{"id":100194,"date":"2026-02-15T20:26:05","date_gmt":"2026-02-15T20:26:05","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100194"},"modified":"2026-07-13T04:25:41","modified_gmt":"2026-07-13T04:25:41","slug":"press-fit-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/zh\/calculators\/press-fit-calculator\/","title":{"rendered":"Elastic Cylindrical Interference-Fit Worksheet"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Elastic Cylindrical Interference-Fit Worksheet\",\"description\":\"Calculate ideal elastic contact pressure and separate Coulomb slip limits for concentric cylindrical interference fits with explicit plane-stress assumptions.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/press-fit-calculator\/\",\"applicationCategory\":\"EngineeringApplication\",\"operatingSystem\":\"Any\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"dateModified\":\"2026-07-13\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Does ISO 286 calculate interference-fit contact pressure?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. ISO 286-1 defines the tolerance-code concepts and ISO 286-2 supplies selected limit-deviation tables. The elastic pressure equation on this page is a Lam\u00e9-Hooke engineering model and is not an ISO formula.\"}},{\"@type\":\"Question\",\"name\":\"Which friction coefficient should I use?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"There is no universal value. Use a coefficient justified for the actual material pair, surface finish, coating, lubricant, assembly process, temperature, contact pressure and life condition; otherwise leave it blank.\"}},{\"@type\":\"Question\",\"name\":\"Can I enter H7\/p6 or H7\/s6 directly?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Determine the applicable shaft and hole limits from a controlled current source, then analyse the minimum and maximum diametral interference at a common reference or operating state.\"}},{\"@type\":\"Question\",\"name\":\"Does this worksheet prove the fit is safe?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. It does not evaluate yielding, plasticity, fatigue, fretting, edge effects, temperature gradients, residual stress, assembly damage, surface flattening, combined loading or a safety factor.\"}},{\"@type\":\"Question\",\"name\":\"What interference does the model use?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"It uses positive diametral interference: free shaft outside diameter minus free hub bore diameter, both defined at the same controlled state. The small diameter difference is ignored in the reference interface geometry.\"}}]}<\/script>\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\":\"Elastic Cylindrical Interference-Fit Worksheet\",\"item\":\"https:\/\/vibromera.eu\/calculators\/press-fit-calculator\/\"}]}<\/script>\n<style>\n:root{--vc-surface:#fff;--vc-alt:#f8f6f2;--vc-ink:#1a1a1a;--vc-secondary:#5a5650;--vc-muted:#807b73;--vc-accent:#b84f22;--vc-accent-light:#fdf0ea;--vc-yellow:#825f00;--vc-yellow-light:#fff8dc;--vc-red:#9d2b24;--vc-red-light:#fff0ee;--vc-border:#d9d4cc;--vc-border-light:#e8e4dd;--vc-shadow:0 1px 3px rgba(26,26,26,.06),0 4px 12px 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var(--vc-accent);background:linear-gradient(135deg,var(--vc-accent-light),#fff)}.vc-result-label{font:600 10px\/1.4 var(--vc-mono);letter-spacing:.08em;text-transform:uppercase;color:var(--vc-muted);margin-bottom:5px}.vc-result-value{font:600 19px\/1.3 var(--vc-mono);overflow-wrap:anywhere}.vc-result-primary .vc-result-value{font-size:27px;color:var(--vc-accent)}.vc-section-toggle{width:100%;display:flex;justify-content:space-between;align-items:center;padding:17px 22px;border:0;background:transparent;text-align:left;cursor:pointer}.vc-section-title{font:700 18px var(--vc-display)}.vc-chevron{transition:transform .2s}.vc-section.vc-open .vc-chevron{transform:rotate(180deg)}.vc-section-body{display:none}.vc-section.vc-open .vc-section-body{display:block}.vc-section-inner{padding:0 22px 22px;border-top:1px solid var(--vc-border-light);color:var(--vc-secondary)}.vc-section-inner h3{font:700 17px var(--vc-display);color:var(--vc-ink);margin:22px 0 9px}.vc-section-inner p,.vc-section-inner li{font-size:14px}.vc-formula{font:500 13px\/1.75 var(--vc-mono);padding:13px 15px;border:1px solid var(--vc-border);border-radius:6px;background:var(--vc-alt);overflow-x:auto}.vc-warning{padding:13px 15px;border-left:4px solid var(--vc-yellow);background:var(--vc-yellow-light);color:#5d4708;border-radius:4px;margin:14px 0}.vc-table{width:100%;border-collapse:collapse;margin:14px 0;font-size:13px}.vc-table th,.vc-table td{padding:9px 10px;border:1px solid var(--vc-border-light);text-align:left;vertical-align:top}.vc-table th{background:var(--vc-alt);color:var(--vc-ink)}.vc-faq{border:1px solid var(--vc-border-light);border-radius:6px;margin-top:8px}.vc-faq button{width:100%;padding:13px 14px;border:0;background:var(--vc-alt);font-weight:700;text-align:left;cursor:pointer}.vc-faq div{display:none;padding:13px 14px;border-top:1px solid var(--vc-border-light)}.vc-faq.vc-open div{display:block}.vc-related{display:flex;gap:9px;flex-wrap:wrap;margin-top:14px}.vc-related a{padding:7px 12px;border:1px solid var(--vc-border);border-radius:6px;text-decoration:none;color:var(--vc-secondary)}.vc-footer{text-align:center;padding:28px 12px;color:var(--vc-muted);font-size:12px}.vc-footer a{color:var(--vc-accent)}@media(max-width:720px){.vc-grid,.vc-result-grid{grid-template-columns:1fr}.vc-result-primary{grid-column:auto}.vc-form,.vc-results{padding:18px}}@media print{.vc-section-body,.vc-results{display:block!important}.vc-copy,.vc-chevron{display:none}}\n<\/style>\n<div class=\"vc-calculator\">\n<header class=\"vc-header\"><p class=\"vc-eyebrow\">Source-gated elastic screening arithmetic<\/p><h1 class=\"vc-title\">Elastic Cylindrical Interference-Fit Worksheet<\/h1><p class=\"vc-subtitle\">Ideal Lam\u00e9-Hooke contact pressure for two concentric cylinders with separate material properties and a solid or hollow shaft. Optional friction outputs are separate uniform-pressure Coulomb limits, not rated joint capacity.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">Diametral interference<\/span><span class=\"vc-badge\">Open ends \/ plane stress<\/span><span class=\"vc-badge\">Not an ISO pressure formula<\/span><\/div><\/header>\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" novalidate><div class=\"vc-grid\">\n<div class=\"vc-field vc-wide\"><label class=\"vc-label\" for=\"vc-system\">Input unit system<\/label><select class=\"vc-select\" id=\"vc-system\"><option value=\"metric\">Metric: mm and GPa<\/option><option value=\"imperial\">US customary: in and Mpsi<\/option><\/select><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-d\">Reference interface diameter d <span class=\"vc-hint vc-len-unit\">(mm)<\/span><\/label><input class=\"vc-input\" id=\"vc-d\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-delta\">Diametral interference \u03b4 <span class=\"vc-hint vc-len-unit\">(mm)<\/span><\/label><input class=\"vc-input\" id=\"vc-delta\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-di\">Shaft bore diameter D\u1d62 <span