Lumped parameter approaches for the description of the flow displaced by hydrostatic pumps and motors have proven to be very effective for both analysis and design purposes. However, while these methods are relatively easy to implement for most of the existing design architectures for positive displacement machines, the case of a crescent-type internal gear machine (CIGM) presents clear challenges as it pertains to the definition of lumped control volumes within the machine. This paper proposes an original scheme for defining lumped control volumes within a CIGM with involute teeth profiles, which is suitable for developing fluid dynamic simulation models for CIGMs. The proposed method strictly obeys fundamental rules on continuous volumes required by lumped parameters models. This is achieved by defining not only multiple control volumes for each displacement chamber but also two variable porting volumes to respect the volume conservation. To prove the validity of the proposed numerical method, the paper provides comparisons between the displaced volume found by the proposed lumped parameter approach and the theoretical kinematic flow ripple provided by an analytical formula available from literature. The results show how the method can be used as a design tool for CIGMs, and particularly to further develop lumped parameter simulation models for detailed fluid dynamic analysis of CIGMs.

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