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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maszyny parowej przenoszącej moment na wentylator |
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N [kW] = |
14 |
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Przełożenie: |
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Wykonać: |
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i =1: |
10 |
1. Kompletne obliczenia. |
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Obroty wejścia: |
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2. Rysunek zestawieniowy w skali 1:1. |
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n[1/min]= |
1000 |
3. Dobrać samodzielnie materiały. |
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4. Rysunki detali. |
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Schemat kinematyczny: |
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I |
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D |
E
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F
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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: |
2,5 |
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iI = 1: |
2,5 |
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iII = 1: |
2 |
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iII = 1: |
2 |
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iIII = 1: |
2 |
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iIII = 1: |
2 |
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Teoretyczne przełożenie całkowite: |
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ic = 1: |
10 |
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ic = 1: |
10 |
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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= |
45 |
koło A z= |
18 |
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koło C z= |
19 |
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koło D z= |
38 |
koło C z= |
19 |
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koło E z= |
19 |
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koło F z= |
38 |
koło E z= |
19 |
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Przełożenie rzeczywiste: |
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koło B z= |
45 |
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ir = 1: |
10 |
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koło D z= |
38 |
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Obliczam prędkości obrotowe poszczególnych wałków |
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koło F z= |
38 |
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w/g wzoru: |
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ir = 1: |
10 |
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koło A z= |
18 |
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koło C z= |
19 |
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koło E z= |
19 |
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nI[1/min]= |
1000 |
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koło B z= |
45 |
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nII[1/min]= |
400 |
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nII[1/min]= |
400 |
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koło D z= |
38 |
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nIII[1/min]= |
200 |
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nIII[1/min]= |
200 |
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koło F z= |
38 |
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nIV[1/min]= |
100 |
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nIV[1/min]= |
100 |
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Korzystając ze wzoru : |
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nI[1/min]= |
1000 |
obliczam prędkości kątowe wałków: |
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nII[1/min]= |
400 |
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wI[1/s]= |
104,72 |
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nIII[1/min]= |
200 |
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wII[1/s]= |
41,89 |
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wII[1/s]= |
41,89 |
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nIV[1/min]= |
100 |
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wIII[1/s]= |
20,94 |
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wIII[1/s]= |
20,94 |
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wIV[1/s]= |
10,47 |
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wIV[1/s]= |
10,47 |
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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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68,12 |
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68,2 |
dB[o]= |
68,12 |
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Dla koła małego dA= |
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21,48 |
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21,8 |
dA[o]= |
21,48 |
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Na podstawie wzoru IV/36 obliczam zastępcze liczby |
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zębów: |
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dB= |
68,12 |
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19,39 |
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ZvA= |
19,39 |
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dA= |
21,48 |
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#DIV/0! |
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121,17 |
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ZvB= |
121,17 |
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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] = |
14 |
Mając wszystkie dane obliczam moduł koła małego w/g |
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dA= |
21,48 |
wzoru XI-10 dla zębów prostych: |
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bm= |
0 |
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Cb= |
1 |
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2,188 |
mnm= |
2,188 |
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lzast= |
0,387 |
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ZvA= |
19,39 |
Dobieram znormalizowany czołowy moduł zewnętrzny |
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nI[1/min]= |
1000 |
mte[mm]= |
3 |
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mte[mm]= |
3 |
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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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54 |
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deA= |
54 |
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ZB= |
45 |
Dla koła dużego: |
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135 |
