Evaluating the Stress and Vibration Conditions of the Rotor of Steam Turbine with the Defect

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Consideration was given to the vibrations of the two-bearing weighty rotor of the steam turbine with the acquired defect in the form of cross crack caused by the working fluid temperature field. Rotor vibration equations were derived during the three-D simulation using the method of finite elements taking thus into consideration the temperature field in the form of additional volume forces. The equations are supplemented by a special mass matrix whose introduction allows us to take into consideration a change in centrifugal forces in a linear statement caused by the offsets and retain their radial directionality. The alternating two-dimensional temperature field is defined by the solution of the nonstationary problem of heat conductivity. The stressed state, the coefficients of stress intensity along the crack front and the crack edge contact conditions were defined for different rotor rotation phases. The stress intensity coefficient values calculated using asymptotic formulas for the rotor with the 50 % cross-section crack depth are much lower than critical and present no danger for the quasistatic state. However, these values can increase significantly in the case of the resonance state. The rotor vibration state was studied for different rotation frequencies in the presence and absence of temperature field. A maximum effect of the influence of nonstationary temperature field in the rotor with the cross crack on its vibrations is manifested at a maximum radial temperature difference. The temperature field reduces considerably maximum inflection values and peak-to-peak values. The superresonance 2/1 that occurred in the rotor in the absence of temperature field disappears and the vibrations approach a monoharmonic type and it is explained by the constancy of the contact area of crack edges during the rotor rotation.