{"id":100099,"date":"2026-02-15T20:16:35","date_gmt":"2026-02-15T20:16:35","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100099"},"modified":"2026-07-12T06:08:56","modified_gmt":"2026-07-12T06:08:56","slug":"flexible-coupling-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/tr\/calculators\/flexible-coupling-calculator\/","title":{"rendered":"Two-Inertia Coupling Torsional Arithmetic"},"content":{"rendered":"\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Two-Inertia Coupling Torsional Arithmetic\",\"description\":\"Calculate exact power-speed torque and an ideal undamped two-inertia torsional mode from sourced user inputs. No coupling selection or resonance verdict.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/flexible-coupling-calculator\/\",\"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 select or rate a flexible coupling?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. It performs transparent arithmetic using user-supplied power, speed, multiplier, inertias, dynamic torsional stiffness and excitation order. Manufacturer limits and the governing design procedure remain required.\"}},{\"@type\":\"Question\",\"name\":\"Does the frequency ratio prove that torsional resonance is avoided?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. It compares one ideal undamped two-inertia mode with one entered synchronous order. 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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; }\r\n.vc-related-link:hover { border-color:var(--vc-accent); color:var(--vc-accent); background:var(--vc-accent-light); }\r\n\r\n\/* \u2500\u2500 PROMO \u2500\u2500 *\/\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; }\r\n.vc-promo-text { flex:1; font-size:14px; color:var(--vc-ink-secondary); }\r\n.vc-promo-text strong { color:var(--vc-ink); }\r\n.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; }\r\n.vc-promo-link:hover { background:var(--vc-accent-hover); }\r\n\r\n\/* \u2500\u2500 FOOTER \u2500\u2500 *\/\r\n.vc-footer { text-align:center; padding:32px 16px; font-size:13px; color:var(--vc-ink-muted); }\r\n.vc-footer a { color:var(--vc-accent); text-decoration:none; }\r\n.vc-footer a:hover { text-decoration:underline; }\r\n.vc-footer-links { margin-top:8px; font-size:12px; }\r\n.vc-footer-links a { margin:0 8px; }\r\n\r\n\/* \u2500\u2500 PRINT \u2500\u2500 *\/\r\n@media print {\r\n    .vc-section-body { max-height:none!important; }\r\n    .vc-faq-a { max-height:none!important; }\r\n    .vc-results { max-height:none!important; padding:24px!important; }\r\n    .vc-copy-btn, .vc-section-chevron, .vc-faq-chevron, .vc-presets, .vc-promo { display:none!important; }\r\n}\r\n\r\n.vc-form-grid-coupling{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-coupling{grid-template-columns:1fr}.vc-field-full{grid-column:auto}}\r\n<\/style>\r\n<div class=\"vc-calculator\" id=\"vc-coupling-arithmetic\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Sourced parameters required \u2014 ideal two-inertia model<\/p><h1 class=\"vc-header-title\">Two-Inertia Coupling Torsional Arithmetic<\/h1><p class=\"vc-header-subtitle\">Calculate power-speed torque and one ideal undamped torsional mode from documented dynamic stiffness,inertias and excitation order.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">No coupling selection<\/span><span class=\"vc-badge\">No generic stiffness<\/span><span class=\"vc-badge\">No resonance verdict<\/span><\/div><\/header>\r\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\"><div class=\"vc-form-grid-coupling\">\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-power\">Transmitted power <span class=\"vc-label-hint\">(kW)<\/span><\/label><input class=\"vc-input\" id=\"vc-power\" type=\"text\" inputmode=\"decimal\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-speed\">Rotational 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\"><label class=\"vc-label\" for=\"vc-k\">User-supplied torque multiplier K <span class=\"vc-label-hint\">(dimensionless)<\/span><\/label><input class=\"vc-input\" id=\"vc-k\" type=\"text\" inputmode=\"decimal\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-order\">Identified synchronous excitation order q<\/label><input