{"id":100049,"date":"2026-02-15T20:09:20","date_gmt":"2026-02-15T20:09:20","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100049"},"modified":"2026-02-15T20:09:20","modified_gmt":"2026-02-15T20:09:20","slug":"campbell-diagram-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bn\/calculators\/campbell-diagram-calculator\/","title":{"rendered":"\u0995\u09cd\u09af\u09be\u09ae\u09cd\u09aa\u09ac\u09c7\u09b2 \u09a1\u09be\u09af\u09bc\u09be\u0997\u09cd\u09b0\u09be\u09ae \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0 | \u0997\u09c1\u09b0\u09c1\u09a4\u09cd\u09ac\u09aa\u09c2\u09b0\u09cd\u09a3 \u0997\u09a4\u09bf\u09b0 \u09b9\u09b8\u09cd\u09a4\u0995\u09cd\u09b7\u09c7\u09aa | \u09ac\u09bf\u09a8\u09be\u09ae\u09c2\u09b2\u09cd\u09af\u09c7 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u099f\u09c1\u09b2"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Campbell Diagram Calculator\",\"alternateName\":[\"Critical Speed Calculator\",\"Interference Diagram Calculator\"],\"description\":\"Free online Campbell diagram calculator. Plots harmonic excitation orders against natural frequencies to find critical speed crossing points.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/campbell-diagram-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\":[\"Up to 5 natural frequencies\",\"Harmonic orders 1\u00d7\u201310\u00d7\",\"Critical speed crossing points\",\"Speed range analysis\",\"Auto-calculation\"],\"keywords\":\"Campbell diagram, critical speed, harmonic order, natural frequency, resonance\"}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"What is a Campbell diagram?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"A Campbell diagram (also called interference diagram) plots excitation frequencies (harmonics of running speed) against natural frequencies. Where harmonic lines cross natural frequency lines, a potential resonance or critical speed exists.\"}},\n{\"@type\":\"Question\",\"name\":\"What are harmonic orders?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Harmonic orders represent multiples of the rotational speed. 1\u00d7 is the fundamental (1 per revolution), 2\u00d7 is twice per revolution (common for misalignment), and higher orders relate to blade pass, gear mesh, etc.\"}},\n{\"@type\":\"Question\",\"name\":\"How do I find critical speeds from the diagram?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Critical speeds occur where harmonic order lines intersect natural frequency lines. The crossing RPM = fn \u00d7 60 \/ order, where fn is the natural frequency in Hz and order is the harmonic number.\"}},\n{\"@type\":\"Question\",\"name\":\"Why are critical speeds dangerous?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"At critical speeds, a harmonic excitation coincides with a natural frequency, causing resonance. This leads to amplified vibration, potential structural damage, and accelerated bearing\/component wear.\"}},\n{\"@type\":\"Question\",\"name\":\"How do I avoid critical speeds?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Ensure operating speed is at least 20% away from any critical speed. 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id=\"vc-campbell-diagram\">\n\n<header class=\"vc-header\">\n    <p class=\"vc-header-eyebrow\">Free Engineering Tool \u2014 #015<\/p>\n    <h1 class=\"vc-header-title\">Campbell Diagram Calculator<\/h1>\n    <p class=\"vc-header-subtitle\">Plot interference between harmonic excitation orders and natural frequencies. Identify critical speed crossing points for rotating machinery.