{"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":"2026-07-12T12:20:31","modified_gmt":"2026-07-12T12:20:31","slug":"harmonic-frequency-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bn\/calculators\/harmonic-frequency-calculator\/","title":{"rendered":"Shaft-Speed Order Frequency Calculator"},"content":{"rendered":"\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Documented Shaft-Speed Order Frequency Calculator\",\"description\":\"Convert documented shaft RPM and requested integer or fractional orders to Hz, CPM, period and angular frequency without fault diagnosis.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/harmonic-frequency-calculator\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any (Web 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print{.vc-section-body{max-height:none!important}.vc-faq-a{max-height:none!important}.vc-results{max-height:none!important;padding:24px!important}.vc-copy-btn,.vc-section-chevron,.vc-faq-chevron,.vc-presets,.vc-promo{display:none!important}}.vc-doc-grid{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:18px}.vc-wide{grid-column:1\/-1}.vc-result-note{font-size:13px;color:var(--vc-ink-secondary);margin:0}@media(max-width:600px){.vc-doc-grid{grid-template-columns:1fr}.vc-wide{grid-column:auto}}.vc-doc-grid{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:18px}.vc-wide{grid-column:1\/-1}.vc-textarea{min-height:150px;resize:vertical;font-family:var(--vc-mono);line-height:1.5}.vc-formula-box{font-family:var(--vc-mono);background:var(--vc-surface-alt);border:1px solid var(--vc-border-light);border-radius:6px;padding:14px;margin:12px 0}.vc-result-note{font-size:13px;color:var(--vc-ink-secondary);margin:0}@media(max-width:600px){.vc-doc-grid{grid-template-columns:1fr}.vc-wide{grid-column:auto}}<\/style>\r\n<div class=\"vc-calculator\" id=\"vc-order-frequency\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Documented shaft speed and requested orders<\/p><h1 class=\"vc-header-title\">Shaft-Speed Order Frequency Calculator<\/h1><p class=\"vc-header-subtitle\">Convert a documented shaft speed and any positive integer or fractional orders to frequency, cycles per minute, period and angular frequency.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">f\u2081\u00d7 = RPM\/60<\/span><span class=\"vc-badge\">f\u2096 = kf\u2081\u00d7<\/span><span class=\"vc-badge\">No fault diagnosis<\/span><\/div><\/header>\r\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\"><div class=\"vc-doc-grid\"><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-id\">Machine \/ shaft identifier<\/label><input class=\"vc-input\" id=\"vc-id\" type=\"text\" maxlength=\"220\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-speed-source\">Speed source, time window and revision<\/label><input class=\"vc-input\" id=\"vc-speed-source\" type=\"text\" maxlength=\"350\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-rpm\">Documented shaft speed <span class=\"vc-label-hint\">(rpm)<\/span><\/label><input class=\"vc-input\" id=\"vc-rpm\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-context\">Tach\/reference and analysis context<\/label><input class=\"vc-input\" id=\"vc-context\" type=\"text\" maxlength=\"350\"><\/div><div class=\"vc-field vc-wide\"><label class=\"vc-label\" for=\"vc-orders\">Requested positive orders, one per line<\/label><textarea class=\"vc-input vc-textarea\" id=\"vc-orders\" maxlength=\"10000\" spellcheck=\"false\" placeholder=\"0.5&#10;1&#10;2&#10;3.5\"><\/textarea><\/div><\/div><p id=\"vc-error\" role=\"alert\" style=\"margin:.75rem 0 0;color:#b42318\"><\/p><div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Interpretation gate:<\/strong> frequency coincidence alone does not identify a fault. Confirm the correct shaft\/reference, speed variation, spectral resolution, amplitude, phase, direction, load and machine construction before diagnosis.<\/p><\/div><\/form>\r\n<div class=\"vc-results\" id=\"vc-results\" aria-live=\"polite\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Order-frequency arithmetic<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">Copy<\/button><\/div><div class=\"vc-result-grid\"><div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">1\u00d7 rotational frequency<\/div><div class=\"vc-rcard-value\" id=\"vc-r-f1\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">1\u00d7 period<\/div><div class=\"vc-rcard-value\" id=\"vc-r-t1\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">1\u00d7 angular frequency<\/div><div class=\"vc-rcard-value\" id=\"vc-r-w1\">\u2014<\/div><\/div><\/div><div style=\"overflow-x:auto\"><table class=\"vc-table\"><thead><tr><th>Order k<\/th><th>Frequency Hz<\/th><th>CPM<\/th><th>Period ms<\/th><th>Angular frequency rad\/s<\/th><\/tr><\/thead><tbody id=\"vc-tbody\"><\/tbody><\/table><\/div><p class=\"vc-result-note\" id=\"vc-r-note\"><\/p><\/div><\/div>\r\n<div class=\"vc-section vc-open\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udcd8<\/span><span class=\"vc-section-title\">Equations and diagnostic boundary<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\"><h3>Implemented unit arithmetic<\/h3><div class=\"vc-formula-box\">f<sub>1\u00d7<\/sub> = n\/60<br>f<sub>k<\/sub> = kf<sub>1\u00d7<\/sub><br>CPM<sub>k<\/sub> = kn<br>T<sub>k<\/sub> = 1\/f<sub>k<\/sub><br>\u03c9<sub>k<\/sub> = 2\u03c0f<sub>k<\/sub><\/div><p>n is the documented shaft speed in revolutions per minute, k is the dimensionless order, f is hertz, T is seconds (displayed in milliseconds) and \u03c9 is radians per second. These are exact unit\/period relations apart from finite numerical representation; they are general mathematics, not an ISO diagnostic formula.