Thermal expansion and backlash calculation<\/title>\n\n <link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n <link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin=\"\">\n <link href=\"https:\/\/fonts.googleapis.com\/css2?family=Inter:wght@400;500;600;700&display=swap\" rel=\"stylesheet\">\n\n <link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.10\/dist\/katex.min.css\">\n <script defer=\"\" src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.10\/dist\/katex.min.js\"><\/script>\n <script defer=\"\" src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.10\/dist\/contrib\/auto-render.min.js\" onload=\"renderMathInElement(document.body, {\n delimiters: [\n { left: '$$', right: '$$', display: true },\n { left: '$', right: '$', display: false }\n ]\n });\"><\/script>\n\n <style>\n *, *::before, *::after { box-sizing: border-box; margin: 0; padding: 0; }\n\n :root {\n --green: #1a6b3c;\n --green-dark: #0f4a28;\n --green-mid: #2d8a55;\n --green-light: #e8f4ed;\n --green-xlight: #f2faf5;\n --amber: #b45309;\n --amber-light: #fef3c7;\n\n --bg: #ffffff;\n --bg-soft: #f8f9fa;\n --bg-muted: #f1f3f5;\n --border: #e5e7eb;\n --border-mid: #d1d5db;\n\n --text-primary: #111827;\n --text-secondary: #4b5563;\n --text-muted: #9ca3af;\n\n --radius-sm: 6px;\n --radius-md: 8px;\n --radius-lg: 12px;\n --shadow-sm: 0 1px 3px rgba(0,0,0,.06), 0 1px 2px rgba(0,0,0,.04);\n --shadow-md: 0 4px 12px rgba(0,0,0,.08), 0 2px 4px rgba(0,0,0,.04);\n }\n\n body { min-height: 100vh; 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}\n\n .badge {\n display: inline-block;\n font-size: 12px;\n font-weight: 600;\n padding: 2px 8px;\n border-radius: 20px;\n background: var(--green-light);\n color: var(--green-dark);\n }\n\n \/* ============================================================\n RESPONSIVE\n ============================================================ *\/\n @media (max-width: 900px) {\n .article-body { flex-direction: column; padding: 20px 20px 48px; }\n }\n \n \/* Formula blocks *\/\n .formula-block {\n background: var(--bg-soft);\n border: 1px solid var(--border);\n border-radius: var(--radius-md);\n padding: 16px 20px;\n margin: 16px 0;\n text-align: center;\n overflow-x: auto;\n }\n .katex { font-size: 1.1em; }\n .formula-block .katex { font-size: 1.25em; }\n .formula-block .katex-display { margin: 0; }\n\n \/* Glossary tooltips *\/\n .glossary-term {\n border-bottom: 1px dotted var(--green);\n color: var(--green);\n font-style: italic;\n cursor: help;\n }\n .glossary-tooltip {\n position: fixed;\n z-index: 9999;\n background: #fff;\n border: 1px solid var(--border-mid);\n border-radius: var(--radius-md);\n box-shadow: var(--shadow-md);\n padding: 10px 14px;\n max-width: 300px;\n font-family: 'Inter', sans-serif;\n font-size: 13px;\n }\n .glossary-tooltip__title {\n font-weight: 600;\n color: var(--text-primary);\n margin-bottom: 4px;\n }\n .glossary-tooltip__def {\n font-size: 12.5px;\n color: var(--text-secondary);\n line-height: 1.6;\n }\n .glossary-tooltip__tag {\n display: inline-block;\n margin-top: 6px;\n font-size: 9px;\n font-weight: 600;\n padding: 2px 7px;\n border-radius: 20px;\n background: var(--green-light);\n color: var(--green-dark);\n text-transform: uppercase;\n letter-spacing: 0.04em;\n }\n\n <\/style>\n<\/head>\n<body>\n\n<div id=\"tt-gioco-di-flanchi-backlash\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Backlash<\/div>\n <div class=\"glossary-tooltip__def\">Free clearance between the flanks of two mating teeth, measured at the pitch circle. It prevents jamming due to thermal expansion or assembly errors.