Although crown gear couplings are widely used in rotating machinery, very little is known about their contact behavior and load distribution characteristics. In this study, the manufacturing methods are presented for crown gear coupling. Complete geometrical mathematical models from tools to crown gear coupling are proposed based on the theories of differential geometry and gear mesh. Then, a high-fidelity finite element model verified by tooth contact analysis under light load is employed to investigate load distribution along the crown gear coupling interfaces. The effects of meshing position, torque, and angular misalignment are investigated on load distributions along with crowning amount depending on the displacement circle radius. Finally, it is observed that when the contact position is 0.2 times the width of the tooth, the radius of the displacement circle is the optimal result for the performance of the crown gear coupling.

L-shaped flexible ring gear is a new solution to the non-uniform load distribution of planetary transmission systems. At present, the research on L-shaped flexible ring gear is still focused on its meshing characteristics and dynamic load sharing performance, and its structural vibration characteristics and dynamic coupling vibration characteristics with the system are not involved. Considering that the structural flexibility of the L-shaped flexible ring gear is significantly higher than that of the traditional ring gear, the structural vibration will obviously affect the load sharing and dynamic load factor performance of the transmission system, as well as the safety and reliability of the mechanism. Due to its strong structural flexibility and structural particularity, the existing dynamic analysis model is difficult to meet the requirements of analysis and design. In this paper, the coupling vibration model of L-shaped flexible ring gear planetary transmission systems is established, and the structural vibration characteristics of L-shaped flexible ring gear and its influence on the dynamic performance of the systems are deeply analyzed. The model foundation and theoretical guidance are provided for the design of L-shaped flexible ring gear and the analysis of the dynamic characteristics of flexible ring gear systems.

The meshing impact on transmission system and internal meshing gear pair and its impact on the load sharing and dynamic characteristics of the system are not well understood yet. In this paper, the meshing impact models of internal gear pairs and planetary transmission system were successfully constructed, and the meshing impact point, meshing impact time and meshing impact force were accurately obtained. Meshing impact in gear transmission system is obviously affected by eccentricity error, installation error, and other errors. Due to the difference in error of each component, the internal and external gears of each branch lead to different meshing positions, which causes the constant change in meshing impact point, meshing impact time and meshing impact force. This creates difficulties in the analysis of meshing impact characteristics of gear transmission system. Load Tooth Contact Analysis (LTCA) method can be used to accurately analyse the change in position of gear tooth under load condition. Through the dynamic model of planetary transmission system, the influence in component errors on the contact position of tooth surface is obtained. Combining the loaded transmission error of the tooth surface under load and the geometric transmission errors under the influence of component errors, the model of meshing impact for accurately solving the system is deduced, and the influence of meshing impact on the system's load sharing coefficient and dynamic load factor coefficient is analysed. By comparing the planetary transmission system before and after considering the meshing impact of the system, it is found that the system's load-sharing coefficient increases slightly, dynamic load factor coefficient fluctuates significantly, and meshing force becomes more clutter after considering meshing impact.

To avoid the occurrence of the hub tooth tip edge contact with the sleeve tooth root flank and the sleeve tooth tip edge contact with the hub tooth root flank, a novel crown gear coupling composed of a hub with profile crowning, longitude crowning, and tip sphere teeth, and a sleeve with straight internal teeth is presented in this paper. The generating procedure of the hub with profile parabolic modification for the novel crown gear coupling is proposed. And the meshing model with angular misalignment of the novel crown gear coupling is developed. Tooth contact analysis (TCA) based on the theory of gearing and loaded tooth contact analysis (LTCA) based on finite element method (FEM) are employed to simulate contact path and to calculate contact stress distributions of the novel crown gear coupling. An example crown gear coupling is presented. The effects of profile parabolic modification coefficient and misalignment angle on contact path are investigated both for the conventional and novel crown gear couplings. Also, contact stress distributions are analyzed both for them with the maximum misalignment angle. The performed research proves that an appropriate amount of profile modification for the hub of the crown gear coupling permits the avoidance of edge contact in presence of angular misalignment, and can significantly reduce the maximum contact stress, compared with the conventional one.