{"id":100106,"date":"2026-02-15T20:16:52","date_gmt":"2026-02-15T20:16:52","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100106"},"modified":"2026-07-12T07:34:34","modified_gmt":"2026-07-12T07:34:34","slug":"foundation-vibration-from-machine","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/fi\/calculators\/foundation-vibration-from-machine\/","title":{"rendered":"Rotating-Unbalance SDOF Force-Transmission Check"},"content":{"rendered":"\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Rotating-Unbalance SDOF Force-Transmission Check\",\"description\":\"Calculate peak rotating-unbalance force, steady-state displacement and transmitted support-force amplitude for a documented linear viscously damped force-excited SDOF model.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/foundation-vibration-from-machine\/\",\"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 result approve a machine foundation or isolation system?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. It is a reference calculation for one documented linear force-excited degree of freedom. It does not apply an ISO acceptance criterion or include coupled modes,base compliance,soil impedance,transients or structural stress.\"}},{\"@type\":\"Question\",\"name\":\"What happens at exact resonance with zero damping?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"The ideal steady-state transfer denominator is zero. The calculator reports the singularity explicitly instead of displaying a finite response,NaN or Infinity.\"}}]}<\/script>\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/vibromera.eu\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculators\",\"item\":\"https:\/\/vibromera.eu\/calculators\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Rotating-unbalance SDOF force transmission\",\"item\":\"https:\/\/vibromera.eu\/calculators\/foundation-vibration-from-machine\/\"}]}<\/script>\r\n<link rel=\"preconnect\" 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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}}\r\n\r\n.vc-form-grid-sdof{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:18px}.vc-result-note{margin:0;color:var(--vc-ink-secondary);font-size:13px}.vc-singular{color:var(--vc-red)!important;font-size:15px!important;line-height:1.3}@media(max-width:600px){.vc-form-grid-sdof{grid-template-columns:1fr}}\r\n<\/style>\r\n<div class=\"vc-calculator\" id=\"vc-sdof-transmission\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Linear force-excited model \u2014 one degree of freedom<\/p><h1 class=\"vc-header-title\">Rotating-Unbalance SDOF Force-Transmission Check<\/h1><p class=\"vc-header-subtitle\">Calculate peak 1\u00d7 excitation force,steady-state displacement and transmitted support force for one documented equivalent mass\u2013spring\u2013damper mode.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">F\u2080=U\u03c9\u00b2<\/span><span class=\"vc-badge\">Peak amplitudes<\/span><span class=\"vc-badge\">Reference model \u2014 no acceptance decision<\/span><\/div><\/header>\r\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\"><div class=\"vc-form-grid-sdof\">\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-mm\">Machine participating mass (kg)<\/label><input class=\"vc-input\" id=\"vc-mm\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 500\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-mf\">Foundation\/block participating mass (kg)<\/label><input class=\"vc-input\" id=\"vc-mf\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 2000\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-u\">Total phase-coherent unbalance U (g\u00b7mm)<\/label><input class=\"vc-input\" id=\"vc-u\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 3000\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-rpm\">Rotational speed n (rpm)<\/label><input class=\"vc-input\" id=\"vc-rpm\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 3000\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-k\">Equivalent support stiffness K<\/label><input class=\"vc-input\" id=\"vc-k\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 5000\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-kunit\">Stiffness unit<\/label><select class=\"vc-select\" id=\"vc-kunit\"><option