Meshing impact analysis of the gear and rack of the pumping machine based on the SPH–FEM coupling method

This paper explores the feasibility of using the coupled smooth particle hydrodynamics–finite element method (SPH–FEM) to study the gear rack and meshing impact problem. Firstly, a numerical model containing both SPH and FEM units is established, and its accuracy is verified. Then, the principle of gear rack meshing impact is analyzed from the perspective of impact dynamics theory, and the formula of maximum meshing impact force is derived. Finally, the meshing impact process of the rack and pinion is simulated using the coupled SPH–FEM method, and experiments are designed to verify it. The analysis results show that the SPH–FEM coupling method can simulate the meshing impact behavior of the gear mechanism more accurately. On the other hand, the severity of the impact in each operating section was obtained. It is also found that the impact stress has reached the material's tensile limit, revealing the mechanism of tooth surface wear caused by the impact. The results of the study provide a choice of research methods for gear mechanism meshing impact and also provide some reference for gear rack tooth shape optimization.