{"id":4062,"date":"2026-10-15T02:19:47","date_gmt":"2026-10-15T01:19:47","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/muhendislik\/mil-burulmasi\/"},"modified":"2026-10-15T02:19:47","modified_gmt":"2026-10-15T01:19:47","slug":"mil-burulmasi","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/muhendislik\/mil-burulmasi\/","title":{"rendered":"Mil burulmas\u0131"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Dairesel bir milin kayma gerilmesini ve burulma a\u00e7\u0131s\u0131n\u0131 kontrol edin<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"4062\" data-favorite-title=\"Mil burulmas\u0131\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/muhendislik\/mil-burulmasi\/\" data-favorite-excerpt=\"Dolu veya i\u00e7i bo\u015f dairesel bir milda en b\u00fcy\u00fck kayma gerilmesini ve burulma a\u00e7\u0131s\u0131n\u0131 hesaplay\u0131n. Torku, boyutlar\u0131, uzunlu\u011fu ve kayma mod\u00fcl\u00fcn\u00fc girin; mil tasar\u0131m\u0131n\u0131z\u0131 saniyeler i\u00e7inde denetleyin.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-civil\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/muhendislik\/mil-burulmasi\/\" method=\"POST\" class=\"calculator\" id=\"calculator-4062\" data-post=\"4062\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"is-single field\" id=\"input-1\"><span class=\"font-semibold\">Y\u00fckleme<\/span><\/div><div class=\"field is-single has-term\" id=\"input-2\"><label for=\"field-2\">Uygulanan tork (T)<\/label><div class=\"term\">T<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"uygulanan_tork_t\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1000\" min=\"0\" value=\"1000\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"birim\" aria-label=\"Birim\"><option value=\"nm\" selected>N\u00b7m<\/option><option value=\"knm\">kN\u00b7m<\/option><option value=\"lbft\">lb\u00b7ft<\/option><option value=\"lbin\">lb\u00b7in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-2\">Mil taraf\u0131ndan iletilen sabit tork.<\/small><\/div><div class=\"is-single field\" id=\"input-3\"><span class=\"font-semibold\">Mil geometrisi<\/span><\/div><div class=\"field is-single\" id=\"input-4\"><label for=\"field-5\">Mil t\u00fcr\u00fc<\/label><div class=\"grid grid-cols-1\"><select id=\"field-5\" name=\"mil_tr\"><option value=\"solid\" selected>Dolu dairesel mil<\/option><option value=\"hollow\">\u0130\u00e7i bo\u015f dairesel mil (boru)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field is-single has-term\" id=\"input-5\"><label for=\"field-6\">D\u0131\u015f \u00e7ap (D)<\/label><div class=\"term\">D<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"d_ap_d\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 40\" min=\"0\" value=\"40\"\/><div class=\"grid grid-cols-1\"><select id=\"field-7\" name=\"birim\" aria-label=\"Birim\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><option value=\"ft\">ft<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-6\">Mil kesitinin d\u0131\u015f \u00e7ap\u0131.