Использование компьютерных технологий при модернизации крышек гидротурбин типа ПЛ 20-В-500
Одной из проблем, возникающих перед конструктором при модернизации действующих гидроагрегатов, является анализ возможности обеспечения прочности и надежности узлов и деталей турбины в условиях дальнейшей продолжительной работы под действием динамической нагрузки или их замена, оптимальная как по мас...
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| Опубліковано в: : | Проблеми машинобудування |
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| Дата: | 2018 |
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| Мова: | Russian |
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Інстиут проблем машинобудування ім. А.М. Підгорного НАН України
2018
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| Цитувати: | Использование компьютерных технологий при модернизации крышек гидротурбин типа ПЛ 20-В-500 / Е.А. Стрельникова, Т.Ф. Медведовская, Е.Л. Медведева, А.В. Линник, О.Н. Зеленская // Проблеми машинобудування. — 2018. — Т. 21, № 1. — С. 35-44. — Бібліогр.: 15 назв. — рос., англ. |
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Стрельникова, Е.А. Медведовская, Т.Ф. Медведева, Е.Л. Линник, А.В. Зеленская, О.Н. 2018-09-15T16:54:37Z 2018-09-15T16:54:37Z 2018 Использование компьютерных технологий при модернизации крышек гидротурбин типа ПЛ 20-В-500 / Е.А. Стрельникова, Т.Ф. Медведовская, Е.Л. Медведева, А.В. Линник, О.Н. Зеленская // Проблеми машинобудування. — 2018. — Т. 21, № 1. — С. 35-44. — Бібліогр.: 15 назв. — рос., англ. 0131-2928 https://nasplib.isofts.kiev.ua/handle/123456789/141895 539.3 Одной из проблем, возникающих перед конструктором при модернизации действующих гидроагрегатов, является анализ возможности обеспечения прочности и надежности узлов и деталей турбины в условиях дальнейшей продолжительной работы под действием динамической нагрузки или их замена, оптимальная как по массе, так и по динамическим характеристикам. Решение этой проблемы возможно с использованием компьютерных технологий для исследования динамики несущих конструкций гидротурбин при разных режимах эксплуатации. В работе описаны методики, разработанные для исследования динамического напряженно-деформированного состояния крышки гидротурбины, которая воспринимает гидродинамическое давление, действующее на ее контактирующую с водой поверхность, а также веса размещенных на ее поверхности узлов и деталей. Впервые в трехмерной постановке учтено влияние присоединенных масс воды конструкции с применением математических моделей, основанных на гиперсингулярных уравнениях и сочетании методов конечных и граничных элементов. Разработаны пакеты прикладных программ, являющиеся мощным инструментом автоматизации при определении динамического напряженно-деформированного состояния крышки гидротурбины. Получены численные результаты, позволяющие оценить динамическое напряженно-деформированное состояние с учетом влияния воды находящейся в эксплуатации и подлежащей замене литой чугунной крышки гидротурбины ПЛ 20-В-500, а также разработанной для ее замены стальной сварной крышки. Выполнен анализ численного исследования и даны рекомендации для проектирования сварной крышки, динамические характеристики которой позволяют исключить резонансные явления и обеспечить эксплуатационную надежность. Примененные методики обоснованы нормативным документом «Розрахунок залишкового ресурсу елементів проточної частини гідротурбін ГЕС та ГАЕС. Методичні вказівки» СОУ-Н МЕВ 40.1 –21677681–51: 2011. Описані методики, розроблені для дослідження динамічного напружено-деформованого стану кришки гідротурбіни, застосування яких обґрунтовано нормативним документом «Розрахунок залишкового ресурсу елементів проточної части гідротурбін ГЕС та ГАЕС. Методичні вказівки» СОУ-Н МЕВ 40.1 -21677681-51:2011. Вперше в тривимірній постановці враховано вплив приєднаних мас води конструкції із застосуванням математичних моделей, що грунтуються на гіперсингулярних рівняннях і поєднанні методів скінченних та граничних елементів. Отримано чисельні результати, що дозволяють оцінити з урахуванням впливу води динамічний напружено-деформований стан литої чавунної кришки гідротурбіни ПЛ 20 В-500, а також розробленої для її заміни конструкції сталевої зварної кришки. Виконано аналіз чисельного дослідження та надано рекомендації для проектування зварної кришки, динамічні характеристики якої дозволяють виключити резонансні явища та забезпечити експлуатаційну надійність One of the problems faced by a designer in the modernization of operating generating units is the analysis of the feasibility of ensuring the strength and reliability of turbine parts and components in their further continuous operation under dynamic load or replacement of the turbine parts and components which would by optimal in terms of weight and dynamic behavior. It is possible to solve the above problem using computer technologies for dynamic study of load bearing structures of hydraulic turbines in various operating modes. This paper describes techniques developed to study the dynamic mode of deformation of hydraulic turbine head cover taking up the hydrodynamic