{"id":849,"date":"2020-12-11T18:45:43","date_gmt":"2020-12-11T18:45:43","guid":{"rendered":"https:\/\/pickedshares.com\/?p=849"},"modified":"2021-03-03T16:29:47","modified_gmt":"2021-03-03T16:29:47","slug":"engineering-mechanics-1-exercise-31-calculate-belt-force-and-wrap-angle","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-31-calculate-belt-force-and-wrap-angle\/","title":{"rendered":"Calculate belt force and wrap angle"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Task<\/h2>\n\n\n\n<p>A belt drives a roller with a force A = 890 N in the load side and a wrap angle \u03b1 = 160 \u00b0. The <a href=\"https:\/\/pickedshares.com\/en\/static-and-sliding-friction-values\/\">coefficient of static friction<\/a> is \u00b5<sub>0<\/sub> = 0.3.<\/p>\n\n\n\n<p>a) How big is the force L in the loose belt?<\/p>\n\n\n\n<p>b) How big must the wrap angle \u03b1' be if the force in the work belt is increased to A' = 1,100 N while the force L in the loose belt remains the same?<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"743\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-31big-1024x743.jpg\" alt=\"Belt with pulley and tension pulley\" class=\"wp-image-842\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-31big-1024x743.jpg 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-31big-300x218.jpg 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-31big-768x557.jpg 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-31big-400x290.jpg 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-31big-800x581.jpg 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2020\/12\/tm1-31big.jpg 1068w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Belt with pulley and tension pulley<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p>The relationship between the forces in the work belt and in the loose belt is described by the <a href=\"https:\/\/pickedshares.com\/en\/belt-friction-calculator\/\">belt friction formula<\/a> (Euler-Eytelwein).<\/p>\n\n\n\n<script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-AMS_HTML\" async=\"async\">  \/\/ A comment that hinders wxWidgets from optimizing this tag too much.\n<\/script>\n\\[ \\require{cancel} \\]\n<p><strong>reg. a), value of the force L<\/strong><\/p>\n<p>\\[ \\tag{1} A \\leq L \\cdot e^{\u00b5_0 \\cdot \\alpha} \\]<\/p>\n\n<p>The inequalition is simplified in the following to<\/p>\n\n<p>\\[ \\tag{2} L = A \\cdot e^{-\u00b5_0 \\cdot \\alpha} \\]<\/p>\n<p>\\[ \\tag{3} L = 890 N \\cdot e^{-0.3 \\cdot \\frac{8}{9} \\cdot \\pi} \\]<\/p>\n<p>\\[ \\tag{4} L = 385 N \\]<\/p>\n\n<p><strong>reg. b), increased force in the work belt<\/strong><\/p>\n<p>The calculation of the required wrap angle for the increased tensile force in the load side is carried out using the following relationship<\/p>\n\n<p>\\[ \\tag{5} L = A' \\cdot e^{-\u00b5_0 \\cdot \\alpha\\,'} \\]<\/p>\n<p>\\[ \\tag{6} \\frac{A'}{L} = e^{\u00b5_0 \\cdot \\alpha\\,'} \\]<\/p>\n<p>\\[ \\tag{7} \\alpha\\,' = \\frac{\\ln \\left( \\frac{A'}{L} \\right)}{\u00b5_0}  \\]<\/p>\n<p>\\[ \\tag{8} \\alpha\\,' = \\frac{\\ln \\left( \\frac{1100 N}{385 N} \\right)}{0.3}  \\]<\/p>\n\n<p>The necessary wrap angle is therefore in radians<\/p>\n\n<p>\\[ \\tag{9} \\alpha\\,' = 3,5 rad  \\]<\/p>\n\n<p>or converted into \u00b0<\/p>\n\n<p>\\[ \\tag{10} \\alpha\\,' = 200\u00b0  \\]<\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Calculate belt force and wrap angle\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-31-calculate-belt-force-and-wrap-angle\/\" aria-label=\"Read more about Calculate belt force and wrap angle\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":844,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,60],"tags":[27,29],"class_list":["post-849","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-engineering-mechanics-i","category-exercises","tag-friction","tag-statics","infinite-scroll-item","masonry-post","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-33"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Calculate belt force and wrap angle &#8226; pickedshares<\/title>\n<meta name=\"description\" content=\"A belt drives a roller with a given wrap angle. 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