The termal deformation of isotropic beam elements of technological equipment in the manufacturing of carbon-carbon composite materials in furnaces of direct heating

For the isotropic beam elements of the technological equipment (BETE), which are used in the production of carbon-carbon composite materials (CCCM) in direct heating furnaces, the analytical solution of the temperature stress-strain state, taking into account the stiffness of the spring of the curre...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Problems of Atomic Science and Technology
Datum:2023
Hauptverfasser: Meltyukhov, M.V., Kravtsov, Y.V.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2023
Schlagworte:
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/196111
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:The termal deformation of isotropic beam elements of technological equipment in the manufacturing of carbon-carbon composite materials in furnaces of direct heating / M.V. Meltyukhov, Y.V. Kravtsov // Problems of Atomic Science and Technology. — 2023. — № 2. — С. 143-147. — Бібліогр.: 2 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
_version_ 1859817858599485440
author Meltyukhov, M.V.
Kravtsov, Y.V.
author_facet Meltyukhov, M.V.
Kravtsov, Y.V.
citation_txt The termal deformation of isotropic beam elements of technological equipment in the manufacturing of carbon-carbon composite materials in furnaces of direct heating / M.V. Meltyukhov, Y.V. Kravtsov // Problems of Atomic Science and Technology. — 2023. — № 2. — С. 143-147. — Бібліогр.: 2 назв. — англ.
collection DSpace DC
container_title Problems of Atomic Science and Technology
description For the isotropic beam elements of the technological equipment (BETE), which are used in the production of carbon-carbon composite materials (CCCM) in direct heating furnaces, the analytical solution of the temperature stress-strain state, taking into account the stiffness of the spring of the current collector, was obtained for the first time in the work. Formulas for calculating the critical diameters of loss of compressive strength are given. Using the example of graphite and molybdenum rods, it was established in the work that the decisive factor of the load-bearing capacity is the loss of stability of the elements under consideration. Для ізотропних стержневих елементів технологічного оснащення (СЕТО), яке використовується при виготовленні вуглець-вуглецевих композиційних матеріалів (ВВКМ) у печах прямого нагріву, в роботі вперше отримане аналітичне рішення температурного напружено-деформованого стану з урахуванням жорсткості пружини струмовідводу. Наводяться формули для обчислення критичних діаметрів втрати міцності на стискання. На прикладі графітових і молібденових стержнів у роботі встановлено, що вирішальним фактором несучої здатності є втрата стійкості елементів, що розглядаються.
first_indexed 2025-12-07T15:23:38Z
format Article
fulltext ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144) 143 https://doi.org/10.46813/2023-144-143 UDC 621.762 THE TERMAL DEFORMATION OF ISOTROPIC BEAM ELEMENTS OF TECHNOLOGICAL EQUIPMENT IN THE MANUFACTURING OF CARBON-CARBON COMPOSITE MATERIALS IN FURNACES OF DIRECT HEATING M.V. Meltyukhov, Y.V. Kravtsov National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine E-mail: meltyukhov_m@kipt.kharkov.ua; tel./fax +38(057)349-10-61 For the isotropic beam elements of the technological equipment (BETE), which are used in the production of carbon-carbon composite materials (CCCM) in direct heating furnaces, the analytical solution of the temperature stress-strain state, taking into account the stiffness of the spring of the current collector, was obtained for the first time in the work. Formulas for calculating the critical diameters of loss of compressive strength are given. Using the example of graphite and molybdenum rods, it was established in the work that the decisive factor of the load-bearing capacity