value=\"\">Select\u2026<\/option><option value=\"Nm\">N\/m<\/option><option value=\"Nmm\">N\/mm<\/option><option value=\"MNm\">MN\/m<\/option><\/select><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-zeta\">Viscous damping ratio \u03b6<\/label><input class=\"vc-input\" id=\"vc-zeta\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 0.05\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-mode\">Mode and direction represented<\/label><input class=\"vc-input\" id=\"vc-mode\" type=\"text\" placeholder=\"e.g. vertical rigid-body translation\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-source\">Input provenance<\/label><input class=\"vc-input\" id=\"vc-source\" type=\"text\" placeholder=\"e.g. modal test and balance report,rev 2\"><\/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 boundary:<\/strong> machine and foundation are one rigid participating mass on a linear parallel K\u2013c support,excited by one phase-coherent rotating-unbalance component at 1\u00d7 against a fixed receiving base. Inputs must describe the same mode and direction. The model excludes coupled\/structural modes,base or soil compliance,frequency-dependent properties,transients,nonlinearity and acceptance criteria.<\/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\">Peak-amplitude SDOF result<\/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\"><div class=\"vc-rcard-label\">Excitation force F\u2080,peak<\/div><div class=\"vc-rcard-value\" id=\"vc-r-f0\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Undamped natural frequency f\u2099<\/div><div class=\"vc-rcard-value\" id=\"vc-r-fn\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Frequency ratio r<\/div><div class=\"vc-rcard-value\" id=\"vc-r-ratio\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Displacement X,peak<\/div><div class=\"vc-rcard-value\" id=\"vc-r-x\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Force transmissibility T<sub>F<\/sub><\/div><div class=\"vc-rcard-value\" id=\"vc-r-tf\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Transmitted support force F<sub>T<\/sub>,peak<\/div><div class=\"vc-rcard-value\" id=\"vc-r-ft\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Force reduction (negative = amplification)<\/div><div class=\"vc-rcard-value\" id=\"vc-r-red\">\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,definitions and applicability<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\">\r\n<h3>Implemented steady-state model<\/h3><div class=\"vc-formula-box\">m\u1e8d+c\u1e8b+Kx=F\u2080cos(\u03c9t)<br>\u03c9=2\u03c0n\/60 &nbsp;;&nbsp; F\u2080=U\u03c9\u00b2<br>\u03c9\u2099=\u221a(K\/m) &nbsp;;&nbsp; r=\u03c9\/\u03c9\u2099 &nbsp;;&nbsp; \u03b6=c\/(2m\u03c9\u2099)<br>D=\u221a[(1\u2212r\u00b2)\u00b2+(2\u03b6r)\u00b2]<br>X=(F\u2080\/K)\/D<br>T<sub>F<\/sub>=\u221a[1+(2\u03b6r)\u00b2]\/D &nbsp;;&nbsp; F<sub>T<\/sub>=F\u2080T<sub>F<\/sub><\/div>\r\n<p>m is the combined participating mass in kg,K is the equivalent stiffness in N\/m,U is converted from g\u00b7mm to kg\u00b7m by 10\u207b\u2076,n is rpm,\u03c9 and \u03c9\u2099 are rad\/s,X is the peak displacement amplitude in metres,and F\u2080 and F<sub>T<\/sub> are peak force amplitudes in newtons. Force reduction is (1\u2212T<sub>F<\/sub>)\u00d7100%; a negative value explicitly means amplification.<\/p>\r\n<h3>Source and dimensional check<\/h3><p><a href=\"https:\/\/ocw.mit.edu\/courses\/2-003sc-engineering-dynamics-fall-2011\/e02beb4dfc72b8a329174f6e94f45d90_QHTJK0v404U.pdf\" target=\"_blank\" rel=\"noopener\">MIT OpenCourseWare,Rotating Imbalance<\/a> derives the harmonic force components with amplitude me\u03c9\u00b2. <a href=\"https:\/\/ocw.mit.edu\/courses\/2-003sc-engineering-dynamics-fall-2011\/25c6ac26dc063bac51de474185a14b74_f1pxiNDTyHc.pdf\" target=\"_blank\" rel=\"noopener\">MIT OpenCourseWare,Vibration Isolation<\/a> derives the force-excited SDOF response and transmitted-force ratio. Units check:F\u2080=(kg\u00b7m)\/s\u00b2=N;F\u2080\/K=N\/(N\/m)=m.<\/p>\r\n<h3>Interpretation limits<\/h3><p>The result is not a balance tolerance,a vibration-severity value,a foundation design or a safe\/unsafe verdict. Enter only equivalent mass,stiffness,damping and unbalance supported by project data. Total phase-coherent U means the vector-equivalent unbalance producing the modeled 1\u00d7 force component; unrelated rotors or phases cannot simply be added as scalars. Peak amplitudes must not be compared directly with RMS or peak-to-peak limits.