{"id":3710,"date":"2021-03-03T16:26:01","date_gmt":"2021-03-03T16:26:01","guid":{"rendered":"https:\/\/pickedshares.com\/?p=3710"},"modified":"2021-03-13T17:32:55","modified_gmt":"2021-03-13T17:32:55","slug":"belt-friction-calculator","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/belt-friction-calculator\/","title":{"rendered":"Belt friction calculator"},"content":{"rendered":"\n<p>The belt friction calculator is based on the Euler-Eytelwein equation and can be used to calculate the pulling force, holding force, the coefficient of friction or the wrap angle online.<\/p>\n\n\n\n<p>Enter three known sizes and the missing size will be calculated. Basically, the following applies:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>the holding force is always smaller than the pulling force,<\/li><li>the wrap angle is always positive,<\/li><li>the coefficient of friction is always positive and<\/li><li>the coefficient of friction is usually less than 1.<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/03\/seilreibungpost-1024x903.png\" alt=\"\" class=\"wp-image-3687\" width=\"512\" height=\"452\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/03\/seilreibungpost-1024x903.png 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/03\/seilreibungpost-300x265.png 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/03\/seilreibungpost-768x678.png 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/03\/seilreibungpost-400x353.png 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/03\/seilreibungpost-800x706.png 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/03\/seilreibungpost.png 1121w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure>\n\n\n\n<div id=\"wrapinput\" style=\"display: grid\">\n<label for=\"f2\">Pulling force F<sub>2<\/sub> in N<\/label>\n<p><input id=\"f2\" type=\"text\"><\/p>\n\n<label for=\"f1\">Holding force F<sub>1<\/sub> in N<\/label>\n<p><input id=\"f1\" type=\"text\"><\/p>\n\n<label for=\"my\">Coefficient of friction \u00b5<\/label>\n<p><input id=\"my\" type=\"text\"><\/p>\n\n<label for=\"alpha\">Wrap angle \u03b1 in \u00b0<\/label>\n<p><input id=\"alpha\" type=\"text\"><\/p>\n<\/div>\n<div id=\"wrapoutput\" style=\"font-size:x-large;\">\n<p id=\"of1\"><\/p>\n<p id=\"of2\"><\/p>\n<p id=\"omy\"><\/p>\n<p id=\"oalpha\"><\/p>\n<\/div>\n<!--noptimize-->\n<script src=\"https:\/\/ajax.googleapis.com\/ajax\/libs\/jquery\/3.5.1\/jquery.min.js\"><\/script>\n<script>\n\n$('input').keyup(function(){     \nf1 = document.getElementById('f1').value;    \nf2 = document.getElementById('f2').value;\nalpha = document.getElementById('alpha').value;\nmy = document.getElementById('my').value;\n\n\nf1 = f1.replace( \/,\/,\".\" );\nf2 = f2.replace( \/,\/,\".\" );\nmy = my.replace( \/,\/,\".\" );\nalpha = alpha.replace( \/,\/,\".\" );\nalpha = alpha * Math.PI\/180;\n\n\/\/ check if 3 fields are filled\n\ncounter = 0;\nif (f1 != ''){counter++;}\nif (f2 != ''){counter++;}\nif (my != ''){counter++;}\nif (alpha != ''){counter++;}\n\n\/\/console.log(counter);\n\n\/\/ equation\n\/\/ f2 = f1 * e^(\u00b5*alpha)\n\n\/\/ who does this call?