{"id":70,"date":"2025-10-31T00:25:51","date_gmt":"2025-10-31T00:25:51","guid":{"rendered":"https:\/\/vibromera.eu\/glossary\/campbell-diagram\/"},"modified":"2026-06-08T04:12:26","modified_gmt":"2026-06-08T04:12:26","slug":"campbell-diagram","status":"publish","type":"glossary","link":"https:\/\/vibromera.eu\/nb\/glossary\/campbell-diagram\/","title":{"rendered":"Hva er et Campbell-diagram? Kritisk hastighetsanalyse"},"content":{"rendered":"
\n\n\n\n\nCampbell Diagram in Rotor Dynamics \u2014 Complete Guide to Critical Speed Analysis | Vibromera<\/title>\n<meta name=\"description\" content=\"Campbell diagram explained: how to read whirl speed maps, identify critical speeds, interpret forward\/backward whirl modes. Includes interactive SVG diagram, API 617 separation margins, bearing effects, and practical examples for turbines, compressors, and pumps.\">\n<meta name=\"keywords\" content=\"Campbell diagram, whirl speed map, interference diagram, critical speed, rotor dynamics, natural frequency, gyroscopic effect, forward whirl, backward whirl, API 617, separation margin, Bode plot, waterfall plot\">\n<meta name=\"author\" content=\"Nikolai Shelkovenko\">\n<meta name=\"robots\" content=\"index, follow, max-image-preview:large, max-snippet:-1\">\n\n\n<!-- Open Graph -->\n<meta property=\"og:type\" content=\"article\">\n<meta property=\"og:url\" content=\"https:\/\/vibromera.eu\/glossary\/campbell-diagram\/\">\n<meta property=\"og:title\" content=\"Campbell Diagram in Rotor Dynamics \u2014 Complete Guide to Critical Speed Analysis\">\n<meta property=\"og:description\" content=\"How to read and interpret Campbell diagrams. Forward\/backward whirl, gyroscopic splitting, API 617 separation margins, practical examples.\">\n<meta property=\"og:site_name\" content=\"Vibromera\">\n<meta property=\"og:locale\" content=\"en_US\">\n\n<!-- Twitter -->\n<meta name=\"twitter:card\" content=\"summary_large_image\">\n<meta name=\"twitter:title\" content=\"Campbell Diagram \u2014 Critical Speed Analysis Guide\">\n<meta name=\"twitter:description\" content=\"Complete guide to Campbell diagrams in rotor dynamics. Interactive diagram, API standards, practical examples.\">\n\n<!-- Schema.org -->\n<script type=\"application\/ld+json\">\n{\n \"@context\": \"https:\/\/schema.org\",\n \"@graph\": [\n {\n \"@type\": \"TechArticle\",\n \"@id\": \"https:\/\/vibromera.eu\/glossary\/campbell-diagram\/#article\",\n \"headline\": \"Campbell Diagram in Rotor Dynamics \u2014 Complete Guide to Critical Speed Analysis\",\n \"description\": \"Comprehensive guide to Campbell diagrams: how to read whirl speed maps, identify critical speeds, interpret gyroscopic splitting, and apply API 617 separation margin requirements.\",\n \"author\": {\n \"@type\": \"Person\",\n \"name\": \"Nikolai Shelkovenko\",\n \"jobTitle\": \"CEO & Field Engineer\",\n \"worksFor\": { \"@type\": \"Organization\", \"name\": \"Vibromera\" }\n },\n \"publisher\": {\n \"@type\": \"Organization\",\n \"name\": \"Vibromera\",\n \"url\": \"https:\/\/vibromera.eu\"\n },\n \"datePublished\": \"2024-10-31\",\n \"dateModified\": \"2026-02-11\",\n \"mainEntityOfPage\": \"https:\/\/vibromera.eu\/glossary\/campbell-diagram\/\",\n \"about\": [\n { \"@type\": \"Thing\", \"name\": \"Campbell diagram\", \"sameAs\": \"https:\/\/www.wikidata.org\/wiki\/Q5026944\" },\n { \"@type\": \"Thing\", \"name\": \"Rotor dynamics\", \"sameAs\": \"https:\/\/www.wikidata.org\/wiki\/Q2296646\" },\n { \"@type\": \"Thing\", \"name\": \"Critical speed\", \"sameAs\": \"https:\/\/www.wikidata.org\/wiki\/Q5186265\" },\n { \"@type\": \"Thing\", \"name\": \"Resonance\", \"sameAs\": \"https:\/\/www.wikidata.org\/wiki\/Q49007\" }\n ],\n \"speakable\": {\n \"@type\": \"SpeakableSpecification\",\n \"cssSelector\": [\".cd-hero__subtitle\", \".cd-definition__text\"]\n },\n \"inLanguage\": \"en\"\n },\n {\n \"@type\": \"FAQPage\",\n \"@id\": \"https:\/\/vibromera.eu\/glossary\/campbell-diagram\/#faq\",\n \"mainEntity\": [\n {\n \"@type\": \"Question\",\n \"name\": \"What is the difference between a Campbell diagram and a Bode plot?\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"A Campbell diagram plots natural frequencies versus rotational speed to predict where critical speeds will occur. A Bode plot shows measured vibration amplitude and phase versus speed during an actual run-up or coastdown, confirming actual critical speed locations and amplification factors.\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"What separation margin does API 617 require from critical speeds?\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"API 617 uses the formula SM = 17 \u00d7 {1 \u2212 [1\/(AF \u2212 1.5)]} where AF is the amplification factor. If AF < 2.5, the response is considered critically damped and no separation margin is required. If AF \u2265 2.5, the calculated SM typically yields 15\u201326% depending on damping, with a cap of 16% for critical speeds below minimum operating speed.\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Why do natural frequencies split on a Campbell diagram?\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"Gyroscopic moments cause each non-rotating natural frequency to split into a forward whirl mode (frequency increases with speed) and a backward whirl mode (frequency decreases with speed). The splitting magnitude depends on the polar-to-diametral moment of inertia ratio of the disks.\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"Can you create a Campbell diagram from field measurements?\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"Yes. Record vibration during a startup or coastdown run, generate a waterfall (cascade) plot of the vibration spectrum at each RPM step, then extract the peak frequencies. Plotting those peaks against rotational speed produces an experimental Campbell diagram.\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"What excitation orders should be included on a Campbell diagram?\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"Always include 1\u00d7 (unbalance). Add 2\u00d7 for misalignment, coupling defects, or cracked shafts. Include higher orders (3\u00d7, blade-pass, vane-pass) based on the specific machine type. For machines with fluid-film bearings, add a 0.43\u20130.48\u00d7 line for oil whirl.\"\n }\n },\n {\n \"@type\": \"Question\",\n \"name\": \"How does bearing type affect the shape of a Campbell diagram?\",\n \"acceptedAnswer\": {\n \"@type\": \"Answer\",\n \"text\": \"Rolling-element bearings provide nearly constant stiffness, producing flat natural frequency curves. Fluid-film (journal) bearings increase stiffness with speed, causing natural frequency curves to rise. 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color: #000 !important; }\n .cd-toc, .cd-cta { display: none; }\n .cd-content h2 { break-before: page; }\n}\n<\/style>\n<\/head>\n<body>\n\n<!