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deB= |
135 |
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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]= |
3 |
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72,7 |
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Re= |
72,7 |
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dA= |
21,48 |
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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= |
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atm[o]= |
20 |
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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]= |
3 |
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ham= |
3 |
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3,6 |
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hfm= |
3,6 |
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Średnice wierzchołkowe [IV-32]: |
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deA= |
54 |
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59,57 |
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daeA= |
59,57 |
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deB= |
135 |
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137,23 |
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daeB= |
137,23 |
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ham= |
3 |
Wysokości stożków wierzchołkowych [IV-33] |
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hfm= |
3,6 |
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dB[o]= |
68,12 |
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66,39 |
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BB= |
24,21 |
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dA[o]= |
21,48 |
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24,21 |
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BA= |
66,39 |
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Kąty wysokości głowy zęba [IV-25]: |
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0,041265474552957 |
[o] |
2,22 |
Qa[o]= |
2,22 |
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Re= |
72,7 |
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2,36 |
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oraz stopy zęba [IV-26]: |
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0,049518569463549 |
[o] |
2,5 |
Qf[o]= |
2,5 |
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2,84 |
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Kąty stożków wierzchołkowych [IV-27]: |
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tgQa[o]= |
2,22 |
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tgQf[o]= |
2,5 |
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24,16 |
setne |
24,1 |
daA[o]= |
24,1 |
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daB[o]= |
70,34 |
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70,56 |
setne |
70,34 |
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dB[o]= |
68,12 |
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dA[o]= |
21,48 |
i dna wrębów [IV-28]: |
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18,97 |
setne |
18,58 |
dfA[o]= |
18,58 |
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dfB[o]= |
65,22 |
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65,37 |
setne |
65,22 |
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Dobieram szerokość wieńca około b=1/3,5 Re: |
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b[mm]= |
21 |
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b[mm]= |
21 |
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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= |
46,2008253094911 |
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49,76 |
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dvmnA= |
49,76 |
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dA[o]= |
21,48 |
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oraz przełożenie czołowe [IV-9]: |
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ZA= |
18 |
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ZB= |
45 |
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0,16 |
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iv= |
0,16 |
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Przyjmuję materiałowy współczynnik Cm,a= |
478,2 |
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dobrałem |
z tablic: |
Dopuszczalny nacisk jednostkowy w/g Hertza [X-25]: |
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|
X-8, X/10, |
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|
X/11, IX-48 |
|
|
|
1322 |
MPa |
|
kH[Mpa]= |
1322 |
|
|
|
|
|
ZHj[MPa]= |
1600 |
|
|
|
|
|
|
|
|
|
|
|
|
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= |
1,53 |
|
|
eA= |
1,53 |
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eB= |
1,73 |
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|
|
Zatem ze wzoru I-55: |
|
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eB= |
1,73 |
|
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|
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eA= |
1,53 |
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eB= |
1,73 |
1,63 |
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|
Cm,a= |
478,2 |
|
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|
ea= |
1,63 |
|
|
|
|
|
nI[1/min]= |
1000 |
|
|
|
|
|
|
|
|
|
|
|
|
kH[Mpa]= |
1322 |
|
|
|
|
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|
|
|
|
ea= |
1,63 |
30,63 |
N[kW]= |
30,63 |
|
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|
b[mm]= |
21 |
|
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dvmnA= |
49,76 |
Warunek Hertza jest spełniony. |
|
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|
bm= |
0 |
Prędkość obwodowa dla ustalenia nadwyżki dynamicznej: |
|
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|
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|
|
|
iv= |
0,16 |
|
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|
dC= |
1,73 |
|
|
2,61 |
m/s |
|
n= |
2,61 |
|
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|
|
|
nII= |
1 |
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|
Wartość współczynnika nadwyżek dynamicznych Cd |
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|
1,4 |
IX/13-V |
Cd= |
1,4 |
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|
|
|
|
n= |
2,61 |
Z tablicy IX/11 odczytuję współczynnik przeciążenia Cp |
|
|
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|
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|
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|
Cp= |
1,25 |
|
|
Cp= |
1,25 |
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|
Ze wzoru IX-9 wyznaczam siłę statyczną: |
|
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|
DANE |
|
|
|
OBLICZENIA |
|
|
WYNIKI |
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N[kW]= |
14 |
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5363,98 |
