Hu, Lingnan (2018-12). Improved Finite Element Modeling and Dynamic Analysis of Rotating Machinery and a Drillstring with Impact Dampers. Doctoral Dissertation.
Accurate modeling and analysis approaches have long been important concerns for designers of rotating machinery. This work is focused on the improvement of high-fidelity finite element (FE) modeling approaches and software algorithms for analysis of a rotor dynamic system that is comprised of rotors, bearings, and support structures. First, improved formulations for the axisymmetric solid harmonic FE method are developed, which account for the centrifugal stress-stiffening effects and spin-softening effects. A thorough comparison of beam-type FE and axisymmetric solid FE is conducted based on various non-dimensional rotor topologies. In addition to the simulation of rotors, an improved modeling approach is developed to simulate coupled rotor-support systems. This modeling approach utilizes multiple-input and multiple-output (MIMO) transfer functions (TFs) to represent a flexible support structure. The TFs are derived by curve-fitting the frequency response functions of the support model at bearing locations, and then transform into a state-space model to perform general rotor dynamic analyses. Moreover, improvements are made in modeling a rotor system that undergoes large support motion. The shaft continuum is discretized with beam FEs and connected to the support structure via hydrodynamic journal bearings. The bearing forces acting on the rotor are determined by solving the Reynold's equation for lubricant film pressure utilizing a two-dimensional (2D) FE fluid film model. The influences of the time-varying parameters and unloaded bearings on the dynamic behavior of the rotor system are investigated. This work also contributes to the development of novel centralized impact and torsional dampers for suppression of lateral and torsional stick-slip vibrations of drillstrings. The rotor model of the drillstring utilizes the beam FEs that account for the gravity and axial loading effects on the transverse string stiffness and includes the radial and tangential contact forces that occur when the impactors contact the drill collar or sub. An improved contact force model containing nonlinear Hertzian contact restoring forces and nonlinear, viscous contact damping force is developed, in place of the conventional coefficient of restitution (COR) model that cannot provide the required normal and tangential contact forces.