{"id":770,"date":"2020-11-18T13:48:41","date_gmt":"2020-11-18T13:48:41","guid":{"rendered":"https:\/\/pickedshares.com\/?p=770"},"modified":"2021-05-08T11:18:04","modified_gmt":"2021-05-08T11:18:04","slug":"engineering-mechanics-1-exercise-26-drum-with-brake","status":"publish","type":"post","link":"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-26-drum-with-brake\/","title":{"rendered":"Drum brake"},"content":{"rendered":"\n<p>This exercise is about the determination of drum braking torques in different rotation directions. See an <a href=\"https:\/\/en.wikipedia.org\/wiki\/Railway_brake\" target=\"_blank\" rel=\"noreferrer noopener\">example for this kind of brakes<\/a> here.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Task<\/h2>\n\n\n\n<p>A drum is braked with a brake pad that is pressed on with an operating lever. The drum can be operated in both left and right rotation.<\/p>\n\n\n\n<p>a) What drum braking torques are achieved for left and right rotation?<\/p>\n\n\n\n<p>b)  What value does the height b must have so that the braking torques for right and left rotation are the same?<\/p>\n\n\n\n<p>c) At what height b does the brake \u201cseize\u201d? Does this happen in clockwise or counterclockwise rotation?<\/p>\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\/01\/tm1-26-1-1024x717.png\" alt=\"Drum with operating lever and brake block in clockwise or counter-clockwise rotation\" class=\"wp-image-2240\" width=\"512\" height=\"359\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-1-1024x717.png 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-1-300x210.png 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-1-768x537.png 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-1-400x280.png 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-1-800x560.png 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-1.png 1459w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><figcaption>Drum with operating lever and brake pad in clockwise or counter-clockwise rotation<\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<p>The following video is in German language, but English subtitles are available.<\/p>\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"lyte-wrapper\" title=\"Bremse im Rechts- und Linkslauf - Technische Mechanik 1, &Uuml;bung 26\" style=\"width:640px;max-width:100%;margin:5px auto;\"><div class=\"lyMe hidef\" id=\"WYL_fkZMYGuOlDw\" itemprop=\"video\" itemscope itemtype=\"https:\/\/schema.org\/VideoObject\"><div><meta itemprop=\"thumbnailUrl\" content=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FfkZMYGuOlDw%2Fmaxresdefault.jpg\" \/><meta itemprop=\"embedURL\" content=\"https:\/\/www.youtube.com\/embed\/fkZMYGuOlDw\" \/><meta itemprop=\"duration\" content=\"PT7M22S\" \/><meta itemprop=\"uploadDate\" content=\"2021-01-25T12:14:32Z\" \/><\/div><meta itemprop=\"accessibilityFeature\" content=\"captions\" \/><div id=\"lyte_fkZMYGuOlDw\" data-src=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FfkZMYGuOlDw%2Fmaxresdefault.jpg\" class=\"pL\"><div class=\"tC\"><div class=\"tT\" itemprop=\"name\">Bremse im Rechts- und Linkslauf - Technische Mechanik 1, \u00dcbung 26<\/div><\/div><div class=\"play\"><\/div><div class=\"ctrl\"><div class=\"Lctrl\"><\/div><div class=\"Rctrl\"><\/div><\/div><\/div><noscript><a href=\"https:\/\/youtu.be\/fkZMYGuOlDw\" rel=\"nofollow\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pickedshares.com\/wp-content\/plugins\/wp-youtube-lyte\/lyteCache.php?origThumbUrl=https%3A%2F%2Fi.ytimg.com%2Fvi%2FfkZMYGuOlDw%2F0.jpg\" alt=\"Bremse im Rechts- und Linkslauf - Technische Mechanik 1, &Uuml;bung 26\" width=\"640\" height=\"340\" \/><br \/>Watch this video on YouTube<\/a><\/noscript><meta itemprop=\"description\" content=\"F\u00fcr eine Bremse mit Handhebel und Bremsklotz werden folgende Punkte untersucht: Wie gro\u00df sind die Bremsmomente im Rechts- und Linkslauf? Wie hoch muss der Bremsklotz sein (Ma\u00df b), damit die Bremsmomente in beiden Drehrichtungen gleich hoch sind? Wann frisst sich die Bremse fest und bei welcher Drehrichtung passiert das? Diese \u00dcbung gibt es auch hier zum Nachlesen: https:\/\/pickedshares.com\/technische-mechanik-1-uebung-26-trommel-mit-bremse\/\"><\/div><\/div><div class=\"lL\" style=\"max-width:100%;width:640px;margin:5px auto;\"><\/div><figcaption><\/figcaption><\/figure>\n\n\n<h3 class=\"wp-block-heading\">Determination of the drum braking torques<\/h3>\n\n\n\n<p>The two braking torques for clockwise and counter-clockwise rotation are calculated from the <a href=\"https:\/\/pickedshares.com\/en\/static-and-sliding-friction-values\/\">friction<\/a> force F<sub>Bx<\/sub> and half the drum diameter.<\/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>\\[ M_{BL}=-F_{Bx} \\cdot \\frac{d}{2} \\]\n<\/p>\n<p>\\[ M_{BR}=F_{Bx} \\cdot \\frac{d}{2} \\]\n<\/p>\n<p>The relationship between the frictional force and the normal force leads to<\/p><p>\n<\/p><p>\\[ F_{Bx}=\u00b5 \\cdot F_{By} \\]\n<\/p>\n<p>\\[ F_{By} = \\frac{F_{Bx}}{\u00b5} \\]\n<\/p>\n\n\n\n<p>The moment balances set out below are set up with regard to point A on the operating lever.