{"id":2407,"date":"2026-06-26T05:15:50","date_gmt":"2026-06-26T05:15:50","guid":{"rendered":"https:\/\/helicalcutgears.top\/?p=2407"},"modified":"2026-06-26T05:15:50","modified_gmt":"2026-06-26T05:15:50","slug":"helical-gear-helix-angle-selection-guide","status":"publish","type":"post","link":"https:\/\/helicalcutgears.top\/cs\/helical-gear-helix-angle-selection-guide\/","title":{"rendered":"V\u00fdb\u011br \u00fahlu stoup\u00e1n\u00ed \u0161roubovice \u0161ikm\u00e9ho ozuben\u00e9ho kola"},"content":{"rendered":"
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V\u00fdb\u011br \u00fahlu stoup\u00e1n\u00ed \u0161roubovice \u0161ikm\u00e9ho ozuben\u00e9ho kola \u2013 technick\u00e9 kompromisy od \u03b2 = 8\u00b0 do \u03b2 = 35\u00b0<\/h1>\n

\u00dahel \u0161roubovice \u03b2 je jedin\u00e1 konstruk\u010dn\u00ed prom\u011bnn\u00e1, kter\u00e1 nejv\u00edce odli\u0161uje spir\u00e1lov\u00e9 ozuben\u00e9 kolo<\/strong> z \u010deln\u00edho ozuben\u00e9ho kola \u2013 a volba \u03b2 ur\u010duje kontaktn\u00ed pom\u011br ozuben\u00e9ho kola, hladinu hluku, axi\u00e1ln\u00ed axi\u00e1ln\u00ed zat\u00ed\u017een\u00ed, \u00fa\u010dinnost a v\u00fdb\u011br lo\u017eiska. Neexistuje univerz\u00e1ln\u011b spr\u00e1vn\u00fd \u00fahel stoup\u00e1n\u00ed \u0161roubovice: spr\u00e1vn\u00e9 \u03b2 pro tiska\u0159sk\u00fd stroj spir\u00e1lov\u00e9 ozuben\u00e9 kolo<\/strong> (maxim\u00e1ln\u00ed hladkost, \u03b2 = 25\u00b0) je nespr\u00e1vn\u00e1 pro robotick\u00e9 z\u00e1p\u011bstn\u00ed soukol\u00ed (minim\u00e1ln\u00ed axi\u00e1ln\u00ed tlak, \u03b2 = 12\u00b0) a zcela odli\u0161n\u00e1 od dvojit\u00e9ho spir\u00e1lov\u00e9ho lodn\u00edho soukol\u00ed (maxim\u00e1ln\u00ed \u0161roubovice, \u03b2 = 35\u00b0 na sekci). Tato p\u0159\u00edru\u010dka poskytuje r\u00e1mec zalo\u017een\u00fd na vzorc\u00edch pro spr\u00e1vn\u00fd v\u00fdb\u011br \u03b2 pro ka\u017edou aplikaci.<\/p>\n

Z\u00edskejte doporu\u010den\u00ed pro \u00fahel \u0161roubovice \u2192<\/a><\/p>\n<\/div>\n<\/div>\n

\u010cty\u0159i \u00fa\u010dinky \u00fahlu \u0161roubovice \u2013 co se m\u011bn\u00ed s rostouc\u00edm \u03b2<\/h2>\n

Ka\u017ed\u00e9 rozhodnut\u00ed o spir\u00e1lov\u00e9 ozuben\u00e9 kolo<\/strong> \u00dahel \u0161roubovice zahrnuje \u010dty\u0159i simult\u00e1nn\u00ed efekty, kter\u00e9 se vz\u00e1jemn\u011b ovliv\u0148uj\u00ed. Pochopen\u00ed v\u0161ech \u010dty\u0159 \u2013 nejen efektu \u0161umu \u2013 je nezbytn\u00e9 pro spr\u00e1vn\u00fd v\u00fdb\u011br parametru \u03b2:<\/p>\n

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\u2191 Pom\u011br p\u0159ekryt\u00ed kontaktu \u03b5_\u03b2<\/p>\n