class=\"vc-hint vc-len-unit\">(mm; 0 = solid)<\/span><\/label><input class=\"vc-input\" id=\"vc-di\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-do\">Hub outside diameter D\u2092 <span class=\"vc-hint vc-len-unit\">(mm)<\/span><\/label><input class=\"vc-input\" id=\"vc-do\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-length\">Uniform contact length L <span class=\"vc-hint vc-len-unit\">(mm)<\/span><\/label><input class=\"vc-input\" id=\"vc-length\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-mu\">Documented friction coefficient \u03bc <span class=\"vc-hint\">(optional)<\/span><\/label><input class=\"vc-input\" id=\"vc-mu\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-es\">Shaft Young&#8217;s modulus E\u209b <span class=\"vc-hint vc-e-unit\">(GPa)<\/span><\/label><input class=\"vc-input\" id=\"vc-es\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-nus\">Shaft Poisson ratio \u03bd\u209b <span class=\"vc-hint\">(\u22121 &lt; \u03bd &lt; 0.5)<\/span><\/label><input class=\"vc-input\" id=\"vc-nus\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-eh\">Hub Young&#8217;s modulus E\u2095 <span class=\"vc-hint vc-e-unit\">(GPa)<\/span><\/label><input class=\"vc-input\" id=\"vc-eh\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-nuh\">Hub Poisson ratio \u03bd\u2095 <span class=\"vc-hint\">(\u22121 &lt; \u03bd &lt; 0.5)<\/span><\/label><input class=\"vc-input\" id=\"vc-nuh\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field vc-wide\"><label class=\"vc-label\" for=\"vc-source\">Controlled basis \/ source <span class=\"vc-hint\">(required: dimensions and state; materials; and \u03bc basis if used)<\/span><\/label><input class=\"vc-input\" id=\"vc-source\"><\/div>\n<label class=\"vc-check vc-wide\"><input type=\"checkbox\" id=\"vc-confirm\"><span>I confirm that \u03b4 is positive diametral interference at one controlled state; the bodies are concentric, sufficiently long away from ends, open\/unrestrained axially, isotropic and linearly elastic; full contact and uniform pressure are reasonable; \u03b4 is very small relative to d; and separate yielding, hollow-shaft buckling, fatigue, fretting, thermal, tolerance and assembly checks will be made.<\/span><\/label>\n<\/div><\/form><div class=\"vc-error\" id=\"vc-error\" role=\"alert\"><\/div>\n<div class=\"vc-results\" id=\"vc-results\" aria-live=\"polite\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Ideal model results<\/h2><button type=\"button\" class=\"vc-copy\" id=\"vc-copy\">Copy<\/button><\/div><div class=\"vc-result-grid\">\n<div class=\"vc-result vc-result-primary\"><div class=\"vc-result-label\">Uniform contact pressure p<\/div><div class=\"vc-result-value\" id=\"vc-r-p\">\u2014<\/div><\/div>\n<div class=\"vc-result\"><div class=\"vc-result-label\">Interference ratio \u03b4\/d<\/div><div class=\"vc-result-value\" id=\"vc-r-ratio\">\u2014<\/div><\/div>\n<div class=\"vc-result\"><div class=\"vc-result-label\">Hub bore hoop stress \u03c3\u03b8,h<\/div><div class=\"vc-result-value\" id=\"vc-r-hubstress\">\u2014<\/div><\/div>\n<div class=\"vc-result\"><div class=\"vc-result-label\">Shaft contact hoop stress \u03c3\u03b8,s<\/div><div class=\"vc-result-value\" id=\"vc-r-shaftstress\">\u2014<\/div><\/div>\n<div class=\"vc-result\"><div class=\"vc-result-label\">Hub diametral expansion<\/div><div class=\"vc-result-value\" id=\"vc-r-hubdef\">\u2014<\/div><\/div>\n<div class=\"vc-result\"><div class=\"vc-result-label\">Shaft diametral contraction<\/div><div class=\"vc-result-value\" id=\"vc-r-shaftdef\">\u2014<\/div><\/div>\n<div class=\"vc-result\"><div