Study of Euler’s Belt Formula
Euler’s belt formula for a fixed circular drum is well known and is an important formula for mechanical engineers. However, there is little book in which belt equation for a drum of any contour is discussed precisely. This study was carried out to confirm the validity of the Euler&rsqu...
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Japanese Society of Tribologists
2017
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oai:doaj.org-article:ead288a64871418cade1a9752554af1c2021-11-05T09:20:03ZStudy of Euler’s Belt Formula1881-219810.2474/trol.12.187https://doaj.org/article/ead288a64871418cade1a9752554af1c2017-08-01T00:00:00Zhttps://www.jstage.jst.go.jp/article/trol/12/4/12_187/_pdf/-char/enhttps://doaj.org/toc/1881-2198Euler’s belt formula for a fixed circular drum is well known and is an important formula for mechanical engineers. However, there is little book in which belt equation for a drum of any contour is discussed precisely. This study was carried out to confirm the validity of the Euler’s belt formula applied to a drum of any contour. The calculated result was verified to ascertain whether it satisfied the static equilibrium equations of the force and moment. The results perfectly satisfied the static equilibrium equations of the force. As for an equilibrium of the moment, it was found in the case of a belt wrapped around an elliptical drum that the moment from the belt tension was equal to the integrated moment caused by frictional force and normal force along wrapped length. Normal force distribution under a belt on a cylindrical surface was evaluated experimentally by a pressure sensitive film which was found to correspond qualitatively to the theory. As an example, an equation to calculate the normal pressure and tension of a belt wrapped on an elliptical drum was derived.Keiji ImadoTakefumi OtsuJapanese Society of Tribologistsarticlebelt frictioncurvaturecontact pressurestaticscontour integralPhysicsQC1-999Engineering (General). Civil engineering (General)TA1-2040Mechanical engineering and machineryTJ1-1570ChemistryQD1-999ENTribology Online, Vol 12, Iss 4, Pp 187-192 (2017) |
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DOAJ |
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DOAJ |
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EN |
| topic |
belt friction curvature contact pressure statics contour integral Physics QC1-999 Engineering (General). Civil engineering (General) TA1-2040 Mechanical engineering and machinery TJ1-1570 Chemistry QD1-999 |
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belt friction curvature contact pressure statics contour integral Physics QC1-999 Engineering (General). Civil engineering (General) TA1-2040 Mechanical engineering and machinery TJ1-1570 Chemistry QD1-999 Keiji Imado Takefumi Otsu Study of Euler’s Belt Formula |
| description |
Euler’s belt formula for a fixed circular drum is well known and is an important formula for mechanical engineers. However, there is little book in which belt equation for a drum of any contour is discussed precisely. This study was carried out to confirm the validity of the Euler’s belt formula applied to a drum of any contour. The calculated result was verified to ascertain whether it satisfied the static equilibrium equations of the force and moment. The results perfectly satisfied the static equilibrium equations of the force. As for an equilibrium of the moment, it was found in the case of a belt wrapped around an elliptical drum that the moment from the belt tension was equal to the integrated moment caused by frictional force and normal force along wrapped length. Normal force distribution under a belt on a cylindrical surface was evaluated experimentally by a pressure sensitive film which was found to correspond qualitatively to the theory. As an example, an equation to calculate the normal pressure and tension of a belt wrapped on an elliptical drum was derived. |
| format |
article |
| author |
Keiji Imado Takefumi Otsu |
| author_facet |
Keiji Imado Takefumi Otsu |
| author_sort |
Keiji Imado |
| title |
Study of Euler’s Belt Formula |
| title_short |
Study of Euler’s Belt Formula |
| title_full |
Study of Euler’s Belt Formula |
| title_fullStr |
Study of Euler’s Belt Formula |
| title_full_unstemmed |
Study of Euler’s Belt Formula |
| title_sort |
study of euler’s belt formula |
| publisher |
Japanese Society of Tribologists |
| publishDate |
2017 |
| url |
https://doaj.org/article/ead288a64871418cade1a9752554af1c |
| work_keys_str_mv |
AT keijiimado studyofeulerrsquosbeltformula AT takefumiotsu studyofeulerrsquosbeltformula |
| _version_ |
1718444442281574400 |