DANE |
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OBLICZENIA |
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WYNIKI |
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Zaprojektować przekładnię redukcyjną dla napędu z |
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Moc silnika: |
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silnika elektrycznego przenoszącą moment na suwnicę |
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N [kW] = |
8 |
Wykonać: |
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Przełożenie: |
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1. Kompletne obliczenia. |
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i =1: |
32 |
2. Rysunek zestawieniowy w skali 1:1. |
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Obroty wejścia: |
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3. Dobrać samodzielnie materiały. |
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n[1/min]= |
2400 |
4. Rysunki detali. |
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Schemat kinematyczny: |
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I |
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D |
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F
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ROZWIĄZANIE |
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1.Obliczam wstępnie przełożenia kół. |
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Dobieram przełożenia dla kolejnych par kół odpowiednio: |
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iI = 1: |
3,2 |
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iI = 1: |
3,2 |
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iII = 1: |
3,2 |
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iII = 1: |
3,2 |
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iIII = 1: |
3,1 |
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iIII = 1: |
3,1 |
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Teoretyczne przełożenie całkowite: |
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ic = 1: |
31,74 |
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ic = 1: |
31,74 |
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Dobieram ilości zębów na współpracujących kołach: |
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koło A z= |
18 |
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koło B z= |
58 |
koło A z= |
18 |
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koło C z= |
21 |
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koło D z= |
67 |
koło C z= |
21 |
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koło E z= |
21 |
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koło F z= |
65 |
koło E z= |
21 |
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Przełożenie rzeczywiste: |
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koło B z= |
58 |
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ir = 1: |
31,82 |
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koło D z= |
67 |
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Obliczam prędkości obrotowe poszczególnych wałków |
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koło F z= |
65 |
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w/g wzoru: |
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ir = 1: |
31,82 |
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koło A z= |
18 |
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koło C z= |
21 |
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koło E z= |
21 |
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nI[1/min]= |
2400 |
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koło B z= |
58 |
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nII[1/min]= |
744,83 |
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nII[1/min]= |
744,83 |
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koło D z= |
67 |
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nIII[1/min]= |
233,45 |
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nIII[1/min]= |
233,45 |
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koło F z= |
65 |
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nIV[1/min]= |
75,42 |
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nIV[1/min]= |
75,42 |
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Korzystając ze wzoru : |
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nI[1/min]= |
2400 |
obliczam prędkości kątowe wałków: |
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nII[1/min]= |
744,83 |
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wI[1/s]= |
251,33 |
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nIII[1/min]= |
233,45 |
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wII[1/s]= |
78 |
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wII[1/s]= |
78 |
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nIV[1/min]= |
75,42 |
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wIII[1/s]= |
24,45 |
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wIII[1/s]= |
24,45 |
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wIV[1/s]= |
7,9 |
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wIV[1/s]= |
7,9 |
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DANE |
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OBLICZENIA |
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WYNIKI |
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2. Obliczenia wytrzymałościowe kół. |
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I. Para pierwsza - koła stożkowe. |
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Dobieram na koła materiał o dopuszczalnej wytrzymałości |
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na zginanie (obciążenie zmienne jednostronne) |
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kgj [MPa]= |
310 |
16HG |
w/g tabeli IX/17. Ochęd. |
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kgj [MPa]= |
310 |
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Dla koła małego przyjąłem ilość zębów ZA= |
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18 |
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Kąt S między osiami kół wynosi S=90o. |
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Z tabeli IV/2. |
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dobieram kąty stożków podziałowych: |
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Dla koła dużego dB= |
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72,46 |
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72,76 |
dB[o]= |
72,46 |
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Dla koła małego dA= |
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17,14 |
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17,24 |
dA[o]= |
17,14 |
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Na podstawie wzoru IV/36 obliczam zastępcze liczby |
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zębów: |
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dB= |
72,46 |
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18,85 |
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ZvA= |
18,85 |
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dA= |
17,14 |
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#DIV/0! |
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195,7 |
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ZvB= |
195,7 |
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0 |
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Dla znanej zastępczej liczby zębów koła małego dobieram |
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z tabeli X/1 |
w/g Czasownikowa współczynnik wytrzymałości |
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zęba u podstawy: |
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lzast= |
0,387 |
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lzast= |
0,387 |
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N [kW] = |
8 |
Mając wszystkie dane obliczam moduł koła małego w/g |
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dA= |
17,14 |
wzoru XI-10 dla zębów prostych: |
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bm= |
0 |
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Cb= |
1 |
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1,471 |
mnm= |
1,471 |
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lzast= |
0,387 |
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ZvA= |
18,85 |
Dobieram znormalizowany czołowy moduł zewnętrzny |
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nI[1/min]= |
2400 |
mte[mm]= |
2,5 |
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mte[mm]= |
2,5 |
