Oscillation suppression of a steam turbine shaft using the exact analytical solution of the equivalent frequency equation

Abstract

This study proposes a new analytical framework for identifying the optimal parameters of a tuned mass damper (TMD) aimed at mitigating torsional oscillations in steam turbine shafts. Improper TMD design may induce eccentric shaft rotation, which becomes particularly hazardous for high-speed shafts due to the substantial Coriolis and centrifugal forces generated during operation. These inertial forces can significantly degrade shaft performance and structural integrity. To address this issue, the present work formulates an analytical approach based on the exact solution of the equivalent frequency equation, enabling the determination of the optimal TMD parameters in closed form. Obtaining analytical expressions for these parameters is crucial, as it allows designers to configure an optimal TMD directly from the initial physical characteristics of the turbine shaft, without relying on computationally expensive numerical optimization. Numerical simulations are conducted to validate the proposed method, demonstrating that the analytically optimized TMD can effectively eliminate torsional oscillations in steam turbine shafts.