class=\"vc-input\" id=\"vc-order\" type=\"text\" inputmode=\"decimal\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-j1\">Inertia J\u2081 referred to coupling shaft <span class=\"vc-label-hint\">(kg\u00b7m\u00b2)<\/span><\/label><input class=\"vc-input\" id=\"vc-j1\" type=\"text\" inputmode=\"decimal\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-j2\">Inertia J\u2082 referred to coupling shaft <span class=\"vc-label-hint\">(kg\u00b7m\u00b2)<\/span><\/label><input class=\"vc-input\" id=\"vc-j2\" type=\"text\" inputmode=\"decimal\"><\/div>\r\n<div class=\"vc-field vc-field-full\"><label class=\"vc-label\" for=\"vc-ct\">Documented dynamic torsional stiffness C<sub>t,dyn<\/sub> <span class=\"vc-label-hint\">(N\u00b7m\/rad at the applicable amplitude,frequency and temperature)<\/span><\/label><input class=\"vc-input\" id=\"vc-ct\" type=\"text\" inputmode=\"decimal\"><\/div>\r\n<div class=\"vc-field vc-field-full\"><label class=\"vc-label\" for=\"vc-torque-source\">Power\/speed\/multiplier operating basis<\/label><input class=\"vc-input\" id=\"vc-torque-source\" type=\"text\" maxlength=\"500\" placeholder=\"Operating case and exact multiplier source\"><\/div>\r\n<div class=\"vc-field vc-field-full\"><label class=\"vc-label\" for=\"vc-model-source\">Inertia,stiffness and excitation model source<\/label><input class=\"vc-input\" id=\"vc-model-source\" type=\"text\" maxlength=\"500\" placeholder=\"Manufacturer data\/model revision and parameter conditions\"><\/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>Model gate:<\/strong> use only when two rigid inertias connected by one linear torsional spring are an accepted idealization and all inputs are referred to the coupling shafts. K is only an entered sensitivity multiplier;this page does not derive a service factor or required coupling rating.<\/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 results<\/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\"><div class=\"vc-rcard-label\">Nominal transmitted torque,P\/\u03c9<\/div><div class=\"vc-rcard-value\" id=\"vc-r-torque\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">K-scaled torque arithmetic<\/div><div class=\"vc-rcard-value\" id=\"vc-r-scaled\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Reduced inertia,J\u2081J\u2082\/(J\u2081+J\u2082)<\/div><div class=\"vc-rcard-value\" id=\"vc-r-jred\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Ideal undamped torsional frequency<\/div><div class=\"vc-rcard-value\" id=\"vc-r-fn\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Entered synchronous-order frequency<\/div><div class=\"vc-rcard-value\" id=\"vc-r-fexc\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Frequency ratio,f\u2099\/f<sub>exc<\/sub><\/div><div class=\"vc-rcard-value\" id=\"vc-r-ratio\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Signed frequency difference,f\u2099\u2212f<sub>exc<\/sub><\/div><div class=\"vc-rcard-value\" id=\"vc-r-delta\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Absolute separation relative to f<sub>exc<\/sub><\/div><div class=\"vc-rcard-value\" id=\"vc-r-separation\">\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\">Formula,applicability and DIN context<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\">\r\n<h3>Exact power-speed torque<\/h3><div class=\"vc-formula-box\">\u03c9=2\u03c0n\/60<br>T=P\/\u03c9=(30000\/\u03c0)\u00b7P<sub>kW<\/sub>\/n<sub>rpm<\/sub><br>T<sub>K<\/sub>=K\u00b7T<\/div><p>The former rounded constant9549 is replaced by the direct SI relation. T<sub>K<\/sub> is only multiplication by a user-supplied K;it is not labelled a DIN-required torque or coupling rating.<\/p>\r\n<h3>Ideal undamped two-inertia mode<\/h3><div class=\"vc-formula-box\">J<sub>red<\/sub>=J\u2081J\u2082\/(J\u2081+J\u2082)<br>f\u2099=(1\/2\u03c0)\u221a(C<sub>t,dyn<\/sub>\/J<sub>red<\/sub>)<br>f<sub>exc<\/sub>=q\u00b7n\/60<\/div><p>The displayed ratio and separation compare only this one ideal mode with one entered synchronous order. They do not prove resonance avoidance.