pressure acting on its surface in contact with water and the weights of parts and components located on its surface. For the first time, the influence of added water masses of the structure is three-dimensionally considered using mathematical models based on hypersingular equations and combination of the finite element method and boundary element method. Application program packages are developed which are a powerful tool of automation in the determination of dynamic mode of deformation of the hydraulic turbine head cover. Numerical results are obtained allowing the evaluation of the dynamic mode of deformation taking into consideration the effect of water on the cast iron head cover of hydraulic turbine ПЛ 20-В-500 inoperation and subject to replacement as well as that on the welded steel head cover developed to replace the cast iron one. The numerical study is analyzed and recommendations are given for designing of the welded head cover which dynamical behavior allows preventing resonance phenomena and ensuring the operating reliability. The techniques used are validated by the regulatory document «Residual life prediction for water passage components of hydraulic turbines of HPPs and PSPs – Methodical Guidelines» SOU-N MEV 40.1–21677681–51: 2011. ru Інстиут проблем машинобудування ім. А.М. Підгорного НАН України Проблеми машинобудування Динаміка та міцність машин Использование компьютерных технологий при модернизации крышек гидротурбин типа ПЛ 20-В-500 Використання комп'ютерних технологій при модернізації кришок гідротурбін типу ПЛ 20-В-500 Use of Computer Technology in Modernization of Head Covers for ПЛ 20-В-500 Kaplan Turbines Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Использование компьютерных технологий при модернизации крышек гидротурбин типа ПЛ 20-В-500 |
| spellingShingle |
Использование компьютерных технологий при модернизации крышек гидротурбин типа ПЛ 20-В-500 Стрельникова, Е.А. Медведовская, Т.Ф. Медведева, Е.Л. Линник, А.В. Зеленская, О.Н. Динаміка та міцність машин |
| title_short |
Использование компьютерных технологий при модернизации крышек гидротурбин типа ПЛ 20-В-500 |
| title_full |
Использование компьютерных технологий при модернизации крышек гидротурбин типа ПЛ 20-В-500 |
| title_fullStr |
Использование компьютерных технологий при модернизации крышек гидротурбин типа ПЛ 20-В-500 |
| title_full_unstemmed |
Использование компьютерных технологий при модернизации крышек гидротурбин типа ПЛ 20-В-500 |
| title_sort |
использование компьютерных технологий при модернизации крышек гидротурбин типа пл 20-в-500 |
| author |
Стрельникова, Е.А. Медведовская, Т.Ф. Медведева, Е.Л. Линник, А.В. Зеленская, О.Н. |
| author_facet |
Стрельникова, Е.А. Медведовская, Т.Ф. Медведева, Е.Л. Линник, А.В. Зеленская, О.Н. |
| topic |
Динаміка та міцність машин |
| topic_facet |
Динаміка та міцність машин |
| publishDate |
2018 |
| language |
Russian |
| container_title |
Проблеми машинобудування |
| publisher |
Інстиут проблем машинобудування ім. А.М. Підгорного НАН України |
| format |
Article |
| title_alt |
Використання комп'ютерних технологій при модернізації кришок гідротурбін типу ПЛ 20-В-500 Use of Computer Technology in Modernization of Head Covers for ПЛ 20-В-500 Kaplan Turbines |
| description |
Одной из проблем, возникающих перед конструктором при модернизации действующих гидроагрегатов, является анализ возможности обеспечения прочности и надежности узлов и деталей турбины в условиях дальнейшей продолжительной работы под действием динамической нагрузки или их замена, оптимальная как по массе, так и по динамическим характеристикам. Решение этой проблемы возможно с использованием компьютерных технологий для исследования динамики несущих конструкций гидротурбин при разных режимах эксплуатации. В работе описаны методики, разработанные для исследования динамического напряженно-деформированного состояния крышки гидротурбины, которая воспринимает гидродинамическое давление, действующее на ее контактирующую с водой поверхность, а также веса размещенных на ее поверхности узлов и деталей. Впервые в трехмерной постановке учтено влияние присоединенных масс воды конструкции с применением математических моделей, основанных на гиперсингулярных уравнениях и сочетании методов конечных и граничных элементов. Разработаны пакеты прикладных программ, являющиеся мощным инструментом автоматизации при определении динамического напряженно-деформированного состояния крышки гидротурбины. Получены численные результаты, позволяющие оценить динамическое напряженно-деформированное состояние с учетом влияния воды находящейся в эксплуатации и подлежащей замене литой чугунной крышки гидротурбины ПЛ 20-В-500, а также разработанной для ее замены стальной сварной крышки. Выполнен анализ численного исследования и даны рекомендации для проектирования сварной крышки, динамические характеристики которой позволяют исключить резонансные явления и обеспечить эксплуатационную надежность. Примененные методики обоснованы нормативным документом «Розрахунок залишкового ресурсу елементів проточної частини гідротурбін ГЕС та ГАЕС. Методичні вказівки» СОУ-Н МЕВ 40.1 –21677681–51: 2011.