[N] |
|
Pstat= |
5363,98 |
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9386,97 |
[N] |
Pzast= |
9386,97 |
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|
Siła obliczeniowa [IX-13]: |
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Pzast= |
9386,97 |
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ea= |
1,63 |
5689,07 |
N |
|
Pobl= |
5689,07 |
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Sprawdzam naprężenia: |
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Pobl= |
5689,07 |
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l= |
0,387 |
|
|
233,34 |
<kgj[MPa]= |
310 |
sgzast[MPa]= |
233,34 |
|
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b[mm]= |
21 |
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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]= |
14 |
Obliczam minimalny moduł [X-4]: |
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y= |
20 |
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l= |
0,387 |
|
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|
2,44 |
mm |
mo= |
2,44 |
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nII= |
400 |
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ZC= |
19 |
Dobieram moduł czołowy m= |
|
|
3,5 |
|
m= |
3,5 |
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|
Średnice podziałowe kół : |
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|
66,5 |
|
|
dC= |
66,5 |
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|
ZD= |
38 |
|
|
133 |
|
|
dD= |
133 |
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|
m= |
3,5 |
Średnice głów zębów: |
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|
dC= |
66,5 |
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|
73,5 |
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dD= |
133 |
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daC= |
73,5 |
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y= |
1 |
|
|
140 |
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daD= |
140 |
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|
Średnice stóp zębów: |
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c=0,2m |
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|
58,1 |
|
dfC= |
58,1 |
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124,6 |
|
dfD= |
124,6 |
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y= |
20 |
Szerokość wieńca: |
|
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|
m= |
3,5 |
|
70 |
|
|
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b[mm]= |
70 |
|
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|
|
Prędkość obwodowa dla ustalenia nadwyżki dynamicznej: |
|
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dC= |
66,5 |
|
|
1,39 |
m/s |
|
n= |
1,39 |
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nII= |
400 |
|
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|
|
Wartość współczynnika nadwyżek dynamicznych Cd |
|
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|
1,29 |
IX/13-V |
Cd= |
1,29 |
|
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|
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|
|
|
n= |
1,39 |
Z tablicy IX/11 odczytuję współczynnik przeciążenia Cp |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cp= |
1,25 |
|
|
Cp= |
1,25 |
|
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|
|
Ze wzoru IX-9 wyznaczam siłę statyczną: |
|
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|
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|
|
N[kW]= |
14 |
|
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|
10071,94 |
[N] |
|
Pstat= |
10071,94 |
|
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|
16241 |
[N] |
Pzast= |
16241 |
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|
eC= |
1,53 |
|
|
eC= |
1,53 |
|
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|
|
eD= |
1,7 |
|
|
eD= |
1,7 |
|
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|
|
Zatem ze wzoru I-55: |
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|
eC= |
1,53 |
|
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eD= |
1,7 |
1,62 |
|
|
ea= |
1,62 |
|
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|
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|
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|
|
|
|
|
|
|
|
|
|
Siła obliczeniowa [IX-13]: |
|
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|
|
|
|
|
|
|
|
Pzast= |
16241 |
|
|
|
|
|
|
|
|
|
|
|
ea= |
1,62 |
10025,31 |
N |
|
Pobl= |
10025,31 |
|
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|
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|
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|
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|
|
Sprawdzam naprężenia: |
|
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|
|
|
|
|
|
|
|
Pobl= |
10025,31 |
|
|
|
|
|
|
|
|
|
|
|
|
l= |
0,387 |
|
|
105,74 |
<kgj[MPa]= |
310 |
sgzast[MPa]= |
105,74 |
|
|
|
|
|
b[mm]= |
70 |
|
|
|
|
|
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|
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|
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|
|
m= |
3,5 |
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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|
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|
|
|
|
|
|
dC= |
66,5 |
|
|
|
|
|
|
|
|
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|
|
dD= |
133 |
|
|
|
34,6 |
kW |
N= |
34,6 |
|
|
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|
|
kH[Mpa]= |
1322 |
|
|
|
|
|
|
|
|
|
|
|
|
b[mm]= |
70 |
Warunek Hertza jest spełniony. |
|
|
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|
|
|
|
|
|
|
|
nII= |
400 |
|
|
|
|
|
|
|
|
|
|
|
|
Cm,a= |
478,2 |
III. Para kół EF- koła walcowe o zębach prostych. |
|
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|
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|
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|
|
|
|
|
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|
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|
|
Na materiał dobieram stal jak dla kół stożkowych |
|
|
|
|
|
|
|
|
|
|
|
|
|
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]= |
14 |
Obliczam minimalny moduł [X-4]: |
|
|
|
|
|
|
|
|
|
|
|
y= |
20 |
|
|
|
|
|
|
|
|
|
|
|
|
l= |
0,387 |
|
|
|
3,08 |
mm |
mo= |
3,08 |
|
|
|
|
|
kgj [MPa]= |
310 |
|
|
|
|
|
|
|
|
|
|
|
|
nIII[1/min]= |
200 |
Dobieram moduł czołowy m= |
|
|
4 |
|
m= |
4 |
|
|
|
|
|
ZE= |
19 |
Średnice podziałowe kół : |
|
|
|
|
|
|
|
|
|
|
|
ZF= |
38 |
|
76 |
|
|
dE= |
76 |
|
|
|
|
|
|
|
152 |
|
|
dF= |
152 |
|
|
|
|
|
m= |
4 |
Średnice głów zębów: |
|
|
|
|
|
|
|
|
|
|
|
dE= |
76 |
|
|
84 |
|
|
|
|
|
|
|
|
|
dF= |
152 |
|
|
|
daE= |
84 |
|
|
|
|
|
y= |
1 |
|
|
daF= |
160 |
|
|
|
|
|
|
|
Średnice stóp zębów: |
|
|
|
|
|
|
|
|
|
|
|
c=0,2m |
|
|
66,4 |
|
|
|
|
|
|
|
|
|
|
|
|
dfE= |
66,4 |
|
|
|
|
|
|
|
142,4 |
|
dfF= |
142,4 |
|
|
|
|
|
DANE |
|
|
|
