{"id":100147,"date":"2026-02-15T20:21:02","date_gmt":"2026-02-15T20:21:02","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100147"},"modified":"2026-07-12T18:52:32","modified_gmt":"2026-07-12T18:52:32","slug":"machine-vibration-isolation","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/ro\/calculators\/machine-vibration-isolation\/","title":{"rendered":"Machine Vibration Isolation SDOF Screening Worksheet"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Machine Vibration Isolation SDOF Screening Worksheet\",\"description\":\"Solve a linear viscously damped single-degree-of-freedom force-isolation target and report the required natural frequency, stiffness, static deflection and transmitted-force amplitude with explicit scope limits.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/machine-vibration-isolation\/\",\"applicationCategory\":\"Engineering Reference\",\"operatingSystem\":\"Any\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"dateModified\":\"2026-07-13\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\n<style>:root{--vi:#295f86;--vil:#eaf3f9;--ink:#181817;--sec:#595750;--mut:#817e76;--b:#d8d4cc;--bl:#e9e5dd;--alt:#f8f6f1;--red:#b42318;--yel:#fff8df;--amb:#8a6500;--font:'DM Sans',-apple-system,BlinkMacSystemFont,'Segoe UI',sans-serif}.vi-wrap{font-family:var(--font);color:var(--ink);max-width:1060px;margin:0 auto;border:1px solid var(--bl);border-radius:16px;overflow:hidden;background:#fff}.vi-wrap *,.vi-wrap *:before,.vi-wrap *:after{box-sizing:border-box}.vi-hero{padding:34px 38px 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20px}.vi-rtitle{font-size:20px;font-weight:900;color:var(--vi)}.vi-rsub{font-size:13px;color:var(--sec);margin-top:4px}.vi-rgrid{display:grid;grid-template-columns:repeat(3,1fr);gap:1px;background:var(--bl)}.vi-card{background:#fff;padding:18px}.vi-card h3{font-size:12px;text-transform:uppercase;letter-spacing:.06em;color:var(--mut);margin:0 0 8px}.vi-val{font-size:20px;font-weight:900;overflow-wrap:anywhere}.vi-unit{font-size:12px;color:var(--mut);margin-top:4px}.vi-alert{border-left:4px solid var(--amb);background:var(--yel);padding:14px 16px;margin-top:18px;font-size:14px;line-height:1.55}.vi-section{border-top:1px solid var(--bl);padding:28px 38px}.vi-section h2{font-size:24px;margin:0 0 10px}.vi-section h3{font-size:18px;margin:22px 0 8px}.vi-section p,.vi-section li{font-size:14px;line-height:1.65;color:var(--sec)}.vi-table-wrap{overflow-x:auto;border:1px solid var(--b);border-radius:10px}.vi-table{width:100%;border-collapse:collapse;min-width:760px}.vi-table th,.vi-table td{padding:12px 13px;text-align:left;vertical-align:top;border-bottom:1px solid var(--bl);font-size:13px;line-height:1.45}.vi-table th{background:var(--alt);font-weight:900}.vi-table tr:last-child td{border-bottom:0}.vi-code{font-family:ui-monospace,SFMono-Regular,Consolas,monospace}.vi-footer{padding:20px 38px;background:var(--alt);font-size:12px;color:var(--mut)}.vi-footer a,.vi-section a{color:var(--vi)}@media(max-width:700px){.vi-hero,.vi-main,.vi-section{padding-left:20px;padding-right:20px}.vi-grid,.vi-rgrid{grid-template-columns:1fr}.vi-wide{grid-column:auto}.vi-panel{padding:18px}.vi-table{min-width:680px}}<\/style>\n<div class=\"vi-wrap\"><header class=\"vi-hero\"><div class=\"vi-kicker\">Linear SDOF force-isolation screening \u00b7 not mount selection<\/div><h1>Machine Vibration Isolation Screening Worksheet<\/h1><p class=\"vi-lead\">For one harmonic force acting on a rigid mass supported by ideal linear springs and viscous dampers, solve the frequency ratio required to meet a user-specified force-transmissibility target. The worksheet does not certify an isolator, machine, foundation or installation.