{"id":347,"date":"2023-06-21T02:27:31","date_gmt":"2023-06-21T02:27:31","guid":{"rendered":"https:\/\/physigeek.com\/pt\/relacao-de-velocidade\/"},"modified":"2023-06-21T02:27:31","modified_gmt":"2023-06-21T02:27:31","slug":"relacao-de-velocidade","status":"publish","type":"post","link":"https:\/\/physigeek.com\/pt\/relacao-de-velocidade\/","title":{"rendered":"Rela\u00e7\u00e3o de transmiss\u00e3o"},"content":{"rendered":"<p>Neste artigo voc\u00ea aprender\u00e1 o que \u00e9 a rela\u00e7\u00e3o de transmiss\u00e3o, como a rela\u00e7\u00e3o de transmiss\u00e3o \u00e9 calculada e, al\u00e9m disso, um exerc\u00edcio resolvido de rela\u00e7\u00e3o de transmiss\u00e3o para entender completamente o conceito. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-la-relacion-de-transmision\"><\/span> O que \u00e9 rela\u00e7\u00e3o de transmiss\u00e3o?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>rela\u00e7\u00e3o de transmiss\u00e3o<\/strong> \u00e9 a rela\u00e7\u00e3o entre as velocidades de rota\u00e7\u00e3o de duas engrenagens. Especificamente, a rela\u00e7\u00e3o de transmiss\u00e3o de duas engrenagens \u00e9 definida como a raz\u00e3o entre a velocidade angular da engrenagem de sa\u00edda e a velocidade angular da engrenagem de entrada.<\/p>\n<p> Normalmente, quando duas engrenagens est\u00e3o conectadas, uma delas \u00e9 maior que a outra. Portanto, as velocidades angulares das duas rodas s\u00e3o diferentes. Assim, a rela\u00e7\u00e3o de transmiss\u00e3o \u00e9 um par\u00e2metro que indica a rela\u00e7\u00e3o entre as velocidades de rota\u00e7\u00e3o das duas rodas.<\/p>\n<p> Primeiramente, a rela\u00e7\u00e3o de transmiss\u00e3o \u00e9 usada para mostrar o fator pelo qual a velocidade de rota\u00e7\u00e3o em um sistema de engrenagens \u00e9 aumentada ou diminu\u00edda. Por\u00e9m, a rela\u00e7\u00e3o de transmiss\u00e3o tamb\u00e9m mostra a <a href=\"https:\/\/physigeek.com\/pt\/vantagem-mecanica\/\">vantagem mec\u00e2nica<\/a> do sistema, pois quanto menor o valor da rela\u00e7\u00e3o de transmiss\u00e3o, maior o momento transmitido. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-de-la-relacion-de-transmision\"><\/span> F\u00f3rmula de rela\u00e7\u00e3o de transmiss\u00e3o<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de ver a defini\u00e7\u00e3o da rela\u00e7\u00e3o de transmiss\u00e3o, veremos nesta se\u00e7\u00e3o como calcular este par\u00e2metro caracter\u00edstico das engrenagens.<\/p>\n<p> A rela\u00e7\u00e3o de transmiss\u00e3o \u00e9 igual \u00e0 raz\u00e3o entre a velocidade angular de sa\u00edda e a velocidade angular de entrada. Portanto, para calcular a rela\u00e7\u00e3o de transmiss\u00e3o, a velocidade angular da roda de sa\u00edda deve ser dividida pela velocidade angular da roda de entrada.<\/p>\n<p> Portanto, a <strong>f\u00f3rmula para calcular a rela\u00e7\u00e3o de transmiss\u00e3o<\/strong> de um sistema de engrenagens \u00e9: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/rapport-de-transmission.png\" alt=\"f\u00f3rmula de rela\u00e7\u00e3o de transmiss\u00e3o\" class=\"wp-image-6189\" width=\"286\" height=\"286\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/rapport-de-transmission-300x300.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/rapport-de-transmission-150x150.png 150w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/rapport-de-transmission.png 568w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\"><\/figure>\n<p> Da mesma forma, a rela\u00e7\u00e3o de transmiss\u00e3o tamb\u00e9m pode ser calculada a partir do n\u00famero de dentes das rodas e dos seus di\u00e2metros. Assim, a f\u00f3rmula da rela\u00e7\u00e3o de transmiss\u00e3o pode ser estendida para a seguinte express\u00e3o:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-97af0b24bdb831157b691d9508c313a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i=\\cfrac{\\omega_2}{\\omega_1}=\\cfrac{Z_1}{Z_2}=\\cfrac{D_1}{D_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"144\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-31318c5dcb226c69e0818e5f7d2422b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a rela\u00e7\u00e3o de transmiss\u00e3o. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-237a06d6ffb9ecf1b88604147901eaa5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\omega_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 a velocidade angular da roda de entrada. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-dda68f357f0855d943e55febd00343b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\omega_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 a velocidade angular da roda de sa\u00edda. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-7efd17fcc5a28b2aa83dbdfc45a99e1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z_1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o n\u00famero de dentes da engrenagem de entrada. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-f0a623c5e60ca8ad55847b5ae8b74589_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z_2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o n\u00famero de dentes da engrenagem de sa\u00edda. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-e263b7d8b237ebc903b5820b6c594a43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D_1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"21\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o di\u00e2metro da roda de entrada. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-c21fc78dd1af9a1401c06279b02a57cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D_2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"22\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o di\u00e2metro da roda de sa\u00edda.<\/span><\/li>\n<\/ul>\n<p> Finalmente, se desprezarmos as perdas de energia na transmiss\u00e3o do movimento circular, a rela\u00e7\u00e3o de transmiss\u00e3o tamb\u00e9m \u00e9 igual ao momento de entrada (M <sub>1<\/sub> ) dividido pelo momento de sa\u00edda (M <sub>2<\/sub> ).<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-9055659a3040d49efe7aa12f151d4412_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i=\\cfrac{\\omega_2}{\\omega_1}=\\cfrac{M_1}{M_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"101\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> Lembre-se que a rela\u00e7\u00e3o de transmiss\u00e3o \u00e9 um par\u00e2metro adimensional, ou seja, n\u00e3o possui unidade.<\/p>\n<p> Finalmente, da f\u00f3rmula da rela\u00e7\u00e3o de transmiss\u00e3o, podemos deduzir o seguinte:<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>i&gt;1<\/strong> : Se a rela\u00e7\u00e3o de transmiss\u00e3o for maior que 1, significa que a velocidade angular de sa\u00edda \u00e9 maior que a velocidade angular de entrada. Assim, o n\u00famero de dentes e o di\u00e2metro da engrenagem de sa\u00edda s\u00e3o menores que o n\u00famero de dentes e o di\u00e2metro da engrenagem de entrada.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>i&lt;1<\/strong> : se a rela\u00e7\u00e3o de transmiss\u00e3o for menor que 1, significa que a velocidade angular de sa\u00edda \u00e9 menor que a velocidade angular de entrada. Portanto, o n\u00famero de dentes e o di\u00e2metro da engrenagem de sa\u00edda s\u00e3o maiores que o n\u00famero de dentes e o di\u00e2metro da engrenagem de entrada.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>i=1<\/strong> : se a rela\u00e7\u00e3o de transmiss\u00e3o for igual a 1, isso implica que a velocidade angular de sa\u00edda \u00e9 equivalente \u00e0 velocidade angular de entrada. Assim, o n\u00famero de dentes e o di\u00e2metro das duas rodas s\u00e3o id\u00eanticos.<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Relacion-de-transmision-de-un-tren-de-engranajes\"><\/span> Rela\u00e7\u00e3o de transmiss\u00e3o de um trem de engrenagens<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Um <strong>trem de engrenagens<\/strong> \u00e9 um sistema composto por diversas engrenagens conectadas entre si. Em outras palavras, um trem de engrenagens \u00e9 composto por mais de duas rodas. <\/p>\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"300\" height=\"298\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/rapport-de-transmission-du-train-dengrenages.png\" alt=\"rela\u00e7\u00e3o de transmiss\u00e3o de um trem de engrenagens\" class=\"wp-image-6200\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/rapport-de-transmission-du-train-dengrenages.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/rapport-de-transmission-du-train-dengrenages-150x150.png 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\"><\/figure>\n<p> Assim, a rela\u00e7\u00e3o de transmiss\u00e3o total de um trem de engrenagens \u00e9 equivalente ao produto das rela\u00e7\u00f5es de transmiss\u00e3o entre os pares de engrenagens.