{"id":1463,"date":"2019-04-20T16:07:00","date_gmt":"2019-04-20T16:07:00","guid":{"rendered":"http:\/\/boyanmfg.com\/?p=1463"},"modified":"2024-05-27T17:16:30","modified_gmt":"2024-05-27T17:16:30","slug":"gear-terminology-teeth-calculation-formulas-easy-guide","status":"publish","type":"post","link":"https:\/\/boyanmfg.com\/ar\/gear-terminology-teeth-calculation-formulas-easy-guide\/","title":{"rendered":"\u062f\u0644\u064a\u0644 \u0633\u0647\u0644 \u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u062a\u0631\u0648\u0633 \u0648\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062d\u0633\u0627\u0628 \u0627\u0644\u0623\u0633\u0646\u0627\u0646"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"1463\" class=\"elementor elementor-1463\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-72e0e04 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"72e0e04\" 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-d83670f\" data-id=\"d83670f\" 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-b901de2 elementor-widget elementor-widget-heading\" data-id=\"b901de2\" 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\/ar\/gear-terminology-teeth-calculation-formulas-easy-guide\/#This_is_a_simpler_version_of_gear_terminology_and_teeth_calculation_formulas\" >This is a simpler version of gear terminology and teeth calculation formulas<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/boyanmfg.com\/ar\/gear-terminology-teeth-calculation-formulas-easy-guide\/#Table_of_content\" >Table of content<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/boyanmfg.com\/ar\/gear-terminology-teeth-calculation-formulas-easy-guide\/#1_Teeth_number_z\" >1.  Teeth number (z)<\/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\/ar\/gear-terminology-teeth-calculation-formulas-easy-guide\/#2_Reference_circle_and_reference_diameter_d\" >2. Reference circle and reference diameter (d)<\/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\/ar\/gear-terminology-teeth-calculation-formulas-easy-guide\/#3_Module_m\" >3. Module (m)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/boyanmfg.com\/ar\/gear-terminology-teeth-calculation-formulas-easy-guide\/#4_Center_distance_a\" >4. Center distance (a)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/boyanmfg.com\/ar\/gear-terminology-teeth-calculation-formulas-easy-guide\/#5_Pressure_angle_%CE%B1\" >5. Pressure angle (\u03b1)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/boyanmfg.com\/ar\/gear-terminology-teeth-calculation-formulas-easy-guide\/#6_Minimum_teeth_number_zmin_without_undercutting_in_gear\" >6. Minimum teeth number (zmin) without undercutting in gear<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/boyanmfg.com\/ar\/gear-terminology-teeth-calculation-formulas-easy-guide\/#7_Profile_shift_coefficient_x\" >7. Profile shift coefficient (x)<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/boyanmfg.com\/ar\/gear-terminology-teeth-calculation-formulas-easy-guide\/#In_summary\" >In summary:<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/boyanmfg.com\/ar\/gear-terminology-teeth-calculation-formulas-easy-guide\/#Frequently_Asked_Questions%E2%80%8B\" >Frequently Asked Questions\u200b<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/boyanmfg.com\/ar\/gear-terminology-teeth-calculation-formulas-easy-guide\/#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=\"This_is_a_simpler_version_of_gear_terminology_and_teeth_calculation_formulas\"><\/span>This is a simpler version of gear terminology and teeth calculation formulas<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-2469168 elementor-widget elementor-widget-text-editor\" data-id=\"2469168\" 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<div class=\"fusion-text\"><p>This post is to explain the gear terminologies and teeth calculation formulas in an easier way for beginners, and also for those who have learned gears long ago but want to pick up again quickly.<\/p><p>The gears have many parameters that will take a bit of mathematics and geometrical training to fully understand them. However, You do not need to go too deep into the basic concepts of gear knowledge, after you have read this post, <strong>you should be able to make preliminary gear designs or have an effective communication with gear designers<\/strong>.<\/p><\/div><div class=\"fusion-text\"><p>Let\u2019s get started from the basic gear form, the spur gears:<\/p><\/div>\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-0dca945 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"0dca945\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/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-2b360c1 elementor-widget elementor-widget-menu-anchor\" data-id=\"2b360c1\" 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=\"topic\"><\/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-b0549a9 elementor-widget elementor-widget-heading\" data-id=\"b0549a9\" 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=\"Table_of_content\"><\/span>Table of content<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-bda9662 elementor-widget elementor-widget-text-editor\" data-id=\"bda9662\" 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>1. Teeth number (z);\u00a0 2. Reference circle and reference diameter (d);\u00a0 3. <a href=\"#module\">Module (m)<\/a>;\u00a0 4. <a href=\"#center_distance\">Center distance (a)<\/a>;\u00a0 5.<a href=\"#pressure_angle\"> Pressure angle (\u03b1)<\/a>; 6.<a href=\"#z_minimun\"> Minimum teeth number (z<sub>min<\/sub>)<\/a>; 7.<a href=\"#profile_shift\"> Profile shift coefficient (x)<\/a>; 8. <a href=\"#summary\">Summary table<\/a>.<\/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-081afe0 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"081afe0\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\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-08f5726 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"08f5726\" 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-f508d7d\" data-id=\"f508d7d\" 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-f8dbe80 elementor-widget elementor-widget-heading\" data-id=\"f8dbe80\" 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=\"1_Teeth_number_z\"><\/span>1.  Teeth number (z)\n<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-20bdde5 elementor-widget elementor-widget-text-editor\" data-id=\"20bdde5\" 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>This is pretty straightforward, it is the number of teeth of the gear.