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kgj [MPa]= |
310 |
Obliczam okrąg zewnętrznej podstawy stożka podziałowe- |
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go w/g wzoru IV-1 |
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ZA= |
18 |
Dla koła małego: |
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45 |
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deA= |
45 |
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ZB= |
58 |
Dla koła dużego: |
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145 |
mm |
deB= |
145 |
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Długość tworzącej stożków podziałowych w/g wzoru IV-7a |
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ZA= |
18 |
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mte[mm]= |
2,5 |
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75,92 |
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Re= |
75,92 |
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dA= |
17,14 |
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Sprawdzam graniczną liczbę zębów w/g wzoruIV-37. |
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Zakładam dla zębów prostych współczynnik wysokości zę- |
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ba ytm= |
1 |
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ytm= |
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ytm= |
1 |
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atm[o]= |
20 |
17,1 |
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Zgtm= |
17,1 |
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Zatem korekcja jest zbędna. |
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Obliczam wysokość głów i stóp zębów niekorygowanych |
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[IV-20, IV-21]dla czoła zewnętrznego wieńca: |
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ytm= |
1 |
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mte[mm]= |
2,5 |
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2,5 |
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ham= |
2,5 |
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DANE |
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OBLICZENIA |
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WYNIKI |
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3 |
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hfm= |
3 |
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49,78 |
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daeA= |
49,78 |
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deA= |
45 |
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146,48 |
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daeB= |
146,48 |
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deB= |
145 |
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ham= |
2,5 |
Wysokości stożków wierzchołkowych [IV-33] |
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hfm= |
3 |
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dB[o]= |
72,46 |
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71,76 |
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BB= |
20,11 |
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dA[o]= |
17,14 |
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20,11 |
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BA= |
71,76 |
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Kąty wysokości głowy zęba [IV-25]: |
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0,032929399367756 |
[o] |
1,53 |
Qa[o]= |
1,53 |
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Re= |
75,92 |
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1,89 |
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oraz stopy zęba [IV-26]: |
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0,039515279241307 |
[o] |
2,16 |
Qf[o]= |
2,16 |
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2,26 |
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Kąty stożków wierzchołkowych [IV-27]: |
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Qa[o]= |
1,53 |
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Qf[o]= |
2,16 |
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19,08 |
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daA[o]= |
19,08 |
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19,13 |
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daB[o]= |
74,39 |
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74,39 |
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dB[o]= |
72,46 |
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74,65 |
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dA[o]= |
17,14 |
i dna wrębów [IV-28]: |
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14,59 |
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dfA[o]= |
14,59 |
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14,98 |
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dfB[o]= |
70,3 |
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70,3 |
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70,5 |
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Dobieram szerokość wieńca około b=1/3,5 Re: |
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b[mm]= |
22 |
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b[mm]= |
22 |
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Obliczanie zębów na naciski. |
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Dla potrzeb wzorów Hertza obliczam średnicę zastępczą |
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zębnika [XI-12] |
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bm= |
0 |
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dmA= |
38,4799789251844 |
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40,29 |
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dvmnA= |
40,29 |
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dA[o]= |
17,14 |
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oraz przełożenie czołowe [IV-9]: |
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ZA= |
18 |
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ZB= |
58 |
|
|
0,096 |
|
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iv= |
0,096 |
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Przyjmuję materiałowy współczynnik Cm,a= |
478,2 |
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dobrałem |
|
Dopuszczalny nacisk jednostkowy w/g Hertza [X-25]: |
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|
z tablic:X-8, X/10, |
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X/11, IX-48 |
|
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|
1322 |
MPa |
|
kH[Mpa]= |
1322 |
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|
|
ZHj[MPa]= |
1600 |
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DANE |
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|
OBLICZENIA |
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|
WYNIKI |
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Co= |
1 |
Ze wzoru Hertza obliczam największą moc jaka może |
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CcH= |
1 |
być przeniesiona: |
|
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xzH= |
1,21 |
Z tablicy I-55 wyznaczam stopnie pokrycia kół: |
|
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eA= |
1,55 |
|
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eA= |
1,55 |
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eB= |
1,78 |
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eB= |
1,78 |
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eA= |
1,55 |
Zatem ze wzoru I-55: |
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eB= |
1,78 |
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Cm,a= |
478,2 |
1,67 |
|
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ea= |
1,67 |
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nI[1/min]= |
2400 |
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kH[Mpa]= |
1322 |
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ea= |
1,67 |
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|
54,74 |
N[kW]= |
54,74 |
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b[mm]= |
22 |
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dvmnA= |
40,29 |
Warunek Hertza jest spełniony. |
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bm= |
0 |
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iv= |
0,096 |
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Prędkość obwodowa dla ustalenia nadwyżki dynamicznej: |
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dmA= |
38,4799789251844 |
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4,84 |
m/s |
|
n= |
4,84 |