<\/p>\n    <div class=\"vc-badges\">\n        <span class=\"vc-badge\">Up to 5 Natural Frequencies<\/span>\n        <span class=\"vc-badge\">Harmonics 1\u00d7\u201310\u00d7<\/span>\n        <span class=\"vc-badge\">Critical Speeds<\/span>\n    <\/div>\n<\/header>\n\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-rpm-min\">Min Speed <span class=\"vc-label-hint\">(RPM)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-rpm-min\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"e.g. 0\" value=\"0\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-rpm-max\">Max Speed <span class=\"vc-label-hint\">(RPM)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-rpm-max\" inputmode=\"decimal\" step=\"any\" min=\"1\" placeholder=\"e.g. 6000\" value=\"6000\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\">Natural Frequencies <span class=\"vc-label-hint\">(Hz, up to 5)<\/span><\/label>\n                <div style=\"display:flex;gap:6px;flex-wrap:wrap;\">\n                    <input class=\"vc-input\" type=\"number\" id=\"vc-fn1\" style=\"flex:1;min-width:80px\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"fn\u2081\" value=\"25\">\n                    <input class=\"vc-input\" type=\"number\" id=\"vc-fn2\" style=\"flex:1;min-width:80px\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"fn\u2082\" value=\"48\">\n                    <input class=\"vc-input\" type=\"number\" id=\"vc-fn3\" style=\"flex:1;min-width:80px\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"fn\u2083\" value=\"85\">\n                    <input class=\"vc-input\" type=\"number\" id=\"vc-fn4\" style=\"flex:1;min-width:80px\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"fn\u2084\">\n                    <input class=\"vc-input\" type=\"number\" id=\"vc-fn5\" style=\"flex:1;min-width:80px\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"fn\u2085\">\n                <\/div>\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-harmonics\">Harmonic Orders <span class=\"vc-label-hint\">(comma-separated)<\/span><\/label>\n                <input class=\"vc-input\" type=\"text\" id=\"vc-harmonics\" placeholder=\"e.g. 1,2,3,4\" value=\"1,2,3,4\">\n            <\/div>\n        <\/div>\n\n        <div class=\"vc-presets\">\n            <div class=\"vc-presets-label\">Quick presets<\/div>\n            <button type=\"button\" class=\"vc-preset-btn\" data-min=\"0\" data-max=\"3600\" data-fn=\"25,48,85\" data-h=\"1,2,3\">Pump 0\u20133600 RPM<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-min=\"0\" data-max=\"12000\" data-fn=\"55,120,210\" data-h=\"1,2,3,4\">Turbo 0\u201312000 RPM<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-min=\"0\" data-max=\"6000\" data-fn=\"30,62\" data-h=\"1,2,3,6\">Fan 0\u20136000 RPM<\/button>\n        <\/div>\n    <\/form>\n\n    <div class=\"vc-results\" id=\"vc-results\">\n        <div class=\"vc-results-head\">\n            <h2 class=\"vc-results-title\">Critical Speed Crossings<\/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\">Total Crossings in Speed Range<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-total\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Speed Range<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-range\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Natural Frequencies<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-fns\">\u2014<\/div>\n            <\/div>\n        <\/div>\n        <div id=\"vc-crossing-table\"><\/div>\n        <div class=\"vc-viz\" id=\"vc-viz\"><div class=\"vc-viz-title\">Campbell Diagram<\/div><div id=\"vc-viz-svg\"><\/div><\/div>\n    <\/div>\n<\/div>\n\n<!