<\/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-6b58af6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6b58af6\" 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-65c9e65\" data-id=\"65c9e65\" 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-dfa30fa elementor-widget elementor-widget-menu-anchor\" data-id=\"dfa30fa\" 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=\"reference_circle\"><\/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-e221efd elementor-widget elementor-widget-heading\" data-id=\"e221efd\" 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=\"2_Reference_circle_and_reference_diameter_d\"><\/span>2. Reference circle and reference diameter (d)<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-f11136e elementor-widget elementor-widget-text-editor\" data-id=\"f11136e\" 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<div class=\"fusion-layout-column fusion_builder_column fusion_builder_column_1_2 fusion-builder-column-3 fusion-one-half fusion-column-first 1_2\"><div class=\"fusion-column-wrapper\" data-bg-url=\"\"><div class=\"fusion-text\"><p>The tip diameter (da) and root diameter (df) correspond to the top and bottom of the teeth.<\/p><p>The reference diameter is used in gear designing and calculation. It has direct connections with other important gear parameters like the module (m), center distance (c) and pressure angle (\u03b1).<\/p><\/div><\/div><\/div>\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-a93c4f7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a93c4f7\" 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-7c4b964\" data-id=\"7c4b964\" 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-71ec420 elementor-widget elementor-widget-text-editor\" data-id=\"71ec420\" 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 tip diameter (da) and root diameter (df) correspond to the top and bottom of the teeth.<\/p><p>The reference diameter is used in gear designing and calculation. It has direct connections with other important gear parameters like the module (m), center distance (c) and pressure angle (\u03b1).<\/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<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-7ab43b5\" data-id=\"7ab43b5\" 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-db267fb elementor-widget elementor-widget-image\" data-id=\"db267fb\" 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=\"398\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-reference-circle.jpg\" class=\"attachment-large size-large wp-image-1466\" alt=\"gear reference circle\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-reference-circle.jpg 500w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-reference-circle-300x239.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-8023e1f elementor-widget elementor-widget-text-editor\" data-id=\"8023e1f\" 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 turning of 2 gears can be considered engaged turning of 2 reference circles without slippage. The gear ratio i=d2\/d1. d1 and d2 refer to the reference diameters of 2 mating gears (gear 1 is the driving gear, and gear 2 is the driven gear).<\/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-b960a09 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b960a09\" 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-3af2760\" data-id=\"3af2760\" 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-f1a7373 elementor-widget elementor-widget-image\" data-id=\"f1a7373\" 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=\"355\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/reference-circles-on-2-meshing-gears.jpg\" class=\"attachment-large size-large wp-image-1469\" alt=\"\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/reference-circles-on-2-meshing-gears.jpg 500w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/reference-circles-on-2-meshing-gears-300x213.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<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-52815da\" data-id=\"52815da\" 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-51f5042 elementor-widget elementor-widget-image\" data-id=\"51f5042\" 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=\"414\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-reference-circles-in-3D.jpg\" class=\"attachment-large size-large wp-image-1468\" alt=\"gear reference circles in 3D\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-reference-circles-in-3D.jpg 550w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-reference-circles-in-3D-300x226.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\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-inner-section elementor-element elementor-element-4c2d421 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4c2d421\" 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-619413c\" data-id=\"619413c\" 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-deb19e6 elementor-widget elementor-widget-text-editor\" data-id=\"deb19e6\" 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 reference circle is located somewhere between the tip and bottom of the teeth, usually it is where the tooth thickness equals to the spacing, but this is not always the case (we will talk about profile shifting later in this post).<\/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<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-fd0ee2a\" data-id=\"fd0ee2a\" 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-170b764 elementor-widget elementor-widget-image\" data-id=\"170b764\" 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=\"500\" height=\"316\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/location-of-reference-circle.jpg\" class=\"attachment-large size-large wp-image-1470\" alt=\"location of reference circle for gear\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/location-of-reference-circle.jpg 500w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/location-of-reference-circle-300x190.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\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-5745c3b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5745c3b\" 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-3c8b853\" data-id=\"3c8b853\" 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-51a46b6 elementor-widget elementor-widget-menu-anchor\" data-id=\"51a46b6\" 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=\"module\"><\/div>\n\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-7578c79 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7578c79\" 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-254349a\" data-id=\"254349a\" 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-2fbb268 elementor-widget elementor-widget-heading\" data-id=\"2fbb268\" 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=\"3_Module_m\"><\/span>3. Module (m)<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-50 elementor-inner-column elementor-element elementor-element-a9a96d4\" data-id=\"a9a96d4\" 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-a3a5a8b elementor-button-info elementor-align-right elementor-widget elementor-widget-button\" data-id=\"a3a5a8b\" 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-sm\" href=\"#topic\">\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\">Back to topic \u2191<\/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<div class=\"elementor-element elementor-element-3033124 elementor-widget elementor-widget-text-editor\" data-id=\"3033124\" 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 module is probably the most important gear parameter, and it appears almost everywhere in teeth calculation formulas. Actually, it is not so difficult to understand as you might imagine. First let\u2019s understand what the pitch is, Pitch is the arc length between corresponding points on adjacent teeth, usually on the reference circle.