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Wartość współczynnika nadwyżek dynamicznych Cd |
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1,55 |
IX/13-V |
Cd= |
1,55 |
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n= |
4,84 |
Z tablicy IX/11 odczytuję współczynnik przeciążenia Cp |
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Cp= |
1 |
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Cp= |
1 |
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|
Ze wzoru IX-9 wyznaczam siłę statyczną: |
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DANE |
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|
OBLICZENIA |
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|
WYNIKI |
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N[kW]= |
8 |
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1652,89 |
[N] |
|
Pstat= |
1652,89 |
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2561,98 |
[N] |
Pzast= |
2561,98 |
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Siła obliczeniowa [IX-13]: |
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Pzast= |
2561,98 |
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ea= |
1,67 |
1534,12 |
N |
|
Pobl= |
1534,12 |
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Sprawdzam naprężenia: |
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Pobl= |
1534,12 |
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l= |
0,387 |
|
|
72,08 |
<kgj[MPa]= |
310 |
sgzast[MPa]= |
72,08 |
|
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b[mm]= |
22 |
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m= |
2,5 |
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II. Para kół CD- koła walcowe o zębach prostych. |
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Na materiał dobieram stal jak dla kół stożkowych |
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kgj [MPa]= |
310 |
16HG |
w/g tabeli IX/17. Ochęd. |
|
kgj [MPa]= |
310 |
|
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|
|
Przyjmuję szerokość wieńca y= |
|
|
20 |
|
y= |
20 |
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Dla znanej zastępczej liczby zębów koła małego dobieram |
|
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|
z tabeli X/1 |
w/g Czasownikowa współczynnik wytrzymałości |
|
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|
|
zęba u podstawy: |
|
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|
kgj [MPa]= |
310 |
l= |
0,387 |
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l= |
0,387 |
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N[kW]= |
8 |
Obliczam minimalny moduł [X-4]: |
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y= |
20 |
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l= |
0,387 |
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|
1,59 |
mm |
mo= |
1,59 |
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nII= |
744,83 |
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ZC= |
21 |
Dobieram moduł czołowy m= |
|
|
2 |
|
m= |
2 |
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|
Średnice podziałowe kół : |
|
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|
42 |
|
|
dC= |
42 |
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ZD= |
67 |
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|
134 |
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dD= |
134 |
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m= |
2 |
Średnice głów zębów: |
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dC= |
42 |
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|
46 |
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dD= |
134 |
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daC= |
46 |
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y= |
1 |
|
|
138 |
|
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daD= |
138 |
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|
Średnice stóp zębów: |
|
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c=0,2m |
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|
37,2 |
|
dfC= |
37,2 |
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|
129,2 |
|
dfD= |
129,2 |
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y= |
20 |
Szerokość wieńca: |
|
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|
|
m= |
2 |
|
40 |
|
|
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b[mm]= |
40 |
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|
|
Prędkość obwodowa dla ustalenia nadwyżki dynamicznej: |
|
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|
dC= |
42 |
|
|
1,64 |
m/s |
|
n= |
1,64 |
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nII= |
744,83 |
|
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|
|
Wartość współczynnika nadwyżek dynamicznych Cd |
|
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|
1,32 |
IX/13-V |
Cd= |
1,32 |
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|
n= |
1,64 |
Z tablicy IX/11 odczytuję współczynnik przeciążenia Cp |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cp= |
1 |
|
|
Cp= |
1 |
|
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|
|
Ze wzoru IX-9 wyznaczam siłę statyczną: |
|
|
|
|
|
|
|
|
|
|
|
DANE |
|
|
|
OBLICZENIA |
|
|
WYNIKI |
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|
N[kW]= |
8 |
|
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|
4878,05 |
[N] |
|
Pstat= |
4878,05 |
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|
6439,03 |
[N] |
Pzast= |
6439,03 |
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|
eC= |
1,57 |
|
|
eC= |
1,57 |
|
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|
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|
|
eD= |
1,8 |
|
|
eD= |
1,8 |
|
|
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|
|
|
|
Zatem ze wzoru I-55: |
|
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|
eC= |
1,57 |
|
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|
eD= |
1,8 |
1,69 |
|
|
ea= |
1,69 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Siła obliczeniowa [IX-13]: |
|
|
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|
|
|
|
|
|
|
|
Pzast= |
6439,03 |
|
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|
|
ea= |
1,69 |
3810,08 |
N |
|
Pobl= |
3810,08 |
|
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|
|
Sprawdzam naprężenia: |
|
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|
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|
|
|
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|
|
Pobl= |
3810,08 |
|
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|
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l= |
0,387 |
|
|
123,06 |
<kgj[MPa]= |
310 |
sgzast[MPa]= |
123,06 |
|
|
|
|
|
b[mm]= |
40 |
|
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|
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|
m= |
2 |
Na podstawie wzoru X-13 określam moc jaką może prze- |
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|
|
nieść przekładnia ze względu na warunek Hertza |
|
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|
dC= |
42 |
|
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dD= |
134 |
|
|
|
16,77 |
kW |
N= |
16,77 |
|
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|
|
kH[Mpa]= |
1322 |
|
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|
|
|
|
|
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|
|
b[mm]= |
40 |
Warunek Hertza jest spełniony. |
|
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|
|
nII= |
744,83 |
|
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|
|
Cm,a= |
478,2 |
III. Para kół EF- koła walcowe o zębach prostych. |
|
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|
|
Na materiał dobieram stal jak dla kół stożkowych |
|
|
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|
|
|
|
|
|
|
|
|
|
kgj [MPa]= |
310 |
16HG |
w/g tabeli IX/17. Ochęd. |
|
kgj [MPa]= |
310 |
|
|
|
|
|
|
|
Przyjmuję szerokość wieńca y= |
|
|
20 |
|
y= |
20 |
|
|
|
|
|
|
|
Dla znanej zastępczej liczby zębów koła małego dobieram |
|
|
|
|
|
|
|
|
|
|
|
|
|
z tabeli X/1 |
w/g Czasownikowa współczynnik wytrzymałości |
|
|
|
|
|
|
|
|
|
|
|
|
zęba u podstawy: |
|
|
|
|
|
|
|
|
|
|
|
|
|
l= |
0,387 |
|
|
|
l= |
0,387 |
|
|
|
|
|
N[kW]= |
8 |
Obliczam minimalny moduł [X-4]: |
|
|
|
|
|
|
|
|
|
|
|
y= |
20 |
|
|
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|
|
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|
|
l= |
0,387 |
|
|
|
2,35 |
mm |
mo= |
2,35 |
|
|
|
|
|
kgj [MPa]= |
310 |
|
|
|
|
|
|
|
|
|
|
|
|
nIII[1/min]= |
233,45 |
Dobieram moduł czołowy m= |
|
|
2,5 |
|
m= |
2,5 |
|
|
|
|
|
ZE= |
21 |
Średnice podziałowe kół : |
|
|
|
|
|
|
|
|
|
|
|
ZF= |
65 |
|
52,5 |
|
|
dE= |
52,5 |
|
|
|
|
|
|
|
162,5 |
|
|
dF= |
162,5 |
|
|
|
|
|
m= |
2,5 |
Średnice głów zębów: |
|
|
|
|
|
|
|
|
|
|
