{"id":100137,"date":"2026-02-15T20:19:43","date_gmt":"2026-02-15T20:19:43","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100137"},"modified":"2026-07-17T21:02:02","modified_gmt":"2026-07-17T21:02:02","slug":"influence-coefficient-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/es\/calculators\/influence-coefficient-calculator\/","title":{"rendered":"Documented Single-Plane Influence-Coefficient Calculator"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Documented Single-Plane Influence-Coefficient Calculator\",\"description\":\"Calculate a replacement correction unbalance from documented synchronous vibration vectors and a trial mass-radius-angle vector, with explicit phase convention and no predicted residual 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var(--b);border-radius:6px;background:#fff;cursor:pointer}.vc-rgrid{display:grid;grid-template-columns:1fr 1fr;gap:12px}.vc-r{background:#fff;border:1px solid var(--bl);border-radius:8px;padding:16px}.vc-primary{grid-column:1\/-1;border:2px solid var(--c);background:linear-gradient(135deg,var(--cl),#fff)}.vc-rl{font:10px var(--mono);letter-spacing:.1em;text-transform:uppercase;color:var(--mut)}.vc-rv{font:600 19px\/1.3 var(--mono);overflow-wrap:anywhere}.vc-primary .vc-rv{font-size:27px;color:var(--c)}.vc-note{font-size:13px;color:var(--sec);margin:18px 0 0;overflow-wrap:anywhere}.vc-toggle{width:100%;padding:18px 24px;border:0;background:#fff;text-align:left;font:700 18px var(--display);cursor:pointer}.vc-body{max-height:0;overflow:hidden}.vc-section.vc-open .vc-body{max-height:30000px}.vc-inner{padding:0 24px 24px;border-top:1px solid var(--bl);color:var(--sec)}.vc-inner h3{font-family:var(--display);color:var(--ink);margin:24px 0 10px}.vc-formula{font:14px\/1.9 var(--mono);padding:14px;background:var(--alt);border:1px solid var(--bl);border-radius:6px;overflow-x:auto}.vc-example{background:var(--alt);border:1px solid var(--bl);padding:16px;border-radius:6px}.vc-footer{text-align:center;padding:30px;color:var(--mut);font-size:13px}.vc-section a,.vc-footer a{color:var(--c)}@media(max-width:650px){.vc-grid,.vc-rgrid{grid-template-columns:1fr}.vc-wide,.vc-group,.vc-primary{grid-column:auto}.vc-form{padding:18px}.vc-calculator{padding-left:12px;padding-right:12px}.vc-header{padding:34px 12px 30px}.vc-rv{font-size:16px}.vc-primary .vc-rv{font-size:21px}}<\/style>\n<div class=\"vc-calculator\" id=\"vc-influence\"><header class=\"vc-header\"><p class=\"vc-eyebrow\">One plane \u00b7 one measurement point \u00b7 one speed\/state<\/p><h1 class=\"vc-title\">Documented Single-Plane Influence-Coefficient Calculator<\/h1><p class=\"vc-sub\">Compute a replacement correction after removing the trial mass. Trial angle and mass radius are part of the complex unbalance vector; phase convention, synchronous quantity and unchanged run conditions are mandatory records.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">Trial angle retained<\/span><span class=\"vc-badge\">m\u00b7r unbalance basis<\/span><span class=\"vc-badge\">No residual prediction<\/span><\/div><\/header>\n<div class=\"vc-card\"><form id=\"vc-form\" class=\"vc-form\" autocomplete=\"off\"><div class=\"vc-grid\"><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-id\">Balance job \/ run identifier<\/label><input class=\"vc-input\" id=\"vc-id\" type=\"text\" maxlength=\"240\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-asset\">Machine, rotor and correction plane<\/label><input class=\"vc-input\" id=\"vc-asset\" type=\"text\" maxlength=\"700\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-point\">Measurement point \/ sensor \/ mounting<\/label><input class=\"vc-input\" id=\"vc-point\" type=\"text\" maxlength=\"700\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-speed\">Common run speed (r\/min)<\/label><input