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n<div id=\"tt-angolo-di-pressione\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Pressure angle<\/div>\n <div class=\"glossary-tooltip__def\">Angle between the direction of the contact force between mating teeth and the tangent to the pitch circle at the point of contact. The standard value is 20\u00b0.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n\n <div class=\"article-page\">\n <div class=\"article-body\">\n <div class=\"article-body__main\"><script type=\"application\/ld+json\">\n{\n \"@context\": \"https:\/\/schema.org\",\n \"@graph\": [\n {\n \"@type\": \"TechArticle\",\n \"@id\": \"#article\",\n \"headline\": \"Thermal expansion and backlash calculation\",\n \"description\": \"A technopolymer gear, mounted with care, that seizes after a few hours of operation. The cause, almost always, is the same: the gap between the teeth wasn't calculated taking into account how the material expands with temperature. Backlash isn't an assembly imperfection. It's a design parameter, and it must be calculated before assembling.\",\n \"inLanguage\": \"en\",\n \"mentions\": [\n {\n \"@id\": \"#term-gioco-di-flanchi-backlash\"\n },\n {\n \"@id\": \"#term-angolo-di-pressione\"\n }\n ]\n },\n {\n \"@type\": \"DefinedTermSet\",\n \"@id\": \"#glossario\",\n \"name\": \"Glossario - Thermal expansion and backlash calculation\",\n \"hasDefinedTerm\": [\n {\n \"@type\": \"DefinedTerm\",\n \"@id\": \"#term-gioco-di-flanchi-backlash\",\n \"name\": \"Backlash\",\n \"description\": \"Free clearance between the flanks of two mating teeth, measured at the pitch circle. It prevents jamming due to thermal expansion or assembly errors.\",\n \"inDefinedTermSet\": \"#glossario\"\n },\n {\n \"@type\": \"DefinedTerm\",\n \"@id\": \"#term-angolo-di-pressione\",\n \"name\": \"Pressure angle\",\n \"description\": \"Angle between the direction of the contact force between mating teeth and the tangent to the pitch circle at the point of contact. The standard value is 20\u00b0.\",\n \"inDefinedTermSet\": \"#glossario\"\n }\n ]\n }\n ]\n}\n<\/script>\n\n\n\n <h1 class=\"article__title\">Thermal expansion and backlash calculation<\/h1>\n<p class=\"article__subtitle\">A technopolymer gear, mounted with care, that seizes after a few hours of operation. The cause, almost always, is the same: the gap between the teeth wasn’t calculated taking into account how the material expands with temperature. <strong><dfn id=\"def-gioco-di-flanchi-backlash\"><span class=\"glossary-term\" data-tooltip=\"tt-gioco-di-flanchi-backlash\" title=\"Free clearance between the flanks of two mating teeth, measured at the pitch circle. It prevents jamming due to thermal expansion or assembly errors.\">Backlash<\/span><\/dfn><\/strong> isn’t an assembly imperfection. It’s a design parameter, and it must be calculated before assembling.<\/p>\n<h2 class=\"article__h2\" id=\"what-backlash-is-and-why-its-needed\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><polyline points=\"5 9 2 12 5 15\"><\/polyline><polyline points=\"9 5 12 2 15 5\"><\/polyline><polyline points=\"15 19 12 22 9 19\"><\/polyline><polyline points=\"19 9 22 12 19 15\"><\/polyline><line x1=\"2\" y1=\"12\" x2=\"22\" y2=\"12\"><\/line><line x1=\"12\" y1=\"2\" x2=\"12\" y2=\"22\"><\/line><\/svg><\/span>\n What backlash is and why it’s needed\n<\/h2>\n<p class=\"article__p\">Flank backlash, or backlash, is the space separating the non-meshing flanks of two mating teeth when the opposite flanks are in contact. It isn’t a machining error or a defect: it’s a deliberate distance, calculated at the design stage.<\/p>\n<p class=\"article__p\">Without backlash, the system becomes statically indeterminate: the teeth lock kinematically as soon as the real conditions (temperature, tolerances, deformation) deviate from the theoretical value. The result is damage to the transmission.