{"id":840,"date":"2026-10-03T20:31:11","date_gmt":"2026-10-03T19:31:11","guid":{"rendered":"https:\/\/wpcalc.com\/de\/feder-resonanzfrequenz-rechner\/"},"modified":"2026-10-03T20:31:11","modified_gmt":"2026-10-03T19:31:11","slug":"feder-resonanzfrequenz-rechner","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/de\/ingenieurwesen\/feder-resonanzfrequenz-rechner\/","title":{"rendered":"Resonanzfrequenz-Rechner f\u00fcr Federn mit Schubmodul"},"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\">Federresonanz-Sch\u00e4tzer mit Schubmodul<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"840\" data-favorite-title=\"Feder-Resonanzfrequenz mit Schubmodul\" data-favorite-url=\"https:\/\/wpcalc.com\/de\/ingenieurwesen\/feder-resonanzfrequenz-rechner\/\" data-favorite-excerpt=\"Dieser Rechner sch\u00e4tzt die Resonanzfrequenz einer Feder anhand geometrischer Parameter, der Materialdichte und des Schubmoduls (G). Er eignet sich ideal zur Bewertung der Dynamik von Schraubenfedern in Pr\u00e4zisionsmechanik, Fahrzeugtechnik und Schwingungssystemen.\" aria-label=\"Zu Favoriten hinzuf\u00fcgen\" data-favorite-icon=\"icon icon-electrical\">\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\/de\/ingenieurwesen\/feder-resonanzfrequenz-rechner\/\" method=\"POST\" class=\"calculator\" id=\"calculator-840\" data-post=\"840\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Eingabefelder<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Mittlerer Windungsdurchmesser<\/label><div class=\"term\">D<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"mittlerer_windungsdurchmesser\" id=\"field-1\" aria-describedby=\"calc-unit-1 calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.0001\" value=\"0.05\"\/><div class=\"unit\" id=\"calc-unit-1\">m<\/div><small id=\"calc-info-1\">Mittlerer Durchmesser der Windungen<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Drahtdurchmesser<\/label><div class=\"term\">d<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"drahtdurchmesser\" id=\"field-2\" aria-describedby=\"calc-unit-2 calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.0001\" value=\"0.002\"\/><div class=\"unit\" id=\"calc-unit-2\">m<\/div><small id=\"calc-info-2\">Durchmesser des Drahtes<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Anzahl der Windungen<\/label><div class=\"term\">n<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"anzahl_der_windungen\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1\" value=\"6\"\/><small id=\"calc-info-3\">Anzahl der aktiven Windungen<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Materialdichte<\/label><div class=\"term\">\u03c1<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"materialdichte\" id=\"field-4\" aria-describedby=\"calc-unit-4 calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1\" value=\"7850\"\/><div class=\"unit\" id=\"calc-unit-4\">kg\/m\u00b3<\/div><small id=\"calc-info-4\">Dichte des Federmaterials (z. B. 7850 f\u00fcr Stahl)<\/small><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-5\">Schubmodul<\/label><div class=\"term\">G<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"schubmodul\" id=\"field-5\" aria-describedby=\"calc-unit-5 calc-info-5\" step=\"any\" value=\"79000000000\"\/><div class=\"unit\" id=\"calc-unit-5\">Pa<\/div><small id=\"calc-info-5\">Schubmodul des Materials<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Neu berechnen\" id=\"calculate-button\" data-post=\"840\">Berechnen<\/button><button type=\"reset\">Zur\u00fccksetzen<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Automatisch berechnen<\/label><small>Wenn aktiviert, wird das Ergebnis automatisch aktualisiert, sobald Sie einen Wert \u00e4ndern.<\/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> Ihre Ergebnisse<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Resonanzfrequenz<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"Hz\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Ergebnis kopieren\" aria-label=\"Ergebnis kopieren\"><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\">Link zu dieser Berechnung kopieren<\/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>Kommentar schreiben<\/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=\"840\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Wie finden Sie dieses Ergebnis?