{"id":8014,"date":"2024-03-01T16:06:18","date_gmt":"2024-03-01T16:06:18","guid":{"rendered":"http:\/\/boyanmfg.com\/?p=8014"},"modified":"2024-05-27T17:11:08","modified_gmt":"2024-05-27T17:11:08","slug":"insights-gear-common-normal-involute-line","status":"publish","type":"post","link":"https:\/\/boyanmfg.com\/it\/insights-gear-common-normal-involute-line\/","title":{"rendered":"Esplorazione della normale degli ingranaggi: approfondimenti sulla meccanica delle linee involute"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"8014\" class=\"elementor elementor-8014\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-83ad5df elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"83ad5df\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3d2c9ca\" data-id=\"3d2c9ca\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2d63993 elementor-widget elementor-widget-heading\" data-id=\"2d63993\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_88 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/boyanmfg.com\/it\/insights-gear-common-normal-involute-line\/#Measurement_of_Common_Normal_Length_in_Gear_Inspection_Methods\" >Measurement of Common Normal Length in Gear Inspection Methods<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/boyanmfg.com\/it\/insights-gear-common-normal-involute-line\/#The_Basic_Concept_of_Involute\" >The Basic Concept of Involute<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/boyanmfg.com\/it\/insights-gear-common-normal-involute-line\/#Introduction_to_Involute_Simplified_Understanding_and_Basic_Knowledge\" >Introduction to Involute: Simplified Understanding and Basic Knowledge<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/boyanmfg.com\/it\/insights-gear-common-normal-involute-line\/#The_Concept_of_Pressure_Angle_%CE%B1_and_Its_Variability\" >The Concept of Pressure Angle \u03b1 and Its Variability<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/boyanmfg.com\/it\/insights-gear-common-normal-involute-line\/#Common_Normal_Function\" >Common Normal Function<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/boyanmfg.com\/it\/insights-gear-common-normal-involute-line\/#The_Concept_of_the_Gears_Common_Normal\" >The Concept of the Gear's Common Normal<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/boyanmfg.com\/it\/insights-gear-common-normal-involute-line\/#spanned_tooth_number\" >spanned tooth number<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/boyanmfg.com\/it\/insights-gear-common-normal-involute-line\/#Conclusion\" >Conclusion<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/boyanmfg.com\/it\/insights-gear-common-normal-involute-line\/#If_youre_looking_for_plastic_gear_solutions_we_might_be_able_to_assist_Let_us_know_how_we_can_help\" >If you're looking for plastic gear solutions, we might be able to assist. Let us know how we can help.<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Measurement_of_Common_Normal_Length_in_Gear_Inspection_Methods\"><\/span>Measurement of Common Normal Length in Gear Inspection Methods<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a360d85 elementor-widget elementor-widget-text-editor\" data-id=\"a360d85\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>When discussing gear inspection methods, measuring <strong>the length of the common normal line<\/strong> presents a simple and cost-effective technique widely used in<strong> gear production <\/strong>and <strong>reverse engineering inspections. <\/strong><\/p><p>This method, compared to the traditional measurement of individual tooth thickness, not only simplifies the operation but also effectively avoids issues related to local elastic deformation caused by point contact, thus enhancing the accuracy of the measurements. When measuring with <strong>gear tooth vernier calipers<\/strong> for tooth thickness, it is essential to ensure that the calipers remain parallel to the tooth&#8217;s surface, which undoubtedly increases the difficulty of measurement. Moreover, although using CNC (Computer Numerical Control) equipment for measurement is precise, it is also costly and the process is cumbersome.<\/p><p>This article will start by introducing the basic concept of the<strong> involute line<\/strong>, gradually delving deeper into the concept of the <strong>gear&#8217;s common normal.<\/strong> By the end of this article, you should have a comprehensive understanding of it and be able to apply this knowledge effectively in your work.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e301cae elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e301cae\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4099f72\" data-id=\"4099f72\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fdfd19d elementor-widget elementor-widget-menu-anchor\" data-id=\"fdfd19d\" data-element_type=\"widget\" data-widget_type=\"menu-anchor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-menu-anchor\" id=\"involute\"><\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6b30397 elementor-widget elementor-widget-heading\" data-id=\"6b30397\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"The_Basic_Concept_of_Involute\"><\/span>The Basic Concept of Involute<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c235c49 elementor-widget elementor-widget-text-editor\" data-id=\"c235c49\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Introduction_to_Involute_Simplified_Understanding_and_Basic_Knowledge\"><\/span>Introduction to Involute: Simplified Understanding and Basic Knowledge<span class=\"ez-toc-section-end\"><\/span><\/h3><p>The involute, a concept frequently mentioned in mathematics and engineering, can be understood through a simple experiment: imagine we have a non-elastic thin string wrapped around a circular object (think of it as a perfect circle). As we begin to slowly unwind this string while keeping it taut, the path that the end of the string takes forms what is called an <a href=\"https:\/\/mathworld.wolfram.com\/Involute.html\" target=\"_blank\" rel=\"noopener\">involute<\/a>. In this process, the circular object is referred to as the &#8220;<strong>base circle<\/strong>,&#8221; and the unwinding string is known as the &#8220;<strong>generating line<\/strong>.