{"id":100100,"date":"2026-02-15T20:16:38","date_gmt":"2026-02-15T20:16:38","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100100"},"modified":"2026-07-12T06:19:44","modified_gmt":"2026-07-12T06:19:44","slug":"flexible-rotor-balancing","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/el\/calculators\/flexible-rotor-balancing\/","title":{"rendered":"Documented Flexible-Rotor Criterion Arithmetic Check"},"content":{"rendered":"\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Documented Flexible-Rotor Criterion Arithmetic Check\",\"description\":\"Compare one measured flexible-rotor balance quantity with one documented limit for the same quantity, mode, speed and state. No ISO tolerance generation or balancing-plane prescription.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/flexible-rotor-balancing\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"dateModified\":\"2026-07-12\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Does this page calculate an ISO 21940-12 flexible-rotor tolerance?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Enter a criterion already established for the exact rotor, mode or tolerance plane, speed, state, quantity and procedure. 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p:last-child{margin-bottom:0}.vc-faq-a-inner ul{margin:4px 0 8px 16px;padding:0}.vc-faq-a-inner li{margin-bottom:3px}\r\n.vc-related{display:flex;flex-wrap:wrap;gap:10px;margin-top:16px}.vc-related-link{display:inline-block;padding:8px 16px;font-family:var(--vc-font);font-size:13px;font-weight:600;background:var(--vc-surface-alt);color:var(--vc-ink-secondary);border:1px solid var(--vc-border);border-radius:var(--vc-radius);text-decoration:none;transition:all 0.15s}.vc-related-link:hover{border-color:var(--vc-accent);color:var(--vc-accent);background:var(--vc-accent-light)}\r\n.vc-promo{margin-top:24px;padding:20px;background:linear-gradient(135deg,var(--vc-accent-light),var(--vc-surface));border:1px solid var(--vc-border);border-radius:var(--vc-radius-lg);display:flex;align-items:center;gap:16px}.vc-promo-text{flex:1;font-size:14px;color:var(--vc-ink-secondary)}.vc-promo-text strong{color:var(--vc-ink)}.vc-promo-link{padding:8px 20px;font-size:13px;font-weight:700;color:#fff;background:var(--vc-accent);border-radius:var(--vc-radius);text-decoration:none;white-space:nowrap;transition:background 0.15s}.vc-promo-link:hover{background:var(--vc-accent-hover)}\r\n.vc-footer{text-align:center;padding:32px 16px;font-size:13px;color:var(--vc-ink-muted)}.vc-footer a{color:var(--vc-accent);text-decoration:none}.vc-footer a:hover{text-decoration:underline}.vc-footer-links{margin-top:8px;font-size:12px}.vc-footer-links a{margin:0 8px}\r\n@media 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}}\r\n\r\n.vc-form-grid-criterion{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:18px}.vc-field-full{grid-column:1\/-1}.vc-result-note{margin:0;color:var(--vc-ink-secondary);font-size:13px}@media(max-width:650px){.vc-form-grid-criterion{grid-template-columns:1fr}.vc-field-full{grid-column:auto}}\r\n<\/style>\r\n<div class=\"vc-calculator\" id=\"vc-flexible-criterion\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Documented criterion required \u2014 no ISO tolerance generation<\/p><h1 class=\"vc-header-title\">Documented Flexible-Rotor Criterion Arithmetic Check<\/h1><p class=\"vc-header-subtitle\">Compare one measured balance quantity with one documented limit that already applies to the same rotor,mode or tolerance plane,speed,state and quantity definition.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">No G-grade conversion<\/span><span class=\"vc-badge\">No equal modal split<\/span><span class=\"vc-badge\">No plane-count rule<\/span><\/div><\/header>\r\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\"><div class=\"vc-form-grid-criterion\">\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-measured\">Measured value <span class=\"vc-label-hint\">(nonnegative)<\/span><\/label><input class=\"vc-input\" id=\"vc-measured\" type=\"text\" inputmode=\"decimal\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-limit\">Documented maximum value <span class=\"vc-label-hint\">(positive)<\/span><\/label><input class=\"vc-input\" id=\"vc-limit\" type=\"text\" inputmode=\"decimal\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-unit\">Exact quantity and unit label<\/label><input class=\"vc-input\" id=\"vc-unit\" type=\"text\" maxlength=\"160\" placeholder=\"e.g. documented modal quantity and unit\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-speed\">Evaluation\/test