Vy\u0161\u0161\u00ed \u03b2 \u2192 v\u00edce sou\u010dasn\u00fdch kontaktn\u00edch p\u00e1r\u016f zub\u016f \u2192 plynulej\u0161\u00ed p\u0159enos s\u00edly \u2192 ni\u017e\u0161\u00ed chyba p\u0159enosu \u2192 m\u00e9n\u011b hluku a vibrac\u00ed. To je hlavn\u00ed d\u016fvod, pro\u010d in\u017een\u00fd\u0159i vol\u00ed vy\u0161\u0161\u00ed \u00fahly \u0161roubovice pro p\u0159esnost a tich\u00fd chod. spir\u00e1lov\u00e9 ozuben\u00e9 kolo<\/strong> aplikace.<\/p>\n<\/div>\n

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\u2191 Axi\u00e1ln\u00ed axi\u00e1ln\u00ed s\u00edla F_a<\/p>\n

Vy\u0161\u0161\u00ed \u03b2 \u2192 v\u011bt\u0161\u00ed slo\u017eka axi\u00e1ln\u00ed s\u00edly na rozte\u010dn\u00e9 kru\u017enici \u2192 n\u00e1ro\u010dn\u011bj\u0161\u00ed axi\u00e1ln\u00ed lo\u017eiska h\u0159\u00eddele \u2192 v extr\u00e9mn\u00edch p\u0159\u00edpadech je nutn\u00e1 dvojit\u00e1 \u0161roubovicov\u00e1 konfigurace k \u00fapln\u00e9mu vynulov\u00e1n\u00ed axi\u00e1ln\u00ed s\u00edly. Toto je hlavn\u00ed nev\u00fdhoda vysok\u00fdch \u00fahl\u016f \u0161roubovice u jedno\u0161roubovcov\u00fdch lo\u017eisk spir\u00e1lov\u00e9 ozuben\u00e9 kolo<\/strong> pohony.<\/p>\n<\/div>\n

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\u2191 Zlep\u0161en\u00ed dynamick\u00e9ho faktoru K_V<\/p>\n

Vy\u0161\u0161\u00ed \u03b2 zvy\u0161uje \u03b5\u03b2, co\u017e sni\u017euje zm\u011bnu amplitudy zat\u00ed\u017een\u00ed na s\u00ed\u0165ov\u00e9 frekvenci \u2013 zdroji buzen\u00ed pro dynamick\u00fd faktor K_V. Hodnoty K_V dle metody ISO 6336-1 B jsou ni\u017e\u0161\u00ed pro \u0161ikm\u00e1 ozuben\u00e1 kola<\/strong> s vy\u0161\u0161\u00edm \u03b5_\u03b2 p\u0159i stejn\u00e9 rychlosti na ose stoup\u00e1n\u00ed, co\u017e umo\u017e\u0148uje kompaktn\u011bj\u0161\u00ed dimenzov\u00e1n\u00ed ozuben\u00e9ho kola pro stejn\u00fd jmenovit\u00fd v\u00fdkon.<\/p>\n<\/div>\n

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\u2193 \u00da\u010dinnost (mezn\u00ed)<\/p>\n

Vy\u0161\u0161\u00ed \u03b2 zav\u00e1d\u00ed malou slo\u017eku axi\u00e1ln\u00ed kluzn\u00e9 rychlosti v kontaktn\u00ed z\u00f3n\u011b, co\u017e m\u00edrn\u011b zvy\u0161uje koeficient t\u0159en\u00ed v z\u00e1b\u011bru. Pro \u03b2 = 0\u201325\u00b0 je rozd\u00edl \u00fa\u010dinnosti men\u0161\u00ed ne\u017e 0,2% \u2013 zanedbateln\u00fd. Pro \u03b2 = 25\u201335\u00b0 je sn\u00ed\u017een\u00ed p\u0159ibli\u017en\u011b o 0,2\u20130,5%. spir\u00e1lov\u00e9 ozuben\u00e9 kolo<\/strong> \u00fa\u010dinnost s\u00edt\u011b \u2013 skute\u010dn\u00fd, ale mal\u00fd postih ve srovn\u00e1n\u00ed s v\u00fdhodami z hlediska \u0161umu a K_V.<\/p>\n<\/div>\n<\/div>\n

