Case study: designing a reduction with a 62.5 mm center distance<\/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-sottotaglio\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Undercut<\/div>\n <div class=\"glossary-tooltip__def\">Unintentional removal of material at the tooth root during profile generation. It occurs with low tooth counts and weakens the root cross-section.<\/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\": \"Case study: designing a reduction with a 62.5 mm center distance\",\n \"description\": \"A step-by-step example to size a 1:1.5 reduction with a fixed center distance, choosing the correct module and integer tooth counts.\",\n \"inLanguage\": \"en\",\n \"mentions\": [\n {\n \"@id\": \"#term-sottotaglio\"\n },\n {\n \"@id\": \"#term-angolo-di-pressione\"\n }\n ]\n },\n {\n \"@type\": \"DefinedTermSet\",\n \"@id\": \"#glossario\",\n \"name\": \"Glossario - Case study: designing a reduction with a 62.5 mm center distance\",\n \"hasDefinedTerm\": [\n {\n \"@type\": \"DefinedTerm\",\n \"@id\": \"#term-sottotaglio\",\n \"name\": \"Undercut\",\n \"description\": \"Unintentional removal of material at the tooth root during profile generation. It occurs with low tooth counts and weakens the root cross-section.\",\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\">Case study: designing a reduction with a 62.5 mm center distance<\/h1>\n<p class=\"article__subtitle\">A step-by-step example to size a 1:1.5 reduction with a fixed center distance, choosing the correct module and integer tooth counts.<\/p>\n<p class=\"article__p\">The machine frame imposes the center distance: exactly 62.5 mm, no exceptions. The required reduction ratio is 1:1.5, that is, the gear wheel must turn at 2\/3 of the pinion’s speed. Your task is to find the combination of module m, pinion tooth count Z1 and gear-wheel tooth count Z2 that satisfies both constraints, choosing among the standard modules and obtaining integer tooth counts.<\/p>\n<h2 class=\"article__h2\" id=\"finding-the-product-m-z1\">\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=\"M12 20h9\"><\/path><path d=\"M16.5 3.5a2.121 2.121 0 0 1 3 3L7 19l-4 1 1-4L16.5 3.5z\"><\/path><\/svg><\/span>\n Finding the product m \u00d7 Z1\n<\/h2>\n<p class=\"article__p\">Start from the center-distance formula:<\/p>\n<div class=\"formula-block\">$$a = \\frac{m \\times (Z_1 + Z_2)}{2}$$<\/div>\n<p class=\"article__p\">Knowing that Z2 = i \u00d7 Z1, with i = 1.5, you can rewrite the equation and derive the product m \u00d7 Z1:<\/p>\n<div class=\"formula-block\">$$m \\times Z_1 = \\frac{(2 \\times a)}{(1 + i)} = \\frac{(2 \\times 62.5)}{(1 + 1.5)} = \\frac{125}{2.5} = 50$$<\/div>\n<p class=\"article__p\">This number, <strong>50<\/strong>, must be the product of the module and the pinion tooth count. The whole sizing starts from here.<\/p>\n<h2 class=\"article__h2\" id=\"trying-the-standard-modules\">\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\"><rect x=\"2\" y=\"2\" width=\"20\" height=\"20\" rx=\"2\" ry=\"2\"><\/rect><line x1=\"8\" y1=\"6\" x2=\"16\" y2=\"6\"><\/line><line x1=\"8\" y1=\"10\" x2=\"14\" y2=\"10\"><\/line><line x1=\"8\" y1=\"14\" x2=\"16\" y2=\"14\"><\/line><line x1=\"8\" y1=\"18\" x2=\"12\" y2=\"18\"><\/line><\/svg><\/span>\n Trying the standard modules\n<\/h2>\n<p class=\"article__p\">Now break down 50 into the catalog modules, looking for the combinations that produce integer tooth counts for both the pinion and the gear wheel.