<\/p><div class=\"vi-badges\"><span class=\"vi-badge\">Damping included<\/span><span class=\"vi-badge\">SI \/ US customary<\/span><span class=\"vi-badge\">No target presets<\/span><span class=\"vi-badge\">ISO 2017-1 information boundary<\/span><\/div><\/header>\n<main class=\"vi-main\"><section class=\"vi-panel\"><h2>Define the idealized operating case<\/h2><p class=\"vi-note\">Select units first. US customary inputs use avoirdupois pounds mass and pounds-force. Changing the unit selector reinterprets\u2014not converts\u2014numbers already entered. Enter peak, RMS or peak-to-peak force consistently;the transmitted force has the same amplitude convention.<\/p><form id=\"vi-form\" novalidate><div class=\"vi-grid\"><div class=\"vi-field\"><label class=\"vi-label\" for=\"vi-units\">Input\/output unit system<\/label><select class=\"vi-select\" id=\"vi-units\"><option value=\"\">Select\u2026<\/option><option value=\"si\">SI: kg, N, N\/mm, mm<\/option><option value=\"us\">US customary: lbm, lbf, lbf\/in, in<\/option><\/select><\/div><div class=\"vi-field\"><label class=\"vi-label\" for=\"vi-mass\">Supported rigid mass (<span id=\"vi-u-mass\">unit<\/span>)<\/label><input class=\"vi-input\" id=\"vi-mass\" inputmode=\"decimal\" autocomplete=\"off\"><\/div><div class=\"vi-field\"><label class=\"vi-label\" for=\"vi-rpm\">Harmonic excitation speed\/frequency (r\/min)<\/label><input class=\"vi-input\" id=\"vi-rpm\" inputmode=\"decimal\" autocomplete=\"off\"><span class=\"vi-help\">This screen assumes one harmonic at f=n\/60.<\/span><\/div><div class=\"vi-field\"><label class=\"vi-label\" for=\"vi-force\">Exciting-force amplitude at that harmonic (<span id=\"vi-u-force\">unit<\/span>)<\/label><input class=\"vi-input\" id=\"vi-force\" inputmode=\"decimal\" autocomplete=\"off\"><span class=\"vi-help\">May be zero for stiffness-only screening. Do not mix peak,RMS or peak-to-peak conventions.<\/span><\/div><div class=\"vi-field\"><label class=\"vi-label\" for=\"vi-mounts\">Number of identical vertical mounts<\/label><input class=\"vi-input\" id=\"vi-mounts\" inputmode=\"numeric\" autocomplete=\"off\"><span class=\"vi-help\">Equal stiffness and equal static load are assumed.<\/span><\/div><div class=\"vi-field\"><label class=\"vi-label\" for=\"vi-target\">Target force transmissibility T<\/label><input class=\"vi-input\" id=\"vi-target\" inputmode=\"decimal\" autocomplete=\"off\"><span class=\"vi-help\">Dimensionless,0&lt;T&lt;1. This is a project target\u2014not an ISO default.<\/span><\/div><div class=\"vi-field\"><label class=\"vi-label\" for=\"vi-zeta\">Viscous damping ratio \u03b6<\/label><input class=\"vi-input\" id=\"vi-zeta\" inputmode=\"decimal\" autocomplete=\"off\"><span class=\"vi-help\">Dimensionless,0\u2264\u03b6\u22641. Use a supplier\/test value for the stated preload,temperature and frequency.<\/span><\/div><div class=\"vi-field vi-wide\"><label class=\"vi-label\" for=\"vi-source\">Assumption and source record<\/label><textarea class=\"vi-textarea\" id=\"vi-source\" maxlength=\"1800\" placeholder=\"Mass and centre-of-gravity data;operating range\/harmonic and force convention;target criterion;mount dynamic stiffness and damping source;preload,temperature and environment\"><\/textarea><\/div><\/div><p class=\"vi-error\" id=\"vi-error\" role=\"alert\"><\/p><\/form>\n<section class=\"vi-results\" id=\"vi-results\" hidden data-json=\"\"><div class=\"vi-rhead\"><div class=\"vi-rtitle\">Ideal linear SDOF target<\/div><div class=\"vi-rsub\" id=\"vi-summary\">\u2014<\/div><\/div><div class=\"vi-rgrid\"><article class=\"vi-card\"><h3>Required frequency ratio<\/h3><div class=\"vi-val\" id=\"vi-r-ratio\">\u2014<\/div><div class=\"vi-unit\">r=f\/fn;isolation branch<\/div><\/article><article class=\"vi-card\"><h3>Required undamped natural frequency<\/h3><div class=\"vi-val\" id=\"vi-r-fn\">\u2014<\/div><div class=\"vi-unit\" id=\"vi-r-fn-note\">\u2014<\/div><\/article><article