Evaluation of the hydro - Mechanical efficiency of external gear pumps

This paper proposes and describes a model for evaluating the hydro-mechanical efficiency of external gear machines. The model is built considering and evaluating the main friction losses in the machines, including the viscous friction losses at the tooth tip gap, at the bearing blocks-gears gaps, at the journal bearings, and the meshing loss. To calculate the shear stress at each gap interface, the geometry of the gap has to be known. For this reason, the actual position of the gears inside the pump casing and consequent radial pressure distribution are numerically calculated to evaluate the gap height at the tooth tips. Moreover, the variation of the tilt and reference height of the lateral gaps between the gears and the pump bushings are considered. The shear stresses within the lateral gaps are estimated, for different lateral heights and tilt values. At the journal bearings gaps, the half Sommerfeld solution has been applied. The meshing loss has been calculated according to the suggestion of the International Standards. The hydro-mechanical efficiency results are then discussed with reference to commercial pumps experimentally characterized by the authors in a previous work. The average percentage deviation from experimental data was around 2%, without considering the most critical operating conditions (high delivery pressure, low rotational speed). The limits of this approach are also explained. Finally, the role of each source of loss is discussed, considering different operating conditions and two values of fluid viscosity. Lateral gap losses and meshing loss are much more relevant in determining the hydro-mechanical efficiency variation in the pump's operating range, especially at a low delivery pressure. Moreover, while lateral gap losses increase with the rotational speed, the meshing loss shows the opposite behavior. The tooth tip gap losses are never as relevant, but they increase at high pressure. The journal bearings losses become comparable with the lateral and meshing ones at high delivery pressure values. Considering the pumps analyzed and the operating range of delivery pressure values and rotational speed values, the meshing loss made the mechanical efficiency vary in a percentage range of ±7%, with lateral losses in the range of about the ±15%, when also considering the extreme operating points (low speed, high pressure; high speed, low pressure). The weight of the lateral losses slightly reduced when we analyzed the higher temperature results, while the meshing losses slightly increased.