{"id":100030,"date":"2026-02-15T20:07:18","date_gmt":"2026-02-15T20:07:18","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100030"},"modified":"2026-07-11T19:51:55","modified_gmt":"2026-07-11T19:51:55","slug":"bearing-thermal-expansion","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/vi\/calculators\/bearing-thermal-expansion\/","title":{"rendered":"C\u00f4ng c\u1ee5 t\u00ednh to\u00e1n h\u1ec7 s\u1ed1 gi\u00e3n n\u1edf nhi\u1ec7t c\u1ee7a \u1ed5 tr\u1ee5c | \u03b4 = L\u00d7\u03b1\u00d7\u0394T | C\u00f4ng c\u1ee5 tr\u1ef1c tuy\u1ebfn mi\u1ec5n ph\u00ed"},"content":{"rendered":"\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Bearing Thermal Expansion Calculator\",\"description\":\"Calculate separate uniform axial thermal changes of a shaft and housing using user-supplied lengths, average CTE values and temperature changes; report signed differential growth without selecting a bearing arrangement.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/bearing-thermal-expansion\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2025-01-01\",\"dateModified\":\"2026-07-11\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\r\n\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\r\n{\"@type\":\"Question\",\"name\":\"Why does thermal expansion matter for bearings?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"When a shaft heats up during operation, it expands axially. If both bearings are fixed axially (locating), the expansion creates internal preload, increasing friction and temperature. Proper locating\/non-locating arrangement allows thermal growth without damaging the bearings.\"}},\r\n{\"@type\":\"Question\",\"name\":\"What is a locating\/non-locating bearing arrangement?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"In a locating\/non-locating arrangement, one bearing is fixed axially (locating) to position the shaft, while the other bearing is free to slide axially (non-locating) to accommodate thermal expansion. This is the most common arrangement.\"}},\r\n{\"@type\":\"Question\",\"name\":\"Which CTE value should I enter?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Use a mean linear CTE for the exact material grade over the actual temperature interval. CTE varies with composition and temperature; generic material-family values are only rough examples.\"}},\r\n{\"@type\":\"Question\",\"name\":\"How much expansion is typical?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"A 1-meter steel shaft with a 50\u00b0C temperature rise expands about 0.6 mm. This may seem small but can generate enormous forces if both bearing positions are axially fixed.\"}},\r\n{\"@type\":\"Question\",\"name\":\"Does axial differential growth determine bearing fit or clearance?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Axial span growth helps size axial displacement capacity. Radial fit and bearing internal clearance require local diameters, ring\/seat temperatures, material properties and the exact bearing arrangement.\"}}\r\n]}<\/script>\r\n\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\":\"Thermal Expansion\",\"item\":\"https:\/\/vibromera.eu\/calculators\/bearing-thermal-expansion\/\"}]}<\/script>\r\n\r\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\r\n\r\n<link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin>\r\n\r\n<link 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p:last-child{margin-bottom:0}.vc-related{display:flex;flex-wrap:wrap;gap:10px;margin-top:16px}.vc-related-link{display:inline-block;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 .15s}.vc-related-link:hover{border-color:var(--vc-accent);color:var(--vc-accent);background:var(--vc-accent-light)}.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}.vc-promo-text{flex:1;font-size:14px;color:var(--vc-ink-secondary)}.vc-promo-text strong{color:var(--vc-ink)}.