{"id":2301,"date":"2026-06-24T01:54:52","date_gmt":"2026-06-24T01:54:52","guid":{"rendered":"https:\/\/helicalcutgears.top\/?p=2301"},"modified":"2026-06-24T01:56:23","modified_gmt":"2026-06-24T01:56:23","slug":"helical-gear-contact-ratio","status":"publish","type":"post","link":"https:\/\/helicalcutgears.top\/sk\/helical-gear-contact-ratio\/","title":{"rendered":"Kontaktn\u00fd pomer \u0161pir\u00e1lov\u00e9ho ozuben\u00e9ho kolesa \u2013 Ako vypo\u010d\u00edta\u0165 \u03b5_\u03b1 a \u03b5_\u03b2 a pre\u010do je d\u00f4le\u017eit\u00e1 prahov\u00e1 hodnota 1,0"},"content":{"rendered":"
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Kontaktn\u00fd pomer \u0161pir\u00e1lov\u00e9ho ozuben\u00e9ho kolesa \u2013 V\u00fdpo\u010det \u03b5_\u03b1 a \u03b5_\u03b2 s praktick\u00fdm pr\u00edkladom<\/h1>\n

Kontaktn\u00fd pomer sa objavuje takmer v ka\u017edej diskusii o kon\u0161trukcii \u0161pir\u00e1lov\u00fdch ozuben\u00fdch kolies \u2013 no zriedka sa vypo\u010d\u00edtava z prv\u00fdch princ\u00edpov. T\u00e1to pr\u00edru\u010dka odvodzuje \u03b5_\u03b1 a \u03b5_\u03b2 z geometrie ozuben\u00e9ho kolesa, rozober\u00e1 kompletn\u00fd numerick\u00fd pr\u00edklad, vysvet\u013euje kritick\u00fa prahov\u00fa hodnotu \u03b5_\u03b2 \u2265 1 a ukazuje, ako optimalizova\u0165 celkov\u00fd kontaktn\u00fd pomer \u03b5_\u03b3 porovnan\u00edm uhla \u0161pir\u00e1ly so \u0161\u00edrkou \u010delnej plochy.<\/p>\n

Potvr\u010fte kontaktn\u00fd pomer pre va\u0161e zariadenie \u2192<\/a><\/p>\n<\/div>\n<\/div>\n

Pre\u010do je kontaktn\u00fd pomer najd\u00f4le\u017eitej\u0161\u00edm prediktorom v\u00fdkonu<\/h2>\n

Celkov\u00fd kontaktn\u00fd pomer \u03b5_\u03b3 \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koleso<\/strong> Dvojica zubov ur\u010duje viac aspektov v\u00fdkonu ako ktor\u00fdko\u013evek in\u00fd samostatn\u00fd parameter. Stanovuje hladinu hluku (vy\u0161\u0161ia \u03b5_\u03b3 = ni\u017e\u0161ia amplit\u00fada chyby prenosu), nosnos\u0165 (vy\u0161\u0161ia \u03b5_\u03b3 = viac p\u00e1rov zubov zdie\u013eaj\u00facich za\u0165a\u017eenie) a kvalitu plynul\u00e9ho chodu (\u03b5_\u03b3 pod kritickou prahovou hodnotou vytv\u00e1ra cite\u013en\u00fa zmenu kr\u00fatiaceho momentu pri sie\u0165ovej frekvencii). V\u0161etky v\u00fdhody \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koles\u00e1<\/strong> cez \u010deln\u00e9 ozuben\u00e9 koles\u00e1 v kone\u010dnom d\u00f4sledku vypl\u00fdvaj\u00fa z vy\u0161\u0161ieho celkov\u00e9ho kontaktn\u00e9ho pomeru, ktor\u00fd umo\u017e\u0148uje \u0161pir\u00e1lov\u00fd tvar zuba \u2013 konkr\u00e9tne z nenulov\u00e9ho kontaktn\u00e9ho pomeru prekrytia \u03b5_\u03b2, ktor\u00fd \u010deln\u00e9 ozuben\u00e9 koleso nem\u00f4\u017ee dosiahnu\u0165.<\/p>\n

Spolo\u010dnos\u0165 Korea Ever-Power vypo\u010d\u00edtava a nahlasuje celkov\u00fd kontaktn\u00fd pomer ako s\u00fa\u010das\u0165 \u0161tandardn\u00e9ho technick\u00e9ho presk\u00famania pre ka\u017ed\u00fd ozuben\u00e9 koleso so \u0161pir\u00e1lov\u00fdm rezom<\/a> objedn\u00e1vka \u2013 potvrdenie, \u017ee \u0161pecifikovan\u00e1 kombin\u00e1cia modulu, po\u010dtu zubov, uhla \u0161pir\u00e1ly a \u0161\u00edrky \u010dela dosahuje \u03b5_\u03b3 po\u017eadovan\u00fa pre ciele aplik\u00e1cie t\u00fdkaj\u00face sa hluku a rozdelenia za\u0165a\u017eenia.<\/p>\n

Tri zlo\u017eky celkov\u00e9ho kontaktn\u00e9ho pomeru<\/h2>\n

Celkov\u00fd kontaktn\u00fd pomer \u03b5_\u03b3 \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koleso<\/strong> p\u00e1r je s\u00fa\u010dtom dvoch nez\u00e1visl\u00fdch zlo\u017eiek:<\/p>\n