class=\"vi-card\"><h3>Target transmitted-force amplitude<\/h3><div class=\"vi-val\" id=\"vi-r-force\">\u2014<\/div><div class=\"vi-unit\">same peak\/RMS\/p-p convention as input<\/div><\/article><article class=\"vi-card\"><h3>Total vertical stiffness<\/h3><div class=\"vi-val\" id=\"vi-r-kt\">\u2014<\/div><div class=\"vi-unit\" id=\"vi-r-kt-si\">\u2014<\/div><\/article><article class=\"vi-card\"><h3>Per-mount stiffness<\/h3><div class=\"vi-val\" id=\"vi-r-km\">\u2014<\/div><div class=\"vi-unit\">identical equal-load mounts only<\/div><\/article><article class=\"vi-card\"><h3>Static deflection<\/h3><div class=\"vi-val\" id=\"vi-r-defl\">\u2014<\/div><div class=\"vi-unit\">linear stiffness and standard gravity<\/div><\/article><article class=\"vi-card\"><h3>Static load per mount<\/h3><div class=\"vi-val\" id=\"vi-r-load\">\u2014<\/div><div class=\"vi-unit\">vertical weight\/N only<\/div><\/article><article class=\"vi-card\"><h3>Total viscous damping coefficient<\/h3><div class=\"vi-val\" id=\"vi-r-c\">\u2014<\/div><div class=\"vi-unit\" id=\"vi-r-c-si\">\u2014<\/div><\/article><article class=\"vi-card\"><h3>Steady relative displacement amplitude<\/h3><div class=\"vi-val\" id=\"vi-r-x\">\u2014<\/div><div class=\"vi-unit\">at the entered force harmonic<\/div><\/article><\/div><\/section>\n<div class=\"vi-alert\"><strong>Decision boundary:<\/strong> the result is a target for an ideal vertical SDOF model. Real selection requires supplier dynamic stiffness and damping at the actual preload,frequency,amplitude,temperature and ageing state;load-deflection limits;centre-of-gravity distribution;rotational\/coupled modes;support flexibility;transients;stops;clearance;stability and restraint. Do not select mounts from stiffness alone.<\/div><\/section><\/main>\n<section class=\"vi-section\"><h2>Equations and dimensional basis<\/h2><div class=\"vi-table-wrap\"><table class=\"vi-table\"><thead><tr><th>Quantity<\/th><th>Equation<\/th><th>Meaning and limitation<\/th><\/tr><\/thead><tbody><tr><td>Force transmissibility<\/td><td class=\"vi-code\">T=\u221a[(1+(2\u03b6r)\u00b2)\/((1\u2212r\u00b2)\u00b2+(2\u03b6r)\u00b2)]<\/td><td>Linear viscously damped SDOF under a harmonic applied force;T=F<sub>trans<\/sub>\/F<sub>0<\/sub>.<\/td><\/tr><tr><td>Required isolation-branch ratio<\/td><td class=\"vi-code\">x=r\u00b2;T\u00b2x\u00b2+[T\u00b2(\u22122+4\u03b6\u00b2)\u22124\u03b6\u00b2]x+(T\u00b2\u22121)=0<\/td><td>The larger positive root is used. At \u03b6=0,this reduces to r=\u221a(1+1\/T).<\/td><\/tr><tr><td>Frequencies<\/td><td class=\"vi-code\">f=n\/60; f<sub>n<\/sub>=f\/r; \u03c9<sub>n<\/sub>=2\u03c0f<sub>n<\/sub><\/td><td>f<sub>n<\/sub> is the undamped natural frequency of the ideal model.<\/td><\/tr><tr><td>Stiffness<\/td><td class=\"vi-code\">k<sub>total<\/sub>=m\u03c9<sub>n<\/sub>\u00b2; k<sub>mount<\/sub>=k<sub>total<\/sub>\/N<\/td><td>Per-mount division assumes identical mounts and equal load\/stiffness.<\/td><\/tr><tr><td>Damping<\/td><td class=\"vi-code\">c<sub>total<\/sub>=2\u03b6m\u03c9<sub>n<\/sub><\/td><td>Equivalent linear viscous coefficient;not a universal material property.<\/td><\/tr><tr><td>Static quantities<\/td><td class=\"vi-code\">\u03b4<sub>st<\/sub>=mg\u2080\/k<sub>total<\/sub>; W<sub>mount<\/sub>=mg\u2080\/N<\/td><td>Uses g\u2080=9.80665 m\/s\u00b2 and the same linear vertical stiffness.<\/td><\/tr><tr><td>Harmonic response<\/td><td class=\"vi-code\">D=\u221a[(1\u2212r\u00b2)\u00b2+(2\u03b6r)\u00b2]; X=F\u2080\/(k<sub>total<\/sub>D); F<sub>trans<\/sub>=TF\u2080<\/td><td>Steady-state amplitude only;no startup,shutdown,shock or multi-harmonic response.<\/td><\/tr><\/tbody><\/table><\/div><p>Internal calculations use kg,N,m,N\/m and N\u00b7s\/m. Exact definitions:1 lbm=0.45359237 kg and1 lbf=4.4482216152605 N. Therefore1 N\/m=0.00571014715476285 lbf\/in.