Geometric features of gerotor pumps: Analytic vs CAD methods

Accurate simulation models of gerotor pumps require knowledge of geometric features of these units. Instantaneous volumes of chambers as well as their volume derivatives lead to kinematic flow rate, flow ripple index, displacement. Flow passage areas between a chamber and the inlet/delivery volumes during a complete shaft revolution also need to be known. General analytical methods (integral-derivative and derivative-integral) have been developed for the calculation of geometric quantities of gear as well as vane pumps and will be reported in the paper with specific emphasis on gerotor units. The approach leading to these geometric informations has traditionally been grounded on a 2D analysis of involved features. However, in the last decade, there has been a progressive and relentless development and use of 3D CAD software that has led to the possibility of having at hand a virtual representation of these positive displacement machines. Accordingly, a novel method that requires the 3D model of the gerotor pump is presented and the paper demonstrates how geometric features of the unit can be obtained. Main characteristics of this methodology are the use of parametric relations that define the relative position of the rotating gears, and the use of virtual components. A validation of this proposed approach is discussed contrasting analytic and CAD-model based outcomes. This methodology has been successful also in axial piston machines as well as for the determination of flow passage areas of complex proportional direction spool valves.