&#8221;<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-4303449 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4303449\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-ad74522\" data-id=\"ad74522\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c535d14 elementor-widget elementor-widget-image\" data-id=\"c535d14\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"500\" height=\"375\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/forming-of-involute.gif\" class=\"attachment-large size-large wp-image-8023\" alt=\"the forming of involute line\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-7c34e51\" data-id=\"7c34e51\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c76c67e elementor-widget elementor-widget-image\" data-id=\"c76c67e\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"500\" height=\"375\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/composition-of-involute.jpg\" class=\"attachment-large size-large wp-image-8031\" alt=\"The composition of an involute\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/composition-of-involute.jpg 500w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/composition-of-involute-300x225.jpg 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-4817a1b elementor-widget elementor-widget-text-editor\" data-id=\"4817a1b\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>In this action, the<strong> generating line<\/strong> remains <strong>tangent to the base circle<\/strong>, and at any point on the involute, it is <strong>perpendicular to the curve<\/strong>. This angle, which we call the <strong>unwinding angle \u03b8 (\u2220KOK<sub>0<\/sub>)<\/strong>, is the angle formed by the line connecting the point on the involute <strong>(<code>K<\/code>)<\/strong> to the center of the base circle <strong>(<code>O<\/code>)<\/strong> from the starting point of the involute <strong>(<code>K<sub>0<\/sub><\/code>) <\/strong>.<\/p><p>It is worth noting that since the length of the string does not change, <strong>the arc length on the base circle (arc NK<sub>0<\/sub>) and the length of the generating line (NK) are numerically equal<\/strong>.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e8a4a6f elementor-widget elementor-widget-text-editor\" data-id=\"e8a4a6f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"The_Concept_of_Pressure_Angle_%CE%B1_and_Its_Variability\"><\/span>The Concept of Pressure Angle \u03b1 and Its Variability<span class=\"ez-toc-section-end\"><\/span><\/h3><p>Delving deeper, let&#8217;s discuss a concept closely related to the involute\u2014the<strong> pressure angle \u03b1<\/strong>. The pressure angle is the angle between the normal at any point on the involute (i.e., the line perpendicular to the involute) and the direction of velocity through that point. It is important to note that the pressure angle varies at each point along the involute, starting from zero at the beginning of the involute and gradually increasing as it moves outward.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e6e90fd elementor-widget elementor-widget-image\" data-id=\"e6e90fd\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"550\" height=\"413\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/pressure-angle-involute-line.jpg\" class=\"attachment-large size-large wp-image-8036\" alt=\"pressure angle of involute line\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/pressure-angle-involute-line.jpg 550w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/pressure-angle-involute-line-300x225.jpg 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-df49fcb elementor-widget elementor-widget-text-editor\" data-id=\"df49fcb\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Additionally, the distance from a point K on the involute to the center of the circle, <code>r<sub>k<\/sub><\/code>, can be calculated using the formula <code>r<sub>k<\/sub> = r<sub>b<\/sub> \/ cos(\u03b1<sub>k<\/sub>)<\/code>, where <code>r<sub>b<\/sub><\/code> is the radius of the base circle and <code>\u03b1<sub>k<\/sub><\/code> is the pressure angle at point K.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ddbf1ee elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ddbf1ee\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-051d0f8\" data-id=\"051d0f8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b540e37 elementor-widget elementor-widget-heading\" data-id=\"b540e37\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Common_Normal_Function\"><\/span>Common Normal Function<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6809c6b elementor-widget elementor-widget-text-editor\" data-id=\"6809c6b\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The functional relationship between the unwinding angle \u03b8 and the pressure angle \u03b1 is referred to as the involute function, denoted by <code>inv(\u03b1)<\/code>.<\/p><p>As shown in the diagram below, <code>\u03b8<sub>k<\/sub> = \u2220NOK<sub>0<\/sub> - \u03b1<sub>k<\/sub><\/code><\/p><p>Where, the <code>\u2220NOK<sub>0<\/sub><\/code> equals the<code>arc length NK<sub>0<\/sub><\/code>\u00a0divided by the radius <code>r<sub>b<\/sub><\/code>, measured in arc length units, which can also be converted to degrees.