ISSN 2224-5278 (Print)
ҚАЗАҚСТАН РЕСПУБЛИКАСЫ ҰЛТТЫҚ ҒЫЛЫМ АКАДЕМИЯСЫНЫҢ
Қ. И. Сəтпаев атындағы Қазақ ұлттық техникалық зерттеу университеті
Х А Б А Р Л А Р Ы
ИЗВЕСТИЯ
НАЦИОНАЛЬНОЙ АКАДЕМИИ НАУК РЕСПУБЛИКИ КАЗАХСТАН
Казахский национальный исследовательский технический университет им. К. И. Сатпаева
N E W S
OF THE ACADEMY OF SCIENCES OF THE REPUBLIC OF KAZAKHSTAN Kazakh national research technical university named after K. I. Satpayev
SERIES
OF GEOLOGY AND TECHNICAL SCIENCES
5 (437)
SEPTEMBER – OCTOBER 2019
THE JOURNAL WAS FOUNDED IN 1940
PUBLISHED 6 TIMES A YEAR
ALMATY, NAS RK
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NAS RK is pleased to announce that News of NAS RK. Series of geology and technical sciences scientific journal has been accepted for indexing in the Emerging Sources Citation Index, a new edition of Web of Science. Content in this index is under consideration by Clarivate Analytics to be accepted in the Science Citation Index Expanded, the Social Sciences Citation Index, and the Arts & Humanities Citation Index. The quality and depth of content Web of Science offers to researchers, authors, publishers, and institutions sets it apart from other research databases. The inclusion of News of NAS RK. Series of geology and technical sciences in the Emerging Sources Citation Index demonstrates our dedication to providing the most relevant and influential content of geology and engineering sciences to our community.
Қазақстан Республикасы Ұлттық ғылым академиясы "ҚР ҰҒА Хабарлары. Геология жəне техникалық ғылымдар сериясы" ғылыми журналының Web of Science-тің жаңаланған нұсқасы Emerging Sources Citation Index-те индекстелуге қабылданғанын хабарлайды. Бұл индекстелу барысында Clarivate Analytics компаниясы журналды одан əрі the Science Citation Index Expanded, the Social Sciences Citation Index жəне the Arts & Humanities Citation Index-ке қабылдау мəселесін қарастыруда. Webof Science зерттеушілер, авторлар, баспашылар мен мекемелерге контент тереңдігі мен сапасын ұсынады. ҚР ҰҒА Хабарлары. Геология жəне техникалық ғылымдар сериясы Emerging Sources Citation Index-ке енуі біздің қоғамдастық үшін ең өзекті жəне беделді геология жəне техникалық ғылымдар бойынша контентке адалдығымызды білдіреді.
НАН РК сообщает, что научный журнал «Известия НАН РК. Серия геологии и технических наук» был принят для индексирования в Emerging Sources Citation Index, обновленной версии Web of Science. Содержание в этом индексировании находится в стадии рассмотрения компанией Clarivate Analytics для дальнейшего принятия журнала в the Science Citation Index Expanded, the Social Sciences Citation Index и the Arts & Humanities Citation Index. Web of Science предлагает качество и глубину контента для исследователей, авторов, издателей и учреждений.
Включение Известия НАН РК. Серия геологии и технических наук в Emerging Sources Citation Index демонстрирует нашу приверженность к наиболее актуальному и влиятельному контенту по геологии и техническим наукам для нашего сообщества.