<\/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-0efbd5e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0efbd5e\" 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-4eeb674\" data-id=\"4eeb674\" 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-3d43484 elementor-widget elementor-widget-image\" data-id=\"3d43484\" 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=\"500\" height=\"368\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-pitch-and-module.jpg\" class=\"attachment-large size-large wp-image-1473\" alt=\"gear pitch and module\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-pitch-and-module.jpg 500w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-pitch-and-module-300x221.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<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-f3d2696\" data-id=\"f3d2696\" 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-8e28066 elementor-widget elementor-widget-image\" data-id=\"8e28066\" 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=\"550\" height=\"310\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/machining-of-gear-teeth.jpg\" class=\"attachment-large size-large wp-image-1472\" alt=\"\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/machining-of-gear-teeth.jpg 550w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/machining-of-gear-teeth-300x169.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\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-28bceec elementor-widget elementor-widget-text-editor\" data-id=\"28bceec\" 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<div class=\"fusion-layout-column fusion_builder_column fusion_builder_column_1_1 fusion-builder-column-13 fusion-one-full fusion-column-first fusion-column-last 1_1\"><div class=\"fusion-column-wrapper\" data-bg-url=\"\"><div class=\"fusion-text\"><p>Then we have the reference diameter\u00a0<strong>d=circumference\/\u03c0=pitch*z\/\u03c0<\/strong>, to make the calculation easier, we define the\u00a0<strong>pitch\/\u03c0<\/strong>\u00a0as the module, and now we have the equation of\u00a0<strong>d=m*z<\/strong>, this makes the calculation a lot easier, right? The modules have been standardized in the following numbers \uff08<strong>unit: mm<\/strong>\uff09:<\/p><\/div><div class=\"fusion-text\"><p>First series (recommeded): 0.1, 0.12, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.8, 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, 50<\/p><p>Second series (less used): 0.35, 0.7, 0.9, 1.75, 2.25, 2.75, 3.25, 3.5, 3.75, 4.5, 5.5, 6.5, 7, 9, 11, 14, 18, 22, 28, 30, 36, 45<\/p><\/div><div class=\"fusion-clearfix\">\u00a0<\/div><\/div><\/div><div class=\"fusion-layout-column fusion_builder_column fusion_builder_column_1_1 fusion-builder-column-14 fusion-one-full fusion-column-first fusion-column-last 1_1\"><div class=\"fusion-column-wrapper\" data-bg-url=\"\"><div class=\"fusion-text\"><p>However, for injection-molded plastic gears, there is no need to adopt these standard module numbers, since the teeth are not cut by standard tooth cutters.<\/p><\/div><div class=\"fusion-text\"><p>Now we have the gear ratio i=d2\/d1=z2\/z1 (gear 1 is the driving gear, and gear 2 is the driven gear).<\/p><p>The module also has to do with the tooth height, for standard gears, the tooth height equals to 2.25*m:<\/p><p>addendum\u00a0<strong>ha=1*m<\/strong>, dedendum\u00a0<strong>hf=1.25*m<\/strong>, tooth height\u00a0<strong>h=2.25*m<\/strong>.<\/p><\/div><\/div><\/div>\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-7508081 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7508081\" 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-5fc2554\" data-id=\"5fc2554\" 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-0d9f7ef elementor-widget elementor-widget-menu-anchor\" data-id=\"0d9f7ef\" 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=\"center_distance\"><\/div>\n\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-014d4ed elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"014d4ed\" 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-0ec797b\" data-id=\"0ec797b\" 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-63b3d69 elementor-widget elementor-widget-heading\" data-id=\"63b3d69\" 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=\"4_Center_distance_a\"><\/span>4. Center distance (a)<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-50 elementor-inner-column elementor-element elementor-element-e67cbe0\" data-id=\"e67cbe0\" 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-4c651fc elementor-button-info elementor-align-right elementor-widget elementor-widget-button\" data-id=\"4c651fc\" 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-sm\" href=\"#topic\">\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\">Back to topic \u2191<\/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<div class=\"elementor-element elementor-element-b00c071 elementor-widget elementor-widget-text-editor\" data-id=\"b00c071\" 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>2 meshing gears always have the same module otherwise they don\u2019t match. Now we can come to the conclusion that<strong>&nbsp;a=(d1+d2)\/2=m(z1+z2)\/2<\/strong>, but it can be slightly different while making some adjustments on the gear geometries (tooth profile shifting).<\/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-2027b26 elementor-widget elementor-widget-image\" data-id=\"2027b26\" 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=\"700\" height=\"305\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-module-and-tooth-height.jpg\" class=\"attachment-large size-large wp-image-1474\" alt=\"gear module and tooth height\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-module-and-tooth-height.jpg 700w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-module-and-tooth-height-600x261.jpg 600w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-module-and-tooth-height-300x131.jpg 300w\" sizes=\"(max-width: 700px) 100vw, 700px\" \/>\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-f8c6ae9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f8c6ae9\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;none&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\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-4b46768\" data-id=\"4b46768\" data-element_type=\"column\">\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-cc47c98 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cc47c98\" 