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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pressure cylinders are under the influence of the steam flow with significantly reduced values of the steam parameters. At the same time, the steam environment in low-pressure cylinders has high humidity, which significantly affects the appearance of erosive damage to the blades, as shown particularly in the study by Torop et al. (2018). This especially applies to the blades of the last stages of the turbines. As shown earlier, significant damage appears on the surfaces of the leading and trailing edges of these blades after approximately 180,000 hours of operation. Such damage is mainly observed on the blades of the last stages of turbines of 1000 MW nuclear power plants. In the upper part of the blades on the leading edges and in the lower part on the leading edges, saw-tooth erosion damage appears, which significantly affects the reliability of their work. In study conducted by Shulzhenko and Olkhovskyi (2021), it is shown that erosion damage in the lower third of the leading edges significantly affects the maximum equivalent stresses of the blades, more so than in the upper part. One of the possible options for continuing their safe operation is restorative repair or replacement of blades. The results of numerical studies obtained on the effect of removing a portion of blades in the zone of erosion damage after restorative repair are presented earlier by Shulzhenko et al. (2022). The study examines the effect of this removal on the vibration characteristics of individual blades and the bladed disk system as a whole. In such a system, the cyclic symmetry, which is a characteristic feature, is broken due to the difference in the natural vibration frequencies of the repaired blades. As a result, the calculation studies were conducted for the entire system rather than a single period of the bladed disk. The specific characteristics of vibrations in bladed disks of high-power steam turbines with disturbed blade vibration frequencies have recently been investigated in several studies, including Rzadkowski et al. (2022), Siewert et al. (2017), and Kaneko et al. (2022). The objective of this study is to investigate the influence of kinematic excitation, specifically the vibrations of the disk center caused by the rotor's vibrations on sliding bearings, on the vibration stress of the bladed disk. This analysis holds significant practical importance in understanding the effects of broken symmetry in the disk-blade system resulting from restorative repairs on the safe operation of the system. By considering the influence of kinematic excitation, the research aims to provide valuable insights into the behavior and performance of the repaired blades in the bladed disk system. 2. Object of Investigation The assessment of changes in the stress state of individual blades with a length of 1.2 m and the disk-blade system of the last stage of a 1000 MW turbine during restorative repair was considered earlier by Shulzhenko and Olkhovskyi (2021). Calculation studies of the maximum equivalent stresses were performed under conditional distributed loads from the steam flow. It is assumed that the physical and mechanical properties of the material remain unchanged after processing the damage removal zones on the leading edges of the blades. Three-dimensional finite element models of the last stage of a steam turbine with 92 blades on a disc were used. It is shown that during the restorative repair of blades in the lower part, where the chord at the treatment location is not less than 150 mm, the maximum values of equivalent stresses, with the same treatment applied to all blades, do not exceed the stress in the blades of the undamaged stage. In solving the problem, it was assumed that the center of the disk is rigidly fixed, and kinematic excitations of the center were not taken into account. In the present study, the change in the maximum equivalent stresses in the lower third of the blades of the working wheel (Fig. 1) is determined, considering the kinematic excitation of the center of the disk. This excitation is caused by the vibration of the rotor on the sliding bearings. The other parameters of the system were assumed to be the same as those in earlier studies by Shulzhenko et al. (2022) for a working wheel with one damaged blade. The blades of the last stage are attached to the disc using herringbone shanks. The disc, which has a constant thickness, is manufactured as a single unit with a robust shaft. The blades are interconnected at the periphery by shelf ligaments. Based on operational experience, it is observed that the centrifugal forces tightly press the shelf connections together. In the calculation model, these connections are represented by bandage tape. However, the influence of the damper wire placed in the blade holes is not considered in the analysis.