## 1 Introduction
In a gear train, the failure of any one gear or gear tooth will affect the transmission capability of the entire system, so it is a common assumption in reliability analysis that a gear train is a series system with gears or gear teeth as basic functional units [19; 20]. The loads on different individual gears in the system, or even different teeth of the same gear, may be different, but they all have a certain mathematical relationship with the system input power. As a key component carried by the planetary gear transmission system, the ring gear is simultaneously subjected to multiple meshing excitation sources, which causes it to become the main component of gear tooth cracks and fatigue damage in the planetary gear system. In addition, the deformation of the ring gear leads to the change in the meshing relationship of the gears in the planetary gear train. With the development of precision machinery, planetary gear transmission systems tend to be lightweight. To reduce the quality of the transmission system to meet the needs of the project, the thin-walled ring gear has gradually become popular for practical applications [21]. [PERSON] and [PERSON] [22] analyzed the inherent characteristics of the equidistant planetary gear flexible ring gear model by perturbation and a candidate mode method. [PERSON] [23] calculated and analyzed the dynamic characteristics of the planetary gear transmission system considering the flexibility of the ring gear. Tooth root bending fatigue strength is one of the most important strength check indexes in a high-speed and heavy-duty gear system. For the planetary mechanism in heavy lift helicopters, its extreme load conditions and harsh reliability requirements will put forward a higher standard for tooth root bending fatigue resistance. Another main method of tooth root bending stress calculation uses the general finite element tool [24; 25; 26]. However, the general finite element method has high computational cost in a model setting and solution operations, and is usually only suitable for isolated solutions of gear parts or several teeth, but it is difficult to perform global operations at the system level. Providing strength variables for reliability prediction of the large-scale aviation planetary mechanism based on an effective test method is a necessary condition to ensure the analysis accuracy. From the perspective of the feasibility and economy of test implementation, in-depth analysis of the functional logic relationship between the tooth unit and the planetary system, and taking the bending fatigue test data of tooth structure as strength input variables for the system reliability model will be an effective way to realize the accurate prediction of fatigue reliability for this kind of large-scale high-end gear equipment. The double-tooth pulsating loading test using a high-frequency fatigue testing machine is one of the most common test methods to obtain the tooth bending fatigue strength [27; 28; 29]. The test method is simple to operate and has a high utilization rate for the sample, but it cannot simulate the time-varying and multi-axial stress states of the tooth root under actual working conditions, nor can it reflect the significant influence of lubricating oil on tooth bending fatigue strength. In fact, this method can be better applied to comparative analysis for gear performance parameters, but in the reliability prediction task of a gear system, the power flow closed gear rotation testing machine should be able to obtain more effective test results. High reliability and long life have become the core technology development direction for future large aviation planetary mechanisms [30]. Compared to small and medium-sized helicopters, the heavy helicopter planetary mechanisms have larger component sizes, higher structural mechanical index requirements, and more demanding design standards for important geometric elements. In this paper, a heavy helicopter planetary mechanism is studied to improve the bending fatigue reliability level of the planetary wheel system.