<\/p><p>Since the arc length NK<sub>0<\/sub> = NK, so <code>= NK \/ r<sub>b<\/sub> = tg(\u03b1<sub>k<\/sub>)<\/code><\/p><p>Thus, we have <code>\u03b8<sub>k<\/sub> = tg(\u03b1<sub>k<\/sub>) - \u03b1<sub>k<\/sub><\/code><\/p><p>Which means <code>inv(\u03b1<sub>k<\/sub>) = tg(\u03b1<sub>k<\/sub>) - \u03b1<sub>k<\/sub><\/code><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8e2d772 elementor-widget elementor-widget-image\" data-id=\"8e2d772\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"600\" height=\"450\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/Common-Normal-Function-explained.jpg\" class=\"attachment-large size-large wp-image-8042\" alt=\"Common Normal Function explained\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/Common-Normal-Function-explained.jpg 600w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/Common-Normal-Function-explained-300x225.jpg 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4e1d3b0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4e1d3b0\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3613489\" data-id=\"3613489\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0e2f3e4 elementor-widget elementor-widget-heading\" data-id=\"0e2f3e4\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"The_Concept_of_the_Gears_Common_Normal\"><\/span>\nThe Concept of the Gear's Common Normal<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3d4377e elementor-widget elementor-widget-text-editor\" data-id=\"3d4377e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Having understood the basic concept of the involute, we can now delve into the concept of the gear&#8217;s common normal. It refers to any <strong>tangent line on the base circle<\/strong> that <strong>intersects the gear profiles at points separated by several teeth<\/strong>. Due to the characteristics of the involute, we know this line is perpendicular to the involutes that form these two gear profiles, which is why it is called the common normal.<\/p><p>From illustrations, we can observe that the l<strong>ength of the common normal <code>(AB)<\/code><\/strong>, nestled between these two gear profiles, <strong>is equal to<\/strong> the <strong>arc length<code>ab<\/code><\/strong> on the base circle. Even if the angle of the common normal changes, its length remains constant. This feature provides a significant advantage in measurements. It means that even if there is some deviation in the position of the measuring tool, it will not affect the outcome of the measurement.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-03a15da elementor-widget elementor-widget-image\" data-id=\"03a15da\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"600\" height=\"450\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/common-normal-length-explained.jpg\" class=\"attachment-large size-large wp-image-8047\" alt=\"common normal length explained\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/common-normal-length-explained.jpg 600w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/common-normal-length-explained-300x225.jpg 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8fa1353 elementor-widget elementor-widget-heading\" data-id=\"8fa1353\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"spanned_tooth_number\"><\/span>spanned tooth number<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f9a388c elementor-widget elementor-widget-text-editor\" data-id=\"f9a388c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The number of teeth spanned by the gear common normal length is called the &#8220;spanned tooth number,&#8221; which can be determined from the common normal drawn on the blueprint. There is a formula to calculate it, but the calculation process can be somewhat cumbersome, making direct observation from the blueprint simpler and more straightforward. The formula is:<\/p><p><code>k = z\u03b1 \/ 180\u00b0 + 0.5<\/code><\/p><p>Where:<\/p><ul><li><code>k<\/code> is the spanned tooth number,<\/li><li><code>z<\/code> is the number of teeth,<\/li><li><code>\u03b1<\/code> is the pressure angle of the gear on the circumference circle, which is 20\u00b0 in most cases<\/li><li><code>x<\/code> is the gear <a href=\"http:\/\/boyanmfg.com\/gear-terminology-teeth-calculation-formulas-easy-guide\/#profile_shift\">profile shift coefficient.<\/a><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-19df150 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"19df150\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-af7754d\" data-id=\"af7754d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4af1dbc elementor-widget elementor-widget-text-editor\" data-id=\"4af1dbc\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The length of the common normal can also be obtained from CAD drawings, but it can be calculated using a formula as well. For gears with a modification coefficient <code>x = 0<\/code>, the formula for calculating the spanned tooth distance is:<\/p><p><code>L = m cos \u03b1 [(k - 0.5)\u03c0 + z inv \u03b1]<\/code><\/p><p>Where:<\/p><ul><li><code>L<\/code> is the length of the common normal,<\/li><li><code>\u03b1<\/code> is the pressure angle at the<a href=\"http:\/\/boyanmfg.com\/gear-terminology-teeth-calculation-formulas-easy-guid#reference_circle\"> reference circle<\/a>,<\/li><li><code>k<\/code> is the spanned tooth number.<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c7a22a3 elementor-widget elementor-widget-image\" data-id=\"c7a22a3\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"375\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/common-normal-length-stable.jpg\" class=\"attachment-large size-large wp-image-8050\" alt=\"common normal length remains stable\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/common-normal-length-stable.jpg 500w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2024\/03\/common-normal-length-stable-300x225.jpg 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"> Even though the angle of the common normal may vary, its length stays the same.