{"id":100055,"date":"2026-02-15T20:09:36","date_gmt":"2026-02-15T20:09:36","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100055"},"modified":"2026-02-15T20:09:36","modified_gmt":"2026-02-15T20:09:36","slug":"chain-defect-frequencies","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bn\/calculators\/chain-defect-frequencies\/","title":{"rendered":"\u09b0\u09cb\u09b2\u09be\u09b0 \u099a\u09c7\u0987\u09a8 \u09a4\u09cd\u09b0\u09c1\u099f\u09bf \u09ab\u09cd\u09b0\u09bf\u0995\u09cb\u09af\u09bc\u09c7\u09a8\u09cd\u09b8\u09bf \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Roller Chain Defect Frequency Calculator\",\"alternateName\":[\"Chain Frequency Calculator\",\"Tooth Meshing Frequency Calculator\",\"Sprocket Frequency Calculator\"],\"description\":\"Free online engineering calculator for roller chain defect frequencies. Calculate tooth meshing frequency, chain link frequency, driven speed, and harmonic multiples.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/chain-defect-frequencies\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2025-01-01\",\"dateModified\":\"2025-02-15\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true,\"featureList\":[\"Tooth meshing frequency\",\"Chain link frequency\",\"Driven speed calculation\",\"Speed ratio\",\"Harmonics table\",\"Auto-calculation on input change\",\"URL parameter sharing\",\"Calculation history\"],\"keywords\":\"chain frequency, tooth meshing, roller chain, sprocket, chain defect, vibration analysis\"}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"What is tooth meshing frequency in a chain drive?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Tooth meshing frequency (TMF) is the rate at which chain links engage with sprocket teeth. It equals the number of teeth on the driving sprocket multiplied by the shaft rotational frequency: TMF = Z1 \u00d7 RPM \/ 60. This frequency is a dominant vibration source in chain drives and increases with worn or damaged teeth.\"}},\n{\"@type\":\"Question\",\"name\":\"What is chain link frequency?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Chain link frequency is the rate at which one complete revolution of the chain occurs. It equals the tooth meshing frequency divided by the total number of links: f_chain = Z1 \u00d7 RPM \/ (60 \u00d7 N_links). A defect on a single chain link will produce vibration at this frequency.\"}},\n{\"@type\":\"Question\",\"name\":\"How do I diagnose chain wear from vibration?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Chain wear typically increases the amplitude of tooth meshing frequency and its harmonics. A worn or elongated chain may also produce sidebands around TMF spaced at chain link frequency. Impact-type vibration from loose chains produces broadband noise with elevated TMF harmonics.\"}},\n{\"@type\":\"Question\",\"name\":\"What causes chain drive vibration?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Common causes include chain wear and elongation, misaligned sprockets, improper chain tension, worn sprocket teeth, damaged or stiff chain links, and chordal action (polygonal effect). The polygonal effect is inherent to chain drives and produces vibration at tooth meshing frequency.\"}},\n{\"@type\":\"Question\",\"name\":\"What is the polygonal effect in chain drives?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"The polygonal (chordal) effect occurs because a chain wraps around a sprocket as a polygon rather than a smooth circle. This causes periodic speed variation at the tooth meshing frequency. The effect is more pronounced with fewer teeth on the sprocket and can be reduced by using sprockets with more teeth (\u226521).\"}}\n]}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[\n{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/vibromera.eu\/\"},\n{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculators\",\"item\":\"https:\/\/vibromera.eu\/calculators\/\"},\n{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Chain Defect Frequencies\",\"item\":\"https:\/\/vibromera.eu\/calculators\/chain-defect-frequencies\/\"}\n]}\n<\/script>\n\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n\n<link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin>\n\n<link 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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-chain-defect\">\n\n<!