-- Theory -->\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\"><span class=\"vc-section-icon\">\ud83d\udcd8<\/span><span class=\"vc-section-title\">Theory &amp; Formulas<\/span><\/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>Campbell Diagram Principle<\/h3>\n            <p>The Campbell diagram plots excitation frequency vs. rotational speed. For each harmonic order <em>k<\/em>, the excitation frequency at speed <em>n<\/em> is:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n            <p>A crossing (critical speed) occurs when a harmonic excitation matches a natural frequency:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n\n            <h3>Common Harmonic Orders<\/h3>\n            <table class=\"vc-table\">\n                <thead><tr><th>Order<\/th><th>Source<\/th><\/tr><\/thead>\n                <tbody>\n                    <tr><td>1\u00d7<\/td><td>Unbalance, bow, eccentricity<\/td><\/tr>\n                    <tr><td>2\u00d7<\/td><td>Misalignment, elliptical bearing, looseness<\/td><\/tr>\n                    <tr><td>3\u00d7<\/td><td>Misalignment (severe), coupling defects<\/td><\/tr>\n                    <tr><td>k\u00d7 (blade pass)<\/td><td>Number of blades \u00d7 RPM<\/td><\/tr>\n                    <tr><td>k\u00d7 (gear mesh)<\/td><td>Number of teeth \u00d7 RPM<\/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 Centrifugal Pump<\/div>\n                <p><strong>Given:<\/strong> f<sub>n1<\/sub> = 25 Hz, f<sub>n2<\/sub> = 48 Hz, Harmonics: 1\u00d7, 2\u00d7, 3\u00d7<\/p>\n                <p>1\u00d7 crossing at f<sub>n1<\/sub>: RPM = 25 \u00d7 60 \/ 1 = <strong>1500 RPM<\/strong><\/p>\n                <p>2\u00d7 crossing at f<sub>n1<\/sub>: RPM = 25 \u00d7 60 \/ 2 = <strong>750 RPM<\/strong><\/p>\n                <p>1\u00d7 crossing at f<sub>n2<\/sub>: RPM = 48 \u00d7 60 \/ 1 = <strong>2880 RPM<\/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> Keep operating speed at least 20% away from any critical speed. If a critical speed must be passed during run-up, accelerate quickly through the resonance zone.<\/p>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\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\"><span class=\"vc-section-icon\">\ud83d\udd17<\/span><span class=\"vc-section-title\">Related Calculators<\/span><\/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\"><div class=\"vc-related\">\n            <a class=\"vc-related-link\" href=\"\/calculators\/vibration-transmissibility\/\">Vibration Transmissibility<\/a>\n            <a class=\"vc-related-link\" href=\"\/calculators\/residual-unbalance-iso1940\/\">Residual Unbalance (ISO 21940)<\/a>\n            <a class=\"vc-related-link\" href=\"\/calculators\/flexible-rotor-balancing\/\">Flexible Rotor Balancing<\/a>\n            <a class=\"vc-related-link\" href=\"\/calculators\/vibration-overall-level\/\">Overall Vibration Level<\/a>\n        <\/div><\/div>\n    <\/div>\n<\/div>\n\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\"><span class=\"vc-section-icon\">\u2753<\/span><span class=\"vc-section-title\">Frequently Asked Questions<\/span><\/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\"><div class=\"vc-section-inner\"><div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div><\/div><\/div>\n<\/div>\n\n<div class=\"vc-promo\">\n    <div class=\"vc-promo-text\"><strong>Vibromera \u2014 Portable Balancing &amp; Vibration Analysis<\/strong><br>Identify critical speeds and resonances in the field with professional vibration analyzers. Used in 50+ countries.