The calculation of gear pump porting areas by mathematical means

Abstract

Twin pinion gear pumps are used widely in industrial hydraulics and as fuel-delivery pumps for aero engines. The kinematics of the pumping action leads to high-flow rates into and out of the meshing gears, and at the high speeds used with aerospace fuel pumps cavitation can occur. One-dimensional ‘lumped parameter’ models are often used to analyse this type of pump. These methods rely on an accurate description of the volume trapped by the meshing teeth and the flow areas during the meshing cycle. Typically, multiple computer-aided design models have to be created to calculate these values during the meshing cycle. This paper presents a mathematical method for calculating these parameters based on a parametric definition of the gear and inlet and outlet porting. Green's theorem is used to allow line integrals around the periphery of the tooth spaces to be used to calculate the volumes and flow areas. Winding numbers are used to calculate the inflow and outflow areas that are formed by the intersection of the trapped volume and the side area porting. The method is validated against computer-aided design model data. This method is well suited for incorporation in an optimisation algorithm since the geometry is defined parametrically.