{"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\/sk\/helical-gear-helix-angle-selection-guide\/","title":{"rendered":"V\u00fdber uhla \u0161pir\u00e1ly ozuben\u00e9ho kolesa so \u0161pir\u00e1lov\u00fdm ozuben\u00fdm kolesom"},"content":{"rendered":"
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V\u00fdber uhla \u0161pir\u00e1ly ozuben\u00e9ho kolesa so \u0161pir\u00e1lou \u2013 technick\u00e9 kompromisy od \u03b2 = 8\u00b0 do \u03b2 = 35\u00b0<\/h1>\n

Uhol skrutkovice \u03b2 je jedin\u00e1 kon\u0161truk\u010dn\u00e1 premenn\u00e1, ktor\u00e1 najviac odli\u0161uje \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koleso<\/strong> z \u010deln\u00e9ho ozuben\u00e9ho kolesa \u2013 a vo\u013eba \u03b2 ur\u010duje kontaktn\u00fd pomer ozuben\u00e9ho kolesa, hladinu hluku, axi\u00e1lne axi\u00e1lne za\u0165a\u017eenie, \u00fa\u010dinnos\u0165 a v\u00fdber lo\u017eiska. Neexistuje univerz\u00e1lne spr\u00e1vny uhol skrutkovice: spr\u00e1vny \u03b2 pre tla\u010diarensk\u00fd stroj \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koleso<\/strong> (maxim\u00e1lna hladkos\u0165, \u03b2 = 25\u00b0) je nespr\u00e1vna pre z\u00e1p\u00e4stn\u00e9 ozuben\u00e9 koleso robota (minim\u00e1lny axi\u00e1lny tlak, \u03b2 = 12\u00b0) a \u00faplne odli\u0161n\u00e1 od dvojit\u00e9ho \u0161pir\u00e1lov\u00e9ho lodn\u00e9ho ozuben\u00e9ho kolesa (maxim\u00e1lna \u0161pir\u00e1la, \u03b2 = 35\u00b0 na sekciu). T\u00e1to pr\u00edru\u010dka poskytuje r\u00e1mec zalo\u017een\u00fd na vzorcoch pre spr\u00e1vny v\u00fdber \u03b2 pre ka\u017ed\u00fa aplik\u00e1ciu.<\/p>\n

Z\u00edskajte odpor\u00fa\u010danie uhla \u0161pir\u00e1ly \u2192<\/a><\/p>\n<\/div>\n<\/div>\n

\u0160tyri \u00fa\u010dinky uhla \u0161pir\u00e1ly \u2013 \u010do sa men\u00ed so zvy\u0161uj\u00facim sa \u03b2<\/h2>\n

Ka\u017ed\u00e9 rozhodnutie o \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koleso<\/strong> Uhol \u0161pir\u00e1ly zah\u0155\u0148a \u0161tyri simult\u00e1nne efekty, ktor\u00e9 sa navz\u00e1jom ovplyv\u0148uj\u00fa. Pochopenie v\u0161etk\u00fdch \u0161tyroch \u2013 nielen efektu \u0161umu \u2013 je nevyhnutn\u00e9 pre spr\u00e1vny v\u00fdber \u03b2:<\/p>\n

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\u2191 Pomer prekrytia kontaktu \u03b5_\u03b2<\/p>\n

Vy\u0161\u0161ie \u03b2 \u2192 viac s\u00fa\u010dasn\u00fdch kontaktn\u00fdch p\u00e1rov zubov \u2192 plynulej\u0161\u00ed prenos sily \u2192 ni\u017e\u0161ia chyba prenosu \u2192 menej hluku a vibr\u00e1ci\u00ed. Toto je hlavn\u00fd d\u00f4vod, pre\u010do in\u017einieri volia vy\u0161\u0161ie uhly skrutkovice pre presnos\u0165 a tich\u00fd chod. \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koleso<\/strong> aplik\u00e1cie.<\/p>\n<\/div>\n

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\u2191 Axi\u00e1lna axi\u00e1lna sila F_a<\/p>\n

