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.

中文翻译：

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渐开线内齿轮泵困油压力的仿真研究

内齿轮泵的主要结构由一对内齿轮组成，其中包括内齿轮和外齿轮。与其他液压齿轮泵一样，内齿轮泵也有油捕集现象。为了解决带有内啮合齿形的渐开线齿轮泵的滞油现象，根据产生原理，建立了齿轮外轮廓的数学方程，并确定了啮合时滞油面积的变化规律。通过扫描法获得的理论瞬时流量推导过程。然后，通过图解法求解最小的被困油量和卸载面积。最后，基于流体力学和动力学，获得了被困油压模型。用MATLAB模拟了啮合周期中滞留油面积和滞留油压的变化。结果表明，被捕集的油区呈抛物线形变化，被捕集的压力在山脉和山谷中波动。当捕集面积最小时，捕集的油压在相应的拐角处​​达到峰值。研究结果可为高性能内啮合齿轮泵的开发提供指导。