TORSIONAL VIBRATION ANALYSIS OF GEARED TURBOMACHINERY TRAINS USING THE FINITE ELEMENT METHOD

Resumo

This work presents the application of finite element method to the torsional analysis of geared turbomachinery trains based on the guidelines of the API (American Petroleum Institute). The implemented code is applied to a case study of a fixed-speed electric motor driven compressor and its modified variable-speed version by the inclusion of a VFD (Variable Frequency Drive). Undamped Torsional, Steady-State Forced Response and Transient Response Analyses are performed to obtain the system natural frequencies, mode shapes and Campbell (Interference Points) Diagrams; steady-state alternating shear stresses; transient response caused by a 3-phase motor short-circuit. The linear model of the turbomachinery train consists of rotational inertias and stiffnesses of motor, shafts, couplings, gears and compressor, with modal damping provided by combined sources such as bearings and material hysteresis. Torsional excitations due to the machine operating loads are considered. The governing discrete equations of the system are derived using the state variable modeling. Transient response of a 3-phase short-circuit is obtained by numerical integration using the 4th order Runge-Kutta method on the time domain. On the Undamped Torsional Analysis, the torsional natural frequencies (TNFs) and the mode shapes are computed for the machine train. Critical speeds, i.e., the train speeds at which the excitations frequencies meet any of the system TNFs, are determined. For the identified interference points within the operational range, the Steady-State Torsional Analysis is performed and magnitude and phase of the twisting angle and alternating shear stresses are computed. Finally, the results of transient and steady-state torsional analyses are used to perform the mechanical integrity assessment of the turbomachinery train.