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-139bf91\" data-id=\"139bf91\" 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-d576b74 elementor-widget elementor-widget-heading\" data-id=\"d576b74\" 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<h5 class=\"elementor-heading-title elementor-size-default\"><a href=\"http:\/\/boyanmfg.com\/finding-custom-plastic-gear-manufacturer\/\">Related post: The design and manufacturing of plastic gears<\/a><\/h5>\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-18dc9df\" data-id=\"18dc9df\" 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-ce956ab elementor-widget elementor-widget-image\" data-id=\"ce956ab\" 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\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/elementor\/thumbs\/plastic-gear-with-spline-shaft-r8r87xrp508mp2ygwcl220wd3nsjnraecpf05gs3fg.png\" title=\"plastic gear with spline shaft\" alt=\"plastic gear with spline shaft\" loading=\"lazy\" \/>\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\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-69adcd8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"69adcd8\" 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-c6b7286\" data-id=\"c6b7286\" 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-01f735e elementor-widget elementor-widget-menu-anchor\" data-id=\"01f735e\" 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=\"pressure_angle\"><\/div>\n\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-3c8fb4f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3c8fb4f\" 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-c2bc577\" data-id=\"c2bc577\" 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-1403877 elementor-widget elementor-widget-heading\" data-id=\"1403877\" 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=\"5_Pressure_angle_%CE%B1\"><\/span><a href=\"http:\/\/boyanmfg.com\/insights-gear-common-normal-involute-line\/#\u03b1\">5. Pressure angle (\u03b1)<\/a><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-50 elementor-inner-column elementor-element elementor-element-990cb22\" data-id=\"990cb22\" 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-7f58fe5 elementor-button-info elementor-align-right elementor-widget elementor-widget-button\" data-id=\"7f58fe5\" 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-sm\" href=\"#topic\">\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\">Back to topic \u2191<\/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<div class=\"elementor-element elementor-element-e893067 elementor-widget elementor-widget-text-editor\" data-id=\"e893067\" 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>Simply put, as its name suggests, it is the angle between the direction of contacting force <span style=\"text-decoration: underline;\">on the contact point<\/span> of the tooth and direction of motion of that point on the tooth profile.<\/p><p>In geometry, it is the angle between the line normal to the involute tooth profile and the line normal to its radial line.<\/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-8c5ee2b elementor-widget elementor-widget-image\" data-id=\"8c5ee2b\" 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=\"550\" height=\"476\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/center-distance-of-meshing-gears.jpg\" class=\"attachment-large size-large wp-image-1475\" alt=\"center distance of meshing gears\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/center-distance-of-meshing-gears.jpg 550w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/center-distance-of-meshing-gears-300x260.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-026b264 elementor-widget elementor-widget-image\" data-id=\"026b264\" 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=\"413\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/pressure-angle-of-gear.jpg\" class=\"attachment-large size-large wp-image-1477\" alt=\"pressure angle of gear\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/pressure-angle-of-gear.jpg 600w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/pressure-angle-of-gear-300x207.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-fc59d2b elementor-widget elementor-widget-text-editor\" data-id=\"fc59d2b\" 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>\u00a0<\/p><p>If you want to fully understand the pressure angle then you need to go deeper to understand the <a href=\"http:\/\/boyanmfg.com\/insights-gear-common-normal-involute-line\/#involute\">involute line<\/a> of the tooth profile. This is just an easier way of explanation.<\/p><p>Different points on the tooth profile have different pressure angles, but when we talk about the pressure angle of a gear, it usually refers to that on the reference circle. Most gear use 20\u00b0as the pressure angle, some are 14.5\u00b0or 25\u00b0. 2 mating gears must have the same module and pressure angle.<\/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-f3515c0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f3515c0\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;none&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\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-fd3451a\" data-id=\"fd3451a\" data-element_type=\"column\">\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-fcc6ad8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fcc6ad8\" 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-55825ed\" data-id=\"55825ed\" 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-fc51522 elementor-widget elementor-widget-spacer\" data-id=\"fc51522\" 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<div class=\"elementor-element elementor-element-e168084 elementor-widget elementor-widget-heading\" data-id=\"e168084\" 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<h6 class=\"elementor-heading-title elementor-size-default\"><a href=\"http:\/\/boyanmfg.com\/insights-gear-common-normal-involute-line\/\">Related post: The Involute and Gear Common Normal Length Explained<\/a><\/h6>\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-153b2e4\" data-id=\"153b2e4\" 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-0956342 elementor-widget elementor-widget-image\" data-id=\"0956342\" 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\t<a href=\"http:\/\/boyanmfg.com\/insights-gear-common-normal-involute-line\/\">\n\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<\/a>\n\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\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-a8053e6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a8053e6\" 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-d0fd790\" data-id=\"d0fd790\" 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-5e848f4 elementor-widget elementor-widget-menu-anchor\" data-id=\"5e848f4\" 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=\"z_minimum\"><\/div>\n\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-19a953f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"19a953f\" 