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Б а с р е д а к т о р ы
э. ғ. д., профессор, ҚР ҰҒА академигі И.К. Бейсембетов
Бас редакторының орынбасары Жолтаев Г.Ж. проф., геол.-мин. ғ. докторы
Р е д а к ц и я а л қ а с ы:
Абаканов Т.Д. проф. (Қазақстан)
Абишева З.С. проф., академик (Қазақстан) Агабеков В.Е. академик (Беларусь)
Алиев Т. проф., академик (Əзірбайжан) Бакиров А.Б. проф., (Қырғыстан) Беспаев Х.А. проф. (Қазақстан)
Бишимбаев В.К. проф., академик (Қазақстан) Буктуков Н.С. проф., академик (Қазақстан) Булат А.Ф. проф., академик (Украина) Ганиев И.Н. проф., академик (Тəжікстан) Грэвис Р.М. проф. (АҚШ)
Ерғалиев Г.К. проф., академик (Қазақстан) Жуков Н.М. проф. (Қазақстан)
Қожахметов С.М. проф., академик (Казахстан) Конторович А.Э. проф., академик (Ресей) Курскеев А.К. проф., академик (Қазақстан) Курчавов А.М. проф., (Ресей)
Медеу А.Р. проф., академик (Қазақстан)
Мұхамеджанов М.А. проф., корр.-мүшесі (Қазақстан) Нигматова С.А. проф. (Қазақстан)
Оздоев С.М. проф., академик (Қазақстан) Постолатий В. проф., академик (Молдова) Ракишев Б.Р. проф., академик (Қазақстан) Сейтов Н.С. проф., корр.-мүшесі (Қазақстан)
Сейтмуратова Э.Ю. проф., корр.-мүшесі (Қазақстан) Степанец В.Г. проф., (Германия)
Хамфери Дж.Д. проф. (АҚШ) Штейнер М. проф. (Германия)
«ҚР ҰҒА Хабарлары. Геология мен техникалық ғылымдар сериясы».
ISSN 2518-170X (Online), ISSN 2224-5278 (Print)
Меншіктенуші: «Қазақстан Республикасының Ұлттық ғылым академиясы» РҚБ (Алматы қ.).
Қазақстан республикасының Мəдениет пен ақпарат министрлігінің Ақпарат жəне мұрағат комитетінде 30.04.2010 ж. берілген №10892-Ж мерзімдік басылым тіркеуіне қойылу туралы куəлік.
Мерзімділігі: жылына 6 рет.
Тиражы: 300 дана.
Редакцияның мекенжайы: 050010, Алматы қ., Шевченко көш., 28, 219 бөл., 220, тел.: 272-13-19, 272-13-18, http://www.geolog-technical.kz/index.php/en/
© Қазақстан Республикасының Ұлттық ғылым академиясы, 2019 Редакцияның Қазақстан, 050010, Алматы қ., Қабанбай батыра көш., 69а.
мекенжайы: Қ. И. Сəтбаев атындағы геология ғылымдар институты, 334 бөлме. Тел.: 291-59-38.
Типографияның мекенжайы: «Аруна» ЖК, Алматы қ., Муратбаева көш., 75.
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Г л а в н ы й р е д а к т о р д. э. н., профессор, академик НАН РК
И. К. Бейсембетов Заместитель главного редактора Жолтаев Г.Ж. проф., доктор геол.-мин. наук
Р е д а к ц и о н н а я к о л л е г и я:
Абаканов Т.Д. проф. (Казахстан)
Абишева З.С. проф., академик (Казахстан) Агабеков В.Е. академик (Беларусь)
Алиев Т. проф., академик (Азербайджан) Бакиров А.Б. проф., (Кыргызстан) Беспаев Х.А. проф. (Казахстан)
Бишимбаев В.К. проф., академик (Казахстан) Буктуков Н.С. проф., академик (Казахстан) Булат А.Ф. проф., академик (Украина) Ганиев И.Н. проф., академик (Таджикистан) Грэвис Р.М. проф. (США)
Ергалиев Г.К.проф., академик (Казахстан) Жуков Н.М. проф. (Казахстан)
Кожахметов С.М. проф., академик (Казахстан) Конторович А.Э. проф., академик (Россия) Курскеев А.К. проф., академик (Казахстан) Курчавов А.М. проф., (Россия)
Медеу А.Р. проф., академик (Казахстан)
Мухамеджанов М.А. проф., чл.-корр. (Казахстан) Нигматова С.А. проф. (Казахстан)
Оздоев С.М. проф., академик (Казахстан) Постолатий В. проф., академик (Молдова) Ракишев Б.Р. проф., академик (Казахстан) Сеитов Н.С. проф., чл.-корр. (Казахстан)
Сейтмуратова Э.Ю. проф., чл.-корр. (Казахстан) Степанец В.Г. проф., (Германия)
Хамфери Дж.Д. проф. (США) Штейнер М. проф. (Германия)
«Известия НАН РК. Серия геологии и технических наук».
