{"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\/sw\/calculators\/flexible-coupling-calculator\/","title":{"rendered":"Kikokotoo cha Kiungo Kinachonyumbuka | DIN 740 | Zana ya Bure ya Mtandaoni"},"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>Kikokotoo cha bure cha mtandaoni cha muunganiko laini wa DIN 740. Ingiza nguvu, kasi, kipengele cha huduma, na aina ya muunganiko ili kukokotoa ukadiriaji wa torque unaohitajika, ugumu wa torsional, na mzunguko wa asili.<\/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\/sw\/wp-json\/wp\/v2\/calculator\/100099","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":1,"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/calculator\/100099\/revisions"}],"predecessor-version":[{"id":100401,"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/calculator\/100099\/revisions\/100401"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/media?parent=100099"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/categories?post=100099"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/tags?post=100099"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}