<\/p>\n<h2 class=\"article__h2\" id=\"the-thermal-expansion-formula\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M14 14.76V3.5a2.5 2.5 0 0 0-5 0v11.26a4.5 4.5 0 1 0 5 0z\"><\/path><\/svg><\/span>\n The thermal expansion formula\n<\/h2>\n<p class=\"article__p\">The dimensional change of a component due to temperature follows this relation:<\/p>\n<div class=\"formula-block\">$$\\Delta{}L = L_0 \\times \\alpha \\times \\Delta{}T$$<\/div>\n<p class=\"article__p\">Where $L_0$ is the initial length, \u03b1 is the material’s thermal expansion coefficient (expressed in 10\u207b\u2076\/K) and \u0394T is the temperature change in degrees Celsius.<\/p>\n<p class=\"article__p\">In technopolymers, the coefficient \u03b1 is about <strong>ten times higher<\/strong> than in steel. A POM-C gear 100 mm in diameter that heats up by 50 \u00b0C expands by 0.55 mm: more than half a millimeter. Without a clearance adequate at the time of assembly, this expansion brings the tooth flanks into continuous contact on both sides, the seizing condition.<\/p>\n<div class=\"infobox infobox--grey\">\n <div class=\"infobox__title\">\n <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M14.7 6.3a1 1 0 0 0 0 1.4l1.6 1.6a1 1 0 0 0 1.4 0l3.77-3.77a6 6 0 0 1-7.94 7.94l-6.91 6.91a2.12 2.12 0 0 1-3-3l6.91-6.91a6 6 0 0 1 7.94-7.94l-3.76 3.76z\"><\/path><\/svg>\n Technical note\n <\/div>\n <p class=\"infobox__text\">The thermal expansion coefficient of POM-C is about <strong>110 \u00d7 10\u207b\u2076\/K<\/strong>, against the 10-12 \u00d7 10\u207b\u2076\/K of steel. For PA6 the value is similar to POM-C; for PK it settles around <strong>85 \u00d7 10\u207b\u2076\/K<\/strong>. Always verify the figure on the supplier’s datasheet. The values change with the formulations and the presence of fiber reinforcement.<\/p>\n<\/div>\n<h2 class=\"article__h2\" id=\"table-of-recommended-minimum-clearances\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><line x1=\"18\" y1=\"20\" x2=\"18\" y2=\"10\"><\/line><line x1=\"12\" y1=\"20\" x2=\"12\" y2=\"4\"><\/line><line x1=\"6\" y1=\"20\" x2=\"6\" y2=\"14\"><\/line><\/svg><\/span>\n Table of recommended minimum clearances\n<\/h2>\n<p class=\"article__p\">The following values are minimum clearances for standard industrial applications with thermal swings up to 50-60 \u00b0C. For more severe conditions, increase the clearance proportionally.<\/p>\n<div class=\"article__table-wrap\">\n<table class=\"article__table\">\n<thead><tr><th>Module m (mm)<\/th><th>Recommended minimum clearance (mm)<\/th><th>Notes<\/th><\/tr><\/thead>\n<tbody><tr><td>0.5 \u2013 1.5<\/td><td>+0.03 \/ +0.10<\/td><td>Typical small transmissions<\/td><\/tr>\n<tr><td>> 1.5<\/td><td>+0.08 \/ +0.30<\/td><td>Standard machines and power transmissions<\/td><\/tr><\/tbody>\n<\/table>\n<\/div>\n<h2 class=\"article__h2\" id=\"how-to-set-the-clearance\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M10.29 3.86L1.82 18a2 2 0 0 0 1.71 3h16.94a2 2 0 0 0 1.71-3L13.71 3.86a2 2 0 0 0-3.42 0z\"><\/path><line x1=\"12\" y1=\"9\" x2=\"12\" y2=\"13\"><\/line><line x1=\"12\" y1=\"17\" x2=\"12.01\" y2=\"17\"><\/line><\/svg><\/span>\n How to set the clearance\n<\/h2>\n<p class=\"article__p\">In practice, you set the clearance by slightly increasing the center distance relative to the theoretical value, which is the sum of the pitch radii of the two paired gears. For standard gears with a 20\u00b0 <dfn id=\"def-angolo-di-pressione\"><span class=\"glossary-term\" data-tooltip=\"tt-angolo-di-pressione\" title=\"Angle between the direction of the contact force between mating teeth and the tangent to the pitch circle at the point of contact. The standard value is 20\u00b0.