PSI - Issue 59

M.G. Shulzhenko et al. / Procedia Structural Integrity 59 (2024) 337–343 M.G. Shulzhenko et al. / Structural Integrity Procedia 00 (2023) 000 – 000

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Fig. 1. General view of the model of the mistuned bladed disk of the last stage of a high-power steam turbine ( a ) and damaged blade ( b ).

The vibration analysis of the disk-blade system is conducted with the inclusion of one damaged blade located in the lower third of the system after undergoing a restorative process. The chord length in the damaged area is set at a minimum value of 150 mm, as determined in the previous study by Shulzhenko and Olkhovskyi (2021). The presence of the damaged blade disrupts the cyclic symmetry that is typically observed in systems with identical blades. The trajectory of the disk center is elliptical, corresponding to stable forms of rotor movement on sliding bearings. This observation is supported by the results of experimental and computational studies conducted by Kicinski (2006), and others. The maximum allowable vibration amplitude of the rotor center was set at 260 μm, in accordance with regulatory recommendations. The perpendicular span value was chosen to be half the size of the maximum amplitude. These values were selected considering the proximity of the last stages to the sliding bearings, where the centers exhibit similar movement patterns to those observed in the shaft support sections. The three-dimensional finite element model developed for the system (Fig. 1) comprises over 60 thousand elements and 175 thousand nodes. It utilizes a combination of prismatic and tetrahedral finite elements. The force load exerted by the steam flow on each blade was set to vary linearly, starting from 0 at the root of the blades and increasing to 1 kPa at the top. This load acts perpendicularly on the points of the blades' working surfaces. Additionally, a kinematic excitation in the form of an elliptical motion, representing the movement of the disk center within its plane, was applied at a frequency of 50 Hz. 3. Results of Numerical Investigations and Their Analysis In the stationary mode, the excitation frequency from the steam flow, considering the presence of 42 guide vanes, is 2100 Hz. As a result, the calculation studies were conducted within the frequency range of 2000 to 2200 Hz to encompass the relevant frequency range for the system's behavior. According to the analysis of the obtained data, it has been found that certain groups of blades exhibit similar magnitudes and patterns of changes in stresses within the range of vibration excitation frequencies. The frequency response of the maximum equivalent stresses in the blades within the specified range is shown in Figure 2. The curves in the figure are labeled as follows: the first digit represents the blade number (with 0 indicating the damaged blade). The numbers in parentheses indicate the blade numbers that have similar maximum stress values to the blades indicated by the first number. Thus, it can be observed that the blades located to the left (Fig. 2, a ) and right (Fig. 2, b ) of the damaged blade exhibit different character of stress variation. Some blades may have higher stresses in the lower third of the blades than the damaged