Determination of the maximum mechanical stresses in the insulating material around a defect with a high dielectric permittivity in an electrostatic field
Introduction. All insulating macrohomogeneous solid materials change shape under the influence of an electric field. Problem. The presence of minor defects changes the distribution of an electric field and causes a significant concentration of mechanical stresses in a given section of the material,...
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| Видавець: | National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine” |
|---|---|
| Дата: | 2024 |
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| Формат: | Стаття |
| Мова: | English Ukrainian |
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National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine”
2024
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| Онлайн доступ: | http://eie.khpi.edu.ua/article/view/293407 |
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Electrical Engineering & Electromechanics| id |
eiekhpieduua-article-293407 |
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| record_format |
ojs |
| institution |
Electrical Engineering & Electromechanics |
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OJS |
| language |
English Ukrainian |
| topic |
insulating material internal and surface defect electrostatics structural mechanics von Mises stress finite element method ізоляційний матеріал внутрішній і поверхневий дефект електростатика структурна механіка механічні напруження за фон Мізесом метод скінченних елементів |
| spellingShingle |
insulating material internal and surface defect electrostatics structural mechanics von Mises stress finite element method ізоляційний матеріал внутрішній і поверхневий дефект електростатика структурна механіка механічні напруження за фон Мізесом метод скінченних елементів Palchykov, O. О. Determination of the maximum mechanical stresses in the insulating material around a defect with a high dielectric permittivity in an electrostatic field |
| topic_facet |
insulating material internal and surface defect electrostatics structural mechanics von Mises stress finite element method ізоляційний матеріал внутрішній і поверхневий дефект електростатика структурна механіка механічні напруження за фон Мізесом метод скінченних елементів |
| format |
Article |
| author |
Palchykov, O. О. |
| author_facet |
Palchykov, O. О. |
| author_sort |
Palchykov, O. О. |
| title |
Determination of the maximum mechanical stresses in the insulating material around a defect with a high dielectric permittivity in an electrostatic field |
| title_short |
Determination of the maximum mechanical stresses in the insulating material around a defect with a high dielectric permittivity in an electrostatic field |
| title_full |
Determination of the maximum mechanical stresses in the insulating material around a defect with a high dielectric permittivity in an electrostatic field |
| title_fullStr |
Determination of the maximum mechanical stresses in the insulating material around a defect with a high dielectric permittivity in an electrostatic field |
| title_full_unstemmed |
Determination of the maximum mechanical stresses in the insulating material around a defect with a high dielectric permittivity in an electrostatic field |
| title_sort |
determination of the maximum mechanical stresses in the insulating material around a defect with a high dielectric permittivity in an electrostatic field |
| title_alt |
Визначення максимальних механічних напружень в ізоляційному матеріалі навколо дефекту з високою діелектричною проникністю в електростатичному полі |
| description |
Introduction. All insulating macrohomogeneous solid materials change shape under the influence of an electric field. Problem. The presence of minor defects changes the distribution of an electric field and causes a significant concentration of mechanical stresses in a given section of the material, which, under certain circumstances, can cause partial or complete destruction of this material. Goal. The purpose of the work is to determine maximum mechanical stresses according to the von Mises criterion in insulating materials around defects with ionized air and water in an electrostatic field. Also, to analyze the influence of the following parameters on the indicated stresses: the location of the defect, the orientation angle of the semi-major axis of the defect cross-section, the ratio of semi-major and semi-minor axes, elastic and dielectric properties of the insulating material and the defect. Methodology. The study is based on the interrelated equations of electrostatics and structural mechanics for an isotropic piecewise homogeneous medium. The solution of these equations is obtained by the finite element method. Results. Graphs of dependences of maximum mechanical stresses on the ratio of semi-major and semi-minor axes of the ellipsoidal cross-section of the defect have been obtained. The minimum ratio of the greatest stresses in the insulating materials around the surface cracks and pores for ionized air has been 9.3 times for the maximum ratio of major and minor semi-axes of the cross-section of the defect considered in the work, which is 10. For a water defect, the similar ratio has been 2...5.6 times, increasing when the relative dielectric permittivity of the insulating material changes from 7 to 2. When Young’s modulus of the insulating material increases from 1 MPa to 100 GPa, the angles of the inclination of the linearized dependences of maximum mechanical stresses around bounded pores with ionized air (water) to the axis of the ratio of major and minor semi-axes of the defect cross-section have been increased by 35.9° (58.0°) and 18.6° (20.1°) at orientations of major semi-axes at angles of 0° and 45°, respectively. Originality. The numerical-field mathematical two-dimensional model has been developed for the first time, which consists of sequentially solved equations of electrostatics and structural mechanics, for the determination of the distribution of mechanical stresses in an insulating material with a liquid or gaseous defect. It has been established for the first time that the ratio of the elastic properties of the insulating material and the defect determines the angle of the inclination of the linearized dependence of the maximum mechanical stress to the axis of the ratio of major and minor semi-axes of the defect cross-section. Practical value. The types of defects that contribute to the aging of insulation materials under the combined action of an electric field and a stress field to the greatest extent have been established. |