OBLICZENIA |
|
|
WYNIKI |
|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
|
|
y= |
20 |
Szerokość wieńca: |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
80 |
|
|
|
b= |
80 |
|
|
|
|
|
|
|
Prędkość obwodowa dla ustalenia nadwyżki dynamicznej: |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0,8 |
m/s |
|
n= |
0,8 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Wartość współczynnika nadwyżek dynamicznych Cd |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
n= |
0,8 |
|
|
|
1,22 |
IX/13-V |
Cd= |
1,22 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Z tablicy IX/11 odczytuję współczynnik przeciążenia Cp |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cp= |
1,25 |
|
|
Cp= |
1,25 |
|
|
|
|
|
|
|
Ze wzoru IX-9 wyznaczam siłę statyczną: |
|
|
|
|
|
|
|
|
|
|
|
N= |
14 |
|
|
|
|
|
|
|
|
|
|
|
|
|
17500 |
[N] |
|
Pstat= |
17500 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
26687,5 |
[N] |
Pzast= |
26687,5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
eE= |
1,53 |
|
|
eE= |
1,53 |
|
|
|
|
|
|
|
|
eF= |
1,7 |
|
|
eF= |
1,7 |
|
|
|
|
|
eE= |
1,53 |
Zatem ze wzoru I-55: |
|
|
|
|
|
|
|
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|
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eF= |
1,7 |
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1,62 |
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ea= |
1,62 |
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Pzast= |
26687,5 |
Siła obliczeniowa [IX-13]: |
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ea= |
1,62 |
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16473,77 |
N |
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Pobl= |
16473,77 |
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Pobl= |
16473,77 |
Sprawdzam naprężenia: |
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l= |
0,387 |
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133,02 |
<kgj[MPa]= |
310 |
sgzast[MPa]= |
133,02 |
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b[mm]= |
80 |
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m= |
4 |
Na podstawie wzoru X-13 określam moc jaką może prze- |
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ZE= |
19 |
nieść przekładnia ze względu na warunek Hertza |
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ZF= |
38 |
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kH[MPa]= |
1322 |
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25,83 |
kW |
N= |
25,83 |
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b[mm]= |
80 |
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nIII= |
200 |
Warunek Hertza jest spełniony. |
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Cm,a= |
478,2 |
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dE= |
76 |
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]= |
14 |
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wI[1/s]= |
104,72 |
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4951 |
N |
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PAo= |
4951 |
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deA= |
54 |
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Siłę poosiową koła napędzającego [XV-11]: |
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dA= |
21,48 |
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N |
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PoA= |
669 |
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an[o]= |
20 |
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PAo= |
4951 |
Koła napędzanego: |
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dB= |
68,12 |
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1673 |
N |
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PoB= |
1673 |
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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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1673 |
N |
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PrA= |
1673 |
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PAo= |
4951 |
Koła napędzanego: |
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N |
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PrB= |
669 |
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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]= |
24 |
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B2 [mm]= |
24 |
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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= |
21,48 |
Obliczeniowa szerokość koła A: |
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b= |
21 |
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e= |
19 |
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Zakładam rozstaw między łożyskami: |
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49 |
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b= |
49 |
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Odległość między łożyskiem ł1, a osią koła: |
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27,5 |
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a= |
27,5 |
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Reakcje w płaszczyźnie poziomej H: |
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Z równania momentów: |
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R2H= |
570 |
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b= |
49 |
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570 |
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a= |
27,5 |
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PrA= |
1673 |
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PAo= |
4951 |
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|
-2243 |
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R1H= |
-2243 |
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deA= |
54 |
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Momenty gnące w płaszczyźnie poziomej H: |
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Dla koła A: |
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PoA= |
669 |
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18,063 |
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Mk= |
18,063 |
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Dla łożyska ł1: |
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b= |
49 |
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a= |
27,5 |
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-27,9445 |
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Mk= |
18,063 |
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R1H= |
-2243 |
Dla łożyska ł2: |
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Mł1H= |
-27,9445 |
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PrA= |
1673 |
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0 |
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Mł2= |
0 |
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Reakcje w płaszczyźnie pionowej V: |
