## 4 Conclusions  
Taking the three planetary gear sets transmission system as the research object, considering the characteristics of various parts, as well as the complex structure and changeable gear position of the planetary gear transmission system, a generalized dynamic model of the planetary gear set transmissions is established using the lump mass method, which can provide a reference for the subsequent automatic model establishment. This work contributes to the efficiency of dynamic modeling of multi-gear planets when they switch gears.  
Through analysis of the variable speed of each frequency components of meshing force, the correctness of the above dynamic model is further verified. Analyzing the current gear set of meshing force, another gear set of meshing frequency components only appeared in the part of low rotational speed, and with the increase in rotational speed, some other low-frequency component in low speed could reduce or even disappear, but because of the characteristic of the structure, some other meshing frequency components will continue to exist, and will be unaffected by the speed change. In addition, the influence of different planetary gear sets on each other is strong or weak, indicating that the coupling relationship between meshing forces of different planetary gear sets is not equal; that is, the coupling relationship between meshing forces of different planetary gear sets is not symmetrical, and the coupling phenomenon of parallel row is more obvious. The results are similar to those of other literature. Resonance rotating speeds excited by meshing frequencies and their coupling frequencies are mainly concentrated in the range of middle-low rotating speed [20]. The frequency coupling of parallel row is more serious than that of series row [21].  
In addition, in the establishment of a general dynamics modeling method, relevant matrix parameters still need to be manually input in the establishment process of a dynamic parameter gear matrix and shaft element connection, which can be combined with the development of related software in the subsequent correlation matrix of motion and torque analysis to complete the fully automated calculation and dynamics building process. Furthermore, based on linear time-varying models (LTVM), this paper focuses on the rapid dynamic model shifting method of a planetary gear sets system. Therefore, non-linear influencing factors such as gear backlash, impact and friction between gear pairs were ignored in the process of building the dynamic model in this paper, and the lack of persuasive analysis of dynamic characteristics gave this paper certain limitations in the subsequent analytical process. For spur gears, the impact of contact, disengagement, and re-contact between teeth caused by gear backlash mainly occurs in high-speed operation under light load, and the analysis of the LTVM model is not sufficient. It is necessary to further analyze the dynamic characteristics of the system by adding non-linear factors and combining with the LTVM model.  
Conceptualization, H.W.; methodology, C.J.; software, C.J.; validation, C.J. and C.W.; formal analysis, H.W.; investigation, F.L.; resources, C.W. and F.L.; data curation X.S.; writing--original draft preparation, C.J.; writing--review and editing, H.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Laboratory of Science and Technology on Helicopter Transmission (Grant No. HTL-O-21G01).  
The authors declare no conflict of interest.