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 .15s}.vc-promo-link:hover{background:var(--vc-accent-hover)}.vc-footer{text-align:center;padding:32px 16px;font-size:13px;color:var(--vc-ink-muted)}.vc-footer a{color:var(--vc-accent);text-decoration:none}.vc-footer a:hover{text-decoration:underline}.vc-footer-links{margin-top:8px;font-size:12px}.vc-footer-links a{margin:0 8px}@media 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}}<\/style>\r\n\r\n<div class=\"vc-calculator\">\r\n<header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Free Engineering Tool #054<\/p><h1 class=\"vc-header-title\">Bearing Thermal Expansion Calculator<\/h1><p class=\"vc-header-subtitle\">Calculate separate uniform axial thermal changes of shaft and housing and their signed difference. Enter actual lengths, mean CTE values and temperature changes.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">\u03b4 = L \u00d7 \u03b1 \u00d7 \u0394T<\/span><span class=\"vc-badge\">Signed Heating\/Cooling<\/span><span class=\"vc-badge\">No Automatic Bearing Selection<\/span><\/div><\/header>\r\n<div class=\"vc-card\">\r\n    <form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\">\r\n        <div class=\"vc-form-grid\">\r\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-Ls\">Shaft Effective Length L<sub>s<\/sub> <span class=\"vc-label-hint\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"text\" id=\"vc-Ls\" inputmode=\"decimal\" autocomplete=\"off\" value=\"500\"><\/div>\r\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-dTs\">Shaft Temperature Change \u0394T<sub>s<\/sub> <span class=\"vc-label-hint\">(K or \u00b0C difference; signed)<\/span><\/label><input class=\"vc-input\" type=\"text\" id=\"vc-dTs\" inputmode=\"decimal\" autocomplete=\"off\" value=\"50\"><\/div>\r\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-as\">Shaft Mean CTE \u03b1<sub>s<\/sub> <span class=\"vc-label-hint\">(\u03bcm\/(m\u00b7K))<\/span><\/label><input class=\"vc-input\" type=\"text\" id=\"vc-as\" inputmode=\"decimal\" autocomplete=\"off\" value=\"11.7\"><\/div>\r\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-Lh\">Housing Effective Length L<sub>h<\/sub> <span class=\"vc-label-hint\">(mm)<\/span><\/label><input class=\"vc-input\" type=\"text\" id=\"vc-Lh\" inputmode=\"decimal\" autocomplete=\"off\" value=\"500\"><\/div>\r\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-dTh\">Housing Temperature Change \u0394T<sub>h<\/sub> <span class=\"vc-label-hint\">(K or \u00b0C difference; signed)<\/span><\/label><input class=\"vc-input\" type=\"text\" id=\"vc-dTh\" inputmode=\"decimal\" autocomplete=\"off\" value=\"50\"><\/div>\r\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-ah\">Housing Mean CTE \u03b1<sub>h<\/sub> <span class=\"vc-label-hint\">(\u03bcm\/(m\u00b7K))<\/span><\/label><input class=\"vc-input\" type=\"text\" id=\"vc-ah\" inputmode=\"decimal\" autocomplete=\"off\" value=\"11.7\"><\/div>\r\n        <\/div>\r\n        <div class=\"vc-warning-box\"><p><strong>Uniform-temperature estimate:<\/strong> use mean CTE over each actual temperature interval. For temperature gradients or constrained structures, integrate thermal strain or use a thermo-mechanical model.<\/p><\/div>\r\n    <\/form>\r\n    <div class=\"vc-results\" id=\"vc-results\">\r\n        <div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Results<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\"><svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy<\/button><\/div>\r\n        <div class=\"vc-result-grid\">\r\n            <div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Shaft Axial Expansion \u03b4_shaft<\/div><div class=\"vc-rcard-value\" id=\"vc-r-ds\">\u2014<\/div><\/div>\r\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Housing Axial Expansion \u03b4_housing<\/div><div class=\"vc-rcard-value\" id=\"vc-r-dh\">\u2014<\/div><\/div>\r\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Differential Expansion<\/div><div class=\"vc-rcard-value\" id=\"vc-r-diff\">\u2014<\/div><\/div>\r\n        <\/div>\r\n    <\/div>\r\n<\/div>\r\n<div class=\"vc-section vc-open\" id=\"vc-sec-theory\"><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\">Theory &amp; Formulas<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\r\n    <div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\">\r\n        <h3>Thermal Expansion Formula<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\r\n        <ul><li><strong>L<\/strong> \u2014 effective initial span (mm)<\/li><li><strong>\u03b1<\/strong> \u2014 mean linear CTE over the stated interval (\u03bcm\/(m\u00b7K), numerically \u00d710\u207b\u2076\/K)<\/li><li><strong>\u0394T<\/strong> \u2014 signed temperature change from the reference state (K or \u00b0C difference)<\/li><\/ul>\r\n        <h3>CTE input<\/h3>\r\n        <p>CTE is material-grade and temperature dependent. Obtain a mean value over the actual interval from controlled material data rather than choosing a broad material-family label.