3D Solid Finite Element Rotordynamics: Parametric Stability Analysis and Contact Modelling

Abstract

Conventional rotordynamic analyses generally simplify the rotor, neglecting detailed geometrical characteristics. However, in modern rotating machines, rotors consist of multiple complex-shaped parts that are usually non-axisymmetric with preloads to ensure the assembly. These effects may significantly affect rotordynamic behavior of high-performance rotating machinery. The present study aims to take them into account in rotordynamic analyses, by presenting an efficient rotordynamic stability approach for non-axisymmetric rotor-bearing systems with complex shapes using three-dimensional solid finite elements. The 10-node quadratic tetrahedron element is used for the finite element formulation of the rotor. A rotor-bearing system, matrix differential equation is derived in the rotor-fixed coordinate system. The system matrices are reduced by using Guyan reduction. The current study utilizes the Floquet theory to determine the stability of solutions for parametrically excited rotor-bearing systems. Computational efficiency is improved by discretization and parallelization, taking advantage of the discretized Monodromy matrix of Hsu’s method. The method is verified by an analytical model with the Routh-Hurwitz stability criteria, and by direct time-transient, numerical integration for large order models. The proposed and Hill’s methods are compared with respect to accuracy and computational efficiency, and the results indicate the limitations of the Hill’s method when applied to 3D solid rotor-bearing systems. A parametric investigation is performed for an asymmetric Root’s blower type shaft, varying bearing asymmetry and bearing damping. In addition to the non-axisymmetric rotor-bearing system analysis, a new contact model for rotordynamic analysis of an assembled rotor-bearing system with multiple parts connected by multiple joints is suggested. A contact element formulation is presented using solid finite elements and statistics-based contact theories. A test arrangement was developed to validate the proposed contact model for varying interface surface roughness and preloads. An iterative computation algorithm is introduced to solve the implicit relation between contact stiffness and stress distribution. Prediction results, using the contact model, are compared with measured natural frequencies for multiple configurations of a test rotor assembly. A case study is performed for an overhung type rotor-bearing system to investigate the effect of contact interfaces, between an overhung impeller and a rotor shaft, on critical speeds.