\nid = ($(this).attr('id')) ;\n\n\/\/calculate\n\n\/\/ case selection\n\/\/ check which field is empty\n\nif (counter == 3){\n\nif (f1 == ''){\ntry{\n\nf1 = f2 * (Math.E)**(-my*alpha);\nf1 = Math.round(f1*100)\/100;\n$('#of1').html('Holding force F<sub>1<\/sub>: '+f1+' N');\n$('#of1').show();\n$('#of2').hide();\n$('#omy').hide();\n$('#oalpha').hide();\n}\n\ncatch{}\nfinally{}\n\n}\n\nif (f2 == ''){\ntry{\n\nf2 = f1 * (Math.E)**(my*alpha);\nf2 = Math.round(f2*100)\/100;\n$('#of2').html('Pulling force F<sub>2<\/sub>: '+f2+' N');\n$('#of2').show();\n$('#of1').hide();\n$('#omy').hide();\n$('#oalpha').hide();\n}\n\ncatch{}\nfinally{}\n\n}\n\nif (my == ''){\ntry{\n\nmy = Math.log(f2\/f1)\/(Math.log(Math.E)*alpha);\nmy = Math.round(my*100)\/100;\n\n$('#omy').html('Coefficient of friction \u00b5: '+my);\nif (my >= 1){$('#omy').append(' This value is too high, the wrap angle should be set higher.');}\n$('#omy').show();\n$('#of2').hide();\n$('#of1').hide();\n$('#oalpha').hide();\n}\n\ncatch{}\nfinally{}\n\n}\n\nif (alpha == ''){\n\ntry{\n\nalpha = Math.log(f2\/f1)\/(Math.log(Math.E)*my);\nalpha = alpha\/Math.PI * 180;\nalpha = Math.round(alpha*100)\/100;\n\n$('#oalpha').html('Wrap angle &alpha;: '+alpha+' \u00b0');\nif (alpha < 0){$('#oalpha').append(' Something seems to be wrong with the input data.');}\n$('#oalpha').show();\n$('#of2').hide();\n$('#omy').hide();\n$('#of1').hide();\n}\n\ncatch{}\nfinally{}\n\n}\n\n\n} else {\n$('#of2').hide();\n$('#my').hide();\n$('#of1').hide();\n$('#oalpha').hide();\n}\n \n\n});\n\n\n\n\n  \n<\/script>\n\n<!--\/noptimize-->\n\n\n\n<h2 class=\"wp-block-heading\">About the math<\/h2>\n\n\n\n<p>The tool calculates the values based on the following equations.<\/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<p>Equation for pulling force<\/p><p>\n<\/p><p>\\[ F_2 = F_1 \\cdot e^{\u00b5 \\alpha}\\]<\/p>\n<p>Equation for holding force<\/p><p>\n<\/p><p>\\[ F_1 = F_2 \\cdot e^{-\u00b5 \\alpha}\\]<\/p>\n<p>Equation for the coefficient of friction<\/p><p>\n<\/p><p>\\[ \u00b5 = \\frac{ln \\frac{F_2}{F_1}}{\\alpha} \\]<\/p>\n<p>Equation for the wrap angle<\/p><p>\n<\/p><p>\\[ \\alpha = \\frac{ln \\frac{F_2}{F_1}}{ \u00b5} \\]<\/p>\n\n\n\n<p>Please note that the angle must be given in radians.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">An expample<\/h2>\n\n\n\n<p>A rope is wrapped around a bollard. The rope is pulled with a force F<sub>2<\/sub> of 1000 N. How big must the wrap angle \u03b1 be so that the holding force F<sub>1<\/sub> is only 50 N with a coefficient of friction of \u00b5 = 0.3?<\/p>\n\n\n\n<p>The values \u200b\u200bcan be entered directly into the calculation tool. In order to be able to calculate the wrap angle online, the corresponding input field is simply left blank.<\/p>\n\n\n\n<p>The result for the wrap angle is 572 \u00b0, i.e. the rope must be wrapped around the pile a little more than 1.5 times.<\/p>\n\n\n\n<p><a href=\"https:\/\/pickedshares.com\/en\/tag\/friction\/\">Exercises on the subject of friction can be found under the keyword friction.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Belt friction calculator\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/belt-friction-calculator\/\" aria-label=\"Read more about Belt friction calculator\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":3686,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[79,54],"tags":[27],"class_list":["post-3710","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-engineering-en","category-tools-en","tag-friction","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>Belt friction calculator &#8226; 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