Vy\u0161\u0161ie \u03b2 \u2192 v\u00e4\u010d\u0161ia zlo\u017eka axi\u00e1lnej sily na rozstupovej kru\u017enici \u2192 n\u00e1ro\u010dnej\u0161ie axi\u00e1lne lo\u017eisk\u00e1 hriade\u013ea \u2192 v extr\u00e9mnych pr\u00edpadoch je potrebn\u00e1 dvojit\u00e1 \u0161pir\u00e1lov\u00e1 konfigur\u00e1cia na \u00fapln\u00e9 zru\u0161enie axi\u00e1lnej sily. Toto je prim\u00e1rna nev\u00fdhoda vysok\u00fdch uhlov \u0161pir\u00e1ly v jedno\u0161pir\u00e1lov\u00fdch lo\u017eisk\u00e1ch. \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koleso<\/strong> pohony.<\/p>\n<\/div>\n

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\u2191 Zlep\u0161enie dynamick\u00e9ho faktora K_V<\/p>\n

Vy\u0161\u0161ie \u03b2 zvy\u0161uje \u03b5_\u03b2, \u010do zni\u017euje zmenu amplit\u00fady za\u0165a\u017eenia pri sie\u0165ovej frekvencii \u2013 zdroji budenia pre dynamick\u00fd faktor K_V. Hodnoty K_V pod\u013ea met\u00f3dy B pod\u013ea normy ISO 6336-1 s\u00fa ni\u017e\u0161ie pre \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koles\u00e1<\/strong> s vy\u0161\u0161ou hodnotou \u03b5_\u03b2 pri rovnakej r\u00fdchlosti na osi rozstupu, \u010do umo\u017e\u0148uje kompaktnej\u0161ie dimenzovanie ozuben\u00e9ho kolesa pri rovnakom menovitom v\u00fdkone.<\/p>\n<\/div>\n

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\u2193 \u00da\u010dinnos\u0165 (hrani\u010dn\u00e1)<\/p>\n

Vy\u0161\u0161ie \u03b2 zav\u00e1dza mal\u00fa axi\u00e1lnu zlo\u017eku r\u00fdchlosti posuvu v kontaktnej z\u00f3ne, \u010d\u00edm mierne zvy\u0161uje koeficient trenia v sieti. Pre \u03b2 = 0\u201325\u00b0 je rozdiel \u00fa\u010dinnosti men\u0161\u00ed ako 0,2% \u2013 zanedbate\u013en\u00fd. Pre \u03b2 = 25\u201335\u00b0 je zn\u00ed\u017eenie pribli\u017ene o 0,2\u20130,5%. \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koleso<\/strong> \u00fa\u010dinnos\u0165 siete \u2013 re\u00e1lny, ale mal\u00fd postih v porovnan\u00ed s v\u00fdhodami z h\u013eadiska \u0161umu a K_V.<\/p>\n<\/div>\n<\/div>\n

Pomer prekrytia \u03b5_\u03b2 \u2013 vzorec a minim\u00e1lna \u0161\u00edrka plochy<\/h2>\n

Pomer prekrytia kontaktu \u03b5_\u03b2 a \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koleso<\/strong> p\u00e1r \u2013 po\u010det \u010fal\u0161\u00edch \u201epl\u00e1tkov\u201c \u0161\u00edrky zubov v s\u00fa\u010dasnom kontakte nad r\u00e1mec prie\u010dneho kontaktn\u00e9ho pomeru \u2013 je kritick\u00fdm parametrom ur\u010den\u00fdm v\u00fdberom uhla skrutkovice:<\/p>\n

\u03b5_\u03b2 = b \u00d7 sin \u03b2 \/ (\u03c0 \u00d7 M_n)
\nkde: b = \u0161\u00edrka \u010delnej plochy [mm]
\n\u03b2 = uhol \u0161pir\u00e1ly [stup\u0148ov]
\nM_n = norm\u00e1lny modul [mm]<\/p>\n

Minim\u00e1lna \u0161\u00edrka \u010delnej plochy pre \u03b5_\u03b2 \u2265 1,0 (prekrytie zubov \u0161pir\u00e1lov\u00e9ho ozuben\u00e9ho kolesa):
\nb_min = \u03c0 \u00d7 M_n \/ sin \u03b2<\/p>\n

