{"id":100126,"date":"2026-02-15T20:19:11","date_gmt":"2026-02-15T20:19:11","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100126"},"modified":"2026-02-15T20:19:11","modified_gmt":"2026-02-15T20:19:11","slug":"harmonic-frequency-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bn\/calculators\/harmonic-frequency-calculator\/","title":{"rendered":"\u09b8\u09c1\u09b0\u09c7\u09b2\u09be \u09ab\u09cd\u09b0\u09bf\u0995\u09cb\u09af\u09bc\u09c7\u09a8\u09cd\u09b8\u09bf \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0 | RPM \u09a5\u09c7\u0995\u09c7 Hz | 1\u00d7\u201310\u00d7 \u0985\u09b0\u09cd\u09a1\u09be\u09b0"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Harmonic Frequency Calculator\",\"alternateName\":[\"RPM to Hz Converter\",\"Vibration Harmonics Calculator\",\"Order Frequency Calculator\"],\"description\":\"Free online harmonic frequency calculator. Convert RPM to Hz and display harmonics 1\u00d7 through 20\u00d7 with period, angular velocity, and CPM.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/harmonic-frequency-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\":[\"RPM to Hz conversion\",\"Harmonics 1\u00d7 to 20\u00d7\",\"Period and angular velocity\",\"CPM display\",\"Auto-calculation on input change\",\"URL parameter sharing\"],\"keywords\":\"harmonic frequency, RPM to Hz, vibration orders, harmonics, CPM\"}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"How do I convert RPM to Hz?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Divide RPM by 60. For example, 3000 RPM = 3000\/60 = 50 Hz. This gives the fundamental (1\u00d7) frequency. Hz means cycles per second, while RPM means revolutions per minute.\"}},\n{\"@type\":\"Question\",\"name\":\"What are harmonics in vibration analysis?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Harmonics are integer multiples of the fundamental (1\u00d7) frequency. The 2\u00d7 harmonic is twice the fundamental, 3\u00d7 is three times, etc. Different fault types generate specific harmonic patterns \u2014 for example, misalignment often shows strong 2\u00d7 components.\"}},\n{\"@type\":\"Question\",\"name\":\"What does the 1\u00d7 vibration frequency indicate?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"The 1\u00d7 frequency corresponds to one event per revolution. The most common source of 1\u00d7 vibration is mass unbalance. Other 1\u00d7 sources include bent shaft, eccentric rotor, and resonance excited at running speed.\"}},\n{\"@type\":\"Question\",\"name\":\"Why are higher harmonics important?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Higher harmonics help diagnose specific faults: 2\u00d7 often indicates misalignment or looseness, blade\/vane pass frequency is the number of blades \u00d7 RPM, gear mesh frequency is the number of teeth \u00d7 RPM. Each harmonic pattern points to a specific root cause.\"}},\n{\"@type\":\"Question\",\"name\":\"What is the difference between Hz, CPM, and orders?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Hz (Hertz) = cycles per second. CPM (Cycles Per Minute) = Hz \u00d7 60 = same value as RPM for 1\u00d7 order. Orders are multiples of the shaft speed: 1\u00d7 = one per revolution, 2\u00d7 = two per revolution, etc. Orders are speed-independent, while Hz\/CPM change with RPM.\"}}\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\":\"Harmonic Frequency Calculator\",\"item\":\"https:\/\/vibromera.eu\/calculators\/harmonic-frequency-calculator\/\"}\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 href=\"https:\/\/fonts.googleapis.com\/css2?family=DM+Sans:ital,opsz,wght@0,9..40,300;0,9..40,400;0,9..40,500;0,9..40,600;0,9..40,700;1,9..40,400&#038;family=JetBrains+Mono:wght@400;500;600&#038;family=Fraunces:opsz,wght@9..144,700;9..144,800&#038;display=swap\" rel=\"stylesheet\">\n\n<link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.css\">\n\n<style>\n:root {\n    --vc-bg: #f4f1ec;\n    --vc-surface: #ffffff;\n    --vc-surface-alt: #f8f6f2;\n    --vc-ink: #1a1a1a;\n    --vc-ink-secondary: #5a5650;\n    --vc-ink-muted: #8a857e;\n    --vc-accent: #c85a2a;\n    --vc-accent-hover: #b04d22;\n    --vc-accent-light: #fdf0ea;\n    --vc-blue: #2a5c8c;\n    --vc-blue-light: #eaf1f8;\n    --vc-green: #2a7a4b;\n    --vc-green-light: #eaf8ef;\n    --vc-yellow: #a67c00;\n    --vc-yellow-light: #fef9e8;\n    --vc-red: #b91c1c;\n    --vc-red-light: #fef2f2;\n    --vc-border: #d9d4cc;\n    --vc-border-light: #e8e4dd;\n    --vc-shadow: 0 1px 3px rgba(26,26,26,0.06), 0 4px 12px rgba(26,26,26,0.04);\n    --vc-shadow-lg: 0 4px 12px rgba(26,26,26,0.08), 0 16px 40px rgba(26,26,26,0.06);\n    --vc-radius: 8px;\n    --vc-radius-lg: 12px;\n    --vc-font: 'DM Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', sans-serif;\n    --vc-mono: 'JetBrains Mono', 'Consolas', 'Monaco', monospace;\n    --vc-display: 'Fraunces', Georgia, serif;\n}\n\n.vc-calculator {\n    font-family: var(--vc-font);\n    font-size: 15px;\n    line-height: 1.65;\n    color: var(--vc-ink);\n    max-width: 960px;\n    margin: 0 auto;\n    padding: 20px 16px 40px;\n    -webkit-font-smoothing: antialiased;\n}\n.vc-calculator *, .vc-calculator *::before, .vc-calculator *::after { box-sizing: border-box; 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}\n.vc-faq-a-inner ul { margin:4px 0 8px 16px; padding:0; }\n.vc-faq-a-inner li { margin-bottom:3px; }\n\n\/* \u2500\u2500 RELATED \u2500\u2500 *\/\n.vc-related { display:flex; flex-wrap:wrap; gap:10px; margin-top:16px; }\n.vc-related-link { display:inline-block; padding:8px 16px; font-family:var(--vc-font); font-size:13px; font-weight:600; background:var(--vc-surface-alt); color:var(--vc-ink-secondary); border:1px solid var(--vc-border); border-radius:var(--vc-radius); text-decoration:none; transition:all 0.15s; }\n.vc-related-link:hover { border-color:var(--vc-accent); color:var(--vc-accent); background:var(--vc-accent-light); }\n\n\/* \u2500\u2500 PROMO \u2500\u2500 *\/\n.vc-promo { margin-top:24px; padding:20px; background:linear-gradient(135deg, var(--vc-accent-light), var(--vc-surface)); border:1px solid var(--vc-border); border-radius:var(--vc-radius-lg); display:flex; align-items:center; gap:16px; }\n.vc-promo-text { flex:1; font-size:14px; color:var(--vc-ink-secondary); }\n.vc-promo-text strong { color:var(--vc-ink); }\n.vc-promo-link { padding:8px 20px; font-size:13px; font-weight:700; color:#fff; background:var(--vc-accent); border-radius:var(--vc-radius); text-decoration:none; white-space:nowrap; transition:background 0.15s; }\n.vc-promo-link:hover { background:var(--vc-accent-hover); }\n\n\/* \u2500\u2500 FOOTER \u2500\u2500 *\/\n.vc-footer { text-align:center; padding:32px 16px; 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-harmonic-frequency-calculator\">\n\n<!-- Header -->\n<header class=\"vc-header\">\n    <p class=\"vc-header-eyebrow\">Free Engineering Tool \u00b7 #008<\/p>\n    <h1 class=\"vc-header-title\">Harmonic Frequency Calculator<\/h1>\n    <p class=\"vc-header-subtitle\">Convert RPM to Hz and display harmonics 1\u00d7 through 20\u00d7. Essential for vibration analysis and machine diagnostics.<\/p>\n    <div class=\"vc-badges\">\n        <span class=\"vc-badge\">RPM \u2192 Hz<\/span>\n        <span class=\"vc-badge\">1\u00d7\u201320\u00d7 Orders<\/span>\n        <span class=\"vc-badge\">Hz &amp; CPM<\/span>\n    <\/div>\n<\/header>\n\n<!-- Calculator Card -->\n<div class=\"vc-card\">\n\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-speed\">Rotational Speed <span class=\"vc-label-hint\">(RPM)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-speed\" inputmode=\"decimal\" step=\"any\" min=\"0.1\" placeholder=\"e.g. 3000\" value=\"3000\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-harmonics\">Number of Harmonics<\/label>\n                <select class=\"vc-select\" id=\"vc-harmonics\">\n                    <option value=\"5\">5 harmonics<\/option>\n                    <option value=\"10\" selected>10 harmonics<\/option>\n                    <option value=\"15\">15 harmonics<\/option>\n                    <option value=\"20\">20 harmonics<\/option>\n                <\/select>\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-s=\"3000\" data-h=\"10\">3000 RPM motor<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-s=\"1500\" data-h=\"10\">1500 RPM pump<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-s=\"750\" data-h=\"10\">750 RPM fan<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-s=\"3000\" data-h=\"5\">50 Hz (3000 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\">1\u00d7 Fundamental Frequency<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-freq1x\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Period (1\u00d7 cycle)<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-period\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Angular Velocity \u03c9<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-omega\">\u2014<\/div>\n            <\/div>\n        <\/div>\n\n        <!