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Left rotation<\/h4>\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\/01\/tm1-26-2-1024x961.png\" alt=\"Drum with operating lever and brake block in counter-clockwise rotation\" class=\"wp-image-2246\" width=\"512\" height=\"481\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-2-1024x961.png 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-2-300x281.png 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-2-768x720.png 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-2-1536x1441.png 1536w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-2-400x375.png 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-2-800x750.png 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-2.png 1549w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><figcaption>Drum with operating lever and brake block in counter-clockwise rotation<\/figcaption><\/figure>\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\n<div style=\"overflow:auto;\">\n<p>\\[ \\sum M(A)=0=- F_{Bx} \\cdot b + F_{By} \\cdot a - F \\cdot l \\]\n<\/p>\n<\/div>\n<p>\\[ 0=-F_{Bx} \\cdot b + \\frac{F_{Bx}}{\u00b5} \\cdot a - F \\cdot l \\]\n<\/p>\n<p>\\[ F \\cdot l=-F_{Bx} \\cdot \\left( b - \\frac{a}{\u00b5} \\right)  \\]\n<\/p>\n<p>\\[ F_{Bx} = - \\frac{F \\cdot l}{\\left( b - \\frac{a}{\u00b5} \\right)}   \\]\n<\/p>\n<p>The braking torque for left turning rotation is<\/p>\n<p>\\[ M_{BL}=\\frac{F \\cdot l \\cdot d}{2 \\cdot \\left( b - \\frac{a}{\u00b5} \\right)}  \\]\n<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Right rotation<\/h4>\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\/01\/tm1-26-3-1024x965.png\" alt=\"Drum with operating lever and brake block in clockwise rotation\" class=\"wp-image-2248\" width=\"512\" height=\"483\" srcset=\"https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-3-1024x965.png 1024w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-3-300x283.png 300w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-3-768x724.png 768w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-3-400x377.png 400w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-3-800x754.png 800w, https:\/\/pickedshares.com\/wp-content\/uploads\/2021\/01\/tm1-26-3.png 1537w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><figcaption>Drum with operating lever and brake block in clockwise rotation<\/figcaption><\/figure>\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\n<div style=\"overflow:auto;\">\n<p>\\[ \\sum M(A)=0= F_{Bx} \\cdot b + F_{By} \\cdot a - F \\cdot l \\]\n<\/p>\n<\/div>\n<p>\\[ 0= F_{Bx} \\cdot b + \\frac{F_{Bx}}{\u00b5} \\cdot a - F \\cdot l \\]\n<\/p>\n<p>\\[ F \\cdot l= F_{Bx} \\cdot \\left( b + \\frac{a}{\u00b5} \\right)  \\]\n<\/p>\n<p>\\[ F_{Bx} = \\frac{F \\cdot l}{\\left( b + \\frac{a}{\u00b5} \\right)}  \\]\n<\/p>\n<p>The braking torque for right turning rotation is<\/p>\n<p>\\[ M_{BR}= \\frac{F \\cdot l \\cdot d}{2 \\cdot \\left( b + \\frac{a}{\u00b5} \\right)}  \\]\n<\/p>\n\n\n\n<p>The amount of braking torque in anti-clockwise rotation is higher than in clockwise rotation because the divisor is larger in clockwise rotation. The brake is therefore more effective in anti-clockwise rotation than in clockwise rotation.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Determination of the height b for equally large drum braking torques both rotation directions<\/h3>\n\n\n\n<p>The condition is: M<sub>BR<\/sub> = -M<sub>BL<\/sub>. From this follows<\/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>\\[ M_{BR} = M_{BL}\\] <\/p>\n<p>\\[ \\frac{F \\cdot l \\cdot d}{2 \\cdot \\left( b + \\frac{a}{\u00b5} \\right)} = -\\frac{F \\cdot l \\cdot d}{2 \\cdot \\left( b - \\frac{a}{\u00b5} \\right)}\\] <\/p>\n<p>\\[ b + \\frac{a}{\u00b5} = - b + \\frac{a}{\u00b5} \\] <\/p>\n<p>\\[ b =0 \\] <\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Determination of the height b and direction of rotation for seizing<\/h3>\n\n\n\n<p>The brake seizes when the braking torque approaches infinity. This can only occur in counter-clockwise operation when the expression below the fraction line approaches zero.<\/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\n<p>\\[ M_B  \\rightarrow \\infty \\]<\/p>\n\n\n<p>\\[ M_{BL}=\\frac{F \\cdot l \\cdot d}{2 \\cdot \\left( b - \\frac{a}{\u00b5} \\right)}  \\]\n<\/p>\n\n<p>\\[  b - \\frac{a}{\u00b5} = 0  \\]\n<\/p>\n<p>\\[  b = \\frac{a}{\u00b5}  \\]\n<\/p>\n\n\n\n<p>Here we have some more <a href=\"https:\/\/pickedshares.com\/en\/tag\/friction\/\">exercises regarding friction in engineering mechanics<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p> ... <a title=\"Drum brake\" class=\"read-more\" href=\"https:\/\/pickedshares.com\/en\/engineering-mechanics-1-exercise-26-drum-with-brake\/\" aria-label=\"Read more about Drum brake\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":2242,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,60],"tags":[45,27,46,48,29],"class_list":["post-770","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-engineering-mechanics-i","category-exercises","tag-bearing-loads","tag-friction","tag-reaction-forces","tag-resulting-moments","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>Drum brake &#8226; pickedshares<\/title>\n<meta name=\"description\" content=\"This exercise investigates the drum braking torques of lever operated brake in left and right hand rotation. 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