## 7 Conclusions  
(1) The frictional heat flux generated by the 3D topology modified internal helical gear pair during transmission is lower than that of the standard gear unmodified. The temperature of the modified gears is lower than the unmodified gears in the meshing area. Under the condition of a light load (200 r/min), the simulation analysis shows that the tooth surface temperature is reduced by 6.38% and the thermal deformation is reduced by 36.5% after modification. When the internal helical gears pair with a three-dimensional topology modification is engaged in the meshing transmission, there is a certain gap between the meshing tooth surfaces, and there are more contact areas between the lubricating oil and the tooth surface, which takes away more friction heat, thereby reducing the contact temperature of the tooth surface. Therefore, the gear after three-dimensional topology modification is helpful to improve the heat dissipation efficiency. (2) Thermoelastic coupling simulation analysis of the topological design of the internal helical gears pair is carried out and reveals that both the temperature distribution and thermal deformation of the internal helical gear are significantly reduced under various revolving speeds and load conditions. To the modified gear, the meshing region within the high-temperature band tends to concentrate at the nodes, resulting in a more uniform temperature distribution across the addendum, pitch circle, and dedendum. Compared to the standard gear, modification can reduce the maximum deformation under the temperature field, lower the transmission error, and improve the transmission accuracy. (3) The temperature of the internal helical gear pair under steady-state working conditions increases with the rising of the load during transmission. Simultaneously, the maximum temperature in the tooth contact area increases with the load. At 400 and 800 r/min, the tooth surface temperature increased by 41.2%. Although the specific temperature value will change, the overall trend in the temperature change is consistent with the trend in the load increase. Although the specific temperature values may vary, the overall temperature change trend remains consistent with the increasing load. (4) Under the same working conditions, the transmission error comparison experiments of modified and unmodified gears was carried out through experiments. It was verified that the transmission error of the internal helical gear pair would gradually increase with the increase in the working temperature. Taking the unmodified gear as an example, the transmission error increased by 51.3% on average when working for 30 min and 90 min, which proved the reliability of the simulation part. It is also verified that the modification can reduce the transmission error of the planetary reducer, and the overall transmission error after modification is reduced by 62.35% on average, which provides a reference for the design and stability of different types of planetary gear reducers. Figure 21: Comparison of simulation and experimental results. **Author Contributions:** Conceptualization, G.Y. and G.L. ; methodology, J.S. and H.Y. ; software, G.Y. and X.W. ; validation, [PERSON], M.J. and X.W. ; formal analysis, [PERSON] and G.L. ; investigation, [PERSON] and G.Y. ; resources, [PERSON] and G.L. ; data curation, [PERSON], M.J. and X.W. ; writing--original draft preparation, [PERSON] and H.Y. ; writing--review and editing, [PERSON] and J.S. ; visualization, [PERSON] and M.J.; supervision, [PERSON] and H.Y. ; project administration, [PERSON]; funding acquisition, [PERSON] and H.Y. All authors have read and agreed to the published version of the manuscript. **Funding:** The research was funded by the National Natural Science Foundation of China (52375052) and the Natural Science Foundation of Henan Province (242300421183). Key R&D projects in Henan Province (241111230300); support for the frontier exploration project of Longmen Laboratory (LMQYTSKT027).