|
dE= |
52,5 |
|
|
57,5 |
|
|
|
|
|
|
|
|
|
dF= |
162,5 |
|
|
|
daE= |
57,5 |
|
|
|
|
|
y= |
1 |
|
|
daF= |
167,5 |
|
|
|
|
|
|
|
Średnice stóp zębów: |
|
|
|
|
|
|
|
|
|
|
|
c=0,2m |
|
|
46,5 |
|
|
|
|
|
|
|
|
|
|
|
|
dfE= |
46,5 |
|
|
|
|
|
|
|
156,5 |
|
dfF= |
156,5 |
|
|
|
|
|
DANE |
|
|
|
OBLICZENIA |
|
|
WYNIKI |
|
|
|
|
|
|
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|
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|
|
|
|
|
|
|
|
|
|
|
y= |
20 |
Szerokość wieńca: |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
50 |
|
|
|
b= |
50 |
|
|
|
|
|
|
|
Prędkość obwodowa dla ustalenia nadwyżki dynamicznej: |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0,64 |
m/s |
|
n= |
0,64 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Wartość współczynnika nadwyżek dynamicznych Cd |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
n= |
0,64 |
|
|
|
1,2 |
IX/13-V |
Cd= |
1,2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Z tablicy IX/11 odczytuję współczynnik przeciążenia Cp |
|
|
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Cp= |
1 |
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Cp= |
1 |
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Ze wzoru IX-9 wyznaczam siłę statyczną: |
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N= |
8 |
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12500 |
[N] |
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Pstat= |
12500 |
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15000 |
[N] |
Pzast= |
15000 |
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eE= |
1,57 |
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eE= |
1,57 |
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eF= |
1,8 |
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eF= |
1,8 |
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eE= |
1,57 |
Zatem ze wzoru I-55: |
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eF= |
1,8 |
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1,69 |
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ea= |
1,69 |
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Pzast= |
15000 |
Siła obliczeniowa [IX-13]: |
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ea= |
1,69 |
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8875,74 |
N |
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Pobl= |
8875,74 |
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Pobl= |
8875,74 |
Sprawdzam naprężenia: |
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l= |
0,387 |
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|
183,48 |
<kgj[MPa]= |
310 |
sgzast[MPa]= |
183,48 |
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b[mm]= |
50 |
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m= |
2,5 |
Na podstawie wzoru X-13 określam moc jaką może prze- |
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dE= |
21 |
nieść przekładnia ze względu na warunek Hertza |
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dF= |
65 |
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kH[Mpa]= |
1322 |
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10,19 |
kW |
N= |
10,19 |
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b[mm]= |
50 |
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nIII= |
233,45 |
Warunek Hertza jest spełniony. |
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Cm,a= |
478,2 |
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3. Obliczanie nacisków w kołach i wałków na zginanie. |
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I. Ustalam siły w kołach stożkowych. |
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Z rysunku XV-14. Dla zębów prostych znaduję siły: |
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Obwodową: |
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N[kW]= |
8 |
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wI[1/s]= |
251,33 |
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1415 |
N |
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PAo= |
1415 |
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deA= |
45 |
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Siłę poosiową koła napędzającego [XV-11]: |
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dA= |
17,14 |
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153 |
N |
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PoA= |
153 |
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an[o]= |
20 |
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DANE |
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OBLICZENIA |
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WYNIKI |
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PAo= |
1415 |
Koła napędzanego: |
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dB= |
72,46 |
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492 |
N |
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PoB= |
492 |
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Siły są skierowane od wierzchołka do podstawy stożka. |
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Siły promieniowe: |
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Koła napędzającego: |
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492 |
N |
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PrA= |
492 |
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PAo= |
1415 |
Koła napędzanego: |
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N |
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PrB= |
153 |
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Dla wału I obliczam reakcje w podporach w 2 płaszczyznach |
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z kołem osadzonym poza łożyskami [rys. XV-17] |
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Szerokość łożyska: |
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B1 [mm]= |
14 |
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B2 [mm]= |
14 |
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Odległość między łożyskami: |
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L1[mm]= |
25 |
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Odległość między łożyskiem 1, a kołem A: |
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L2[mm]= |
6 |
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dA= |
17,14 |
Obliczeniowa szerokość koła A: |
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b= |
22 |
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e= |
21 |
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Zakładam rozstaw między łożyskami: |
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39 |
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b= |
39 |
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Odległość między łożyskiem ł1, a osią koła: |
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23,5 |
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a= |
23,5 |
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Reakcje w płaszczyźnie poziomej H: |
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b= |
39 |
Z równania momentów: |
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a= |
23,5 |
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PrA= |
492 |
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|
-208 |
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R2H= |
-208 |
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PAo= |
1415 |
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deA= |
45 |
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700 |
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R1H= |
700 |
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Momenty gnące w płaszczyźnie poziomej: |
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Dla koła A: |
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PoA= |
153 |
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3,4425 |
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Mk= |
3,4425 |
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Dla łożyska ł1: |
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b= |
39 |
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a= |
23,5 |
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-8,1195 |
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Mk= |
3,4425 |
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R1H= |
700 |
Dla łożyska ł2: |
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Mł1H= |
-8,1195 |
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PrA= |
492 |
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0 |
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Mł2= |
0 |
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Reakcje w płaszczyźnie pionowej V: |
