<p>Positive displacement gear machines are widely used in a variety of industrial applications ranging from fuel injection applications to fluid handling systems to fluid power machinery. Simulation models for these machines are increasingly being developed with greater applicability and more accuracy to meet the industry needs. In this work, a research study is done on contact forces in positive displacement gear machines towards improving the accuracy of the simulation models, which can help gain insights on the underlying physics that govern the performance of the machines.</p> <p><br></p> <p>First, the importance of considering contact forces in simulating a positive displacement gear machine is addressed. For this purpose, an orbit motor reference unit is chosen. A multi-domain simulation tool to evaluate the performance of this reference unit, considering contact features, is developed. The approach for creating the simulation tool is based on coupling of different models: pre-processor tools are created that can provide information needed by fluid dynamic model; a 2D CFD model is created that can evaluate leakages through the lubricating gaps based on pressures from fluid dynamic model; and a fluid dynamic model that can accept inputs from other models and evaluate the primary flow of the unit using a lumped parameter approach. This approach allows an accurate prediction of performance characteristics of orbit unit and the results are compared with those of experiments in terms of flow rate (maximum deviation up to 2.5%) and torque (maximum deviation up to 10%). Variation of performance of the unit by modification of contact features is presented, thus drawing the importance of contact forces in simulating a positive displacement gear machine.</p> <p><br></p> <p>After presenting the importance of contact forces, emphasis is placed on creating an accurate model of the traction contact force, in terms of traction coefficient. The traction coefficient is evaluated  by solving a mixed thermal EHL system, for the case of lubricated non-conformal contacts, considering possible asperity effects and temperature change. A few required characteristics of the reference lubricant are obtained using experiments, along with asperity friction coefficient for the lubricant-solid combination for two different roughnesses. The solver is further validated, both in magnitude and trend, against experimental results for the variation of roughness and slide-to-roll ratio of the surfaces. The solver is further used to obtain curve-fit relations of the traction coefficient components with reasonable accuracy.</p> <p><br></p> <p>Lastly, the curve-fit relations of the traction coefficient are used to evaluate the meshing torque loss, and thus the hydro-mechanical efficiency for the case of two external gear machine units, having different gear flank roughnesses. The simulated hydro-mechanical efficiencies are further validated using the results from experiments, with a maximum deviation of up to 3%, but less than 0.5% deviation at many operating conditions. The experimentally obtained variation of hydro-mechanical efficiency with respect to gear flank roughness is captured in the simulations at majority of the operating conditions, thus laying emphasis on the importance of accurate contact force models.</p> <p><br></p> <p>The approaches followed in this work, along with the findings and proven accuracy with experiments, can be considered valuable and can be used to create simulation models that can capture the effects of interference/clearance and gear flank roughness on the performance of positive displacement gear units.</p>

External gear machines (EGMs) are used in a variety of industries ranging from fluid power machinery to fluid handling systems and fuel injection applications. Energy efficiency requirements and new trends in hydraulic technology necessitate the development of novel EGMs optimized for efficiency and reliability in all of these applications. A crucial piece in the novel EGM development process is a numerical model that can simulate the operation of EGM and predict its volumetric and hydro-mechanical performance.<div><br></div><div>The EGM simulation models developed in the past have focused mostly on the challenges related to the modeling of the theoretical behavior and elementary fluid dynamics, and determining appropriate modeling schemes. Key aspects related to the flow and geometry are either considered in a simplified manner or not considered at all. In particular, the current simulation models assume the fluid to be Newtonian and the leakage flows to be laminar. However, EGMs working in fluid handling applications operate with non-Newtonian fluids. Further, in fuel injection applications, due to low fluid viscosity and high operating speed, the internal leakage flows may not remain laminar.</div><div><br></div><div>With respect to the geometric aspects, the gears in EGMs are prone to manufacturing errors that are not accounted by any simulation model. In addition, there is no method available in the literature for accurately modeling the leakage flows through curve-constricted geometries in EGMs. Further, the goal of current simulation tools is related to the prediction of the volumetric performance of EGMs. However, an equally important characteristic, hydro-mechanical performance, is often ignored. Finally, the energy flow during EGM operation can result in the variation of the fluid temperature. Thus, the isothermal assumption of current simulation tools is another major limitation.</div><div><br></div><div>The work presented in this dissertation is focused on developing numerical methodologies for the modeling of EGMs that addresses all the aforementioned limitations of the current models. In this work, techniques for evaluating non-Newtonian internal flows in EGMs is developed to permit an accurate modelling of EGMs working with non-Newtonian fluids. For fuel injection EGMs, flow regime at the tooth tips of the gears is investigated and it is shown that the flow becomes turbulent for such EGMs. A methodology for modeling this turbulent flow is proposed and its impact on the performance of EGMs is described. To include gear manufacturing errors in the simulation model, numerical techniques are developed for modeling the effects of two common gear manufacturing errors: conicity and concentricity. These two errors are shown to have an opposite impact on the volumetric efficiency of the EGM. For the evaluation of flows through curve-constricted leakage paths in EGMs, a novel flow model is developed in this work that is applicable for a wide range of geometry and flow conditions. Modeling of the hydro-mechanical efficiency of EGMs is accomplished by developing methodologies for the evaluation of torque losses at key interfaces. Finally, to account for the thermal effects in EGMs, a thermal model is developed to predict the temperature distribution in the EGM and its impact on the EGM performance.