Описані методики, розроблені для дослідження динамічного напружено-деформованого стану кришки гідротурбіни, застосування яких обґрунтовано нормативним документом «Розрахунок залишкового ресурсу елементів проточної части гідротурбін ГЕС та ГАЕС. Методичні вказівки» СОУ-Н МЕВ 40.1 -21677681-51:2011. Вперше в тривимірній постановці враховано вплив приєднаних мас води конструкції із застосуванням математичних моделей, що грунтуються на гіперсингулярних рівняннях і поєднанні методів скінченних та граничних елементів. Отримано чисельні результати, що дозволяють оцінити з урахуванням впливу води динамічний напружено-деформований стан литої чавунної кришки гідротурбіни ПЛ 20 В-500, а також розробленої для її заміни конструкції сталевої зварної кришки. Виконано аналіз чисельного дослідження та надано рекомендації для проектування зварної кришки, динамічні характеристики якої дозволяють виключити резонансні явища та забезпечити експлуатаційну надійність
One of the problems faced by a designer in the modernization of operating generating units is the analysis of the feasibility of ensuring the strength and reliability of turbine parts and components in their further continuous operation under dynamic load or replacement of the turbine parts and components which would by optimal in terms of weight and dynamic behavior. It is possible to solve the above problem using computer technologies for dynamic study of load bearing structures of hydraulic turbines in various operating modes. This paper describes techniques developed to study the dynamic mode of deformation of hydraulic turbine head cover taking up the hydrodynamic pressure acting on its surface in contact with water and the weights of parts and components located on its surface. For the first time, the influence of added water masses of the structure is three-dimensionally considered using mathematical models based on hypersingular equations and combination of the finite element method and boundary element method. Application program packages are developed which are a powerful tool of automation in the determination of dynamic mode of deformation of the hydraulic turbine head cover. Numerical results are obtained allowing the evaluation of the dynamic mode of deformation taking into consideration the effect of water on the cast iron head cover of hydraulic turbine ПЛ 20-В-500 inoperation and subject to replacement as well as that on the welded steel head cover developed to replace the cast iron one. The numerical study is analyzed and recommendations are given for designing of the welded head cover which dynamical behavior allows preventing resonance phenomena and ensuring the operating reliability. The techniques used are validated by the regulatory document «Residual life prediction for water passage components of hydraulic turbines of HPPs and PSPs – Methodical Guidelines» SOU-N MEV 40.1–21677681–51: 2011.
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0131-2928 |
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https://nasplib.isofts.kiev.ua/handle/123456789/141895 |
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Использование компьютерных технологий при модернизации крышек гидротурбин типа ПЛ 20-В-500 / Е.А. Стрельникова, Т.Ф. Медведовская, Е.Л. Медведева, А.В. Линник, О.Н. Зеленская // Проблеми машинобудування. — 2018. — Т. 21, № 1. — С. 35-44. — Бібліогр.: 15 назв. — рос., англ. |
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ДИНАМІКА ТА МІЦНІСТЬ МАШИН
ISSN 0131–2928. Проблеми машинобудування, 2018, Т. 21, № 1 35
1 E. A. Strelnikova, Doctor of Technical
Sciences
2 T. F. Medvedovskaya, Candidate of
Technical Sciences
2 E. L. Medvedeva
3 A. V. Linnik
3 O. N. Zelenskaya
1 A. Podgorny Institute of Mechanical
Engineering Problems of NASU,
Kharkiv, Ukraine,
2 Kharkov Turbo Engineering,
Kharkiv, Ukraine,
e-mail: khte@online.kharkov.ua
3 PJSC 'Turboatom', Kharkiv, Ukraine,
e-mail: lynnyk@turboatom.com.ua
UDC 539.3
USE OF COMPUTER TECHNOLOGIES IN
MODERNIZATION OF HEAD COVERS
FOR ПЛ 20-В-500 KAPLAN TURBINES
Описані методики, розроблені для дослідження динамічного
напружено-деформованого стану кришки гідротурбіни,
застосування яких обґрунтовано нормативним документом
«Розрахунок залишкового ресурсу елементів проточної части
гідротурбін ГЕС та ГАЕС. Методичні вказівки» СОУ-Н МЕВ
40.1 -21677681-51:2011. Вперше в тривимірній постановці
враховано вплив приєднаних мас води конструкції із
застосуванням математичних моделей, що ґрунтуються на
гіперсингулярних рівняннях і поєднанні методів скінченних та
граничних елементів. Отримано чисельні результати, що
дозволяють оцінити з урахуванням впливу води динамічний
напружено-деформований стан литої чавунної кришки
гідротурбіни ПЛ 20 В-500, а також розробленої для її заміни
конструкції сталевої зварної кришки. Виконано аналіз
чисельного дослідження та надано рекомендації для
проектування зварної кришки, динамічні характеристики якої
дозволяють виключити резонансні явища та забезпечити
експлуатаційну надійність.