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DANE |
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OBLICZENIA |
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WYNIKI |
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P= |
1415 |
|
2267,62820512821 |
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R1V= |
2267,62820512821 |
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-852,628205128205 |
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R2V= |
-852,628205128205 |
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Momenty gnące w płaszczyźnie pionowej: |
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Dla koła A MgA: |
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0 |
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MgA= |
0 |
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Dla łożyska ł1: |
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Mgł1= |
33,2525 |
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33,2525 |
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Mgł2= |
0 |
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Dla łożyska ł2: |
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0 |
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Moment skręcający na wałku: |
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N[kW]= |
8 |
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wI[1/s]= |
251,33 |
32 |
Nm |
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Ms= |
32 |
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Momenty zastępcze do obliczeń średnic wałków: |
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Dla koła: |
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Mk= |
3,4425 |
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27,9 |
Nm |
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MZk= |
27,9 |
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Ms= |
32 |
Dla łożyska ł1: |
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MZł1= |
44 |
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Mgł1V= |
33,2525 |
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44 |
Nm |
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Mł1H= |
-8,1195 |
Dla łożyska ł2 moment zastępczy jest równy momentowi |
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skręcającemu: |
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Nm |
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MZł2= |
32 |
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Minimalne średnice wałka dla obciążeń złożonych: |
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Na wałek dobieram stal do nawęglania: |
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15 |
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stal |
15 |
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MZk= |
27,9 |
Pod koło zębate z warunku na skręcanie: |
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dla stali |
15 |
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Kt[MPa]= |
90 |
18,4 |
dobieram |
20 |
Dk[mm]= |
20 |
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kgj[MPa]= |
140 |
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Pod łozysko ł1 z warunku na zginanie: |
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MZł1= |
44 |
14,6 |
dobieram |
20 |
Dł1= |
20 |
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Pod łozysko ł2 z warunku na skręcanie: |
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19,2 |
dobieram |
20 |
Dł2= |
20 |
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1. Obliczenie wałka II |
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Siły pochodzące od koła B: |
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POB= |
492 |
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PrB= |
153 |
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PBo= |
1415 |
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Siła obwodowa koła C: |
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N[kW]= |
8 |
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wII[1/s]= |
78 |
4884 |
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PCo= |
4884 |
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dpC= |
42 |
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an[o]= |
20 |
Siła promieniowa: |
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PCo= |
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PCo= |
4884 |
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|
1778 |
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PrC= |
1778 |
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DANE |
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OBLICZENIA |
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WYNIKI |
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Dla wału II obliczam reakcje w podporach w 2 płaszczyznach |
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z kołem stożkowym osadzonym między łożyskami wraz |
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z kołem walcowym |
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Dla potrzeb obliczeń zakładam: |
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Szerokość łożyska: |
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B1 [mm]= |
14 |
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B2 [mm]= |
14 |
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Odległość między łożyskiem B1 a kołem B: |
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L1[mm]= |
16 |
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Odległość między kołami: |
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L2[mm]= |
10 |
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Odległość między łożyskiemB2, a kołem C: |
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L3[mm]= |
70 |
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Obliczeniowa szerokość koła B e: |
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b[mm]= |
22 |
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e[mm]= |
7 |
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Zakładam rozstaw między łożyskiem B1 a kołem B: |
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L1[mm]= |
16 |
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26,5 |
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Zakładam rozstaw między kołami B i C: |
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a[mm]= |
26,5 |
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L2[mm]= |
10 |
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33,5 |
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b[mm]= |
33,5 |
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Odległość między łożyskiem B2, a osią koła C: |
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c[mm]= |
97 |
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L3[mm]= |
70 |
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97 |
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Długość wałka między osiami łożysk: |
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a[mm]= |
26,5 |
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157 |
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Lc[mm]= |
157 |
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b[mm]= |
33,5 |
Reakcje w płaszczyźnie poziomej H: |
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c[mm]= |
97 |
Z równania momentów: |
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PrC= |
1778 |
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PrB= |
153 |
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881 |
N |
R2H= |
881 |
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deB= |
145 |
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Lc[mm]= |
157 |
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POB= |
492 |
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Przemysłw Kowalak:
siła skierowana w dół jest
dodatnia
744 |
N |
R1H= |
744 |
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Momenty gnące w płaszczyźnie poziomej: |
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Dla łożyska ł1: |
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0 |
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Mł1= |
0 |
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Dla koła B: |
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R2H= |
881 |
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R1H= |
744 |
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-55 |
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MKB= |
-55 |
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Dla koła C: |
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-85 |
MKC= |
-85 |