Pr\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

Dve praktick\u00e9 postrehy: (1) \u0160pir\u00e1lov\u00e9 ozuben\u00e9 koles\u00e1<\/strong> s \u03b5_\u03b2 < 1,0 st\u00e1le prekon\u00e1vaj\u00fa \u010deln\u00e9 ozuben\u00e9 koles\u00e1 (\u03b5_\u03b2 = 0) v hluku a rozdelen\u00ed za\u0165a\u017eenia, ale prechod kontaktu z jednozub\u00e9ho do viaczub\u00e9ho z\u00e1beru nie je \u00faplne spojit\u00fd \u2013 st\u00e1le existuje kr\u00e1tky moment kontaktu jedn\u00e9ho zuba na st\u00fapanie. (2) Pre cie\u013eov\u00fa hodnotu \u03b5_\u03b2 \u2265 2,0 (\u00fapln\u00e9 dvojit\u00e9 prekrytie, \u0161tandard pre presn\u00e9 aplik\u00e1cie s n\u00edzkou hlu\u010dnos\u0165ou) je po\u017eadovan\u00e1 \u0161\u00edrka \u010delnej plochy alebo uhol \u0161pir\u00e1ly ove\u013ea v\u00e4\u010d\u0161ia \u2013 pri M5, \u03b2 = 20\u00b0, dosiahnutie \u03b5_\u03b2 = 2,0 vy\u017eaduje b = 92 mm.<\/p>\n

Axi\u00e1lny \u0165ah F_a \u2013 V\u00fdpo\u010det a d\u00f4sledky pre lo\u017eisk\u00e1<\/h2>\n

Axi\u00e1lny tlak generovan\u00fd \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koleso<\/strong> sie\u0165 je priamo \u00famern\u00e1 tangenci\u00e1lnej sile a tangencii uhla \u0161pir\u00e1ly:<\/p>\n

F_a = F_t \u00d7 tan \u03b2
\nF_t = 2 \u00d7 T \/ d [tangenci\u00e1lna sila na rozstupovej kru\u017enici; T v N\u00b7m, d v m]<\/p>\n

Pre pohon s v\u00fdkonom 75 kW pri 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\u00e1lny \u0165ah pri r\u00f4znych uhloch \u0161pir\u00e1ly:
\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\u00f4sledky v\u00fdberu axi\u00e1lneho lo\u017eiska:<\/strong> V uvedenom pr\u00edklade zv\u00fd\u0161enie \u03b2 z 15\u00b0 na 25\u00b0 zvy\u0161uje axi\u00e1lnu silu z 2 001 N na 3 479 N \u2013 \u010do predstavuje n\u00e1rast o 74%. Lo\u017eisko hriade\u013ea mus\u00ed t\u00fato silu absorbova\u0165 v kombin\u00e1cii s radi\u00e1lnou z\u00e1berovou silou. Pre \u013eahk\u00e9 pohony to \u0161tandardn\u00e9 gu\u013e\u00f4\u010dkov\u00e9 lo\u017eisko s hlbokou dr\u00e1\u017ekou pohodlne zvl\u00e1da. Pre \u0165a\u017ek\u00e9 pohony (vysok\u00e1 hodnota Ft) sa limituj\u00facim faktorom st\u00e1va axi\u00e1lna \u00fanosnos\u0165 lo\u017eiska, ktor\u00e1 si pri \u03b2 = 20\u00b0 a viac \u010dasto vy\u017eaduje uhlov\u00e9 alebo ku\u017eel\u00edkov\u00e9 lo\u017eisk\u00e1, alebo dvojit\u00fa \u0161pir\u00e1lov\u00fa konfigur\u00e1ciu nad \u03b2 = 30\u00b0.<\/div>\n

Vplyv uhla \u0161pir\u00e1ly na \u0161um \u2013 kvantifikovan\u00fd vz\u0165ah<\/h2>\n