<\/p><h3>Harmonic versus order<\/h3><p>Integer orders 1\u00d7, 2\u00d7, 3\u00d7\u2026 are harmonics of the 1\u00d7 rotational frequency. Order analysis can also use fractional or non-integer orders; those are not integer harmonics. An order label is speed-normalized, while its absolute frequency changes with shaft speed.<\/p><h3>Why automatic fault labels were removed<\/h3><p>The former FAQ assigned unbalance, misalignment, looseness, cracked shafts, blade problems and gear faults to individual orders as if frequency alone established cause. Real spectra can share frequencies across mechanisms, and resonance, modulation, geometry and operating state affect amplitudes and phase. This calculator therefore produces only traceable frequency arithmetic.<\/p><div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Not a diagnosis:<\/strong> blade-pass or gear-mesh order must be derived from the correct component count and the speed of the associated shaft. Phase is meaningful only with a defined reference and measurement chain; it does not directly reveal a heavy-spot angle without the machine response and balancing procedure.<\/p><\/div><\/div><\/div><\/div><footer class=\"vc-footer\"><p>\u00a9 2024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><p>Documented order-frequency arithmetic only. Scientific review: July 2026.<\/p><\/footer><\/div>\r\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}var map={of_id:'vc-id',of_speed_source:'vc-speed-source',of_rpm:'vc-rpm',of_context:'vc-context',of_orders:'vc-orders'};function num(raw){var s=String(raw).trim().replace(',','.');if(s.length>80||!\/^[-+]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+-]?\\d+)?$\/.test(s))return NaN;return Number(s)}function fmt(v){if(!Number.isFinite(v))return'\u2014';if(v===0)return'0';return Number(v.toPrecision(12)).toString()}function clear(){$('vc-r-f1').textContent='\u2014';$('vc-r-t1').textContent='\u2014';$('vc-r-w1').textContent='\u2014';$('vc-tbody').innerHTML='';$('vc-r-note').textContent='';$('vc-results').classList.remove('vc-visible')}function fail(m){clear();$('vc-error').textContent=m}function setUrl(){var u=new URL(location);Object.keys(map).forEach(function(q){var v=$(map[q]).value.trim();if(v)u.searchParams.set(q,v);else u.searchParams.delete(q)});history.replaceState(null,'',u.toString())}function calc(){setUrl();var x={};Object.keys(map).forEach(function(q){x[q]=$(map[q]).value.trim()});var any=Object.keys(x).some(function(q){return x[q]});if(!any){$('vc-error').textContent='';clear();return}if(!Object.keys(map).every(function(q){return x[q]})){fail('Enter the shaft record, speed source, RPM, context and requested orders.');return}var rpm=num(x.of_rpm);if(!Number.isFinite(rpm)||rpm<=0||rpm>1e30){fail('RPM must be a complete finite strict positive number no greater than 10\u00b3\u2070.');return}var lines=x.of_orders.split(\/\\r?\\n\/).filter(function(s){return s.trim()});if(!lines.length||lines.length>200){fail('Enter between 1 and 200 nonblank order rows.');return}var orders=[],seen=new Set();for(var i=0;i<lines.length;i++){var k=num(lines[i]);if(!Number.isFinite(k)||k<=0||k>1e9){fail('Order on line '+(i+1)+' must be finite, strict positive and no greater than 10\u2079.');return}var key=k.toPrecision(15);if(seen.has(key)){fail('Duplicate order on line '+(i+1)+'.');return}seen.add(key);orders.push(k)}var f1=rpm\/60,t1=1000\/f1,w1=2*Math.PI*f1;if(![f1,t1,w1].every(Number.isFinite)){fail('Base result exceeds the finite numerical range.');return}var html='';for(var j=0;j<orders.length;j++){var o=orders[j],f=o*f1,cpm=o*rpm,t=1000\/f,w=2*Math.PI*f;if(![f,cpm,t,w].every(Number.isFinite)||Math.max(f,cpm,t,w)>1e100){fail('Order result on line '+(j+1)+' exceeds the finite numerical range.');return}html+='<tr><td>'+fmt(o)+'\u00d7<\/td><td>'+fmt(f)+'<\/td><td>'+fmt(cpm)+'<\/td><td>'+fmt(t)+'<\/td><td>'+fmt(w)+'<\/td><\/tr>'}$('vc-error').textContent='';$('vc-r-f1').textContent=fmt(f1)+' Hz \/ '+fmt(rpm)+' CPM';$('vc-r-t1').textContent=fmt(t1)+' ms';$('vc-r-w1').textContent=fmt(w1)+' rad\/s';$('vc-tbody').innerHTML=html;$('vc-r-note').textContent='Shaft: '+x.of_id+' | Speed source: '+x.of_speed_source+' | Context: '+x.of_context+' | '+orders.length+' requested orders. Frequency arithmetic only; no fault classification.';$('vc-results').classList.add('vc-visible')}$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',calc);$('vc-copy-btn').addEventListener('click',function(){if(navigator.clipboard)navigator.clipboard.writeText($('vc-results').innerText)});document.querySelectorAll('.vc-section-toggle').forEach(function(b){b.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'))})});var q=new URLSearchParams(location.search);Object.keys(map).forEach(function(x){if(q.has(x))$(map[x]).value=q.get(x)});calc()})();<\/script>\r\n","protected":false},"excerpt":{"rendered":"<p>Convert documented shaft RPM and positive integer or fractional orders to Hz, CPM, period and angular frequency. 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