## 1 Introduction  
Due to the demand for technical indicators of high speed and heavy load equipment, the performance requirements of planetary gear transmission are becoming higher and higher. At the same time, it must meet the requirements of compact structure, high power density, and high reliability. Therefore, the planetary transmission technology with compact structure and high power density also needs to be further improved. In view of the shortcomings of planetary transmission technology, such as the uneven load between multiple planetary gears caused by the deformation of manufacturing and installation load, and the low efficiency of the external meshing gear pair in the ordinary planetary gear train, some scholars have adopted the double internal meshing coplanar planetary gear transmission, which has made major improvements in three aspects: First, the positive planetary gear train is adopted, and the sun gear, planetary gear and gear ring all adopt the internal meshing form. Compared with the external meshing gear in the negative sign row, the coincidence degree is higher and the efficiency is higher. Second, improvements result from changing the tooth profile of planetary gears, replacing the traditional involute tooth profile with the tooth profile with a long tooth mesh line, and replacing the conventional involute tooth profile with the addendum tooth profile and its conjugate meshing tooth profile. In the direction of the meshing line (straight line) of the traditional involute gear, the tooth top and tooth root of the driving gear and the tooth root and tooth top of the passive gear, respectively, realize the meshing transmission mainly in the form of rolling friction. The tooth profile of the double internal meshing coplanar gear is replaced by the conjugate tooth profile of the tooth top profile on the tooth root profile. The meshing of the driving gear and the passive gear is realized by a sliding contact on a segment of arc meshing line. For a single pair of gears, the number of teeth engaged by the new tooth profile gear is much more than that of the traditional involute tooth profile gear, with increased coincidence and high efficiency, as shown in Figure 1a. The third aspect is the use of coplanar planetary array structure. In the positive planetary array, two pairs of internal meshing gear pairs that are usually not in a plane are designed to work in a plane, reducing the axial size. One internal meshing gear pair is embedded in the ring gear planetary gear, and another internal meshing gear pair is embedded in the ring gear planetary gear (ring gear and planetary gear, see Figure 1b). Because the embedded ring gear becomes the internal gear in the planetary gear, the embedded planetary gear also becomes the sun gear. In order to make the structure clear, the frame model is not built. The brake frame or any two components in the planetary array form two transmission ratios (including 1:1). This coplanar structure design meets the requirements of a small size, fewer parts, and a compact structure while ensuring the transmission ratio. As a common mechanical transmission device, planetary gear transmission is widely used in machinery, engineering and automotive fields. In the tank transmission system, planetary gear has a very important role, including driving tank track system, speed control, steering system, etc. The purpose of the application of planetary gear transmission in tanks is to provide efficient, flexible and reliable power transmission to meet the diverse needs of tanks in different battlefield environments. The planetary gear is mainly composed of several key components, including a sun wheel, planet wheel, ring wheel, double row roller bearing and load distribution mechanism. Due to prolonged heavy loading and harsh working conditions, planetary gears may inevitably experience failure forms such as gear tooth surface wear. [PERSON] et al.