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-e458587\" data-id=\"e458587\" 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-06ea34f elementor-widget elementor-widget-heading\" data-id=\"06ea34f\" 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=\"6_Minimum_teeth_number_zmin_without_undercutting_in_gear\"><\/span>6. Minimum teeth number (<strong>z<sub>min<\/sub><\/strong>) without undercutting in gear<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-50 elementor-inner-column elementor-element elementor-element-0447cee\" data-id=\"0447cee\" 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-4b49592 elementor-button-info elementor-align-right elementor-widget elementor-widget-button\" data-id=\"4b49592\" 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-sm\" href=\"#topic\">\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\">Back to topic \u2191<\/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<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-b140b45 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b140b45\" 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-546ea83\" data-id=\"546ea83\" 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-8f16027 elementor-widget elementor-widget-text-editor\" data-id=\"8f16027\" 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>You can not have any teeth number of the gear as you want. If there are too few teeth, the bottom of the teeth will be below the limit point, as a consequence, when the teeth are made by tooth cutters, an excess part of the teeth root will be cut off.<\/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<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-e2606c0\" data-id=\"e2606c0\" 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-7f6f3e2 elementor-widget elementor-widget-image\" data-id=\"7f6f3e2\" 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=\"450\" height=\"250\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/undercutting-of-gear-tooth.jpg\" class=\"attachment-large size-large wp-image-1479\" alt=\"undercutting of gear tooth\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/undercutting-of-gear-tooth.jpg 450w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/undercutting-of-gear-tooth-300x167.jpg 300w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/>\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-ca24231 elementor-widget elementor-widget-text-editor\" data-id=\"ca24231\" 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\tIf the teeth are not machined by tooth cutters, and the teeth profiles are still kept intact, then the 2 gears will get jammed in transmission.\n\nThe formula for calculating the minimum teeth number without undercutting is:\n\n<strong>z<sub>min<\/sub>=2ha*\/sin<sup>2<\/sup>\u03b1<\/strong>\n\nWhen ha*=1, and \u03b1=20\u00b0\uff0cwe will have the z<sub>min<\/sub>=2*1\/(sin20\u00b0\uff09<sup>2<\/sup>=17.09=17\uff08always round down\uff09. So, the minimum teeth number for standard gears is 17.\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-0c02df0 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0c02df0\" 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-4dbba31\" data-id=\"4dbba31\" data-element_type=\"column\">\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-a79660c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a79660c\" 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-4cc485e\" data-id=\"4cc485e\" 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-0d33bc9 elementor-widget elementor-widget-heading\" data-id=\"0d33bc9\" 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=\"7_Profile_shift_coefficient_x\"><\/span>7. Profile shift coefficient (x)<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-1a3de6b elementor-widget elementor-widget-menu-anchor\" data-id=\"1a3de6b\" 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=\"profile_shift\"><\/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<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-a8d70a9\" data-id=\"a8d70a9\" 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-6b67862 elementor-button-info elementor-align-right elementor-widget elementor-widget-button\" data-id=\"6b67862\" 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-sm\" href=\"#topic\">\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\">Back to topic \u2191<\/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<div class=\"elementor-element elementor-element-d6bfcca elementor-widget elementor-widget-text-editor\" data-id=\"d6bfcca\" 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>Usually for the tooth profile, the teeth addendum ha=1*m, and the dedendum hf=1.25*m, however the teeth profile can be moved up or down a little bit:<\/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-b569973 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b569973\" 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-2aac869\" data-id=\"2aac869\" 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-d2b941b elementor-widget elementor-widget-image\" data-id=\"d2b941b\" 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=\"550\" height=\"290\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-profile-shift-cofficient.jpg\" class=\"attachment-large size-large wp-image-1481\" alt=\"gear profile shift coefficient\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-profile-shift-cofficient.jpg 550w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/gear-profile-shift-cofficient-300x158.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\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-206c8d7\" data-id=\"206c8d7\" 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-d26fdae elementor-widget elementor-widget-image\" data-id=\"d26fdae\" 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=\"410\" height=\"500\" src=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/machining-of-plastic-gear-teeth.jpg\" class=\"attachment-large size-large wp-image-1482\" alt=\"\" srcset=\"https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/machining-of-plastic-gear-teeth.jpg 410w, https:\/\/boyanmfg.com\/wp-content\/uploads\/2020\/01\/machining-of-plastic-gear-teeth-246x300.jpg 246w\" sizes=\"(max-width: 410px) 100vw, 410px\" \/>\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-810687b elementor-widget elementor-widget-text-editor\" data-id=\"810687b\" 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<div class=\"fusion-text\"><p>Now we have the profile shift coefficient (x). When the profile is moved upwards, the value of x is positive (x&gt;0), and if the profile is moved downwards, the value of x is negative (x&lt;0).<\/p><p>With the movement of teeth profile, now we have:<\/p><ul><li>addendum ha=(1+x)*m<\/li><li>dedendum hf=(1.25-x)*m<\/li><\/ul><p>Tooth height h=ha+hf=2.25*m, it is still the same as standard teeth.