Ключові слова: кришка, гідротурбіна,
модернізація, метод скінченних елементів,
метод граничних елементів, динамічний
напружено-деформований стан.
Introduction
In recent years, the level of requirements for the efficiency and reliability of energy equipment has
increased sharply, and a considerable use of energy potential in many countries of the world, including
Ukraine, has resulted in the necessity to modernize and replace the HPS turbine equipment which has been in
operation for a long time. Evaluation of the efficiency and scope of the reconstruction requires computer
technologies using specialized software to study the strength and dynamics of the parts and components of
the turbines.
When deciding on the scope of modernization, in particular, one considers the necessity to replace or
extend the service life of the head covers of turbines, which are one of its most metal consuming units. In the
previous designs of the turbines, the head covers were usually made in the form of cast iron castings, where-
as at present, they are welded from carbon steel sheets. It should be emphasized that the elastic properties of
gray cast iron used for the castings earlier depend on the amounts of graphite inclusions: a modulus of elas-
ticity can amount to 40 − 75 % of the elastic modulus of steel, about 67 % of Poisson's ratio, and the density
of cast iron − to 90 − 95 % of the density of steel. If in the process of modernization of the turbine a decision
has been made to replace the head cover, it is of interest to carry out a comparative numerical analysis of the
stress-strain state of the head cover used and the head cover being designed.
The main requirements for the design of the head cover are to provide not only strength but also ri-
gidity, as well as vibration reliability since the head cover vibrations in both axial and radial directions must
meet the existing standards. A special feature of the problem is the necessity to fit the new cover into the ex-
isting flow section.
A regulatory document has been developed to assess the service life of the elements of the flow sec-
tion, including the head covers for the said turbines [1]. The reliability of the results obtained by the devel-
oped procedure is confirmed in [2]. This approach was developed in [3 − 4] to determine the stress-strain
state of a constructive and orthotropic body under asymmetric stress, which makes it possible to reduce the
computations of the required displacements to the solution of independent problems for each term in the
Fourier series expansion. One of the important tasks solved both in forecasting the service life of the head
covers, and in the case of replacing cast iron head covers with steel ones, is an accurate determination of
their eigenfrequencies, taking into account the effect of a liquid. This paper describes a technique in which,
E. A. Strelnikova, T. F. Medvedovskaya, E. L. Medvedeva, A. V. Linnik, O. N. Zelenskaya, 2018
mailto:khte@online.kharkov.ua
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in contrast to [5 − 7], the modes of vibration of the head cover in a liquid are represented as the eigenmode
expansion of its vibrations in a vacuum. The developed technique for constructing matrices of the additional
masses of the load-bearing structures interacting with a liquid is described in [8 − 9] and is given below. This
approach makes it possible to reduce the computations of the required displacements to the solution of inde-
pendent problems for each term in the Fourier series expansion.
Free hydroelastic vibrations of turbine head covers
We write the system of equations of motion of a deformable construction symbolically as
PUU )()( ML , (1)
where L and M are the operators of elastic and mass forces; P is the pressure of the liquid on the structural
element in question (blade); U = (u1, u2, w) is a vector-function of displacements. The speed of the oncoming
stream is assumed to be zero. The liquid motion is studied in a 3D formulation by the methods in potential
theory. It is assumed that the liquid is ideal, free vortices are not formed and they do not descend from the
lifting surface. In this case, there exists a velocity potential that satisfies the harmonic equation everywhere
outside the plate, and on the face surfaces of the plate S − the no-flow condition. For a potential flow, the
perturbed velocity of the liquid is represented as
),,,(grad),,,( tzyxtzyx Фv , (2)
where (x, y, z, t) is the potential of velocities induced by small free vibrations of the plate. To determine the
pressure of a liquid on wetted surfaces, the Cauchy-Lagrange integral is used. To find the pressure on the de-
formable surface from the liquid side, it is necessary to determine function (x, y, z, t) by solving the Laplace
equation with the following boundary condition:
t
w
S
nΦgrad , (3)
Thus, it is required to determine functions U, (x, y, z, t), satisfying the system of differential equa-
tions (1) − (2), the no-flow conditions (3), the conditions for fixing and damping the perturbed velocity of the
liquid at infinity. The literature has no numerical studies to determine the eigenfrequencies and vibration
modes of such structural elements in a liquid. Earlier, to estimate the influence of a liquid on the frequency
of eigen-vibrations, the results obtained using the approximate Rayleigh-Lamb approach were used. In this
case, shapes of the radial plate were taken as forms of free vibrations for the turbine head cover, while 2D
models were used for the turbine blade array.
In this paper, a method for calculating the frequencies and forms of free vibrations of the structures
interacting with a liquid is proposed, based on the attraction of the apparatus of singular and hypersingular
integral equations.
