Влияние предварительно напряженного состояния на частоты несущих конструкций гидротурбин
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Дата
2018
ORCID
DOI
10.20998/2078-9130.2018.38.152480
Науковий ступінь
Рівень дисертації
Шифр та назва спеціальності
Рада захисту
Установа захисту
Науковий керівник
Члени комітету
Видавець
НТУ "ХПІ"
Анотація
Целью работы является создание методики расчета собственных частот колебаний крышки гибротурбины в вакууме и при взаимодействии с водой с учетом предварительно напряженного состояния конструкции. Задача решается методом конечных элементов и состоит в нахождении частот и форм колебаний. Влияние инерционных сил от масс и оборудования, расположенного на крышке, учитывается приведенной плотностью. Также в динамическом процессе учитывается влияние жидкости. Предварительно напряженное состояние моделируется путем введения так называемой геометрической матрицы жесткости, которая получена на основе тензора предварительных напряжений и нелинейной части тензора деформаций. Решена задача по определению частот собственных колебаний стальной цилиндрической оболочки, находящейся под действием внутреннего давления. Для выбора размера конечного элемента выполнена серия расчетов и проведена оценка сходимости развязку. Установлено, что внутреннее давление приводит к увеличению собственных частот колебаний цилиндрической оболочки, а внешний их снижает. На тестовом примере проверена работоспособность предложенного подхода и подтверждена достоверность результатов, полученных на его основе. Результаты, полученные с разработанным подходом, отличаются от экспериментальных данных от 0,5 до 11%. На основе предложенного подхода исследованы свободные колебания крышки гидротурбины, изготовленной из листового проката стали.
The goal of the work is to develop a method for calculating the modal frequencies of hydroturbine cover in a vacuum and in interaction with water, taking into account the prestressed state of the structure. Due to the complexity of the design form, the problem is solved by the finite element method and consists in finding the frequencies and modes of vibration. The consideration of inertial forces from masses, equipment located on the cover is modeled by the reduced density. Also, the dynamic process takes into account the water influence. The prestressed state is modeled by involving the so-called geometric rigidity matrix, which is derived on the basis of the previous stresses tensor and the nonlinear part of the strain tensor. The problem of determining natural frequencies of a steel cylindrical shell which is under the influence of internal pressure is solved. Calculations have been performed for choosing a finite element size and an estimation of the solution convergence is carried out. It has been established that internal pressure leads to an increase in the natural frequencies of vibration of the cylindrical shell, and the outer one reduces them. The robustness of the proposed approach has tested and verified the reliability of the results obtained on its basis. The results obtained from the developed approach differ from the experimental data from 0.5 to 11%. Based on the proposed approach free vibrations of the hydroturbine cover made of steel sheets were investigated. The greatest interest is the first natural frequency, because it is closest to the excitation frequency. In the study of the proper vibrations of the cover, the inertial forces from the equipment mass installed on the cover were modeled by the reduced density of the ring. It is determined that the mass change affects its own cover frequency. It has been established that with increasing depth of water, the frequency of hydroelastic vibrations decreases; with increasing weight loads the frequency of oscillations decreases; with increasing water pressure the frequency of vibrations decreases; taking into account the prestressed state does not significantly affect the frequency at the first proper frequency of the cover.
The goal of the work is to develop a method for calculating the modal frequencies of hydroturbine cover in a vacuum and in interaction with water, taking into account the prestressed state of the structure. Due to the complexity of the design form, the problem is solved by the finite element method and consists in finding the frequencies and modes of vibration. The consideration of inertial forces from masses, equipment located on the cover is modeled by the reduced density. Also, the dynamic process takes into account the water influence. The prestressed state is modeled by involving the so-called geometric rigidity matrix, which is derived on the basis of the previous stresses tensor and the nonlinear part of the strain tensor. The problem of determining natural frequencies of a steel cylindrical shell which is under the influence of internal pressure is solved. Calculations have been performed for choosing a finite element size and an estimation of the solution convergence is carried out. It has been established that internal pressure leads to an increase in the natural frequencies of vibration of the cylindrical shell, and the outer one reduces them. The robustness of the proposed approach has tested and verified the reliability of the results obtained on its basis. The results obtained from the developed approach differ from the experimental data from 0.5 to 11%. Based on the proposed approach free vibrations of the hydroturbine cover made of steel sheets were investigated. The greatest interest is the first natural frequency, because it is closest to the excitation frequency. In the study of the proper vibrations of the cover, the inertial forces from the equipment mass installed on the cover were modeled by the reduced density of the ring. It is determined that the mass change affects its own cover frequency. It has been established that with increasing depth of water, the frequency of hydroelastic vibrations decreases; with increasing weight loads the frequency of oscillations decreases; with increasing water pressure the frequency of vibrations decreases; taking into account the prestressed state does not significantly affect the frequency at the first proper frequency of the cover.
Опис
Ключові слова
гидротурбины, собственные колебания, предварительно напряженное состояние, внутреннее давление, prestressed state, hydroturbine Bearing structures, modal frequencies, hydroturbine cover, internal pressure
Бібліографічний опис
Сметанкина Н. В. Влияние предварительно напряженного состояния на частоты несущих конструкций гидротурбин / Н. В. Сметанкина, С. Ю. Мисюра, А. В. Линник // Вісник Національного технічного університету "ХПІ". Сер. : Динаміка і міцність машин = Bulletin of the National Technical University "KhPI". Ser. : Dynamics and Strength of Machines : зб. наук. пр. – Харків : НТУ "ХПІ", 2018. – № 38 (1314). – С. 42-48.