ISSN 2518-170X (Online), ISSN 2224-5278 (Print)
Собственник: Республиканское общественное объединение «Национальная академия наук Республики Казахстан (г. Алматы)
Свидетельство о постановке на учет периодического печатного издания в Комитете информации и архивов Министерства культуры и информации Республики Казахстан №10892-Ж, выданное 30.04.2010 г.
Периодичность: 6 раз в год Тираж: 300 экземпляров
Адрес редакции: 050010, г. Алматы, ул. Шевченко, 28, ком. 219, 220, тел.: 272-13-19, 272-13-18, http://nauka-nanrk.kz /geology-technical.kz
Национальная академия наук Республики Казахстан, 2019 Адрес редакции: Казахстан, 050010, г. Алматы, ул. Кабанбай батыра, 69а.
Институт геологических наук им. К. И. Сатпаева, комната 334. Тел.: 291-59-38.
Адрес типографии: ИП «Аруна», г. Алматы, ул. Муратбаева, 75
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E d i t o r i n c h i e f
doctor of Economics, professor, academician of NAS RK I. K. Beisembetov
Deputy editor in chief
Zholtayev G.Zh. prof., dr. geol-min. sc.
E d i t o r i a l b o a r d:
Abakanov Т.D. prof. (Kazakhstan)
Abisheva Z.S. prof., academician (Kazakhstan) Agabekov V.Ye. academician (Belarus) Aliyev Т. prof., academician (Azerbaijan) Bakirov А.B. prof., (Kyrgyzstan)
Bespayev Kh.А. prof. (Kazakhstan)
Bishimbayev V.K. prof., academician (Kazakhstan) Buktukov N.S. prof., academician (Kazakhstan) Bulat А.F. prof., academician (Ukraine)
Ganiyev I.N. prof., academician (Tadjikistan) Gravis R.М. prof. (USA)
Yergaliev G.K. prof., academician (Kazakhstan) Zhukov N.М. prof. (Kazakhstan)
Kozhakhmetov S.М. prof., academician (Kazakhstan) Kontorovich А.Ye. prof., academician (Russia) Kurskeyev А.K. prof., academician (Kazakhstan) Kurchavov А.М. prof., (Russia)
Medeu А.R. prof., academician (Kazakhstan)
Muhamedzhanov M.A. prof., corr. member. (Kazakhstan) Nigmatova S.А. prof. (Kazakhstan)
Ozdoyev S.М. prof., academician (Kazakhstan) Postolatii V. prof., academician (Moldova) Rakishev B.R. prof., academician (Kazakhstan) Seitov N.S. prof., corr. member. (Kazakhstan)
Seitmuratova Ye.U. prof., corr. member. (Kazakhstan) Stepanets V.G. prof., (Germany)
Humphery G.D. prof. (USA) Steiner М. prof. (Germany)
News of the National Academy of Sciences of the Republic of Kazakhstan. Series of geology and technology sciences.
ISSN 2518-170X (Online), ISSN 2224-5278 (Print)
Owner: RPA "National Academy of Sciences of the Republic of Kazakhstan" (Almaty)
The certificate of registration of a periodic printed publication in the Committee of information and archives of the Ministry of culture and information of the Republic of Kazakhstan N 10892-Ж, issued 30.04.2010
Periodicity: 6 times a year Circulation: 300 copies
Editorial address: 28, Shevchenko str., of. 219, 220, Almaty, 050010, tel. 272-13-19, 272-13-18, http://nauka-nanrk.kz/geology-technical.kz
© National Academy of Sciences of the Republic of Kazakhstan, 2019 Editorial address: Institute of Geological Sciences named after K.I. Satpayev
69a, Kabanbai batyr str., of. 334, Almaty, 050010, Kazakhstan, tel.: 291-59-38.
Address of printing house: ST "Aruna", 75, Muratbayev str, Almaty
60 N E W S
OF THE NATIONAL ACADEMY OF SCIENCES OF THE REPUBLIC OF KAZAKHSTAN SERIES OF GEOLOGY AND TECHNICAL SCIENCES
ISSN 2224-5278
Volume 5, Number 437 (2019), 60 – 73 https://doi.org/10.32014/2019.2518-170X.126
UDC 539.4
А. U. Nurimbetov1, S. A. Orynbayev2, M. Sh. Junisbekov2, Zh. T. Omarov3
1Moscow Aviation Institute, Russia,
2Taraz State University after M. Kh. Dulaty, Kazakhstan,
3Karaganda State Technical University, Kazakhstan.