speed <span class=\"vc-label-hint\">(rev\/min)<\/span><\/label><input class=\"vc-input\" id=\"vc-speed\" type=\"text\" inputmode=\"decimal\"><\/div>\r\n<div class=\"vc-field vc-field-full\"><label class=\"vc-label\" for=\"vc-criterion\">Criterion identity <span class=\"vc-label-hint\">(mode\/tolerance plane,speed,state and quantity basis)<\/span><\/label><input class=\"vc-input\" id=\"vc-criterion\" type=\"text\" maxlength=\"500\"><\/div>\r\n<div class=\"vc-field vc-field-full\"><label class=\"vc-label\" for=\"vc-rotor\">Rotor configuration\/category and balancing procedure<\/label><input class=\"vc-input\" id=\"vc-rotor\" type=\"text\" maxlength=\"500\"><\/div>\r\n<div class=\"vc-field vc-field-full\"><label class=\"vc-label\" for=\"vc-error-source\">Measurement\/balancing-error assessment reference<\/label><input class=\"vc-input\" id=\"vc-error-source\" type=\"text\" maxlength=\"500\" placeholder=\"Assessment report or applicable ISO 21940-14 procedure reference\"><\/div>\r\n<div class=\"vc-field vc-field-full\"><label class=\"vc-label\" for=\"vc-source\">Exact criterion source<\/label><input class=\"vc-input\" id=\"vc-source\" type=\"text\" maxlength=\"500\" placeholder=\"Licensed standard clause\/table or approved specification revision\"><\/div>\r\n<\/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>Same-basis gate:<\/strong> the measured value and entered limit must use the same physical quantity,normalization,unit,mode\/tolerance plane,speed,state and error treatment. This page does not determine whether the criterion is applicable or correctly derived.<\/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\">Arithmetic comparison<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">Copy<\/button><\/div><div class=\"vc-result-grid\">\r\n<div class=\"vc-rcard vc-rcard-primary\" id=\"vc-condition-card\"><div class=\"vc-rcard-label\">Condition relative to entered documented value<\/div><div class=\"vc-rcard-value\" id=\"vc-r-condition\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Utilization,measured\/documented<\/div><div class=\"vc-rcard-value\" id=\"vc-r-util\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Margin,documented\u2212measured<\/div><div class=\"vc-rcard-value\" id=\"vc-r-margin\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Speed frequency<\/div><div class=\"vc-rcard-value\" id=\"vc-r-hz\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Angular speed<\/div><div class=\"vc-rcard-value\" id=\"vc-r-omega\">\u2014<\/div><\/div>\r\n<\/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\">Arithmetic and ISO scope boundary<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\">\r\n<h3>Arithmetic only<\/h3><div class=\"vc-formula-box\">utilization=measured\/documented\u00d7100%<br>margin=documented\u2212measured<br>f=n\/60;&nbsp;\u03c9=2\u03c0n\/60<\/div><p>\u201cWithin entered limit\u201d means only that one entered number does not exceed another entered number on the declared same basis. It is not an ISO acceptance result or proof of satisfactory running behaviour.<\/p>\r\n<h3>ISO21940-12 flexible-rotor scope<\/h3><p><a href=\"https:\/\/www.iso.org\/standard\/50429.html\" target=\"_blank\" rel=\"noopener\">ISO21940-12:2016<\/a>,edition1,was confirmed in2025 and remains current. It presents typical flexible-rotor configurations,balancing procedures,final-state assessment methods and guidelines for balance-quality criteria. ISO states that it is not an acceptance specification,that structural resonances are outside its scope,and that its industrial experience may not apply directly to specialized equipment. <a href=\"https:\/\/www.iso.org\/standard\/86180.html\" target=\"_blank\" rel=\"noopener\">Edition2 is under development<\/a> and will replace the2016 edition when published.<\/p>\r\n<h3>Why the former formulas were removed<\/h3><p><a href=\"https:\/\/www.iso.org\/standard\/54074.html\" target=\"_blank\" rel=\"noopener\">ISO21940-11:2016<\/a> with <a href=\"https:\/\/www.iso.org\/standard\/78116.html\" target=\"_blank\" rel=\"noopener\">Amendment1:2022<\/a> covers rotors with rigid behaviour and explicitly excludes flexible behaviour. Therefore its G-grade residual-unbalance relation cannot be relabelled as a flexible-rotor modal tolerance. No official source was found for dividing that result equally by \u201cmodes+1\u201d or prescribing \u201cmodes+2\u201d correction planes universally.