</div><div><br></div><div><div>To validate the numerical methodologies developed in this work, several experiments are conducted on commercial gear pumps as well as on a custom apparatus designed and manufactured in the course of this research work. The results from the experiments are found to match those obtained from the simulations which indicates the validity of the methodologies developed in this work. </div><div><br></div><div>These numerical methodologies are based on the lumped parameter approach to allow the coupling with mechanical models for gear micromotion and permit fast computations so that the model can be used in optimization algorithms to develop energy efficient and reliable EGMs.</div><div><br></div><div>The methodologies described in the dissertation are useful for accurate analysis of a variety of EGMs working with different types of fluids and at wide range of operating conditions. This capability will be valuable for pump designers in developing novel better performing EGM designs optimized for various applications.</div><div><br></div></div>

<div>Positive displacement machines are used in a wide variety of applications, ranging from fluid power where they act as a transmission of power, to lubrication and fluid transport. As the core of the fluid system responsible for mechanical--hydraulic energy conversion, the efficiencies of these units are a major driver of the total efficiency of the system. Furthermore, the durability of these units is a strong decider in the useful life of the system in which they operate.</div><div><br></div><div>The key challenge in designing these units comes from understanding their working principles and designing their lubricating interfaces, which must simultaneously perform a load carrying and sealing function as the unit operates. While most of the physical phenomena relevant to these machines have been studied previously in some capacity, the significance of their mutual interactions has not. For this reason, the importance of these mutual interactions is a fundamental question in these machines that this thesis answers for the first time. In analysis of two different machine types, it is confirmed that mutual interactions of both physical phenomena and neighboring fluid domains of the unit contribute significantly to the overall performance of the machine. Namely, these analyses demonstrate load sharing owing to mutual interactions on average of 20% and as high as 50%, and mutual flow interactions of at least 10%.</div><div><br></div><div>In this thesis, the behavior of the thin films of fluid in the lubricating interfaces of the units, the bodies that make up these films, and the volumes which interface with them will be considered. The resulting coupled problem requires a model that can consider the effects of motion of all floating bodies on all films and volumes, and collect the resulting loads applied by the fluid as it responds. This will require a novel 6 degree of freedom dynamics model including the inertia of the bodies and the transient pressure and shear loads of all interfaces of the body and the fluid domain.</div><div><br></div><div>During operation, fluid cavitation and aeration can occur in both the displacement chambers of the machine and its lubricating interfaces. To capture this, a novel cavitation algorithm is developed in this thesis, which considers the release of bubbles due to both gas trapped within the fluid and vaporization of the operating fluid in localized low pressure regions of the films. In the absence of cavitation, this model will also be used to find the pressures and flows over the film, communicating this information with the remainder of the fluid domain.</div><div><br></div><div>Due to the high pressures that form in these units, the bodies deform. The resulting deformation changes the shape of the films and therefore its pressure distribution. This coupled effect will be captured in one of two ways, the first relying on existing geometric information of the unit, and the other using a novel analytical approach that is developed to avoid this necessity. In either case, the added damping due to the shear of the materials will be considered for the first time. Additionally in regions of low gap height, mixed lubrication occurs and the effects of the surface asperities of the floating bodies cannot be neglected. Accurate modeling of this condition is necessary to predict wear that leads to failure in these units. This work will then develop a novel implementation for mixed lubrication modeling that is directly integrated into the cavitation modeling approach.</div><div><br></div><div>Finally, effort is made to maintain a generic tools, such that the model can be applied to any positive displacement machine. This thesis will present the first toolbox of its kind, which accounts for all the mentioned aspects in such a way that they can be captured for any machine. Using both multithreaded and sequential implementations, the tool will be capable of fully utilizing a machine on which it is run for both low latency (design) and high throughput (optimization) applications respectively. In order to make these applications feasible, the various modules of the tool will be strongly coupled using asynchronous time stepping. This approach is made possible with the development of a novel impedance tensor of the mixed universal Reynolds equation, and shows marked improvements in simulation time by requiring at most 50% of the simulation time of existing approaches.</div><div><br></div><div>In the present thesis, the developed tool will be validated using experimental data collected from 3 fundamentally different machines. Individual advancements of the tool will also be verified in isolation with comparison to the state of the art and commercial software in the relevant fields. As a demonstration of the use of the tool for design, detailed analysis of the displacing actions and lubricating interfaces of these same units will be performed. These validations demonstrate the ability of the tool to predict machine efficiencies with error averaging around 1% over all operating conditions for multiple machine types, and capture transient behavior of the units. To demonstrate the utility as a virtual optimization tool, design of a complete external gear machine design will be performed. This demonstration will start from only analytical parameters, and will track a route to a complete prototype.</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>