E-mail: [email protected], [email protected], [email protected], [email protected]
NUMERICAL SOLUTION STRESSED DEFRESSED CONDITION OF MULTILAYER COMPOSITION BLADES
IN THE FIELD OF CENTRIFUGAL FORCES
Abstract. One of the main tasks of the mechanics of composite materials (CM) is the calculation of the effective characteristics of the elasticity of CM based on information about the physicomechanical properties of their components and the laws of the distribution of components over the volume of the material. The possible scattering of the properties of a layer of multilayer CM is not taken into account when constructing models of structurally inhomogeneous media and when calculating their effective characteristics. Therefore, it is necessary to assess the influence of the properties of the layer on the effective characteristics of the material, as well as on the reliability of the structure as a whole.
The paper considers program, allowing numerically determine stress and strain state of a layered composite blade in the centrifugal force field, has been compiled using proved engineering torsion theory of the random section composite layered rod. The naturally twisted layered composite blade lies under combined action of stretching for- ces, bending and twisting moments or under the influence of centrifugal forces. The program has solved engineering problem on cutting of the blade to leaves (these leaves appear in a result of variable section along the blade length) in planes, parallel to the rod axis. The blade, studied in this paper, is presented by eight sections.
Keywords: blade, torsion, stretching, bend, deformation, strain, cutting.
Introduction. Rotodynamic machine blade outline in potential engines becomes more complex.
There is a change from outlines, close to the rods with twist and high relative elongation, to outlines like plates with low relative elongation, high twist and flexure, in the blade structures of fans, compressors and turbines. Intermetallic compounds, metal-matrix composites and ceramic-matrix composites come into use instead of modern metal alloys. With development of analysis methods of modern jet engines, geometrical characteristics, aerodynamic and thermal loads of bladed disks and drums become more specific. This allows use numerical method to determine the blades’ stress and strain state [1, 6-21].
Research. Prospective models of air screws have blades with high sweep angle, twisted by the span and bended towards the axis of rotation. These blades should function in rather complicated and heavy aeromechanic conditions.
Similar designs are known for a long time, however, up till now there were no methods for their cal- culation and materials for their manufacture. Currently, the emergence of high-performance computers and complicated engineering software, as well as the availability of modern composite materials allow carry out more thorough and detailed analysis of the prospective turboprop engine blades. Therefore, using materials, received in [1], the analysis computer program, allowing numerically determine stress and strain state of the blades from the composite material, has been compiled.
The program is designed for investigation of the stress and strain state of naturally twisted layered rod structures, which lie under combined action of stretching forces, bending and twisting moments or under the influence of centrifugal forces. Each layer of the rod section under the investigation consists of
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orthotropic material with 9 independent elastic constants. At that, purposeful general property regulation of the specific material can be carried out by choice of both fiber pattern in a separate layer and layer arrangement with known properties in section. This is achieved by alteration of angles φi between the material elastic symmetry principal directions in the layer and axes, where the body’s stress and strain state is investigated. At that, amount of independent elastic constants (elastic modulus, shearing modulus, Poisson’s constants, etc.) of the layer material in the general case will be equal to 13 [1].
The relevant rod structure cross section is arbitrary. The input program parameters are coordinates of the line, limiting separate arbitrary plane section, usually set in the working drawings of projects. This line is divided into two parts (further conditionally called “back” and “backet”), to which two outer lines are adjacent in the layer section. Coordinates of the layers’ superficies are specified. Proceeding from these data, with the help of special procedure, the arbitrary configuration section is divided into separate layers by defined thickness tc of the monolayer [3]. At that, numbers of each layer origin and end are formed.
Such designs are carried out for a series of following one after another rod sections (figure 1). As dimen- sions of the section may vary along the rod length, then number of the layers in each section can be dif- ferent. This predetermines the emergence of short layers inside the section. Taken from different sections, the coordinates of origin and end of one layer determine the leaf length in the current rod section.