<\/div>\n    <a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a>\n<\/div>\n\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;\">Campbell diagram &#038; critical speed analysis. Last updated: February 2025<\/p>\n    <div class=\"vc-footer-links\"><a href=\"\/calculators\/engineering-calculators\/\">All Calculators<\/a><a href=\"https:\/\/vibromera.eu\/contacts\/\">Contact<\/a><\/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    var SLUG='campbell-diagram-calculator';\n    function $(id){return document.getElementById(id)}\n    function fmt(n,d){if(isNaN(n)||!isFinite(n))return '\u2014';return n.toFixed(d===undefined?1:d).replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,'')}\n\n    function calculate(){\n        var rpmMin=parseFloat($('vc-rpm-min').value)||0;\n        var rpmMax=parseFloat($('vc-rpm-max').value);\n        if(!rpmMax||rpmMax<=rpmMin){$('vc-results').classList.remove('vc-visible');return}\n\n        var fns=[];\n        for(var i=1;i<=5;i++){var v=parseFloat($('vc-fn'+i).value);if(v&&v>0)fns.push(v)}\n        if(fns.length===0){$('vc-results').classList.remove('vc-visible');return}\n\n        var hStr=$('vc-harmonics').value;\n        var harmonics=hStr.split(',').map(function(s){return parseFloat(s.trim())}).filter(function(v){return v&&v>0});\n        if(harmonics.length===0){$('vc-results').classList.remove('vc-visible');return}\n\n        var crossings=[];\n        harmonics.forEach(function(h){\n            fns.forEach(function(fn){\n                var rpm=fn*60\/h;\n                if(rpm>=rpmMin&&rpm<=rpmMax){\n                    crossings.push({order:h,fn:fn,rpm:rpm});\n                }\n            });\n        });\n        crossings.sort(function(a,b){return a.rpm-b.rpm});\n\n        $('vc-r-total').innerHTML=crossings.length+' <span class=\"vc-rcard-unit\">crossing'+(crossings.length!==1?'s':'')+'<\/span>';\n        $('vc-r-range').innerHTML=fmt(rpmMin,0)+'\u2013'+fmt(rpmMax,0)+' <span class=\"vc-rcard-unit\">RPM<\/span>';\n        $('vc-r-fns').innerHTML=fns.map(function(f){return fmt(f,1)}).join(', ')+' <span class=\"vc-rcard-unit\">Hz<\/span>';\n\n        var html='';\n        if(crossings.length>0){\n            html='<table class=\"vc-table vc-crossing-table\"><thead><tr><th>Order<\/th><th>Natural Freq (Hz)<\/th><th>Critical Speed (RPM)<\/th><\/tr><\/thead><tbody>';\n            crossings.forEach(function(c){\n                html+='<tr><td>'+c.order+'\u00d7<\/td><td>'+fmt(c.fn,1)+'<\/td><td><strong>'+fmt(c.rpm,0)+'<\/strong><\/td><\/tr>';\n            });\n            html+='<\/tbody><\/table>';\n        } else {\n            html='<div class=\"vc-info-box\"><p>No crossings found in the specified speed range.<\/p><\/div>';\n        }\n        $('vc-crossing-table').innerHTML=html;\n        $('vc-results').classList.add('vc-visible');\n        drawCampbellViz(rpmMin, rpmMax, fns, harmonics, crossings);\n\n        saveHistory({fns:fns.join(','),harmonics:harmonics.join(','),crossings:crossings.length,_summary:crossings.length+' crossings in '+fmt(rpmMin,0)+'\u2013'+fmt(rpmMax,0)+' RPM'});\n    }\n\n    function drawCampbellViz(rpmMin, rpmMax, fns, harmonics, crossings) {\n        var el = $('vc-viz-svg'); if (!el) return;\n        var W = 560, H = 300, mx = 55, my = 25, pw = W - 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3) + '\" text-anchor=\"middle\" font-size=\"9\" font-family=\"var(--vc-mono)\" fill=\"var(--vc-ink-muted)\">Speed (RPM)<\/text>';\n        s += '<text x=\"12\" y=\"' + (my + ph \/ 2) + '\" text-anchor=\"middle\" font-size=\"9\" font-family=\"var(--vc-mono)\" fill=\"var(--vc-ink-muted)\" transform=\"rotate(-90,12,' + (my + ph \/ 2) + ')\">Freq (Hz)<\/text>';\n        \/\/ Natural frequency horizontal lines\n        fns.forEach(function(fn, i) {\n            var y = yF(fn);\n            s += '<line x1=\"' + mx + '\" y1=\"' + y.toFixed(1) + '\" x2=\"' + (mx + pw) + '\" y2=\"' + y.toFixed(1) + '\" stroke=\"var(--vc-red,#b91c1c)\" stroke-width=\"1.5\" stroke-dasharray=\"6,4\"\/>';\n            s += '<text x=\"' + (mx + pw + 3) + '\" y=\"' + (y + 3).toFixed(1) + '\" font-size=\"8\" font-family=\"var(--vc-mono)\" fill=\"var(--vc-red,#b91c1c)\">fn' + (i + 1) + '<\/text>';\n        });\n        \/\/ Harmonic lines\n        harmonics.forEach(function(h, i) {\n            var c = hColors[i % hColors.length];\n            var y1 = yF(h * rpmMin \/ 60), y2 = yF(h * rpmMax \/ 60);\n            s += '<line x1=\"' + xR(rpmMin).toFixed(1) + '\" y1=\"' + y1.toFixed(1) + '\" x2=\"' + xR(rpmMax).toFixed(1) + '\" y2=\"' + y2.toFixed(1) + '\" stroke=\"' + c + '\" stroke-width=\"1.5\"\/>';\n            s += '<text x=\"' + (xR(rpmMax) + 3).toFixed(1) + '\" y=\"' + (y2 + 3).toFixed(1) + '\" font-size=\"8\" font-family=\"var(--vc-mono)\" fill=\"' + c + '\">' + h + '\u00d7<\/text>';\n        });\n        \/\/ Crossing dots\n        crossings.forEach(function(cr) {\n            var x = xR(cr.rpm), y = yF(cr.fn);\n            s += '<circle cx=\"' + x.toFixed(1) + '\" cy=\"' + y.toFixed(1) + '\" r=\"5\" fill=\"var(--vc-red,#b91c1c)\" stroke=\"#fff\" stroke-width=\"1.5\"\/>';\n        });\n        s += '<\/svg>';\n        el.innerHTML = s;\n    }\n\n    document.querySelectorAll('.vc-preset-btn').forEach(function(btn){\n        btn.addEventListener('click',function(e){\n            e.preventDefault();\n            $('vc-rpm-min').value=this.getAttribute('data-min');\n            $('vc-rpm-max').value=this.getAttribute('data-max');\n            var fnv=this.getAttribute('data-fn').split(',');\n            for(var i=1;i<=5;i++) $('vc-fn'+i).value=fnv[i-1]||'';\n            $('vc-harmonics').value=this.getAttribute('data-h');\n            calculate();\n        });\n    });\n\n    $('vc-form').addEventListener('input',calculate);\n    $('vc-form').addEventListener('change',calculate);\n\n    $('vc-copy-btn').addEventListener('click',function(){\n        var rows=document.querySelectorAll('.vc-crossing-table tbody tr');\n        var text='Campbell Diagram \u2014 Critical Speed Crossings\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nSpeed Range: '+$('vc-r-range').textContent+'\\n';\n        rows.forEach(function(r){var cells=r.querySelectorAll('td');text+=cells[0].textContent+' at '+cells[1].textContent+' Hz \u2192 '+cells[2].textContent+' RPM\\n'});\n        text+='\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nvibromera.eu\/calculators\/campbell-diagram-calculator\/';\n        if(navigator.clipboard){navigator.clipboard.writeText(text).then(function(){var b=$('vc-copy-btn');b.classList.add('vc-copied');b.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!';setTimeout(function(){b.classList.remove('vc-copied');b.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'},2000)})}\n    });\n\n    document.querySelectorAll('.vc-section-toggle').forEach(function(btn){btn.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'))})});\n\n    var faqData=[\n        {q:'What is a Campbell diagram?',a:'<p>A Campbell diagram plots excitation frequencies (harmonics of running speed) against natural frequencies. Intersections indicate potential resonance \u2014 critical speeds where amplified vibration may occur.<\/p>'},\n        {q:'What are harmonic orders?',a:'<p>Harmonic orders are multiples of the shaft rotation frequency. 