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Dla łożyska ł2: |
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0 |
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Mł2= |
0 |
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Reakcje w płaszczyźnie pionowej V: |
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4194 |
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R1V= |
4194 |
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2105 |
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R2V= |
2105 |
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DANE |
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OBLICZENIA |
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WYNIKI |
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Momenty gnące w płaszczyźnie pionowej: |
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Dla łożyska ł1: |
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0 |
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Mł1= |
0 |
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111,141 |
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MKB= |
111,141 |
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Dla koła C: |
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204,2375 |
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MKC= |
204,2375 |
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Dla łożyska ł2: |
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0 |
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Moment skręcający na wałku: |
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102,6 |
Nm |
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MsII= |
102,6 |
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Momenty zastępcze do obliczeń średnic wałków: |
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Dla łożyska ł1: |
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MKBV= |
111,141 |
Mzł1= |
0 |
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Mzł1= |
0 |
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MKBH= |
-55 |
Dla koła B: |
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MsII= |
102,6 |
|
152,6 |
MzB= |
152,6 |
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Dla koła C: |
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MKCH= |
-85 |
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238,4 |
MzC= |
238,4 |
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MKCV= |
204,2375 |
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Dla łożyska ł2: |
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MZł2= |
0 |
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Minimalne średnice wałka dla obciążeń złożonych: |
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MzB= |
152,6 |
Pod koło zębate B: |
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MzC= |
238,4 |
22,2 |
dobieram |
28 |
DB[mm]= |
28 |
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dla stali |
15 |
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Kt[MPa]= |
90 |
Pod koło C: |
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kgj[MPa]= |
140 |
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25,7 |
dobieram |
34 |
Dc[mm]= |
34 |
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WAŁEK -III- |
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Obliczam siły działające na koło D |
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N[kW]= |
8 |
-obwodową |
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wIII[1/s]= |
24,45 |
|
4883,55767176388 |
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PDo= |
4883,55767176388 |
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dD= |
134 |
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-promieniową |
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PDo= |
4883,55767176388 |
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|
1777 |
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PDr= |
1777 |
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an[o]= |
20 |
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Obliczam siły działające na koło E |
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-obwodową |
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dE= |
52,5 |
|
12465 |
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PEo= |
12465 |
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-promieniową |
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PEo= |
12465 |
|
4537 |
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PEr= |
4537 |
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Obliczam długość wałka |
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60 |
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DANE |
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OBLICZENIA |
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WYNIKI |
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-szerokość łożyska A |
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|
55 |
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BA= |
14 |
[mm] |
47 |
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-odstęp pomiędzy łożyskiem A a kołem zębatym D |
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L1= |
33 |
[mm] |
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-szerokość wieńca zębatego koła D |
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bD= |
40 |
[mm] |
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-odstęp pomiędzy kołem zębatym D a kołem zębatym E |
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L2= |
10 |
[mm] |
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-szerokość wieńca zębatego koła E |
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bE= |
50 |
[mm] |
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-odstęp pomiędzy łożyskiem B a kołem zębatym E |
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L3= |
10 |
[mm] |
0 |
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-szerokość łożyska B |
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|
60 |
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BB= |
24 |
[mm] |
115 |
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|
162 |
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Zakładam rozstaw między łożyskiem A a kołem D: |
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|
60 |
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Zakładam rozstaw między kołami D i E: |
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a[mm]= |
60 |
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L1= |
33 |
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|
55 |
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b[mm]= |
55 |
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L2= |
10 |
Odległość między łożyskiem B2, a osią koła C: |
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c[mm]= |
47 |
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L3= |
10 |
|
47 |
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a[mm]= |
60 |
Długość wałka między osiami łożysk: |
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b[mm]= |
55 |
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|
162 |
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Lc= |
162 |
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c[mm]= |
47 |
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bD= |
40 |
Obliczam reakcję łożysk w płaszczyźnie |
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bE= |
50 |
-pionowej |
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PDo= |
4883,55767176388 |
10657 |
R2V= |
10657 |
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PEo= |
12465 |
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R2V= |
10657 |
6692 |
R1V= |
6692 |
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PDr= |
1777 |
|
2563 |
R2H= |
2563 |
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PEr= |
4537 |
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R2H= |
2563 |
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|
-197 |
R1H= |
-197 |
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Obliczam momenty gnące działającena wałek: |
|
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Mł1= |
0 |
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- w płaszczyźnie pionowej |
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Mg1H= |
0 |
|
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R1V= |
6692 |
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|
401,5 |
MgDV= |
401,5 |
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|
1038,2 |
MgEV= |
1038,2 |
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Mg2H= |
0 |
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|
- w płaszczyźnie poziomej |