Figure 1 –
The compressor blade cross section set layers; numbers of the blade sections
correspond to the sections, distant from its root section
Therefore, the program has solved the engineering problem of “cutting” of each rod layer on the leaves in planes, parallel to the rod axis.
Basic relations of the developed engineering theory on layered rods [1-6] are used to investigate the layered rod stress and strain state. Based on this theory, stretching strain , curvature changes 1, 2 and unwinding , as well as strains 11i ,22i ,33i ,23i ,13i ,12i in separate points of the layer i are calculated for each section.
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The input program parameters are stretching force Р, bending М1, М2 and twisting Мt moments, as well as 13 elastic constants of each layer [1] for the current layer. The layers’ set points coordinates and numbers are also input parameters for the current section.
To investigate the rod stress and strain state in the centrifugal force field, stretching force, applied in the current section, is calculated by formula:
R r F r
r P dF rdr
P 1
) ( 2 1
1
)
(
, (1) where F(r1) – cross sectional area; r, R – distance from the rotational axis to the gravitational center of the current r and peripheral R section respectively (figure 2); – angular velocity (rad.turns/sec.), where N – rotational velocity (turns/min); r1 – integration variable; - the section layer material density.
Figure 2 – The distance from the rotation axis to the center of gravity of the current r and peripheral R section
Thus, the force Р in the current section r is equal by the centrifugal inertial force value, to the developed layered rod part, concluded between the considered section r and peripheral section R [22].
Data about geometrical characteristics of all sections are necessary to calculate the centrifugal effort by formula (1) and the current section gravity center coordinates. To this end, with the help of special procedure, 15 geometrical characteristics and set densities of all sections are calculated at first [22].
The centrifugal effort for the current section r by the approximate value for (1) is calculated by formula:
i 1
i
r
r 1
1
2 F rdr
P R
r i , (2) where the current section area and density are measured linearly towards the previous section. i.e.
).
/(
) )(
(
), /(
) )(
(
1 1
1
1 1
1
i i i i i i
i i i i i i
r r r
r
r r F F r r F F
(3) Further, the layered rod stress and strain state is studied for the current section. The stretching strain
, curvature changes 1, 2 and unwinding are determined, physical and geometrical characteristics of the layer and the whole section are calculated.
The program for described lower calculations is currently used to analyze the blade stress and strain state at the preliminary design stage.
1. The studied blade description. The considered blade model is a reduced version of the full scale compressor blade. This blade has been designed and manufactured with a view to follow the real blade structural and aerodynamic equivalency. The blade, studied in the paper, is presented by eight sections (figure 1). Figure 3 presents changes in the area (curve 2 on figure 3), in the highest thickness (curve 1 on figure 3), in the chord в (curve 3 on figure 3) of the blade and relation cmax/в depending on r/R0. The root
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Figure 3 – Change of сmax ,area F, chord в and сmax/в by the compressor blade length
blade section consists of 12 layers of uniform thickness tc=0,4 mm, however, the peripheral section
consists of 6 layers. The reference swirl angle per one unit of the blade length 0 – is equal to 0.006 rad./mm.
2. Calculation variants. As an example, the blade from the composite material in the centrifugal force field has been calculated by the described program. At that, investigation for three different com- binations of the elastic constants in the package of the composite blade layers has been carried out.
The blade consisting of boron aluminum (BAL) layers interstratified from the side of back and backet has been considered.
3. Calculation result analysis. The stretching force P in the blade rotation has been calculated by formula (1) for each its section r/R0. Averaged values of the tension stresses cp in the conditional untwisted blade achieve the highest value in the third section. This is related to the fact that the force P in the third section differs from the force in the root section on 17%, while their areas differ on 45%.
W, U, V displacement pattern isograms by the blade length for the back and backet (figure 4) have been drawn by the calculation results. As is clear from the Figure, normal displacements W on the peri- pheral section have maximal values (MX point). W displacements rise on 4-5 times on the entry edge of
the back from the root section to the third section. They rise on 10 times on the feathered entry edges.
W normal displacement and U, V displacement patterns on the back are more proportional in comparison with the blade backet. On the backet, concentration of the high displacements W is already observed in the fourth blade section. Therefore, to increase the blade strength, it is necessary to change the layers from the backet side by materials more rigid in the stretching.
