{"id":100099,"date":"2026-02-15T20:16:35","date_gmt":"2026-02-15T20:16:35","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100099"},"modified":"2026-02-15T20:16:35","modified_gmt":"2026-02-15T20:16:35","slug":"flexible-coupling-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bn\/calculators\/flexible-coupling-calculator\/","title":{"rendered":"\u09a8\u09ae\u09a8\u09c0\u09af\u09bc \u09af\u09c1\u0997\u09b2 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0 | DIN 740 | \u09ac\u09bf\u09a8\u09be\u09ae\u09c2\u09b2\u09cd\u09af\u09c7 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09b8\u09b0\u099e\u09cd\u099c\u09be\u09ae"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Flexible Coupling Calculator\",\"alternateName\":[\"DIN 740 Coupling Calculator\",\"Coupling Selection Calculator\",\"Elastic Coupling Calculator\"],\"description\":\"Free online DIN 740 flexible coupling calculator. Enter power, speed, service factor, and coupling type to calculate required torque rating, torsional stiffness, and natural frequency.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/flexible-coupling-calculator\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2024-01-01\",\"dateModified\":\"2025-02-14\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true,\"featureList\":[\"DIN 740 compliant\",\"Service factor selection\",\"Multiple coupling types\",\"Natural frequency calculation\",\"Torsional stiffness\",\"Auto-calculation on input change\"],\"keywords\":\"flexible coupling, DIN 740, coupling torque, torsional stiffness, natural frequency\"}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"What is a flexible coupling and why use one?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"A flexible coupling connects two shafts while accommodating misalignment (angular, parallel, axial) and damping vibrations. They protect connected equipment from shock loads and torsional vibration, extending bearing and seal life.\"}},\n{\"@type\":\"Question\",\"name\":\"How do I select the right service factor?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Service factors account for load characteristics. Uniform loads (fans, pumps) use 1.0-1.5. Moderate shock (compressors, mixers) use 1.5-2.0. Heavy shock (crushers, presses) use 2.0-3.0 or higher. Always check manufacturer catalogs for specific applications.\"}},\n{\"@type\":\"Question\",\"name\":\"What is torsional stiffness in a coupling?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Torsional stiffness (Ct) is the torque required per unit angle of twist, measured in Nm\/rad. Higher stiffness means more accurate motion transmission but less vibration damping. DIN 740 defines dynamic and static stiffness values.\"}},\n{\"@type\":\"Question\",\"name\":\"Why is natural frequency important for coupling selection?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"The torsional natural frequency of the coupling-shaft system must be separated from excitation frequencies (typically shaft speed and its multiples) by at least 20%. Resonance causes excessive vibration and coupling failure.\"}},\n{\"@type\":\"Question\",\"name\":\"What is DIN 740 and how does it apply to couplings?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"DIN 740 is a German standard for flexible shaft couplings. 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font-size:13px; color:var(--vc-ink-muted); }\n.vc-footer a { color:var(--vc-accent); text-decoration:none; }\n.vc-footer a:hover { text-decoration:underline; }\n.vc-footer-links { margin-top:8px; font-size:12px; }\n.vc-footer-links a { margin:0 8px; }\n\n\/* \u2500\u2500 PRINT \u2500\u2500 *\/\n@media print {\n    .vc-section-body { max-height:none!important; }\n    .vc-faq-a { max-height:none!important; }\n    .vc-results { max-height:none!important; padding:24px!important; }\n    .vc-copy-btn, .vc-section-chevron, .vc-faq-chevron, .vc-presets, .vc-promo { display:none!important; }\n}\n<\/style>\n\n<div class=\"vc-calculator\" id=\"vc-flexible-coupling\">\n\n<!