-- Breadcrumb -->\n<nav class=\"cd-breadcrumb\" aria-label=\"Breadcrumb\">\n <a href=\"https:\/\/vibromera.eu\/\">Home<\/a><span>\u203a<\/span>\n <a href=\"https:\/\/vibromera.eu\/glossary\/\">Glossary<\/a><span>\u203a<\/span>\n Campbell Diagram\n<\/nav>\n\n<!-- HERO -->\n<header class=\"cd-hero\">\n <div class=\"cd-hero__inner\">\n <div class=\"cd-hero__badge\">Rotor Dynamics Glossary<\/div>\n <h1>Campbell Diagram<\/h1>\n <p class=\"cd-hero__subtitle\">A frequency-vs-speed map that reveals critical speeds, gyroscopic splitting, and resonance hazard zones in rotating machinery \u2014 from micro-turbines to multi-megawatt compressor trains.<\/p>\n <\/div>\n<\/header>\n\n<!-- LAYOUT: TOC + Content -->\n<div class=\"cd-layout\">\n\n <!-- TOC -->\n <aside class=\"cd-toc\" aria-label=\"Table of contents\">\n <div class=\"cd-toc__title\">Contents<\/div>\n <ol>\n <li><a href=\"#definition\">Definition<\/a><\/li>\n <li><a href=\"#history\">Historical Background<\/a><\/li>\n <li><a href=\"#structure\">Anatomy of the Diagram<\/a><\/li>\n <li><a href=\"#interactive\">Interactive Campbell Diagram<\/a><\/li>\n <li><a href=\"#how-to-read\">How to Read & Interpret<\/a><\/li>\n <li><a href=\"#gyroscopic\">Gyroscopic Effects<\/a><\/li>\n <li><a href=\"#bearings\">Bearing Effects<\/a><\/li>\n <li><a href=\"#standards\">API 617 & Separation Margins<\/a><\/li>\n <li><a href=\"#creating\">Analytical vs Experimental<\/a><\/li>\n <li><a href=\"#applications\">Applications by Machine Type<\/a><\/li>\n <li><a href=\"#comparisons\">Related Diagrams & Plots<\/a><\/li>\n <li><a href=\"#practical\">Practical Example<\/a><\/li>\n <li><a href=\"#software\">Software Tools<\/a><\/li>\n <li><a href=\"#common-mistakes\">Common Mistakes<\/a><\/li>\n <li><a href=\"#faq\">FAQ<\/a><\/li>\n <\/ol>\n <\/aside>\n\n <!-- CONTENT -->\n <main class=\"cd-content\">\n\n <!-- 1. DEFINITION -->\n <section id=\"definition\">\n <h2>Definition<\/h2>\n <div class=\"cd-definition\">\n <div class=\"cd-definition__label\">Technical Definition<\/div>\n <p class=\"cd-definition__text\">\n A <strong>Campbell diagram<\/strong> (also called a <em>whirl speed map<\/em> or <em>interference diagram<\/em>) is a graph that plots the <a href=\"\/glossary\/natural-frequency\/\">natural frequencies<\/a> of a rotor-bearing system on the vertical axis against rotational speed on the horizontal axis. Diagonal excitation-order lines (1\u00d7, 2\u00d7, 3\u00d7\u2026) are superimposed; wherever an excitation line crosses a natural-frequency curve, a <a href=\"\/glossary\/critical-speed\/\">critical speed<\/a> exists. The diagram is the primary tool for determining whether a machine's operating range is safely separated from <a href=\"\/glossary\/resonance\/\">resonance<\/a> conditions.\n <\/p>\n <\/div>\n <p>In a sentence: the Campbell diagram answers one question \u2014 <em>\"At which speeds will this rotor resonate, and how close are those speeds to where I plan to operate?\"<\/em><\/p>\n <\/section>\n\n <!-- 2. HISTORY -->\n <section id=\"history\">\n <h2>Historical Background<\/h2>\n <p>Wilfred Campbell published the concept in 1924 while studying circumferential waves in steam-turbine discs at General Electric. His original chart plotted disc vibration modes against rotational speed to predict where destructive resonances would appear during operation.<\/p>\n <p>The approach filled a gap that had troubled engineers since the 1890s. W. J. M. Rankine's 1869 shaft-whirling analysis had incorrectly predicted that supercritical operation was impossible. Gustaf de Laval proved otherwise by running a steam turbine above its first critical speed in 1889. Henry Jeffcott's landmark 1919 paper finally explained <em>why<\/em> supercritical operation is stable, but Campbell's diagram gave engineers the <em>visual tool<\/em> to predict exactly where those dangerous speeds lie \u2014 and how to design around them.<\/p>\n <p>Over the following decades, the concept expanded from disc vibrations to full lateral rotor analysis, torsional analysis, and even acoustics. Today, every major API, ISO, and IEC standard for rotating machinery either requires or recommends Campbell-diagram analysis.<\/p>\n <\/section>\n\n <!-- 3. STRUCTURE -->\n <section id=\"structure\">\n <h2>Anatomy of the Diagram<\/h2>\n <p>A Campbell diagram carries four families of information on a single plot. Understanding each layer is necessary before you can read intersections correctly.<\/p>\n\n <h3>Axes<\/h3>\n <p>The horizontal axis is rotational speed, typically in RPM or Hz. The vertical axis is frequency, in Hz or CPM. When both axes use the same unit, the 1\u00d7 excitation line runs at exactly 45\u00b0 \u2014 a useful visual check that the scale is correct.<\/p>\n\n <h3>Natural-Frequency Curves<\/h3>\n <p>Each curve represents one vibration mode of the rotor-bearing-support system. In the simplest case (rigid bearings, no gyroscopic effects), these curves are horizontal lines because the natural frequencies do not change with speed. In reality, gyroscopic moments and speed-dependent bearing stiffness cause the curves to slope, split, or both.<\/p>\n <p>Modes are labeled by deflection shape: first bending (one antinode), second bending (two antinodes with one node), third bending, and so on. Torsional and axial modes may also be plotted if relevant.<\/p>\n\n <h3>Forward and Backward Whirl<\/h3>\n <p>When gyroscopic effects are significant, each non-spinning natural frequency splits into two curves as speed increases:<\/p>\n <ul>\n <li><strong>Forward whirl (FW):<\/strong> the mode precesses in the same direction as the shaft rotation. Gyroscopic stiffening pushes its frequency <em>up<\/em>.<\/li>\n <li><strong>Backward whirl (BW):<\/strong> the mode precesses opposite to rotation. Gyroscopic softening pushes its frequency <em>down<\/em>.<\/li>\n <\/ul>\n <p>Forward whirl modes are the primary concern for <a href=\"\/glossary\/unbalance\/\">unbalance<\/a>-driven resonance because unbalance excites synchronous forward precession.