Zn\u00ed\u017eenie hluku zv\u00fd\u0161en\u00edm \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koleso<\/strong> Uhol sklonu \u0161pir\u00e1ly poch\u00e1dza z dvoch mechanizmov: vy\u0161\u0161ie \u03b5_\u03b2 rozde\u013euje za\u0165a\u017eenie s\u00fa\u010dasne na viac kontaktn\u00fdch \u010diar zubov (zn\u00ed\u017eenie maxim\u00e1lnej kontaktnej sily na p\u00e1r zubov) a vy\u0161\u0161ie \u03b5_\u03b2 zni\u017euje amplit\u00fadu zmeny tuhosti pri frekvencii z\u00e1beru (prim\u00e1rne budenie \u0161umom). Kombinovan\u00fd vplyv na hladinu \u0161umu z\u00e1beru ozuben\u00e9ho kolesa pri rovnakej r\u00fdchlosti na osi rozstupu zubov a pren\u00e1\u0161anom kr\u00fatiacom momente:<\/p>\n

\n\n\n\n\n\n\n\n\n\n
Uhol \u0161pir\u00e1ly \u03b2<\/th>\n\u03b5_\u03b2 (M5, b=60 mm)<\/th>\n\u0160um vs. impulz (\u03b5_\u03b2=0)<\/th>\n\u0160um vs. \u03b2=15\u00b0<\/th>\nTypick\u00e9 priemyseln\u00e9 pou\u017eitie<\/th>\n<\/tr>\n<\/thead>\n
Ostroha (\u03b2 = 0\u00b0)<\/td>\n0<\/td>\n0 dB(A) referen\u010dn\u00e1 hodnota<\/td>\n+8 a\u017e +12 dB(A)<\/td>\nPomal\u00fd priemysel, po\u013enohospod\u00e1rstvo (ohrozen\u00e9 n\u00e1kladmi)<\/td>\n<\/tr>\n
\u03b2 = 8\u00b0\u201312\u00b0<\/td>\n0,26 \u2013 0,42<\/td>\n\u22123 a\u017e \u22125 dB(A)<\/td>\n+4 a\u017e +7 dB(A)<\/td>\nServo a presnos\u0165 (priorita minim\u00e1lneho axi\u00e1lneho posunu)<\/td>\n<\/tr>\n
\u03b2 = 15\u00b0\u201318\u00b0<\/td>\n0,65 \u2013 0,95<\/td>\n\u22125 a\u017e \u22128 dB(A)<\/td>\nReferencia<\/td>\n\u0160tandardn\u00e9 priemyseln\u00e9: dopravn\u00edky, mie\u0161a\u010dky, \u010derpadl\u00e1<\/td>\n<\/tr>\n
\u03b2 = 20\u00b0\u201325\u00b0<\/td>\n1,08 \u2013 1,62<\/td>\n\u22128 a\u017e \u221212 dB(A)<\/td>\n\u22123 a\u017e \u22125 dB(A)<\/td>\nReduktory pre elektromobily, automobilov\u00fd priemysel, tla\u010diarensk\u00e9 stroje, kompresory<\/td>\n<\/tr>\n
\u03b2 = 28\u00b0\u201335\u00b0 (dvojit\u00e1 \u0161pir\u00e1la)<\/td>\n2,3 \u2013 3,6<\/td>\n\u221214 a\u017e \u221218 dB(A)<\/td>\n\u22127 a\u017e \u221210 dB(A)<\/td>\nLodn\u00fd pohon, n\u00e1morn\u00e9, prevodovky s n\u00edzkou hlu\u010dnos\u0165ou<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Vplyv \u03b2 na mletie \u2013 praktick\u00e1 horn\u00e1 hranica<\/h2>\n

CNC gener\u00e1torov\u00e9 br\u00fasky H\u00d6FLER \u2013 \u0161tandardn\u00fd stroj pre presnos\u0165 \u0161pir\u00e1lov\u00e9 ozuben\u00e9 koleso<\/strong> br\u00fasenie zubov \u2013 maj\u00fa mechanick\u00fd maxim\u00e1lny uhol skrutkovice pre generuj\u00faci pohyb. V\u00e4\u010d\u0161ina modelov umo\u017e\u0148uje \u03b2 a\u017e do pribli\u017ene 30\u201335\u00b0. Nad \u03b2 = 30\u00b0 si generuj\u00faci pohyb br\u00fasneho kot\u00fa\u010da vy\u017eaduje ve\u013emi \u0161ikm\u00fd pr\u00edstup k zubu, \u010do:<\/p>\n