| publisher |
National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine” |
| publishDate |
2024 |
| url |
http://eie.khpi.edu.ua/article/view/293407 |
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AT palchykovoo determinationofthemaximummechanicalstressesintheinsulatingmaterialaroundadefectwithahighdielectricpermittivityinanelectrostaticfield AT palchykovoo viznačennâmaksimalʹnihmehaníčnihnapruženʹvízolâcíjnomumateríalínavkolodefektuzvisokoûdíelektričnoûproniknístûvelektrostatičnomupolí |
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2024-06-01T14:40:43Z |
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2024-06-01T14:40:43Z |
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1800670117785239552 |
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eiekhpieduua-article-2934072024-01-01T09:17:37Z Determination of the maximum mechanical stresses in the insulating material around a defect with a high dielectric permittivity in an electrostatic field Визначення максимальних механічних напружень в ізоляційному матеріалі навколо дефекту з високою діелектричною проникністю в електростатичному полі Palchykov, O. О. insulating material internal and surface defect electrostatics structural mechanics von Mises stress finite element method ізоляційний матеріал внутрішній і поверхневий дефект електростатика структурна механіка механічні напруження за фон Мізесом метод скінченних елементів Introduction. All insulating macrohomogeneous solid materials change shape under the influence of an electric field. Problem. The presence of minor defects changes the distribution of an electric field and causes a significant concentration of mechanical stresses in a given section of the material, which, under certain circumstances, can cause partial or complete destruction of this material. Goal. The purpose of the work is to determine maximum mechanical stresses according to the von Mises criterion in insulating materials around defects with ionized air and water in an electrostatic field. Also, to analyze the influence of the following parameters on the indicated stresses: the location of the defect, the orientation angle of the semi-major axis of the defect cross-section, the ratio of semi-major and semi-minor axes, elastic and dielectric properties of the insulating material and the defect. Methodology. The study is based on the interrelated equations of electrostatics and structural mechanics for an isotropic piecewise homogeneous medium. The solution of these equations is obtained by the finite element method. Results. Graphs of dependences of maximum mechanical stresses on the ratio of semi-major and semi-minor axes of the ellipsoidal cross-section of the defect have been obtained. The minimum ratio of the greatest stresses in the insulating materials around the surface cracks and pores for ionized air has been 9.3 times for the maximum ratio of major and minor semi-axes of the cross-section of the defect considered in the work, which is 10. For a water defect, the similar ratio has been 2...5.6 times, increasing when the relative dielectric permittivity of the insulating material changes from 7 to 2. When Young’s modulus of the insulating material increases from 1 MPa to 100 GPa, the angles of the inclination of the linearized dependences of maximum mechanical stresses around bounded pores with ionized air (water) to the axis of the ratio of major and minor semi-axes of the defect cross-section have been increased by 35.9° (58.0°) and 18.6° (20.1°) at orientations of major semi-axes at angles of 0° and 45°, respectively. Originality. The numerical-field mathematical two-dimensional model has been developed for the first time, which consists of sequentially solved equations of electrostatics and structural mechanics, for the determination of the distribution of mechanical stresses in an insulating material with a liquid or gaseous defect. It has been established for the first time that the ratio of the elastic properties of the insulating material and the defect determines the angle of the inclination of the linearized dependence of the maximum mechanical stress to the axis of the ratio of major and minor semi-axes of the defect cross-section. Practical value. The types of defects that contribute to the aging of insulation materials under the combined action of an electric field and a stress field to the greatest extent have been established. В роботі методом скінченних елементів розроблено двовимірну математичну модель розрахунку розподілу механічних напружень під дією електростатичного поля в ізоляційному матеріалі з дефектом. Модель являє собою послідовно розв’язувані задачі електростатики та структурної механіки. У якості матеріалу дефекту виступали іонізоване повітря і вода. Розглядалися варіанти з внутрішніми та поверхневими дефектами, з врахуванням і без пружних властивостей дефекту. Поле механічних напружень розраховувалось на основі критерію фон Мізеса. Встановлено, що мінімальне відношення найбільших напружень в ізоляційних матеріалах з поверхневими тріщинами і порами для іонізованого повітря склало 9,3 рази для максимального співвідношення півосей поперечного перерізу дефекту 10. Для водного дефекту аналогічне відношення склало 2…5,6 разів, збільшуючись при зміні відносної діелектричної проникності ізоляційного матеріалу від 7 до 2. Визначено, що при збільшенні модуля Юнга ізоляційного матеріалу від 1 МПа до 100 ГПа кути нахилу до вісі лінеаризованих залежностей максимальних механічних напружень навколо обмежених пор з іонізованим повітрям (водою) збільшуються на 35,9° (58,0°) і 18,6° (20,1°) при орієнтаціях великих півосей під кутами 0° і 45° відповідно. National Technical University "Kharkiv Polytechnic Institute" and State Institution “Institute of Technical Problems of Magnetism of the National Academy of Sciences of Ukraine” 2024-01-01 Article Article application/pdf application/pdf http://eie.khpi.edu.ua/article/view/293407 10.20998/2074-272X.2024.1.09 Electrical Engineering & Electromechanics; No. 1 (2024); 69-76 Электротехника и Электромеханика; № 1 (2024); 69-76 Електротехніка і Електромеханіка; № 1 (2024); 69-76 2309-3404 2074-272X en uk http://eie.khpi.edu.ua/article/view/293407/286230 http://eie.khpi.edu.ua/article/view/293407/286232 Copyright (c) 2023 O. О. Palchykov http://creativecommons.org/licenses/by-nc/4.0 |