## 7 Conclusions  
In this paper, the digital twin technique was used to investigate the vibration spectrum characteristics of planetary gearboxes. The physical model of the system vibration was constructed and the characteristic frequency of the system fault was calculated taking into consideration that the planetary gearbox system is prone to faults. A digital twin model of the planetary gearbox structure was established with reference to the existing primary planetary gearbox test bench in the laboratory. Firstly, a combined fault model of the sun gear and planetary gear was built in SOLIDWORKS, and then a rigid-flexible coupled multi-body dynamic model was built in ADAMS, which was close to the actual operating state of the physical object. Then, the model was imported into MATLAB, and the electrical model was built using the motor module that comes with Simulink. Finally, each module was connected to form the digital twin model of the planetary gearbox. The sun gear fault frequency \(f_{s}\) and planetary gear fault frequency \(f_{p}\) appear in the experiment, similarly, the sun gear fault frequency \(f_{s}\) and planetary gear failure frequency \(f_{p}\) appear in the simulation. Through the comparison of the experiment and simulation results, it was verified that the digital twin model can accurately simulate the motion state of the physical object and still has good accuracy even under multi-fault working conditions. Meanwhile, according to the root-mean-square metrics used to characterize the faults, the root-mean-square characteristic metrics of the digital twin model are better than the root-mean-square index of the traditional model. In the future, based on this model, the predictive maintenance of planetary gear can be studied to provide a solution to the problem of obtaining data during the degradation process of actual gear equipment. At the same time, through the ideas of positive derivation and inverse identification, accurate meshing parameters, transmission errors, and other mechanical parameters during the fault evolution can be obtained, based on which a more realistic digital twin gear degradation model can be established as a substitute for partial experiments. This research can be applied in the aerospace and automotive fields, and in large-scale industrial equipment to provide solutions for fault diagnosis and predictive maintenance in the above fields.  
Conceptualization, D.Z. and Z.L.; methodology, D.Z.; software, D.Z.; validation, D.Z., N.H. and Z.L.; formal analysis, N.H.; data curation, D.Z.; writing--original draft preparation, D.Z.; writing--review and editing, Z.L. and N.H.; visualization, Z.L.; supervision, Z.L.; funding acquisition, Z.L., N.H. All authors have read and agreed to the published version of the manuscript. This work supported by the grant from National Natural Science Foundation of China (Grant No. 51975576), National Key R and D Program of China (Grant No.2018 YFB1702401), Key projects of Natural Science Foundation of Jiangxi Province (Grant No. 20212 ACB202005), and Postgraduate Innovation Special Fund of Jiangxi Province (Grant No. YC2021-5692).  
Not applicable.  
The authors declare no conflict of interest.