class=\"vc-result-label\">Separate ideal axial slip limit<\/div><div class=\"vc-result-value\" id=\"vc-r-force\">\u2014<\/div><\/div>\n<div class=\"vc-result\"><div class=\"vc-result-label\">Separate ideal torque slip limit<\/div><div class=\"vc-result-value\" id=\"vc-r-torque\">\u2014<\/div><\/div>\n<\/div><\/div><\/div>\n\n<section class=\"vc-section vc-open\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\"><span class=\"vc-section-title\">Definitions, equations and scope<\/span><span class=\"vc-chevron\">\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\">\n<h3>Elastic compatibility<\/h3><p>The model uses one reference interface diameter d because the free preassembly diameter difference is assumed very small. \u03b4 is <strong>diametral<\/strong> interference: free shaft OD minus free hub bore, evaluated at the same controlled state.<\/p>\n<div class=\"vc-formula\">k\u209b = (d\u00b2 + D\u1d62\u00b2)\/(d\u00b2 \u2212 D\u1d62\u00b2)&nbsp;&nbsp;&nbsp; k\u2095 = (D\u2092\u00b2 + d\u00b2)\/(D\u2092\u00b2 \u2212 d\u00b2)<br>C\u209b = (k\u209b \u2212 \u03bd\u209b)\/E\u209b&nbsp;&nbsp;&nbsp; C\u2095 = (k\u2095 + \u03bd\u2095)\/E\u2095<br>p = \u03b4\/[d(C\u209b + C\u2095)]<br>\u0394d\u209b = p d C\u209b&nbsp;&nbsp;&nbsp; \u0394d\u2095 = p d C\u2095&nbsp;&nbsp;&nbsp; \u03b4 = \u0394d\u209b + \u0394d\u2095<br>\u03c3\u03b8,s at contact = \u2212p k\u209b&nbsp;&nbsp;&nbsp; \u03c3\u03b8,h at bore = +p k\u2095<\/div>\n<p>E is in pressure units; all four diameters\/lengths use one length unit. The result p and displayed hoop stresses then use the same pressure basis. These equations follow axisymmetric Lam\u00e9 stresses plus plane-stress Hooke strain compatibility; they are general engineering elasticity equations, not ISO fit equations.<\/p>\n<h3>Optional friction arithmetic<\/h3><div class=\"vc-formula\">A = \u03c0dL&nbsp;&nbsp;&nbsp; F<sub>slip<\/sub> = \u03bcpA&nbsp;&nbsp;&nbsp; T<sub>slip<\/sub> = \u03bcpA(d\/2)<\/div><p>F and T are separate ideal incipient-slip limits for uniform normal pressure and constant Coulomb \u03bc. They are not simultaneous independent capacities and contain no safety factor. Leave \u03bc blank unless its basis is controlled for the real surfaces and service state.<\/p>\n<table class=\"vc-table\"><thead><tr><th>Input<\/th><th>Definition<\/th><\/tr><\/thead><tbody><tr><td>d<\/td><td>Common reference diameter at the fit interface<\/td><\/tr><tr><td>\u03b4<\/td><td>Positive diametral interference at one state<\/td><\/tr><tr><td>D\u1d62<\/td><td>Shaft bore; zero selects the solid-shaft limit<\/td><\/tr><tr><td>D\u2092<\/td><td>Hub outside diameter<\/td><\/tr><tr><td>L<\/td><td>Length over which uniform p and \u03bc are assumed<\/td><\/tr><tr><td>E\u209b E\u2095<\/td><td>Young&#8217;s moduli at the relevant state<\/td><\/tr><tr><td>\u03bd\u209b \u03bd\u2095<\/td><td>Poisson ratios for stable isotropic elasticity: \u22121 &lt; \u03bd &lt; 0.5<\/td><\/tr><\/tbody><\/table>\n<div class=\"vc-warning\"><strong>No acceptance verdict:<\/strong> interface stresses are not a complete stress field or a yield\/fatigue check. Short hubs, shoulders, grooves, keys, splines, tapers, surface asperity flattening, residual stress, plasticity, hollow-shaft external-pressure buckling, temperature gradients, centrifugal effects, fretting, assembly damage and combined axial\/torque\/bending loads can invalidate the uniform elastic model.