Abstract: Accurate, efficient, and high-precision modeling and calculation methods are the foundation of digital twin technology for hydraulic components and systems, taking the involute external meshing spur gear pump as an example to explore an accurate calculation method for its instantaneous geometric flow rate. The axial projection areas of the pump’s discharge chamber and the trapped oil chamber are viewed respectively as a simple connected domain enclosed by piecewise smooth curves, and a parameterized mathematical model of the piecewise curve of the calculation domain is established by the principle of coordinate transformation, using Green's formula, the variation law of the area of the domain with the gear rotation angle can be accurately calculated, and then the geometric instantaneous flow characteristics of the gear pump can be obtained. Through case verification, the results obtained by this method are completely consistent with those based on CAD assisted measurement, compared with traditional approximate calculation methods, the instantaneous geometric flow pulsation rate of the pump obtained by this method is higher than the approximate calculation results, and the displacement of the pump obtained is lower than the approximate calculation results.This method has a certain degree of universality and can be extended to calculate and analyze the instantaneous geometric flow characteristics of gear pumps with other tooth profiles.

Key words: positive displacement pump, external meshing spur gear pump, involute profile, instantaneous geometric flow characteristics, calculation method