-- Header -->\n<header class=\"vc-header\">\n    <p class=\"vc-header-eyebrow\">Free Engineering Tool<\/p>\n    <h1 class=\"vc-header-title\">Roller Chain Defect Frequency Calculator<\/h1>\n    <p class=\"vc-header-subtitle\">Calculate tooth meshing frequency, chain link frequency, driven speed, and harmonics for roller chain drive systems.<\/p>\n    <div class=\"vc-badges\">\n        <span class=\"vc-badge\">Roller Chain<\/span>\n        <span class=\"vc-badge\">Tooth Meshing<\/span>\n        <span class=\"vc-badge\">Chain Link Freq<\/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-z1\">Driving Sprocket Teeth Z\u2081<\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-z1\" inputmode=\"numeric\" step=\"1\" min=\"1\" placeholder=\"e.g. 17\" value=\"17\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-z2\">Driven Sprocket Teeth Z\u2082<\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-z2\" inputmode=\"numeric\" step=\"1\" min=\"1\" placeholder=\"e.g. 51\" value=\"51\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-links\">Total Number of Chain Links<\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-links\" inputmode=\"numeric\" step=\"1\" min=\"1\" placeholder=\"e.g. 120\" value=\"120\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-rpm\">Driver Speed <span class=\"vc-label-hint\">(RPM)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-rpm\" inputmode=\"decimal\" step=\"any\" min=\"1\" placeholder=\"e.g. 1450\" value=\"1450\">\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-z1=\"17\" data-z2=\"51\" data-links=\"120\" data-rpm=\"1450\">17\/51 teeth 120 links 1450 RPM<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-z1=\"21\" data-z2=\"63\" data-links=\"96\" data-rpm=\"750\">21\/63 teeth 96 links 750 RPM<\/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\">Tooth Meshing Frequency<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-tmf\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Chain Link Frequency (1 chain revolution)<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-fchain\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Driver Shaft Frequency<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-fdriver\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Driven Speed<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-n2\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Speed Ratio (Z\u2081\/Z\u2082)<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-ratio\">\u2014<\/div>\n            <\/div>\n        <\/div>\n\n        <!-- Harmonics Table -->\n        <h3 style=\"font-family:var(--vc-display);font-size:17px;font-weight:700;margin:0 0 10px;\">Tooth Meshing Harmonics<\/h3>\n        <table class=\"vc-table\" id=\"vc-harmonics-table\">\n            <thead><tr><th>Harmonic<\/th><th>Frequency (Hz)<\/th><th>CPM<\/th><th>Note<\/th><\/tr><\/thead>\n            <tbody id=\"vc-harmonics-body\"><\/tbody>\n        <\/table>\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>Tooth Meshing Frequency<\/h3>\n            <p>The tooth meshing frequency (TMF) is the rate at which chain links engage with sprocket teeth:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n            <ul>\n                <li><strong>Z\u2081<\/strong> \u2014 number of teeth on driving sprocket<\/li>\n                <li><strong>n\u2081<\/strong> \u2014 driver shaft speed (RPM)<\/li>\n            <\/ul>\n\n            <h3>Chain Link Frequency<\/h3>\n            <p>The chain link frequency represents one complete revolution of the chain loop:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n            <ul>\n                <li><strong>N<sub>links<\/sub><\/strong> \u2014 total number of chain links<\/li>\n            <\/ul>\n\n            <h3>Driven Speed<\/h3>\n            <div