\u03b5_\u03b3 = \u03b5_\u03b1 + \u03b5_\u03b2<\/p>\n

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\u03b5_\u03b1 \u2014 Pomer kontaktu profilu (prie\u010dny)<\/strong><\/p>\n

Meria, ko\u013eko p\u00e1rov zubov je s\u00fa\u010dasne v kontakte pozd\u013a\u017e v\u00fd\u0161ky zuba (dodatok k dedendumu). Pre \u0161tandardn\u00e9 ozuben\u00e9 koles\u00e1 pri \u03b1_n = 20\u00b0 je \u03b5_\u03b1 \u2248 1,4\u20131,8. Je to rovnak\u00fd parameter, ak\u00fd plat\u00ed pre \u010deln\u00e9 ozuben\u00e9 koles\u00e1 \u2013 z\u00e1vis\u00ed od modulu, po\u010dtu zubov a uhla z\u00e1beru, ale nie od uhla sklonu \u0161pir\u00e1ly. \u03b5_\u03b1 je pr\u00edtomn\u00fd v ka\u017edom type ozuben\u00e9ho kolesa.<\/p>\n<\/div>\n

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\u03b5_\u03b2 \u2014 Pomer prekrytia (axi\u00e1lny) kontakt<\/strong><\/p>\n

Meria, ko\u013eko rozstupov zubov v d\u013a\u017eke zuba je s\u00fa\u010dasne zapojen\u00fdch po \u0161\u00edrke \u010delnej plochy. Pre \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koleso<\/strong>, \u03b5_\u03b2 = b \u00d7 sin \u03b2 \/ (\u03c0 \u00d7 Mn). Toto je jedine\u010dn\u00fd parameter \u0161pir\u00e1ly \u2013 \u010deln\u00e9 ozuben\u00e9 koleso (\u03b2 = 0) m\u00e1 v\u017edy \u03b5_\u03b2 = 0. Ka\u017ed\u00e1 \u010fal\u0161ia jednotka \u03b5_\u03b2 nad nulou predstavuje jeden \u010fal\u0161\u00ed rozstup zubov \u0161pir\u00e1lov\u00e9ho kontaktu, \u010do prispieva k rozdeleniu za\u0165a\u017eenia a zn\u00ed\u017eeniu hluku.<\/p>\n<\/div>\n<\/div>\n

Vzorec a v\u00fdpo\u010det kontaktn\u00e9ho pomeru profilu \u03b5_\u03b1<\/h2>\n

Presn\u00fd vzorec<\/h3>\n

Kontaktn\u00fd pomer profilu pre \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koleso<\/strong> p\u00e1r (meran\u00e9 v prie\u010dnej rovine) je:<\/p>\n

\u03b5_\u03b1 = [\u221a(r_a1\u00b2 \u2212 r_b1\u00b2) + \u221a(r_a2\u00b2 \u2212 r_b2\u00b2) \u2212 C \u00d7 sin \u03b1_t] \/ (\u03c0 \u00d7 m_t \u00d7 cos \u03b1_t)<\/p>\n

kde: r_a = polomer hrotu (doplnkovej kru\u017enice), r_b = polomer z\u00e1kladnej kru\u017enice = d\/2 \u00d7 cos \u03b1_t, C = stredov\u00e1 vzdialenos\u0165, \u03b1_t = prie\u010dny tlakov\u00fd uhol = arctan(tan \u03b1_n \/ cos \u03b2), m_t = prie\u010dny modul = Mn \/ cos \u03b2.<\/p>\n

Praktick\u00e1 aproxim\u00e1cia pre \u0161tandardn\u00e9 ozuben\u00e9 koles\u00e1<\/h3>\n

Pre \u0161tandardn\u00e9 ozuben\u00e9 koles\u00e1 s koncovkou (ha = Mn, \u03b1_n = 20\u00b0) je vhodn\u00e1 aproxim\u00e1cia s presnos\u0165ou na \u00b10,02:<\/p>\n

\u03b5_\u03b1 \u2248 1,88 \u2212 3,2 \u00d7 (1\/z\u2081 + 1\/z\u2082) [plat\u00ed pre \u03b1_n = 20\u00b0, \u0161tandardn\u00fd dodatok]<\/p>\n

T\u00e1to aproxim\u00e1cia ud\u00e1va prie\u010dny kontaktn\u00fd pomer priamo z po\u010dtu zubov \u2013 nie s\u00fa potrebn\u00e9 \u017eiadne v\u00fdpo\u010dty polomeru. Pre n\u00edzky po\u010det zubov (pastorok z\u2081 < 17) aproxim\u00e1cia mierne nadhodnocuje \u03b5_\u03b1; pre z\u2081 \u2265 20 je dostato\u010dne presn\u00e1 pre predbe\u017en\u00fd n\u00e1vrh.<\/p>\n

Pomer prekrytia kontaktu \u03b5_\u03b2 \u2013 vzorec a kritick\u00e1 prahov\u00e1 hodnota<\/h2>\n

\u03b5_\u03b2 = b \u00d7 sin \u03b2 \/ (\u03c0 \u00d7 Mn)<\/p>\n

Kde b = \u0161\u00edrka plochy (mm), \u03b2 = uhol skrutkovice (stupne), Mn = norm\u00e1lov\u00fd modul (mm). Vzorec odha\u013euje tri vz\u00e1jomn\u00e9 z\u00e1vislosti:<\/p>\n