To solve this problem, we apply the method of given forms [10]. At the first stage, in a 3D formula-
tion, a calculation of the frequencies and modes of vibration of the structure in a vacuum is carried out with
the help of the finite element method and its modification for the body of revolution. The obtained modes of
free vibrations are chosen as the basic system of functions, by which they are decomposed into a series of the
vibration modes of the structure in question in a liquid.
Let us study the case of harmonic vibrations. Then the problem under consideration reduces to
2,0,0 iML uu , 02 ; wi
S
n
. (4)
We represent the function (x, y, z) as a potential of a double layer with an unknown density. Then
the problem of determining the pressure (4) reduces to solving the integral equation
widS
xS
xnn
1
)(
4
1 2
. (5)
Suppose that the eigenmodes of vibrations in a liquid are representable as
N
k
kk wcw
1
.
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Let the functions k () be solutions of the hypersingular equation (5) with appropriately chosen
right-hand sides:
kww .
To solve the hypersingular equation (5), the discrete singularity method was applied [5, 6]. In this
case, the integration domain was divided into a finite number of quadrangular subdomains NS, in each of
which an unknown density was replaced with a constant value. When calculating the finite part according to
Adamar for the integrals in (5) across the quadrangle arbitrarily oriented in space, the formula obtained in [5]
was used. The elements of the matrix of the additional masses were found by the formula
S
kiik dSxwxP )()( ,
where )(xi are the amplitude values of the pressure induced by its eigenform xwk . After determining the
elements of the matrix of the additional masses, the eigenvalue problem can be solved according to the
method developed in [5, 10].
Investigation of the vibration frequency spectra of the head covers for the ПЛ 20-В-500 turbines,
taking into account the influence of a liquid
The design of the head covers for the
ПЛ 20-В-500 turbines in service consists of
bodies of revolution and a system of multiply-
connected meridional plates (Fig. 1).
For calculations, the mechanical proper-
ties of materials were used in accordance with
the data given in [11−13].
For grey cast iron Сч20 it was assumed
that the modulus of elasticity
E (0.81.2)×105 MPa, the Poisson ratio
= 0.210.25, the tensile strength В = 210 MPa,
the material density = 7,100 kg/m3.
For steel Ст3 the modulus of elasticity E = 2.1×105 MPa, the Poisson ratio = 0.3, the tensile
strength В = 380 MPa, the material density = 7,800 kg/m3 were considered.
The calculation of the eigenfrequencies of the head cover vibrations was carried out for two variants
of fixation, imitating, depending on the tightening force of the fasteners, a possible contact of the head cover
flange surface with the stator surface: resting along the line of its fastening to the stator with studs (ur = 0,
uz = 0, u = 0) and a rigid fastening of the flange cover to the stator (ur = 0, uz = 0, u = 0).
The eigenfrequencies and vibration modes were calculated, taking into account the masses of the
turbine parts and units placed on the head cover (added masses of the parts): the regulating ring
(Greg r = 5,365 kg), half of the stator shackles (Gsh = 366 kg), half of the pins of the of the stator
(Gpin =96 kg), the rod (Grod =495 kg), guide bearing (Ggd brg =114,690 N), the turbine shaft
(Gturb sft = 23,220 kg), the generator rotor (Ggen rtr = 137,650 кг), the shaft extension (Gsft ext = 900 kg), the ex-
citer rotor (Gexc rtr =5.160 kg), the thrust block (Gthr bl = 9,500 kg), the thrust (Gthr = 2,800 kg), the cowl cone
(Gcc = 11,469 kg).
The design diagram of the ПЛ 20 В-500 turbine head cover is shown in Fig. 2. The values of the
masses of the parts and units located on the turbine head cover (Fig. 2) are as follows:
G2 = Greg r +½ Gsh +½ Gpin + Grod = 6,322 kg;
G3 = Ggen rtr + Gturb sft + Gsft ext + Gexc rtr + Gthr bl + Gthr = 247,330 kg;
G4 = Gсс = 1,469 kg.
The additional masses of the parts Gi (i = 2, 3, 4) are uniformly distributed over the annular portions
of the head cover as shown in Fig. 2.
The influence of mass forces is taken into account by adjusting the density of the head cover sections
along the boundary of their application [14]. The material densities for the primary discretization zones of
the head cover 1, 2, 3, 4 and the body of revolution -1, -2, -3, -4 (Fig. 2) are given in Table 1.
Fig. 1. Head cover of the ПЛ 20-В-500 turbine
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The eigen and forced vibrations
of both the head cover in service and the
new steel cover made of materials with
different elastic characteristics, namely
of steel Ст3 (E = 2.1×105 MPa, = 0.3),
cast iron '1' (Е = 0.8×105 MPa, = 0.3),
cast iron '2' (Е = 1.2×105 MPa, =0.21),
were calculated both in a vacuum and in
liquid.
The influence of the additional
liquid masses on the eigenfrequencies of
the head cover was investigated both in a
vacuum and liquid, with the head cover
resting on the stator along the line of the
head cover fastening. The results of the
calculations are given in Tables 2 − 4.
