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>