{"id":563,"date":"2015-07-27T21:12:12","date_gmt":"2015-07-27T19:12:12","guid":{"rendered":"http:\/\/www.a-ueberbach.de\/cnc\/?p=563"},"modified":"2016-10-15T18:59:12","modified_gmt":"2016-10-15T16:59:12","slug":"exkurs-berechnung-der-zahnstangen","status":"publish","type":"post","link":"https:\/\/cnc.a-ueberbach.de\/en\/mechanik\/exkurs-berechnung-der-zahnstangen\/","title":{"rendered":"Exkurs: Berechnung der Zahnstangen"},"content":{"rendered":"<p>Heute mal ein kleiner Exkurs in die Berechnung der Zahnstangenantriebe (Auch als eigene Gedankenst\u00fctze).<\/p>\n<p><a href=\"http:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-560\" src=\"http:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-1024x521.jpg\" alt=\"IMG_4001 copy\" width=\"648\" height=\"330\" srcset=\"https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-1024x521.jpg 1024w, https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-300x152.jpg 300w, https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-620x315.jpg 620w, https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-1536x781.jpg 1536w, https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-2048x1041.jpg 2048w\" sizes=\"auto, (max-width: 648px) 100vw, 648px\" \/><\/a><\/p>\n<p>Grunds\u00e4tzlich rechnet sich der Zahnstangenantrieb wie ein normales Zahnrad&#8230;<\/p>\n<p>Wir brauchen zun\u00e4chst vom Antriebszahnrad folgende Daten:<\/p>\n<ul>\n<li>Die Anzahl der Z\u00e4hne<\/li>\n<li>Das Modul (Gr\u00f6\u00dfe der Z\u00e4hne)<\/li>\n<\/ul>\n<p>Unsere Zahnr\u00e4der haben ein Modul von 2,0 sowie 15 Z\u00e4hne.<\/p>\n<p>Hieraus errechnet sich ein Teilkreisdurchmesser (Modul x Anzahl der Z\u00e4hne) von 30mm sowie eine Abrollstrecke (Teilkreisdurchmesser x pi) von 94,25mm pro voller Umdrehung des Zahnrades oder in anderen Worten 6,28mm Bewegung je Zahn (Abrollstrecke \/ Anzahl der Z\u00e4hne).<\/p>\n<p>Das w\u00e4ren bei 1.000 <span class=\"explanatory-dictionary-highlight\" data-definition=\"explanatory-dictionary-definition-26\">U\/min<\/span> dann 94 Meter in der Minute oder 26Km\/h und das Portal w\u00fcrde die 2 Meter Verfahrweg auf der Y Achse rechnerisch in nur 1,3 Sekunden &#8220;abspulen&#8221;. Die Leadshine 86HS80-EC Schrittmotoren erreichen maximal etwa 2.000 <span class=\"explanatory-dictionary-highlight\" data-definition=\"explanatory-dictionary-definition-26\">U\/min<\/span>, vergleichbare Servo Systeme sogar 3.000 <span class=\"explanatory-dictionary-highlight\" data-definition=\"explanatory-dictionary-definition-26\">U\/min<\/span> und mehr. Somit w\u00e4ren wir schon bei 50 bzw. 78Km\/h.<\/p>\n<p>Alles viel zu schnell, weswegen eine Getriebeuntersetzung im Verh\u00e4ltnis 1:5 zwischengeschaltet wird. Die Geschwindigkeit reduziert sich damit auf 19m\/min bei 1.000 bzw. 38m\/min bei 2.000 Umdrehungen des Motors bei gesteigertem Drehmoment.<\/p>\n<p>Hier noch unsere Excel Berechnung: <a href=\"http:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/Zahnrad_v4.xlsx\">Zahnrad_v4.<\/a><\/p>\n<p><a href=\"http:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4034-100-768x10241.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone  wp-image-727\" src=\"http:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4034-100-768x10241-768x1024.jpg\" alt=\"IMG_4034-100-768x1024\" width=\"648\" height=\"864\" srcset=\"https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4034-100-768x10241.jpg 768w, https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4034-100-768x10241-225x300.jpg 225w\" sizes=\"auto, (max-width: 648px) 100vw, 648px\" \/><\/a><\/p>\n<h3><\/h3>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Berechnung der Verfahrgeschwindigkeit und des Verfahrweges pro