<div>Gerotor units are widely used in low-pressure (up to 30 bar) </div><div>fluid power applications, injection and lubrication systems, due to their compact package and low cost. Their performance in terms of volumetric efficiency, flow pulsations, internal pressure peaks or localized cavitation depends on many parameters, such as the rotors profiles and the manufacturing tolerances. In this work, a multi-domain simulation approach for the numerical analysis of the performance of Gerotor units is proposed. The model can be used for analysis and virtual prototyping of units considering the actual geometry of the rotors, their geometrical tolerances and the properties of the working fluid and materials.</div><div><br></div><div><div>The approach is based on the coupling of different models: a numerical geometric model evaluating the instantaneous volumes and flow areas inside the unit; a lumped parameter fluid dynamic model describing the displacing process of the tooth space volumes; and a mechanical model evaluating the internal micro-motions of the rotors axes according to their tolerances. In this way, the model determines the actual loading of the rotors, considering also the actual location of the points of contact. Advanced 2D CFD models for the analysis of lubricated interfaces have been developed to study the axial and the radial gaps. This approach allows an accurate prediction of the power losses and radial micro-motion of the rotors taking into account fluidstructure interaction effects. A line contact model is used to describe the contact interface using an elastohydrodynamic approach and non-Newtonian fluid behavior for the prediction of the friction between the rotors.</div></div><div><br></div><div><div>Specic experiments were performed by connecting the pump outlet to a variable loading orifice and by measuring the delivered flow, pressure ripple and required torque under dfferent operating conditions of speed and outlet pressure. These experiments allowed a detailed model validation through the comparisons with simulation data in terms of signicant steady-state as well as transient pressure, flow and torque features. After the model validation, gaps compensation solutions to minimize the volumetric losses are developed and studied showing the potential improvements on the performances of a prototype unit by reaching up to 55% volumetric effciency at high pressure (pmax > 100bar).</div><div><br></div><div>The approach used in the current work along with its proven accuracy through experiments can be considered a valuable tool when studying the impact of real-life technological clearances and gears geometry on the fluid-dynamic performance of the pump.</div></div>

<p dir="ltr">Positive displacement machines are used in various industries spanning the power spectrum, from industrial robotics to heavy construction equipment to aviation. These machines should be highly efficient, compact, and reliable. It is very advantageous for designers to use virtual simulations to design and improve the performance of these units as they significantly reduce cost and downtime. The recent trends of electrification and the goal to increase power density force these units to work at higher pressures and higher rotational speeds while maintaining their efficiencies and reliability. This push means that the simulation models need to advance to account for various aspects during the operation of these machines. </p><p dir="ltr">These machines typically have several bodies in relative motion with each other. Quantifying these motions and solving for their effect on the fluid enclosed are vital as they influence the machine's performance. The push towards higher rotational speeds introduces unwanted cavitation and aeration in these units. To model these effects, keeping the design evaluation time low is key for a designer. The lumped parameter approach offers the benefit of computational speed, but a major drawback that comes along with it is that it typically assumes fluid inertia to be negligible. These effects cannot be ignored, as quantifying and making design considerations to negate these effects can be beneficial. Therefore, this thesis addresses these key challenges of cavitation dynamics, body dynamics, and accounting for fluid inertia effects using a lumped parameter formulation.</p><p dir="ltr">To account for dynamics features related to cavitation, this thesis proposes a novel approach combining the two types of cavitation, i.e., gaseous and vaporous, by considering that both vapor and undissolved gas co-occupy a spherical bubble. The size of the spherical bubble is solved using the Rayleigh-Plesset equation, and the transfer of gas through the bubble interface is solved using Henry's Law and diffusion of the dissolved gas in the liquid. These equations are coupled with a novel pressure derivative equation. To account for body dynamics, this thesis introduces a novel approach for solving the positions of the bodies of a hydraulic machine while introducing new methods to solve contact dynamics and the application of Elasto Hydrodynamic Lubrication (EHL) friction at those contact locations. This thesis also proposes strategies to account for fluid inertia effects in a lumped parameter-based approach, taking as a reference an External Gear Machine. This thesis proposes a method to study the effects of fluid inertia on the pressurization and depressurization of the tooth space volumes of these units. The approach is based on considering the fluid inertia in the pressurization grooves and inside the control volumes with a peculiar sub-division. Further, frequency-dependent friction is also modeled to provide realistic damping of the fluid inside these channels.</p><p dir="ltr">To show the validity of the proposed dynamic cavitation model, the instantaneous pressure of a closed fluid volume undergoing expansion/compression is compared with multiple experimental sources, showing an improvement in accuracy compared to existing models. This modeling is then further applied to a gerotor machine and validated with experiments. Integrating this modeling technique with current displacement chamber simulation can further improve the understanding of cavitation in hydraulic systems. Formulations for body dynamics are tested on a prototype Gerotor and Vane unit. For both gerotor and vane units, comparisons of simulation results to experimental results for various dynamic quantities, such as pressure ripple, volumetric, and hydromechanical efficiency for multiple operating conditions, have been done. Extensive validation is performed for the case of gerotors where shaft torque ripple and the motion of the outer gear is experimentally validated. The thesis also comments on the distribution of the different torque loss contributions. The model for fluid inertia effects has been validated by comparing the lumped parameter model with a full three-dimensional Navier Stokes solver. The quantities compared, such as tooth space volume pressures and outlet volumetric flow rate, show a good match between the two approaches for varying operating speeds. A comparison with the experiments supports the modeling approach as well. The thesis also discusses which operating conditions and geometries play a significant role that governs the necessity to model such fluid inertia effects in the first place.</p>