class=\"vc-input\" id=\"vc-speed\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div><div class=\"vc-field vc-wide\"><label class=\"vc-label\" for=\"vc-vbasis\">Synchronous vibration quantity, unit and amplitude basis<\/label><input class=\"vc-input\" id=\"vc-vbasis\" type=\"text\" maxlength=\"600\"><\/div><div class=\"vc-field vc-wide\"><label class=\"vc-label\" for=\"vc-phase\">Phase reference, positive direction, viewing side and instrument convention<\/label><input class=\"vc-input\" id=\"vc-phase\" type=\"text\" maxlength=\"900\"><\/div>\n<div class=\"vc-group\">Initial run \u2014 no trial mass<\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-a0\">Initial synchronous amplitude A\u2080<\/label><input class=\"vc-input\" id=\"vc-a0\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-p0\">Initial phase \u03c6\u2080 (degrees)<\/label><input class=\"vc-input\" id=\"vc-p0\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div>\n<div class=\"vc-group\">Trial unbalance and trial run<\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-munit\">Mass unit<\/label><select class=\"vc-select\" id=\"vc-munit\"><option value=\"\">Select\u2026<\/option><option value=\"g\">g<\/option><option value=\"oz\">oz (avoirdupois)<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-runit\">Radius unit<\/label><select class=\"vc-select\" id=\"vc-runit\"><option value=\"\">Select\u2026<\/option><option value=\"mm\">mm<\/option><option value=\"in\">in<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-mt\">Trial mass m\u209c<\/label><input class=\"vc-input\" id=\"vc-mt\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-rt\">Trial radius r\u209c<\/label><input class=\"vc-input\" id=\"vc-rt\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-tt\">Trial angle \u03b8\u209c (degrees)<\/label><input class=\"vc-input\" id=\"vc-tt\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-trial-state\">Correction interpretation<\/label><select class=\"vc-select\" id=\"vc-trial-state\"><option value=\"\">Select\u2026<\/option><option value=\"remove\">Trial mass will be removed; output is replacement added mass<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-a1\">Trial-run synchronous amplitude A\u2081<\/label><input class=\"vc-input\" id=\"vc-a1\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-p1\">Trial-run phase \u03c6\u2081 (degrees)<\/label><input class=\"vc-input\" id=\"vc-p1\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div>\n<div class=\"vc-group\">Correction location and applicability<\/div><div class=\"vc-field vc-wide\"><label class=\"vc-label\" for=\"vc-rc\">Correction radius r\ua700 (same selected radius unit)<\/label><input class=\"vc-input\" id=\"vc-rc\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div><div class=\"vc-field vc-wide\"><label class=\"vc-label\" for=\"vc-review\">Repeatability, linearity, rotor behaviour, runout, thermal state, trial attachment, ratings, guarding and safety review<\/label><input class=\"vc-input\" id=\"vc-review\" type=\"text\" maxlength=\"1200\"><\/div><\/div><p class=\"vc-error\" id=\"vc-error\" role=\"alert\"><\/p><div class=\"vc-warning\"><strong>Applicability gate:<\/strong> one suitable balance plane and one measurement point, stable synchronous response, identical speed\/configuration\/thermal state, unchanged phase convention, linear response and securely engineered trial\/correction masses. Stop, isolate and follow the machine\/tool procedure before changing weights. This arithmetic does not authorize a trial mass, prove rotor rigidity, set an acceptance limit or predict the measured residual.