Table 1. Densities of materials of primary discretization zones of head cover
Zone sign Gi, kg R2, m R1, m Fi, m2 hi, m
1
ii
i
i
hF
G
i, kg/m3
1, 2, 3, 4 – – – – – steel 7,800 / cast iron 7,100
-1 – – – – – steel 7,800 / cast iron 7,100
-2 G2=6,322 1.925 1.760 1.91017 7.0 5,513 / 5,438
-3 G3=24,7330 1.710 1.470 2.39766 7.0 14,814.9 / 14,807.4
-4 G4=11,469 1.568 1.200 3.20010 6.0 6,753 / 6,683
Table 2. Eigen vibration frequencies of steel cover (Ст3), taking into account additional masses of parts, resting
Harmonic number, KF Medium
Vibration frequency, Hz
1 2 3
0
vacuum 29.341 94.941 179.621
liquid 29.102 94.925 173.978
1
vacuum 23.169 49.471 101.569
liquid 23.068 49.405 101.545
2
vacuum 23.142 68.512 134.764
liquid 23.032 68.420 133.440
Table 3. Eigen vibration frequencies of cast iron cover (cast iron '1'), taking into account additional masses of parts, resting
Harmonic number, KF Medium
Vibration frequency, Hz
1 2 3
0
vacuum 15.328 50.373 128.097
liquid 15.186 50.365 114.879
1
vacuum 12.539 25.419 53.460
liquid 12.477 25.385 53.454
2
vacuum 12.687 36.695 69.340
liquid 12.620 36.651 69.198
Fig. 2. Peculiarities of the design scheme and the loading
of the ПЛ 20 В-500 turbine head cover
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Table 4. Eigen vibration frequencies of cast iron cover (cast iron '2'), taking into account additional masses of parts, resting
Harmonic number, KF Medium
Vibration frequency, Hz
1 2 3
0
vacuum 18.623 62.306 157.287
liquid 18.449 62.296 140.539
1
vacuum 15.419 30.862 66.202
liquid 15.342 30.823 66.193
2
vacuum 15.606 44.853 85.848
liquid 15.523 44.803 85.726
The influence of the additional masses of the parts on the eigenfrequencies of the head covers was
investigated both in a vacuum and in liquid. The results of calculating the eigenfrequencies of the vibrations
of the cast iron head covers (cast iron '2') without taking into account the additional masses of the parts, with
the head cover resting on the stator, are given in Table 5.
Table 5. Eigen vibration frequencies of cast iron cover (cast iron '2'), without taking into account additional masses
of parts, resting
Harmonic number, KF Medium
Vibration frequency, Hz
1 2 3
0
vacuum 108.324 287.873 351.912
liquid 80.388 225.678 317.934
1
vacuum 78.852 176.833 250.943
liquid 68.334 166.779 245.280
2
vacuum 71.312 173.965 272.786
liquid 63.232 168.137 266.285
The results of calculating the eigenfrequencies of the vibrations of the head covers, taking into ac-
count the additional masses of the parts, with the head cover fastened rigidly along the flange cover to the
stator, are given in Tables 6 − 8.
Table 6. Eigen frequencies of vibrations of steel head cover (Ст3), taking into account additional masses of parts,
rigid fastening
Harmonic number, KF Medium
Vibration frequency, Hz
1 2 3
0
vacuum 31.303 103.008 181.841
liquid 31.093 102.977 175.425
1
vacuum 26.435 51.617 108.212
liquid 26.314 51.567 108.189
2
vacuum 24.997 76.546 135.258
liquid 24.875 76.455 133.862
Table 7. Eigen frequencies of the vibrations of the cast iron head cover (cast iron '1'), taking into account the
additional masses of the parts, rigid fastening
Harmonic number, KF Medium
Vibration frequency, Hz
1 2 3
0
vacuum 16.445 54.215 129.208
liquid 16.301 54.211 114.652
1
vacuum 14.297 26.401 56.607
liquid 14.222 26.376 56.604
2
vacuum 13.606 40.672 69.801
liquid 13.532 40.634 69.619
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Table 8. Eigen frequencies of vibrations of cast iron head cover (cast iron '2'), taking into account additional masses
of parts, rigid fastening
Harmonic number, KF Medium
Vibration frequency, Hz
1 2 3
0
vacuum 20.016 66.994 158.763
liquid 19.839 66.989 140.239
1
vacuum 17.578 32.031 70.076
liquid 17.485 32.003 70.072
2
vacuum 16.732 49.613 86.521
liquid 16.641 49.572 86.323
Analysis of the results of calculating the forced vibrations of the head covers for the ПЛ 20 В-500
turbines
The forced vibrations of the construction under harmonic loading in time are described by the equa-
tion [10].
Quu MK 2 , (6)
where K, M − the stiffness matrix and the mass matrix of the structure, respectively; ω − frequency of vibra-
tions; u, Q − time-varying displacement t vectors and external node load t vectors, respectively.