1\u00d7 = once per revolution (unbalance), 2\u00d7 = twice per revolution (misalignment), higher orders relate to blade pass, gear mesh, etc.<\/p>'},\n        {q:'How do I find critical speeds?',a:'<p>Critical speed RPM = f<sub>n<\/sub> \u00d7 60 \/ order. For example, if f<sub>n<\/sub> = 50 Hz and order = 2\u00d7, critical speed = 50 \u00d7 60 \/ 2 = 1500 RPM.<\/p>'},\n        {q:'Why are critical speeds dangerous?',a:'<p>At critical speeds, excitation frequency matches a natural frequency causing resonance, amplified vibration, possible structural damage, and accelerated bearing wear.<\/p>'},\n        {q:'How do I avoid critical speeds?',a:'<p>Maintain at least 20% separation margin. Options: change stiffness\/mass (shift natural frequencies), add damping, modify operating speed range, or pass through resonance quickly during run-up\/down.<\/p>'}\n    ];\n    var fl=$('vc-faq-list');faqData.forEach(function(f){fl.innerHTML+='<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>'+f.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\">'+f.a+'<\/div><\/div><\/div>'});\n    fl.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(!b)return;b.closest('.vc-faq-item').classList.toggle('vc-open')});\n\n    function saveHistory(entry){var key='vc_history_'+SLUG;var arr=[];try{arr=JSON.parse(localStorage.getItem(key))||[]}catch(e){}entry._ts=new Date().toISOString();arr.unshift(entry);if(arr.length>10)arr=arr.slice(0,10);try{localStorage.setItem(key,JSON.stringify(arr))}catch(e){}}\n\n    function renderFormulas(){try{\n        katex.render('f_{exc} = k \\\\times \\\\frac{n}{60} \\\\quad [\\\\text{Hz}]',$('vc-katex-1'),{displayMode:true,throwOnError:false});\n        katex.render('n_{crit} = \\\\frac{f_n \\\\times 60}{k} \\\\quad [\\\\text{RPM}]',$('vc-katex-2'),{displayMode:true,throwOnError:false});\n    }catch(e){}}\n\n    function init(){renderFormulas();calculate()}\n    if(document.readyState==='loading'){document.addEventListener('DOMContentLoaded',init)}else{init()}\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 \u0995\u09cd\u09af\u09be\u09ae\u09cd\u09aa\u09ac\u09c7\u09b2 \u09a1\u09be\u09af\u09bc\u09be\u0997\u09cd\u09b0\u09be\u09ae \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0\u0964 \u09b8\u09c1\u09b0\u09c7\u09b2\u09be \u0995\u09cd\u09b0\u09ae \u098f\u09ac\u0982 \u09aa\u09cd\u09b0\u09be\u0995\u09c3\u09a4\u09bf\u0995 \u09ab\u09cd\u09b0\u09bf\u0995\u09cb\u09af\u09bc\u09c7\u09a8\u09cd\u09b8\u09bf\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b9\u09b8\u09cd\u09a4\u0995\u09cd\u09b7\u09c7\u09aa \u09aa\u09cd\u09b2\u099f \u0995\u09b0\u09c1\u09a8\u0964 \u0998\u09c2\u09b0\u09cd\u09a3\u09be\u09af\u09bc\u09ae\u09be\u09a8 \u09af\u09a8\u09cd\u09a4\u09cd\u09b0\u09aa\u09be\u09a4\u09bf\u09b0 \u099c\u09a8\u09cd\u09af \u0997\u09c1\u09b0\u09c1\u09a4\u09cd\u09ac\u09aa\u09c2\u09b0\u09cd\u09a3 \u0997\u09a4\u09bf\u09b0 \u0995\u09cd\u09b0\u09b8\u09bf\u0982 \u09aa\u09af\u09bc\u09c7\u09a8\u09cd\u099f \u0996\u09c1\u0981\u099c\u09c1\u09a8\u0964<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100049","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100049","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\/100049\/revisions"}],"predecessor-version":[{"id":100360,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100049\/revisions\/100360"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/media?parent=100049"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/categories?post=100049"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/tags?post=100049"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}