<\/div><\/form>\n<div class=\"vc-results\" id=\"vc-results\" aria-live=\"polite\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Replacement correction result<\/h2><button type=\"button\" class=\"vc-copy\" id=\"vc-copy\">Copy<\/button><\/div><div class=\"vc-rgrid\"><div class=\"vc-r vc-primary\"><div class=\"vc-rl\">Added correction mass and angle<\/div><div class=\"vc-rv\" id=\"vc-r-correction\">\u2014<\/div><\/div><div class=\"vc-r\"><div class=\"vc-rl\">Correction unbalance<\/div><div class=\"vc-rv\" id=\"vc-r-unbalance\">\u2014<\/div><\/div><div class=\"vc-r\"><div class=\"vc-rl\">Trial unbalance<\/div><div class=\"vc-rv\" id=\"vc-r-trial\">\u2014<\/div><\/div><div class=\"vc-r\"><div class=\"vc-rl\">Vibration change \u0394V<\/div><div class=\"vc-rv\" id=\"vc-r-dv\">\u2014<\/div><\/div><div class=\"vc-r\"><div class=\"vc-rl\">Response coefficient \u03b1=\u0394V\/U\u209c<\/div><div class=\"vc-rv\" id=\"vc-r-alpha\">\u2014<\/div><\/div><div class=\"vc-r\"><div class=\"vc-rl\">Effect ratio |\u0394V|\/max(A\u2080,A\u2081)<\/div><div class=\"vc-rv\" id=\"vc-r-ratio\">\u2014<\/div><\/div><\/div><p class=\"vc-note\" id=\"vc-note\"><\/p><\/div><\/div>\n<div class=\"vc-section vc-open\"><button type=\"button\" class=\"vc-toggle\" aria-expanded=\"true\">Equations, published example and ISO boundary<\/button><div class=\"vc-body\"><div class=\"vc-inner\"><h3>Implemented complex-vector model<\/h3><div class=\"vc-formula\">V(A,\u03c6)=A[cos\u03c6+i sin\u03c6]<br>U\u209c=m\u209cr\u209c[cos\u03b8\u209c+i sin\u03b8\u209c]<br>\u0394V=V\u2081\u2212V\u2080<br>\u03b1=\u0394V\/U\u209c<br>U\ua700=\u2212V\u2080\/\u03b1=\u2212V\u2080U\u209c\/\u0394V<br>m\ua700=|U\ua700|\/r\ua700<\/div><p>\u03b1 is a vibration-response coefficient per unbalance. Some references use its reciprocal; the convention must always be stated. The output is an added replacement mass after the entered trial mass is removed. Removal corrections, retained-trial corrections, fixed-hole decomposition, multiple measurement points\/planes\/speeds and least-squares balancing are outside this calculator.<\/p><h3>Published numerical example<\/h3><div class=\"vc-example\"><p>The <a href=\"https:\/\/oaktrust.library.tamu.edu\/server\/api\/core\/bitstreams\/25fa34ef-11d0-45fd-b528-ee6d4b650ebd\/content\" target=\"_blank\" rel=\"noopener\">Texas A&amp;M Turbomachinery Laboratory Rotor Balancing Tutorial (2016)<\/a> gives V\u2080=5.6 mil pk-pk\u2220135\u00b0, V\u2081=3.3 mil pk-pk\u2220238\u00b0 and trial unbalance 74 oz\u00b7in\u2220315\u00b0. Using the printed polar inputs gives \u0394V=7.110850\u2220288.116\u00b0 and U\ua700=58.277138 oz\u00b7in\u2220341.883971\u00b0, consistent with the tutorial\u2019s rounded 58.24 oz\u00b7in\u2220341.9\u00b0. The former code omitted \u03b8\u209c from U\ua700 and would have reported approximately 26.9\u00b0.<\/p><\/div><h3>Independent method sources<\/h3><p>A peer-reviewed <a href=\"https:\/\/www.mdpi.com\/2075-1702\/9\/5\/89\" target=\"_blank\" rel=\"noopener\">review of rotor balancing methods<\/a> defines influence coefficients using trial mass, radius and phase. The official <a href=\"https:\/\/www.schenck-rotec.com\/fileadmin\/Downloads\/1._Products\/EN\/1.4_Handhelds\/1.4.1_SmartBalancer4\/BE-90969-ENG-V2.0.pdf\" target=\"_blank\" rel=\"noopener\">Schenck SmartBalancer 4 manual<\/a> describes the initial\/trial-run method and limits its instructions to rotors behaving rigidly at balance speed.<\/p><h3>ISO scope\/status<\/h3><p><a href=\"https:\/\/www.iso.org\/standard\/56561.html\" target=\"_blank\" rel=\"noopener\">ISO 21940-13:2012<\/a>, edition 1, is Published and confirmed; it covers criteria, instrumentation, safety, reporting and records for in-situ balancing of medium\/large rotors, and its official abstract explicitly says it does not guide correction-mass calculations. <a href=\"https:\/\/www.iso.org\/standard\/54074.html\" target=\"_blank\" rel=\"noopener\">ISO 21940-11:2016<\/a> with Amendment 1:2022 covers procedures\/tolerances for rigid behaviour and is under systematic review. <a href=\"https:\/\/www.iso.org\/standard\/50429.html\" target=\"_blank\" rel=\"noopener\">ISO 21940-12:2016<\/a>, confirmed in 2025, covers flexible behaviour. This page\u2019s complex arithmetic is not labelled an ISO formula; exact clauses remain <strong>NEEDS_LICENSED_SOURCE<\/strong>.