<\/p><\/div><div class=\"fusion-text\"><p>Main reasons for profile shift are:<\/p><p>1) With profile shifted, we can avoid teeth undercutting with fewer teeth number. The formula is as follows:<\/p><p><strong>x<sub>min<\/sub>=(17-z)\/17<\/strong><\/p><p>For example, if you want to the teeth number to be 14, then X=(17-14)\/17=0.176<\/p><p>2)Fine tune of center distance<\/p><p><strong>a=[(m+x1)z1+(m+x2)z2]\/2<\/strong>, so the center distance does not have to be (z1+z2)*m<\/p><p>3)Make the pinion stronger. Usually, the pinion fails prior to the gear, by adding a positive profile shift, the bottom the pinion becomes wider (while the tip becomes narrower) thus making it stronger.<\/p><\/div>\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-9b828f9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9b828f9\" 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-0226883\" data-id=\"0226883\" 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-6c9b4fa elementor-widget elementor-widget-menu-anchor\" data-id=\"6c9b4fa\" 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=\"summary\"><\/div>\n\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-c563f04 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c563f04\" 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-6d9cc3a\" data-id=\"6d9cc3a\" 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-d5eb6e9 elementor-widget elementor-widget-heading\" data-id=\"d5eb6e9\" 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=\"In_summary\"><\/span>In summary:\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\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-38c155b\" data-id=\"38c155b\" 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-3564fdd elementor-button-info elementor-align-right elementor-widget elementor-widget-button\" data-id=\"3564fdd\" 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-sm\" href=\"#topic\">\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\">Back to topic \u2191<\/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<div class=\"elementor-element elementor-element-b3437d0 elementor-widget elementor-widget-text-editor\" data-id=\"b3437d0\" 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>\n<table id=\"tablepress-1\" class=\"tablepress tablepress-id-1\">\n<thead>\n<tr class=\"row-1\">\n\t<th class=\"column-1\">#<\/th><th class=\"column-2\">Item<\/th><th class=\"column-3\">Symbol<\/th><th class=\"column-4\">Formula<\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"row-striping row-hover\">\n<tr class=\"row-2\">\n\t<td class=\"column-1\">1<\/td><td class=\"column-2\">teeth number<\/td><td class=\"column-3\">z<\/td><td class=\"column-4\"><\/td>\n<\/tr>\n<tr class=\"row-3\">\n\t<td class=\"column-1\">2<\/td><td class=\"column-2\">module<\/td><td class=\"column-3\">m<\/td><td class=\"column-4\">m=pitch\/\u03c0<\/td>\n<\/tr>\n<tr class=\"row-4\">\n\t<td class=\"column-1\">3<\/td><td class=\"column-2\">gear ratio<\/td><td class=\"column-3\">i<\/td><td class=\"column-4\">i=d2\/d1=z2\/z1<br \/>\n1: driving gear, and 2: driven gear<\/td>\n<\/tr>\n<tr class=\"row-5\">\n\t<td class=\"column-1\">4<\/td><td class=\"column-2\">addendum coefficient<\/td><td class=\"column-3\">da*<\/td><td class=\"column-4\">da*=1+x<br \/>\nx=0 for standard gears<\/td>\n<\/tr>\n<tr class=\"row-6\">\n\t<td class=\"column-1\">5<\/td><td class=\"column-2\">dedendum coefficient<\/td><td class=\"column-3\">df*<\/td><td class=\"column-4\">df*=1.25-x<\/td>\n<\/tr>\n<tr class=\"row-7\">\n\t<td class=\"column-1\">6<\/td><td class=\"column-2\">profile shift coefficient<\/td><td class=\"column-3\">x<\/td><td class=\"column-4\">For standard gears,, x=0<\/td>\n<\/tr>\n<tr class=\"row-8\">\n\t<td class=\"column-1\">7<\/td><td class=\"column-2\">pressure angle<\/td><td class=\"column-3\">\u03b1<\/td><td class=\"column-4\">\u03b1=20\u00b0 for most gears<br \/>\nOther less used are 14.5\u00b0 and 25\u00b0.<\/td>\n<\/tr>\n<tr class=\"row-9\">\n\t<td class=\"column-1\">8<\/td><td class=\"column-2\">referernce diameter<\/td><td class=\"column-3\">d<\/td><td class=\"column-4\">d=mz<\/td>\n<\/tr>\n<tr class=\"row-10\">\n\t<td class=\"column-1\">9<\/td><td class=\"column-2\">tip diameter<\/td><td class=\"column-3\">da<\/td><td class=\"column-4\">da=d+2Ha* x m, da=(z+2ha*) m<br \/>\nFor standard gears, da=(z+2) x m<\/td>\n<\/tr>\n<tr class=\"row-11\">\n\t<td class=\"column-1\">10<\/td><td class=\"column-2\">root diameter<\/td><td class=\"column-3\">df<\/td><td class=\"column-4\">df=d-2Hf* x m, df=(z-2hf*) x m<br \/>\nFor standard gears, df=(z-2.5) x m<\/td>\n<\/tr>\n<tr class=\"row-12\">\n\t<td class=\"column-1\">11<\/td><td class=\"column-2\">addendum<\/td><td class=\"column-3\">ha<\/td><td class=\"column-4\">ha=m x ha*<br \/>\nFor standard gears, ha=m<\/td>\n<\/tr>\n<tr class=\"row-13\">\n\t<td class=\"column-1\">12<\/td><td class=\"column-2\">dedendum<\/td><td class=\"column-3\">hf<\/td><td class=\"column-4\">hf=m x hf*<br \/>\nFor standard gears, hf=1.25m<\/td>\n<\/tr>\n<tr class=\"row-14\">\n\t<td class=\"column-1\">13<\/td><td class=\"column-2\">tooth height<\/td><td class=\"column-3\">h<\/td><td class=\"column-4\">h=m x (ha*+hf*)<br \/>\nha*+Hf*=2.25 for most gears<\/td>\n<\/tr>\n<tr class=\"row-15\">\n\t<td class=\"column-1\">14<\/td><td class=\"column-2\">center distance<\/td><td class=\"column-3\">a<\/td><td class=\"column-4\">a=m x (z1+z2)\/2 for standard gears<br \/>\na=[(m+x1)z1+(m+x2)z2]\/2 for profile shifted gears<\/td>\n<\/tr>\n<tr class=\"row-16\">\n\t<td class=\"column-1\">15<\/td><td class=\"column-2\">Mininum teeth number without undercutting<\/td><td class=\"column-3\">Zmin<\/td><td class=\"column-4\">Zmin=2ha*\/sin\u03b1^2<br \/>\nZmin=17 when ha*=1,  \u03b1=20\u00b0<\/td>\n<\/tr>\n<tr class=\"row-17\">\n\t<td class=\"column-1\">16<\/td><td class=\"column-2\">Minimun profile shift without undercutting<\/td><td class=\"column-3\">Xmin<\/td><td class=\"column-4\">Xmin=(17-z)\/17<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<!-- #tablepress-1 from cache --><\/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-65c8e6b elementor-widget elementor-widget-spacer\" data-id=\"65c8e6b\" 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-e590b75 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e590b75\" 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-6030336\" data-id=\"6030336\" data-element_type=\"column\">\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-a1d4c84 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a1d4c84\" 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-05a6338\" data-id=\"05a6338\" 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-0c3af75 elementor-view-default elementor-widget elementor-widget-icon\" data-id=\"0c3af75\" data-element_type=\"widget\" data-widget_type=\"icon.