The area of powertrain dynamics has received considerable attention over a number of years. The recent introduction of more stringent emission requirements together with economic pressure has led to a particular focus on increasing powertrain efficiency. This has seen the incorporation of on-board, real-time measurements to predict system behaviour and engine condition. In this domain, accurate models for all powertrain components are important. One strategy to improve accuracy is to evaluate the assumptions made when deriving each model and then to address the simplifications that may introduce large errors. To this end, the aim of the work presented in this dissertation was to investigate the consequences of some of the more common assumptions and simplifications made in low frequency torsional powertrain models, and to propose improved models where appropriate. In particular, the effects of piston-tocylinder friction, crank/gudgeon pin offset, and the torsional behaviour of tyres were studied. Frequency and time domain models were used to investigate system behaviour and model predictions were compared with measurements on a small single cylinder engine. All time domain engine and powertrain models also include a variable inertia function for each reciprocating mechanism. It was found that piston-to-cylinder friction can increase the apparent inertia variation of a single reciprocating engine mechanism. This has implications for the nonlinear behaviour of engines and the drivetrains they are connected to. The effect of crank/gudgeon pin offset also modified the nonlinear behaviour of the mechanism. Though, for typical (small) gudgeon offset values these effects are small. However, for large offset values, achievable practically with crank offset, the modification to the nonlinear behaviour should not be ignored. The low frequency torsional damping properties of a small pneumatic tyre were found to be more accurately represented as hysteretic rather than viscous. Time domain modelling was then used to extend the results to a multi-cylinder engine powertrain and was achieved using the Time Domain Receptance (TDR) method. Various powertrain component TDRs were developed using Laplacians. Powertrain simulations showed that piston-to-cylinder friction can provide additional excitation to the system.

<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>