-- Header -->\n<header class=\"vc-header\">\n    <p class=\"vc-header-eyebrow\">Free Engineering Tool #081<\/p>\n    <h1 class=\"vc-header-title\">Flexible Coupling Calculator<\/h1>\n    <p class=\"vc-header-subtitle\">Calculate the required torque rating, torsional stiffness, and natural frequency for flexible couplings per DIN 740. Select coupling type and enter operating conditions.<\/p>\n    <div class=\"vc-badges\">\n        <span class=\"vc-badge\">DIN 740<\/span>\n        <span class=\"vc-badge\">Coupling Selection<\/span>\n        <span class=\"vc-badge\">Torsional Analysis<\/span>\n    <\/div>\n<\/header>\n\n<!-- Calculator Card -->\n<div class=\"vc-card\">\n    <form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\">\n        <div class=\"vc-form-grid\">\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-power\">Power <span class=\"vc-label-hint\">(kW)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-power\" inputmode=\"decimal\" step=\"any\" min=\"0.01\" placeholder=\"e.g. 15\" value=\"15\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-speed\">Speed <span class=\"vc-label-hint\">(RPM)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-speed\" inputmode=\"decimal\" step=\"any\" min=\"1\" placeholder=\"e.g. 1500\" value=\"1500\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-sf\">Service Factor <span class=\"vc-label-hint\">(K<sub>A<\/sub>)<\/span><\/label>\n                <select class=\"vc-select\" id=\"vc-sf\">\n                    <option value=\"1.0\">1.0 \u2014 Uniform load (fans, pumps)<\/option>\n                    <option value=\"1.25\">1.25 \u2014 Light shocks (conveyors)<\/option>\n                    <option value=\"1.5\" selected>1.5 \u2014 Moderate shocks (compressors)<\/option>\n                    <option value=\"1.75\">1.75 \u2014 Heavy shocks (mixers, mills)<\/option>\n                    <option value=\"2.0\">2.0 \u2014 Extreme shocks (crushers)<\/option>\n                    <option value=\"2.5\">2.5 \u2014 Severe reversing loads<\/option>\n                    <option value=\"3.0\">3.0 \u2014 Presses, shears<\/option>\n                <\/select>\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-type\">Coupling Type<\/label>\n                <select class=\"vc-select\" id=\"vc-type\">\n                    <option value=\"jaw\" data-ct=\"12000\" data-j=\"0.005\" selected>Jaw coupling (elastomer insert)<\/option>\n                    <option value=\"tyre\" data-ct=\"5000\" data-j=\"0.012\">Tyre coupling (rubber element)<\/option>\n                    <option value=\"disc\" data-ct=\"50000\" data-j=\"0.003\">Disc coupling (metallic flex)<\/option>\n                    <option value=\"grid\" data-ct=\"25000\" data-j=\"0.008\">Grid coupling (spring grid)<\/option>\n                    <option value=\"pin\" data-ct=\"8000\" data-j=\"0.006\">Pin &amp; bush coupling<\/option>\n                <\/select>\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-j1\">Inertia \u2014 Drive Side <span class=\"vc-label-hint\">(kg\u00b7m\u00b2)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-j1\" inputmode=\"decimal\" step=\"any\" min=\"0.0001\" placeholder=\"e.g. 0.5\" value=\"0.5\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-j2\">Inertia \u2014 Driven Side <span class=\"vc-label-hint\">(kg\u00b7m\u00b2)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-j2\" inputmode=\"decimal\" step=\"any\" min=\"0.0001\" placeholder=\"e.g. 1.2\" value=\"1.2\">\n            <\/div>\n        <\/div>\n\n        <!