|
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Mg1H= |
0 |
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|
-11,82 |
|
MgDH= |
-11,82 |
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R1H= |
-197 |
75,08 |
|
MgEH= |
75,08 |
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|
0 |
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|
Obliczam moment skręcający na wałku |
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N[kW]= |
8 |
Ms1= |
0 |
Ms2= |
0 |
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wIII[1/s]= |
24,45 |
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MsE=MsD= |
|
327,2 |
|
Ms= |
327,2 |
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327,2 |
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DANE |
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OBLICZENIA |
|
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WYNIKI |
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MgDV= |
401,5 |
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MgEV= |
1038,2 |
Obliczam rzeczywisty moment zginający wałki |
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401,7 |
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MgD= |
401,7 |
|
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MgDH= |
-11,82 |
1040,9 |
MgE= |
1040,9 |
|
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MgEH= |
75,08 |
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Dla łożysk moment gnący nie występuje Mg= |
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|
0 |
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Korzystając z teorii Hubera wytrzymałości materiałów |
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obliczam naprężenia zastępcze |
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MgD= |
401,7 |
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MgE= |
1040,9 |
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491,6 |
MZD= |
491,6 |
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Ms= |
327,2 |
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MZE= |
1078,8 |
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1078,8 |
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Dla łożysk moment gnący nie występuje Mg= |
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0 |
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Minimalne średnice wałka dla obciążeń złożonych: |
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Pod koło zębate B: |
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Na wałek dobieram stal do nawęglania: |
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15 |
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stal |
15 |
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MZD= |
491,6 |
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MZE= |
1078,8 |
32,7 |
dobieram |
36 |
DD= |
36 |
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kgj[MPa]= |
140 |
Pod koło C: |
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42,6 |
dobieram |
44 |
DE= |
44 |
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WAŁEK -IV- |
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Obliczam siły działające na koło F |
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-obwodową |
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PFo= |
12463,5 |
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N[kW]= |
8 |
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12463,5 |
[N] |
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wIV[1/s]= |
7,9 |
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dpF= |
162,5 |
-promieniową |
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PFo= |
12463,5 |
|
4536,34301477681 |
[N] |
PFr= |
4536,34301477681 |
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an[o]= |
20 |
Obliczam długość wałka |
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-szerokość łożyska 1 |
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B1= |
27 |
[mm] |
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-odstęp pomiędzy łożyskiem 1 a kołem zębatym F |
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L1= |
83 |
[mm] |
121,5 |
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-szerokość wieńca zębatego koła F |
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42,5 |
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bF= |
50 |
[mm] |
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-odstęp pomiędzy łożyskiem 2 a kołem zębatym F |
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L2= |
10 |
[mm] |
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-szerokość łożyska 2 |
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B2= |
15 |
[mm] |
0 |
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-długość wałka pod sprzęgło |
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121,5 |
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L3= |
50 |
[mm] |
164 |
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DANE |
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OBLICZENIA |
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WYNIKI |
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L1= |
83 |
Zakładam rozstaw między łożyskiem 1 a kołem F: |
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L2= |
10 |
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121,5 |
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a[mm]= |
121,5 |
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L3= |
50 |
Odległość między łożyskiem 2, a osią koła F: |
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b[mm]= |
42,5 |
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42,5 |
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Długość wałka między osiami łożysk: |
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164 |
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Lc= |
164 |
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Obliczam reakcję łożysk w płaszczyźnie |
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a[mm]= |
121,5 |
-pionowej |
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b[mm]= |
42,5 |
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9233,6 |
[N] |
R2V= |
9233,6 |
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R2V= |
9233,6 |
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R1V= |
3229,9 |
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R1V= |
3229,9 |
3229,9 |
[N] |
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PFo= |
12463,5 |
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-poziomej |
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3360,8 |
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R2H= |
3360,8 |
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R1H= |
1175,54301477681 |
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Obliczam momenty gnące działające na wałek: |
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- w płaszczyźnie pionowej |
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Mg1H= |
0 |
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R1V= |
3229,9 |
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408,3 |
MgFV= |
408,3 |
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a[mm]= |
121,5 |
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Mg2H= |
0 |
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PEo= |
0 |
- w płaszczyźnie poziomej |
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Mg1H= |
0 |
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R1H= |
1175,54301477681 |
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142,8 |
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MgFH= |
142,8 |
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Mg2H= |
0 |
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Obliczam moment skręcający na wałku |
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Dla łożyska 1: |
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Ms1= |
0 |
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N[kW]= |
8 |
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wIV[1/s]= |
7,9 |
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MsF= |
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1012,7 |
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Ms= |
1012,7 |
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1012,7 |
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Ms2= |
1012,7 |
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Obliczam rzeczywisty moment zginający wałki |
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MgFV= |
408,3 |
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MgFH= |
142,8 |
432,6 |
MgF= |
432,6 |
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Dla łożysk moment gnący nie występuje Mg= |