<\/p>\n\n <h3>Excitation-Order Lines<\/h3>\n <p>These are straight diagonal lines radiating from the origin. Each line represents an excitation whose frequency is a fixed multiple of rotational speed:<\/p>\n\n <div class=\"cd-table-wrap\">\n <table class=\"cd-table\">\n <thead>\n <tr><th>Line<\/th><th>Relationship<\/th><th>Typical Source<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td><strong>1\u00d7<\/strong><\/td><td>f = 1 \u00d7 RPM\/60<\/td><td><a href=\"\/glossary\/unbalance\/\">Mass unbalance<\/a>, shaft bow<\/td><\/tr>\n <tr><td><strong>2\u00d7<\/strong><\/td><td>f = 2 \u00d7 RPM\/60<\/td><td><a href=\"\/glossary\/misalignment\/\">Misalignment<\/a>, cracked shaft, ovality<\/td><\/tr>\n <tr><td><strong>3\u00d7, 4\u00d7\u2026<\/strong><\/td><td>f = n \u00d7 RPM\/60<\/td><td>Gear mesh, vane\/blade pass, coupling defects<\/td><\/tr>\n <tr><td><strong>0.43\u20130.48\u00d7<\/strong><\/td><td>f \u2248 0.45 \u00d7 RPM\/60<\/td><td>Oil whirl in fluid-film bearings<\/td><\/tr>\n <tr><td><strong>Blade-pass<\/strong><\/td><td>f = Z \u00d7 RPM\/60<\/td><td>Number of blades Z \u00d7 running speed<\/td><\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h3>Intersection Points = Critical Speeds<\/h3>\n <p>Each intersection between an excitation line and a natural-frequency curve marks a potential resonance. The RPM value at that intersection is a critical speed for that particular mode-excitation combination. If the operating range includes or is close to that RPM, the machine risks high vibration amplitudes.<\/p>\n <\/section>\n\n <!-- 4. INTERACTIVE DIAGRAM -->\n <section id=\"interactive\">\n <h2>Interactive Campbell Diagram<\/h2>\n <p>The SVG below shows a typical Campbell diagram for a two-bearing, flexible-shaft rotor. Hover over elements to identify modes, excitation lines, and critical speed intersections.<\/p>\n\n <div class=\"cd-diagram-wrap\">\n <svg viewBox=\"0 0 720 460\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" font-family=\"IBM Plex Sans, sans-serif\" role=\"img\" aria-label=\"Campbell diagram showing natural frequency curves, excitation lines, and critical speed intersections\">\n <title>Campbell Diagram \u2014 Interactive Example<\/title>\n\n <!-- Background grid -->\n <defs>\n <pattern id=\"cdGrid\" width=\"60\" height=\"40\" patternUnits=\"userSpaceOnUse\">\n <path d=\"M 60 0 L 0 0 0 40\" fill=\"none\" stroke=\"#e0ddd5\" stroke-width=\"0.5\"\/>\n <\/pattern>\n <\/defs>\n <rect x=\"80\" y=\"20\" width=\"600\" height=\"400\" fill=\"url(#cdGrid)\" rx=\"2\"\/>\n\n <!-- Axes -->\n <line x1=\"80\" y1=\"420\" x2=\"680\" y2=\"420\" stroke=\"#0f1b2d\" stroke-width=\"1.5\"\/>\n <line x1=\"80\" y1=\"420\" x2=\"80\" y2=\"20\" stroke=\"#0f1b2d\" stroke-width=\"1.5\"\/>\n\n <!-- X-axis labels -->\n <text x=\"380\" y=\"455\" text-anchor=\"middle\" font-size=\"12\" fill=\"#5a5a5a\" font-weight=\"600\">Rotational Speed (RPM)<\/text>\n <text x=\"80\" y=\"438\" text-anchor=\"middle\" font-size=\"9\" fill=\"#5a5a5a\">0<\/text>\n <text x=\"200\" y=\"438\" text-anchor=\"middle\" font-size=\"9\" fill=\"#5a5a5a\">3,000<\/text>\n <text x=\"320\" y=\"438\" text-anchor=\"middle\" font-size=\"9\" fill=\"#5a5a5a\">6,000<\/text>\n <text x=\"440\" y=\"438\" text-anchor=\"middle\" font-size=\"9\" fill=\"#5a5a5a\">9,000<\/text>\n <text x=\"560\" y=\"438\" text-anchor=\"middle\" font-size=\"9\" fill=\"#5a5a5a\">12,000<\/text>\n <text x=\"680\" y=\"438\" text-anchor=\"middle\" font-size=\"9\" fill=\"#5a5a5a\">15,000<\/text>\n\n <!-- Y-axis label -->\n <text x=\"28\" y=\"220\" text-anchor=\"middle\" font-size=\"12\" fill=\"#5a5a5a\" font-weight=\"600\" transform=\"rotate(-90 28 220)\">Frequency (Hz)<\/text>\n <text x=\"72\" y=\"420\" text-anchor=\"end\" font-size=\"9\" fill=\"#5a5a5a\">0<\/text>\n <text x=\"72\" y=\"340\" text-anchor=\"end\" font-size=\"9\" fill=\"#5a5a5a\">50<\/text>\n <text x=\"72\" y=\"260\" text-anchor=\"end\" font-size=\"9\" fill=\"#5a5a5a\">100<\/text>\n <text x=\"72\" y=\"180\" text-anchor=\"end\" font-size=\"9\" fill=\"#5a5a5a\">150<\/text>\n <text x=\"72\" y=\"100\" text-anchor=\"end\" font-size=\"9\" fill=\"#5a5a5a\">200<\/text>\n <text x=\"72\" y=\"25\" text-anchor=\"end\" font-size=\"9\" fill=\"#5a5a5a\">250<\/text>\n\n <!-- Operating range band -->\n <rect x=\"400\" y=\"20\" width=\"120\" height=\"400\" fill=\"rgba(201,149,43,0.1)\" rx=\"0\"\/>\n <text x=\"460\" y=\"38\" text-anchor=\"middle\" font-size=\"9\" fill=\"#c9952b\" font-weight=\"600\">OPERATING RANGE<\/text>\n\n <!-- 1\u00d7 Excitation line -->\n <line x1=\"80\" y1=\"420\" x2=\"680\" y2=\"20\" stroke=\"#3a7bd5\" stroke-width=\"1.5\" stroke-dasharray=\"6 3\" opacity=\"0.7\"\/>\n <text x=\"668\" y=\"32\" font-size=\"9\" fill=\"#3a7bd5\" font-weight=\"600\">1\u00d7<\/text>\n\n <!-- 2\u00d7 Excitation line -->\n <line x1=\"80\" y1=\"420\" x2=\"380\" y2=\"20\" stroke=\"#3a7bd5\" stroke-width=\"1\" stroke-dasharray=\"4 4\" opacity=\"0.5\"\/>\n <text x=\"370\" y=\"32\" font-size=\"9\" fill=\"#3a7bd5\" font-weight=\"600\">2\u00d7<\/text>\n\n <!-- 0.5\u00d7 Excitation line (oil whirl) -->\n <line x1=\"80\" y1=\"420\" x2=\"680\" y2=\"220\" stroke=\"#9b59b6\" stroke-width=\"1\" stroke-dasharray=\"3 5\" opacity=\"0.5\"\/>\n <text x=\"672\" y=\"216\" font-size=\"8\" fill=\"#9b59b6\">0.5\u00d7<\/text>\n\n <!-- \u2550\u2550\u2550 Mode 1: Forward Whirl \u2550\u2550\u2550 -->\n <path d=\"M 80,340 Q 200,335 320,320 Q 440,300 560,270 Q 620,252 680,230\"\n fill=\"none\" stroke=\"#2d8a56\" stroke-width=\"2.5\"\/>\n <text x=\"686\" y=\"228\" font-size=\"9\" fill=\"#2d8a56\" font-weight=\"600\">1st FW<\/text>\n\n <!-- Mode 1: Backward Whirl -->\n <path d=\"M 80,340 Q 200,345 320,356 Q 440,370 560,385 Q 620,392 680,398\"\n fill=\"none\" stroke=\"#c44d3f\" stroke-width=\"2\" stroke-dasharray=\"8 4\"\/>\n <text x=\"686\" y=\"396\" font-size=\"9\" fill=\"#c44d3f\" font-weight=\"600\">1st BW<\/text>\n\n <!-- \u2550\u2550\u2550 Mode 2: Forward Whirl \u2550\u2550\u2550 -->\n <path d=\"M 80,180 Q 200,176 320,164 Q 440,145 560,115 Q 620,96 680,72\"\n fill=\"none\" stroke=\"#2d8a56\" stroke-width=\"2.5\"\/>\n <text x=\"686\" y=\"72\" font-size=\"9\" fill=\"#2d8a56\" font-weight=\"600\">2nd FW<\/text>\n\n <!-- Mode 2: Backward Whirl -->\n <path d=\"M 80,180 Q 200,184 320,194 Q 440,208 560,226 Q 620,237 680,248\"\n fill=\"none\" stroke=\"#c44d3f\" stroke-width=\"2\" stroke-dasharray=\"8 4\"\/>\n <text x=\"686\" y=\"253\" font-size=\"9\" fill=\"#c44d3f\" font-weight=\"600\">2nd BW<\/text>\n\n <!-- \u2550\u2550\u2550 Critical Speed Markers \u2550\u2550\u2550 -->\n <!-- 1st FW \u00d7 1\u00d7 intersection \u2248 5000 RPM -->\n <circle cx=\"278\" cy=\"325\" r=\"6\" fill=\"none\" stroke=\"#c9952b\" stroke-width=\"2\"\/>\n <circle cx=\"278\" cy=\"325\" r=\"2\" fill=\"#c9952b\"\/>\n <text x=\"290\" y=\"320\" font-size=\"8.5\" fill=\"#c9952b\" font-weight=\"600\">CS\u2081 \u2248 5,000 RPM<\/text>\n\n <!-- 2nd FW \u00d7 1\u00d7 intersection \u2248 11500 RPM -->\n <circle cx=\"540\" cy=\"122\" r=\"6\" fill=\"none\" stroke=\"#c9952b\" stroke-width=\"2\"\/>\n <circle cx=\"540\" cy=\"122\" r=\"2\" fill=\"#c9952b\"\/>\n <text x=\"460\" y=\"112\" font-size=\"8.5\" fill=\"#c9952b\" font-weight=\"600\">CS\u2082 \u2248 11,500 RPM<\/text>\n\n <!-- 1st FW \u00d7 2\u00d7 intersection \u2248 2800 RPM -->\n <circle cx=\"192\" cy=\"338\" r=\"5\" fill=\"none\" stroke=\"#3a7bd5\" stroke-width=\"1.5\"\/>\n <circle cx=\"192\" cy=\"338\" r=\"2\" fill=\"#3a7bd5\"\/>\n <text x=\"130\" y=\"355\" font-size=\"8\" fill=\"#3a7bd5\">2\u00d7 CS \u2248 2,800<\/text>\n\n <!