Frictional Energy Dissipation in Partial Slip Contacts of Axisymmetric Power-Law Graded Elastic Solids under Oscillating Tangential Loads: Effect of the Geometry and the In-Depth Grading
Due to the rapid development of additive manufacturing, a growing number of components in mechanical engineering are made of functionally graded materials. Compared to conventional materials, they exhibit improved properties in terms of strength, thermal, wear or corrosion resistance. However, becau...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/19/3641 |
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| author | Josefine Wilhayn Markus Heß |
| author_facet | Josefine Wilhayn Markus Heß |
| author_sort | Josefine Wilhayn |
| collection | DOAJ |
| description | Due to the rapid development of additive manufacturing, a growing number of components in mechanical engineering are made of functionally graded materials. Compared to conventional materials, they exhibit improved properties in terms of strength, thermal, wear or corrosion resistance. However, because of the varying material properties, especially the type of in-depth grading of Young’s modulus, the solution of contact problems including the frequently encountered tangential fretting becomes significantly more difficult. The present work is intended to contribute to this context. The partial-slip contact of axisymmetric, power-law graded elastic solids under classical loading by a constant normal force and an oscillating tangential force is investigated both numerically and analytically. For this purpose, a fictitious equivalent contact model in the mathematical space of the Abel transform is used since it simplifies the solution procedure considerably without being an approximation. For different axisymmetric shaped solids and various elastic inhomogeneities (types of in-depth grading), the hysteresis loops are numerically generated and the corresponding dissipated frictional energies per cycle are determined. Moreover, a closed-form analytical solution for the dissipated energy is derived, which is applicable for a breadth class of axisymmetric shapes and elastic inhomogeneities. The famous solution of Mindlin et al. emerges as a special case. |
| first_indexed | 2024-03-09T21:27:41Z |
| format | Article |
| id | doaj.art-88c708333779402daf313e7bc7d558e7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T21:27:41Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-88c708333779402daf313e7bc7d558e72023-11-23T21:04:57ZengMDPI AGMathematics2227-73902022-10-011019364110.3390/math10193641Frictional Energy Dissipation in Partial Slip Contacts of Axisymmetric Power-Law Graded Elastic Solids under Oscillating Tangential Loads: Effect of the Geometry and the In-Depth GradingJosefine Wilhayn0Markus Heß1Department of System Dynamics and Friction Physics, Technische Universität Berlin, Sekr. C8-4, Straße des 17. Juni 135, 10623 Berlin, GermanyDepartment of System Dynamics and Friction Physics, Technische Universität Berlin, Sekr. C8-4, Straße des 17. Juni 135, 10623 Berlin, GermanyDue to the rapid development of additive manufacturing, a growing number of components in mechanical engineering are made of functionally graded materials. Compared to conventional materials, they exhibit improved properties in terms of strength, thermal, wear or corrosion resistance. However, because of the varying material properties, especially the type of in-depth grading of Young’s modulus, the solution of contact problems including the frequently encountered tangential fretting becomes significantly more difficult. The present work is intended to contribute to this context. The partial-slip contact of axisymmetric, power-law graded elastic solids under classical loading by a constant normal force and an oscillating tangential force is investigated both numerically and analytically. For this purpose, a fictitious equivalent contact model in the mathematical space of the Abel transform is used since it simplifies the solution procedure considerably without being an approximation. For different axisymmetric shaped solids and various elastic inhomogeneities (types of in-depth grading), the hysteresis loops are numerically generated and the corresponding dissipated frictional energies per cycle are determined. Moreover, a closed-form analytical solution for the dissipated energy is derived, which is applicable for a breadth class of axisymmetric shapes and elastic inhomogeneities. The famous solution of Mindlin et al. emerges as a special case.https://www.mdpi.com/2227-7390/10/19/3641structural dampingfrettingfrictional energy dissipationtangential contactfunctionally graded materialsAbel transform |
| spellingShingle | Josefine Wilhayn Markus Heß Frictional Energy Dissipation in Partial Slip Contacts of Axisymmetric Power-Law Graded Elastic Solids under Oscillating Tangential Loads: Effect of the Geometry and the In-Depth Grading Mathematics structural damping fretting frictional energy dissipation tangential contact functionally graded materials Abel transform |
| title | Frictional Energy Dissipation in Partial Slip Contacts of Axisymmetric Power-Law Graded Elastic Solids under Oscillating Tangential Loads: Effect of the Geometry and the In-Depth Grading |
| title_full | Frictional Energy Dissipation in Partial Slip Contacts of Axisymmetric Power-Law Graded Elastic Solids under Oscillating Tangential Loads: Effect of the Geometry and the In-Depth Grading |
| title_fullStr | Frictional Energy Dissipation in Partial Slip Contacts of Axisymmetric Power-Law Graded Elastic Solids under Oscillating Tangential Loads: Effect of the Geometry and the In-Depth Grading |
| title_full_unstemmed | Frictional Energy Dissipation in Partial Slip Contacts of Axisymmetric Power-Law Graded Elastic Solids under Oscillating Tangential Loads: Effect of the Geometry and the In-Depth Grading |
| title_short | Frictional Energy Dissipation in Partial Slip Contacts of Axisymmetric Power-Law Graded Elastic Solids under Oscillating Tangential Loads: Effect of the Geometry and the In-Depth Grading |
| title_sort | frictional energy dissipation in partial slip contacts of axisymmetric power law graded elastic solids under oscillating tangential loads effect of the geometry and the in depth grading |
| topic | structural damping fretting frictional energy dissipation tangential contact functionally graded materials Abel transform |
| url | https://www.mdpi.com/2227-7390/10/19/3641 |
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