<\/p><\/section>\n<section class=\"vi-section\"><h2>What was corrected<\/h2><p>The former page inverted the undamped formula <span class=\"vi-code\">T=1\/(r\u00b2\u22121)<\/span> but described the result as a complete isolation design. It did not ask for damping even though its own text acknowledged that damping controls resonance and worsens high-frequency isolation. Fixed 0.20,0.10,0.05,0.03 and0.01 targets were presented as generic machinery recommendations without a controlled project or normative source. They have been removed.<\/p><p>The exciting-force input was labelled \u201cunbalance force\u201d,although it could be any harmonic force amplitude and the page did not derive it from residual unbalance. The new wording separates the force-isolation screen from ISO 21940 balance-quality calculations. Approximate pound conversions,9.81 m\/s\u00b2,prefix-tolerant parsing,pre-filled results and quick presets were also removed.<\/p><\/section>\n<section class=\"vi-section\"><h2>Source and applicability boundary<\/h2><p><a href=\"https:\/\/dspace.mit.edu\/bitstream\/handle\/1721.1\/60691\/16-07-fall-2004\/contents\/lecture-notes\/d33.pdf\" target=\"_blank\" rel=\"noopener\">MIT 16.07 Dynamics, Lecture D33: Forced Vibration<\/a> gives the damped force-transmissibility relation used here and shows the damping tradeoff above r=\u221a2. The algebraic inversion for r is derived on this page from that general engineering equation;it is not an ISO formula.<\/p><p><a href=\"https:\/\/www.iso.org\/standard\/28919.html\" target=\"_blank\" rel=\"noopener\">ISO 2017-1:2005<\/a>,edition1,is published and was last confirmed in2019;the ISO lifecycle currently shows stage90.60 (close of review). Its public scope concerns the technical information exchanged among users,manufacturers and suppliers when applying resilient mounting systems. It does not establish the former universal target percentages. Exact clauses and required data fields need the licensed standard and are marked <strong>NEEDS_LICENSED_SOURCE<\/strong>.<\/p><p><a href=\"https:\/\/www.nist.gov\/pml\/special-publication-811\/nist-guide-si-appendix-b-conversion-factors\" target=\"_blank\" rel=\"noopener\">NIST SP811 Appendix B<\/a> supplies the exact pound and inch\/foot conversion basis used for SI\/US equivalence tests.<\/p><h3>Information still needed before selection<\/h3><ul><li>Supported mass,centre of gravity,rotary inertia and load carried by each mount.<\/li><li>All excitation harmonics and force\/moment amplitudes across startup,normal operation,variable speed and shutdown.<\/li><li>Dynamic\u2014not merely static\u2014stiffness and damping versus preload,frequency,amplitude,temperature,ageing and tolerances.<\/li><li>Six-degree-of-freedom natural frequencies,coupled modes,support\/foundation flexibility and piping\/duct\/cable forces.<\/li><li>Allowable motion,clearances,snubbing,shock\/seismic\/wind restraint,stability,creep,fatigue and environment.<\/li><li>Acceptance criteria and commissioning measurements agreed by the responsible parties.<\/li><\/ul><\/section>\n<footer class=\"vi-footer\">\u00a9 2024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u00b7 Scientific review July2026<\/footer><\/div>\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}var G0=9.80665,LBKG=.45359237,LBFN=4.4482216152605,NM_LBFIN=.00571014715476285,MIN=.0254;function num(s){s=String(s).trim();if(!s||s.includes('.')&&s.includes(',')||!\/^[+-]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)(?:[eE][+-]?\\d+)?$\/.test(s))return NaN;var n=Number(s.replace(',','.'));return Number.isFinite(n)&&Math.abs(n)<=1e15?n:NaN}function out(x,d){return x.toLocaleString('en-US',{minimumFractionDigits:d,maximumFractionDigits:d})}function 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