Residual-Flexibility Corrections for Transient Modal Rotordynamic Models

An extension is presented to a modal formulation for the dynamics of flexible rotors. To date, rotordynamic modal formulations have retained for integration those modes of vibration whose natural frequencies are within or slightly above the operating speed range of the rotor, with higher-order modes simply discarded. In this study, the residual-flexibility technique is employed to account for the “static” contribution of these higher-frequency modes without requiring their integration. The residual-flexibility technique accounts directly for the static contribution of higher frequency modes due to imbalance and external transient loading, and has been adapted to account for reaction forces which are not accounted for by the nominal rotor/bearing stiffness matrix, e.g., bearing damping forces or speed-dependent bearing stiffnesses. The High-Pressure-Oxygen Turbopump of the Space Shuttle Main Engine (SSME) is analyzed. The maximum operating speed of this turbopump lies between its first and second critical speeds. Comparisons are made without residual-flexibility corrections for two through six modes retained for integration. Simulation runs are made for (a) a deceleration through the first critical speed and (b) a constant speed run at FPL (full power level). The results demonstrate that the residual-flexibility approach yields a significant improvement in accuracy for a comparatively modest increase in computer-time requirements.