\">pressure angle<\/span><\/dfn>, a radial increase of the center distance of 0.1 mm generates an increase of the flank backlash of about 0.07 mm.<\/p>\n<h2 class=\"article__h2\" id=\"what-happens-without-adequate-clearance\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><circle cx=\"12\" cy=\"12\" r=\"10\"><\/circle><\/svg><\/span>\n What happens without adequate clearance\n<\/h2>\n<p class=\"article__p\">A gear mounted without sufficient clearance is destined for rapid failure. When the temperature rises and the material expands, the flanks come into continuous contact. Local friction increases, the temperature rises further, the material expands even more, the friction rises again. It’s a positive-feedback mechanism, the so-called <strong>thermal runaway<\/strong>, which ends in a few minutes with plastic deformation and collapse of the material.<\/p>\n<div class=\"warnbox\">\n <div class=\"warnbox__title\">\n <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M10.29 3.86L1.82 18a2 2 0 0 0 1.71 3h16.94a2 2 0 0 0 1.71-3L13.71 3.86a2 2 0 0 0-3.42 0z\"><\/path><line x1=\"12\" y1=\"9\" x2=\"12\" y2=\"13\"><\/line><line x1=\"12\" y1=\"17\" x2=\"12.01\" y2=\"17\"><\/line><\/svg>\n Warning\n <\/div>\n <p class=\"warnbox__text\"><strong>No technopolymer application should be designed with zero clearance.<\/strong> If positioning precision is critical and you can’t tolerate even a small backlash, the technopolymer gear isn’t the suitable solution. Evaluate a metal profile or a transmission with an elastic element that absorbs the expansion.<\/p>\n<\/div>\n<div class=\"infobox\">\n <div class=\"infobox__title\">\n <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M4 4h16c1.1 0 2 .9 2 2v12c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V6c0-1.1.9-2 2-2z\"><\/path><polyline points=\"22,6 12,13 2,6\"><\/polyline><\/svg>\n Ask us\n <\/div>\n <p class=\"infobox__text\">If your application involves thermal swings above 60 \u00b0C or materials with off-standard expansion coefficients, <a href=\"https:\/\/shop.stagnoligears.com\/en\/contacts\/\" target=\"_blank\" rel=\"noopener\" class=\"cta-link\">write<\/a> to the technical office. We calculate the correct clearance for your real operating conditions.<\/p>\n<\/div>\n\n <\/div>\n <\/div>\n <\/div>\n\n\n<script>\n (function () {\n var hideTimers = {};\n function positionTooltip(trigger, tooltip) {\n var margin = 8;\n tooltip.style.visibility = 'hidden';\n tooltip.style.top = '-9999px';\n tooltip.style.left = '-9999px';\n tooltip.removeAttribute('hidden');\n var ttRect = tooltip.getBoundingClientRect();\n var trRect = trigger.getBoundingClientRect();\n var vw = window.innerWidth, vh = window.innerHeight;\n var top = trRect.bottom + margin;\n var left = trRect.left;\n if (top + ttRect.height + margin > vh) {\n var above = trRect.top - ttRect.height - margin;\n top = above >= margin ? above : Math.max(margin, vh - ttRect.height - margin);\n }\n if (left + ttRect.width + margin > vw) left = vw - ttRect.width - margin;\n if (left < margin) left = margin;\n tooltip.style.top = top + 'px';\n tooltip.style.left = left + 'px';\n tooltip.style.visibility = '';\n }\n function 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{"id":25616,"date":"2026-06-30T14:16:53","date_gmt":"2026-06-30T12:16:53","guid":{"rendered":"https:\/\/shop.stagnoligears.com\/?post_type=centro-tecnico&p=25616"},"modified":"2026-07-10T13:51:38","modified_gmt":"2026-07-10T11:51:38","slug":"thermal-expansion-and-backlash-calculation","status":"publish","type":"centro-tecnico","link":"https:\/\/shop.stagnoligears.com\/en\/technical-hub\/thermal-expansion-and-backlash-calculation\/","title":{"rendered":"Thermal expansion and