-- Operating speed arrows -->\n <line x1=\"400\" y1=\"418\" x2=\"400\" y2=\"422\" stroke=\"#c9952b\" stroke-width=\"1\"\/>\n <text x=\"400\" y=\"432\" text-anchor=\"middle\" font-size=\"8\" fill=\"#c9952b\">9,000<\/text>\n <line x1=\"520\" y1=\"418\" x2=\"520\" y2=\"422\" stroke=\"#c9952b\" stroke-width=\"1\"\/>\n <text x=\"520\" y=\"432\" text-anchor=\"middle\" font-size=\"8\" fill=\"#c9952b\">12,000<\/text>\n\n <\/svg>\n\n <div class=\"cd-legend\">\n <span><span class=\"cd-legend-swatch\" style=\"background:#2d8a56;\"><\/span> Forward Whirl<\/span>\n <span><span class=\"cd-legend-swatch\" style=\"background:#c44d3f; border-top: 2px dashed #c44d3f; height:0; margin-top:2px;\"><\/span> Backward Whirl<\/span>\n <span><span class=\"cd-legend-swatch\" style=\"background:#3a7bd5;\"><\/span> Excitation Lines<\/span>\n <span><span class=\"cd-legend-swatch\" style=\"background:#c9952b; width:10px; height:10px; border-radius:50%;\"><\/span> Critical Speed<\/span>\n <span><span class=\"cd-legend-swatch\" style=\"background:rgba(201,149,43,0.2); width:20px;\"><\/span> Operating Range<\/span>\n <\/div>\n <p class=\"cd-diagram-caption\">Fig. 1 \u2014 Campbell diagram for a flexible two-bearing rotor. Gold circles mark critical speeds (CS\u2081, CS\u2082). The amber band shows the operating-speed range 9,000\u201312,000 RPM.<\/p>\n <\/div>\n <\/section>\n\n <!-- 5. HOW TO READ -->\n <section id=\"how-to-read\">\n <h2>How to Read and Interpret a Campbell Diagram<\/h2>\n\n <h3>Step-by-Step Reading Procedure<\/h3>\n <div class=\"cd-steps\">\n <div class=\"cd-step\">\n <div class=\"cd-step__num\">01<\/div>\n <div class=\"cd-step__body\">\n <h4>Identify the Operating Speed Range<\/h4>\n <p>Locate the vertical band or tick marks indicating minimum and maximum continuous operating speeds. In Fig. 1, this is 9,000\u201312,000 RPM.<\/p>\n <\/div>\n <\/div>\n <div class=\"cd-step\">\n <div class=\"cd-step__num\">02<\/div>\n <div class=\"cd-step__body\">\n <h4>Trace the 1\u00d7 Line First<\/h4>\n <p>The 1\u00d7 synchronous line is the most critical because unbalance \u2014 present in every rotor \u2014 excites at 1\u00d7 running speed. Find every point where it crosses a forward-whirl curve.<\/p>\n <\/div>\n <\/div>\n <div class=\"cd-step\">\n <div class=\"cd-step__num\">03<\/div>\n <div class=\"cd-step__body\">\n <h4>Read Horizontal Coordinates at Intersections<\/h4>\n <p>Each intersection's x-coordinate is a critical speed. Record each one along with the mode number it involves.<\/p>\n <\/div>\n <\/div>\n <div class=\"cd-step\">\n <div class=\"cd-step__num\">04<\/div>\n <div class=\"cd-step__body\">\n <h4>Check 2\u00d7 and Higher-Order Intersections<\/h4>\n <p>Repeat for 2\u00d7, 3\u00d7, blade-pass, and sub-synchronous lines. These intersections are secondary critical speeds \u2014 lower energy than 1\u00d7 but still capable of causing vibration problems, especially if the excitation source is strong.<\/p>\n <\/div>\n <\/div>\n <div class=\"cd-step\">\n <div class=\"cd-step__num\">05<\/div>\n <div class=\"cd-step__body\">\n <h4>Calculate Separation Margins<\/h4>\n <p>For each critical speed, compute the percentage distance to the nearest edge of the operating range. Compare against applicable standards (API 617, API 612, ISO, OEM spec).<\/p>\n <\/div>\n <\/div>\n <div class=\"cd-step\">\n <div class=\"cd-step__num\">06<\/div>\n <div class=\"cd-step__body\">\n <h4>Evaluate Curve Slopes<\/h4>\n <p>Steep upward-sloping FW curves indicate strong gyroscopic effects \u2014 common in overhung rotors. Nearly flat curves suggest the system is bearing-stiffness dominated.<\/p>\n <\/div>\n <\/div>\n <div class=\"cd-step\">\n <div class=\"cd-step__num\">07<\/div>\n <div class=\"cd-step__body\">\n <h4>Identify Hazard Zones<\/h4>\n <p>If two critical speeds bracket the operating range with insufficient margins, the design must be modified: bearing stiffness, shaft diameter, support stiffness, or operating speed must change.<\/p>\n <\/div>\n <\/div>\n <\/div>\n\n <div class=\"cd-callout\">\n <p><span class=\"cd-callout__icon\">\u26a0\ufe0f<\/span> <strong>A common misunderstanding:<\/strong> backward-whirl modes rarely respond to unbalance excitation because unbalance produces only forward precession. Intersections with BW curves are usually not true operational critical speeds \u2014 they are included on the diagram for completeness and for cases where other excitation sources exist (e.g., reverse-rotating flow in seals).<\/p>\n <\/div>\n\n <h3>Understanding Separation Margins<\/h3>\n <p>Safe operation demands that the operating speed range lies far enough from every critical speed so that the resonance amplification is tolerable. The required margin depends on the sharpness of the resonance peak, quantified by the <strong>amplification factor (AF)<\/strong>.<\/p>\n <ul>\n <li>A low AF (< 2.5) means heavy damping \u2014 the rotor can operate close to or even at the critical speed without excessive vibration.<\/li>\n <li>A high AF (> 8) means a sharp peak \u2014 even a few percent deviation from the critical speed causes dangerous amplitude growth.<\/li>\n <\/ul>\n <p>Typical industrial practice calls for 15\u201330% separation, but the exact requirement depends on the governing standard and the AF value.<\/p>\n <\/section>\n\n <!-- 6. GYROSCOPIC -->\n <section id=\"gyroscopic\">\n <h2>Gyroscopic Effects and Frequency Splitting<\/h2>\n <p>When a spinning disc precesses (wobbles), gyroscopic moments arise that couple the motion in two perpendicular planes. This coupling splits what would be a single natural frequency at zero speed into two distinct frequencies at any non-zero speed.<\/p>\n\n <h3>The Physics<\/h3>\n <p>The equation of motion for a rotor with gyroscopic effects takes the form:<\/p>\n <div class=\"cd-formula\">\n <strong>M<\/strong>q\u0308 + (<strong>C<\/strong> + \u03a9<strong>G<\/strong>)q\u0307 + <strong>K<\/strong>q = f(t)\n <\/div>\n <p>where <strong>M<\/strong> is the mass matrix, <strong>C<\/strong> the damping matrix, <strong>G<\/strong> the skew-symmetric gyroscopic matrix (proportional to spin speed \u03a9), and <strong>K<\/strong> the stiffness matrix. Because <strong>G<\/strong> is speed-dependent, the eigenvalues \u2014 and therefore the natural frequencies \u2014 change with \u03a9.<\/p>\n\n <h3>What Determines the Splitting Magnitude?<\/h3>\n <p>The ratio of polar moment of inertia (I<sub>p<\/sub>) to diametral moment of inertia (I<sub>d<\/sub>) controls how strongly the gyroscopic effect acts. Disc-like components (I<sub>p<\/sub>\/I<sub>d<\/sub> > 1) produce strong splitting. Long, slender shaft sections (I<sub>p<\/sub>\/I<sub>d<\/sub> \u2248 0) produce negligible splitting.