniques to ensure computational efficiency and investigated the influence of planet carrier flexibility on the quasi-static and dynamic responses of planetary gear sets. [PERSON] et al. [20] proposed a flexible-rigid coupling dynamics (FRCD) model for Ravigneaux planetary gear sets (RPGS) with unloaded floating sun gears and studied the influence of the sun gear position on planet dynamic responses, revealing the mechanism of floating ring gear vibration. [PERSON] et al. [21] proposed a novel split-type structure for first- and second-stage gears of planetary reducers. Through rigid body dynamics theory, dynamic simulations, noise tests, and dynamic stability tests were conducted to determine the dynamic characteristics of the entire system. [PERSON] et al. [22], focusing on compound planetary gears, established a bending-torsional coupled dynamic model of the system based on [PERSON]'s equations, investigating the bending-torsional coupled meshingdeformations and translations and torsions of various engagements. [PERSON] et al.