Mathematical model of the rubber-cord shell of rotation for pneumatic dampers
The review of the fundamental scientific works on the mechanics of pneumatic tires is given. A mathematical model is proposed for a rubber-cord shell, taking into account the tensile properties of the cord threads and the elastic resistance of the rubber matrix without limiting the magnitude of th...
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| Format: | Article |
| Language: | English |
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Omsk State Technical University, Federal State Autonomous Educational Institution of Higher Education
2019-04-01
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| Series: | Омский научный вестник: Серия "Авиационно-ракетное и энергетическое машиностроение" |
| Subjects: | |
| Online Access: | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2019/%D0%A2.%203,%20%E2%84%96%201%20(%D0%90%D0%A0%D0%B8%D0%AD%D0%9C)/22-41%20%D0%9A%D0%BE%D1%80%D0%BD%D0%B5%D0%B5%D0%B2%20%D0%92.%20%D0%A1.,%20%D0%A8%D0%B0%D0%BB%D0%B0%D0%B9%20%D0%92.%20%D0%92..pdf |
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| _version_ | 1832557755360083968 |
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| author | V. S. Korneyev V. V. Shalay |
| author_facet | V. S. Korneyev V. V. Shalay |
| author_sort | V. S. Korneyev |
| collection | DOAJ |
| description | The review of the fundamental scientific works on the mechanics of pneumatic tires is given.
A mathematical model is proposed for a rubber-cord shell, taking into account the tensile properties of
the cord threads and the elastic resistance of the rubber matrix without limiting the magnitude of the
deformations, which differs from the mathematical model of the moment-free theory of mesh shells used
in pneumatic tires mechanics. The applied loads are assumed to be static and axisymmetric. Equilibrium
equations are compiled in the form that excludes the emergence of a singularity at special points and
does not require special techniques and tools for integration. To construct the constitutive relations
reflecting the structural heterogeneity of the material and described by smooth functions of spatial
coordinates, the principle of virtual displacements is used. The order of solving the equations of the
mathematical model is indicated.
A critical analysis of the known variants of the theoretical description of the initial geometry of
the rubber-cord shell after its manufacture is given. A modified method is proposed, based on the
consideration of the process of deformation of the representative element of the workpiece and
generally accepted assumptions. The redundancy and inadmissibility of the assumption of the constancy
of the pitch between the cords or the assumption of the constancy of the area of the elementary
rhombic cell of the workpiece are indicated.
The developed mathematical model is designed to design air springs with optimal performance |
| format | Article |
| id | doaj-art-0656e90a6a6c45c4b6240fc3063f1f13 |
| institution | Kabale University |
| issn | 2588-0373 2587-764X |
| language | English |
| publishDate | 2019-04-01 |
| publisher | Omsk State Technical University, Federal State Autonomous Educational Institution of Higher Education |
| record_format | Article |
| series | Омский научный вестник: Серия "Авиационно-ракетное и энергетическое машиностроение" |
| spelling | doaj-art-0656e90a6a6c45c4b6240fc3063f1f132025-02-03T02:30:21ZengOmsk State Technical University, Federal State Autonomous Educational Institution of Higher EducationОмский научный вестник: Серия "Авиационно-ракетное и энергетическое машиностроение"2588-03732587-764X2019-04-0131224110.25206/2588-0373-2019-3-1-22-41Mathematical model of the rubber-cord shell of rotation for pneumatic dampersV. S. Korneyev0https://orcid.org/0000-0003-1694-1190V. V. Shalay1https://orcid.org/0000-0003-0635-4849Omsk State Technical UniversityOmsk State Technical UniversityThe review of the fundamental scientific works on the mechanics of pneumatic tires is given. A mathematical model is proposed for a rubber-cord shell, taking into account the tensile properties of the cord threads and the elastic resistance of the rubber matrix without limiting the magnitude of the deformations, which differs from the mathematical model of the moment-free theory of mesh shells used in pneumatic tires mechanics. The applied loads are assumed to be static and axisymmetric. Equilibrium equations are compiled in the form that excludes the emergence of a singularity at special points and does not require special techniques and tools for integration. To construct the constitutive relations reflecting the structural heterogeneity of the material and described by smooth functions of spatial coordinates, the principle of virtual displacements is used. The order of solving the equations of the mathematical model is indicated. A critical analysis of the known variants of the theoretical description of the initial geometry of the rubber-cord shell after its manufacture is given. A modified method is proposed, based on the consideration of the process of deformation of the representative element of the workpiece and generally accepted assumptions. The redundancy and inadmissibility of the assumption of the constancy of the pitch between the cords or the assumption of the constancy of the area of the elementary rhombic cell of the workpiece are indicated. The developed mathematical model is designed to design air springs with optimal performancehttps://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2019/%D0%A2.%203,%20%E2%84%96%201%20(%D0%90%D0%A0%D0%B8%D0%AD%D0%9C)/22-41%20%D0%9A%D0%BE%D1%80%D0%BD%D0%B5%D0%B5%D0%B2%20%D0%92.%20%D0%A1.,%20%D0%A8%D0%B0%D0%BB%D0%B0%D0%B9%20%D0%92.%20%D0%92..pdfpneumatic tire mechanicsair springsrubber-cord shelmathematical modelcalculation method |
| spellingShingle | V. S. Korneyev V. V. Shalay Mathematical model of the rubber-cord shell of rotation for pneumatic dampers Омский научный вестник: Серия "Авиационно-ракетное и энергетическое машиностроение" pneumatic tire mechanics air springs rubber-cord shel mathematical model calculation method |
| title | Mathematical model of the rubber-cord shell of rotation for pneumatic dampers |
| title_full | Mathematical model of the rubber-cord shell of rotation for pneumatic dampers |
| title_fullStr | Mathematical model of the rubber-cord shell of rotation for pneumatic dampers |
| title_full_unstemmed | Mathematical model of the rubber-cord shell of rotation for pneumatic dampers |
| title_short | Mathematical model of the rubber-cord shell of rotation for pneumatic dampers |
| title_sort | mathematical model of the rubber cord shell of rotation for pneumatic dampers |
| topic | pneumatic tire mechanics air springs rubber-cord shel mathematical model calculation method |
| url | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2019/%D0%A2.%203,%20%E2%84%96%201%20(%D0%90%D0%A0%D0%B8%D0%AD%D0%9C)/22-41%20%D0%9A%D0%BE%D1%80%D0%BD%D0%B5%D0%B5%D0%B2%20%D0%92.%20%D0%A1.,%20%D0%A8%D0%B0%D0%BB%D0%B0%D0%B9%20%D0%92.%20%D0%92..pdf |
| work_keys_str_mv | AT vskorneyev mathematicalmodeloftherubbercordshellofrotationforpneumaticdampers AT vvshalay mathematicalmodeloftherubbercordshellofrotationforpneumaticdampers |