When solving the dynamics problem (6) by the finite element method, the method of direct integra-
tion and the displacement eigenfunction expansion method are usually applied [4, 5].
When using the direct integration method, we build the mass matrix Mк and the rigidity matrix Кк of
the construction for any kth harmonic of the expansion with respect to the vector of the amplitude values dis-
placements uik, applying the developed finite element approach [4].
The dynamic stress-strain state of the head covers of the existing and the new design, made of mate-
rials with different elastic characteristics, was investigated under the action of hydrodynamic loads on the
head cover at the maximum values of liquid pressure Нmax = 21 m and power Nmax = 24.5 MW.
In addition to the mass forces Gi (i = 2, 3, 4) and the hydrodynamic liquid pressure q1, acting on the
liquid contacting surface of the head cover, the latter receives the hydrodynamic axial thrust Q3, acting on the
impeller through the thrust block, and the hydrodynamic force Q4 from the flow-washed cowl cone. The law
of change in hydrodynamic pressure was accepted in the form of q = qi cos(ωt), where t is the time and ω is
the loading frequency. The scheme of application of the acting dynamic loads is shown in Fig. 3.
The values of the dynamic loads qi (i = 1, 3, 4) accepted during the calculation are given in table 9.
Table 9. Dynamic loads
Load
variant
Total hydrodynamic load
qi, MPa
Qi, N Action area, m2
1 – – 0.2100
3 Q3. =3,500,000 2.397664 1.4598
4 Q4 =1,536,942 3.200102 0.4803
Depending on the frequency of loading, dynamic displacements as well as dynamic stresses are defined
both as when the cover is supported along the circumference formed by the studs (option 1 − loading frequency
ω1 = 2.08 Hz, option 2 − loading frequency ω2 = 8.33 Hz), and when the head cover is fastened rigidly onto the
flange surface (option 3 − loading frequency ω1 = 2.08 Hz, option 4 − loading frequency ω2 = 8.33 Hz).
The discretization of the meridional section of the design model of the steel head cover on the finite
elements for the investigation of the dynamic stress-strain state is shown in Fig. 4, which shows the nodes
necessary for an analysis of dynamic displacements.
The values of the dynamic displacements of the steel cover, in the fixed mesh nodes of the finite el-
ements, are shown in Table 10.
The values of the dynamic displacements of the cast iron head cover (cast iron '1'), in the fixed mesh
nodes of the finite elements, are shown in Table 11.
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Fig. 3. Dynamic loading on head cover
Fig. 4. Fixed mesh nodes of finite elements of
design model of head cover
Table 10. Dynamic movements of steel cover depending on type of loading
No. of
variant of
loading
Displacements
Displacements in nodes (ur103, uz103), m
No. of nodal point
1 2 3 4 5
1
ur 0.000 -0.0042 -0.0052 0.0031 0.00315
uz 0.000 0.00098 0.0172, 0.0113 0.0201
2
ur 0.000 -0.0043 -0.0056 0.0035 0.00358
uz 0.000 0.00110 0.0185, 0.0125 0.0218
3
ur 0.000 -0.00424 -0.00478 0.00291 0.00297
uz 0.000 0.00044 0.0162 0.0104 0.0189
4
ur 0.000 -0.00430 -0.00516 0.00327 0.00335
uz 0.000 0.00046 0.0173 0.0115 0.0204
Table 11. Dynamic movements of the cast iron head cover (cast iron '1'), depending on the type of loading
No. of
variant of
loading
Displacements
Displacements in nodes (ur103, uz103), m
No. of nodal point
1 2 3 4 5
1
ur 0.000 -0.0134 -0.0014 -0.00309 0.00358
uz 0.000 -0.01028 0.0208 -0.00117 0.0145
2
ur 0.000 -0.014 -0.00284 -0.00149 0.00191
uz 0.000 -0.00041 0.0271 0.00463 0.0224
3
ur 0.000 -0.0134 -0.00237 -0.00269 0.00316
uz 0.000 0.00041 0.0232 -0.00085 0.0173
4
ur 0.000 -0.014 -0.00135 -0.00112 0.00151
uz 0.000 0.000534 0.0291 0.00631 0.0247
The values of the dynamic displacements of the cast iron head cover (cast iron '1'), in the fixed
meshed nodes of the finite elements, are shown in table 12.
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Table 12. Dynamic movements of the cast iron head cover (cast iron '2'), depending on the type of loading
No. of
variant of
loading
Displacements
Displacements in nodes (ur103, uz103), m
No. of nodal point
1 2 3 4 5
1
ur 0.000 -0.009460 -0.000979 -0.002140 0.00241
uz 0.000 -0.000743 0.013600 -0.001200 0.00925
2
ur 0.000 -0.009670 -0.001540 -0.001500 0.00176
uz 0.000 -0.000504 0.016000 0.001060 0.01230
3
ur 0.000 -0.009410 -0.001600 -0.001860 0.00213
uz 0.000 0.000210 0.015200 0.000133 0.01110
4
ur 0.000 -0.009640 -0.002050 -0.001230 0.00148
uz 0.000 0.000260 0.017500 0.002300 0.01400
The signs of displacement correspond to the direction of the R, Z axes (Fig. 4). For illustration, the
level of dynamic stresses and the nature of their distribution along the meridional section of the head cover,
depending on the characteristics of the material, fastening conditions and the loading frequency, is shown in
Figs. 5 − 8.
