As a key part of vibration generation and transmission of planetary gear transmissions, thin‐walled inner ring gear deforms under the influence of meshing excitation and seriously affects the reliability and fatigue life of the transmission system. The effect of the flexibility of the inner ring gear on the transmission system is ignored in the calculation of making the inner ring gear as a rigid body in the lumped parameter model, while the calculation amount of the finite element model is too large. Therefore, it is very important to establish an accurate and reasonable model to solve the flexibility of the inner ring gear. In this paper, according to the supporting mode, supporting quantity, thickness, and sectional shape of the inner ring gear, the inner ring gear is reasonably separated into the form of multisection curved beam. The displacement of the gear teeth in the meshing line caused by the flexibility of the inner ring gear is obtained rapidly and accurately. It lays an important theoretical foundation for the dynamic analysis of planetary gear transmission.

Considering flexibility of the support shafts as well as bearing supports, the effect of meshing impact force and meshing stiffness on the dynamic behavior of a gear transmission system in electric vehicle is investigated in this paper using the proposed hybrid user-defined element method. First, a structured grid generation method is introduced to establish accurate mesh models of the pinion and gear teeth. Second, coupling the tooth mesh models and the flexible shafts as well as bearings, two finite element models are, respectively, constructed for the two helical gear pairs of the electric vehicle reduction unit to calculate the meshing impact force. Next, the basic mechanism of meshing impact is explained in detail according to the finite element results, and the impact force is determined as one of the main internal excitations substituted into the dynamic model established by the hybrid user-defined element method. Under 50 N m input torque and 12,010 r/min rotational speed of the input shaft, the simulation results by the hybrid user-defined element method indicate that the example system reaches a steady state and the vibrations primarily occur at the meshing frequencies. With an increment of 600 r/min of the input rotational speed, it is also concluded from the results that (1) the calculated impact force approximately presents linear growth with the increase of the input shaft rotational speed and (2) the root mean square values of the vibration acceleration generally grow with the increase of the speed.

Meshing impact is an important factor that affects gear vibration and noise. Therefore, it is of great theoretical and practical significance to study the characteristics of offline meshing impact to reduce the vibration caused by meshing impact. Currently, a single-pair gear is the research goal, ignoring complex coupling relationships between systems, and the established numerical solution formula of the meshing impact cannot be verified. By using Hilbert demodulation and instantaneous frequency, this study obtained the meshing impact signal from the dynamic transmission error signal of the experiment and obtained the maximum deformation caused by the meshing impact. The meshing stiffness of a single tooth was obtained by loaded tooth contact analysis and tooth contact analysis, and the meshing impact force was calculated. The dynamic model of the meshing impact considering the contact ratio was established to compare with the obtained force in the experiment. The method of measuring the meshing impact signal from experiments has not been reported in relevant literature. The method has the advantages of being extensive, accurate and convenient, and it is not affected by the complexity of the system. At the same time, this method can be used to determine the gear teeth with meshing impact in the course of operation and provide a basis for real-time shape modification and design. Therefore, it is of great significance.

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.

As a key component of the vibration generation and transmission of planetary transmission system, the design of ring gear will directly affect the vibration of the system. After considering the advantages and disadvantages of the traditional ring gear structure, the new flexible ring gear was designed by scholars and applied to helicopter reducer. There is a dearth of reported analysis in the meshing characteristics of the new flexible ring gear, which leads to the blind selection of the ring gear. By building an accurate parametric finite element model, the meshing characteristics of the new flexible ring gear and the difference in dynamic characteristics between the new flexible ring gear and the traditional ring gear are obtained. The analysis shows that the new ring gear is superior to the traditional ring gear in many aspects, but it also has the characteristic of unbalance loading on the tooth surface. In addition, a test method is proposed to accurately measure the load sharing coefficient and dynamic load factor of planetary transmission and the simulation results of flexible ring gear are verified by comparison.