<\/p>\n\n <div class=\"cd-engineer-note\">\n <div class=\"cd-engineer-note__label\">Practical Implication<\/div>\n <p>Overhung rotors (single-stage pump impellers, turbocharger wheels, cantilevered grinding wheels) exhibit the most pronounced gyroscopic splitting. In these designs, the forward-whirl first critical speed can be 20\u201340% higher than the zero-speed natural frequency, meaning the Campbell diagram differs dramatically from a simple \"flat-line\" model. Running a flat-line analysis for an overhung rotor will underpredict the first FW critical and overpredict the first BW critical, potentially leading to incorrect operating-speed decisions.<\/p>\n <\/div>\n <\/section>\n\n <!-- 7. BEARINGS -->\n <section id=\"bearings\">\n <h2>How Bearing Type Shapes the Campbell Diagram<\/h2>\n <p>Bearings connect the rotor to the stator and define the boundary conditions that determine natural frequencies. Different bearing technologies produce fundamentally different diagram shapes.<\/p>\n\n <div class=\"cd-table-wrap\">\n <table class=\"cd-table\">\n <thead>\n <tr><th>Bearing Type<\/th><th>Stiffness Behavior<\/th><th>Effect on Campbell Curves<\/th><th>Additional Concerns<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td><strong>Rolling Element<\/strong> (ball, roller)<\/td>\n <td>Nearly constant with speed<\/td>\n <td>Natural frequency curves are approximately flat (horizontal) unless gyroscopic effects dominate<\/td>\n <td>Defect frequencies (BPFO, BPFI, BSF) add excitation lines at non-integer orders<\/td>\n <\/tr>\n <tr>\n <td><strong>Fluid-Film (Journal)<\/strong><\/td>\n <td>Stiffness and damping increase with speed (Sommerfeld number changes)<\/td>\n <td>Curves slope upward more steeply than gyroscopic effect alone would produce<\/td>\n <td>Cross-coupled stiffness can cause instability (oil whirl\/whip); add 0.43\u20130.48\u00d7 sub-synchronous line<\/td>\n <\/tr>\n <tr>\n <td><strong>Tilting-Pad Journal<\/strong><\/td>\n <td>Stiffness increases with speed; minimal cross-coupling<\/td>\n <td>Similar slope to plain journal but with better stability<\/td>\n <td>Preferred for high-speed compressors per API 617<\/td>\n <\/tr>\n <tr>\n <td><strong>Active Magnetic<\/strong><\/td>\n <td>Programmable via control algorithm; can be constant, increasing, or adaptive<\/td>\n <td>Curves can be intentionally shaped to move critical speeds away from operating range<\/td>\n <td>Control-loop bandwidth limits maximum achievable stiffness at high frequencies<\/td>\n <\/tr>\n <tr>\n <td><strong>Gas (Foil\/Aerostatic)<\/strong><\/td>\n <td>Stiffness increases sharply with speed; very low damping<\/td>\n <td>Steeply rising curves; high-Q resonances<\/td>\n <td>Low damping makes separation margins even more critical<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h3>Anisotropic Supports<\/h3>\n <p>When the bearing support pedestal or foundation has different stiffness in the horizontal and vertical directions, each mode further splits into horizontal and vertical variants. The Campbell diagram then shows even more curves \u2014 a horizontal FW, a vertical FW, a horizontal BW, and a vertical BW for each mode. This is typical in horizontal machines with flexible foundations.<\/p>\n <\/section>\n\n <!-- 8. API 617 -->\n <section id=\"standards\">\n <h2>API 617 and Separation-Margin Requirements<\/h2>\n <p>For centrifugal and axial compressors in petroleum, chemical, and gas service, API Standard 617 (8th Ed., 2014; 9th Ed., 2022) mandates a rigorous Campbell-diagram analysis as part of the lateral rotordynamic study.<\/p>\n\n <h3>The API 617 Separation-Margin Formula<\/h3>\n <div class=\"cd-formula\">\n SM = 17 \u00d7 { 1 \u2212 [ 1 \/ (AF \u2212 1.5) ] }\n <\/div>\n <p>where <strong>SM<\/strong> is the required separation margin (%) and <strong>AF<\/strong> is the amplification factor from the unbalance-response (Bode) plot at that critical speed.<\/p>\n\n <div class=\"cd-table-wrap\">\n <table class=\"cd-table\">\n <thead>\n <tr><th>AF Value<\/th><th>SM per Formula<\/th><th>Interpretation<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>< 2.5<\/td><td>No SM required<\/td><td>Critically damped; may operate at the critical speed<\/td><\/tr>\n <tr><td>3.5<\/td><td>8.5%<\/td><td>Moderate damping; small margin sufficient<\/td><\/tr>\n <tr><td>5.0<\/td><td>12.1%<\/td><td>Typical for tilting-pad bearings<\/td><\/tr>\n <tr><td>8.0<\/td><td>14.4%<\/td><td>Sharp peak; larger margin needed<\/td><\/tr>\n <tr><td>12.0<\/td><td>15.4%<\/td><td>Very sharp; approaching 16% cap<\/td><\/tr>\n <tr><td>> ~11<\/td><td>\u2264 16% (capped)<\/td><td>API caps SM at 16% for CS below min speed<\/td><\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h3>Applying This to the Campbell Diagram<\/h3>\n <p>During design review, the engineer reads each critical speed from the Campbell diagram, then checks the corresponding AF from the Bode plot. If SM<sub>actual<\/sub> \u2265 SM<sub>required<\/sub>, the design passes. If not, the engineer must modify bearings, shaft geometry, or operating range until all margins are met.<\/p>\n\n <div class=\"cd-callout\">\n <p><strong>Other standards with similar requirements:<\/strong> API 612 (steam turbines), API 613 (gear units), API 672 (packaged air compressors), ISO 10814 (tolerance of critical-speed proximity), ISO 22266 (mechanical vibration of non-reciprocating machines). Each uses slightly different formulas or fixed-percentage thresholds, but all rely on the Campbell diagram as the source data.<\/p>\n <\/div>\n <\/section>\n\n <!-- 9. CREATING -->\n <section id=\"creating\">\n <h2>Creating a Campbell Diagram: Analytical vs. Experimental<\/h2>\n\n <h3>Analytical (FEA \/ Transfer Matrix) Approach<\/h3>\n <div class=\"cd-steps\">\n <div class=\"cd-step\">\n <div class=\"cd-step__num\">01<\/div>\n <div class=\"cd-step__body\">\n <h4>Build the Rotor Model<\/h4>\n <p>Discretize the shaft, discs, impellers, couplings, and sleeves into beam elements (Timoshenko or Euler-Bernoulli) or 3D solid\/shell elements. Include mass, stiffness, and gyroscopic terms.<\/p>\n <\/div>\n <\/div>\n <div class=\"cd-step\">\n <div class=\"cd-step__num\">02<\/div>\n <div class=\"cd-step__body\">\n <h4>Define Bearing Properties<\/h4>\n <p>Input speed-dependent stiffness and damping coefficients (8 coefficients for each fluid-film bearing: K<sub>xx<\/sub>, K<sub>xy<\/sub>, K<sub>yx<\/sub>, K<sub>yy<\/sub>, C<sub>xx<\/sub>, C<sub>xy<\/sub>, C<sub>yx<\/sub>, C<sub>yy<\/sub>). For rolling-element bearings, use constant stiffness values.<\/p>\n <\/div>\n <\/div>\n <div class=\"cd-step\">\n <div class=\"cd-step__num\">03<\/div>\n <div class=\"cd-step__body\">\n <h4>Set Speed Range and Increments<\/h4>\n <p>Define a speed sweep from 0 to at least 115% of maximum continuous speed (per API 617 trip-speed requirement), with fine enough RPM increments (typically 100\u2013500 RPM steps) to capture curve shapes accurately.