<\/p><p><a href=\"https:\/\/www.iso.org\/standard\/50430.html\" target=\"_blank\" rel=\"noopener\">ISO21940-14:2012+Amd1:2022<\/a> addresses identifying,assessing and accounting for balance-measurement errors;edition2 is under development. This page does not implement its closed procedures.<\/p>\r\n<div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Not evaluated:<\/strong> rotor category,modal decomposition,mode shapes,modal mass,influence coefficients,critical speeds,run-up\/coast-down response,correction-plane effectiveness,thermal state,assembly state,repeatability,measurement errors,structural resonance,operating vibration or specialized-equipment requirements.<\/p><\/div><\/div><\/div><\/div><footer class=\"vc-footer\"><p>\u00a92024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><p>Documented-criterion arithmetic only;not ISO tolerance generation or rotor acceptance. Scientific review:July2026.<\/p><\/footer><\/div>\r\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}var ids=['vc-measured','vc-limit','vc-unit','vc-speed','vc-criterion','vc-rotor','vc-error-source','vc-source'],keys=['measured_value','documented_limit','quantity_unit','speed_rpm','criterion_identity','rotor_procedure','error_assessment','criterion_source'],outs=['vc-r-condition','vc-r-util','vc-r-margin','vc-r-hz','vc-r-omega'];function num(raw){var s=String(raw).trim().replace(',','.');return \/^[+]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+-]?\\d+)?$\/.test(s)?Number(s):NaN}function fmt(x){if(Object.is(x,-0))x=0;return Number(x.toPrecision(12)).toString()}function clear(){outs.forEach(function(id){$(id).textContent='\u2014'});$('vc-r-note').textContent='';$('vc-condition-card').className='vc-rcard vc-rcard-primary';$('vc-results').classList.remove('vc-visible')}function calc(){var raw=ids.map(function(id){return $(id).value.trim()}),any=raw.some(Boolean),url=new URL(location);keys.forEach(function(key,i){if(raw[i])url.searchParams.set(key,raw[i]);else url.searchParams.delete(key)});history.replaceState(null,'',url.toString());if(!raw.every(Boolean)){clear();$('vc-error').textContent=any?'Complete all8 fields.':'';return}var measured=num(raw[0]),limit=num(raw[1]),speed=num(raw[3]);if(!Number.isFinite(measured)||measured<0||measured>1e18){clear();$('vc-error').textContent='Measured value must be a strict,finite,nonnegative number no more than10\u00b9\u2078.';return}if(!Number.isFinite(limit)||limit<=0||limit>1e18){clear();$('vc-error').textContent='Documented maximum must be a strict,finite,positive number no more than10\u00b9\u2078.';return}if(!Number.isFinite(speed)||speed<=0||speed>1e9){clear();$('vc-error').textContent='Speed must be a strict,finite,positive number no more than10\u2079rev\/min.';return}var util=measured\/limit*100,margin=limit-measured,hz=speed\/60,omega=2*Math.PI*speed\/60;if(![util,margin,hz,omega].every(Number.isFinite)){clear();$('vc-error').textContent='The result exceeds the finite numerical range.';return}var condition,cls;if(measured<limit){condition='Within entered numeric limit';cls='vc-fit-clearance'}else if(measured===limit){condition='At entered numeric limit';cls='vc-fit-transition'}else{condition='Exceeds entered numeric limit';cls='vc-fit-interference'}$('vc-error').textContent='';$('vc-r-condition').textContent=condition;$('vc-condition-card').className='vc-rcard vc-rcard-primary '+cls;$('vc-r-util').textContent=fmt(util)+'%';$('vc-r-margin').textContent=fmt(margin)+' '+raw[2];$('vc-r-hz').textContent=fmt(hz)+' Hz';$('vc-r-omega').textContent=fmt(omega)+' rad\/s';$('vc-r-note').textContent='Criterion:'+raw[4]+' | Rotor\/procedure:'+raw[5]+' | Error assessment:'+raw[6]+' | Source:'+raw[7]+' | Arithmetic only;criterion applicability and ISO acceptance are not verified.';$('vc-results').classList.add('vc-visible')}$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',calc);$('vc-copy-btn').addEventListener('click',function(){if(navigator.clipboard)navigator.clipboard.writeText($('vc-results').innerText)});document.querySelectorAll('.vc-section-toggle').forEach(function(button){button.addEventListener('click',function(){var section=this.closest('.vc-section');section.classList.toggle('vc-open');this.setAttribute('aria-expanded',section.classList.contains('vc-open'))})});var query=new URLSearchParams(location.search);keys.forEach(function(key,i){if(query.has(key))$(ids[i]).value=query.get(key)});calc()})();<\/script>\r\n","protected":false},"excerpt":{"rendered":"<p>Compare one measured flexible-rotor balance quantity with one documented limit for the same mode or tolerance plane, speed, state and quantity. 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