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-icon-wrapper\">\n\t\t\t<div class=\"elementor-icon\">\n\t\t\t<i aria-hidden=\"true\" class=\"fas fa-question-circle\"><\/i>\t\t\t<\/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<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-b7302d7\" data-id=\"b7302d7\" 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-e6d890b elementor-widget elementor-widget-heading\" data-id=\"e6d890b\" 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=\"Frequently_Asked_Questions%E2%80%8B\"><\/span>Frequently Asked Questions\u200b<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\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-9498ff8 elementor-widget elementor-widget-toggle\" data-id=\"9498ff8\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1551\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1551\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">What is the most appropriate pressure angle for gears?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1551\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1551\"><h4>Introduction to Gear Forces<\/h4><p>In the meshing process between two gears, the force exerted by the driving gear on the driven gear can be decomposed into a normal force perpendicular to the surface of the driven gear and a tangential force perpendicular to the normal force. The tangential force does not participate in driving the driven gear, and it causes wear between the two gears. The angle at the meshing point of the driving and driven gears is largest at the beginning and end of engagement and smaller in the middle. When the meshing point is on the centerline of the two gears, it equals zero. Therefore, a smaller angle can improve transmission efficiency and reduce wear.<\/p><h4>Relation Between Pressure Angle and Meshing Angle<\/h4><p>The pressure angle is directly related to the meshing angle. On the other hand, a smaller pressure angle results in thinner gear roots, which reduces the strength of the gears. Therefore, it&#8217;s important to find a balance.<\/p><h4><strong>Industrial Standards for Gear Pressure Angles<\/strong><\/h4><ol><li>In current industrial production, most standard gears use a 20\u00b0 pressure angle.<\/li><li>Gears designed for light loads and high speeds often use a 14.5\u00b0 pressure angle, which has the advantages of lower noise and higher transmission efficiency.<\/li><li>Gears designed for low-speed and heavy-load applications use a 25\u00b0 pressure angle, which offers higher tooth strength but at the cost of lower transmission efficiency and higher noise.<\/li><\/ol><h4>Plastic Gears<\/h4><p>For plastic gears, any pressure angle can be chosen since standard cutting tools are not required for their manufacturing. However, for simplicity in design, it&#8217;s common to stick with these standard values.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1552\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-1552\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">What is the difference between the circumference circle and the pitch circle?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1552\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-1552\"><p>The circumference circle is the basis for gear calculations. Its diameter is calculated as the module (m) multiplied by the number of teeth (Z). Essentially, it&#8217;s a theoretical circle used mainly for calculations, with other gear parameters derived from it.<\/p><p>The pitch diameter, on the other hand, is defined during the actual meshing of two gears. It&#8217;s the circle formed by the intersection of the gears&#8217; common normal and the line connecting their centers, passing through the point of tangency. The pitch circles of two meshing gears are tangent to each other. However, the circumference circles might not always be tangent<\/p><p>In standard gear designs, the circumference circle and the pitch circle typically overlap. However, if the center distance is adjusted to increase backlash or if the gears have been modified, the circumference circle and the pitch circle may differ.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1553\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-1553\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Are the tooth thickness and slot width on the circumference circle equal?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1553\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-1553\"><p>Yes. In standard designs, the tooth thickness and slot width on the circumference circle are equal.<\/p><p>However, in practical applications, to allow for some backlash while maintaining the standard center distance, the tooth thickness is made slightly thinner.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1554\" class=\"elementor-tab-title\" data-tab=\"4\" role=\"button\" aria-controls=\"elementor-tab-content-1554\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">How can appropriate backlash be ensured in gear meshing?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1554\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"4\" role=\"region\" aria-labelledby=\"elementor-tab-title-1554\"><p>One method is to make the tooth thickness slightly smaller than the slot width on the circumference circle.<\/p><p>Another method is to install the gears at a center distance slightly larger than the standard.<\/p><p>The required size of the backlash depends on the manufacturing precision of the gears; higher precision reduces the need for backlash.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1555\" class=\"elementor-tab-title\" data-tab=\"5\" role=\"button\" aria-controls=\"elementor-tab-content-1555\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">What is the base circle pitch of a gear?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1555\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"5\" role=\"region\" aria-labelledby=\"elementor-tab-title-1555\"><p>The base circle of a gear is the circle from which its involute is generated. Its pitch is the arc length between identical points on the profiles of two adjacent teeth on the base circle, so:<\/p><p style=\"padding-left: 40px;\">Pb = Db\/Z.<\/p><p>Here, Db is the diameter of the base circle.<\/p><p style=\"padding-left: 40px;\">Or Pb = Df * cos(\u03b1) \/ Z = m\u03c0 * cos(\u03b1),<\/p><p>where Df is the diameter of the circumference circle, m is the module of the gear, and \u03b1 is the pressure angle of the circumference circle.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1556\" class=\"elementor-tab-title\" data-tab=\"6\" role=\"button\" aria-controls=\"elementor-tab-content-1556\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">What are the conditions for correct engagement of two gears?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1556\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"6\" role=\"region\" aria-labelledby=\"elementor-tab-title-1556\"><p>1. For spur gears, it&#8217;s required that the meshing of one pair of teeth is synchronized with the meshing of the previous pair. This demands that their base circle pitches are equal, meaning:<\/p><p>m1 * cos(\u03b11) = m2 * cos(\u03b12).