backlash calculation"},"content":{"rendered":"\n\n \n \n \n Thermal expansion and backlash calculation<\/title>\n\n <link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n <link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin=\"\">\n <link href=\"https:\/\/fonts.googleapis.com\/css2?family=Inter:wght@400;500;600;700&display=swap\" rel=\"stylesheet\">\n\n <link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.10\/dist\/katex.min.css\">\n <script defer=\"\" src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.10\/dist\/katex.min.js\"><\/script>\n <script defer=\"\" src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.10\/dist\/contrib\/auto-render.min.js\" onload=\"renderMathInElement(document.body, {\n delimiters: [\n { left: '$$', right: '$$', display: true },\n { left: '$', right: '$', display: false }\n ]\n });\"><\/script>\n\n <style>\n *, *::before, *::after { box-sizing: border-box; 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}\n\n .badge {\n display: inline-block;\n font-size: 12px;\n font-weight: 600;\n padding: 2px 8px;\n border-radius: 20px;\n background: var(--green-light);\n color: var(--green-dark);\n }\n\n \/* ============================================================\n RESPONSIVE\n ============================================================ *\/\n @media (max-width: 900px) {\n .article-body { flex-direction: column; padding: 20px 20px 48px; }\n }\n \n \/* Formula blocks *\/\n .formula-block {\n background: var(--bg-soft);\n border: 1px solid var(--border);\n border-radius: var(--radius-md);\n padding: 16px 20px;\n margin: 16px 0;\n text-align: center;\n overflow-x: auto;\n }\n .katex { font-size: 1.1em; }\n .formula-block .katex { font-size: 1.25em; }\n .formula-block .katex-display { margin: 0; }\n\n \/* Glossary tooltips *\/\n .glossary-term {\n border-bottom: 1px dotted var(--green);\n color: var(--green);\n font-style: italic;\n cursor: help;\n }\n .glossary-tooltip {\n position: fixed;\n z-index: 9999;\n background: #fff;\n border: 1px solid var(--border-mid);\n border-radius: var(--radius-md);\n box-shadow: var(--shadow-md);\n padding: 10px 14px;\n max-width: 300px;\n font-family: 'Inter', sans-serif;\n font-size: 13px;\n }\n .glossary-tooltip__title {\n font-weight: 600;\n color: var(--text-primary);\n margin-bottom: 4px;\n }\n .glossary-tooltip__def {\n font-size: 12.5px;\n color: var(--text-secondary);\n line-height: 1.6;\n }\n .glossary-tooltip__tag {\n display: inline-block;\n margin-top: 6px;\n font-size: 9px;\n font-weight: 600;\n padding: 2px 7px;\n border-radius: 20px;\n background: var(--green-light);\n color: var(--green-dark);\n text-transform: uppercase;\n letter-spacing: 0.04em;\n }\n\n <\/style>\n<\/head>\n<body>\n\n<div id=\"tt-gioco-di-flanchi-backlash\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Backlash<\/div>\n <div class=\"glossary-tooltip__def\">Free clearance between the flanks of two mating teeth, measured at the pitch circle. It prevents jamming due to thermal expansion or assembly errors.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n<div id=\"tt-angolo-di-pressione\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Pressure angle<\/div>\n <div class=\"glossary-tooltip__def\">Angle between the direction of the contact force between mating teeth and the tangent to the pitch circle at the point of contact. The standard value is 20\u00b0.