{"id":100181,"date":"2026-02-15T20:25:27","date_gmt":"2026-02-15T20:25:27","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100181"},"modified":"2026-07-13T01:51:34","modified_gmt":"2026-07-13T01:51:34","slug":"paper-machine-roll-balance","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/hi\/calculators\/paper-machine-roll-balance\/","title":{"rendered":"Documented Roll Residual-Unbalance Arithmetic"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Documented Roll Residual-Unbalance Arithmetic\",\"description\":\"Converts documented roll speed and either a documented G value or specific residual-unbalance limit into total residual-unbalance arithmetic without selecting a balance grade or correction planes.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/paper-machine-roll-balance\/\",\"applicationCategory\":\"EngineeringApplication\",\"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\":\"2026-07-13\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true,\"featureList\":[\"Surface-speed or RPM basis\",\"Documented G or e basis\",\"Total residual-unbalance arithmetic\",\"Explicit no plane allocation\"],\"keywords\":\"paper roll residual unbalance,ISO 21940 scope,balance grade arithmetic,specific unbalance,rigid rotor\"}<\/script>\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Does this choose a balance grade for a paper roll?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Enter a G value or specific residual-unbalance limit already selected by the responsible specification or engineering process.\"}},{\"@type\":\"Question\",\"name\":\"Does it split total unbalance between two planes?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. The number of correction and tolerance planes and allocation among them require the applicable rotor geometry and controlled procedure.\"}},{\"@type\":\"Question\",\"name\":\"Does it calculate a correction mass?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Correction requires vector magnitude and phase at defined planes\/radii and cannot be inferred from a scalar total tolerance.\"}},{\"@type\":\"Question\",\"name\":\"Does it set vibration limits?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Machine vibration acceptance and paper-quality criteria are separate from residual-unbalance arithmetic.\"}}]}<\/script>\n<style>:root{--s:#fff;--sa:#f8f6f2;--i:#1a1a1a;--is:#5a5650;--im:#8a857e;--a:#c85a2a;--al:#fdf0ea;--b:#d9d4cc;--bl:#e8e4dd;--y:#8a6500;--yl:#fef9e8;--r:#a12b2b;--f:'DM Sans',sans-serif;--m:'JetBrains Mono',monospace;--d:'Fraunces',serif}.vc-calculator{font-family:var(--f);font-size:15px;line-height:1.65;color:var(--i);max-width:960px;margin:auto;padding:20px 16px 40px}.vc-calculator *{box-sizing:border-box}.vc-header{text-align:center;padding:48px 20px 40px;border-bottom:3px solid var(--a)}.vc-header-eyebrow{font:500 11px var(--m);letter-spacing:.15em;text-transform:uppercase;color:var(--a)}.vc-header-title{font:800 clamp(24px,4vw,36px)\/1.15 var(--d);margin:10px 0 14px}.vc-header-subtitle{max-width:720px;margin:auto;color:var(--is)}.vc-badges{display:flex;gap:8px;justify-content:center;flex-wrap:wrap;margin-top:18px}.vc-badge{font:500 11px var(--m);padding:4px 10px;border:1px solid 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var(--bl);background:var(--sa);padding:0;max-height:0;overflow:hidden}.vc-results.vc-visible{max-height:1400px;padding:24px}.vc-result-grid{display:grid;grid-template-columns:repeat(2,1fr);gap:12px}.vc-rcard{background:var(--s);border:1px solid var(--bl);border-radius:8px;padding:16px}.vc-primary{grid-column:1\/-1;border:2px solid var(--a);background:var(--al)}.vc-rcard-label{font:500 10px var(--m);letter-spacing:.1em;text-transform:uppercase;color:var(--im)}.vc-rcard-value{font:600 20px var(--m);overflow-wrap:anywhere}.vc-primary .vc-rcard-value{font-size:24px;color:var(--a)}.vc-status{grid-column:1\/-1;padding:12px;background:var(--yl);border-left:3px solid var(--y);font-size:13px;color:var(--is)}.vc-section-toggle{width:100%;display:flex;justify-content:space-between;padding:18px 24px;border:0;background:transparent;cursor:pointer;text-align:left}.vc-section-title{font:700 18px var(--d)}.vc-section-body{max-height:0;overflow:hidden}.vc-section.vc-open .vc-section-body{max-height:15000px}.vc-section-inner{padding:0 24px 24px;border-top:1px solid var(--bl)}.vc-theory h3{font:700 17px var(--d);margin:24px 0 8px}.vc-theory p,.vc-theory li{font-size:14px;color:var(--is)}.vc-formula{padding:14px;border:2px solid var(--b);border-radius:6px;background:var(--sa);text-align:center;font:500 14px var(--m);margin:12px 