{"id":100112,"date":"2026-02-15T20:17:11","date_gmt":"2026-02-15T20:17:11","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100112"},"modified":"2026-02-15T20:17:11","modified_gmt":"2026-02-15T20:17:11","slug":"gear-mesh-frequency","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bn\/calculators\/gear-mesh-frequency\/","title":{"rendered":"\u0997\u09bf\u09af\u09bc\u09be\u09b0 \u09ae\u09c7\u09b6 \u09ab\u09cd\u09b0\u09bf\u0995\u09cb\u09af\u09bc\u09c7\u09a8\u09cd\u09b8\u09bf \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0 | GMF \u098f\u09ac\u0982 \u09b8\u09be\u0987\u09a1\u09ac\u09cd\u09af\u09be\u09a8\u09cd\u09a1"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Gear Mesh Frequency Calculator\",\"alternateName\":[\"GMF Calculator\",\"Gear Sideband Calculator\",\"Gear Ratio Calculator\"],\"description\":\"Free online engineering calculator for gear mesh frequency (GMF), sidebands, gear ratio, and shaft speeds. Essential for gear vibration diagnostics.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/gear-mesh-frequency\/\",\"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\":\"2026-02-14\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true,\"featureList\":[\"Gear mesh frequency calculation\",\"Sideband frequencies (\u00b11, \u00b12, \u00b13)\",\"Gear ratio and shaft 2 speed\",\"Common gear presets\",\"Auto-calculation on input change\",\"URL parameter sharing\"],\"keywords\":\"gear mesh frequency, GMF, sideband, gear ratio, 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 gear mesh frequency?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Gear mesh frequency (GMF) is the rate at which gear teeth engage. It equals the number of teeth on a gear multiplied by its rotational frequency (RPM\/60). GMF = Z \u00d7 RPM\/60. Both meshing gears produce the same GMF.\"}},\n{\"@type\":\"Question\",\"name\":\"What do sidebands indicate?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Sidebands around GMF are spaced at shaft rotational frequencies. They indicate gear faults like eccentricity, tooth wear, or cracking. Sidebands at the input shaft frequency suggest a fault on the input gear, while sidebands at the output shaft frequency suggest a fault on the output gear.\"}},\n{\"@type\":\"Question\",\"name\":\"How to identify gear faults using vibration?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Common gear fault indicators: elevated GMF with sidebands indicates tooth wear or damage; non-synchronous sidebands suggest a cracked tooth; ghost frequencies (non-integer multiples) indicate manufacturing errors; natural frequency excitation with GMF modulation suggests advanced damage.\"}},\n{\"@type\":\"Question\",\"name\":\"What is hunting tooth frequency?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Hunting tooth frequency (HTF) is the rate at which a specific tooth on one gear meshes with a specific tooth on the other gear. HTF = GMF \/ (Z1 \u00d7 Z2 \/ GCD(Z1, Z2)). It is used to detect assembly-related faults and pattern wear.\"}},\n{\"@type\":\"Question\",\"name\":\"What are assembly phase considerations for gears?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Assembly phasing refers to the specific tooth-to-tooth alignment when gears are installed. Marking and maintaining the original phasing during maintenance ensures the same wear pattern continues. 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{\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-gear-mesh\">\n\n<!-- Header -->\n<header class=\"vc-header\">\n    <p class=\"vc-header-eyebrow\">Free Engineering Tool #036<\/p>\n    <h1 class=\"vc-header-title\">Gear Mesh Frequency Calculator<\/h1>\n    <p class=\"vc-header-subtitle\">Calculate gear mesh frequency (GMF), gear ratio, driven shaft speed, and sideband frequencies for vibration diagnostics.<\/p>\n    <div class=\"vc-badges\">\n        <span class=\"vc-badge\">GMF<\/span>\n        <span class=\"vc-badge\">Sidebands<\/span>\n        <span class=\"vc-badge\">Gear Ratio<\/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 Gear Teeth <span class=\"vc-label-hint\">(Z\u2081)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-z1\" inputmode=\"numeric\" step=\"1\" min=\"1\" placeholder=\"e.g. 23\" value=\"23\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-z2\">Driven Gear Teeth <span class=\"vc-label-hint\">(Z\u2082)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-z2\" inputmode=\"numeric\" step=\"1\" min=\"1\" placeholder=\"e.g. 