MATHEMATICAL MODEL OF THE FUNCTIONING PROCESS OF A RUBBER BUSHING ON THE HOOKE AND SAINT-VENANT ELEMENTS’ BASIS
Introduction. Rubber bushings are important parts of the spring systems of modern vehicles. The properties determine not only the comfort of car movement, but also affect the elastic suspension characteristics. When a bushing is deformed, linear sections appear in characteristics. It is advisable to...
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| Format: | Article |
| Language: | Russian |
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Siberian State Automobile and Highway University
2019-12-01
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| Series: | Вестник СибАДИ |
| Subjects: | |
| Online Access: | https://vestnik.sibadi.org/jour/article/view/985 |
| _version_ | 1797873483015782400 |
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| author | D. A. Tikhov-Tinnikov V. S. Baradiev A. I. Fedotov A. V. Alekseev |
| author_facet | D. A. Tikhov-Tinnikov V. S. Baradiev A. I. Fedotov A. V. Alekseev |
| author_sort | D. A. Tikhov-Tinnikov |
| collection | DOAJ |
| description | Introduction. Rubber bushings are important parts of the spring systems of modern vehicles. The properties determine not only the comfort of car movement, but also affect the elastic suspension characteristics. When a bushing is deformed, linear sections appear in characteristics. It is advisable to describe such characteristics using a mathematical model based on the classical elements of Hooke and Saint-Venant. The paper presents a mathematical description of the bushing simulation functioning results, accuracy of approach, areas of application of the mathematical model.Materials and methods. The initial data was the experimental characteristic of a cylindrical automobile rubber bushing, obtained in harmonic mode at the 0.03 to 51 Hz frequency and the 0.4 to 10 mm amplitude. The force balance of the two Hooke elements and one Saint-Venant element interacting with each other determined the mathematical model description. The authors carried out the calculations using numerical and optimization methods.Results. As a result, the authors determined functions characterizing the change in the parameters of the Hooke and Saint-Venant elements from the rubber bushings’ deformation amplitude. Moreover, the authors calculated power characteristics in the form of dependences of the rubber bushing effort and also found quantitative indicators of the reliability of the experimental data approximation by the developed mathematical model.Discussion and conclusions. The analysis of the operating modes shows the possibility of the model application to describe the rubber bushing functioning in a stationary harmonic mode with small and medium strain amplitudes. The simulation results of the Hooke’s and Saint-Venant’s parameters reveals the theoretical prerequisites for the possibility of using the model to calculate the bushing force in an unsteady mode.The authors have read and approved the final manuscript. Financial transparency: the authors have no financial interest in the presented materials or methods. There is no conflict of interest. |
| first_indexed | 2024-04-10T01:15:49Z |
| format | Article |
| id | doaj.art-fd85a10d00cf4a15870d10f719e568f6 |
| institution | Directory Open Access Journal |
| issn | 2071-7296 2658-5626 |
| language | Russian |
| last_indexed | 2024-04-10T01:15:49Z |
| publishDate | 2019-12-01 |
| publisher | Siberian State Automobile and Highway University |
| record_format | Article |
| series | Вестник СибАДИ |
| spelling | doaj.art-fd85a10d00cf4a15870d10f719e568f62023-03-13T09:52:49ZrusSiberian State Automobile and Highway UniversityВестник СибАДИ2071-72962658-56262019-12-0116670671610.26518/2071-7296-2019-6-706-716598MATHEMATICAL MODEL OF THE FUNCTIONING PROCESS OF A RUBBER BUSHING ON THE HOOKE AND SAINT-VENANT ELEMENTS’ BASISD. A. Tikhov-Tinnikov0V. S. Baradiev1A. I. Fedotov2A. V. Alekseev3Восточно-Сибирский государственный университет технологий и управленияВосточно-Сибирский государственный университет технологий и управленияИркутский национальный исследовательский технический университетВосточно-Сибирский государственный университет технологий и управленияIntroduction. Rubber bushings are important parts of the spring systems of modern vehicles. The properties determine not only the comfort of car movement, but also affect the elastic suspension characteristics. When a bushing is deformed, linear sections appear in characteristics. It is advisable to describe such characteristics using a mathematical model based on the classical elements of Hooke and Saint-Venant. The paper presents a mathematical description of the bushing simulation functioning results, accuracy of approach, areas of application of the mathematical model.Materials and methods. The initial data was the experimental characteristic of a cylindrical automobile rubber bushing, obtained in harmonic mode at the 0.03 to 51 Hz frequency and the 0.4 to 10 mm amplitude. The force balance of the two Hooke elements and one Saint-Venant element interacting with each other determined the mathematical model description. The authors carried out the calculations using numerical and optimization methods.Results. As a result, the authors determined functions characterizing the change in the parameters of the Hooke and Saint-Venant elements from the rubber bushings’ deformation amplitude. Moreover, the authors calculated power characteristics in the form of dependences of the rubber bushing effort and also found quantitative indicators of the reliability of the experimental data approximation by the developed mathematical model.Discussion and conclusions. The analysis of the operating modes shows the possibility of the model application to describe the rubber bushing functioning in a stationary harmonic mode with small and medium strain amplitudes. The simulation results of the Hooke’s and Saint-Venant’s parameters reveals the theoretical prerequisites for the possibility of using the model to calculate the bushing force in an unsteady mode.The authors have read and approved the final manuscript. Financial transparency: the authors have no financial interest in the presented materials or methods. There is no conflict of interest.https://vestnik.sibadi.org/jour/article/view/985система подрессоривания автомобилярезинометаллический шарнирмодель тела гукамодель тела сен-венанаматематическое моделированиеамплитудачастота |
| spellingShingle | D. A. Tikhov-Tinnikov V. S. Baradiev A. I. Fedotov A. V. Alekseev MATHEMATICAL MODEL OF THE FUNCTIONING PROCESS OF A RUBBER BUSHING ON THE HOOKE AND SAINT-VENANT ELEMENTS’ BASIS Вестник СибАДИ система подрессоривания автомобиля резинометаллический шарнир модель тела гука модель тела сен-венана математическое моделирование амплитуда частота |
| title | MATHEMATICAL MODEL OF THE FUNCTIONING PROCESS OF A RUBBER BUSHING ON THE HOOKE AND SAINT-VENANT ELEMENTS’ BASIS |
| title_full | MATHEMATICAL MODEL OF THE FUNCTIONING PROCESS OF A RUBBER BUSHING ON THE HOOKE AND SAINT-VENANT ELEMENTS’ BASIS |
| title_fullStr | MATHEMATICAL MODEL OF THE FUNCTIONING PROCESS OF A RUBBER BUSHING ON THE HOOKE AND SAINT-VENANT ELEMENTS’ BASIS |
| title_full_unstemmed | MATHEMATICAL MODEL OF THE FUNCTIONING PROCESS OF A RUBBER BUSHING ON THE HOOKE AND SAINT-VENANT ELEMENTS’ BASIS |
| title_short | MATHEMATICAL MODEL OF THE FUNCTIONING PROCESS OF A RUBBER BUSHING ON THE HOOKE AND SAINT-VENANT ELEMENTS’ BASIS |
| title_sort | mathematical model of the functioning process of a rubber bushing on the hooke and saint venant elements basis |
| topic | система подрессоривания автомобиля резинометаллический шарнир модель тела гука модель тела сен-венана математическое моделирование амплитуда частота |
| url | https://vestnik.sibadi.org/jour/article/view/985 |
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