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In this paper, the theoretical flow ripple of an external gear pump is studied for pumps of similar size using different numbers of teeth on the driving and driven gears. In this work, the flow ripple equation is derived based upon the flow of incompressible fluid across the changing boundaries of a control volume. From this method, it is shown that the instantaneous length of action within the gear mesh determines the instantaneous flow ripple. A numerical and a closed-form approximation are presented for the instantaneous length of action and it is shown that the difference between these two solutions is negligible. Fast Fourier transform analysis is employed for identifying the harmonic frequencies and amplitudes of the flow pulse and these results are compared for 16 different pump designs. In summary, the results of this study show that the driving gear dictates the flow ripple characteristics of the pump while the driven gear dictates the pump size. As a result, it may be advantageous to design an external gear pump with a large number of teeth on the driving gear and a fewer number of teeth on the driven gear. This design configuration will tend to reduce both the physical pump size (without reducing the volumetric displacement of the pump) and the amplitude of the flow pulsation, while increasing the natural harmonic frequencies of the machine.
Manring et al. (Mon,) studied this question.