67\" value=\"67\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-rpm1\">Shaft 1 Speed <span class=\"vc-label-hint\">(RPM)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-rpm1\" inputmode=\"decimal\" step=\"any\" min=\"1\" placeholder=\"e.g. 1500\" value=\"1500\">\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=\"23\" data-z2=\"67\" data-rpm=\"1500\">Helical 23\/67 teeth, 1500 RPM<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-z1=\"17\" data-z2=\"51\" data-rpm=\"3000\">Spur 17\/51 teeth, 3000 RPM<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-z1=\"1\" data-z2=\"40\" data-rpm=\"1800\">Worm 1\/40 teeth, 1800 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\">Gear Mesh Frequency (GMF)<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-gmf\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">GMF as Order of Shaft 1<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-gmf-order\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Shaft 2 Speed<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-rpm2\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Gear Ratio (Z\u2082\/Z\u2081)<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-ratio\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Shaft 1 Frequency<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-f1\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Shaft 2 Frequency<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-f2\">\u2014<\/div>\n            <\/div>\n        <\/div>\n\n        <h3 style=\"font-family:var(--vc-display);font-size:17px;font-weight:700;margin:8px 0 12px;\">Sideband Frequencies<\/h3>\n        <div style=\"overflow-x:auto;\">\n            <table class=\"vc-sb-table\" id=\"vc-sb-tbl\">\n                <thead>\n                    <tr>\n                        <th>Sideband<\/th>\n                        <th>GMF \u2212 n\u00d7f\u2081 (Hz)<\/th>\n                        <th>GMF + n\u00d7f\u2081 (Hz)<\/th>\n                        <th>GMF \u2212 n\u00d7f\u2082 (Hz)<\/th>\n                        <th>GMF + n\u00d7f\u2082 (Hz)<\/th>\n                    <\/tr>\n                <\/thead>\n                <tbody id=\"vc-sb-body\"><\/tbody>\n            <\/table>\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>Gear Mesh Frequency<\/h3>\n            <p>The gear mesh frequency (GMF) is the rate at which teeth engage between two meshing gears. It is the same for both gears:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-gmf\"><\/div>\n\n            <h3>Gear Ratio &amp; Shaft 2 Speed<\/h3>\n            <div class=\"vc-formula-box\" id=\"vc-katex-ratio\"><\/div>\n            <div class=\"vc-formula-box\" id=\"vc-katex-rpm2\"><\/div>\n\n            <h3>Sidebands<\/h3>\n            <p>Sidebands appear around GMF spaced at shaft rotational frequencies. They are key indicators of gear health:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-sb\"><\/div>\n            <ul>\n                <li><strong>Sidebands at f\u2081:<\/strong> Indicate a fault on the driving gear<\/li>\n                <li><strong>Sidebands at f\u2082:<\/strong> Indicate a fault on the driven gear<\/li>\n                <li><strong>Asymmetric sidebands:<\/strong> Suggest cracked or broken teeth<\/li>\n            <\/ul>\n\n            <h3>Practical Example<\/h3>\n            <div class=\"vc-example-box\">\n                <div class=\"vc-example-title\">Example \u2014 Helical Gear Pair 23\/67, 1500 RPM<\/div>\n                <p><strong>Given:<\/strong> Z\u2081 = 23, Z\u2082 = 67, RPM\u2081 = 1500<\/p>\n                <p>f\u2081 = 1500\/60 = 25 Hz<\/p>\n                <p>GMF = 23 \u00d7 25 = <strong>575 Hz<\/strong><\/p>\n                <p>Gear ratio = 67\/23 = <strong>2.913:1<\/strong><\/p>\n                <p>RPM\u2082 = 1500 \u00d7 23\/67 = <strong>514.9 RPM<\/strong> \u2192 f\u2082 = 8.58 Hz<\/p>\n                <p>Sidebands: 575 \u00b1 25 Hz, 575 \u00b1 8.58 Hz, etc.<\/p>\n            <\/div>\n\n            <div class=\"vc-info-box\">\n                <p><strong>Tip:<\/strong> A healthy gear typically shows GMF with low-amplitude, symmetric sidebands. Growing sidebands, especially asymmetric ones, indicate developing faults.