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P= |
4951 |
|
-7729,62244897959 |
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R1V= |
-7729,62244897959 |
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2778,62244897959 |
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R2V= |
2778,62244897959 |
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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= |
136,1525 |
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136,1525 |
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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]= |
14 |
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wI[1/s]= |
104,72 |
134 |
Nm |
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Ms= |
134 |
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Momenty zastępcze do obliczeń średnic wałków: |
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Dla koła: |
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Mk= |
18,063 |
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117,4 |
Nm |
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MZk= |
117,4 |
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Ms= |
134 |
Dla łożyska ł1: |
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MZł1= |
181,1 |
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Mgł1V= |
136,1525 |
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181,1 |
Nm |
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Mł1H= |
-27,9445 |
Dla łożyska ł2 moment zastępczy jest równy momentowi |
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skręcającemu: |
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134 |
Nm |
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MZł2= |
134 |
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Minimalne średnice wałka dla obciążeń złożonych: |
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Na wałek dobieram stal do nawęglania: |
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16HG |
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stal |
16HG |
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MZk= |
117,4 |
Pod koło zębate z warunku na skręcanie: |
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dla stali |
16HG |
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Kt[MPa]= |
200 |
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kgj[MPa]= |
310 |
22,7 |
dobieram |
25 |
Dk[mm]= |
25 |
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dla stali |
16HG |
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Kt[MPa]= |
90 |
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kgj[MPa]= |
140 |
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MZł1= |
181,1 |
18 |
|
25 |
Dł1= |
18 |
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Pod łozysko ł2 z warunku na skręcanie: |
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23,8 |
|
25 |
Dł2= |
23,8 |
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1. Obliczenie wałka II |
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Siły pochodzące od koła B: |
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POB= |
1673 |
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PrB= |
669 |
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PBo= |
4951 |
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Siła obwodowa koła C: |
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N[kW]= |
14 |
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wII[1/s]= |
41,89 |
10051 |
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PCo= |
10051 |
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dpC= |
66,5 |
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an[o]= |
20 |
Siła promieniowa: |
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PCo= |
10051 |
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|
3658 |
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PrC= |
3658 |
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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]= |
24 |
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B2 [mm]= |
15 |
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Odległość między łożyskiem B1 a kołem B: |
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L1[mm]= |
20 |
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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]= |
92,5 |
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Obliczeniowa szerokość koła B e: |
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b[mm]= |
21 |
|
8 |
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e[mm]= |
8 |
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Zakładam rozstaw między łożyskiem B1 a kołem B: |
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36 |
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L1[mm]= |
20 |
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Zakładam rozstaw między kołami B i C: |
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a[mm]= |
36 |
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L2[mm]= |
10 |
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|
49 |
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b[mm]= |
49 |
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Odległość między łożyskiem B2, a osią koła C: |
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c[mm]= |
135 |
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L3[mm]= |
92,5 |
|
135 |
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Długość wałka między osiami łożysk: |
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a[mm]= |
36 |
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|
220 |
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Lc[mm]= |
220 |
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b[mm]= |
49 |
Reakcje w płaszczyźnie poziomej H: |
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c[mm]= |
135 |
Z równania momentów: |
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PrC= |
3658 |
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PrB= |
669 |
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1817 |
N |
R2H= |
1817 |
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deB= |
135 |
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Lc[mm]= |
220 |
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POB= |
1673 |
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Przemysłw Kowalak:
siła skierowana w dół jest
dodatnia
1172 |
N |
R1H= |
1172 |
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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= |
1817 |
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R1H= |
1172 |
-155 |
|
MKB= |
-155 |
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Dla koła C: |
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-245 |
MKC= |
-245 |