class=\"vc-formula-box\" id=\"vc-katex-3\"><\/div>\n\n            <h3>Vibration Indicators<\/h3>\n            <table class=\"vc-table\">\n                <thead><tr><th>Frequency<\/th><th>Source<\/th><th>Indication<\/th><\/tr><\/thead>\n                <tbody>\n                    <tr><td>1\u00d7 TMF<\/td><td>Tooth engagement<\/td><td>Normal chain operation, polygonal effect<\/td><\/tr>\n                    <tr><td>2\u00d7, 3\u00d7 TMF<\/td><td>Harmonics<\/td><td>Chain wear, worn sprocket teeth, excessive slack<\/td><\/tr>\n                    <tr><td>1\u00d7 chain link freq<\/td><td>Chain revolution<\/td><td>Single defective link, tight link<\/td><\/tr>\n                    <tr><td>Sidebands around TMF<\/td><td>Modulation<\/td><td>Worn\/elongated chain, misalignment<\/td><\/tr>\n                <\/tbody>\n            <\/table>\n\n            <div class=\"vc-example-box\">\n                <div class=\"vc-example-title\">Example \u2014 17\/51 Chain Drive<\/div>\n                <p><strong>Given:<\/strong> Z\u2081 = 17, Z\u2082 = 51, Links = 120, n\u2081 = 1450 RPM<\/p>\n                <p>TMF = 17 \u00d7 1450 \/ 60 = <strong>410.83 Hz<\/strong><\/p>\n                <p>Chain freq = 17 \u00d7 1450 \/ (60 \u00d7 120) = <strong>3.42 Hz<\/strong><\/p>\n                <p>Driven speed = 1450 \u00d7 17\/51 = <strong>483.3 RPM<\/strong><\/p>\n                <p>Speed ratio = 17\/51 = <strong>0.333<\/strong><\/p>\n            <\/div>\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> For sprockets with fewer than 21 teeth, the polygonal (chordal) effect becomes significant, producing higher TMF harmonics even in healthy chain drives. Use 21+ teeth sprockets when smooth operation is critical.<\/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\/belt-defect-frequencies\/\">Belt Defect Frequencies<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/bearing-defect-frequencies\/\">Bearing Defect Frequencies<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/gear-mesh-frequency\/\">Gear Mesh Frequency<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/vibration-velocity\/\">Vibration Velocity (ISO 10816)<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/journal-bearing-frequencies\/\">Journal Bearing Frequencies<\/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 vibration analysis instruments and software. Diagnose chain drive issues on-site. Used in 50+ countries.\n    <\/div>\n    <a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a>\n<\/div>\n\n<!-- Footer -->\n<footer class=\"vc-footer\">\n    <p>\u00a9 2024\u20132025 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u2014 Engineering Calculators<\/p>\n    <p style=\"font-size:12px;margin-top:4px;\">Roller chain defect frequency reference. 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 = 'chain-defect-frequencies';\n\n    function $(id) { return document.getElementById(id); }\n    function fmt(n, d) { if(isNaN(n)) return '\u2014'; var f=n.toFixed(d===undefined?2:d); return f.replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,''); }\n\n    \/* \u2500\u2500 CALCULATION \u2500\u2500 *\/\n    function calculate() {\n        var z1 = parseInt($('vc-z1').value);\n        var z2 = parseInt($('vc-z2').value);\n        var links = parseInt($('vc-links').value);\n        var rpm = parseFloat($('vc-rpm').value);\n\n        if (!z1 || z1 <= 0 || !z2 || z2 <= 0 || !links || links <= 0 || !rpm || rpm <= 0) {\n            $('vc-results').classList.remove('vc-visible');\n            return;\n        }\n\n        \/\/ Tooth meshing frequency = Z1 \u00d7 n1 \/ 60\n        var tmf = z1 * rpm \/ 60;\n        \/\/ Chain link frequency = Z1 \u00d7 n1 \/ (60 \u00d7 N_links)\n        var fChain = z1 * rpm \/ (60 * links);\n        \/\/ Driver frequency\n        var fDriver = rpm \/ 60;\n        \/\/ Driven speed\n        var n2 = rpm * z1 \/ z2;\n        \/\/ Speed ratio\n        var ratio = z1 \/ z2;\n\n        \/\/ Display\n        $('vc-r-tmf').innerHTML = fmt(tmf, 2) + ' <span class=\"vc-rcard-unit\">Hz<\/span> <span class=\"vc-rcard-unit\">(' + fmt(tmf * 60, 0) + ' CPM)<\/span>';\n        $('vc-r-fchain').innerHTML = fmt(fChain, 3) + ' <span class=\"vc-rcard-unit\">Hz<\/span> <span class=\"vc-rcard-unit\">(' + fmt(fChain * 60, 1) + ' CPM)<\/span>';\n        $('vc-r-fdriver').innerHTML = fmt(fDriver, 3) + ' <span class=\"vc-rcard-unit\">Hz<\/span> <span class=\"vc-rcard-unit\">(' + fmt(rpm, 0) + ' CPM)<\/span>';\n        $('vc-r-n2').innerHTML = fmt(n2, 1) + ' <span class=\"vc-rcard-unit\">RPM<\/span> <span class=\"vc-rcard-unit\">(' + fmt(n2 \/ 60, 3) + ' Hz)<\/span>';\n        $('vc-r-ratio').innerHTML = fmt(ratio, 4);\n\n        \/\/ Harmonics table\n        var tbody = $('vc-harmonics-body');\n        tbody.innerHTML = '';\n        var notes = [\n            'Fundamental tooth meshing \u2014 normal engagement',\n            '2nd harmonic \u2014 chain wear, sprocket wear',\n            '3rd harmonic \u2014 severe wear, excessive slack',\n            '4th harmonic \u2014 advanced deterioration'\n        ];\n        for (var i = 1; i <= 4; i++) {\n            var f = tmf * i;\n            tbody.innerHTML += '<tr><td><strong>' + i + '\u00d7 TMF<\/strong><\/td><td>' + fmt(f, 2) + ' Hz<\/td><td>' + fmt(f * 60, 0) + '<\/td><td>' + notes[i - 1] + '<\/td><\/tr>';\n        }\n        \/\/ Add chain link frequency row\n        tbody.innerHTML += '<tr style=\"border-top:2px solid var(--vc-border);\"><td><strong>1\u00d7 Chain<\/strong><\/td><td>' + fmt(fChain, 3) + ' Hz<\/td><td>' + fmt(fChain * 60, 1) + '<\/td><td>Single defective\/tight link<\/td><\/tr>';\n\n        $('vc-results').classList.add('vc-visible');\n\n        \/\/ URL params\n        var u = new URL(window.location);\n        u.searchParams.set('z1', z1);\n        u.searchParams.set('z2', z2);\n        u.searchParams.set('links', links);\n        u.searchParams.set('rpm', rpm);\n        history.replaceState(null, '', u.toString());\n\n        \/\/ History\n        saveHistory({ z1: z1, z2: z2, links: links, rpm: rpm, _summary: z1 + '\/' + z2 + ' teeth, ' + links + ' links, ' + rpm + ' RPM' });\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-z1').value = this.getAttribute('data-z1');\n            $('vc-z2').value = this.getAttribute('data-z2');\n            $('vc-links').value = this.getAttribute('data-links');\n            $('vc-rpm').value = this.getAttribute('data-rpm');\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 = 'Roller Chain Defect Frequency Calculation\\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            'Driving sprocket Z1: ' + $('vc-z1').value + ' teeth\\n' +\n            'Driven sprocket Z2: ' + $('vc-z2').value + ' teeth\\n' +\n            'Chain links: ' + $('vc-links').value + '\\n' +\n            'Driver Speed: ' + $('vc-rpm').value + ' RPM\\n' +\n            'Tooth Meshing Freq: ' + $('vc-r-tmf').textContent + '\\n' +\n            'Chain Link Freq: ' + $('vc-r-fchain').textContent + '\\n' +\n            'Driven Speed: ' + $('vc-r-n2').textContent + '\\n' +\n            'Speed Ratio: ' + $('vc-r-ratio').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\/chain-defect-frequencies\/';\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 tooth meshing frequency in a chain drive?', a: '<p>Tooth meshing frequency (TMF) is the rate at which chain links engage with sprocket teeth. It equals the number of teeth on the driving sprocket multiplied by the shaft rotational frequency: TMF = Z\u2081 \u00d7 RPM \/ 60.<\/p><p>This frequency is a dominant vibration source in chain drives and its amplitude increases with worn or damaged teeth.<\/p>' },\n        { q: 'What is chain link frequency?', a: '<p>Chain link frequency is the rate at which one complete revolution of the chain loop occurs. It equals the tooth meshing frequency divided by the total number of links:<\/p><p>f<sub>chain<\/sub> = Z\u2081 \u00d7 RPM \/ (60 \u00d7 N<sub>links<\/sub>)<\/p><p>A defect on a single chain link (tight link, damaged roller) will produce vibration at this frequency.