<\/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\/bearing-defect-frequencies\/\">Bearing Defect Frequencies<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/blade-pass-frequency\/\">Blade Pass Frequency<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/motor-electrical-frequencies\/\">Motor Electrical Frequencies<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/vibration-velocity\/\">Vibration Velocity (ISO 10816)<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/residual-unbalance-iso1940\/\">Residual Unbalance (ISO 1940)<\/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 for gearbox diagnostics, field balancing, and condition monitoring. 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>&copy; 2024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u2014 Engineering Calculators<\/p>\n    <p style=\"font-size:12px;margin-top:4px;\">Gear mesh frequency formulas per standard kinematic equations. Last updated: February 2026<\/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 = 'gear-mesh-frequency';\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 Z1 = parseInt($('vc-z1').value);\n        var Z2 = parseInt($('vc-z2').value);\n        var RPM1 = parseFloat($('vc-rpm1').value);\n\n        if (!Z1 || Z1 < 1 || !Z2 || Z2 < 1 || !RPM1 || RPM1 <= 0) {\n            $('vc-results').classList.remove('vc-visible');\n            return;\n        }\n\n        var f1 = RPM1 \/ 60;\n        var GMF = Z1 * f1;\n        var RPM2 = RPM1 * Z1 \/ Z2;\n        var f2 = RPM2 \/ 60;\n        var ratio = Z2 \/ Z1;\n\n        \/\/ Display results\n        $('vc-r-gmf').innerHTML = fmt(GMF, 2) + ' <span class=\"vc-rcard-unit\">Hz<\/span>';\n        $('vc-r-gmf-order').innerHTML = fmt(GMF \/ f1, 1) + '<span class=\"vc-rcard-unit\">\u00d7 shaft 1<\/span>';\n        $('vc-r-rpm2').innerHTML = fmt(RPM2, 1) + ' <span class=\"vc-rcard-unit\">RPM<\/span> <span class=\"vc-rcard-unit\">(' + fmt(f2, 2) + ' Hz)<\/span>';\n        $('vc-r-ratio').innerHTML = fmt(ratio, 3) + '<span class=\"vc-rcard-unit\"> : 1<\/span>';\n        $('vc-r-f1').innerHTML = fmt(f1, 2) + ' <span class=\"vc-rcard-unit\">Hz<\/span> <span class=\"vc-rcard-unit\">(' + fmt(RPM1) + ' RPM)<\/span>';\n        $('vc-r-f2').innerHTML = fmt(f2, 2) + ' <span class=\"vc-rcard-unit\">Hz<\/span> <span class=\"vc-rcard-unit\">(' + fmt(RPM2, 1) + ' RPM)<\/span>';\n\n        \/\/ Sideband table\n        var tbody = $('vc-sb-body');\n        tbody.innerHTML = '';\n        for (var n = 1; n <= 3; n++) {\n            var row = '<tr>';\n            row += '<td><strong>n = ' + n + '<\/strong><\/td>';\n            row += '<td>' + fmt(GMF - n * f1, 2) + '<\/td>';\n            row += '<td>' + fmt(GMF + n * f1, 2) + '<\/td>';\n            row += '<td>' + fmt(GMF - n * f2, 2) + '<\/td>';\n            row += '<td>' + fmt(GMF + n * f2, 2) + '<\/td>';\n            row += '<\/tr>';\n            tbody.innerHTML += row;\n        }\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('rpm1', RPM1);\n        history.replaceState(null, '', u.toString());\n\n        \/\/ History\n        saveHistory({\n            z1: Z1, z2: Z2, rpm1: RPM1,\n            _summary: 'Z1=' + Z1 + ', Z2=' + Z2 + ', ' + RPM1 + ' RPM'\n        });\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-rpm1').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 = 'Gear Mesh 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\u2501\u2501\u2501\u2501\u2501\u2501\\n' +\n            'Driving gear teeth (Z1): ' + $('vc-z1').value + '\\n' +\n            'Driven gear teeth (Z2): ' + $('vc-z2').value + '\\n' +\n            'Shaft 1 speed: ' + $('vc-rpm1').value + ' RPM\\n' +\n            '\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\n' +\n            'GMF: ' + $('vc-r-gmf').textContent + '\\n' +\n            'Gear ratio: ' + $('vc-r-ratio').textContent + '\\n' +\n            'Shaft 2 speed: ' + $('vc-r-rpm2').textContent + '\\n' +\n            '\u2501\u2501\u2501\u2501\u2501\u2501\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\/gear-mesh-frequency\/';\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 gear mesh frequency?', a: '<p>Gear mesh frequency (GMF) is the rate at which gear teeth come into contact. For any pair of meshing gears, GMF = Z \u00d7 RPM\/60, where Z is the number of teeth and RPM is the rotational speed of that gear. Both gears produce the same GMF.<\/p><p>GMF is one of the most important frequencies in gearbox vibration analysis. A healthy gearbox shows a stable GMF; changes indicate developing faults.<\/p>' },\n        { q: 'What do sidebands indicate?', a: '<p>Sidebands are spectral peaks that appear on either side of GMF, spaced at shaft rotational frequencies:<\/p><ul><li><strong>Sidebands at shaft 1 frequency:<\/strong> Fault on the driving (input) gear<\/li><li><strong>Sidebands at shaft 2 frequency:<\/strong> Fault on the driven (output) gear<\/li><li><strong>Symmetric sidebands:<\/strong> Uniform wear or eccentricity<\/li><li><strong>Asymmetric sidebands:<\/strong> Cracked or broken tooth<\/li><\/ul><p>The number and amplitude of sidebands increase with fault severity.