Numerical analysis of theoretical flow in external gear machines

With their advantages of low-cost, high-reliability and simplicity, external gear machines (EGMs) are among the most common pumps or motors in high pressure applications. As all positive displacement machines, EGMs are characterized by a substantial flow non-uniformity, which is given by the gear meshing and results in vibrations and noises. Several analytical methods are available but require the knowledge of the tooth profile, involute or cycloidal, and are not directly applicable to unconventional gears. This paper presents a numerical approach for the analysis of the theoretical flow through spur gear EGMs which does not require a-priori knowledge of the gear profile. Starting from a CAD input, the proposed approach automatically determines control volumes for every angular position of the gears to describe the displacing action realized by the unit. After describing the method, the paper shows its application to different geometric morphologies for the gear profiles to calculate the theoretical flow rate. The verification of the numerical model is demonstrated by comparing its results with those provided by the analytical methods available in literature for the case of involute gears.