0}.vc-warning{padding:14px;background:var(--yl);border-left:3px solid var(--y);color:var(--is)}.vc-faq-item{border:1px solid var(--bl);margin-top:8px}.vc-faq-q{width:100%;padding:14px;border:0;background:var(--sa);text-align:left;font-weight:600}.vc-faq-a{display:none;padding:14px;color:var(--is)}.vc-faq-item.vc-open .vc-faq-a{display:block}.vc-footer{text-align:center;padding:30px;color:var(--im);font-size:13px}@media(max-width:600px){.vc-grid,.vc-result-grid{grid-template-columns:1fr}.vc-full,.vc-primary,.vc-status{grid-column:1}}<\/style>\n<div class=\"vc-calculator\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Source-gated rigid-rotor arithmetic<\/p><h1 class=\"vc-header-title\">Documented Roll Residual-Unbalance Arithmetic<\/h1><p class=\"vc-header-subtitle\">Convert a documented speed and documented G or specific-unbalance limit into total scalar residual-unbalance arithmetic. No paper-roll grade,plane allocation or correction vector is invented.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">No automatic G grade<\/span><span class=\"vc-badge\">No 50\/50 plane split<\/span><span class=\"vc-badge\">No correction mass<\/span><\/div><\/header><div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\" novalidate><div class=\"vc-grid\"><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-mass\">Rotor mass <span class=\"vc-hint\">(kg)<\/span><\/label><input class=\"vc-input\" id=\"vc-mass\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-speed-mode\">Speed basis<\/label><select class=\"vc-select\" id=\"vc-speed-mode\"><option value=\"surface\">Surface speed and diameter<\/option><option value=\"rpm\">Direct rotational speed<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-speed\">Speed value<\/label><input class=\"vc-input\" id=\"vc-speed\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-speed-unit\">Speed unit<\/label><select class=\"vc-select\" id=\"vc-speed-unit\"><option value=\"mmin\">m\/min surface speed<\/option><option value=\"ftmin\">ft\/min surface speed<\/option><option value=\"rpm\">r\/min<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-diameter\">Roll operating diameter <span class=\"vc-hint\">(surface mode only)<\/span><\/label><input class=\"vc-input\" id=\"vc-diameter\" inputmode=\"decimal\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-diameter-unit\">Diameter unit<\/label><select class=\"vc-select\" id=\"vc-diameter-unit\"><option value=\"mm\">mm<\/option><option value=\"in\">in<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-limit-mode\">Documented limit basis<\/label><select class=\"vc-select\" id=\"vc-limit-mode\"><option value=\"g\">G value (mm\/s)<\/option><option value=\"e\">Specific residual unbalance e (\u03bcm)<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-limit\">Documented G or e value<\/label><input class=\"vc-input\" id=\"vc-limit\" inputmode=\"decimal\"><\/div><div class=\"vc-field vc-full\"><label class=\"vc-label\" for=\"vc-source\">Rotor,grade\/limit and speed source<\/label><input class=\"vc-input\" id=\"vc-source\" type=\"text\" placeholder=\"rotor ID\/configuration;rigid-behaviour evidence;specification\/edition;selected G\/e;service speed\"><\/div><div class=\"vc-field vc-full\"><label class=\"vc-check\" for=\"vc-gate\"><input id=\"vc-gate\" type=\"checkbox\"><span>The rotor configuration and mass are controlled;rigid behaviour and service speed are established.The responsible specification selected the entered G or e.The number\/location of tolerance and correction planes,allocation,phase,balancing errors,measurement uncertainty and acceptance are determined separately under the applicable current procedure.<\/span><\/label><\/div><\/div><div class=\"vc-validation\" id=\"vc-validation\" role=\"status\" aria-live=\"polite\"><\/div><\/form><div class=\"vc-results\" id=\"vc-results\"><div class=\"vc-result-grid\"><div class=\"vc-rcard vc-primary\"><div class=\"vc-rcard-label\">Total scalar residual-unbalance arithmetic<\/div><div class=\"vc-rcard-value\" id=\"vc-r-u\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Rotational speed<\/div><div class=\"vc-rcard-value\" id=\"vc-r-rpm\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Angular speed<\/div><div class=\"vc-rcard-value\" id=\"vc-r-omega\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Specific residual unbalance e<\/div><div class=\"vc-rcard-value\" id=\"vc-r-e\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Entered basis<\/div><div class=\"vc-rcard-value\" id=\"vc-r-basis\">\u2014<\/div><\/div><div class=\"vc-status\" id=\"vc-r-note\">Scalar arithmetic only.