is the loss of stability of the elements under consideration. INTRODUCTION In the production of CCCM by the method of ther- mogradient gas-phase densification in direct heating furnaces, beam elements are often used as equipment, which are in conditions of high temperatures (up to 1500 °C) and compression, which occurs as a result of thermal expansion. It is advisable to study the stress- strain state of such elements at the stage of densification processes planning. Fig. 1. General view of the direct heating furnace: 1 – upper power supply; 2 – equipment element (heater rod); 3 – lower power supply; 4 – camera body; 5 – product made of CCCM; 6 – spring of the upper current supply The general view of the direct heating furnace is shown in Fig. 1. It is a chamber 4 that is cooled. During the operation of the furnace, the initial heating of the CCCM frame for densification is often carried out using the rod element of the equipment 2, which is heated to a temperature of 900 °C. For reliable electrical contact, the spring 6 is pressed using a screw mechanism. This spring should also compensate for the thermal expan- sion of rod 2 and CCCM. At the end of the process, the temperature in the rod and in the center of the product reaches 1300…1500 °С. At the same time, the central areas of the finished product will be compressed be- tween the current leads due to thermal expansion with a temperature difference along the radius of about 600 °C. The equipment element 2 can be a molybdenum rod with a diameter of 6…8 mm or a rod made of carbon material. 1. STRESS-STRAIN STATE (SSS) OF THE FREE HEATER ROD WITHOUT TAKING INTO ACCOUNT THE CURRENT SUPPLY SPRING First, free expansion of BETE due to heating is con- sidered. The calculation diagram of the deformation of rod element 2 for this case is presented in Fig. 2. It is a rod of constant cross-section fixed from below, which is heated to a temperature of ΔT. Let's determine the dis- placement of the free end of the rod. If the diameter of the BETE is small, then a hole is made in the upper cur- rent lead, which should compensate for the elongation of the rod, provided that electrical contact is maintained. Then moving the free end of the rod will give us infor- mation about what the depth of this hole should be. Fig. 2. Calculation diagram the free extension of the heater rod: 1 – BETE; 2 – lower current supply The elongation of BETE can be found using the ex- pression for temperature deformations t [1]: l l T t t   , (1) 1 2 3 4 ∆Т 5 6 ∆lt 1 2 ∆Т l 144 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144) where  is the coefficient of temperature linear expan- sion of the material (CTLE); t l – elongation of the free end of the rod due to its heating. Table 1 shows the initial data and calculation results of the movement of the free end of the heater rod (l = 1 m), which is made of MPG-7 graphite at different temperatures [2]. Table 1 Temperature movements of a BETE free end of the MPG-7 graphite Т, °C 610 , 1/deg Δ l, mm 1 2 3 200 9.0 1.8 400 13.0 4.8 600 16.0 9.6 800 19.0 15.2 2. SSS OF THE COMPRESSED HEATING ROD WITHOUT TAKING INTO ACCOUNT THE SPRING OF THE CURRENT SUPPLY Fig. 3 shows a rod of constant cross-section, which is located between two current leads. Its ends cannot move vertically. The temperature has changed by ΔT. Let's determine the axial stress σ [1]:          T l l Е  , (2) where Е – modulus of elasticity of the rod material. In (2) in the case of fixed ends Δl = 0. Thus we have: TЕ   . (3) As can be seen from equation (3), the compressive stresses in the rod do not depend on its diameter and length. Fig. 3. Calculation diagram of the heating rod deformation without taking into account the spring of the current supply: 1 – upper current lead; 2 – equipment element; 3 – lower current lead Table 2 shows the initial data and the results of cal- culations of the axial stress of BETE at different tem- peratures, from 200 to 800 °C. The length of the rod is 1 m. Data for MPG-7 graphite [2] were taken for CLTE. The compressive strength of MPG-7 graphite of the highest grade is 103.00 MPa [2]. Fig. 4 shows the graphical dependence of the axial stress on the tempera- ture, which is non-linear due to the fact that the CLTE and the modulus of elasticity depend on the tempera- ture. Table 2 Calculation of the stresses of the BETE due to heating Т, °C 610 , 1/deg E, GPа σ(Т), МPа 1 2 3 4 200 9.0 7.10 12.78 400 13.0 7.35 38.22 600 16.0 7.50 72.00 800 19.0 7.84 119.17 Fig. 4. Dependence of the axial stress of the rod on the temperature without taking into account the stiffness of the current lead spring 3. STRESSED-STRAIN STATE OF BETE, TAKING INTO ACCOUNT THE SPRING OF THE CURRENT SUPPLY The calculation scheme for this case is shown in Fig. 5. It consists of a heating rod with a diameter d (BETE), length l1 and a spring with stiffness C. The values characterizing the stressed-strain state of the rod will be denoted by the subscript “1”. Thus, we get a static nondeterministic system con- sisting of two parts. The first section is a heating rod, and the second is a spring with stiffness C. This system deforms in the axial direction due to the heating of the first section. The generalized view of the calculation scheme in this case is shown in Fig. 6,a. Fig. 5. Calculation scheme of the heating rod taking into account the spring of the current supply: 1 – upper current supply; 2 – BETE; 3 – lower current supply; 4 – spring of the upper current supply As can be seen from Figs. 6,b and c, the thermal elongation of the first section will consist of the sum of the elastic elongations of the first and second sections: 1 2.tl l l    (4) 1 2 3 ∆Т l 2 3 ∆Т 4 С l1 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144) 145 Fig. 6. Deformation of the heater rod together with the spring: a – the system consists of two sections; b – the first section is heated and lengthens by the amount tl ; c – thermoelastic deformation of the entire system In other words, the spring prevents the first section from elongating, (4) is the geometric side of the prob- lem. The static side of the problem is that the longitudinal force xN on all sections of the system will be the same and will be equal to the reactions in the resistances (in the current leads). If there is a previous longitudinal compression of the system, then it will be added to the chart of longitudinal forces according to the principle of superpositions [1]. The physical side of the problem [1]: Tllt  1 , 11 1 1 1 1111 FE Nl E lll T x   , (5) C N l T x 2 . where – cross-sectional area of BETE. After substituting equations (5) into (4), we get the expression for calculating the longitudinal force T xN : 1 1 1 1 , T T x xl N N l T E F C    1 1 1 1 . 1 T x Tl N l E F C    (6) In the case when 0С , 0xN we have a free end. When С , we have a rigid support, 11FTENx  , the formula for the longitudinal force turns into the one resulting from (2). To obtain the stress in the rod, it is enough to divide the value of the axial force by the cross-sectional area [1]: 1F N x x   . (7) In the case of preliminary compression by force 𝑁𝑥 П, formula (6) takes the form: П xx N CFE l Tl N     1 11 1 1 . (8) In order to verify that at С , 11FTENx  calculations of axial stresses were carried out at E = 7.84 GPa; 61019  1/deg; ΔT = 800 °C for different values of the stiffness of the spring C and the diameter of rod. The results are given in Table 3. Table 3 The value of BETE stresses x , MPa at different diameters and stiffness of the spring d, mm С, kN/m 2 20 200 2000 20000 25 0.03 0.31 3.02 24.58 86.05 15 0.09 0.85 8.02 49.96 104.6 5 0.77 7.27 46.9 103.3 117.4 As can be seen from the data shown in Table 3, with a spring stiffness of 20000 kN/m and a rod diameter of 5 mm, the axial stress of the BETE is close to that obtained earlier with absolutely rigid resistances 17,119x MPa (see Table 2). Table 4 contains