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-6\" hidden><label for=\"field-8\">\u0130\u00e7 \u00e7ap (d)<\/label><div class=\"term\">d<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"_ap_d\" id=\"field-8\" aria-describedby=\"calc-info-8\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 20\" min=\"0\" value=\"20\"\/><div class=\"grid grid-cols-1\"><select id=\"field-9\" name=\"birim\" aria-label=\"Birim\"><option value=\"mm\" selected>mm<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><option value=\"ft\">ft<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-8\">Yaln\u0131zca i\u00e7i bo\u015f mil i\u00e7in: delik \u00e7ap\u0131. D\u0131\u015f \u00e7aptan k\u00fc\u00e7\u00fck olmal\u0131d\u0131r.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-7\"><label for=\"field-10\">Mil boyu (L)<\/label><div class=\"term\">L<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"mil_boyu_l\" id=\"field-10\" aria-describedby=\"calc-info-10\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1\" min=\"0\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-11\" name=\"birim\" aria-label=\"Birim\"><option value=\"m\" selected>m<\/option><option value=\"cm\">cm<\/option><option value=\"mm\">mm<\/option><option value=\"ft\">ft<\/option><option value=\"in\">in<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-10\">Torkun uyguland\u0131\u011f\u0131 nokta ile sabit u\u00e7 aras\u0131ndaki mil uzunlu\u011fu.<\/small><\/div><div class=\"is-single field\" id=\"input-8\"><span class=\"font-semibold\">Malzeme<\/span><\/div><div class=\"field is-single has-term\" id=\"input-9\"><label for=\"field-13\">Kayma mod\u00fcl\u00fc (G)<\/label><div class=\"term\">G<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"kayma_modl_g\" id=\"field-13\" aria-describedby=\"calc-info-13\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 80\" min=\"0\" value=\"80\"\/><div class=\"grid grid-cols-1\"><select id=\"field-14\" name=\"birim\" aria-label=\"Birim\"><option value=\"gpa\" selected>GPa<\/option><option value=\"mpa\">MPa<\/option><option value=\"psi\">psi<\/option><option value=\"ksi\">ksi<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-13\">Mil malzemesinin kayma mod\u00fcl\u00fc. Tipik de\u011ferler: \u00e7elik \u2248 80 GPa (11,6\u00b710\u2076 psi), al\u00fcminyum \u2248 27 GPa, bak\u0131r \u2248 45 GPa.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"4062\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Burulma sonu\u00e7lar\u0131<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>En b\u00fcy\u00fck kayma gerilmesi (\u03c4max)<\/span><span class=\"result-term\">\u03c4max<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-2\"><span class=\"field-title\"><span>Burulma a\u00e7\u0131s\u0131 (\u03c6)<\/span><span class=\"result-term\">\u03c6<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"4062\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Mil burulmas\u0131 form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ J = \\frac{\\pi D^4}{32} \\quad (\\text{dolu}) \\qquad J = \\frac{\\pi (D^4 - d^4)}{32} \\quad (\\text{bo\u015f}) \\]\n\\[ \\tau_{max} = \\frac{T \\cdot c}{J}, \\quad c = \\frac{D}{2} \\qquad \\varphi = \\frac{T \\cdot L}{J \\cdot G} \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(T\\) \u2014 uygulanan tork (N\u00b7m)<\/li>\n<li>\\(D\\) \u2014 