<\/div>\n<\/div><\/div><\/section>\n<section class=\"vc-section\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-title\">Standards and source classification<\/span><span class=\"vc-chevron\">\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\">\n<h3>ISO fit codes do not supply this pressure formula<\/h3><p><a href=\"https:\/\/www.iso.org\/standard\/45975.html\" target=\"_blank\" rel=\"noopener\">ISO 286-1:2010<\/a>, edition 2 with Cor 1:2013, is current and was confirmed in 2026. It defines the ISO code system concepts and fit terminology. <a href=\"https:\/\/www.iso.org\/standard\/54915.html\" target=\"_blank\" rel=\"noopener\">ISO 286-2:2010<\/a>, edition 2 with Cor 1:2013, supplies selected limit-deviation tables; its official record is currently under systematic review. Neither public scope establishes the Lam\u00e9 pressure equation or selects a fit for a load case.<\/p>\n<p>Exact H7\/p6, H7\/s6 or other designation limits must come from the controlled applicable ISO 286-2 table and size step. They are deliberately not reconstructed here and remain <strong>NEEDS_LICENSED_SOURCE<\/strong>. Analyse both minimum and maximum interference after temperature, coating, surface and measurement effects.<\/p>\n<p><a href=\"https:\/\/www.iso.org\/standard\/80702.html\" target=\"_blank\" rel=\"noopener\">ISO 1:2022<\/a>, edition 4, defines the standard reference-temperature concept for dimensional properties. This worksheet does not convert a drawing-state interference to an operating-state interference.<\/p>\n<h3>Open technical sources<\/h3><p>University of Washington ME 354, <a href=\"https:\/\/courses.washington.edu\/me354a\/Thick%20Walled%20Cylinders.pdf\" target=\"_blank\" rel=\"noopener\">Thick Walled Cylinders<\/a>, gives the same-material two-cylinder shrink-fit reduction and states the small-interference\/no-axial-stress assumptions. NASA contractor report BRL 6048 (1972), <a href=\"https:\/\/ntrs.nasa.gov\/api\/citations\/19720023849\/downloads\/19720023849.pdf\" target=\"_blank\" rel=\"noopener\">Appendix F<\/a>, gives the dissimilar-material radial compatibility and the ideal torque relation with a worked actuator example. Exact unit conversions use NIST SP 811 Appendix B. Sources accessed 13 July 2026.<\/p>\n<\/div><\/div><\/section>\n<section class=\"vc-section\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-title\">Frequently asked questions<\/span><span class=\"vc-chevron\">\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\">\n<div class=\"vc-faq\"><button type=\"button\">Does ISO 286 calculate contact pressure?<\/button><div>No. ISO 286 codes and tables describe size tolerances and deviations. Pressure requires a separate structural model with geometry and material properties.<\/div><\/div>\n<div class=\"vc-faq\"><button type=\"button\">Which friction coefficient should I use?<\/button><div>No universal dry\/oiled value is supplied. Use controlled evidence for the actual pair, finish, coating, lubricant, process, pressure, temperature and life condition, or leave \u03bc blank.<\/div><\/div>\n<div class=\"vc-faq\"><button type=\"button\">Why are H7\/p6 and H7\/s6 presets absent?<\/button><div>A designation alone is not one interference value. The basic size step and both shaft\/hole limits determine a range, and service-state effects can change it.<\/div><\/div>\n<div class=\"vc-faq\"><button type=\"button\">Does a result below yield mean the joint is safe?<\/button><div>No. This page reports only ideal interface quantities and no allowable. A complete multiaxial\/local stress, assembly, fatigue, fretting, tolerance and service analysis is still required.