-- Presets -->\n        <div class=\"vc-presets\">\n            <div class=\"vc-presets-label\">Quick presets<\/div>\n            <button type=\"button\" class=\"vc-preset-btn\" data-p=\"7.5\" data-s=\"1500\" data-sf=\"1.5\" data-t=\"jaw\" data-j1=\"0.2\" data-j2=\"0.5\">Pump 7.5 kW<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-p=\"15\" data-s=\"1500\" data-sf=\"1.5\" data-t=\"jaw\" data-j1=\"0.5\" data-j2=\"1.2\">Compressor 15 kW<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-p=\"55\" data-s=\"1000\" data-sf=\"1.75\" data-t=\"grid\" data-j1=\"2.0\" data-j2=\"5.0\">Mixer 55 kW<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-p=\"110\" data-s=\"1500\" data-sf=\"2.0\" data-t=\"disc\" data-j1=\"3.0\" data-j2=\"8.0\">Crusher 110 kW<\/button>\n        <\/div>\n    <\/form>\n\n    <!-- Results -->\n    <div class=\"vc-results\" id=\"vc-results\">\n        <div class=\"vc-results-head\">\n            <h2 class=\"vc-results-title\">Results<\/h2>\n            <button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">\n                <svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg>\n                Copy\n            <\/button>\n        <\/div>\n        <div class=\"vc-result-grid\">\n            <div class=\"vc-rcard vc-rcard-primary\">\n                <div class=\"vc-rcard-label\">Required Coupling Torque Rating<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-treq\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Nominal Torque (T<sub>n<\/sub>)<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-tnom\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Torsional Stiffness (C<sub>t<\/sub>)<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-stiff\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Natural Frequency (f<sub>n<\/sub>)<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-freq\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Operating Frequency<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-fop\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Frequency Ratio (f<sub>n<\/sub>\/f<sub>op<\/sub>)<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-ratio\">\u2014<\/div>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- Theory & Reference -->\n<div class=\"vc-section vc-open\" id=\"vc-sec-theory\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\">\n        <span class=\"vc-section-toggle-text\">\n            <span class=\"vc-section-icon\">\ud83d\udcd8<\/span>\n            <span class=\"vc-section-title\">Theory &amp; Formulas<\/span>\n        <\/span>\n        <svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg>\n    <\/button>\n    <div class=\"vc-section-body\">\n        <div class=\"vc-section-inner vc-theory\">\n            <h3>Nominal Torque<\/h3>\n            <p>The nominal torque transmitted by the coupling is derived from power and speed:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n            <ul>\n                <li><strong>P<\/strong> \u2014 transmitted power (kW)<\/li>\n                <li><strong>n<\/strong> \u2014 rotational speed (RPM)<\/li>\n                <li><strong>T<sub>n<\/sub><\/strong> \u2014 nominal torque (N\u00b7m)<\/li>\n            <\/ul>\n\n            <h3>Required Torque Rating<\/h3>\n            <p>Per DIN 740, the coupling must be rated for the design torque including the service factor:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n            <p>Where <strong>K<sub>A<\/sub><\/strong> is the application\/service factor accounting for dynamic loads.