milin d\u0131\u015f \u00e7ap\u0131 (m)<\/li>\n<li>\\(d\\) \u2014 i\u00e7i bo\u015f milde i\u00e7 (g\u00f6bek) \u00e7ap\u0131 (m)<\/li>\n<li>\\(c\\) \u2014 merkezden d\u0131\u015f y\u00fczeye olan uzakl\u0131k (m)<\/li>\n<li>\\(J\\) \u2014 kesitin polar atalet momenti (m\u2074)<\/li>\n<li>\\(G\\) \u2014 malzemenin kayma mod\u00fcl\u00fc (Pa)<\/li>\n<li>\\(L\\) \u2014 torkun uyguland\u0131\u011f\u0131 kesitten sabit uca kadar olan mil uzunlu\u011fu (m)<\/li>\n<li>\\(\\tau_{max}\\) \u2014 d\u0131\u015f y\u00fczeydeki en b\u00fcy\u00fck kayma gerilmesi (Pa)<\/li>\n<li>\\(\\varphi\\) \u2014 \\(L\\) uzunlu\u011fu boyunca burulma a\u00e7\u0131s\u0131 (rad)<\/li>\n<\/ul>\n<p>\u0130lk iki ifade dairesel bir milin burulmas\u0131n\u0131 tan\u0131mlar: kayma gerilmesi merkezde s\u0131f\u0131rdan ba\u015flay\u0131p d\u0131\u015f y\u00fczeye do\u011fru do\u011frusal olarak artar ve en b\u00fcy\u00fck de\u011fere d\u0131\u015f y\u00fczeyde ula\u015f\u0131r; mil ise torkla ve uzunlukla orant\u0131l\u0131, burulma rijitli\u011fi \\(JG\\) ile ters orant\u0131l\u0131 bir a\u00e7\u0131yla burulur.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Mil burulmas\u0131 \u2013 hesaplama \u00f6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> \u00e7ap\u0131 \\(D = 40\\) mm ve uzunlu\u011fu \\(L = 1\\) m olan dolu bir \u00e7elik mil, \\(T = 1000\\) N\u00b7m sabit bir tork iletiyor. \u00c7eli\u011fin kayma mod\u00fcl\u00fc \\(G = 80\\) GPa'd\u0131r.<\/p>\n<p>\\[ J = \\frac{\\pi (0.04)^4}{32} = 2.513 \\times 10^{-7}\\ \\text{m}^4 \\]<\/p>\n<p>\\[ \\tau_{max} = \\frac{1000 \\times 0.02}{2.513 \\times 10^{-7}} = 79.6 \\times 10^6\\ \\text{Pa} \\approx 79.6\\ \\text{MPa} \\]<\/p>\n<p>\\[ \\varphi = \\frac{1000 \\times 1}{2.513 \\times 10^{-7} \\times 80 \\times 10^9} = 0.04974\\ \\text{rad} \\approx 2.85^\\circ \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> en b\u00fcy\u00fck kayma gerilmesi d\u0131\u015f y\u00fczeyde yakla\u015f\u0131k 79,6 MPa (\u2248 11,5 ksi), mil ise 1 m'lik uzunlu\u011fu boyunca yakla\u015f\u0131k 2,85\u00b0 (0,0497 rad) buruluyor \u2014 yani metre ba\u015f\u0131na yakla\u015f\u0131k 2,85\u00b0.<\/p>\n<p>\n\r\n<\/section>\n<h2>Mil burulmas\u0131 hesaplama arac\u0131 nas\u0131l kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li><strong>Uygulanan torku (T)<\/strong> girin ve birimini se\u00e7in \u2014 N\u00b7m, kN\u00b7m, lb\u00b7ft veya lb\u00b7in.<\/li>\n<li><strong>Mil tipini<\/strong> se\u00e7in: dolu dairesel mil veya i\u00e7i bo\u015f dairesel mil (boru). \u0130\u00e7i bo\u015f mil i\u00e7in ayr\u0131ca, d\u0131\u015f \u00e7aptan k\u00fc\u00e7\u00fck olmas\u0131 gereken <strong>i\u00e7 \u00e7ap\u0131 (d)<\/strong> girin.<\/li>\n<li><strong>D\u0131\u015f \u00e7ap\u0131 (D)<\/strong> ve <strong>mil uzunlu\u011funu (L)<\/strong> birimleriyle birlikte girin (mm, cm, m, in veya ft).<\/li>\n<li>Malzemenin <strong>kayma mod\u00fcl\u00fcn\u00fc (G)<\/strong> girin \u2014 \u00e7elik i\u00e7in \u2248 80 GPa, al\u00fcminyum i\u00e7in \u2248 27 GPa, bak\u0131r i\u00e7in \u2248 45 GPa \u2014 ve birimi se\u00e7in (GPa, MPa, psi veya ksi).