<\/p>\r\n<h3>DIN740-2 context \u2014 no closed load factors implemented<\/h3><p><a href=\"https:\/\/www.dinmedia.de\/en\/standard\/din-740-2\/1298816\" target=\"_blank\" rel=\"noopener\">DIN740-2:1986-08<\/a> is listed by DIN Media as current and is titled \u201cPower transmission engineering;flexible shaft couplings;parameters and design principles\u201d. Public scope information states that its calculation methods contain empirical load factors and apply only to a linear two-mass system under specific operating conditions;more elaborate methods are required when a rough calculation is not permissible. This page does not reproduce or claim any closed factor,table or clause.<\/p>\r\n<div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Not modelled:<\/strong> multiple inertias,shaft\/distributed stiffness,gear-ratio reflection errors,damping,nonlinear elastomer stiffness,backlash,transient start\/stop,fault torque,electrical or reciprocating excitation spectra,harmonics other than entered q,temperature\/load dependence,misalignment,maximum speed,bore\/key\/hub stresses,fatigue,guarding or manufacturer limits.<\/p><\/div><\/div><\/div><\/div><footer class=\"vc-footer\"><p>\u00a92024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><p>Reference arithmetic only;not coupling selection,design approval or proof of resonance avoidance. Scientific review:July2026.<\/p><\/footer><\/div>\r\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}var ids=['vc-power','vc-speed','vc-k','vc-order','vc-j1','vc-j2','vc-ct','vc-torque-source','vc-model-source'],keys=['power_kw','speed_rpm','torque_multiplier','excitation_order','inertia_1_kgm2','inertia_2_kgm2','dynamic_stiffness_nm_per_rad','torque_source','model_source'],outs=['vc-r-torque','vc-r-scaled','vc-r-jred','vc-r-fn','vc-r-fexc','vc-r-ratio','vc-r-delta','vc-r-separation'];function num(raw){var s=String(raw).trim().replace(',','.');return \/^[+]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+-]?\\d+)?$\/.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-results').classList.remove('vc-visible')}function valid(x,max){return Number.isFinite(x)&&x>0&&x<=max}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 all9 fields.':'';return}var P=num(raw[0]),n=num(raw[1]),K=num(raw[2]),q=num(raw[3]),J1=num(raw[4]),J2=num(raw[5]),Ct=num(raw[6]);if(!valid(P,1e9)){clear();$('vc-error').textContent='Power must be a strict,finite,positive number no more than10\u2079kW.';return}if(!valid(n,1e9)){clear();$('vc-error').textContent='Speed must be a strict,finite,positive number no more than10\u2079rev\/min.';return}if(!valid(K,1e6)){clear();$('vc-error').textContent='Torque multiplier must be a strict,finite,positive number no more than10\u2076.';return}if(!valid(q,1e6)){clear();$('vc-error').textContent='Excitation order must be a strict,finite,positive number no more than10\u2076.';return}if(!valid(J1,1e12)||!valid(J2,1e12)){clear();$('vc-error').textContent='Each inertia must be a strict,finite,positive number no more than10\u00b9\u00b2kg\u00b7m\u00b2.';return}if(!valid(Ct,1e18)){clear();$('vc-error').textContent='Dynamic stiffness must be a strict,finite,positive number no more than10\u00b9\u2078N\u00b7m\/rad.';return}var omega=2*Math.PI*n\/60,T=P*1000\/omega,TK=K*T,Jred=(J1*J2)\/(J1+J2),fn=Math.sqrt(Ct\/Jred)\/(2*Math.PI),fexc=q*n\/60,ratio=fn\/fexc,delta=fn-fexc,separation=Math.abs(delta)\/fexc*100;if(![omega,T,TK,Jred,fn,fexc,ratio,delta,separation].every(Number.isFinite)||Jred<=0){clear();$('vc-error').textContent='The result exceeds the finite numerical range;rescale the inputs.';return}$('vc-error').textContent='';$('vc-r-torque').textContent=fmt(T)+' N\u00b7m';$('vc-r-scaled').textContent=fmt(TK)+' N\u00b7m';$('vc-r-jred').textContent=fmt(Jred)+' kg\u00b7m\u00b2';$('vc-r-fn').textContent=fmt(fn)+' Hz';$('vc-r-fexc').textContent=fmt(fexc)+' Hz';$('vc-r-ratio').textContent=fmt(ratio);$('vc-r-delta').textContent=fmt(delta)+' Hz';$('vc-r-separation').textContent=fmt(separation)+'%';$('vc-r-note').textContent='Torque basis:'+raw[7]+' | Model basis:'+raw[8]+' | One ideal undamped mode versus one entered order only;no selection or resonance verdict.';$('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>Calculate exact power-speed torque and one ideal undamped two-inertia torsional mode from sourced dynamic stiffness, inertias and excitation order. 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