Numerical Study on the Instantaneous Theoretical Flow Rate of the Continuous Contact Gear Pump with a New Geometrical Approach

External gear pumps with an involute tooth profile are used in many applications because of their simple shape, low production cost, and excellent reliability. However, they can be characterized by the generation of vibration and noise, due to the pressure pulsation caused by the trapped volume resulting from the gear meshing. In this study, a one-point continuous contact helical gear pump with circular-involute teeth was designed to eliminate the trapped volume. A novel geometrical approach is described to analyze the kinematic flow of this pump. The morphology of the tooth space, which changes depending on the angular position of the rotating gear, is explained by a newly defined algorithm. Algorithms designed for the geometric approach are simple because they define tooth space morphology for specific angular positions and therefore do not require corrections. The area of tooth space calculated through numerical analysis is used to calculate the instantaneous theoretical flow rate. The kinematic flow rate of the numerically analyzed pump can quantify the compressibility effect of the fluid. In addition, the calculated instantaneous theoretical flow rate accurately reflects the physical characteristics compared to previous studies and can be used to identify the cause of flow ripple.