<\/p>\r\n        <h3>Locating \/ Non-Locating Arrangement<\/h3>\r\n        <div class=\"vc-info-box\"><p><strong>\u2139\ufe0f<\/strong> A locating\/non-locating support can accommodate axial displacement from relative shaft\/housing thermal growth, but required travel and bearing type must be selected from the complete arrangement loads, fits, tolerances and manufacturer data.<\/p><\/div>\r\n    <\/div><\/div>\r\n<\/div>\r\n<div class=\"vc-section\" id=\"vc-sec-related\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udd17<\/span><span class=\"vc-section-title\">Related Calculators<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\r\n    <div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-related\"><a class=\"vc-related-link\" href=\"\/calculators\/bearing-fit-tolerance\/\">Bearing Fit Tolerance<\/a><a class=\"vc-related-link\" href=\"\/calculators\/bearing-press-fit-force\/\">Press-Fit Force<\/a><a class=\"vc-related-link\" href=\"\/calculators\/bearing-removal-force\/\">Removal Force<\/a><\/div><\/div><\/div>\r\n<\/div>\r\n<div class=\"vc-section\" id=\"vc-sec-faq\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\u2753<\/span><span class=\"vc-section-title\">Frequently Asked Questions<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\r\n    <div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div><\/div><\/div>\r\n<\/div>\r\n<div class=\"vc-promo\"><div class=\"vc-promo-text\"><strong>Vibromera \u2014 Portable Balancing &amp; Vibration Analysis<\/strong><br>Professional vibration analyzers. Used in 50+ countries.<\/div><a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a><\/div>\r\n<footer class=\"vc-footer\"><p>\u00a9 2024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><p style=\"font-size:12px;margin-top:4px;\">Uniform linear thermal-strain model. Scientific review: July 2026<\/p><div class=\"vc-footer-links\"><a href=\"\/calculators\/engineering-calculators\/\">All Calculators<\/a><a href=\"https:\/\/vibromera.eu\/contacts\/\">Contact<\/a><\/div><\/footer>\r\n<\/div>\r\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.js\"><\/script>\r\n<script>\r\n(function(){\r\n    'use strict';var SLUG='bearing-thermal-expansion';\r\n    function $(id){return document.getElementById(id)}\r\n    function fmt(n,d){if(isNaN(n)||!isFinite(n))return'\u2014';return n.toFixed(d===undefined?3:d).replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,'')}\r\n    function parseLocaleNumber(raw){var normalized=String(raw).trim().replace(\/\\s+\/g,'');if(!\/^[+-]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(normalized))return NaN;return Number(normalized.replace(',','.'));}\r\n\r\n    function calculate(){\r\n        var Ls=parseLocaleNumber($('vc-Ls').value),dTs=parseLocaleNumber($('vc-dTs').value),as=parseLocaleNumber($('vc-as').value);\r\n        var Lh=parseLocaleNumber($('vc-Lh').value),dTh=parseLocaleNumber($('vc-dTh').value),ah=parseLocaleNumber($('vc-ah').value);\r\n        if(!isFinite(Ls)||Ls<=0||!isFinite(Lh)||Lh<=0||!isFinite(dTs)||!isFinite(dTh)||!isFinite(as)||as<=0||!isFinite(ah)||ah<=0){$('vc-results').classList.remove('vc-visible');return;}\r\n        var ds=Ls*as*1e-6*dTs;\r\n        var dh=Lh*ah*1e-6*dTh;\r\n        var diff=ds-dh;\r\n        if(![ds,dh,diff].every(isFinite)){$('vc-results').classList.remove('vc-visible');return;}\r\n\r\n        $('vc-r-ds').innerHTML=fmt(ds,3)+' <span class=\"vc-rcard-unit\">mm<\/span>';\r\n        $('vc-r-dh').innerHTML=fmt(dh,3)+' <span class=\"vc-rcard-unit\">mm<\/span>';\r\n        $('vc-r-diff').innerHTML=fmt(diff,3)+' <span class=\"vc-rcard-unit\">mm (shaft \u2212 housing)<\/span>';\r\n        $('vc-results').classList.add('vc-visible');\r\n        var u=new URL(window.location);u.searchParams.set('Ls',Ls);u.searchParams.set('dTs',dTs);u.searchParams.set('as',as);u.searchParams.set('Lh',Lh);u.searchParams.set('dTh',dTh);u.searchParams.set('ah',ah);history.replaceState(null,'',u.toString());\r\n        saveHistory({Ls:Ls,dTs:dTs,as:as,Lh:Lh,dTh:dTh,ah:ah,_summary:'shaft='+fmt(ds,3)+'mm; housing='+fmt(dh,3)+'mm; diff='+fmt(diff,3)+'mm'});\r\n    }\r\n\r\n    $('vc-form').addEventListener('input',calculate);$('vc-form').addEventListener('change',calculate);\r\n    $('vc-copy-btn').addEventListener('click',function(){var text='Thermal Expansion\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nShaft: '+$('vc-r-ds').textContent+'\\nHousing: '+$('vc-r-dh').textContent+'\\nSigned difference: '+$('vc-r-diff').textContent+'\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nvibromera.eu';if(navigator.clipboard){navigator.clipboard.writeText(text).then(function(){var b=$('vc-copy-btn');b.classList.add('vc-copied');b.innerHTML='<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><polyline points=\"20 6 9 17 4 12\"\/><\/svg> Copied!';setTimeout(function(){b.classList.remove('vc-copied');b.innerHTML='<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy';},2000);});}});\r\n    document.querySelectorAll('.vc-section-toggle').forEach(function(btn){btn.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'));});});\r\n    var faqData=[{q:'Why calculate both shaft and housing?',a:'<p>The non-locating support must accommodate relative axial change, so lengths, temperatures and CTEs may differ.<\/p>'},{q:'What CTE should I enter?',a:'<p>Use mean linear CTE for the exact grade over the actual temperature interval; CTE varies with temperature and composition.<\/p>'},{q:'Can \u0394T be negative?',a:'<p>Yes. Negative \u0394T represents cooling and produces contraction.<\/p>'},{q:'Does this choose a bearing arrangement?',a:'<p>No. It reports signed axial growth only. Arrangement selection requires loads, fits, tolerances, available travel and manufacturer data.<\/p>'},{q:'Does axial growth determine fit or internal clearance?',a:'<p>No. Radial fit and internal clearance require local diameters, ring\/seat temperatures and exact bearing geometry.<\/p>'}];\r\n    var fl=$('vc-faq-list');faqData.forEach(function(f){fl.innerHTML+='<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>'+f.q+'<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\">'+f.a+'<\/div><\/div><\/div>';});\r\n    fl.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(b)b.closest('.vc-faq-item').classList.toggle('vc-open');});\r\n    function saveHistory(entry){var key='vc_history_'+SLUG;var arr=[];try{arr=JSON.parse(localStorage.getItem(key))||[];}catch(e){}entry._ts=new Date().toISOString();arr.unshift(entry);if(arr.length>10)arr=arr.slice(0,10);try{localStorage.setItem(key,JSON.stringify(arr));}catch(e){}}\r\n    function loadParams(){var p=new URLSearchParams(window.location.search);['Ls','dTs','as','Lh','dTh','ah'].forEach(function(k){if(p.has(k)){var el=$('vc-'+k);if(el)el.value=p.get(k);}});}\r\n    function renderFormulas(){try{katex.render('\\\\delta = L \\\\times \\\\alpha \\\\times \\\\Delta T \\\\quad [\\\\text{mm}]',$('vc-katex-1'),{displayMode:true,throwOnError:false});}catch(e){}}\r\n    function init(){loadParams();renderFormulas();calculate();}\r\n    if(document.readyState==='loading'){document.addEventListener('DOMContentLoaded',init);}else{init();}\r\n})();\r\n<\/script>\r\n","protected":false},"excerpt":{"rendered":"<p>M\u00e1y t\u00ednh tr\u1ef1c tuy\u1ebfn mi\u1ec5n ph\u00ed t\u00ednh to\u00e1n s\u1ef1 gi\u00e3n n\u1edf nhi\u1ec7t c\u1ee7a tr\u1ee5c\/v\u1ecf \u1ea3nh h\u01b0\u1edfng \u0111\u1ebfn c\u00e1c ki\u1ec3u b\u1ed1 tr\u00ed \u1ed5 tr\u1ee5c. Nh\u1eadp chi\u1ec1u d\u00e0i tr\u1ee5c, h\u1ec7 s\u1ed1 gi\u00e3n n\u1edf nhi\u1ec7t c\u1ee7a v\u1eadt li\u1ec7u v\u00e0 ch\u00eanh l\u1ec7ch nhi\u1ec7t \u0111\u1ed9. 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