<\/p>\n\n            <h3>Torsional Natural Frequency<\/h3>\n            <p>For a two-inertia system connected by the coupling:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-3\"><\/div>\n            <ul>\n                <li><strong>C<sub>t<\/sub><\/strong> \u2014 dynamic torsional stiffness of coupling (N\u00b7m\/rad)<\/li>\n                <li><strong>J<sub>1<\/sub>, J<sub>2<\/sub><\/strong> \u2014 mass moments of inertia (kg\u00b7m\u00b2)<\/li>\n            <\/ul>\n\n            <h3>Service Factor Guide<\/h3>\n            <table class=\"vc-table\">\n                <thead><tr><th>K<sub>A<\/sub><\/th><th>Load Character<\/th><th>Typical Applications<\/th><\/tr><\/thead>\n                <tbody>\n                    <tr><td>1.0<\/td><td>Uniform<\/td><td>Fans, centrifugal pumps, light conveyors<\/td><\/tr>\n                    <tr><td>1.25<\/td><td>Light shocks<\/td><td>Belt conveyors, generators, centrifugal blowers<\/td><\/tr>\n                    <tr><td>1.5<\/td><td>Moderate shocks<\/td><td>Reciprocating compressors, positive displacement pumps<\/td><\/tr>\n                    <tr><td>1.75<\/td><td>Heavy shocks<\/td><td>Mixers, ball mills, rubber extruders<\/td><\/tr>\n                    <tr><td>2.0\u20133.0<\/td><td>Extreme\/Reversing<\/td><td>Crushers, presses, shears, rolling mills<\/td><\/tr>\n                <\/tbody>\n            <\/table>\n\n            <div class=\"vc-warning-box\">\n                <p style=\"margin:0;font-size:14px;color:var(--vc-ink-secondary);\"><strong>\u26a0\ufe0f Note:<\/strong> The natural frequency should be at least 20% away from the operating frequency and its harmonics to avoid torsional resonance. DIN 740-2 recommends f<sub>n<\/sub>\/f<sub>op<\/sub> &gt; 1.2 or f<sub>n<\/sub>\/f<sub>op<\/sub> &lt; 0.8.<\/p>\n            <\/div>\n\n            <div class=\"vc-example-box\">\n                <div class=\"vc-example-title\">Example \u2014 15 kW Compressor Drive<\/div>\n                <p><strong>Given:<\/strong> P = 15 kW, n = 1500 RPM, K<sub>A<\/sub> = 1.5<\/p>\n                <p>T<sub>n<\/sub> = 9549 \u00d7 15 \/ 1500 = <strong>95.5 N\u00b7m<\/strong><\/p>\n                <p>T<sub>req<\/sub> = 1.5 \u00d7 95.5 = <strong>143.2 N\u00b7m<\/strong><\/p>\n                <p>Select a coupling with T<sub>max<\/sub> \u2265 143.2 N\u00b7m<\/p>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- Related Calculators -->\n<div class=\"vc-section\" id=\"vc-sec-related\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\">\n        <span class=\"vc-section-toggle-text\">\n            <span class=\"vc-section-icon\">\ud83d\udd17<\/span>\n            <span class=\"vc-section-title\">Related Calculators<\/span>\n        <\/span>\n        <svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg>\n    <\/button>\n    <div class=\"vc-section-body\">\n        <div class=\"vc-section-inner\">\n            <div class=\"vc-related\">\n                <a class=\"vc-related-link\" href=\"\/calculators\/coupling-torque-calculator\/\">Coupling Torque Calculator<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/gear-ratio-calculator\/\">Gear Ratio Calculator<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/belt-drive-calculator\/\">Belt Drive Calculator<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/drive-efficiency-calculator\/\">Drive Efficiency Calculator<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/brake-torque-calculator\/\">Brake Torque Calculator<\/a>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- FAQ -->\n<div class=\"vc-section\" id=\"vc-sec-faq\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\">\n        <span class=\"vc-section-toggle-text\">\n            <span class=\"vc-section-icon\">\u2753<\/span>\n            <span class=\"vc-section-title\">Frequently Asked Questions<\/span>\n        <\/span>\n        <svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg>\n    <\/button>\n    <div class=\"vc-section-body\">\n        <div class=\"vc-section-inner\">\n            <div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- Promo -->\n<div class=\"vc-promo\">\n    <div class=\"vc-promo-text\">\n        <strong>Vibromera \u2014 Portable Balancing &amp; Vibration Analysis<\/strong><br>\n        Professional field balancing instruments and software. 