<\/p>\n <\/div>\n <\/div>\n <div class=\"cd-step\">\n <div class=\"cd-step__num\">04<\/div>\n <div class=\"cd-step__body\">\n <h4>Solve the Complex Eigenvalue Problem<\/h4>\n <p>At each speed step, solve det(<strong>K<\/strong> + i\u03a9<strong>G<\/strong> \u2212 \u03c9\u00b2<strong>M<\/strong>) = 0 to find natural frequencies \u03c9<sub>n<\/sub> (imaginary parts) and damping (real parts). The imaginary parts become the y-coordinates on the Campbell diagram.<\/p>\n <\/div>\n <\/div>\n <div class=\"cd-step\">\n <div class=\"cd-step__num\">05<\/div>\n <div class=\"cd-step__body\">\n <h4>Plot and Overlay Excitation Lines<\/h4>\n <p>Plot all modes vs. speed, add 1\u00d7, 2\u00d7, and other relevant excitation lines, and mark intersections.<\/p>\n <\/div>\n <\/div>\n <\/div>\n\n <h3>Experimental Approach (From Field Data)<\/h3>\n <p>When a machine already exists, a Campbell diagram can be extracted from vibration measurements during a run-up or coastdown:<\/p>\n <ol>\n <li>Mount accelerometers or proximity probes at bearing locations.<\/li>\n <li>Record vibration continuously during a slow startup (or coastdown after trip).<\/li>\n <li>Generate a <a href=\"\/glossary\/waterfall-plot\/\">waterfall (cascade) plot<\/a>: a stack of FFT spectra taken at successive RPM values.<\/li>\n <li>Identify frequency peaks at each RPM slice \u2014 these are the natural frequencies excited by whichever order dominates.<\/li>\n <li>Plot the peak frequencies vs. RPM to produce an experimental Campbell diagram.<\/li>\n <\/ol>\n\n <div class=\"cd-engineer-note\">\n <div class=\"cd-engineer-note__label\">Field Tip<\/div>\n <p>Coastdown tests often produce cleaner data than startups because the machine decelerates smoothly without the torque fluctuations of a motor starting. Run the coastdown from trip speed to rest with continuous high-resolution data acquisition (\u2265 4,096 lines, 0.5-second averaging). If the machine uses a VFD, program a linear ramp at 50\u2013100 RPM\/second for best spectral resolution.<\/p>\n <\/div>\n <\/section>\n\n <!-- 10. APPLICATIONS -->\n <section id=\"applications\">\n <h2>Applications by Machine Type<\/h2>\n\n <div class=\"cd-table-wrap\">\n <table class=\"cd-table\">\n <thead>\n <tr><th>Machine<\/th><th>Typical Speed Range<\/th><th>Key Campbell-Diagram Concerns<\/th><th>Governing Standard<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr>\n <td><strong>Centrifugal Compressor<\/strong><\/td>\n <td>3,000\u201360,000 RPM<\/td>\n <td>Multiple critical speeds; fluid-film bearing instability; seal cross-coupling; typically 2\u20134 modes below trip speed<\/td>\n <td>API 617<\/td>\n <\/tr>\n <tr>\n <td><strong>Steam Turbine<\/strong><\/td>\n <td>3,000\u201315,000 RPM<\/td>\n <td>Blade-pass excitation; thermal bow shifting modes during warmup; disc modes at high orders<\/td>\n <td>API 612<\/td>\n <\/tr>\n <tr>\n <td><strong>Gas Turbine<\/strong><\/td>\n <td>3,600\u201330,000 RPM<\/td>\n <td>Dual-spool designs require separate Campbell diagrams for each spool; squeeze-film damper effects<\/td>\n <td>API 616 \/ OEM<\/td>\n <\/tr>\n <tr>\n <td><strong>Electric Motor \/ Generator<\/strong><\/td>\n <td>750\u201336,000 RPM<\/td>\n <td>Electromagnetic excitation at 2\u00d7 line frequency; VFD-driven motors require sweep through resonances<\/td>\n <td>API 541 \/ IEC 60034<\/td>\n <\/tr>\n <tr>\n <td><strong>Pump<\/strong><\/td>\n <td>1,000\u201312,000 RPM<\/td>\n <td>Overhung impeller with strong gyroscopic effects; vane-pass excitation; wear-ring stiffness changes over time<\/td>\n <td>API 610<\/td>\n <\/tr>\n <tr>\n <td><strong>Machine-Tool Spindle<\/strong><\/td>\n <td>5,000\u201360,000+ RPM<\/td>\n <td>Preloaded angular-contact bearings; speed-dependent preload loss softens frequencies at high speed<\/td>\n <td>ISO 15641 \/ OEM<\/td>\n <\/tr>\n <tr>\n <td><strong>Turbocharger<\/strong><\/td>\n <td>30,000\u2013300,000 RPM<\/td>\n <td>Floating-ring bearings with complex inner\/outer film dynamics; sub-synchronous whirl common<\/td>\n <td>OEM \/ SAE<\/td>\n <\/tr>\n <tr>\n <td><strong>Wind Turbine Gearbox<\/strong><\/td>\n <td>10\u201320 RPM (rotor); up to 1,800 RPM (HSS)<\/td>\n <td>Torsional Campbell diagram for gear-mesh resonances; multiple speed ratios<\/td>\n <td>IEC 61400 \/ AGMA<\/td>\n <\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n\n <h3>Design-Phase Uses<\/h3>\n <p>During design, the Campbell diagram guides decisions about shaft diameter, bearing placement, bearing type, and impeller\/disc geometry. Moving a critical speed by just 10% may require changing bearing span by 50 mm or shaft diameter by 5 mm \u2014 the diagram shows engineers exactly how much shift is needed.<\/p>\n\n <h3>Troubleshooting Uses<\/h3>\n <p>If a machine develops high 1\u00d7 vibration at a specific speed, the Campbell diagram quickly shows whether that speed coincides with a predicted critical. If it does, the solution is either to change the operating speed, add damping (e.g., squeeze-film damper), or improve balancing quality. If it does not, the high vibration likely has a different root cause such as mechanical looseness or bearing defect.<\/p>\n\n <h3>Operating Guidance<\/h3>\n <p>The Campbell diagram defines <strong>forbidden speed ranges<\/strong> \u2014 RPM bands where sustained operation is not allowed because a critical speed falls within the band. Variable-speed machines (VFD-driven compressors, turbine-generator sets with load-following) must have their Campbell diagrams reviewed to ensure no continuous-duty operating point sits in a forbidden band. Transient passage through a critical speed during startup or shutdown is acceptable if the acceleration rate is high enough to prevent amplitude buildup.<\/p>\n <\/section>\n\n <!-- CTA 1 -->\n <div class=\"cd-cta\">\n <div>\n <h3>Measure What the Diagram Predicts<\/h3>\n <p>The Balanset-1A portable analyzer records vibration data you need for experimental Campbell diagrams \u2014 spectrum vs. RPM during run-up and coastdown. Two-plane balancing in the field. From \u20ac1,975.<\/p>\n <\/div>\n <a href=\"https:\/\/vibromera.eu\/product\/balanset-1a\/\" class=\"cd-cta__btn\">View Balanset-1A \u2192<\/a>\n <\/div>\n\n <!-- 11. COMPARISONS -->\n <section id=\"comparisons\">\n <h2>Related Diagrams and Plots<\/h2>\n <p>The Campbell diagram is one of several interrelated visualizations in rotordynamic analysis. Each serves a distinct purpose.<\/p>\n\n <div class=\"cd-compare-grid\">\n <div class=\"cd-compare-card\">\n <h4>Campbell Diagram<\/h4>\n <p><strong>Axes:<\/strong> natural frequency vs. rotational speed.<br><strong>Shows:<\/strong> where critical speeds <em>will<\/em> occur (predictive). Based on eigenvalue analysis or extracted from waterfall data.<\/p>\n <\/div>\n <div class=\"cd-compare-card\">\n <h4><a href=\"\/glossary\/bode-plot\/\">Bode Plot<\/a><\/h4>\n <p><strong>Axes:<\/strong> vibration amplitude & phase vs. rotational speed.