<\/div><\/div>\n<\/div><\/div><\/section>\n<section class=\"vc-section\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-title\">Related calculators<\/span><span class=\"vc-chevron\">\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-related\"><a href=\"\/calculators\/shaft-diameter-torsion\/\">Shaft diameter<\/a><a href=\"\/calculators\/keyway-calculator\/\">Keyway<\/a><a href=\"\/calculators\/spline-connection-calculator\/\">Spline connection<\/a><\/div><\/div><\/div><\/section>\n<footer class=\"vc-footer\">Elastic reference calculation only; independent mechanical and metrology review remains necessary. \u00b7 <a href=\"\/calculators\/engineering-calculators\/\">All calculators<\/a><\/footer>\n<\/div>\n<script>\n(function(){\n\"use strict\";\nvar INCH_MM=25.4,PSI_MPA=0.006894757293168361,LBF_N=4.4482216152605,FOOT_MM=304.8;\nfunction byId(id){return document.getElementById(id)}\nfunction parseDecimal(text){var s=String(text).trim();if(!s||\/[eE]\/.test(s)||!\/^[-+]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(s)||s.indexOf('.')>=0&&s.indexOf(',')>=0)return null;var n=Number(s.replace(',','.'));return Number.isFinite(n)?n:null}\nfunction interferenceModel(x){var d=x.d,delta=x.delta,di=x.di,Do=x.Do,L=x.L,Es=x.Es,nus=x.nus,Eh=x.Eh,nuh=x.nuh,mu=x.mu;if(![d,delta,di,Do,L,Es,nus,Eh,nuh].every(Number.isFinite))throw new Error('All required numeric inputs must be finite.');if(!(d>0&&delta>0&&delta<d))throw new Error('Require d > 0 and 0 < diametral interference \u03b4 < d.');if(!(di>=0&&di<d&&Do>d&&L>0))throw new Error('Require 0 \u2264 shaft bore < d < hub OD and contact length > 0.');if(!(Es>0&&Eh>0))throw new Error('Young\\'s moduli must be positive.');if(!(nus>-1&&nus<0.5&&nuh>-1&&nuh<0.5))throw new Error('Each Poisson ratio must satisfy \u22121 < \u03bd < 0.5.');if(mu!==null&&(!Number.isFinite(mu)||mu<0))throw new Error('Friction coefficient must be blank or non-negative.');var d2=d*d,di2=di*di,Do2=Do*Do;var ks=(d2+di2)\/(d2-di2),kh=(Do2+d2)\/(Do2-d2);var cs=(ks-nus)\/Es,ch=(kh+nuh)\/Eh;var p=delta\/(d*(cs+ch));var shaftContraction=p*d*cs,hubExpansion=p*d*ch;var area=Math.PI*d*L;var force=mu===null?null:mu*p*area;var torque=force===null?null:force*d\/2;var out={p:p,ks:ks,kh:kh,shaftHoop:-p*ks,hubHoop:p*kh,shaftContraction:shaftContraction,hubExpansion:hubExpansion,ratio:delta\/d,area:area,force:force,torque:torque};if(!Object.keys(out).every(function(k){return out[k]===null||Number.isFinite(out[k])}))throw new Error('Inputs produced a non-finite result; check geometry and scale.');return out}\nfunction toSI(raw,system){var length=system==='imperial'?INCH_MM:1,modulus=system==='imperial'?1e6*PSI_MPA:1000;return{d:raw.d*length,delta:raw.delta*length,di:raw.di*length,Do:raw.Do*length,L:raw.L*length,Es:raw.Es*modulus,nus:raw.nus,Eh:raw.Eh*modulus,nuh:raw.nuh,mu:raw.mu}}\nwindow.vbmInterferenceModel=interferenceModel;window.vbmInterferenceToSI=toSI;\nfunction fmt(n,d){return n.toLocaleString('en-US',{maximumFractionDigits:d,minimumFractionDigits:0})}\nfunction fail(message){byId('vc-error').textContent=message;byId('vc-error').classList.add('vc-show');byId('vc-results').classList.remove('vc-visible')}\nfunction calculate(){if(!byId('vc-confirm').checked)return fail('Confirm the stated elastic-model applicability before calculating.');if(byId('vc-source').value.trim().length<3)return fail('Identify the controlled dimensional and material basis.');var ids={d:'vc-d',delta:'vc-delta',di:'vc-di',Do:'vc-do',L:'vc-length',Es:'vc-es',nus:'vc-nus',Eh:'vc-eh',nuh:'vc-nuh'},raw={};for(var key in ids){raw[key]=parseDecimal(byId(ids[key]).value);if(raw[key]===null)return fail('Use complete decimal numbers with a point or comma. Do not use exponents or thousands separators.');}var muText=byId('vc-mu').value.trim();raw.mu=muText===''?null:parseDecimal(muText);if(muText!