the initial data for calculations according to formula (8). The results of calculations for BETE, which is made of MPG-7 graphite according to formula (8), are pre- sented in Table 5 at different values of the diameter of the graphite rod. The following notations are accepted: – axial ductility of the graphite rod, ductility of the spring 51051 С m/N, η – coefficient of strength re- serve for axial stresses due to temperature expansion; taking into account the preliminary compression of 500 N at the compressive strength limit of MPG-7 graphite [ ] МPа. Table 4 Input data for temperature SSS calculations Physical quantity Value MPG-7 graphite Molybdenum Temperature drop ∆𝑇, °С 800 800 CLTE 610 , 1/grad 19 6,2 Modulus of elasticity E, GPа 7,84 160 Rod length 𝑙 , m 1 1 Spring stiffness, 410С N/m 2 2 Pre-compression П xN , N 500 500 С ∆Т, l1 , E1, F1 1 2 x а ∆Т b c 146 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144) Fig. 7. Comparison of the compliance of the BETE and the current supply spring for different values of its diameter On the basis of the data entered in Table 5, it can be concluded that the destruction of the BETE due to reaching the strength limit during compression occurs at a diameter of 3 mm. Fig. 7 shows a graph for comparing the axial com- pliance of the BETE for different values of its diameter with the compliance of the current supply spring. As can be seen from the graph, the component corresponding to the compliance of BETE becomes significant at diame- ters that are close to the critical ones for the loss of rod strength. In order to avoid selecting the critical diameter of the BETE, we obtain the cross-sectional area using for- mula (7). Let's write down the strength condition:  x x x F N    1 . (9) Instead of  xN let's substitute its expression (8) in (9). After bringing similar ones, we get a quadratic equation with respect to 1F of the form: 01 2 1  cbFaF , (10) where  1Ea  ;   1111 ENCETlClb П x  ; ClNc П x 1 . One positive root of the equation (10) was obtained 6 1 1002.7 F m 2 = 0.0702 сm 2 . It corresponds to the value of the diameter d = 2.99 mm, which coincides with what was obtained by selection and is given in Ta- ble 5. With a length of 𝑙 = 0.5 m, the failure occurs at d = 2.78 mm. For molybdenum, the critical diameter of temperature compression at a length 11 l m is 2.72 mm, that is, it is almost no different from that ob- tained for graphite. 4. BUCKLING OF THE ROD ELEMENT OF THE EQUIPMENT UNDER CONDITIONS OF THERMAL EXPANSION The analysis of the results regarding the critical di- ameter of graphite BETE failure due to thermal com- pression shows that the obtained diameter values are very small. In addition, the dangerous diameter depends slightly on the length of the rod element. At the same time, the elements under consideration have a sufficient- ly large flexibility, so it is appropriate to consider the buckling problem for them. According to [1], the critical strength of the loss of stability for the rod element of the structure, which has a rigid clamping at the ends (Fig. 8), will be calculated according to the formula: 𝑃𝑐𝑟 4𝜋2 𝐽𝑚𝑖𝑛 2 , (11) where Е – modulus of elasticity at a given temperature; 𝐽𝑚𝑖𝑛 – moment of inertia in the plane of minimum stiff- ness of the section, for a rod of round cross-section: 𝐽𝑚𝑖𝑛 𝜋𝑑4 64 , (12) l – rod lenghth. Fig. 8. Calculation scheme for determining the critical strength of the loss of stability of the rod element The safety margin of the structure under considera- tion is defined as a fraction of the critical force of buck- ling and the axial force of temperature expansion. At the same time, we will reduce the diameter of the rod until the safety margin approaches unity. The calculation re- sults for MPG-7 graphite (at 11 l m) are given in Ta- ble 6, and for molybdenum in Table 7. The data presented in Tables 6 and 7 confirm the general information about the structural buckling. For example, for a graphite