-- Harmonics Table -->\n        <div class=\"vc-harmonics-wrap\">\n            <table class=\"vc-table\" id=\"vc-harm-table\">\n                <thead>\n                    <tr>\n                        <th>Order<\/th>\n                        <th>Frequency (Hz)<\/th>\n                        <th>CPM<\/th>\n                        <th>Period (ms)<\/th>\n                    <\/tr>\n                <\/thead>\n                <tbody id=\"vc-harm-tbody\"><\/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>RPM to Hz Conversion<\/h3>\n            <p>The fundamental frequency (1\u00d7 order) in Hz equals the rotational speed divided by 60:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n\n            <h3>Harmonic Frequencies<\/h3>\n            <p>Each harmonic (order) is an integer multiple of the fundamental frequency:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n            <p>where <strong>n<\/strong> is the harmonic order (1, 2, 3, \u2026).<\/p>\n\n            <h3>Angular Velocity<\/h3>\n            <div class=\"vc-formula-box\" id=\"vc-katex-3\"><\/div>\n\n            <h3>Common Harmonic Sources in Vibration<\/h3>\n            <table class=\"vc-table\">\n                <thead><tr><th>Order<\/th><th>Common Source<\/th><\/tr><\/thead>\n                <tbody>\n                    <tr><td>1\u00d7<\/td><td>Unbalance, bent shaft, eccentricity<\/td><\/tr>\n                    <tr><td>2\u00d7<\/td><td>Misalignment (angular\/parallel), looseness<\/td><\/tr>\n                    <tr><td>3\u00d7<\/td><td>Misalignment (severe), looseness<\/td><\/tr>\n                    <tr><td>N\u00d7<\/td><td>Blade\/vane pass (N = number of blades)<\/td><\/tr>\n                    <tr><td>Z\u00d7<\/td><td>Gear mesh frequency (Z = number of teeth)<\/td><\/tr>\n                    <tr><td>\u00bd\u00d7<\/td><td>Oil whirl, rubbing<\/td><\/tr>\n                    <tr><td>0.43\u00d7<\/td><td>Oil whip<\/td><\/tr>\n                <\/tbody>\n            <\/table>\n\n            <h3>Practical Example<\/h3>\n            <div class=\"vc-example-box\">\n                <div class=\"vc-example-title\">Example \u2014 3000 RPM Motor<\/div>\n                <p><strong>Given:<\/strong> Speed = 3000 RPM<\/p>\n                <p>1\u00d7 = 3000 \/ 60 = <strong>50 Hz<\/strong> (3000 CPM)<\/p>\n                <p>2\u00d7 = 2 \u00d7 50 = <strong>100 Hz<\/strong> (6000 CPM)<\/p>\n                <p>3\u00d7 = 3 \u00d7 50 = <strong>150 Hz<\/strong> (9000 CPM)<\/p>\n                <p>Period = 1 \/ 50 = <strong>20 ms<\/strong><\/p>\n                <p>\u03c9 = 2\u03c0 \u00d7 50 = <strong>314.16 rad\/s<\/strong><\/p>\n            <\/div>\n\n            <div class=\"vc-info-box\">\n                <p><strong>\ud83d\udca1 Tip:<\/strong> In vibration analysis, the harmonic spectrum pattern is a key diagnostic tool. Unbalance shows a dominant 1\u00d7 peak, misalignment shows strong 2\u00d7 (and sometimes 3\u00d7), and bearing defects generate non-synchronous frequencies related to bearing geometry.<\/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\/vibration-velocity\/\">Vibration Velocity (ISO 10816)<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/bearing-defect-frequencies\/\">Bearing Defect Frequencies (upcoming)<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/vibration-unit-converter\/\">Vibration Unit Converter<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/centrifugal-force-unbalance\/\">Centrifugal Force from Unbalance<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/residual-unbalance-iso1940\/\">Residual Unbalance (ISO 21940)<\/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        Identify harmonics, diagnose faults, and balance rotors on-site with our professional vibration analyzers and portable balancing systems.