<\/li>\n<li>Sonu\u00e7lar\u0131 okuyun: MPa, ksi ve psi cinsinden <strong>en b\u00fcy\u00fck kayma gerilmesi (\u03c4max)<\/strong> ile derece, radyan, metre ba\u015f\u0131na derece ve fit ba\u015f\u0131na derece cinsinden <strong>burulma a\u00e7\u0131s\u0131 (\u03c6)<\/strong>.<\/li>\n<\/ol>\n<h2>Mil burulmas\u0131 nedir?<\/h2>\n<p>Milin ekseni boyunca bir tork uyguland\u0131\u011f\u0131nda \u2014 bu, her aktar\u0131m milinde, tahrik hatt\u0131nda, sondaj borusunda ve pervane milinde ya\u015fan\u0131r \u2014 malzeme burulur. Her kesit, kom\u015fu kesite g\u00f6re d\u00f6ner ve bu d\u00f6n\u00fc\u015f\u00fc, kesit \u00fczerine da\u011f\u0131lm\u0131\u015f kayma gerilmeleri kar\u015f\u0131lar. Dairesel millerde (dolu veya merkezli g\u00f6bek delikli) analiz kesindir ve basittir: kayma gerilmesi merkezde s\u0131f\u0131rdan d\u0131\u015f y\u00fczeyde en b\u00fcy\u00fck de\u011fere do\u011frusal olarak de\u011fi\u015fir; millerin ve borular\u0131n bu y\u00fczden ilk olarak d\u0131\u015f y\u00fczeylerinde hasar g\u00f6rd\u00fc\u011f\u00fcn\u00fc veya akt\u0131\u011f\u0131n\u0131 bilmek gerekir.<\/p>\n<p>Burulma denetiminde iki b\u00fcy\u00fckl\u00fck \u00f6nem ta\u015f\u0131r. \u0130lki <strong>en b\u00fcy\u00fck kayma gerilmesidir<\/strong>, \\(\\tau_{max} = Tc\/J\\): bu de\u011fer malzemenin izin verilen kayma gerilmesinin alt\u0131nda kalmal\u0131d\u0131r. S\u00fcnek \u00e7eliklerde kayma alt\u0131ndaki akma dayan\u0131m\u0131, \u00e7ekme akma dayan\u0131m\u0131n\u0131n yakla\u015f\u0131k 0,5\u20130,6 kat\u0131d\u0131r ve \u00fczerine uygun bir emniyet katsay\u0131s\u0131 uygulan\u0131r. \u0130kincisi <strong>burulma a\u00e7\u0131s\u0131d\u0131r<\/strong>, \\(\\varphi = TL\/JG\\): yeterince g\u00fc\u00e7l\u00fc bir mil bile fazla burulabilir; bu da hizas\u0131zl\u0131k, titre\u015fim, kumanda sistemlerinde toplanan burulma veya hassas tahriklerde konum hatas\u0131 yarat\u0131r.<\/p>\n<p>Geometri terimi \\(J\\), yani polar atalet momenti, \u00e7ap\u0131n d\u00f6rd\u00fcnc\u00fc kuvvetiyle \u00f6l\u00e7eklenir. Dolu bir milin \u00e7ap\u0131 iki kat\u0131na \u00e7\u0131kar\u0131l\u0131rsa hem gerilme hem burulma 16 kat azal\u0131r. \u0130\u00e7i bo\u015f millerin bu kadar etkili olmas\u0131n\u0131n nedeni budur: merkez yak\u0131n\u0131nda az gerilmeli malzemeyi kald\u0131rmak rijitlikten \u00e7ok az kaybettirir ama a\u011f\u0131rl\u0131kta b\u00fcy\u00fck tasarruf sa\u011flar; tahrik millerinin, merdane millerinin ve bir\u00e7ok havac\u0131l\u0131k par\u00e7as\u0131n\u0131n boru bi\u00e7iminde olmas\u0131n\u0131n nedeni de budur.<\/p>\n<p>Sonucu yorumlarken \\(\\tau_{max}\\) de\u011ferini malzemenin izin verilen kayma gerilmesiyle, \\(\\varphi\\) de\u011ferini de kendi burulma s\u0131n\u0131r\u0131n\u0131zla kar\u015f\u0131la\u015ft\u0131r\u0131n. Geleneksel bir pratik kural olarak makine millerinde 20 \u00e7ap uzunlukta yakla\u015f\u0131k 1\u00b0 burulmaya izin verilir; hassas ve uzun hat millerinde ise genellikle \u00e7ok daha s\u0131k\u0131 s\u0131n\u0131rlar gerekir.<\/p>\n<h2>Varsay\u0131mlar, s\u0131n\u0131rlamalar ve pratik ipu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>Yaln\u0131zca dairesel kesitler.