<\/p>' },\n        { q: 'How do I diagnose chain wear from vibration?', a: '<p>Chain wear typically increases the amplitude of tooth meshing frequency and its harmonics (2\u00d7, 3\u00d7, 4\u00d7 TMF). Key indicators:<\/p><ul><li>Rising TMF harmonics \u2014 chain elongation, worn sprocket teeth<\/li><li>Sidebands around TMF at chain link frequency \u2014 modulation from chain defects<\/li><li>Broadband noise increase \u2014 severe wear, loose chain<\/li><li>1\u00d7 chain frequency peak \u2014 single defective or tight link<\/li><\/ul>' },\n        { q: 'What causes chain drive vibration?', a: '<p>Common causes include:<\/p><ul><li>Chain wear and elongation (pitch growth)<\/li><li>Misaligned sprockets<\/li><li>Improper chain tension (too tight or too loose)<\/li><li>Worn sprocket teeth (hooked teeth profile)<\/li><li>Damaged or stiff chain links<\/li><li>Polygonal (chordal) effect \u2014 inherent to chain drives<\/li><\/ul>' },\n        { q: 'What is the polygonal effect in chain drives?', a: '<p>The polygonal (chordal) effect occurs because a chain wraps around a sprocket as a polygon rather than a smooth circle. This causes periodic speed variation at the tooth meshing frequency.<\/p><p>The effect is more pronounced with fewer teeth on the sprocket. Using sprockets with 21 or more teeth significantly reduces the chordal action. The speed variation is approximately \u00b1(1 \u2212 cos(180\u00b0\/Z)) \u00d7 100%.<\/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 URL PARAMS \u2500\u2500 *\/\n    function loadParams() {\n        var p = new URLSearchParams(window.location.search);\n        if (p.get('z1')) $('vc-z1').value = p.get('z1');\n        if (p.get('z2')) $('vc-z2').value = p.get('z2');\n        if (p.get('links')) $('vc-links').value = p.get('links');\n        if (p.get('rpm')) $('vc-rpm').value = p.get('rpm');\n    }\n\n    \/* \u2500\u2500 KATEX \u2500\u2500 *\/\n    function renderFormulas() {\n        try {\n            katex.render('f_{TMF} = \\\\frac{Z_1 \\\\times n_1}{60} \\\\quad [\\\\text{Hz}]', $('vc-katex-1'), { displayMode: true, throwOnError: false });\n            katex.render('f_{chain} = \\\\frac{Z_1 \\\\times n_1}{60 \\\\times N_{links}} \\\\quad [\\\\text{Hz}]', $('vc-katex-2'), { displayMode: true, throwOnError: false });\n            katex.render('n_2 = n_1 \\\\times \\\\frac{Z_1}{Z_2} \\\\quad [\\\\text{RPM}]', $('vc-katex-3'), { displayMode: true, throwOnError: false });\n        } catch(e) {}\n    }\n\n    \/* \u2500\u2500 INIT \u2500\u2500 *\/\n    function init() {\n        loadParams();\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>\u09b0\u09cb\u09b2\u09be\u09b0 \u099a\u09c7\u0987\u09a8 \u09a4\u09cd\u09b0\u09c1\u099f\u09bf \u09ab\u09cd\u09b0\u09bf\u0995\u09cb\u09af\u09bc\u09c7\u09a8\u09cd\u09b8\u09bf\u09b0 \u099c\u09a8\u09cd\u09af \u09ac\u09bf\u09a8\u09be\u09ae\u09c2\u09b2\u09cd\u09af\u09c7 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0\u0964 \u099f\u09c1\u09a5 \u09ae\u09c7\u09b6\u09bf\u0982 \u09ab\u09cd\u09b0\u09bf\u0995\u09cb\u09af\u09bc\u09c7\u09a8\u09cd\u09b8\u09bf, \u099a\u09c7\u0987\u09a8 \u09b2\u09bf\u0999\u09cd\u0995 \u09ab\u09cd\u09b0\u09bf\u0995\u09cb\u09af\u09bc\u09c7\u09a8\u09cd\u09b8\u09bf, \u099a\u09be\u09b2\u09bf\u09a4 \u0997\u09a4\u09bf, \u0997\u09a4\u09bf \u0985\u09a8\u09c1\u09aa\u09be\u09a4 \u098f\u09ac\u0982 \u09b0\u09cb\u09b2\u09be\u09b0 \u099a\u09c7\u0987\u09a8 \u09a1\u09cd\u09b0\u09be\u0987\u09ad\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09b9\u09be\u09b0\u09ae\u09a8\u09bf\u0995\u09cd\u09b8 \u0997\u09a3\u09a8\u09be \u0995\u09b0\u09c1\u09a8\u0964<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100055","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100055","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\/100055\/revisions"}],"predecessor-version":[{"id":100365,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100055\/revisions\/100365"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/media?parent=100055"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/categories?post=100055"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/tags?post=100055"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}