rod, the critical value of the di- ameter of the loss of stability is 16 mm (for molyb- denum, 7 mm), although this diameter corresponds to a compressive stress of only 3.98 MPa, and the loss of strength due to thermal expansion occurs at a diameter of 3.0 mm (see Table 5), that is, the destruction caused by the loss of stability occurs at stresses much lower than the strength limit of the material. The following values of the critical diameter of buckling were obtained for the length of the BETE 5,01 l m: graphite MPG-7 11 mm, molybdenum 5 mm. CONCLUSIONS The paper investigates the temperature resistance of beam elements of technological equipment used in the production of CCCM in direct heating furnaces. The calculation scheme of the problem is built taking into account the stiffness of the furnace current supply spring, and the deformation model contains such a type of destruction as loss of stability. In the course of nu- merical studies, it was proved that the buckling is deci- sive for this case. 0,00 1,00 2,00 3,00 4,00 5,00 6,00 0 10 20 30 1/С, m/N d, mm spring BЕТE ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144) 147 Table 5 Axial stresses of a graphite rod at different diameters 𝑙 𝑚 d, mm F, cm 2 ∙ 5, m/N 𝑁𝑥 𝑇, N 𝑁𝑥 Σ, N 𝑥, МPа η 25 4.909 0.026 302 802 1.63 63.01 15 1.77 0.072 300 800 4.53 22.76 5 0.196 0.65 269 769 39.17 2.63 3 0.071 1.8 223 723 102.33 1.006 Table 6 Axial force and critical buckling force of a graphite rod at different diameters (l = 1m) d, mm 9 min 10J , cm 4 𝑁𝑥 ∑ , N 𝑥, МPа 𝑃𝑐𝑟 , N 𝜂 𝑃𝑐𝑟 𝑁𝑥 ∑ 20 7.85 802 2.55 2430 3.03 18 5.153 801 3.15 1594 1.99 16 3.217 800 3.98 996 1.24 15 2.485 800 4.53 769 0.962 Table 7 Axial force and critical buckling force of a molybdenum rod at different diameters (l = 1m) d, mm 10 min 10J , cm 4 𝑁𝑥 ∑ , N 𝑥, МPа 𝑃𝑐𝑟 , N 𝜂 𝑃𝑐𝑟 𝑁𝑥 ∑ 10 4.91 599 7.63 3100 5.18 7 1.18 599 15.56 744.5 1.24 6 0.636 599 21.18 401.8 0.67 The article provides formulas for calculating the crit- ical diameters of the loss of compressive strength due to heating, as well as calculations for determining the buckling critical diameters of rod elements at a tempera- ture of 800 °C, which are made of MPG-7 graphite and molybdenum, and have a length of 1 and 0.5 m. REFERENCES 1. A.P. Yakovlev, V.V. Matveev. Reference book on resistance of materials / Opening ed. Pisarenko H.S. 2nd ed., revised. and add. Kyiv: “Nauk. opinion”, 1988, 736 c. 2. Billets and products from MPG-6 and MPG-7 graphite: TU U 23.9-37494898-001:2018. Article received 14.03.2023 ТЕМПЕРАТУРНІ ДЕФОРМАЦІЇ ІЗОТРОПНИХ СТЕРЖНЕВИХ ЕЛЕМЕНТІВ ТЕХНОЛОГІЧНОГО ОСНАЩЕННЯ ПРИ ВИГОТОВЛЕННІ ВУГЛЕЦЬ-ВУГЛЕЦЕВИХ КОМПОЗИТНИХ МАТЕРІАЛІВ У ПЕЧАХ ПРЯМОГО НАГРІВУ М.В. Мельтюхов, Я.В. Кравцов Для ізотропних стержневих елементів технологічного оснащення (СЕТО), яке використовується при ви- готовленні вуглець-вуглецевих композиційних матеріалів (ВВКМ) у печах прямого нагріву, в роботі вперше отримане аналітичне рішення температурного напружено-деформованого стану з урахуванням жорсткості пружини струмовідводу. Наводяться формули для обчислення критичних діаметрів втрати міцності на стис- кання. На прикладі графітових і молібденових стержнів у роботі встановлено, що вирішальним фактором несучої здатності є втрата стійкості елементів, що розглядаються.
id nasplib_isofts_kiev_ua-123456789-196111
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1562-6016
language English
last_indexed 2025-12-07T15:23:38Z
publishDate 2023
publisher Національний науковий центр «Харківський фізико-технічний інститут» НАН України
record_format dspace
spelling Meltyukhov, M.V.
Kravtsov, Y.V.
2023-12-10T12:58:48Z
2023-12-10T12:58:48Z
2023
The termal deformation of isotropic beam elements of technological equipment in the manufacturing of carbon-carbon composite materials in furnaces of direct heating / M.V. Meltyukhov, Y.V. Kravtsov // Problems of Atomic Science and Technology. — 2023. — № 2. — С. 143-147. — Бібліогр.: 2 назв. — англ.
