In order to obtain the calculation method of the unloading area of the internal gear pump during oil trapping, a pair of internal gears including an external gear and an internal gear was used as the research object to simulate the oil trapping process. The geometric relationship during the meshing process was established, and the unloading area expression was obtained by using the geometric pattern expansion method with the variable f as the independent variable. Guided by a mathematical model, two improved optimization schemes were proposed for the internal gear tooth profile, and the unloading area expressions sud, suda, and sudb were obtained. Taking the meshing gear pair with module 3 and number of teeth 13/19 as examples, the simulation results were very consistent with the existing literature. The reliability of the model and the feasibility of the optimization scheme are obtained based on the theoretical analysis and calculation results. This calculation method of unloading area can be applied to the same type of gear pump design in the future, providing a reference for the design of high pressure and low noise gear pumps.

The main structure of an internal gear pump consisted of an internal gear pair, including an internal gear and an external gear. The internal gear pump had oil trapping phenomenon like other hydraulic gear pumps. In order to solve the oil trapping phenomenon of involute gear pump with internal meshing tooth profile, in this paper, the mathematical equation of gear outer contour is established according to the principle of generation method, and the variation law of the trapped oil area in meshing process is deduced by theoretical instantaneous flow rate obtained by scanning method. Then, the minimum trapped oil volume and unloading area are solved by the graphic method. Finally, based on fluid mechanics and dynamics, the trapped oil pressure model is obtained. The change of the trapped oil area and trapped oil pressure in a meshing cycle is simulated by MATLAB. The results show that the trapped oil area changes in a parabola, and the trapped pressure fluctuates in mountains and valleys. When the trapped area is the smallest, the trapped oil pressure reaches the peak at the corresponding corner. The research results can provide guidance for the development of high-performance internal gear pumps.