<\/div>\n <span class=\"glossary-tooltip__tag\">Glossary<\/span>\n<\/div>\n\n <div class=\"article-page\">\n <div class=\"article-body\">\n <div class=\"article-body__main\"><script type=\"application\/ld+json\">\n{\n \"@context\": \"https:\/\/schema.org\",\n \"@graph\": [\n {\n \"@type\": \"TechArticle\",\n \"@id\": \"#article\",\n \"headline\": \"Thermal expansion and backlash calculation\",\n \"description\": \"A technopolymer gear, mounted with care, that seizes after a few hours of operation. The cause, almost always, is the same: the gap between the teeth wasn't calculated taking into account how the material expands with temperature. Backlash isn't an assembly imperfection. It's a design parameter, and it must be calculated before assembling.\",\n \"inLanguage\": \"en\",\n \"mentions\": [\n {\n \"@id\": \"#term-gioco-di-flanchi-backlash\"\n },\n {\n \"@id\": \"#term-angolo-di-pressione\"\n }\n ]\n },\n {\n \"@type\": \"DefinedTermSet\",\n \"@id\": \"#glossario\",\n \"name\": \"Glossario - Thermal expansion and backlash calculation\",\n \"hasDefinedTerm\": [\n {\n \"@type\": \"DefinedTerm\",\n \"@id\": \"#term-gioco-di-flanchi-backlash\",\n \"name\": \"Backlash\",\n \"description\": \"Free clearance between the flanks of two mating teeth, measured at the pitch circle. It prevents jamming due to thermal expansion or assembly errors.\",\n \"inDefinedTermSet\": \"#glossario\"\n },\n {\n \"@type\": \"DefinedTerm\",\n \"@id\": \"#term-angolo-di-pressione\",\n \"name\": \"Pressure angle\",\n \"description\": \"Angle between the direction of the contact force between mating teeth and the tangent to the pitch circle at the point of contact. The standard value is 20\u00b0.\",\n \"inDefinedTermSet\": \"#glossario\"\n }\n ]\n }\n ]\n}\n<\/script>\n\n\n\n <h1 class=\"article__title\">Thermal expansion and backlash calculation<\/h1>\n<p class=\"article__subtitle\">A technopolymer gear, mounted with care, that seizes after a few hours of operation. The cause, almost always, is the same: the gap between the teeth wasn’t calculated taking into account how the material expands with temperature. <strong><dfn id=\"def-gioco-di-flanchi-backlash\"><span class=\"glossary-term\" data-tooltip=\"tt-gioco-di-flanchi-backlash\" title=\"Free clearance between the flanks of two mating teeth, measured at the pitch circle. It prevents jamming due to thermal expansion or assembly errors.\">Backlash<\/span><\/dfn><\/strong> isn’t an assembly imperfection. It’s a design parameter, and it must be calculated before assembling.<\/p>\n<h2 class=\"article__h2\" id=\"what-backlash-is-and-why-its-needed\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><polyline points=\"5 9 2 12 5 15\"><\/polyline><polyline points=\"9 5 12 2 15 5\"><\/polyline><polyline points=\"15 19 12 22 9 19\"><\/polyline><polyline points=\"19 9 22 12 19 15\"><\/polyline><line x1=\"2\" y1=\"12\" x2=\"22\" y2=\"12\"><\/line><line x1=\"12\" y1=\"2\" x2=\"12\" y2=\"22\"><\/line><\/svg><\/span>\n What backlash is and why it’s needed\n<\/h2>\n<p class=\"article__p\">Flank backlash, or backlash, is the space separating the non-meshing flanks of two mating teeth when the opposite flanks are in contact. It isn’t a machining error or a defect: it’s a deliberate distance, calculated at the design stage.<\/p>\n<p class=\"article__p\">Without backlash, the system becomes statically indeterminate: the teeth lock kinematically as soon as the real conditions (temperature, tolerances, deformation) deviate from the theoretical value. The result is damage to the transmission.<\/p>\n<h2 class=\"article__h2\" id=\"the-thermal-expansion-formula\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M14 14.76V3.5a2.5 2.5 0 0 0-5 0v11.26a4.5 4.5 0 1 0 5 0z\"><\/path><\/svg><\/span>\n The thermal expansion formula\n<\/h2>\n<p class=\"article__p\">The dimensional change of a component due to temperature follows this relation:<\/p>\n<div class=\"formula-block\">$$\\Delta{}L = L_0 \\times \\alpha \\times \\Delta{}T$$<\/div>\n<p class=\"article__p\">Where $L_0$ is the initial length, \u03b1 is the material’s thermal expansion coefficient (expressed in 10\u207b\u2076\/K) and \u0394T is the temperature change in degrees Celsius.