<\/strong> Form\u00fcller, dolu veya merkezli g\u00f6bek delikli i\u00e7i bo\u015f dairesel miller i\u00e7in kesindir. Dairesel olmayan kesitler (dikd\u00f6rtgen \u00e7ubuklar, kama yuvalar\u0131, oluklu [spline] miller) \u00e7ok farkl\u0131 bi\u00e7imde burulur ve ayr\u0131 y\u00f6ntemler gerektirir.<\/li>\n<li><strong>De\u011fi\u015fmeyen kesit, sabit tork.<\/strong> Hesaplama; sabit bir kesiti, tek bir malzemeyi ve uzunluk boyunca de\u011fi\u015fmeyen bir torku varsayar. Kademesi olan miller veya birden fazla tork s\u00f6z konusuysa her par\u00e7ay\u0131 ayr\u0131 hesaplay\u0131p burulma a\u00e7\u0131klar\u0131n\u0131 toplay\u0131n.<\/li>\n<li><strong>Do\u011frusal elastik davran\u0131\u015f.<\/strong> Gerilmelerin elastik s\u0131n\u0131r\u0131n alt\u0131nda kalmas\u0131 gerekir; sonu\u00e7 akma veya plastik \u00e7\u00f6kmeyi \u00f6ng\u00f6rmez.<\/li>\n<li><strong>Kama yuvalar\u0131, delikler ve omuzlar<\/strong> gerilmeyi yo\u011funla\u015ft\u0131r\u0131r. Kama yuvas\u0131 veya omuz bulunan ger\u00e7ek bir milde yerel gerilmeler ad\u00ee de\u011ferin 1,5\u20133 kat\u0131na \u00e7\u0131kabilir; bu nedenle kritik tasar\u0131mlarda gerilme yo\u011funla\u015ft\u0131rma katsay\u0131lar\u0131n\u0131 hesaba kat\u0131n.<\/li>\n<li><strong>Her iki \u00f6l\u00e7\u00fct\u00fc de denetleyin.<\/strong> K\u0131sa ve kal\u0131n bir mil genellikle gerilmeyle, uzun ve ince bir mil ise \u00e7o\u011fu kez burulmayla s\u0131n\u0131rlan\u0131r. Ayr\u0131ca uzun bir milin burkulma veya savrulma (whirling) sonucu da bozulabilece\u011fini unutmay\u0131n \u2014 ilgili bir denetim i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/muhendislik\/euler-burkulma-yuku\/\">Euler burkulma y\u00fck\u00fc hesaplama arac\u0131m\u0131za<\/a> bakabilirsiniz.<\/li>\n<li>E\u011filme y\u00fckleri de ta\u015f\u0131yan millerde (di\u015fli \u00e7arklar, kay\u0131\u015flar, kasnaklar) kiri\u015f analizinden elde edilen e\u011filme gerilmelerini ekleyin \u2014 <a href=\"https:\/\/wpcalc.com\/en\/engineering\/simply-supported-beam-with-center-point-load\/\">ortas\u0131ndan tek kuvvet alan basit mesnetli kiri\u015f<\/a> ve <a href=\"https:\/\/wpcalc.com\/en\/engineering\/simply-supported-beam-with-uniform-load\/\">e\u015fit yay\u0131l\u0131 y\u00fck alt\u0131ndaki kiri\u015f<\/a> hesaplama ara\u00e7lar\u0131m\u0131za bakabilirsiniz.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Dolu veya i\u00e7i bo\u015f dairesel bir milda en b\u00fcy\u00fck kayma gerilmesini ve burulma a\u00e7\u0131s\u0131n\u0131 hesaplay\u0131n. Torku, boyutlar\u0131, uzunlu\u011fu ve kayma mod\u00fcl\u00fcn\u00fc girin; mil tasar\u0131m\u0131n\u0131z\u0131 saniyeler i\u00e7inde denetleyin.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[6],"tags":[84],"class_list":["post-4062","post","type-post","status-publish","format-standard","hentry","category-muhendislik","tag-kirisler"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4062","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=4062"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4062\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=4062"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=4062"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=4062"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}