Pom\u011br p\u0159ekryt\u00ed kontaktu \u03b5_\u03b2 \u2013 vzorec a minim\u00e1ln\u00ed \u0161\u00ed\u0159ka plochy<\/h2>\n

Pom\u011br p\u0159ekryt\u00ed kontakt\u016f \u03b5_\u03b2 a spir\u00e1lov\u00e9 ozuben\u00e9 kolo<\/strong> dvojice \u2013 po\u010det dal\u0161\u00edch \u201e\u0159ez\u016f\u201c \u0161\u00ed\u0159ky zubu v sou\u010dasn\u00e9m kontaktu nad r\u00e1mec p\u0159\u00ed\u010dn\u00e9ho kontaktn\u00edho pom\u011bru \u2013 je kritick\u00fdm parametrem ur\u010den\u00fdm volbou \u00fahlu \u0161roubovice:<\/p>\n

\u03b5_\u03b2 = b \u00d7 sin \u03b2 \/ (\u03c0 \u00d7 M_n)
\nkde: b = \u0161\u00ed\u0159ka \u010deln\u00ed plochy [mm]
\n\u03b2 = \u00fahel stoup\u00e1n\u00ed \u0161roubovice [stupn\u011b]
\nM_n = norm\u00e1ln\u00ed modul [mm]<\/p>\n

Minim\u00e1ln\u00ed \u0161\u00ed\u0159ka \u010deln\u00ed plochy pro \u03b5_\u03b2 \u2265 1,0 (p\u0159ekryt\u00ed zub\u016f \u0161ikm\u00e9ho ozuben\u00e9ho kola):
\nb_min = \u03c0 \u00d7 M_n \/ sin \u03b2<\/p>\n

P\u0159\u00edklady s M_n = 5:
\n\u03b2 = 10\u00b0: b_min = \u03c0 \u00d7 5 \/ sin10\u00b0 = 15,71 \/ 0,174 = 90,4 mm
\np = 15\u00b0: b_min = 15,71 \/ 0,259 = 60,7 mm
\np = 20\u00b0: b_min = 15,71 \/ 0,342 = 45,9 mm
\np = 25\u00b0: b_min = 15,71 \/ 0,423 = 37,2 mm
\np = 30\u00b0: b_min = 15,71 \/ 0,500 = 31,4 mm<\/p>\n

Dv\u011b praktick\u00e1 pozorov\u00e1n\u00ed: (1) \u0160roubov\u00e1 ozuben\u00e1 kola<\/strong> s \u03b5_\u03b2 < 1,0 st\u00e1le p\u0159ekon\u00e1vaj\u00ed \u010deln\u00ed ozuben\u00e1 kola (\u03b5_\u03b2 = 0) v hlu\u010dnosti a sd\u00edlen\u00ed zat\u00ed\u017een\u00ed, ale p\u0159echod kontaktu z jednozub\u00e9ho do v\u00edcezub\u00e9ho z\u00e1b\u011bru nen\u00ed zcela spojit\u00fd \u2013 st\u00e1le existuje kr\u00e1tk\u00fd moment kontaktu jednoho zubu na jednu rozte\u010d. (2) Pro c\u00edlovou hodnotu \u03b5_\u03b2 \u2265 2,0 (pln\u00e9 dvojit\u00e9 p\u0159ekryt\u00ed, standard pro p\u0159esn\u00e9 aplikace s n\u00edzkou hlu\u010dnost\u00ed) je po\u017eadovan\u00e1 \u0161\u00ed\u0159ka \u010deln\u00ed plochy nebo \u00fahel \u0161roubovice mnohem v\u011bt\u0161\u00ed \u2013 p\u0159i M5, \u03b2 = 20\u00b0, dosa\u017een\u00ed \u03b5_\u03b2 = 2,0 vy\u017eaduje b = 92 mm.<\/p>\n

Axi\u00e1ln\u00ed tah F_a \u2014 V\u00fdpo\u010det a d\u016fsledky pro lo\u017eiska<\/h2>\n

Axi\u00e1ln\u00ed tah generovan\u00fd spir\u00e1lov\u00e9 ozuben\u00e9 kolo<\/strong> S\u00ed\u0165 je p\u0159\u00edmo \u00fam\u011brn\u00e1 te\u010dn\u00e9 s\u00edle a tangenci \u00fahlu \u0161roubovice:<\/p>\n

