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.

In the hydraulic servo-cylinders design, the circumferential grooves are used in order to reduce the effect of the locking force. This force arises as a consequence to the distribution of pressure around the piston, when both an eccentric position, caused by the load on the piston, and the manufacturing defects on the piston and cylinder surfaces are present. In this work an approach is presented for the calculation of the contribution of the grooves in the definition of the locking force and of the leakage flow rate. The mathematical model proposed is based on the Reynolds equation, properly combined with the continuity equation applied within the grooves. The results of the analysis are combined together with the ones coming from the analysis at the hydrostatic bearings at the rod ends, which have been analyzed on a previous step of the research. A numerical procedure is then created that, with the appropriate input, allows to study the different design configurations of the servo-cylinder. Results here shown are focused on exploring the effect of number, position, size of the grooves and manufacturing tolerances on the piston and cylinder. Simulations are also run under different operating conditions. For the real servo-cylinder configurations tested here, it is shown that five equally spaced grooves may be sufficient to decrease consistently the locking force while containing the flow losses. The procedure is also functional to investigate the bending and seizing of the piston during the different operating conditions, both in steady state and dynamic conditions.

Hydraulic servo cylinders are widely used in versatile industrial applications such as machine tools, industrial robots, autonomous manufacturing systems and special applications in laboratories. To reduce friction and allow smooth and controllable displacement of the actuator, hydrostatic journal bearings are used at the ends of the rod. The design and manufacturing of this elements is challenging since the good operation relays on the very small tolerances required to bear the load on the cylinder and to reduce leakages. In this work, a virtual design and test tool for hydrostatic journal bearing with pockets, developed in OpenModelica environment, is presented. The influence of eccentricity and manufacturing tolerances is then studied and discussed. The model proposed has the aim to explore the extreme and critical operating conditions of the servo-cylinder and to help and/or improve the design phase.