Study on Impact Excitation and System Dynamic Characteristics of Shield Machine Planetary Gear Train

Objective This study aims to reveal the evolution law of the internal and external meshing state of the sun gear and planetary gear induced by the collision between the sun gear and planetary gear. Clear meshing impact causes changes in the rotational speed of the sun gear, planetary gear, and gear ring, resulting in internal impact between the meshing lines of each gear pair. An impact excitation analysis calculation model is established for the internal meshing of the shield machine planetary gear and external meshing gear sideline of the shield machine. The impact radius is solved through a reverse method, the position of the impact point <italic>C</italic> is determined, and the impact speed at impact point <italic>C</italic> and the synthesized flexibility between the gear pairs are obtained. This allows for determining the maximum impact force between the planetary wheel and gear ring. A solid model of the planetary wheel and gear ring structure is established using 3D modeling software. A shared node is applied between the solid unit and the rigid shell unit, with constraints imposed on the rigid body to restrict all freedoms other than the rotational freedom of the rigid shell unit on the inside of the two-gear wheels. The driving speed is applied to the rigid shell unit of the drive gear, load torque is applied to the rigid shell unit of the driven gear, and the corresponding initial speed is loaded on the drive gear.Methods Explicit dynamic simulation analysis was conducted using the contact automatic surface tosurface contact algorithm, which considered the effects of friction factors and damping. The contact force between a single pair of tooth surfaces was extracted, and the rationality of the analysis model was verified through comparison. In addition, a model of the impact mechanism of internal meshing impact induced by meshing impact on the planetary gear-gear ring and planetary gear-sun gear was built to study the influence of external meshing gear meshing impact. This model examined the meshing state of the planetary gear-gear ring and the outer engagement state of the sun gear-planetary gear. When the sun gear and planetary gear have an offline impact, the rotational speed changes of the sun gear, planetary gear, and gear ring are detected. The multi-point impact excitation of the gear ring exhibited regular changes. A centralized quality model for the planetary gear system of the shield machine was established, and internal excitations such as variable meshing stiffness, damping, and comprehensive transmission errors during loading were calculated. These calculations determined the meshing force between internal and external gear pairs under different impact excitations, clarifying the dynamic evolution between impact excitation and gear pair meshing force. Finally, a planetary wheel system dynamic model was built to extract the meshing force and contact force of the external and internal meshing gears, obtain the magnitude of the impact force of each gear, and identify the peak and valley values that cause fluctuations in meshing force. These results were compared to theoretical analysis to verify the rationality of the theoretical model.Results and Discussions The results indicated that the numerical values of the internal and external meshing impact forces fit well with the analytical solution, with a relative error of 4.09%. When the sun gear and planetary gear have an offline impact, the meshing line between the sun gear and planetary gear changes, causing changes in the planetary gear rotation speed and leading to an impact within the planetary gear and gear ring. The angular velocity of the sun gear fluctuated slightly due to the impact of kinetic energy transmission and frictional energy loss, causing tooth-side clearance between the sun gear and planetary gear. This resulted in a speed difference when the sun gear and planetary gear mesh again, inducing impacts within the sun gear and planetary gear (Ⅱ～Ⅳ) line. Planetary gear system impact incentives exhibited periodic changes, inducing a cyclic shift in the pulley to the galaxy.Conclusions The meshing force between the external meshing gear pairs changes, and the engagement impact excitation reduces the dynamic meshing force between the gear pairs. However, the induced inline impact excitation increases the dynamic meshing force of the gear system, leading to increased vibration of the planetary gear system. Compared to the planetary gear system's finite element simulation numerical solution and the theoretical analysis solution, the relative errors of external and internal meshing impacts were 3.21% and 6.4%, respectively, and the average meshing force errors were 6.93% and 3.8%, respectively. The peak error of the corresponding meshing force wave at the impact time was 17.17% and 13.19%, and the valley error was 11.19% and 13.22%, respectively, verifying the correctness of the theoretical model. In addition, this study uses DAMPING_GLOBAL to set different dampers and discusses the effects of damping on explicit dynamic simulation results. The size of the damping directly in the finite element model of dynamic gear contact affects the degree of convergence of the contact force between a single pair of teeth.