Optimal design for damper of long blade in steam turbine based on dynamic analysis

Adding damped structure can decrease dynamic stress of blade and avoid blade fatigue failure from forced vibration. Based on the structural feature of long blade with friction damper, the numerical model for dynamic analysis of damped blade in steam turbine has been developed. The blade was described by twisted beam element, the usual space beam element was adopted to analyze the frame of damper, and the slip motion between rubbing surface was modeled by a damping connector, The following matrices which are necessary for finite element analysis were obtained: the stiffness matrix, mass matrix and damping matrix of finite element for blade and damper, the stiffness matrix and damping matrix of damping connector. Then the gross finite element motion equation of the blade was got, Meanwhile, harmonic wave propagation method was adopted to improve calculation efficiency. The comparison of calculation results and experimental data of a 360mm blade shows good agreement. The dynamic characteristic of a last stage long blade in steam turbine with damper was analyzed in detail, its responses with different thickness shroud and gap between shrouds were investigated in detail too, then the optimal structure of damped shroud was obtained, the comparison for response between damped blade and freestanding blade shows the maximum response of blade with optimal damper is 42.4% of that of freestanding blade. At last, a tie wire was added to the damped blade, numerical result shows it can decrease blade response further.