<\/p><p>From this, it can be inferred that the modules (m) of a pair of meshing gears do not necessarily have to be equal.<\/p><p>2. At the same time, the degree of engagement (contact ratio \u03b5) is greater than 1<\/p><p>For gears manufactured with standard cutting tools, due to the standardization and serialization of the tools, it&#8217;s common practice to use the same module and pressure angle of the circumference circle for both gears.<\/p><p>3. For helical gears, it&#8217;s also necessary that their helix angles are equal, assuming their axes of installation are parallel.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1557\" class=\"elementor-tab-title\" data-tab=\"7\" role=\"button\" aria-controls=\"elementor-tab-content-1557\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">What is the contact ratio (\u03b5) of two meshing gears?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1557\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"7\" role=\"region\" aria-labelledby=\"elementor-tab-title-1557\"><p>The contact ratio (\u03b5) is the length of the common normal segment between two meshing gears, which is cut by the addendum circles of the gears, divided by the base pitch (Pb) of the gear.<\/p><ul><li style=\"list-style-type: none;\"><ul><li>When \u03b5 &lt;1, the gears cannot function correctly because there are moments when no teeth are in contact.<\/li><li>If 1 &lt; \u03b5 &lt; 2, there are times when only one tooth is in contact. For example, with \u03b5 = 1.63, you can imagine an average of 1.63 pairs of teeth meshing. During 37% of the transmission process, only one tooth is in engagement, while during 63%, two teeth are in engagement, leading to a greater impact during transmission.<\/li><li>If \u03b5 &gt; 2, at any given time, more than two pairs of teeth are in contact, resulting in smoother transmission.<\/li><\/ul><\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1558\" class=\"elementor-tab-title\" data-tab=\"8\" role=\"button\" aria-controls=\"elementor-tab-content-1558\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">How can the contact ratio (\u03b5) of two gears be increased?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1558\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"8\" role=\"region\" aria-labelledby=\"elementor-tab-title-1558\"><p>The number of teeth (Z) on the gears is an important factor affecting the contact ratio.<\/p><p>For smaller gears, helical gears are often used to increase the contact ratio. However, the manufacturing cost of helical gears is significantly higher than that of spur gears.<\/p><p>Another method is to use a smaller pressure angle of the pitch circle, but this has a minor effect.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1559\" class=\"elementor-tab-title\" data-tab=\"9\" role=\"button\" aria-controls=\"elementor-tab-content-1559\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">What determines the lifespan of a gear?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-1559\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"9\" role=\"region\" aria-labelledby=\"elementor-tab-title-1559\"><p>The lifespan of a gear is mainly determined by wear and fatigue fracture. These issues stem from various factors such as low gear precision, inappropriate backlash, poor lubrication, overheating, and more. While it&#8217;s challenging to calculate lifespan with empirical formulas, the precision of the gear and the material used are critical factors for its longevity.<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/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-d226747 elementor-widget elementor-widget-spacer\" data-id=\"d226747\" 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-d2bb396 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d2bb396\" 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-9c8aabe\" data-id=\"9c8aabe\" 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-607dea5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"607dea5\" 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-497a076\" data-id=\"497a076\" 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-e1c4379 elementor-widget elementor-widget-image\" data-id=\"e1c4379\" 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-6312b39\" data-id=\"6312b39\" 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-308bd76 elementor-widget elementor-widget-heading\" data-id=\"308bd76\" 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-5d3f7e1\" data-id=\"5d3f7e1\" 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-57277c7 elementor-align-center elementor-mobile-align-justify elementor-widget elementor-widget-button\" data-id=\"57277c7\" 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>\u0647\u0630\u0647 \u0646\u0633\u062e\u0629 \u0645\u0628\u0633\u0637\u0629 \u0645\u0646 \u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u062a\u0631\u0648\u0633 \u0648\u0635\u064a\u063a \u062d\u0633\u0627\u0628 \u0627\u0644\u0623\u0633\u0646\u0627\u0646. \u0647\u0630\u0627 \u0627\u0644\u0645\u0646\u0634\u0648\u0631 \u064a\u0647\u062f\u0641 \u0625\u0644\u0649 \u0634\u0631\u062d \u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u062a\u0631\u0648\u0633 \u0648\u0635\u064a\u063a \u062d\u0633\u0627\u0628 \u0627\u0644\u0623\u0633\u0646\u0627\u0646 \u0628\u0637\u0631\u064a\u0642\u0629 \u0623\u0633\u0647\u0644 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\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u062a\u0631\u0648\u0633 \u0648\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u062d\u0633\u0627\u0628 \u0627\u0644\u0623\u0633\u0646\u0627\u0646<\/span><\/a><\/p>","protected":false},"author":1,"featured_media":1485,"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":100,"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-1463","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-manufacturing-knowledge"],"acf":[],"_links":{"self":[{"href":"https:\/\/boyanmfg.com\/ar\/wp-json\/wp\/v2\/posts\/1463","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/boyanmfg.com\/ar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/boyanmfg.com\/ar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/boyanmfg.com\/ar\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/boyanmfg.com\/ar\/wp-json\/wp\/v2\/comments?post=1463"}],"version-history":[{"count":0,"href":"https:\/\/boyanmfg.com\/ar\/wp-json\/wp\/v2\/posts\/1463\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/boyanmfg.com\/ar\/wp-json\/wp\/v2\/media\/1485"}],"wp:attachment":[{"href":"https:\/\/boyanmfg.com\/ar\/wp-json\/wp\/v2\/media?parent=1463"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/boyanmfg.com\/ar\/wp-json\/wp\/v2\/categories?post=1463"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/boyanmfg.com\/ar\/wp-json\/wp\/v2\/tags?post=1463"}],"curies":[{"name":"\u062f\u0628\u0644\u064a\u0648 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