<\/p>\r\n<h3>Ideal undamped resonance<\/h3><p>When \u03b6=0 and r=1,the steady-state transfer denominator is zero. The ideal linear model has no finite harmonic steady-state response. The calculator reports that singularity explicitly; real systems require measured\/modelled damping and transient analysis near resonance.<\/p>\r\n<\/div><\/div><\/div><footer class=\"vc-footer\"><p>\u00a92024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><p>Reference linear SDOF arithmetic,not a normative balancing,vibration-acceptance or foundation-design calculation. Scientific review:July2026.<\/p><\/footer><\/div>\r\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}var ids=['vc-r-f0','vc-r-fn','vc-r-ratio','vc-r-x','vc-r-tf','vc-r-ft','vc-r-red'];function num(raw){var s=String(raw).trim().replace(',','.');return \/^[+]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+-]?\\d+)?$\/.test(s)?Number(s):NaN}function fmt(x){return Number(x.toPrecision(12)).toString()}function clear(){ids.forEach(function(id){$(id).textContent='\u2014';$(id).classList.remove('vc-singular')});$('vc-r-note').textContent='';$('vc-results').classList.remove('vc-visible')}function inRange(x,lo,hi){return Number.isFinite(x)&&x>=lo&&x<=hi}function setUrl(){var u=new URL(location),map={mm:'vc-mm',mf:'vc-mf',u:'vc-u',rpm:'vc-rpm',k:'vc-k',kunit:'vc-kunit',zeta:'vc-zeta',mode:'vc-mode',source:'vc-source'};Object.keys(map).forEach(function(key){var value=$(map[key]).value.trim();if(value)u.searchParams.set(key,value);else u.searchParams.delete(key)});history.replaceState(null,'',u.toString())}function fail(message){clear();$('vc-error').textContent=message}function calc(){setUrl();var raw=['vc-mm','vc-mf','vc-u','vc-rpm','vc-k','vc-zeta'].map(function(id){return $(id).value.trim()}),unit=$('vc-kunit').value,mode=$('vc-mode').value.trim(),source=$('vc-source').value.trim();if(raw.every(function(v){return !v})&&!unit&&!mode&&!source){clear();$('vc-error').textContent='';return}if(raw.some(function(v){return !v})||!unit||!mode||!source){fail('Enter every numeric input,select the stiffness unit,and document the mode\/direction and provenance.');return}var mm=num(raw[0]),mf=num(raw[1]),U=num(raw[2]),rpm=num(raw[3]),k=num(raw[4]),zeta=num(raw[5]);if(!inRange(mm,1e-9,1e12)){fail('Machine participating mass must be from 10\u207b\u2079 to 10\u00b9\u00b2 kg.');return}if(!inRange(mf,0,1e12)){fail('Foundation participating mass must be from 0 to 10\u00b9\u00b2 kg.');return}var m=mm+mf;if(!Number.isFinite(m)||m>2e12){fail('Combined participating mass must be finite and no greater than 2\u00d710\u00b9\u00b2 kg.');return}if(!inRange(U,0,1e15)){fail('Unbalance must be from 0 to 10\u00b9\u2075 g\u00b7mm.');return}if(!inRange(rpm,1e-6,1e9)){fail('Speed must be from 10\u207b\u2076 to 10\u2079 rpm.');return}if(!Number.isFinite(k)||k<=0){fail('Stiffness must be a strict positive number.');return}if(!(zeta===0||inRange(zeta,1e-12,10))){fail('Damping ratio must be zero or from 10\u207b\u00b9\u00b2 to 10.');return}var factor=unit==='Nmm'?1000:unit==='MNm'?1e6:1,K=k*factor;if(!inRange(K,1e-6,1e18)){fail('Converted equivalent stiffness must be from 10\u207b\u2076 to 10\u00b9\u2078 N\/m.');return}var omega=2*Math.PI*rpm\/60,Ukgm=U*1e-6,F0=Ukgm*omega*omega,wn=Math.sqrt(K)\/Math.sqrt(m),fn=wn\/(2*Math.PI),r=omega\/wn,a=1-r*r,b=2*zeta*r,D=Math.hypot(a,b);if(![omega,F0,wn,fn,r,a,b,D].every(Number.isFinite)){fail('The calculated state exceeds the finite numerical range.');return}$('vc-error').textContent='';$('vc-r-f0').textContent=fmt(F0)+' N';$('vc-r-fn').textContent=fmt(fn)+' Hz';$('vc-r-ratio').textContent=fmt(r);var singular=zeta===0&&Math.abs(r-1)<=8*Number.EPSILON*Math.max(1,Math.abs(r));if(singular){['vc-r-x','vc-r-tf','vc-r-ft','vc-r-red'].forEach(function(id){$(id).textContent='Unbounded in ideal undamped steady-state model';$(id).classList.add('vc-singular')});$('vc-r-note').textContent='\u03b6=0 and r\u22481 within floating-point resolution:the transfer denominator is treated as singular. 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