Fig.5. Lines of stress intensity levels in steel head
cover, variant 1
Fig.6. Lines of stress intensity levels in steel head
cover, variant 2
Fig.7. Lines of stress intensity levels in cast iron head
cover (cast iron '1' ), variant 3
Fig. 8. Lines of stress intensity levels in cast iron head
cover (cast iron '2'), variant 4.
The minimum i
min and maximum i
max values of the intensity of dynamic stresses in the cast iron
head cover with different ways of fastening it, possible values of the elastic characteristics and excitation
frequencies are given in Table. 13.
The minimum i
min and maximum i
max values of the intensity of dynamic stresses in the cast iron
head cover with different ways of fastening it, possible values of the elastic characteristics and excitation
frequencies are given in Table. 14.
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Table 13. The intensity of dynamic stresses in the steel cover
Type of fastening
Frequency
i , Hz
Minimum stresses
i
min, MPа
Maximum stresses
i
max, MPа
mode 1 mode 1
rigid − along flange line
2.08 0.02240 6.205
8.33 0.02520 6.413
in points of resting along circumference formed
by studs
2.08 0.00849 6.210
8.33 0.01110 6.433
Table 14. Dynamic stress intensity in cast iron head cover
Type of fastening
Frequency
i , Hz
Minimum stresses
i
min, MPа
Maximum stresses
i
max, MPа
E=0.8105 MPa,
=0.3
E=1.2105 MPa,
=0.21
rigid − along flange line
2.08 0.00170 0.00170
8.33 0.00377 0.00200
in points of resting along circumference formed
by studs
2.08 0.01410 0.01763
8.33 0.01610 0.01305
Conclusions
1. The purpose of the investigation was to solve the problem of the possibility of replacing the cast
iron cover of the ПЛ 20-В-500 turbine with the one of Ст3 welded carbon steel sheet.
2. In a 3D formulation, the influence of the additional liquid masses of the structure on the eigenfre-
quencies is taken into account, using mathematical models based on hypersingular equations and a combina-
tion of finite and boundary element methods.
The investigation of design models of the head covers for the ПЛ 20-В-500 turbines, whose design
features are determined by the composition, type, and size of the turbine, showed that the effect of a liquid
on the eigenfrequencies is insignificant (see Tables 2 − 4 and 5 − 8). As the frequency number increases, the
effect of a liquid decreases. At the same time, the eigenfrequency of the covers is significantly affected by
the value of the additional masses of the parts and units placed on them.
The spectra of the eigenfrequencies of the cast iron and steel covers of the ПЛ 20-В-500 turbines are
shifted both relative to each other and the fixed revo-vane frequency ω2=8,33 Hz during full-scale tests. The
detuning of the eigenfrequencies from the excitation frequencies of the steel head cover is higher than that of
the cast iron one, which, considering the damping properties of the cast iron, is an important factor.
3. The conducted numerical investigation of the influence of both the material of the head covers and
the conditions of fastening on their dynamic stress-strain state revealed that the level of dynamic displace-
ments and stresses is insignificant and depends both on the fastening conditions and the loading frequency.
The maximum values of dynamic stresses and displacements occur when the design model of the head cover
is fixed along the circumference formed by the studs and the loading frequency ω2 = 8.33 Hz is fixed during
full-scale tests. The maximum level of dynamic displacements in the steel head cover uz = 0.0218 mm, in the
cast iron one uz = 0.0224 mm. The maximum dynamic stresses in the steel head cover i
max = 6.433 MPа,
while in the cast iron head cover i
max = 6.209 MPa. When the turbine is operating, the dynamic defor-
mations of both steel and cast iron head covers do not disrupt the operation of the shaft seal since the struc-
tural radial clearance between the head cover and the shaft seal housing ∆r is 1.5 to 2.04 mm.
4. The conducted numerical investigations have confirmed the possibility of replacing the cast-iron
head cover with the one welded from Ст3 carbon steel sheets, as well as the necessity of tightening the
flange connection of the head cover to the stator, which is one of the effective ways of increasing rigidity.
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Received 20 November 2017
Introduction
Free hydroelastic vibrations of turbine head covers
Investigation of the vibration frequency spectra of the head covers for the ПЛ 20-В-500 turbines, taking into account the influence of a liquid
Analysis of the results of calculating the forced vibrations of the head covers for the ПЛ 20 В-500 turbines
Conclusions
References:
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