F_a = F_t \u00d7 tan \u03b2
\nF_t = 2 \u00d7 T \/ d [tangenci\u00e1ln\u00ed s\u00edla na rozte\u010dn\u00e9 kru\u017enici; T v N\u00b7m, d v m]<\/p>\n

Pro pohon o v\u00fdkonu 75 kW p\u0159i 1 500 ot.\/min, M5, z=24, \u03b2=20\u00b0:
\nT = 9550 \u00d7 75 \/ 1500 = 477 N\u00b7m
\nd = 5 \u00d7 24 \/ cos20\u00b0 = 127,8 mm = 0,1278 m
\nF_t = 2 \u00d7 477 \/ 0,1278 = 7 465 N<\/p>\n

Axi\u00e1ln\u00ed posuv pod r\u016fzn\u00fdmi \u00fahly \u0161roubovice:
\n\u03b2 = 10\u00b0: F_a = 7 465 \u00d7 tan10\u00b0 = 7 465 \u00d7 0,176 = 1 314 N
\n\u03b2 = 15\u00b0: F_a = 7 465 \u00d7 0,268 = 2 001 N
\n\u03b2 = 20\u00b0: F_a = 7 465 \u00d7 0,364 = 2 717 N
\n\u03b2 = 25\u00b0: F_a = 7 465 \u00d7 0,466 = 3 479 N
\n\u03b2 = 30\u00b0: F_a = 7 465 \u00d7 0,577 = 4 308 N<\/p>\n

D\u016fsledky v\u00fdb\u011bru axi\u00e1ln\u00edho lo\u017eiska:<\/strong> Ve v\u00fd\u0161e uveden\u00e9m p\u0159\u00edkladu se zv\u00fd\u0161en\u00edm \u03b2 z 15\u00b0 na 25\u00b0 zv\u00fd\u0161\u00ed axi\u00e1ln\u00ed axi\u00e1ln\u00ed s\u00edla z 2 001 N na 3 479 N \u2013 co\u017e p\u0159edstavuje n\u00e1r\u016fst o 741 TP3T. H\u0159\u00eddelov\u00e9 lo\u017eisko mus\u00ed tuto s\u00edlu absorbovat v kombinaci s radi\u00e1ln\u00ed z\u00e1b\u011brovou silou. U lehk\u00fdch pohon\u016f to standardn\u00ed kuli\u010dkov\u00e9 lo\u017eisko s hlubokou dr\u00e1\u017ekou pohodln\u011b zvl\u00e1d\u00e1. U t\u011b\u017ek\u00fdch pohon\u016f (s vysok\u00fdm Ft) se limituj\u00edc\u00edm faktorem st\u00e1v\u00e1 axi\u00e1ln\u00ed \u00fanosnost lo\u017eiska, kter\u00e1 p\u0159i \u03b2 = 20\u00b0 a v\u00fd\u0161e \u010dasto vy\u017eaduje lo\u017eiska s koso\u00fahl\u00fdm stykem nebo ku\u017eel\u00edkov\u00e1 lo\u017eiska, nebo dvojitou \u0161roubovicovou konfiguraci nad \u03b2 = 30\u00b0.<\/div>\n

Vliv \u00fahlu \u0161roubovice na \u0161um \u2013 kvantifikovan\u00fd vztah<\/h2>\n

Sn\u00ed\u017een\u00ed hluku zv\u00fd\u0161en\u00edm spir\u00e1lov\u00e9 ozuben\u00e9 kolo<\/strong> \u00dahel stoup\u00e1n\u00ed \u0161roubovice je zp\u016fsoben dv\u011bma mechanismy: vy\u0161\u0161\u00ed \u03b5_\u03b2 rozkl\u00e1d\u00e1 zat\u00ed\u017een\u00ed sou\u010dasn\u011b na v\u00edce kontaktn\u00edch lini\u00ed zub\u016f (sn\u00ed\u017een\u00ed maxim\u00e1ln\u00ed kontaktn\u00ed s\u00edly na p\u00e1r zub\u016f) a vy\u0161\u0161\u00ed \u03b5_\u03b2 sni\u017euje amplitudu zm\u011bny tuhosti p\u0159i frekvenci z\u00e1b\u011bru (prim\u00e1rn\u00ed buzen\u00ed \u0161umem). Kombinovan\u00fd vliv na hladinu \u0161umu z\u00e1b\u011bru ozuben\u00e9ho kola p\u0159i stejn\u00e9 rychlosti na ose stoup\u00e1n\u00ed a p\u0159en\u00e1\u0161en\u00e9m kroutic\u00edm momentu:<\/p>\n

