Pressure balancing in external gear pumps and motors

The paper relates on a numerical method for designing balancing bearing block areas for external gear pumps and motors. At first, a way is presented for obtaining pressure distribution inside spaces between teeth, bearing blocks and casing; the procedure, based on integration of the continuity equation for sealed spaces, permits also the evaluation of some interesting aspects dealing with the influence of rotational speed, dynamic viscosity and gears eccentricity. Then, a method is presented for calculating pressure distribution in the layer bounded by gears sides and bearing blocks. The method, starting from pressure distribution in spaces, is based on the integration of the laspace equation over the whole layer. Axial thrust on bearing blocks and its point of application are then calculated. Finally, the same problem is analysed with a simplified numerical approach, as well based on the integration of the laplace equation, but on the small portion of the layer corresponding to one tooth, with only one boundary condition. At the end, calculations are made for a commercial pump, obtaining balancing aeras very close to the ones designed by the manufacturer.