# Analysis of the Dynamic Characteristics of Coaxial Counter-Rotating Planetary Transmission System
## 6 Conclusions  
A comprehensive dynamic model of the coaxial counter-rotating planetary transmission system is constructed. The model incorporated TMS, transmission errors, and external excitations. The primary objective of the investigation was to conduct an analysis of the meshing forces, displacements of the planet gears, and the performance of the load distribution in the transmission system. Figure 28: Meshing force curves obtained from the ADAMS dynamic simulation: (**a**) left external meshing forces of the fixed axes PGT; (**b**) left external meshing forces of the differential PGT. Figure 27: Constraints of the transmission system in the ADAMS dynamic simulation. Firstly, considering the translational and torsional vibrations of each component, a dynamic model of the coaxial counter-rotating planetary transmission system was established using the concentrated mass method. The dynamic equations of each component were derived based on the relative displacements between gear teeth. Secondly, the dynamic meshing forces, planet gear displacements, and load-sharing characteristics of the coaxial counter-rotating planetary transmission system were investigated. The meshing forces acting on both sides exhibited significant similarities. When considering the external excitations, the variations in the meshing force curves became more pronounced. The radial displacements of the planet gears in the differential PGT were greater than that in the fixed-axes PGT. With an increasing input torque, the average displacements of planet gears in all directions tended to increase. The differential PGT, transmitting higher power, demonstrated a better load-sharing performance compared to the fixed-axes PGT. In summary, this study explored the dynamic responses of the coaxial counter-rotating planetary transmission system under different operating conditions. It is noted that while the quantitative results presented are specific to the system studied, the qualitative findings are generally applicable to coaxial counter-rotating planetary transmission systems. Although the model established by the concentrated mass method may lack the accuracy of a finite element analysis, its computational efficiency is high, and the results are also close to reality. When performing strength, fatigue, reliability analysis, or parameter optimization for coaxial counter-rotating planetary transmission systems, this method can be utilized to quickly obtain data, such as meshing forces, vibration displacements, and load-sharing coefficients, serving as the basis for further work. Mechanical system designers can also use the main findings of this study as general guidelines for designing coaxial counter-rotating planetary transmission systems. Additionally, we recognize the importance of analytical methods in system analysis and optimization. In the future, we plan to combine numerical methods with analytical methods, based on simplified assumptions, to simplify and extend the model developed in this study and to obtain exact solutions and optimization results under certain conditions. This approach not only reduces computational complexity but also provides a theoretical foundation for further optimization. We will continue to explore these directions in future research to enhance and refine the study of the dynamic characteristics of transmission systems. Conceptualization, Z.Y. and Z.C. ; methodology, Z.Y. ; software, J.Q. ; validation, Y.L., M.D., S.M. and G.Y. ; formal analysis, Z.Y. ; investigation, Z.Y. ; resources, Y.L. ; data curation, M.D. ; writing--original draft preparation, Z.Y. ; writing--review and editing, Z.Y. ; visualization, S.M. ; supervision, G.Y. ; project administration, G.Y. ; funding acquisition, G.Y. All authors have read and agreed to the published version of the manuscript.