<\/p>' },\n        { q: 'How to identify gear faults using vibration?', a: '<p>Key indicators of gear faults in vibration spectra:<\/p><ul><li><strong>Elevated GMF:<\/strong> Tooth wear, misalignment, or overload<\/li><li><strong>Growing sidebands:<\/strong> Localized tooth damage (crack, chip)<\/li><li><strong>Ghost frequencies:<\/strong> Manufacturing errors (non-integer multiples of shaft speed)<\/li><li><strong>Natural frequency excitation:<\/strong> Impulse from broken tooth exciting gear natural frequencies<\/li><li><strong>Broadband noise rise:<\/strong> Advanced gear damage<\/li><\/ul>' },\n        { q: 'What is hunting tooth frequency?', a: '<p>The hunting tooth frequency (HTF) is the rate at which a specific tooth on one gear re-meshes with a specific tooth on the other gear:<\/p><p><strong>HTF = GMF \/ LCM(Z\u2081, Z\u2082)<\/strong><\/p><p>Or equivalently: HTF = GMF \/ (Z\u2081 \u00d7 Z\u2082 \/ GCD(Z\u2081, Z\u2082))<\/p><p>HTF is very low (often sub-Hz) and is useful for detecting assembly errors and patterns of wear that repeat over many revolutions.<\/p>' },\n        { q: 'What are assembly phase considerations for gears?', a: '<p>Assembly phasing refers to the specific tooth-to-tooth alignment when gears are mated. Key considerations:<\/p><ul><li>Always mark the meshing position before disassembly<\/li><li>Maintaining original phasing preserves the worn-in contact pattern<\/li><li>Changing phase can introduce new vibration signatures<\/li><li>For precision gears, phasing affects backlash and transmission error<\/li><li>In multi-stage gearboxes, relative phase between stages affects overall vibration<\/li><\/ul>' }\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.has('z1')) $('vc-z1').value = p.get('z1');\n        if (p.has('z2')) $('vc-z2').value = p.get('z2');\n        if (p.has('rpm1')) $('vc-rpm1').value = p.get('rpm1');\n    }\n\n    \/* \u2500\u2500 KATEX \u2500\u2500 *\/\n    function renderFormulas() {\n        try {\n            katex.render('\\\\text{GMF} = Z_1 \\\\times \\\\frac{\\\\text{RPM}_1}{60} = Z_2 \\\\times \\\\frac{\\\\text{RPM}_2}{60} \\\\quad [\\\\text{Hz}]', $('vc-katex-gmf'), { displayMode: true, throwOnError: false });\n            katex.render('\\\\text{Gear Ratio} = \\\\frac{Z_2}{Z_1}', $('vc-katex-ratio'), { displayMode: true, throwOnError: false });\n            katex.render('\\\\text{RPM}_2 = \\\\text{RPM}_1 \\\\times \\\\frac{Z_1}{Z_2}', $('vc-katex-rpm2'), { displayMode: true, throwOnError: false });\n            katex.render('\\\\text{Sidebands} = \\\\text{GMF} \\\\pm n \\\\times f_{\\\\text{shaft}} \\\\quad (n = 1, 2, 3\\\\ldots)', $('vc-katex-sb'), { 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>\u09ac\u09bf\u09a8\u09be\u09ae\u09c2\u09b2\u09cd\u09af\u09c7 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u0997\u09bf\u09af\u09bc\u09be\u09b0 \u09ae\u09c7\u09b6 \u09ab\u09cd\u09b0\u09bf\u0995\u09cb\u09af\u09bc\u09c7\u09a8\u09cd\u09b8\u09bf (GMF) \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0\u0964 \u0995\u09ae\u09cd\u09aa\u09a8 \u09ac\u09bf\u09b6\u09cd\u09b2\u09c7\u09b7\u09a3 \u098f\u09ac\u0982 \u0997\u09bf\u09af\u09bc\u09be\u09b0 \u09a4\u09cd\u09b0\u09c1\u099f\u09bf \u09a1\u09be\u09af\u09bc\u09be\u0997\u09a8\u09b8\u09cd\u099f\u09bf\u0995\u09cd\u09b8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af GMF, \u0997\u09bf\u09af\u09bc\u09be\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4, \u09b6\u09be\u09ab\u099f \u09e8 \u0997\u09a4\u09bf \u098f\u09ac\u0982 \u09b8\u09be\u0987\u09a1\u09ac\u09cd\u09af\u09be\u09a8\u09cd\u09a1 \u09ab\u09cd\u09b0\u09bf\u0995\u09cb\u09af\u09bc\u09c7\u09a8\u09cd\u09b8\u09bf \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-100112","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100112","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\/100112\/revisions"}],"predecessor-version":[{"id":100413,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100112\/revisions\/100413"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/media?parent=100112"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/categories?post=100112"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/tags?post=100112"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}