Theoretical flow rate in crescent pumps

In this paper, a method for evaluating the kinematic flow rate of a crescent oil pump is presented. The procedure also allows calculating the angular derivatives of the delivery, suction and trapped volumes of the pump, which are the prerequisites for the simulation of the unit using a lumped parameters approach. The method is based on the knowledge of the length of the vector rays between the centres of the gears and the contact points. From the volume derivatives, an analytic expression of the pump displacement and of the kinematic flow ripple index is obtained. Moreover, the same formula can also be applied to external gear machines. Finally, in this study the influence of the number of teeth of the driving and driven gears has been assessed. The increase of the number of teeth of the inner gear is beneficial; both for the reduction of the flow ripple and for the increase of the displacement at equal overall pump size.