<\/p>\n<p class=\"article__p\">In technopolymers, the coefficient \u03b1 is about <strong>ten times higher<\/strong> than in steel. A POM-C gear 100 mm in diameter that heats up by 50 \u00b0C expands by 0.55 mm: more than half a millimeter. Without a clearance adequate at the time of assembly, this expansion brings the tooth flanks into continuous contact on both sides, the seizing condition.<\/p>\n<div class=\"infobox infobox--grey\">\n <div class=\"infobox__title\">\n <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M14.7 6.3a1 1 0 0 0 0 1.4l1.6 1.6a1 1 0 0 0 1.4 0l3.77-3.77a6 6 0 0 1-7.94 7.94l-6.91 6.91a2.12 2.12 0 0 1-3-3l6.91-6.91a6 6 0 0 1 7.94-7.94l-3.76 3.76z\"><\/path><\/svg>\n Technical note\n <\/div>\n <p class=\"infobox__text\">The thermal expansion coefficient of POM-C is about <strong>110 \u00d7 10\u207b\u2076\/K<\/strong>, against the 10-12 \u00d7 10\u207b\u2076\/K of steel. For PA6 the value is similar to POM-C; for PK it settles around <strong>85 \u00d7 10\u207b\u2076\/K<\/strong>. Always verify the figure on the supplier’s datasheet. The values change with the formulations and the presence of fiber reinforcement.<\/p>\n<\/div>\n<h2 class=\"article__h2\" id=\"table-of-recommended-minimum-clearances\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><line x1=\"18\" y1=\"20\" x2=\"18\" y2=\"10\"><\/line><line x1=\"12\" y1=\"20\" x2=\"12\" y2=\"4\"><\/line><line x1=\"6\" y1=\"20\" x2=\"6\" y2=\"14\"><\/line><\/svg><\/span>\n Table of recommended minimum clearances\n<\/h2>\n<p class=\"article__p\">The following values are minimum clearances for standard industrial applications with thermal swings up to 50-60 \u00b0C. For more severe conditions, increase the clearance proportionally.<\/p>\n<div class=\"article__table-wrap\">\n<table class=\"article__table\">\n<thead><tr><th>Module m (mm)<\/th><th>Recommended minimum clearance (mm)<\/th><th>Notes<\/th><\/tr><\/thead>\n<tbody><tr><td>0.5 \u2013 1.5<\/td><td>+0.03 \/ +0.10<\/td><td>Typical small transmissions<\/td><\/tr>\n<tr><td>> 1.5<\/td><td>+0.08 \/ +0.30<\/td><td>Standard machines and power transmissions<\/td><\/tr><\/tbody>\n<\/table>\n<\/div>\n<h2 class=\"article__h2\" id=\"how-to-set-the-clearance\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M10.29 3.86L1.82 18a2 2 0 0 0 1.71 3h16.94a2 2 0 0 0 1.71-3L13.71 3.86a2 2 0 0 0-3.42 0z\"><\/path><line x1=\"12\" y1=\"9\" x2=\"12\" y2=\"13\"><\/line><line x1=\"12\" y1=\"17\" x2=\"12.01\" y2=\"17\"><\/line><\/svg><\/span>\n How to set the clearance\n<\/h2>\n<p class=\"article__p\">In practice, you set the clearance by slightly increasing the center distance relative to the theoretical value, which is the sum of the pitch radii of the two paired gears. For standard gears with a 20\u00b0 <dfn id=\"def-angolo-di-pressione\"><span class=\"glossary-term\" data-tooltip=\"tt-angolo-di-pressione\" title=\"Angle between the direction of the contact force between mating teeth and the tangent to the pitch circle at the point of contact. The standard value is 20\u00b0.\">pressure angle<\/span><\/dfn>, a radial increase of the center distance of 0.1 mm generates an increase of the flank backlash of about 0.07 mm.<\/p>\n<h2 class=\"article__h2\" id=\"what-happens-without-adequate-clearance\">\n <span class=\"article__h2-icon\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><circle cx=\"12\" cy=\"12\" r=\"10\"><\/circle><\/svg><\/span>\n What happens without adequate clearance\n<\/h2>\n<p class=\"article__p\">A gear mounted without sufficient clearance is destined for rapid failure. When the temperature rises and the material expands, the flanks come into continuous contact. Local friction increases, the temperature rises further, the material expands even more, the friction rises again. It’s a positive-feedback mechanism, the so-called <strong>thermal runaway<\/strong>, which ends in a few minutes with plastic deformation and collapse of the material.