<\/div><\/div><\/div><\/div>\n<div class=\"vc-section vc-open\"><button class=\"vc-section-toggle\" type=\"button\" aria-expanded=\"true\"><span class=\"vc-section-title\">Equations and ISO boundary<\/span><span>\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\"><div class=\"vc-formula\">surface mode:n=v\/(\u03c0D); \u03c9=2\u03c0n\/60; G mode:e=1000G\/\u03c9 [\u03bcm]; U=eM [g\u00b7mm]<\/div><p>The identity1kg\u00b7\u03bcm=1g\u00b7mm is used.Direct-e mode skips the G conversion.U is a scalar total arithmetic value,not an allocated tolerance-plane vector.<\/p><h3>Current source status<\/h3><p>ISO21940-11:2016,edition1,confirmed2021 and currently under systematic review,with Amd1:2022 establishes procedures\/tolerances for rotors with rigid behaviour.It covers magnitude,necessary correction planes,allocation to tolerance planes and balancing errors.It excludes flexible behaviour,which is addressed by Part12.<\/p><div class=\"vc-warning\"><strong>NEEDS_LICENSED_SOURCE:<\/strong> exact G selection,formula\/constants,plane allocation,acceptance and amendment details.No paper-industry G recommendation is asserted.<\/div><h3>Not calculated<\/h3><ul><li>Paper-roll balance grade or vibration limit.<\/li><li>One\/two-plane selection or a50\/50 split.<\/li><li>Correction mass,phase,radius or couple\/static components.<\/li><li>Bearing force,vibration response,paper quality or field-balancing readiness.<\/li><\/ul><h3>Sources<\/h3><p><a href=\"https:\/\/www.iso.org\/standard\/54074.html\" target=\"_blank\" rel=\"noopener\">ISO21940-11:2016<\/a>; <a href=\"https:\/\/www.iso.org\/standard\/78116.html\" target=\"_blank\" rel=\"noopener\">ISO21940-11:2016\/Amd1:2022<\/a>; <a href=\"https:\/\/www.iso.org\/standard\/73726.html\" target=\"_blank\" rel=\"noopener\">ISO21940-1:2019<\/a>.<\/p><\/div><\/div><\/div><div class=\"vc-section\"><button class=\"vc-section-toggle\" type=\"button\" aria-expanded=\"false\"><span class=\"vc-section-title\">Frequently asked questions<\/span><span>\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div id=\"vc-faq-list\"><\/div><\/div><\/div><\/div><footer class=\"vc-footer\">\u00a92024\u20132026 Vibromera \u2014 reviewed13 July2026<\/footer><\/div>\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}function read(raw){var t=String(raw||'').trim();if(!t||(t.includes(',')&&t.includes('.')))return null;t=t.replace(',','.');if(!\/^(?:\\d+(?:\\.\\d*)?|\\.\\d+)$\/.test(t))return null;var v=Number(t);return Number.isFinite(v)&&v>0?v:null}function fmt(v){if(Math.abs(v)>=1e9||Math.abs(v)<1e-6)return v.toExponential(6);return Number(v.toPrecision(10)).toString()}function hide(m){$('vc-results').classList.remove('vc-visible');$('vc-validation').textContent=m||''}function calc(){if(!$('vc-source').value.trim())return hide('Enter the controlled rotor,limit and speed source.');if(!$('vc-gate').checked)return hide('Confirm rigid-rotor applicability and separate plane\/error decisions.');var mass=read($('vc-mass').value),speed=read($('vc-speed').value),limit=read($('vc-limit').value);if(mass===null||speed===null||limit===null)return hide('Enter positive complete numbers using a decimal point or comma.');var rpm;if($('vc-speed-mode').value==='rpm'){if($('vc-speed-unit').value!=='rpm')return hide('Direct speed mode requires r\/min.');rpm=speed}else{if($('vc-speed-unit').value==='rpm')return hide('Surface mode requires m\/min or ft\/min.');var d=read($('vc-diameter').value);if(d===null)return hide('Enter a positive operating diameter for surface-speed mode.');var dm=d*($('vc-diameter-unit').value==='in'?.0254:.001),v=speed*($('vc-speed-unit').value==='ftmin'?.3048:1);rpm=v\/(Math.PI*dm)}var omega=2*Math.PI*rpm\/60,e=$('vc-limit-mode').value==='g'?1000*limit\/omega:limit,u=e*mass;if(![rpm,omega,e,u].every(Number.isFinite))return hide('The arithmetic did not produce finite results.');$('vc-r-u').textContent=fmt(u)+' g\u00b7mm';$('vc-r-rpm').textContent=fmt(rpm)+' r\/min';$('vc-r-omega').textContent=fmt(omega)+' rad\/s';$('vc-r-e').textContent=fmt(e)+' \u03bcm';$('vc-r-basis').textContent=$('vc-limit-mode').value==='g'?'G='+fmt(limit)+' mm\/s':'e='+fmt(limit)+' \u03bcm';$('vc-r-note').textContent='Total scalar arithmetic only.No grade selection,plane allocation,correction mass,phase,force,vibration or acceptance decision is calculated.';$('vc-validation').textContent='';$('vc-results').classList.add('vc-visible')}$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',calc);document.querySelectorAll('.vc-section-toggle').forEach(function(b){b.addEventListener('click',function(){var 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