Evaluating time dependent pressure forces and torques in external gear machines by means of an analytical approach

Variable pressure loads are one of the main actors in determining the acoustic behavior of gear pumps, together with the meshing phenomenon occurring within the gearpair. Pressure distribution around gears gives birth to various force and torque components which load both the gears and the pump case, and the nature of such actions is strongly correlated to the pump's design. The present paper describes a standardized analytical procedure to calculate pressure loads coming from the pressure course inside gear pockets in external gear pumps. The method indistinctly applies to both spur and helical gears, since pressure force and torque components are determined along all the three coordinate axes. Firstly, pressure loads applied on a single pocket during the entire course are estimated and then the total pressure force and torque loading the gears centers are obtained. Attention is particularly paid in describing the helical gears approach, since such a design choice, despite the small amount of studies related to gear pumps applications, is getting more and more common nowadays. Examples of the application of the proposed methodology are described in this work by taking advantage of an experimentally assessed model to determine the pressure ripple inside external gear pumps. Results of the present procedure are evaluated with respect to the one provided by other methods previously introduced in the literature. The comparison highlights the quality of the estimation guaranteed by the proposed method, which is shown to be highly sensitive to various design parameters by taking into account a wide range of phenomena involved along the meshing evolution. The method gives suitable results to study the acoustic behavior of gear pumps by estimating the variable pressure loads at the basis of this phenomenon.