<\/p>\n<div class=\"warnbox\">\n <div class=\"warnbox__title\">\n <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M10.29 3.86L1.82 18a2 2 0 0 0 1.71 3h16.94a2 2 0 0 0 1.71-3L13.71 3.86a2 2 0 0 0-3.42 0z\"><\/path><line x1=\"12\" y1=\"9\" x2=\"12\" y2=\"13\"><\/line><line x1=\"12\" y1=\"17\" x2=\"12.01\" y2=\"17\"><\/line><\/svg>\n Warning\n <\/div>\n <p class=\"warnbox__text\"><strong>No technopolymer application should be designed with zero clearance.<\/strong> If positioning precision is critical and you can’t tolerate even a small backlash, the technopolymer gear isn’t the suitable solution. Evaluate a metal profile or a transmission with an elastic element that absorbs the expansion.<\/p>\n<\/div>\n<div class=\"infobox\">\n <div class=\"infobox__title\">\n <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"><path d=\"M4 4h16c1.1 0 2 .9 2 2v12c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V6c0-1.1.9-2 2-2z\"><\/path><polyline points=\"22,6 12,13 2,6\"><\/polyline><\/svg>\n Ask us\n <\/div>\n <p class=\"infobox__text\">If your application involves thermal swings above 60 \u00b0C or materials with off-standard expansion coefficients, <a href=\"https:\/\/shop.stagnoligears.com\/en\/contacts\/\" target=\"_blank\" rel=\"noopener\" class=\"cta-link\">write<\/a> to the technical office. We calculate the correct clearance for your real operating conditions.<\/p>\n<\/div>\n\n <\/div>\n <\/div>\n <\/div>\n\n\n<script>\n (function () {\n var hideTimers = {};\n function positionTooltip(trigger, tooltip) {\n var margin = 8;\n tooltip.style.visibility = 'hidden';\n tooltip.style.top = '-9999px';\n tooltip.style.left = '-9999px';\n tooltip.removeAttribute('hidden');\n var ttRect = tooltip.getBoundingClientRect();\n var trRect = trigger.getBoundingClientRect();\n var vw = window.innerWidth, vh = window.innerHeight;\n var top = trRect.bottom + margin;\n var left = trRect.left;\n if (top + ttRect.height + margin > vh) {\n var above = trRect.top - ttRect.height - margin;\n top = above >= margin ? above : Math.max(margin, vh - ttRect.height - margin);\n }\n if (left + ttRect.width + margin > vw) left = vw - ttRect.width - margin;\n if (left < margin) left = margin;\n tooltip.style.top = top + 'px';\n tooltip.style.left = left + 'px';\n tooltip.style.visibility = '';\n }\n function showTooltip(ttId, trigger) {\n if (hideTimers[ttId]) { clearTimeout(hideTimers[ttId]); hideTimers[ttId] = null; }\n positionTooltip(trigger, document.getElementById(ttId));\n }\n function hideTooltip(ttId) {\n hideTimers[ttId] = setTimeout(function () {\n var tt = document.getElementById(ttId);\n if (tt) tt.setAttribute('hidden', '');\n hideTimers[ttId] = null;\n }, 180);\n }\n function cancelHide(ttId) {\n if (hideTimers[ttId]) { clearTimeout(hideTimers[ttId]); hideTimers[ttId] = null; }\n }\n document.querySelectorAll('[data-tooltip]').forEach(function (trigger) {\n var ttId = trigger.getAttribute('data-tooltip');\n trigger.addEventListener('mouseenter', function () { showTooltip(ttId, trigger); });\n trigger.addEventListener('mouseleave', function () { hideTooltip(ttId); });\n });\n ['tt-gioco-di-flanchi-backlash', 'tt-angolo-di-pressione'].forEach(function (ttId) {\n var tt = document.getElementById(ttId);\n if (!tt) return;\n tt.addEventListener('mouseenter', function () { 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