==''&&raw.mu===null)return fail('Friction coefficient must be a complete decimal number or blank.');var system=byId('vc-system').value,result;try{result=interferenceModel(toSI(raw,system))}catch(error){return fail(error.message)}byId('vc-error').classList.remove('vc-show');var imperial=system==='imperial',stressFactor=imperial?PSI_MPA*1000:1,stressUnit=imperial?' ksi':' MPa';byId('vc-r-p').textContent=fmt(result.p\/stressFactor,4)+stressUnit;byId('vc-r-ratio').textContent=fmt(result.ratio*100,6)+' %';byId('vc-r-hubstress').textContent='+'+fmt(result.hubHoop\/stressFactor,4)+stressUnit;byId('vc-r-shaftstress').textContent=fmt(result.shaftHoop\/stressFactor,4)+stressUnit;byId('vc-r-hubdef').textContent=imperial?fmt(result.hubExpansion\/INCH_MM*1000,5)+' mil':fmt(result.hubExpansion*1000,4)+' \u00b5m';byId('vc-r-shaftdef').textContent=imperial?fmt(result.shaftContraction\/INCH_MM*1000,5)+' mil':fmt(result.shaftContraction*1000,4)+' \u00b5m';if(result.force===null){byId('vc-r-force').textContent='Not evaluated (\u03bc blank)';byId('vc-r-torque').textContent='Not evaluated (\u03bc blank)'}else if(imperial){byId('vc-r-force').textContent=fmt(result.force\/LBF_N,3)+' lbf';byId('vc-r-torque').textContent=fmt(result.torque\/(LBF_N*FOOT_MM),3)+' lbf\u00b7ft'}else{byId('vc-r-force').textContent=fmt(result.force\/1000,4)+' kN';byId('vc-r-torque').textContent=fmt(result.torque\/1000,4)+' N\u00b7m'}byId('vc-results').classList.add('vc-visible')}\nfunction clearForUnitChange(){['vc-d','vc-delta','vc-di','vc-do','vc-length','vc-es','vc-nus','vc-eh','vc-nuh','vc-mu'].forEach(function(id){byId(id).value=''});byId('vc-confirm').checked=false;byId('vc-results').classList.remove('vc-visible');byId('vc-error').classList.remove('vc-show');var imperial=byId('vc-system').value==='imperial';document.querySelectorAll('.vc-len-unit').forEach(function(e){e.textContent=imperial?'(in)':'(mm)'});document.querySelectorAll('.vc-e-unit').forEach(function(e){e.textContent=imperial?'(Mpsi)':'(GPa)'})}\nbyId('vc-form').addEventListener('input',calculate);byId('vc-form').addEventListener('change',function(e){if(e.target.id==='vc-system')clearForUnitChange();else calculate()});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')?'true':'false')})});document.querySelectorAll('.vc-faq button').forEach(function(button){button.addEventListener('click',function(){this.parentNode.classList.toggle('vc-open')})});byId('vc-copy').addEventListener('click',function(){var text=byId('vc-results').innerText+'\\nControlled basis: '+byId('vc-source').value.trim();if(navigator.clipboard)navigator.clipboard.writeText(text)});\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Calculate ideal Lam\u00e9-Hooke contact pressure and separate Coulomb slip limits for concentric cylindrical fits with explicit plane-stress assumptions.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100194","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/calculator\/100194","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/calculator\/100194\/revisions"}],"predecessor-version":[{"id":102533,"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/calculator\/100194\/revisions\/102533"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/media?parent=100194"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/categories?post=100194"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/zh\/wp-json\/wp\/v2\/tags?post=100194"}],"curies":[{"name":"\u53ef\u6e7f\u6027\u7c89\u5242","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}