<\/p>\n<div class=\"article__table-wrap\">\n<table class=\"article__table\">\n<thead><tr><th>Module m<\/th><th>Z1 = 50\/m<\/th><th>Z2 = Z1 \u00d7 1.5<\/th><th>Outcome<\/th><\/tr><\/thead>\n<tbody><tr><td>1.0<\/td><td>50<\/td><td>75<\/td><td>OK, but small teeth<\/td><\/tr>\n<tr><td>2.0<\/td><td>25<\/td><td>37.5<\/td><td>Z2 not integer: discarded<\/td><\/tr>\n<tr><td>2.5<\/td><td>20<\/td><td>30<\/td><td>OK: robust solution<\/td><\/tr>\n<tr><td>3.0<\/td><td>16.67<\/td><td>\u2014<\/td><td>Z1 not integer: discarded<\/td><\/tr><\/tbody>\n<\/table>\n<\/div>\n<h2 class=\"article__h2\" id=\"the-solution\">\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=\"18\" cy=\"18\" r=\"3\"><\/circle><circle cx=\"6\" cy=\"6\" r=\"3\"><\/circle><path d=\"M13 6h3a2 2 0 0 1 2 2v7\"><\/path><path d=\"M11 18H8a2 2 0 0 1-2-2V9\"><\/path><path d=\"m8 9-2 2 2 2\"><\/path><\/svg><\/span>\n The solution\n<\/h2>\n<p class=\"article__p\">The winning combination is <strong>module 2.5, Z1 = 20 teeth, Z2 = 30 teeth<\/strong>.<\/p>\n<p class=\"article__p\">Compared with module 1.0, also geometrically valid, module 2.5 guarantees more robust teeth, greater torque capacity and greater tolerance to center-distance errors. This counts especially when the frame is made from laser-cut sheet metal: tolerances can exceed two tenths of a millimeter, and a larger module absorbs these deviations better.<\/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\"><line x1=\"9\" y1=\"18\" x2=\"15\" y2=\"18\"><\/line><line x1=\"10\" y1=\"22\" x2=\"14\" y2=\"22\"><\/line><path d=\"M15.09 14c.18-.98.65-1.74 1.41-2.5A4.65 4.65 0 0 0 18 8 6 6 0 0 0 6 8c0 1 .23 2.23 1.5 3.5A4.61 4.61 0 0 1 8.91 14\"><\/path><\/svg>\n From the field\n <\/div>\n <p class=\"infobox__text\">When you have several geometrically valid solutions, generally choose the largest module compatible with the footprint. You pay a few grams of extra weight and gain robustness, durability and assembly tolerance.<\/p>\n<\/div>\n<h2 class=\"article__h2\" id=\"final-check-undercut-control\">\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=\"9 11 12 14 22 4\"><\/polyline><path d=\"M21 12v7a2 2 0 0 1-2 2H5a2 2 0 0 1-2-2V5a2 2 0 0 1 2-2h11\"><\/path><\/svg><\/span>\n Final check: undercut control\n<\/h2>\n<p class=\"article__p\">Before closing the sizing, verify that <strong>Z1 is greater than 17<\/strong>. Below this threshold, milling the tooth can cut into the foot of the profile, weakening it: this is the <strong><dfn id=\"def-sottotaglio\"><span class=\"glossary-term\" data-tooltip=\"tt-sottotaglio\" title=\"Unintentional removal of material at the tooth root during profile generation. It occurs with low tooth counts and weakens the root cross-section.\">undercut<\/span><\/dfn><\/strong> phenomenon, which in certain cases requires profile corrections to recover strength. In our case Z1 = 20, well above the limit, so no corrections are needed.<\/p>\n<p class=\"article__p\">If your project should take you below this threshold, you don’t need to change the module or center distance: there are profile-correction techniques that eliminate undercut while keeping the transmission geometry unchanged.<\/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 <strong>17-tooth threshold<\/strong> applies to the standard profile at 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>. With different pressure angles or corrected wheels, the limit changes. If you work outside the standard profile, check the minimum tooth count in the catalog or in the sector ISO references.