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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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10308 |
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R1V= |
10308 |
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R2V= |
4694 |
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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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371,088 |
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MKB= |
371,088 |
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Dla koła C: |
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633,581 |
|
MKC= |
633,581 |
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Dla łożyska ł2: |
|
0 |
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Moment skręcający na wałku: |
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334,2 |
Nm |
|
MsII= |
334,2 |
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Momenty zastępcze do obliczeń średnic wałków: |
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Dla łożyska ł1: |
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MKBV= |
371,088 |
Mzł1= |
0 |
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Mzł1= |
0 |
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MKBH= |
-155 |
Dla koła B: |
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MsII= |
334,2 |
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MzB= |
495,5 |
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495,5 |
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Dla koła C: |
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MKCH= |
-245 |
738,4 |
MzC= |
738,4 |
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MKCV= |
633,581 |
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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= |
495,5 |
Pod koło zębate B: |
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MzC= |
738,4 |
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dla stali |
15 |
32,8 |
dobieram |
36 |
DB[mm]= |
36 |
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Kt[MPa]= |
90 |
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kgj[MPa]= |
140 |
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37,5 |
dobieram |
42 |
Dc[mm]= |
42 |
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WAŁEK -III- |
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Obliczam siły działające na koło D |
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N[kW]= |
14 |
-obwodową |
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wIII[1/s]= |
20,94 |
|
10053,7877645403 |
|
PDo= |
10053,7877645403 |
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dD= |
133 |
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-promieniową |
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PDo= |
10053,7877645403 |
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|
3659 |
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PDr= |
3659 |
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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= |
76 |
|
17594 |
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PEo= |
17594 |
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-promieniową |
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PEo= |
17594 |
|
6404 |
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PEr= |
6404 |
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Obliczam długość wałka |
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-szerokość łożyska A |
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|
81 |
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BA= |
15 |
[mm] |
60 |
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-odstęp pomiędzy łożyskiem A a kołem zębatym D |
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L1= |
38 |
[mm] |
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-szerokość wieńca zębatego koła D |
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bD= |
70 |
[mm] |
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-odstęp pomiędzy kołem zębatym D a kołem zębatym E |
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L2= |
6 |
[mm] |
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-szerokość wieńca zębatego koła E |
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bE= |
80 |
[mm] |
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-odstęp pomiędzy łożyskiem B a kołem zębatym E |
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L3= |
6,5 |
[mm] |
0 |
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-szerokość łożyska B |
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|
0 |
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BB= |
27 |
[mm] |
81 |
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|
141 |
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|
Zakładam rozstaw między łożyskiem A a kołem D: |
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|
80,5 |
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Zakładam rozstaw między kołami D i E: |
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a[mm]= |
80,5 |
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L1= |
38 |
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b[mm]= |
81 |
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|
81 |
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Odległość między łożyskiem B2, a osią koła C: |
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L2= |
6 |
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c[mm]= |
60 |
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L3= |
6,5 |
60 |
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|
a[mm]= |
80,5 |
Długość wałka między osiami łożysk: |
|
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b[mm]= |
81 |
|
221,5 |
|
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Lc= |
221,5 |
|
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c[mm]= |
60 |
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bD= |
70 |
Obliczam reakcję łożysk w płaszczyźnie |
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bE= |
80 |
-pionowej |
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PDo= |
10053,7877645403 |
-16482 |
R2V= |
-16482 |
|
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PEo= |
17594 |
|
16482 |
|
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|
|
|
|
R2V= |
-16482 |
-11166 |
R1V= |
-11166 |
|
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|
11166 |
|
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PDr= |
3659 |
|
3339 |
R2H= |
3339 |
|
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PEr= |
6404 |
|
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|
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R2H= |
3339 |
|
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|
594 |
R1H= |
594 |
|
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|
|
Obliczam momenty gnące działającena wałek: |
|
|
Mł1= |