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Last updated: February 2025<\/p>\n    <div class=\"vc-footer-links\">\n        <a href=\"\/calculators\/engineering-calculators\/\">All Calculators<\/a>\n        <a href=\"https:\/\/vibromera.eu\/contacts\/\">Contact<\/a>\n    <\/div>\n<\/footer>\n\n<\/div>\n\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.js\"><\/script>\n<script>\n(function() {\n    'use strict';\n\n    var SLUG = 'flexible-coupling-calculator';\n\n    function $(id) { return document.getElementById(id); }\n    function fmt(n, d) { if(isNaN(n)||!isFinite(n)) return '\u2014'; var f=n.toFixed(d===undefined?2:d); return f.replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,''); }\n\n    \/* \u2500\u2500 CALCULATION \u2500\u2500 *\/\n    function calculate() {\n        var P = parseFloat($('vc-power').value);\n        var n = parseFloat($('vc-speed').value);\n        var KA = parseFloat($('vc-sf').value);\n        var J1 = parseFloat($('vc-j1').value);\n        var J2 = parseFloat($('vc-j2').value);\n        var typeEl = $('vc-type');\n        var opt = typeEl.options[typeEl.selectedIndex];\n        var Ct = parseFloat(opt.getAttribute('data-ct'));\n\n        if (!P || P <= 0 || !n || n <= 0) {\n            $('vc-results').classList.remove('vc-visible');\n            return;\n        }\n\n        var Tn = 9549 * P \/ n; \/\/ N\u00b7m\n        var Treq = KA * Tn;\n\n        \/\/ Natural frequency\n        var fn = 0;\n        var fop = n \/ 60;\n        if (J1 > 0 && J2 > 0 && Ct > 0) {\n            var Jred = (J1 * J2) \/ (J1 + J2);\n            fn = (1 \/ (2 * Math.PI)) * Math.sqrt(Ct \/ Jred);\n        }\n\n        var ratio = fn > 0 ? fn \/ fop : 0;\n\n        $('vc-r-tnom').innerHTML = fmt(Tn, 1) + ' <span class=\"vc-rcard-unit\">N\u00b7m<\/span>';\n        $('vc-r-treq').innerHTML = fmt(Treq, 1) + ' <span class=\"vc-rcard-unit\">N\u00b7m<\/span>';\n        $('vc-r-stiff').innerHTML = fmt(Ct, 0) + ' <span class=\"vc-rcard-unit\">N\u00b7m\/rad<\/span>';\n        $('vc-r-freq').innerHTML = fmt(fn, 1) + ' <span class=\"vc-rcard-unit\">Hz<\/span>';\n        $('vc-r-fop').innerHTML = fmt(fop, 1) + ' <span class=\"vc-rcard-unit\">Hz<\/span> <span class=\"vc-rcard-unit\">(' + fmt(n,0) + ' RPM)<\/span>';\n\n        var ratioColor = '';\n        if (ratio > 0) {\n            if (ratio > 1.2 || ratio < 0.8) ratioColor = 'color:var(--vc-green)';\n            else ratioColor = 'color:var(--vc-red)';\n        }\n        $('vc-r-ratio').innerHTML = '<span style=\"' + ratioColor + '\">' + fmt(ratio, 2) + '<\/span>' + (ratio > 0 ? (ratio > 1.2 || ratio < 0.8 ? ' <span class=\"vc-rcard-unit\" style=\"color:var(--vc-green)\">\u2713 OK<\/span>' : ' <span class=\"vc-rcard-unit\" style=\"color:var(--vc-red)\">\u26a0 Near resonance<\/span>') : '');\n\n        $('vc-results').classList.add('vc-visible');\n\n        saveHistory({ power: P, speed: n, sf: KA, torque: fmt(Treq,1), _summary: 'P=' + P + ' kW, n=' + n + ' RPM, T_req=' + fmt(Treq,1) + ' Nm' });\n    }\n\n    \/* \u2500\u2500 PRESETS \u2500\u2500 *\/\n    document.querySelectorAll('.vc-preset-btn').forEach(function(btn) {\n        btn.addEventListener('click', function(e) {\n            e.preventDefault();\n            $('vc-power').value = this.getAttribute('data-p');\n            $('vc-speed').value = this.getAttribute('data-s');\n            $('vc-sf').value = this.getAttribute('data-sf');\n            $('vc-type').value = this.getAttribute('data-t');\n            $('vc-j1').value = this.getAttribute('data-j1');\n            $('vc-j2').value = this.getAttribute('data-j2');\n            calculate();\n        });\n    });\n\n    \/* \u2500\u2500 AUTO-CALCULATE \u2500\u2500 *\/\n    $('vc-form').addEventListener('input', calculate);\n    $('vc-form').addEventListener('change', calculate);\n\n    \/* \u2500\u2500 COPY \u2500\u2500 *\/\n    $('vc-copy-btn').addEventListener('click', function() {\n        var text = 'Flexible Coupling Calculation (DIN 740)\\n' +\n            '\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\n' +\n            'Power: ' + $('vc-power').value + ' kW\\n' +\n            'Speed: ' + $('vc-speed').value + ' RPM\\n' +\n            'Service Factor: ' + $('vc-sf').value + '\\n' +\n            'Nominal Torque: ' + $('vc-r-tnom').textContent + '\\n' +\n            'Required Torque: ' + $('vc-r-treq').textContent + '\\n' +\n            'Natural Frequency: ' + $('vc-r-freq').textContent + '\\n' +\n            '\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\n' +\n            'vibromera.eu\/calculators\/' + SLUG + '\/';\n\n        if (navigator.clipboard) {\n            navigator.clipboard.writeText(text).then(function() {\n                var btn = $('vc-copy-btn');\n                btn.classList.add('vc-copied');\n                btn.innerHTML = '<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><polyline points=\"20 6 9 17 4 12\"\/><\/svg> Copied!';\n                setTimeout(function() {\n                    btn.classList.remove('vc-copied');\n                    btn.innerHTML = '<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy';\n                }, 2000);\n            });\n        }\n    });\n\n    \/* \u2500\u2500 COLLAPSIBLE SECTIONS \u2500\u2500 *\/\n    document.querySelectorAll('.vc-section-toggle').forEach(function(btn) {\n        btn.addEventListener('click', function() {\n            var section = this.closest('.vc-section');\n            var isOpen = section.classList.contains('vc-open');\n            section.classList.toggle('vc-open');\n            this.setAttribute('aria-expanded', !isOpen);\n        });\n    });\n\n    \/* \u2500\u2500 FAQ \u2500\u2500 *\/\n    var faqData = [\n        { q: 'What is a flexible coupling and why use one?', a: '<p>A flexible coupling connects two shafts while accommodating misalignment (angular, parallel, axial) and damping vibrations. They protect connected equipment from shock loads and torsional vibration, extending bearing and seal life.<\/p>' },\n        { q: 'How do I select the right service factor?', a: '<p>Service factors account for load characteristics beyond the nominal torque:<\/p><ul><li><strong>1.0\u20131.5<\/strong> \u2014 Uniform loads: fans, centrifugal pumps<\/li><li><strong>1.5\u20132.0<\/strong> \u2014 Moderate shock: compressors, mixers<\/li><li><strong>2.0\u20133.0<\/strong> \u2014 Heavy shock: crushers, presses, rolling mills<\/li><\/ul><p>Always check the coupling manufacturer\\'s catalog for application-specific factors.<\/p>' },\n        { q: 'What is torsional stiffness in a coupling?', a: '<p>Torsional stiffness (C<sub>t<\/sub>) is the torque required per unit angle of twist, measured in N\u00b7m\/rad. Higher stiffness means more accurate motion transmission but less vibration damping. DIN 740 defines both dynamic and static stiffness values.<\/p>' },\n        { q: 'Why is natural frequency important for coupling selection?', a: '<p>The torsional natural frequency of the coupling-shaft system must be separated from excitation frequencies (shaft speed and harmonics) by at least 20%. Resonance causes excessive vibration, coupling fatigue, and potential failure. DIN 740-2 recommends f<sub>n<\/sub>\/f<sub>op<\/sub> &gt; 1.2 or &lt; 0.8.