A NUMERICAL SCHEME FOR SIMULATING GEAR PUMPS AND MOTORS WITH FLEXIBLE LUMPED PARAMETER FORMULATION AND SWIFT FLUID-STRUCTURE INTERACTION COUPLING
Creators: name: Pan, Dinghao
Publisher: name: Purdue University Graduate School
Year: 2024
Subjects: classificationCode: 401706
subject: Numerical modelling and mechanical characterisation

description: This research developed a lumped volume-based coupled simulation model for gear pumps and motors, which is employed to analyze a reference machine of a compensated crescent- type internal gear pump. The model is composed of simultaneous simulations of the pump fluid domain pressure, lubricating films, and dynamics of the moving components.The simulation model developed includes four major novel contributions.1. A coupled simulation model was developed for the reference machine which provides (a) a lumped parameter simulation of the fluid pressure within the inter-teeth volumes, (b) CFD simulations of the lubricating interfaces, and (c) a simulation of the micromotion of the pressure compensating components and gear bodies. The simulation tool is developed in C++ and constitutes the simulation core of Multics for internal gear pumps. The model achieved volumetric and mechanical predictions for the reference type of machine, which are validated via experimental investigations.2. A flexible pressure solver was established to solve the pressure transience in the fluid domain in gear pumps with general CV geometry exemplified in the reference machine. The approach allows for ample freedom in defining control volumes, including possible volume discontinuities. The new formulation, derived from mass conservation, avoids the numerical evaluation of the volume derivatives so that it allows for simulating a control volume layout with sudden shape changes. The new formulation also considers the sliding motion from volume boundaries when evaluating internal flows, which improves the accuracy of the control volume pressure solutions. The effectiveness of the proposed formulation was examined by applying the method to the simulation of the reference machine. Compared with the state-of-the-art simulations, several improvements in the pressure simulation were observed : (i) the proposed formulation provides free-of-spike fluid pressure simulations, even for discontinuous volumes; (ii) the proposed formulation properly captures the flow component between volumes that is caused by the volume boundary motions, a term previously neglected, which affects the pressure evaluation accuracy, especially in gear meshing zone.3. The swift film coupling algorithm proposes a novel artificial inertia damping-based method (AIDM) to simulate this coupling. The proposed method considers modifying the physical body dynamics with artificial inertia and damping values that could achieve significant numerical solver accelerations while maintaining extremely low errors. The artificial inertia and damping are determined based on the instantaneous physical system’s Jacobian so that the first-order dynamics in the solution can be conserved from the original dynamic system. The solver acceleration capability is quantified in time-discretization-based derivations, where additional guidelines for determining the artificial inertia and damping values are found. The proposed approach is used to simulate two model problems for a 1-D slider pad under periodic loading conditions, where one pad is fixed inclined and the other free to move vertically and rotate about its center. Simulation results reported an error lower than 0.01 μm in the gap height geometry prediction by the proposed AIDM approach compared to the state-of-the-art Reynolds film damping-based method (RDM). Meanwhile, the numerical solver speed improved 1000 times for the fixed incline pad problem and one hundred thousand times for the free-to-float pad problem. Derivations showed that additional acceleration potential can be achieved in realistic mechanical systems where a higher degree of freedom is present in the body motions. The error behavior of the proposed AIDM approach is discussed, showing the error is positively related to the absolute magnitude of the modification parameter ϕ used for calculating the artificial inertia and damping, and the error is related to the validity of the linearization assumption on the system dynamics.4. Based on a novel experimental set-up to measure the filling characteristics of an internal gear pump under induced gaseous cavitation. An integrated simulation approach was proposed to study the incomplete filling behavior in positive displacement machines. The approach consists of (a) a 1st order predictive model for evaluating the amount of undissolved gas at the pump inlet from the circuit pressure loss, (b) a gas-equilibrium-based cavitation model for predicting the pressure transience in the pump fluid domain, (c) a lumped volume based pump flow evaluation. Experiments performed over a wide range of operating conditions validated the deployment of the first-order gas release prediction (with 8 s time constant for fluid with 6 % total air). The complete simulation approach was validated via a good match with the measured volumetric efficiency for both low-speed and high-speed conditions.The reference compensated crescent-type internal gear pump (CCIGP) unit was simulated with the full scope coupled simulation model, with which the methods proposed in this thesis research were validated with experiments. Simulation results matched with volumetric efficiency as well as mechanical efficiency. The model also reports a breakdown of the energy consumption within the reference CCIGP, which promotes the understanding of the operation of the reference machine.