<br><strong>Shows:<\/strong> measured response during actual run-up\/coastdown. Confirms critical-speed locations and provides amplification factors for margin calculations.<\/p>\n <\/div>\n <div class=\"cd-compare-card\">\n <h4><a href=\"\/glossary\/waterfall-plot\/\">Waterfall (Cascade) Plot<\/a><\/h4>\n <p><strong>Axes:<\/strong> frequency spectrum vs. rotational speed (3D).<br><strong>Shows:<\/strong> full spectral content at each RPM step. Source data for extracting experimental Campbell diagrams. Reveals all excitation orders simultaneously.<\/p>\n <\/div>\n <div class=\"cd-compare-card\">\n <h4>Undamped Critical-Speed Map<\/h4>\n <p><strong>Axes:<\/strong> natural frequency vs. bearing stiffness (not speed).<br><strong>Shows:<\/strong> how critical speeds shift as support stiffness changes. Used in early design to bracket the bearing stiffness range before generating the full Campbell diagram.<\/p>\n <\/div>\n <div class=\"cd-compare-card\">\n <h4>Orbit Plot<\/h4>\n <p><strong>Axes:<\/strong> X-displacement vs. Y-displacement at a single speed.<br><strong>Shows:<\/strong> the shape of shaft motion at a specific RPM. Forward whirl produces a circular orbit; backward whirl produces a retrograde ellipse.<\/p>\n <\/div>\n <div class=\"cd-compare-card\">\n <h4>Stability Map<\/h4>\n <p><strong>Axes:<\/strong> logarithmic decrement (or real eigenvalue) vs. speed.<br><strong>Shows:<\/strong> where the system is stable (positive damping) vs. unstable (negative damping). A Campbell diagram extended by one dimension.<\/p>\n <\/div>\n <\/div>\n <\/section>\n\n <!-- 12. PRACTICAL EXAMPLE -->\n <section id=\"practical\">\n <h2>Practical Example: High-Speed Compressor<\/h2>\n <p>Consider a centrifugal compressor designed for 15,000 RPM continuous operation (250 Hz), with trip speed at 17,250 RPM (115%).<\/p>\n\n <h3>Campbell Diagram Results<\/h3>\n <ul>\n <li><strong>1st FW Critical (1\u00d7):<\/strong> 5,200 RPM (86.7 Hz) \u2014 safely below operating range.<\/li>\n <li><strong>2nd FW Critical (1\u00d7):<\/strong> 19,800 RPM (330 Hz) \u2014 above trip speed.<\/li>\n <li><strong>1st FW \u00d7 2\u00d7:<\/strong> 2,600 RPM \u2014 only relevant during startup; passed through quickly.<\/li>\n <\/ul>\n\n <h3>Margin Check<\/h3>\n <p>Minimum operating speed: 12,000 RPM. Separation from 1st FW critical at 5,200 RPM:<\/p>\n <div class=\"cd-formula\">\n SM<sub>actual<\/sub> = (12,000 \u2212 5,200) \/ 12,000 \u00d7 100 = 56.7%\n <\/div>\n <p>The AF at this critical from the Bode plot is 4.2, yielding a required SM of 10.7% per the API 617 formula. Actual SM of 56.7% far exceeds the requirement \u2014 no issue.<\/p>\n\n <p>Separation from 2nd FW critical at 19,800 RPM to trip speed 17,250 RPM:<\/p>\n <div class=\"cd-formula\">\n SM<sub>actual<\/sub> = (19,800 \u2212 17,250) \/ 17,250 \u00d7 100 = 14.8%\n <\/div>\n <p>The AF at this critical is 6.5, yielding a required SM of 13.6%. Actual SM of 14.8% passes, but marginally. The engineer flags this in the report and recommends verifying the exact AF during shop mechanical running tests.<\/p>\n\n <div class=\"cd-engineer-note\">\n <div class=\"cd-engineer-note__label\">What Could Go Wrong<\/div>\n <p>If fouling increases impeller mass by 3%, the 2nd FW critical drops from 19,800 to approximately 19,200 RPM, reducing the separation margin to 11.3% \u2014 below the required 13.6%. This scenario must be captured in the sensitivity analysis submitted with the API datasheet.<\/p>\n <\/div>\n <\/section>\n\n <!-- 13. SOFTWARE -->\n <section id=\"software\">\n <h2>Software Tools for Campbell Diagrams<\/h2>\n <p>Campbell diagrams are produced by both general-purpose FEA platforms and dedicated rotordynamics packages.<\/p>\n\n <div class=\"cd-table-wrap\">\n <table class=\"cd-table\">\n <thead>\n <tr><th>Tool<\/th><th>Type<\/th><th>Notes<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>ANSYS Mechanical (Rotordynamics)<\/td><td>General FEA<\/td><td>Full 3D solid + beam models; built-in Campbell chart post-processor; requires damped modal analysis with RGYRO<\/td><\/tr>\n <tr><td>Siemens Simcenter 3D<\/td><td>General FEA<\/td><td>Superelement reduction for multi-rotor systems; integrated orbit and stability plots<\/td><\/tr>\n <tr><td>DyRoBeS<\/td><td>Dedicated rotordynamics<\/td><td>Beam-element based; fast; widely used in compressor and turbine OEMs per API 684 tutorial<\/td><\/tr>\n <tr><td>XLTRC\u00b2 (Texas A&M)<\/td><td>Dedicated rotordynamics<\/td><td>Spreadsheet-based workflow; strong bearing coefficient library; popular in pump and compressor analysis<\/td><\/tr>\n <tr><td>MADYN 2000<\/td><td>Dedicated rotordynamics<\/td><td>German-developed; FE + transfer-matrix hybrid; excellent for torsional + lateral coupled analyses<\/td><\/tr>\n <tr><td>COMSOL Multiphysics<\/td><td>General FEA<\/td><td>Rotordynamics module for custom models; programmable post-processing<\/td><\/tr>\n <tr><td>Bently Nevada System 1 \/ ADRE<\/td><td>Condition monitoring<\/td><td>Extracts experimental Campbell diagrams from field vibration data; real-time tracking<\/td><\/tr>\n <\/tbody>\n <\/table>\n <\/div>\n <\/section>\n\n <!-- 14. COMMON MISTAKES -->\n <section id=\"common-mistakes\">\n <h2>Common Mistakes When Using Campbell Diagrams<\/h2>\n\n <h3>1. Ignoring Gyroscopic Effects<\/h3>\n <p>Running an undamped, zero-speed modal analysis and assuming those frequencies are the critical speeds. This produces flat lines that miss forward\/backward splitting entirely. Always solve the speed-dependent eigenvalue problem.<\/p>\n\n <h3>2. Using Too Coarse a Speed Increment<\/h3>\n <p>If the RPM step is 2,000 RPM in a machine running at 10,000, you might miss a narrow crossing entirely. Use increments of 100\u2013500 RPM for reliable curve definition.<\/p>\n\n <h3>3. Confusing Campbell and Bode<\/h3>\n <p>The Campbell diagram predicts <em>where<\/em> criticals are; the Bode plot shows <em>how severe<\/em> they are. Both are required for a complete rotordynamic evaluation per API 617.<\/p>\n\n <h3>4. Neglecting Foundation and Support Flexibility<\/h3>\n <p>A rotor model with rigid supports will produce different critical speeds than the same rotor on a real flexible foundation. Include pedestal and foundation compliance in the model.<\/p>\n\n <h3>5. Forgetting Temperature and Load Effects<\/h3>\n <p>Bearing clearances change with temperature, altering stiffness coefficients. Process-gas density affects seal cross-coupling. The Campbell diagram should be run at both minimum and maximum clearance \/ density conditions.<\/p>\n\n <h3>6. Treating All Intersections as Equally Dangerous<\/h3>\n <p>A 1\u00d7 intersection with the first forward mode is far more dangerous than a 4\u00d7 intersection with a high backward mode. Prioritize by excitation energy and mode type.