<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-a919c875cac16b2c44617ebe1d201cdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle i_T=\\prod_{k=1}^n i_k=i_1\\cdot i_2\\cdot i_3\\cdot \\ldots \\cdot i_n\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"234\" style=\"vertical-align: -22px;\"><\/p>\n<\/p>\n<p> Da mesma forma, a rela\u00e7\u00e3o de transmiss\u00e3o geral de um trem de engrenagens pode ser calculada dividindo o n\u00famero de dentes das rodas motrizes pelo n\u00famero de dentes das rodas motrizes. A f\u00f3rmula para a rela\u00e7\u00e3o de transmiss\u00e3o para um trem de engrenagens \u00e9, portanto:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-7aeac32cc3b2fb4534bf73408a529981_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i_T=\\cfrac{\\displaystyle \\prod_{k=1}^n Z_{\\text{conductive}_k}}{\\displaystyle \\prod_{k=1}^n Z_{\\text{conducted}_k} }\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"158\" style=\"vertical-align: -49px;\"><\/p>\n<\/p>\n<p> Observe que as engrenagens intermedi\u00e1rias devem ser colocadas tanto no numerador quanto no denominador da f\u00f3rmula, porque s\u00e3o rodas motrizes e motrizes.<\/p>\n<p> Por exemplo, o c\u00e1lculo da rela\u00e7\u00e3o de transmiss\u00e3o do trem de engrenagens acima \u00e9 feito da seguinte forma: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-ddd72d8191a3cfa30c42e4fb98b29965_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i_T=\\cfrac{12\\cdot 12}{24\\cdot 18}=0,33\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"149\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicio-resuelto-de-la-relacion-de-transmision\"><\/span> Exerc\u00edcio resolvido sobre a rela\u00e7\u00e3o de transmiss\u00e3o<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li> Duas engrenagens com os seguintes n\u00fameros de dentes est\u00e3o conectadas: Z <sub>1<\/sub> =75 e Z <sub>2<\/sub> =25. Se a engrenagem de entrada girar a 340 rpm, qual ser\u00e1 a rela\u00e7\u00e3o de transmiss\u00e3o e a velocidade angular de sa\u00edda?<\/li>\n<\/ul>\n<p> Aplicando a f\u00f3rmula da rela\u00e7\u00e3o de transmiss\u00e3o, podemos calcular seu valor dividindo o n\u00famero de dentes de entrada pelo n\u00famero de dentes de sa\u00edda.<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-3000814b3ee6b543c2ed3a8c64d08e8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i=\\cfrac{Z_1}{Z_2}=\\cfrac{75}{25}=3\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"127\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> E uma vez que conhecemos a rela\u00e7\u00e3o de transmiss\u00e3o, tamb\u00e9m podemos encontrar a velocidade de rota\u00e7\u00e3o da roda de sa\u00edda usando a equa\u00e7\u00e3o da rela\u00e7\u00e3o de transmiss\u00e3o: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-95f6e8dfa91369c1a581c497f7f6ec9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i=\\cfrac{\\omega_2}{\\omega_1}\\quad \\longrightarrow\\quad \\omega_2=i\\cdot \\omega_1\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"203\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-ec3ce2abd22210fc87b6fd5679f6cb53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\omega_2=i\\cdot \\omega_1=3\\cdot 340=1020 \\rpm\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"212\" style=\"vertical-align: -3px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Neste artigo voc\u00ea aprender\u00e1 o que \u00e9 a rela\u00e7\u00e3o de transmiss\u00e3o, como a rela\u00e7\u00e3o de transmiss\u00e3o \u00e9 calculada e, al\u00e9m disso, um exerc\u00edcio resolvido de rela\u00e7\u00e3o de transmiss\u00e3o para entender completamente o conceito. O que \u00e9 rela\u00e7\u00e3o de transmiss\u00e3o? A rela\u00e7\u00e3o de transmiss\u00e3o \u00e9 a rela\u00e7\u00e3o entre as velocidades de rota\u00e7\u00e3o de duas engrenagens. Especificamente, &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/pt\/relacao-de-velocidade\/\"> <span class=\"screen-reader-text\">Rela\u00e7\u00e3o de transmiss\u00e3o<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[10],"tags":[],"class_list":["post-347","post","type-post","status-publish","format-standard","hentry","category-maquinas-e-mecanismos"],"yoast_head":"<!-- This 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