\n\n\n\n\n\n\n\n\n\n
\u00dahel \u0161roubovice \u03b2<\/th>\n\u03b5_\u03b2 (M5, b=60 mm)<\/th>\n\u0160um vs. odra\u017een\u00e9 vln\u011bn\u00ed (\u03b5_\u03b2=0)<\/th>\n\u0160um vs. \u03b2=15\u00b0<\/th>\nTypick\u00e9 pr\u016fmyslov\u00e9 pou\u017eit\u00ed<\/th>\n<\/tr>\n<\/thead>\n
V\u00fdb\u011b\u017eek (\u03b2 = 0\u00b0)<\/td>\n0<\/td>\n0 dB(A) referen\u010dn\u00ed hodnota<\/td>\n+8 a\u017e +12 dB(A)<\/td>\nPomal\u00fd pr\u016fmysl, zem\u011bd\u011blstv\u00ed (ovl\u00e1dan\u00e9 n\u00e1klady)<\/td>\n<\/tr>\n
\u03b2 = 8\u00b0\u201312\u00b0<\/td>\n0,26\u20130,42<\/td>\n\u22123 a\u017e \u22125 dB(A)<\/td>\n+4 a\u017e +7 dB(A)<\/td>\nServo a p\u0159esnost (priorita minim\u00e1ln\u00edho axi\u00e1ln\u00edho tahu)<\/td>\n<\/tr>\n
\u03b2 = 15\u00b0\u201318\u00b0<\/td>\n0,65\u20130,95<\/td>\n\u22125 a\u017e \u22128 dB(A)<\/td>\nOdkaz<\/td>\nStandardn\u00ed pr\u016fmyslov\u00e9: dopravn\u00edky, m\u00edcha\u010dky, \u010derpadla<\/td>\n<\/tr>\n
\u03b2 = 20\u00b0\u201325\u00b0<\/td>\n1,08\u20131,62<\/td>\n\u22128 a\u017e \u221212 dB(A)<\/td>\n\u22123 a\u017e \u22125 dB(A)<\/td>\nReduktory pro elektromobily, automobilov\u00fd pr\u016fmysl, tiska\u0159sk\u00e9 stroje, kompresory<\/td>\n<\/tr>\n
\u03b2 = 28\u00b0\u201335\u00b0 (dvojit\u00e1 \u0161roubovice)<\/td>\n2,3\u20133,6<\/td>\n\u221214 a\u017e \u221218 dB(A)<\/td>\n\u22127 a\u017e \u221210 dB(A)<\/td>\nLodn\u00ed pohon, n\u00e1mo\u0159n\u00ed, tich\u00e9 p\u0159evodovky<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Vliv \u03b2 na mlet\u00ed \u2013 praktick\u00e1 horn\u00ed hranice<\/h2>\n

CNC gener\u00e1torov\u00e9 brusky H\u00d6FLER \u2013 standardn\u00ed stroj pro p\u0159esnost spir\u00e1lov\u00e9 ozuben\u00e9 kolo<\/strong> brou\u0161en\u00ed zub\u016f \u2013 maj\u00ed mechanick\u00fd maxim\u00e1ln\u00ed \u00fahel stoup\u00e1n\u00ed \u0161roubovice pro generuj\u00edc\u00ed pohyb. V\u011bt\u0161ina model\u016f umo\u017e\u0148uje \u03b2 a\u017e do p\u0159ibli\u017en\u011b 30\u201335\u00b0. Nad \u03b2 = 30\u00b0 vy\u017eaduje generuj\u00edc\u00ed pohyb brusn\u00e9ho kotou\u010de velmi \u0161ikm\u00fd p\u0159\u00edstup k zubu, co\u017e:<\/p>\n