<\/p>\n <\/section>\n\n <!-- CTA 2 -->\n <div class=\"cd-cta\">\n <div>\n <h3>Need On-Site Vibration Data?<\/h3>\n <p>Balanset-1A captures vibration spectra during run-up\/coastdown for waterfall plots and experimental Campbell diagrams. Two-channel, two-plane, ISO 1940 compliant. Ships worldwide via DHL Express.<\/p>\n <\/div>\n <a href=\"https:\/\/wa.me\/351927275567?text=Hello%2C%20I%27m%20interested%20in%20Balanset%20for%20vibration%20analysis\" class=\"cd-cta__btn\" target=\"_blank\" rel=\"noopener\">WhatsApp Us \u2192<\/a>\n <\/div>\n\n <!-- 15. FAQ -->\n <section id=\"faq\">\n <h2>Frequently Asked Questions<\/h2>\n <div class=\"cd-faq\">\n\n <details class=\"cd-faq-item\">\n <summary>What is the difference between a Campbell diagram and a Bode plot?<\/summary>\n <div class=\"cd-faq-answer\">\n <p>A Campbell diagram plots the system's natural frequencies against rotational speed \u2014 it predicts <em>at which speeds<\/em> critical conditions exist. A Bode plot plots actual measured (or calculated) vibration amplitude and phase against rotational speed \u2014 it shows <em>how much<\/em> the rotor vibrates at those critical speeds. Engineers use the Campbell diagram for design and the Bode plot for verification. Both are required by API 617 for compressor certification.<\/p>\n <\/div>\n <\/details>\n\n <details class=\"cd-faq-item\">\n <summary>What separation margin does API 617 require from critical speeds?<\/summary>\n <div class=\"cd-faq-answer\">\n <p>API 617 uses the formula SM = 17 \u00d7 {1 \u2212 [1\/(AF \u2212 1.5)]}, where AF is the amplification factor at that critical speed. If AF < 2.5, no margin is required because the resonance is overdamped. For typical tilting-pad bearings (AF = 4\u20138), required margins range from 10% to 15%. The maximum required SM is capped at 16% for critical speeds below minimum operating speed. For critical speeds above maximum continuous speed, the same formula applies but the margin is calculated as a percentage of the maximum continuous speed.<\/p>\n <\/div>\n <\/details>\n\n <details class=\"cd-faq-item\">\n <summary>Why do natural frequencies split into forward and backward whirl on the Campbell diagram?<\/summary>\n <div class=\"cd-faq-answer\">\n <p>Gyroscopic moments from spinning discs couple the rotor's motion in two perpendicular planes. This coupling creates two distinct precession patterns: forward whirl (precession in the same direction as shaft rotation, stiffened by the gyroscopic effect) and backward whirl (precession opposite to rotation, softened by the effect). The higher the disc's polar-to-diametral inertia ratio, the stronger the splitting. At zero speed, there is no gyroscopic moment, so both modes coalesce to a single frequency.<\/p>\n <\/div>\n <\/details>\n\n <details class=\"cd-faq-item\">\n <summary>Can you create a Campbell diagram from field measurements?<\/summary>\n <div class=\"cd-faq-answer\">\n <p>Yes. Record vibration during a continuous startup (or coastdown) using accelerometers or proximity probes at bearing housings. Process the time-domain data into a waterfall (cascade) plot \u2014 a series of FFT spectra at each RPM increment. Extract the peak frequencies at each RPM step, then plot those peaks against RPM. The result is an experimental Campbell diagram. Coastdowns tend to give cleaner data because there are no motor-starting torque transients. Aim for a deceleration rate of 50\u2013100 RPM\/s and use at least 4,096 FFT lines for good frequency resolution.<\/p>\n <\/div>\n <\/details>\n\n <details class=\"cd-faq-item\">\n <summary>What excitation orders should be included on a Campbell diagram?<\/summary>\n <div class=\"cd-faq-answer\">\n <p>At minimum, always include the 1\u00d7 line (unbalance \u2014 the single most common excitation source in all rotating machinery). Add 2\u00d7 for misalignment, shaft ovality, or cracked shafts. For turbomachinery, include blade-pass frequency (number of blades \u00d7 1\u00d7) and vane-pass frequency. For geared systems, include gear-mesh frequency. For machines with fluid-film bearings, add a 0.43\u20130.48\u00d7 line for oil whirl. If the machine has a known defect pattern (e.g., coupling with 6 jaws), include that order (6\u00d7).<\/p>\n <\/div>\n <\/details>\n\n <details class=\"cd-faq-item\">\n <summary>How does bearing type affect the shape of a Campbell diagram?<\/summary>\n <div class=\"cd-faq-answer\">\n <p>Rolling-element bearings have nearly constant stiffness across the speed range, so natural-frequency curves remain almost flat (horizontal) \u2014 the only slope comes from gyroscopic effects. Fluid-film (journal) bearings increase in stiffness with speed as the oil film thins and becomes stiffer, causing natural-frequency curves to rise more steeply. Tilting-pad journal bearings behave similarly but produce less cross-coupling, improving rotor stability. Active magnetic bearings can be programmed to shift stiffness in real time, allowing engineers to reshape the Campbell diagram dynamically to avoid resonances.<\/p>\n <\/div>\n <\/details>\n\n <\/div>\n <\/section>\n\n <!-- Author Block -->\n <div class=\"cd-author\">\n <div class=\"cd-author__avatar\">NS<\/div>\n <div>\n <div class=\"cd-author__name\">Nikolai Shelkovenko<\/div>\n <div class=\"cd-author__title\">CEO & Field Balancing Engineer, Vibromera \u2014 13+ years in vibration diagnostics and rotor balancing across 20+ countries<\/div>\n <\/div>\n <\/div>\n\n <\/main>\n<\/div>\n\n<!-- Back link -->\n<div class=\"cd-back\">\n <a href=\"https:\/\/vibromera.eu\/glossary\/\">\u2190 Back to Glossary Index<\/a>\n<\/div>\n\n<\/body>\n<\/html><\/div><\/div><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>L\u00e6r om Campbell-diagrammer, grafiske verkt\u00f8y som plotter naturlige frekvenser kontra rotasjonshastighet for \u00e5 identifisere kritiske hastigheter og forutsi resonansforhold i roterende maskineri.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[114,109],"tags":[],"class_list":["post-70","glossary","type-glossary","status-publish","hentry","category-analysis","category-glossary"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/glossary\/70","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/glossary"}],"about":[{"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/types\/glossary"}],"version-history":[{"count":5,"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/glossary\/70\/revisions"}],"predecessor-version":[{"id":101733,"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/glossary\/70\/revisions\/101733"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/media?parent=70"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/categories?post=70"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/tags?post=70"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}