\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;\">Harmonic frequency and RPM-to-Hz conversion. 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 = 'harmonic-frequency-calculator';\n\n    function $(id) { return document.getElementById(id); }\n    function fmt(n, d) {\n        if (isNaN(n) || !isFinite(n)) return '\u2014';\n        if (Math.abs(n) >= 1e6) return n.toExponential(3);\n        var f = n.toFixed(d === undefined ? 2 : d);\n        return f.replace(\/(\\.\\d*?)0+$\/, '$1').replace(\/\\.$\/, '');\n    }\n    function fmtComma(n, d) {\n        var s = fmt(n, d);\n        if (s === '\u2014') return s;\n        return s.replace(\/\\B(?=(\\d{3})+(?!\\d))\/g, ',');\n    }\n\n    \/* \u2500\u2500 CALCULATION \u2500\u2500 *\/\n    function calculate() {\n        var speed = parseFloat($('vc-speed').value);\n        var numHarm = parseInt($('vc-harmonics').value);\n\n        if (!speed || speed <= 0) {\n            $('vc-results').classList.remove('vc-visible');\n            return;\n        }\n\n        var f1x = speed \/ 60;\n        var omega = 2 * Math.PI * f1x;\n        var period = 1 \/ f1x * 1000; \/\/ ms\n\n        \/\/ Primary results\n        $('vc-r-freq1x').innerHTML = fmt(f1x, 4) + ' <span class=\"vc-rcard-unit\">Hz<\/span> <span class=\"vc-rcard-unit\">(' + fmtComma(speed, 0) + ' CPM)<\/span>';\n        $('vc-r-period').innerHTML = fmt(period, 3) + ' <span class=\"vc-rcard-unit\">ms<\/span>';\n        $('vc-r-omega').innerHTML = fmt(omega, 2) + ' <span class=\"vc-rcard-unit\">rad\/s<\/span>';\n\n        \/\/ Harmonics table\n        var tbody = $('vc-harm-tbody');\n        var rows = '';\n        for (var i = 1; i <= numHarm; i++) {\n            var fHz = f1x * i;\n            var cpm = speed * i;\n            var per = 1 \/ fHz * 1000;\n            rows += '<tr>' +\n                '<td>' + i + '\u00d7<\/td>' +\n                '<td>' + fmt(fHz, 3) + '<\/td>' +\n                '<td>' + fmtComma(cpm, 0) + '<\/td>' +\n                '<td>' + fmt(per, 3) + '<\/td>' +\n                '<\/tr>';\n        }\n        tbody.innerHTML = rows;\n\n        $('vc-results').classList.add('vc-visible');\n\n        \/\/ URL params\n        var u = new URL(window.location);\n        u.searchParams.set('speed', speed);\n        u.searchParams.set('harmonics', numHarm);\n        history.replaceState(null, '', u.toString());\n\n        \/\/ History\n        saveHistory({\n            speed: speed,\n            harmonics: numHarm,\n            _summary: speed + ' RPM = ' + fmt(f1x, 2) + ' Hz, ' + numHarm + ' harmonics'\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-speed').value = this.getAttribute('data-s');\n            $('vc-harmonics').value = this.getAttribute('data-h');\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    $('vc-copy-btn').addEventListener('click', function() {\n        var speed = parseFloat($('vc-speed').value);\n        var numHarm = parseInt($('vc-harmonics').value);\n        var f1x = speed \/ 60;\n\n        var text = 'Harmonic 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            'Speed: ' + speed + ' RPM\\n' +\n            '1\u00d7 Frequency: ' + fmt(f1x, 4) + ' Hz\\n' +\n            'Period: ' + $('vc-r-period').textContent + '\\n' +\n            '\u03c9: ' + $('vc-r-omega').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\n        for (var i = 1; i <= numHarm; i++) {\n            text += i + '\u00d7: ' + fmt(f1x * i, 3) + ' Hz (' + fmtComma(speed * i, 0) + ' CPM)\\n';\n        }\n\n        text += '\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\/harmonic-frequency-calculator\/';\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: 'How do I convert RPM to Hz?', a: '<p>Simply divide RPM by 60:<\/p><p><strong>Hz = RPM \/ 60<\/strong><\/p><p>For example: 3000 RPM \/ 60 = 50 Hz. This gives the fundamental (1\u00d7) rotational frequency.<\/p>' },\n        { q: 'What are harmonics in vibration analysis?', a: '<p>Harmonics are integer multiples of the fundamental (1\u00d7) frequency:<\/p><ul><li>1\u00d7 = fundamental = one event per revolution<\/li><li>2\u00d7 = second harmonic = two events per revolution<\/li><li>3\u00d7 = third harmonic = three events per revolution<\/li><\/ul><p>Different faults produce characteristic harmonic patterns. Unbalance is primarily 1\u00d7, misalignment shows strong 2\u00d7 and sometimes 3\u00d7, and blade pass frequency is number-of-blades \u00d7 1\u00d7.