0 |
|
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|
|
- w płaszczyźnie pionowej |
|
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|
|
Mg1H= |
0 |
|
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|
|
R1V= |
-11166 |
|
|
898,9 |
MgDV= |
898,9 |
|
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|
2617,7 |
MgEV= |
2617,7 |
|
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|
0 |
|
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|
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|
|
- w płaszczyźnie poziomej |
|
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|
|
Mg1H= |
0 |
|
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|
47,817 |
|
MgDH= |
47,817 |
|
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|
|
R1H= |
594 |
|
-200,45 |
|
MgEH= |
-200,45 |
|
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|
0 |
|
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|
|
Obliczam moment skręcający na wałku |
|
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|
|
N[kW]= |
14 |
Ms1= |
0 |
Ms2= |
0 |
|
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|
|
wIII[1/s]= |
20,94 |
|
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|
|
MsE=MsD= |
|
668,6 |
|
Ms= |
668,6 |
|
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|
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MgDV= |
898,9 |
|
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|
|
MgEV= |
2617,7 |
Obliczam rzeczywisty moment zginający wałki |
|
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|
900,2 |
|
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|
MgD= |
900,2 |
|
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|
|
MgDH= |
47,817 |
2625,4 |
MgE= |
2625,4 |
|
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|
|
MgEH= |
-200,45 |
|
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|
|
Dla łożysk moment gnący nie występuje Mg= |
|
|
|
0 |
|
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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= |
900,2 |
|
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|
|
MgE= |
2625,4 |
|
1070,3 |
MZD= |
1070,3 |
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Ms= |
668,6 |
|
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MZE= |
2625,4 |
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2625,4 |
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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 D: |
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Na wałek dobieram stal do nawęglania: |
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16HG |
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stal |
16HG |
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MZD= |
1070,3 |
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MZE= |
2625,4 |
32,6 |
dobieram |
40 |
DD= |
40 |
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kgj[MPa]= |
310 |
Pod koło C: |
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43,9 |
dobieram |
46 |
DE= |
46 |
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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= |
17594,1 |
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N[kW]= |
14 |
|
17594,1 |
[N] |
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wIV[1/s]= |
10,47 |
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dpF= |
152 |
-promieniową |
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|
6403,72869870299 |
[N] |
PFr= |
6403,72869870299 |
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PFo= |
17594,1 |
Obliczam długość wałka |
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an[o]= |
20 |
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-szerokość łożyska 1 |
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B1= |
33 |
[mm] |
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-odstęp pomiędzy łożyskiem 1 a kołem zębatym F |
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L1= |
114 |
[mm] |
170,5 |
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-szerokość wieńca zębatego koła F |
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55 |
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bF= |
80 |
[mm] |
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-odstęp pomiędzy łożyskiem 2 a kołem zębatym F |
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L2= |
6,5 |
[mm] |
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-szerokość łożyska 2 |
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B2= |
17 |
[mm] |
0 |
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-długość wałka pod sprzęgło |
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170,5 |
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L3= |
50 |
[mm] |
225,5 |
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L1= |
114 |
Zakładam rozstaw między łożyskiem 1 a kołem F: |
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L2= |
6,5 |
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|
170,5 |
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a[mm]= |
170,5 |
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L3= |
50 |
Odległość między łożyskiem 2, a osią koła F: |
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b[mm]= |
55 |
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55 |
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Długość wałka między osiami łożysk: |
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225,5 |
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Lc= |
225,5 |
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Obliczam reakcję łożysk w płaszczyźnie |
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a[mm]= |
170,5 |
-pionowej |
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b[mm]= |
55 |
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13302,9 |
[N] |
R2V= |
13302,9 |
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R2V= |
13302,9 |
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R1V= |
4291,2 |
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R1V= |
4291,2 |
4291,2 |
[N] |
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PFo= |
17594,1 |
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-poziomej |
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4841,8 |
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R2H= |
4841,8 |
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R1H= |
1561,92869870299 |
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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= |
4291,2 |
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|
825,5 |
MgFV= |
825,5 |
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a[mm]= |
170,5 |
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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= |
1561,92869870299 |
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266,3 |
|
MgFH= |
266,3 |