Figure 5 gives deformation of the blade Ux, Vy, Wz towards the axis 0x, 0y, 0z. The highest changes occur in the second blade section. The compressing deformation value towards the axis 0х on the trailing edge on 3-4 times higher than on the entry blade edge. As a consequence, local strength loss may occur in the tailing feathered layers’ edge. Therefore, these layers should be changed by materials with higher com- pression-resisting properties. The highest blade deformation changes towards the axis 0y occur on the third blade section. The stretching strain value towards the axis 0у in the trailing edge is 2 times higher than in the entry edge of the second blade section and by its value is 3 times higher than the compressing deformation towards the axis 0х. Consequently, to avoid the strength loss from the compressing and stretching strains in the tailing feathered layers’ edge, these layers should be changed by materials with higher tensile and compression-resisting properties.
Figure 6 gives distribution of stresses xx, yy, zz on the back and backet by the blade length. The highest normal stress is distributed on the root blade section (MX point), as the root blade section is rigidly fixed. If not to consider it, then the maximum stress is achieved on the third blade section and concentration of the normal stresses on the backet is higher on 1.5-2 times in comparison with the normal stresses on the back. Concentration of the normal stresses on the third section is lower on 4-5 times in comparison with its values on the root section. The compression stresses, conditioned by bending, twisting and stretching interconnectivity, occur on the peripheral back sections. The average stresses in comparison with the stresses xx, yy, zz on 1.5-2 times higher and it is impossible to determine the compression stresses’ fields by them (figure 7). Therefore, to determine the blade stress and strain state it is necessary to calculate all components of the stresses xx, yy, zz.
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Figure 4 – U, V, W displacement patterns on the back and backet by the boron aluminum blade length
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Figure 5 – Ux, Vy, Wz displacement patterns on the back and backet by the boron aluminum blade length
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Figure 6 – Distribution of the stresses xx, yy, zz on the back and backet by the boron aluminum blade length
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Figure 7 – Distribution of the averaged stress avg on the back and backet by the boron aluminum blade length
Figure 8 gives distribution of tangential stresses xz, yz, xy on the back and backet by the blade length. The highest tangential stress is distributed on the third blade section. The local highest tensile tangential stress xz is achieved on the third section near the entry back edge, and the compression one – on the tailing backet edge and its value (MN point) is higher on 2 times in comparison with values of хz
near the entry back edge (MX point). As is known, in the feathered layers such concentration of the tangential stresses may result in the blade’s local strength loss. As a consequence, the emergence of the above values of the tangential stresses in the blades may be inadmissible. It has been deduced from the experiments that the strength margin by the tangential stresses between the layers currently should not be less than 3 [3]. The tangential stress yz by the value is 2 times lower than the tangential stress хz and is distributed respectively on the thick back and backet layers. Therefore, in comparison with the tangential stress хz, its influence on the general blade strength is insignificant. The highest value of the tangential stress xy is achieved in the third section (MX point) (figure 8). In comparison with the values of the tangential stresses yz, xz the tangential stress xy is insignificant. Therefore, it may not be considered in the calculations.
Figure 9 gives the displacement pattern isograms on the fourth blade section. As is seen from the Figure, displacement area on the backet is higher by its value on 25% from displacement on the back. The highest displacements occur in the middle of the blade back section. The highest displacement U occurs in the back layers neighboring to the gravitational center. V, W displacements occur on the tailing blade edge (MX point). Consequently, it is necessary to select materials of the layers neighboring to the gravitational center and tailing section edges with the tensile properties.
Figure 10 gives distribution isograms of the stresses xx, yy, zz on the fourth blade section. As is seen from the figure, displacement area of the normal stress zz on the backet is higher by its value on 20 times from the normal stress zz on the back. The highest normal stresses occur in the middle of the blade backet section. The highest normal stress zz occurs in the points neighboring to the backet layers’
gravitational center and comparable to the values of the average stress (figure 12). Consequently, it is necessary to select materials of the layers neighboring to the gravitational section center with the tensile properties.