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0 |
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Korzystając z teorii Hubera wytrzymałości materiałów |
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obliczam naprężenia zastępcze |
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MgF= |
432,6 |
|
977,9 |
MZF= |
977,9 |
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Ms= |
1012,7 |
Dla łożysk moment gnący nie występuje Mg= |
0 |
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Dla łożyska ł2 moment zastępczy jest równy momentowi |
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skręcającemu: |
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1012,7 |
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Minimalne średnice wałka dla obciążeń złożonych: |
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Ms= |
1012,7 |
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Na wałek dobieram stal do nawęglania: |
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15HN |
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DANE |
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OBLICZENIA |
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WYNIKI |
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Pod koło zębate z warunku na zginanie: |
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MZF= |
977,9 |
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Ms= |
1012,7 |
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34,4 |
dobieram |
50 |
Df= |
50 |
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dla stali |
15 |
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Kt[MPa]= |
200 |
Pod łożysko ł2 z warunku na skręcanie: |
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kgj[MPa]= |
240 |
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46,6 |
dobieram |
50 |
Dł2= |
50 |
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trwałość |
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V. Obliczam łożyska. |
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LH= |
10000 |
Korzystam ze wzoru z katalogu łożysk tocznych rolkowych: |
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RI1= |
2373,21252244568 |
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RI2= |
877,632529126026 |
21030,295684986 |
N |
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RII1= |
4259,48024998356 |
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RII2= |
2281,92594095426 |
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CI2= |
7777,16762224985 |
N |
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RIII1= |
6694,8990283648 |
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CII1= |
26571,687254324 |
N |
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RIII2= |
10960,8675751512 |
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CII2= |
14235,2162428268 |
N |
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RIV1= |
3437,1725865296 |
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CIII1= |
29488,1529177616 |
N |
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RIV2= |
9826,20708106643 |
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CIII2= |
48277,9109584773 |
N |
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nI[1/min]= |
2400 |
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CIV1= |
10786,8011534906 |
N |
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2400 |
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CIV2= |
30837,3639112206 |
N |
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nII[1/min]= |
744,83 |
Z katalogu łożysk na podstawie dopuszczalnych obciążeń |
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744,83 |
dynamicznych dobieram łożyska: |
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nIII[1/min]= |
233,45 |
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wymiary: |
d[mm] |
D[mm] |
B[mm] |
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233,45 |
łI1= |
30204A |
20 |
47 |
14 |
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nIV[1/min]= |
75,42 |
łI2= |
30204A |
20 |
47 |
14 |
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75,42 |
łII1= |
30204A |
20 |
47 |
14 |
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łII2= |
30204A |
20 |
47 |
14 |
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łIII1= |
NU2305 |
25 |
62 |
24 |
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łIII2= |
NJ2306 |
30 |
72 |
27 |
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łIV1= |
N205 |
25 |
52 |
15 |
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łIV2= |
NJ210 |
50 |
90 |
20 |
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Odległości między osiami kół: |
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łożysk 1 |
łożysk 2 |
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II-III= |
88 |
54,5 |
59,5 |
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III-IV= |
107,5 |
57 |
81 |
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MI[Nm]= |
31,83 |
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MII[Nm]= |
102,56 |
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102,56 |
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MIII[Nm]= |
327,2 |
Pod koła i sprzęgła dobieram następujące średnice: |
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327,2 |
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wymiary: |
t1 |
b |
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MIV[Nm]= |
1012,66 |
sprzęgło wejściowe= |
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20 |
3,5 |
6 |
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1012,66 |
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koło B= |
28 |
4 |
8 |
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koło C= |
34 |
5 |
10 |
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koło D= |
36 |
5 |
10 |
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koło E= |
44 |
5 |
12 |
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koło F= |
50 |
5,5 |
14 |
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sprzęgło wyjściowe= |
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50 |
5,5 |
14 |
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~koło A - wykonane razem z wałkiem. |
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Obliczam siły ścinające wpusty: |
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Dla stali st7 |
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3183 |
N |
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Pdop[MPa]= |
140 |
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FB= |
7325,71428571429 |
N |
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FC= |
6032,94117647059 |
N |
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FD= |
18177,7777777778 |
N |
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FE= |
14872,7272727273 |
N |
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FF= |
40506,4 |
N |
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Fwy= |
40506,4 |
N |
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Obliczam długości wpustów z nacisków powierzchniowych |
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12 |
dobieram |
25 |
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lB= |
21 |
dobieram |
22 |
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lC= |
19 |
dobieram |
26 |
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N[kW]= |
8 |
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lD= |
36 |
dobieram |
38 |
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ir2= |
0,313432835820896 |
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lE= |
33 |
dobieram |
36 |
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ir3= |
0,323076923076923 |
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lF= |
67 |
dobieram |
2x40 |
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lwy= |
67 |
dobieram |
2x40 |
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zC= |
21 |
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zE= |
21 |
V. Obliczam przekładnię na zagrzanie |
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Wyznaczam moc tarcia dla kół stożkowych wg [XI-17] |
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0,0664 |
[kW] |
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0,0715 |
[kW] |
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0,072 |
[kW] |
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0,2099 |
[kW] |
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Zatem współczynnik pewności na zagrzanie: |
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2,3 |
>1 |
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