<\/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\">Gef\u00e4llt mir <\/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\">Hilfreich <\/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\">Verwirrt <\/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\">Entt\u00e4uscht <\/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\">Ungenau <\/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<p><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>Federresonanzfrequenz mit Elastizit\u00e4ts- oder Schubmodul<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formel<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n$$f_{\\text{res}} = \\frac{d}{D^2} \\cdot \\sqrt{ \\frac{9 \\cdot G}{n \\cdot \\rho} }$$\n<\/div>\r\n\t<\/figure>\r\n\t<br \/>\n<strong>Dabei ist:<\/strong><\/p>\n<ul>\n<li>$$f_{\\text{res}}$$ = Resonanzfrequenz (Hz)  <\/li>\n<li>$$d$$ = Drahtdurchmesser (m)  <\/li>\n<li>$$D$$ = Windungsdurchmesser (m)  <\/li>\n<li>$$n$$ = Anzahl der wirksamen Windungen  <\/li>\n<li>$$\\rho$$ = Materialdichte (kg\/m\u00b3)  <\/li>\n<li>$$G$$ = Schubmodul (Pa)<\/li>\n<\/ul>\n<p>Diese Formel folgt aus der Dynamik von Feder-Masse-Systemen und der Materialelastizit\u00e4t unter der Annahme, dass keine D\u00e4mpfung vorhanden ist.<br \/>\r\n<\/section><br \/>\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>Federresonanzfrequenz mit Elastizit\u00e4tsmodul \u2013 Berechnungsbeispiel<\/h2><\/div>\r\n\r\n<\/p>\n<h3>Gegeben:<\/h3>\n<ul>\n<li>$$d$$ = 0,003 m  <\/li>\n<li>$$D$$ = 0,03 m  <\/li>\n<li>$$n$$ = 8  <\/li>\n<li>$$\\rho $$= 7850 kg\/m\u00b3 (Stahl)  <\/li>\n<li>$$G$$ = 79,3 \u00d7 10\u2079 Pa<\/li>\n<\/ul>\n<h3>Berechnung:<\/h3>\n<ol>\n<li>$$f_{\\text{res}} = \\frac{0.003}{0.03^2} \\cdot \\sqrt{ \\frac{9 \\cdot 79.3 \\cdot 10^9}{8 \\cdot 7850} }$$<\/li>\n<li>$$= \\frac{0.003}{0.0009} \\cdot \\sqrt{ \\frac{713.7 \\cdot 10^9}{62800} }$$<\/li>\n<li>$$\u2248 3.33 \\cdot \\sqrt{1136226.11} \u2248 3.33 \\cdot 1065.2 \u2248 3547~\\text{Hz}$$<\/li>\n<\/ol>\n<p>\n\r\n<\/section><br \/>\nDie Resonanzfrequenz einer Schraubenfeder l\u00e4sst sich anhand der Geometrie des Drahtes, der Dichte und des Schubmoduls genau modellieren. Dieser Rechner ist unverzichtbar f\u00fcr Ingenieure, die Federungssysteme, Schwingungsisolierungen und mechanische Resonatoren konstruieren, bei denen eine pr\u00e4zise Frequenzkontrolle erforderlich ist. Er erm\u00f6glicht es Konstrukteuren, zu untersuchen, wie sich \u00c4nderungen des Drahtdurchmessers, der Windungsanzahl oder des Materials auf das dynamische Verhalten auswirken.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dieser Rechner sch\u00e4tzt die Resonanzfrequenz einer Feder anhand geometrischer Parameter, der Materialdichte und des Schubmoduls (G). Er eignet sich ideal zur Bewertung der Dynamik von Schraubenfedern in Pr\u00e4zisionsmechanik, Fahrzeugtechnik und Schwingungssystemen.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[6],"tags":[35],"class_list":["post-840","post","type-post","status-publish","format-standard","hentry","category-ingenieurwesen","tag-elektrotechnik"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/de\/wp-json\/wp\/v2\/posts\/840","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/de\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/de\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/de\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/de\/wp-json\/wp\/v2\/comments?post=840"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/de\/wp-json\/wp\/v2\/posts\/840\/revisions"}],"predecessor-version":[{"id":4295,"href":"https:\/\/wpcalc.com\/de\/wp-json\/wp\/v2\/posts\/840\/revisions\/4295"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/de\/wp-json\/wp\/v2\/media?parent=840"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/de\/wp-json\/wp\/v2\/categories?post=840"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/de\/wp-json\/wp\/v2\/tags?post=840"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}