<\/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 + 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{"id":25321,"date":"2026-06-10T12:51:40","date_gmt":"2026-06-10T10:51:40","guid":{"rendered":"https:\/\/shop.stagnoligears.com\/centro-tecnico\/caso-studio-progettare-una-riduzione-con-interasse-625-mm\/"},"modified":"2026-07-10T14:42:39","modified_gmt":"2026-07-10T12:42:39","slug":"case-study-gears-designing-a-reduction","status":"publish","type":"centro-tecnico","link":"https:\/\/shop.stagnoligears.com\/en\/technical-hub\/case-study-gears-designing-a-reduction\/","title":{"rendered":"Case study: designing a reduction with 62.5 mm center distance"},"content":{"rendered":"\n\n \n \n \n Case study: designing a reduction with a 62.5 mm center distance<\/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-sottotaglio\" class=\"glossary-tooltip\" hidden=\"\">\n <div class=\"glossary-tooltip__title\">Undercut<\/div>\n <div class=\"glossary-tooltip__def\">Unintentional removal of material at the tooth root during profile generation. It occurs with low tooth counts and weakens the root cross-section.<\/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\": \"Case study: designing a reduction with a 62.5 mm center distance\",\n \"description\": \"A step-by-step example to size a 1:1.5 reduction with a fixed center distance, choosing the correct module and integer tooth counts.\",\n \"inLanguage\": \"en\",\n \"mentions\": [\n {\n \"@id\": \"#term-sottotaglio\"\n },\n {\n \"@id\": \"#term-angolo-di-pressione\"\n }\n ]\n },\n {\n \"@type\": \"DefinedTermSet\",\n \"@id\": \"#glossario\",\n \"name\": \"Glossario - Case study: designing a reduction with a 62.5 mm center distance\",\n \"hasDefinedTerm\": [\n {\n \"@type\": \"DefinedTerm\",\n \"@id\": \"#term-sottotaglio\",\n \"name\": \"Undercut\",\n \"description\": \"Unintentional removal of material at the tooth root during profile generation. It occurs with low tooth counts and weakens the root cross-section.\",\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\">Case study: designing a reduction with a 62.5 mm center distance<\/h1>\n<p class=\"article__subtitle\">A step-by-step example to size a 1:1.5 reduction with a fixed center distance, choosing the correct module and integer tooth counts.<\/p>\n<p class=\"article__p\">The machine frame imposes the center distance: exactly 62.5 mm, no exceptions. The required reduction ratio is 1:1.5, that is, the gear wheel must turn at 2\/3 of the pinion’s speed. Your task is to find the combination of module m, pinion tooth count Z1 and gear-wheel tooth count Z2 that satisfies both constraints, choosing among the standard modules and obtaining integer tooth counts.<\/p>\n<h2 class=\"article__h2\" id=\"finding-the-product-m-z1\">\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=\"M12 20h9\"><\/path><path d=\"M16.5 3.5a2.121 2.121 0 0 1 3 3L7 19l-4 1 1-4L16.5 3.5z\"><\/path><\/svg><\/span>\n Finding the product m \u00d7 Z1\n<\/h2>\n<p class=\"article__p\">Start from the center-distance formula:<\/p>\n<div class=\"formula-block\">$$a = \\frac{m \\times (Z_1 + Z_2)}{2}$$<\/div>\n<p class=\"article__p\">Knowing that Z2 = i \u00d7 Z1, with i = 1.5, you can rewrite the equation and derive the product m \u00d7 Z1:<\/p>\n<div class=\"formula-block\">$$m \\times Z_1 = \\frac{(2 \\times a)}{(1 + i)} = \\frac{(2 \\times 62.5)}{(1 + 1.5)} = \\frac{125}{2.5} = 50$$<\/div>\n<p class=\"article__p\">This number, <strong>50<\/strong>, must be the product of the module and the pinion tooth count. The whole sizing starts from here.<\/p>\n<h2 class=\"article__h2\" id=\"trying-the-standard-modules\">\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\"><rect x=\"2\" y=\"2\" width=\"20\" height=\"20\" rx=\"2\" ry=\"2\"><\/rect><line x1=\"8\" y1=\"6\" x2=\"16\" y2=\"6\"><\/line><line x1=\"8\" y1=\"10\" x2=\"14\" y2=\"10\"><\/line><line x1=\"8\" y1=\"14\" x2=\"16\" y2=\"14\"><\/line><line x1=\"8\" y1=\"18\" x2=\"12\" y2=\"18\"><\/line><\/svg><\/span>\n Trying the standard modules\n<\/h2>\n<p class=\"article__p\">Now break down 50 into the catalog modules, looking for the combinations that produce integer tooth counts for both the pinion and the gear wheel.