Motorumdrehung<\/p>\n","protected":false},"author":1,"featured_media":560,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","_analytify_skip_tracking":false,"footnotes":""},"categories":[4],"tags":[134,136,135],"class_list":["post-563","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mechanik","tag-berechnung","tag-zahnrad","tag-zahnstange","has_thumb"],"translation":{"provider":"WPGlobus","version":"3.0.2","language":"en","enabled_languages":["de","en"],"languages":{"de":{"title":true,"content":true,"excerpt":true},"en":{"title":false,"content":false,"excerpt":false}}},"uagb_featured_image_src":{"full":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy.jpg",3124,1588,false],"thumbnail":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-220x165.jpg",220,165,true],"medium":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-300x152.jpg",300,152,true],"medium_large":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy.jpg",3124,1588,false],"large":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-1024x521.jpg",620,315,true],"1536x1536":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-1536x781.jpg",1536,781,true],"2048x2048":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-2048x1041.jpg",2048,1041,true],"wp_review_large":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-300x200.jpg",300,200,true],"wp_review_small":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-60x57.jpg",60,57,true],"post-thumbnail":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-220x162.jpg",220,162,true],"pointpro-featured":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-220x162.jpg",220,162,true],"pointpro-carousel":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-140x130.jpg",140,130,true],"pointpro-bigthumb":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-620x315.jpg",620,315,true],"pointpro-mediumthumb":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-300x200.jpg",300,200,true],"pointpro-smallthumb":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-140x100.jpg",140,100,true],"pointpro-widgetthumb":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-60x57.jpg",60,57,true],"pointpro-widgetfull":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-300x200.jpg",300,200,true],"pointpro-slider":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-980x400.jpg",980,400,true],"pointpro-project-3":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-286x180.jpg",286,180,true],"pointpro-project-4":["https:\/\/cnc.a-ueberbach.de\/wp-content\/uploads\/IMG_4001-copy-215x150.jpg",215,150,true]},"uagb_author_info":{"display_name":"Andr\u00e9","author_link":"https:\/\/cnc.a-ueberbach.de\/en\/author\/andre\/"},"uagb_comment_info":4,"uagb_excerpt":"Berechnung der Verfahrgeschwindigkeit und des Verfahrweges pro Motorumdrehung","_links":{"self":[{"href":"https:\/\/cnc.a-ueberbach.de\/en\/wp-json\/wp\/v2\/posts\/563","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cnc.a-ueberbach.de\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cnc.a-ueberbach.de\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cnc.a-ueberbach.de\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cnc.a-ueberbach.de\/en\/wp-json\/wp\/v2\/comments?post=563"}],"version-history":[{"count":16,"href":"https:\/\/cnc.a-ueberbach.de\/en\/wp-json\/wp\/v2\/posts\/563\/revisions"}],"predecessor-version":[{"id":1727,"href":"https:\/\/cnc.a-ueberbach.de\/en\/wp-json\/wp\/v2\/posts\/563\/revisions\/1727"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cnc.a-ueberbach.de\/en\/wp-json\/wp\/v2\/media\/560"}],"wp:attachment":[{"href":"https:\/\/cnc.a-ueberbach.de\/en\/wp-json\/wp\/v2\/media?parent=563"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cnc.a-ueberbach.de\/en\/wp-json\/wp\/v2\/categories?post=563"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cnc.a-ueberbach.de\/en\/wp-json\/wp\/v2\/tags?post=563"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}