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ebb67af elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ebb67af\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b29a0e7\" data-id=\"b29a0e7\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b85407c elementor-widget elementor-widget-text-editor\" data-id=\"b85407c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The formulas mentioned above are calculated based on the modification coefficient <code>x = 0<\/code>, where the tooth thickness at the pitch circle <code>s = zm\/2<\/code>, which is half of the pitch. However, if <code>x &gt; 0<\/code>, the tooth thickness at the pitch circle increases, leading to an increase in <code>L<\/code>, and conversely, <code>L<\/code> decreases if <code>x &lt; 0<\/code>. Therefore, measuring the length of the common normal is an effective method for gear reverse engineering, allowing for the estimation of the sample gear&#8217;s modification coefficient.<\/p>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-927f8d3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"927f8d3\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5f9e00e\" data-id=\"5f9e00e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-09020d1 elementor-widget elementor-widget-heading\" data-id=\"09020d1\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Conclusion\"><\/span>Conclusion<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2578ff2 elementor-widget elementor-widget-text-editor\" data-id=\"2578ff2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>To keep this article concise, we will not delve into the derivation of these formulas here, but they will be covered in other articles.<\/p><p>We hope this article gives you a clear concept of the common normal. If you have any questions, please leave your comments below.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5fbcfb4 elementor-widget elementor-widget-spacer\" data-id=\"5fbcfb4\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-536b71d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"536b71d\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6fafede\" data-id=\"6fafede\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-adae672 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"adae672\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-af517ad\" data-id=\"af517ad\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5726eca elementor-widget elementor-widget-image\" data-id=\"5726eca\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"273\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2019\/04\/plastic-gear-with-spline-shaft.png\" class=\"attachment-large size-large wp-image-4622\" alt=\"plastic gear with spline shaft\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-67cd013\" data-id=\"67cd013\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7569708 elementor-widget elementor-widget-heading\" data-id=\"7569708\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"If_youre_looking_for_plastic_gear_solutions_we_might_be_able_to_assist_Let_us_know_how_we_can_help\"><\/span>If you're looking for plastic gear solutions, we might be able to assist. Let us know how we can help.<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-0c88463\" data-id=\"0c88463\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7d53280 elementor-align-center elementor-mobile-align-justify elementor-widget elementor-widget-button\" data-id=\"7d53280\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-xl\" href=\"http:\/\/boyanmfg.com\/enquiry-plastic-injection-molding\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Request a quote<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Misura della Lunghezza della Normale Comune nei Metodi di Ispezione degli Ingranaggi Quando si discutono i metodi di ispezione degli ingranaggi, la misurazione della lunghezza della normale comune rappresenta una tecnica semplice ed economica ampiamente utilizzata nella produzione di ingranaggi e nelle ispezioni di ingegneria inversa. Questo metodo, rispetto alla tradizionale misurazione dello spessore del singolo dente, non solo semplifica l'operazione ma anche\u2026&nbsp;<a href=\"https:\/\/boyanmfg.com\/it\/insights-gear-common-normal-involute-line\/\" rel=\"bookmark\">Continua a leggere \u00bb<span class=\"screen-reader-text\">Esplorazione della normale degli ingranaggi: approfondimenti sulla meccanica delle linee involute<\/span><\/a><\/p>","protected":false},"author":1,"featured_media":8058,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"on","neve_meta_content_width":93,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","neve_meta_reading_time":"","_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[55],"tags":[],"class_list":["post-8014","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-manufacturing-knowledge"],"acf":[],"_links":{"self":[{"href":"https:\/\/boyanmfg.com\/it\/wp-json\/wp\/v2\/posts\/8014","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/boyanmfg.com\/it\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/boyanmfg.com\/it\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/boyanmfg.com\/it\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/boyanmfg.com\/it\/wp-json\/wp\/v2\/comments?post=8014"}],"version-history":[{"count":0,"href":"https:\/\/boyanmfg.com\/it\/wp-json\/wp\/v2\/posts\/8014\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/boyanmfg.com\/it\/wp-json\/wp\/v2\/media\/8058"}],"wp:attachment":[{"href":"https:\/\/boyanmfg.com\/it\/wp-json\/wp\/v2\/media?parent=8014"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/boyanmfg.com\/it\/wp-json\/wp\/v2\/categories?post=8014"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/boyanmfg.com\/it\/wp-json\/wp\/v2\/tags?post=8014"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}