<\/p><h3>Required engineering checks<\/h3><p>Confirm that unbalance is the dominant cause and the chosen plane can control the relevant response. Review 1\u00d7 repeatability, runout compensation, phase sign\/viewing convention, sensor orientation and integration convention, speed\/thermal\/configuration equality, structural resonance\/nonlinearity, trial centrifugal force and attachment, rotor\/bearing\/driver limits, clearance, overspeed and guarding. Verify the result with a controlled run; do not treat the algebraic cancellation as a residual-vibration forecast.<\/p><\/div><\/div><\/div><footer class=\"vc-footer\">\u00a9 2024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u00b7 Scientific review July 2026<\/footer><\/div>\n<script>(function(){'use strict';function $(i){return document.getElementById(i)}var mf={g:1,oz:28.349523125},rf={mm:1,in:25.4},ml={g:'g',oz:'oz'},rl={mm:'mm',in:'in'},map={ic_id:'vc-id',ic_asset:'vc-asset',ic_point:'vc-point',ic_speed:'vc-speed',ic_vbasis:'vc-vbasis',ic_phase:'vc-phase',ic_a0:'vc-a0',ic_p0:'vc-p0',ic_munit:'vc-munit',ic_runit:'vc-runit',ic_mt:'vc-mt',ic_rt:'vc-rt',ic_tt:'vc-tt',ic_trial_state:'vc-trial-state',ic_a1:'vc-a1',ic_p1:'vc-p1',ic_rc:'vc-rc',ic_review:'vc-review'};function num(raw){var s=String(raw).trim().replace(',','.');if(s.length>80||!\/^[-+]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+-]?\\d+)?$\/.test(s))return NaN;return Number(s)}function fmt(v){if(!Number.isFinite(v))return'\u2014';if(Object.is(v,-0)||v===0)return'0';return Number(v.toPrecision(12)).toString()}function ang(a){a=a%360;return a<0?a+360:a}function pol(a,d){var r=d*Math.PI\/180;return{re:a*Math.cos(r),im:a*Math.sin(r)}}function sub(a,b){return{re:a.re-b.re,im:a.im-b.im}}function mul(a,b){return{re:a.re*b.re-a.im*b.im,im:a.re*b.im+a.im*b.re}}function div(a,b){var q=b.re*b.re+b.im*b.im;return{re:(a.re*b.re+a.im*b.im)\/q,im:(a.im*b.re-a.re*b.im)\/q}}function neg(a){return{re:-a.re,im:-a.im}}function polar(a){return{mag:Math.hypot(a.re,a.im),phase:ang(Math.atan2(a.im,a.re)*180\/Math.PI)}}function clear(){['vc-r-correction','vc-r-unbalance','vc-r-trial','vc-r-dv','vc-r-alpha','vc-r-ratio'].forEach(function(i){$(i).textContent='\u2014'});$('vc-note').textContent='';$('vc-results').classList.remove('vc-visible')}function fail(m){clear();$('vc-error').textContent=m}function setUrl(){var u=new URL(location);Object.keys(map).forEach(function(k){var v=$(map[k]).value.trim();if(v)u.searchParams.set(k,v);else u.searchParams.delete(k)});history.replaceState(null,'',u.toString())}function calc(){setUrl();var x={};Object.keys(map).forEach(function(k){x[k]=$(map[k]).value.trim()});if(!Object.keys(x).some(function(k){return x[k]})){$('vc-error').textContent='';clear();return}if(!Object.keys(x).every(function(k){return x[k]})){fail('Enter every job, measurement, convention, run, trial, radius and review field.');return}if(!(x.ic_munit in mf)||!(x.ic_runit in rf)||x.ic_trial_state!=='remove'){fail('Select supported mass\/radius units and the remove-trial interpretation.');return}var speed=num(x.ic_speed),a0=num(x.ic_a0),p0=num(x.ic_p0),mt=num(x.ic_mt),rt=num(x.ic_rt),tt=num(x.ic_tt),a1=num(x.ic_a1),p1=num(x.ic_p1),rc=num(x.ic_rc),n=[speed,a0,p0,mt,rt,tt,a1,p1,rc];if(!n.every(Number.isFinite)){fail('Numerical fields must be complete finite decimal numbers.');return}if(speed<=0||mt<=0||rt<=0||rc<=0||a0<0||a1<0){fail('Speed, trial mass and radii must be positive; 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