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Figure 8 – Distribution of the tangential stresses xz, yz, xy on the back and backet by the boron aluminum blade length
69
Figure 9 – U, V, W displacement patterns on the fourth boron aluminum blade section
Figure 10 – Distributions of the stresses xx, yy, zz on the fourth boron aluminum blade section
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Figure 11 – Distributions of the stresses yx, xz, xy on the fourth boron aluminum blade section
Figure 12 – Distributions of the stress avg on the fourth boron aluminum blade section
In the same manner, distributions of the tangential stress ху (figure 11) on the fourth blade section show that the tangential stress xy concentration area is lower by its value on 200%-300% from the normal stress zz. The highest tangential stress xy occur in the backet layers neighboring to the gravitational center. In the feathered layers (4th section) of the entry and tailing blade edge, the compression tangential stresses are equally distributed. Values of the tangential stress xy in the concentration areas are com- parable with values of the stresses yz, xz. Therefore, materials in the layers, neighboring to the gravitational center should have higher tensile and compression-resisting properties.
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The tangential stress yz distribution isograms on the fourth blade section show that the tangential stress уz distribution area is lower by its value on 15-20 times from the normal stress zz. The highest tensile tangential stress yz is distributed in the layers of the entry blade edge and is insignificant by its value.
The tangential stress xz distribution isograms on the fourth blade section show that the tangential stress xz distribution area is lower by its value on 5-7 times from the normal stress zz. The highest tensile tangential stress xz is distributed in the layers in the middle back part, and the compression tangential stress – on the backet. In the feathered layers (4th section) of the tailing blade edge, the compression tangential stresses are equally distributed and insignificant by their value. The highest tangential stress хz by its value is higher on 4-6 times in comparison with values of the tangential stress yz and from value of the normal stress is lower on 5-7 times. Therefore, it is necessary to consider influence of the tangential stress xz for the layered thin rods.
Conclusions. Thus, the studied examples show that selecting material for the separate layers or reinforcing in them, it is possible over a wide range regulate the level of stress and deformation in the same physical rotor cycles. There is no such wide regulation opportunity for the isotropic material blades.
Thus, in the given geometrical blade form, selected from aerodynamic considerations, by two-way reinforcement of its layers, the level of stress zz may be reduced, at the same time avoiding high com- pression stresses on the profile edges and achieving their more uniform distribution (zz) by the section.
The carried out calculations of the blades of specific types showed that the peripheral blade section unwinding angle may be reduced both by increasing the torsional stiffness by the layers’ two-way reinforcement and using the stiff material layers in the package of materials. When increasing the layers’
rigidity curve ratio level (the layers’ curve ratio (elastic modulus, shearing modulus, etc.), difference of the normal stresses in the cross section and value of the tangential stresses between the layers increase.
The high tangential stresses between the layers occur due to the different rigidity of the contacting layers.
Continuous transition of the material properties from layer to layer is required.
The multilayer composite materials’ operation analysis in conditions close to the working conditions of the blades allowed determine a series of the stress distribution features in reinforced materials. It is found that increase in the normal stresses on 2-4 times in comparison with their average values occurs when stretching the blades from the composite materials in the centrifugal force field in external layers.
А. У. Нуримбетов1, С. Ə. Орынбаев2, M. Ш. Джунисбеков2, Ж. Oмаров3
1Мəскеу авиация институты, Ресей,
2М. Х. Дулатиатындағы Тараз мемлекеттік университеті, Қазақстан,
3Қараганды мемлекеттік техникалық университеті, Қазақстан
КӨПҚАБАТТЫ КОМПОЗИТТІК ҚАЛАҚШАЛАРДЫҢ
ОРТАЛЫҚ ТЕБУ КҮШТЕРДІҢ ƏСЕРІНЕН КЕРНЕУ ДЕФОРМАЦИЯЛАНҒАН КҮЙІН САНДЫҚ АНЫҚТАУ
Аннотация. Композиттік материалдардың (КМ) механикасының негізгі мəселелерінің бірі, оның құ- рамдас бөліктерінің физика-механикалық қасиеттеріне жəне олардың материал көлеміндегі таралу заң- дылығына сүйене отырып КМ тиімді серпімділік сипаттамаларын есептеу. Көп қабатты КМ қабатының қасиеттерінің ықтимал шашырауы құрылымдық біркелкі емес орталар үлгілерін құру кезінде жəне олардың тиімді сипаттамаларын есептеу кезінде ескерілмейді. Сондықтан қабат қасиеттерінің материалдың тиімді сипаттамаларына, сондай-ақ тұтастай құрылымның сенімділігіне əсерін бағалау қажет.