<\/p>\n<div class=\"article__table-wrap\">\n<table class=\"article__table\">\n<thead><tr><th>Module m<\/th><th>Z1 = 50\/m<\/th><th>Z2 = Z1 \u00d7 1.5<\/th><th>Outcome<\/th><\/tr><\/thead>\n<tbody><tr><td>1.0<\/td><td>50<\/td><td>75<\/td><td>OK, but small teeth<\/td><\/tr>\n<tr><td>2.0<\/td><td>25<\/td><td>37.5<\/td><td>Z2 not integer: discarded<\/td><\/tr>\n<tr><td>2.5<\/td><td>20<\/td><td>30<\/td><td>OK: robust solution<\/td><\/tr>\n<tr><td>3.0<\/td><td>16.67<\/td><td>\u2014<\/td><td>Z1 not integer: discarded<\/td><\/tr><\/tbody>\n<\/table>\n<\/div>\n<h2 class=\"article__h2\" id=\"the-solution\">\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=\"18\" cy=\"18\" r=\"3\"><\/circle><circle cx=\"6\" cy=\"6\" r=\"3\"><\/circle><path d=\"M13 6h3a2 2 0 0 1 2 2v7\"><\/path><path d=\"M11 18H8a2 2 0 0 1-2-2V9\"><\/path><path d=\"m8 9-2 2 2 2\"><\/path><\/svg><\/span>\n The solution\n<\/h2>\n<p class=\"article__p\">The winning combination is <strong>module 2.5, Z1 = 20 teeth, Z2 = 30 teeth<\/strong>.<\/p>\n<p class=\"article__p\">Compared with module 1.0, also geometrically valid, module 2.5 guarantees more robust teeth, greater torque capacity and greater tolerance to center-distance errors. This counts especially when the frame is made from laser-cut sheet metal: tolerances can exceed two tenths of a millimeter, and a larger module absorbs these deviations better.<\/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\"><line x1=\"9\" y1=\"18\" x2=\"15\" y2=\"18\"><\/line><line x1=\"10\" y1=\"22\" x2=\"14\" y2=\"22\"><\/line><path d=\"M15.09 14c.18-.98.65-1.74 1.41-2.5A4.65 4.65 0 0 0 18 8 6 6 0 0 0 6 8c0 1 .23 2.23 1.5 3.5A4.61 4.61 0 0 1 8.91 14\"><\/path><\/svg>\n From the field\n <\/div>\n <p class=\"infobox__text\">When you have several geometrically valid solutions, generally choose the largest module compatible with the footprint. You pay a few grams of extra weight and gain robustness, durability and assembly tolerance.<\/p>\n<\/div>\n<h2 class=\"article__h2\" id=\"final-check-undercut-control\">\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=\"9 11 12 14 22 4\"><\/polyline><path d=\"M21 12v7a2 2 0 0 1-2 2H5a2 2 0 0 1-2-2V5a2 2 0 0 1 2-2h11\"><\/path><\/svg><\/span>\n Final check: undercut control\n<\/h2>\n<p class=\"article__p\">Before closing the sizing, verify that <strong>Z1 is greater than 17<\/strong>. Below this threshold, milling the tooth can cut into the foot of the profile, weakening it: this is the <strong><dfn id=\"def-sottotaglio\"><span class=\"glossary-term\" data-tooltip=\"tt-sottotaglio\" title=\"Unintentional removal of material at the tooth root during profile generation. It occurs with low tooth counts and weakens the root cross-section.\">undercut<\/span><\/dfn><\/strong> phenomenon, which in certain cases requires profile corrections to recover strength. In our case Z1 = 20, well above the limit, so no corrections are needed.<\/p>\n<p class=\"article__p\">If your project should take you below this threshold, you don’t need to change the module or center distance: there are profile-correction techniques that eliminate undercut while keeping the transmission geometry unchanged.<\/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 <strong>17-tooth threshold<\/strong> applies to the standard profile at 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>. With different pressure angles or corrected wheels, the limit changes. If you work outside the standard profile, check the minimum tooth count in the catalog or in the sector ISO references.<\/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-sottotaglio', 'tt-angolo-di-pressione'].forEach(function (ttId) {\n var tt = document.getElementById(ttId);\n if (!tt) return;\n 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