<\/p>' },\n        { q: 'What is DIN 740 and how does it apply to couplings?', a: '<p>DIN 740 is the German standard for flexible shaft couplings. Part 2 covers torsional vibration characteristics, defining how to measure and specify dynamic torsional stiffness, damping coefficient, and the coupling\\'s influence on system natural frequencies.<\/p>' }\n    ];\n\n    var faqList = $('vc-faq-list');\n    faqData.forEach(function(faq) {\n        faqList.innerHTML += '<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>' + faq.q + '<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\">' + faq.a + '<\/div><\/div><\/div>';\n    });\n    faqList.addEventListener('click', function(e) {\n        var btn = e.target.closest('.vc-faq-q');\n        if (!btn) return;\n        btn.closest('.vc-faq-item').classList.toggle('vc-open');\n    });\n\n    \/* \u2500\u2500 HISTORY \u2500\u2500 *\/\n    function saveHistory(entry) {\n        var key = 'vc_history_' + SLUG;\n        var arr = [];\n        try { arr = JSON.parse(localStorage.getItem(key)) || []; } catch(e) {}\n        entry._ts = new Date().toISOString();\n        arr.unshift(entry);\n        if (arr.length > 10) arr = arr.slice(0, 10);\n        try { localStorage.setItem(key, JSON.stringify(arr)); } catch(e) {}\n    }\n\n    \/* \u2500\u2500 KATEX \u2500\u2500 *\/\n    function renderFormulas() {\n        try {\n            katex.render('T_n = \\\\frac{9549 \\\\times P}{n} \\\\quad [\\\\text{N\u00b7m}]', $('vc-katex-1'), { displayMode: true, throwOnError: false });\n            katex.render('T_{req} = K_A \\\\times T_n', $('vc-katex-2'), { displayMode: true, throwOnError: false });\n            katex.render('f_n = \\\\frac{1}{2\\\\pi}\\\\sqrt{\\\\frac{C_t}{J_{red}}} \\\\quad \\\\text{where} \\\\quad J_{red} = \\\\frac{J_1 \\\\cdot J_2}{J_1 + J_2}', $('vc-katex-3'), { displayMode: true, throwOnError: false });\n        } catch(e) {}\n    }\n\n    \/* \u2500\u2500 INIT \u2500\u2500 *\/\n    function init() {\n        renderFormulas();\n        calculate();\n    }\n\n    if (document.readyState === 'loading') {\n        document.addEventListener('DOMContentLoaded', init);\n    } else {\n        init();\n    }\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>\u09ac\u09bf\u09a8\u09be\u09ae\u09c2\u09b2\u09cd\u09af\u09c7 \u0985\u09a8\u09b2\u09be\u0987\u09a8 DIN 740 \u09a8\u09ae\u09a8\u09c0\u09af\u09bc \u09b8\u0982\u09af\u09cb\u0997 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0\u0964 \u09b6\u0995\u09cd\u09a4\u09bf, \u0997\u09a4\u09bf, \u09aa\u09b0\u09bf\u09b7\u09c7\u09ac\u09be \u09ab\u09cd\u09af\u09be\u0995\u09cd\u099f\u09b0 \u098f\u09ac\u0982 \u09b8\u0982\u09af\u09cb\u0997 \u09aa\u09cd\u09b0\u0995\u09be\u09b0 \u09aa\u09cd\u09b0\u09ac\u09c7\u09b6 \u0995\u09b0\u09c1\u09a8 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u099c\u09a8\u09c0\u09af\u09bc \u099f\u09b0\u09cd\u0995 \u09b0\u09c7\u099f\u09bf\u0982, \u099f\u09b0\u09cd\u09b6\u09a8\u09be\u09b2 \u0995\u09a0\u09cb\u09b0\u09a4\u09be \u098f\u09ac\u0982 \u09aa\u09cd\u09b0\u09be\u0995\u09c3\u09a4\u09bf\u0995 \u09ab\u09cd\u09b0\u09bf\u0995\u09cb\u09af\u09bc\u09c7\u09a8\u09cd\u09b8\u09bf \u0997\u09a3\u09a8\u09be \u0995\u09b0\u09a4\u09c7\u0964<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100099","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100099","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":1,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100099\/revisions"}],"predecessor-version":[{"id":100401,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100099\/revisions\/100401"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/media?parent=100099"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/categories?post=100099"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/tags?post=100099"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}