1562-6016
DOI: https://doi.org/10.46813/2023-144-143
https://nasplib.isofts.kiev.ua/handle/123456789/196111
621.762
For the isotropic beam elements of the technological equipment (BETE), which are used in the production of carbon-carbon composite materials (CCCM) in direct heating furnaces, the analytical solution of the temperature stress-strain state, taking into account the stiffness of the spring of the current collector, was obtained for the first time in the work. Formulas for calculating the critical diameters of loss of compressive strength are given. Using the example of graphite and molybdenum rods, it was established in the work that the decisive factor of the load-bearing capacity is the loss of stability of the elements under consideration.
Для ізотропних стержневих елементів технологічного оснащення (СЕТО), яке використовується при виготовленні вуглець-вуглецевих композиційних матеріалів (ВВКМ) у печах прямого нагріву, в роботі вперше отримане аналітичне рішення температурного напружено-деформованого стану з урахуванням жорсткості пружини струмовідводу. Наводяться формули для обчислення критичних діаметрів втрати міцності на стискання. На прикладі графітових і молібденових стержнів у роботі встановлено, що вирішальним фактором несучої здатності є втрата стійкості елементів, що розглядаються.
en
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
Problems of Atomic Science and Technology
Irradiation installations, diagnostic and research methods
The termal deformation of isotropic beam elements of technological equipment in the manufacturing of carbon-carbon composite materials in furnaces of direct heating
Температурні деформації ізотропних стержневих елементів технологічного оснащення при виготовленні вуглець-вуглецевих композитних матеріалів у печах прямого нагріву
Article
published earlier
spellingShingle The termal deformation of isotropic beam elements of technological equipment in the manufacturing of carbon-carbon composite materials in furnaces of direct heating
Meltyukhov, M.V.
Kravtsov, Y.V.
Irradiation installations, diagnostic and research methods
title The termal deformation of isotropic beam elements of technological equipment in the manufacturing of carbon-carbon composite materials in furnaces of direct heating
title_alt Температурні деформації ізотропних стержневих елементів технологічного оснащення при виготовленні вуглець-вуглецевих композитних матеріалів у печах прямого нагріву
title_full The termal deformation of isotropic beam elements of technological equipment in the manufacturing of carbon-carbon composite materials in furnaces of direct heating
title_fullStr The termal deformation of isotropic beam elements of technological equipment in the manufacturing of carbon-carbon composite materials in furnaces of direct heating
title_full_unstemmed The termal deformation of isotropic beam elements of technological equipment in the manufacturing of carbon-carbon composite materials in furnaces of direct heating
title_short The termal deformation of isotropic beam elements of technological equipment in the manufacturing of carbon-carbon composite materials in furnaces of direct heating
title_sort termal deformation of isotropic beam elements of technological equipment in the manufacturing of carbon-carbon composite materials in furnaces of direct heating
topic Irradiation installations, diagnostic and research methods
topic_facet Irradiation installations, diagnostic and research methods
url https://nasplib.isofts.kiev.ua/handle/123456789/196111
work_keys_str_mv AT meltyukhovmv thetermaldeformationofisotropicbeamelementsoftechnologicalequipmentinthemanufacturingofcarboncarboncompositematerialsinfurnacesofdirectheating
AT kravtsovyv thetermaldeformationofisotropicbeamelementsoftechnologicalequipmentinthemanufacturingofcarboncarboncompositematerialsinfurnacesofdirectheating
AT meltyukhovmv temperaturnídeformacííízotropnihsteržnevihelementívtehnologíčnogoosnaŝennâprivigotovlennívuglecʹvuglecevihkompozitnihmateríalívupečahprâmogonagrívu
AT kravtsovyv temperaturnídeformacííízotropnihsteržnevihelementívtehnologíčnogoosnaŝennâprivigotovlennívuglecʹvuglecevihkompozitnihmateríalívupečahprâmogonagrívu
AT meltyukhovmv termaldeformationofisotropicbeamelementsoftechnologicalequipmentinthemanufacturingofcarboncarboncompositematerialsinfurnacesofdirectheating
AT kravtsovyv termaldeformationofisotropicbeamelementsoftechnologicalequipmentinthemanufacturingofcarboncarboncompositematerialsinfurnacesofdirectheating