Torsional analysis of geared turbomachinery trains

Abstract

This work presents the torsional vibration analysis of geared turbomachinery trains using a computational procedure based on the finite element and lumped parameters methods. The analysis is performed for systems driven by constant speed electric motors or by variable frequency driver (VFD) motors, that induce additional torsional excitations and have wide operational speed range, which makes the task of keeping the separation margins almost impossible. The computational procedure allows the torsional analysis of geared turbomachinery trains to be performed for single or multiple branched systems, based on American Petroleum Institute (API) guidelines. Modeling considerations of the main train components are applied to obtain the finite element model with lumped inertias at the nodes. The computational procedure consists of obtaining the single speed equivalent model from the original geared model and applying the finite element method to obtain mass, stiffness and damping matrices of the train and the system equations of motion. From the equations of motion, the eigenvalue problem is derived to estimate the torsional natural frequencies and mode shapes and to plot the Campbell diagrams. For the interference points identified in the Campbell diagram, steady state forces response analysis is applied to estimate nodal angular displacements, frequency response functions, elements twisting angles and associated torques and shear stresses in each element, being the damping matrix proportional (can be decoupled by the eigenvectors) or not. Transient responses due to 2-phase and 3-phase short circuits are estimated by numerical integration using an adaptative stepsize Runge-Kutta method, considering the non-linearity associated with the turbomachinery resistant torque. Validation cases are presented and results agreement with literature are demonstrated. Finally, the procedure is applied to a case study of a constant speed electric motor driven compressor and its modified version by the inclusion of a VFD, which causes interference points within operational speed range, requiring forced response and fatigue analyses to demonstrate train integrity in steady state regime. Train response to short circuits torques is predicted for different cases and resonance with first torsional mode is identified for the 2-phase short circuit.