Жұмыста, кез келген қимадағы композиттік қабатталған дене бұралуының техникалық теориясын пай- далана отырып, орталықтан тепкіш күштердің əсеріндегі қабатты композиттік қалақшаның кернеу деформа- цияланған күйін сандық анықтауға мүмкіндік беретін бағдарлама құрастырылды.
Табиғи бұралған көпқабатты композитті қалақша созылғыш күштердің, иілу жəне бұралудың бірік- тірілген əрекеті сəттерінде немесе орталықтан тебу күштердің əсерінде қарастырылады. Бағдарламада, қа- лақша осіне параллель орналасқан жазықтықта, қалақшаны қабаттардың жапырақшаларына пішудің технологиялық мəселесі шешілді (бұл қалақшаның ұзындығы бойымен əртүрлі қималары болғандықтан
72
қалақшаның ұзындығы бойынша жапырақтары пайда болады). Бұл жұмыста зерттелген қалақша сегіз қимадан тұрады.
Түйін сөздер: қалақша, бұру, созу, майыстыру, деформация, кернеу, бороаллюминий, қима.
А. У. Нуримбетов1, С. A. Орынбаев2, M. Ш. Джунисбеков2, Ж. Oмаров3
1Московский авиационный институт, Россия,
2Таразский государственный университет им. М. Х. Дулати, Казахстан,
3Карагандинский государственный технический университет, Казахстан
ЧИСЛЕННОЕ РЕШЕНИЕ НАПРЯЖЕННО-ДЕФОРМИРОВАННОГО СОСТОЯНИЯ МНОГОСЛОЙНЫХ КОМПОЗИЦИОННЫХ ЛОПАТОК
В ПОЛЕ ЦЕНТРОБЕЖНЫХ СИЛ
Аннотация. Одной из основных задач механики композиционных материалов (КМ) является вычис- ление эффективных характеристик упругости КМ на основе информации о физико-механических свойствах их компонент и законах распределения компонент по объему материала. Возможное рассеяние свойств слоя многослойного КМ не учитывается при построении моделей структурно-неоднородных сред и при вычис- лении их эффективных характеристик. Поэтому необходима оценка влияния свойств слоя на эффективные характеристики материала, а также на надежность конструкции в целом.
В работе, используя полученную техническую теорию кручения композиционного слоистого стержня произвольного сечения, составлена программа, позволяющая численно определить напряжено-деформиро- ванное состояние (НДС) слоистой композиционной лопатки, находящейся в поле центробежных сил. Естест- венно-закрученная слоистая композиционная лопатка находится под объединенным действием растяги- вающих сил, изгибающих и скручивающих моментов или под влиянием центробежных сил. В программе решена технологическая проблема раскроя лопатки на лепестки (эти лепестки по длине лопатки появляются в результате переменного сечения по длине лопатки) в плоскостях, параллельных оси стержня. Лопатка, исследованная в данной работе, представлена восемью сечениями.
Ключевые слова: лопасть, кручение, растяжение, изгиб, деформация, напряжение, бороаллюминий, сечение.
Information about authors:
Nurimbetov Аlibek Usipbaevich, doctor of technical sciences, Professor of the Moscow Aviation Institute (National Research University) (MAI), Russia; [email protected]; https://orcid.org/0000-0002-8857-1240
Orynbayev Seitzhan Aueszhanovich, PhD, associate professor of the Department of «Power engineering»
M.Kh. Dulaty Taraz State University, Kazakhstan; [email protected];https://orcid.org/0000-0002-5077-7219 Junisbekov Mukhtar Shardarbekovich, candidate of technical sciences, associate professor of the Department of
«Telecommunication systems» M.Kh. Dulaty Taraz State University, Kazakhstan; [email protected];
https://orcid.org/0000-0002-5383-8400
Omarov Zhaksylyk Talgatuly, PhD student, Karaganda State Technical University, Kazakhstan;
[email protected]; https://orcid.org/0000-0003-1897-7875
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