PSI - Issue 59

ScienceDirect Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2023) 000 – 000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2023) 000 – 000 Available online at www.sciencedirect.com Procedia Structural Integrity 59 (2024) 337–343

www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia

© 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2023 Organizers Abstract The study aims to determine the maximum stresses in the steam turbine blades under force and kinematic excitation conditions in a system with broken cyclic symmetry. Three-dimensional finite element models of the disk-blade system were developed for analysis of stationary harmonic vibrations. The calculation was conducted for excitation from the steam flow with a frequency of 2100 Hz and kinematic excitation in the form of an elliptical motion caused by rotor vibration at a frequency of 50 Hz. The steam flow load on each blade was set to vary linearly from 0 at the root to 1 kPa at the top, acting normally on the blade's working surface. The study established the dependence of maximum equivalent stresses in the lower third of the blades on the excitation frequency in the disk-blade system with broken cyclic symmetry under kinematic excitation conditions. The obtained results were compared with data from systems without kinematic excitation and those after restorative repair. The study shows the importance of considering kinematic excitation in assessing the stress state of blades in the last stage of a high-power steam turbine with broken cyclic symmetry, thus contributing to the determination of their operational reliability. © 202 3 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the conference Guest Editors Keywords: mistuned bladed disk, forced vibrations, three-dimensional finite element model, frequency response, restorative repair. 1. Introduction and Problem Statement One of the most stressed elements of steam turbines is the working blades. If the rotor blades of the high and medium pressure cylinders work at high temperatures and pressure of the steam flow, then the blades in the low- The influence of kinematic excitation on the vibrational stress of the mistuned bladed disk of the last stage of a high-power steam turbine M.G. Shulzhenko, А.S. Olkhovskiy, O.L. Derkach* G.S. Pisarenko Institute for Problems of Strength of the NAS of Ukraine, Kyiv 01014, Ukraine Abstract The study aims to determine the maximum stresses in the steam turbine blades under force and kinematic excitation conditions in a system with broken cyclic symmetry. Three-dimensional finite element models of the disk-blade system were developed for analysis of stationary harmonic vibrations. The calculation was conducted for excitation from the steam flow with a frequency of 2100 Hz and kinematic excitation in the form of an elliptical motion caused by rotor vibration at a frequency of 50 Hz. The steam flow load on each blade was set to vary linearly from 0 at the root to 1 kPa at the top, acting normally on the blade's working surface. The study established the dependence of maximum equivalent stresses in the lower third of the blades on the excitation frequency in the disk-blade system with broken cyclic symmetry under kinematic excitation conditions. The obtained results were compared with data from systems without kinematic excitation and those after restorative repair. The study shows the importance of considering kinematic excitation in assessing the stress state of blades in the last stage of a high-power steam turbine with broken cyclic symmetry, thus contributing to the determination of their operational reliability. © 202 3 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the conference Guest Editors Keywords: mistuned bladed disk, forced vibrations, three-dimensional finite element model, frequency response, restorative repair. 1. Introduction and Problem Statement One of the most stressed elements of steam turbines is the working blades. If the rotor blades of the high and medium pressure cylinders work at high temperatures and pressure of the steam flow, then the blades in the low- VII International Conference “In -service Damage of Materials: Diagnostics and Prediction ” (DMDP 2023) The influence of kinematic excitation on the vibrational stress of the mistuned bladed disk of the last stage of a high-power steam turbine M.G. Shulzhenko, А.S. Olkhovskiy, O.L. Derkach* G.S. Pisarenko Institute for Problems of Strength of the NAS of Ukraine, Kyiv 01014, Ukraine VII International Conference “In -service Damage of Materials: Diagnostics and Prediction ” (DMDP 2023)

* Corresponding author. Tel.: +38-044-286-49-57 ; fax: +38-044-286-16-84 . E-mail address: derkach@ipp.kiev.ua * Corresponding author. Tel.: +38-044-286-49-57 ; fax: +38-044-286-16-84 . E-mail address: derkach@ipp.kiev.ua

2452-3216 © 202 3 M.G. Shulzhenko et al. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the conference Guest Editors 2452-3216 © 202 3 M.G. Shulzhenko et al. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the conference Guest Editors

2452-3216 © 2024 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2023 Organizers 10.1016/j.prostr.2024.04.048