<\/p>' },\n        { q: 'What does the 1\u00d7 vibration frequency indicate?', a: '<p>The 1\u00d7 frequency (one-per-revolution) is the most fundamental vibration component. Common 1\u00d7 sources:<\/p><ul><li><strong>Mass unbalance<\/strong> \u2014 the most common source<\/li><li><strong>Bent shaft<\/strong> \u2014 creates 1\u00d7 with axial component<\/li><li><strong>Eccentric rotor<\/strong> \u2014 electrical machines<\/li><li><strong>Resonance<\/strong> \u2014 if natural frequency coincides with 1\u00d7<\/li><\/ul><p>1\u00d7 vibration phase is crucial for balancing \u2014 it tells you the heavy spot direction.<\/p>' },\n        { q: 'Why are higher harmonics important?', a: '<p>Higher harmonics reveal specific mechanical faults:<\/p><ul><li><strong>2\u00d7<\/strong>: Misalignment (angular and parallel), looseness, cracked shaft<\/li><li><strong>3\u00d7 and above<\/strong>: Severe misalignment, mechanical looseness<\/li><li><strong>Blade pass (N\u00d7)<\/strong>: Impeller\/fan blade problems<\/li><li><strong>Gear mesh (Z\u00d7)<\/strong>: Gear tooth problems<\/li><\/ul><p>The ratio of harmonic amplitudes to 1\u00d7 amplitude is a key diagnostic indicator.<\/p>' },\n        { q: 'What is the difference between Hz, CPM, and orders?', a: '<p><strong>Hz (Hertz)<\/strong> = cycles per second. Absolute frequency unit.<\/p><p><strong>CPM (Cycles Per Minute)<\/strong> = Hz \u00d7 60. Numerically equal to RPM for 1\u00d7 order.<\/p><p><strong>Orders (1\u00d7, 2\u00d7, ...)<\/strong> = multiples of shaft speed. Speed-normalized \u2014 they stay the same regardless of RPM.<\/p><p>Example at 3000 RPM: 1\u00d7 = 50 Hz = 3000 CPM; 2\u00d7 = 100 Hz = 6000 CPM.<\/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.has('speed')) $('vc-speed').value = p.get('speed');\n        if (p.has('harmonics')) $('vc-harmonics').value = p.get('harmonics');\n    }\n\n    \/* \u2500\u2500 KATEX \u2500\u2500 *\/\n    function renderFormulas() {\n        try {\n            katex.render('f_{1\\\\times} = \\\\frac{n}{60} \\\\quad [\\\\text{Hz}]\\\\;, \\\\quad n\\\\;\\\\text{in RPM}', $('vc-katex-1'), { displayMode: true, throwOnError: false });\n            katex.render('f_{n\\\\times} = n \\\\cdot f_{1\\\\times} \\\\quad [\\\\text{Hz}]', $('vc-katex-2'), { displayMode: true, throwOnError: false });\n            katex.render('\\\\omega = 2\\\\pi f_{1\\\\times} = \\\\frac{2\\\\pi n}{60} \\\\quad [\\\\text{rad\/s}]', $('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>\u09ac\u09bf\u09a8\u09be\u09ae\u09c2\u09b2\u09cd\u09af\u09c7 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09b8\u09c1\u09b0\u09c7\u09b2\u09be \u09ab\u09cd\u09b0\u09bf\u0995\u09cb\u09af\u09bc\u09c7\u09a8\u09cd\u09b8\u09bf \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0\u0964 RPM \u09a5\u09c7\u0995\u09c7 Hz \u098f \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u0995\u09b0\u09c1\u09a8 \u098f\u09ac\u0982 \u09b8\u09c1\u09b0\u09c7\u09b2\u09be 1\u00d7 \u09a5\u09c7\u0995\u09c7 20\u00d7 \u09aa\u09cd\u09b0\u09a6\u09b0\u09cd\u09b6\u09a8 \u0995\u09b0\u09c1\u09a8\u0964 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u09b8\u09c1\u09b0\u09c7\u09b2\u09be \u0995\u09cd\u09b0\u09ae\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09b8\u09ae\u09af\u09bc\u0995\u09be\u09b2, \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997 \u098f\u09ac\u0982 CPM \u09a6\u09c7\u0996\u09c1\u09a8\u0964<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100126","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100126","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\/100126\/revisions"}],"predecessor-version":[{"id":100440,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100126\/revisions\/100440"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/media?parent=100126"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/categories?post=100126"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/tags?post=100126"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}