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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]= |
14 |
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wIV[1/s]= |
10,47 |
|
MsF= |
|
1337,2 |
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Ms= |
1337,2 |
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|
1337,2 |
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Ms2= |
1337,2 |
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Obliczam rzeczywisty moment zginający wałki |
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MgFV= |
825,5 |
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MgFH= |
266,3 |
867,4 |
MgF= |
867,4 |
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Dla łożysk moment gnący nie występuje Mg= |
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0 |
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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= |
867,4 |
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Ms= |
1337,2 |
|
1446,9 |
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MZF= |
1446,9 |
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Dla łożysk moment gnący nie występuje Mg= |
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|
0 |
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Dla łożyska ł2 moment zastępczy jest równy momentowi |
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skręcającemu: |
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|
1337,2 |
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Minimalne średnice wałka dla obciążeń złożonych: |
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|
|
Ms= |
1337,2 |
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|
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Na wałek dobieram stal do nawęglania: |
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|
16HG |
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|
Pod koło zębate z warunku na zginanie: |
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MZF= |
1446,9 |
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Ms= |
1337,2 |
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|
36 |
dobieram |
40 |
Df= |
40 |
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dla stali |
16HG |
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Kt[MPa]= |
200 |
Pod łożysko ł2 z warunku na skręcanie: |
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kgj[MPa]= |
310 |
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|
51,1 |
dobieram |
55 |
Dł2= |
55 |
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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= |
8048,48508750369 |
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RI2= |
2836,48421712044 |
54847,8387154533 |
N |
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RII1= |
10374,4131400287 |
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RII2= |
5033,40093773584 |
|
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CI2= |
19329,7281622725 |
N |
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|
|
RIII1= |
11181,7884079426 |
|
|
CII1= |
53706,5075018712 |
N |
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|
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RIII2= |
16816,8143534975 |
|
|
CII2= |
26057,029113233 |
N |
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RIV1= |
4566,62005205513 |
|
|
CIII1= |
47018,1615346115 |
N |
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RIV2= |
14156,630095118 |
|
|
CIII2= |
70712,8113074178 |
N |
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|
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nI[1/min]= |
1000 |
|
|
CIV1= |
15596,9706329299 |
N |
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|
1000 |
|
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CIV2= |
48350,9776022289 |
N |
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nII[1/min]= |
400 |
Z katalogu łożysk na podstawie dopuszczalnych obciążeń |
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|
400 |
dynamicznych dobieram łożyska: |
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nIII[1/min]= |
200 |
|
wymiary: |
d[mm] |
D[mm] |
B[mm] |
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|
200 |
łI1= |
32305A |
25 |
62 |
24 |
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nIV[1/min]= |
100 |
łI2= |
32305A |
25 |
62 |
24 |
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|
100 |
łII1= |
32305A |
25 |
62 |
24 |
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łII2= |
30304A |
20 |
52 |
15 |
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łIII1= |
NU2306 |
30 |
72 |
27 |
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łIII2= |
NJ2308 |
40 |
90 |
33 |
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łIV1= |
NJ305 |
25 |
62 |
17 |
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łIV2= |
NJ2211 |
55 |
100 |
25 |
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Odległości między osiami kół: |
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|
łożysk 1 |
łożysk 2 |
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II-III= |
99,75 |
67 |
71 |
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III-IV= |
114 |
67 |
95 |
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|
Pod koła i sprzęgła dobieram następujące średnice: |
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|
wymiary: |
t1 |
b |
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MI[Nm]= |
133,69 |
sprzęgło wejściowe= |
|
25 |
4 |
8 |
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|
|
MII[Nm]= |
334,21 |
|
koło B= |
36 |
5 |
10 |
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koło C= |
42 |
5 |
12 |
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koło D= |
40 |
5 |
12 |
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|
334,21 |
|
koło E= |
46 |
5,5 |
14 |
|
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|
|
|
MIII[Nm]= |
668,58 |
|
koło F= |
40 |
5 |
12 |
|
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|
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|
668,58 |
sprzęgło wyjściowe= |
|
55 |
6 |
16 |
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|
|
MIV[Nm]= |
1337,15 |
~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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|
|
10695,2 |
N |
|
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|
|
Pdop[MPa]= |
140 |
|
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|
|
FB= |
18567,2222222222 |
N |
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|
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FC= |
15914,7619047619 |
N |
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|
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FD= |
33429 |
N |
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|
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FE= |
29068,6956521739 |
N |
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|
|
FF= |
66857,5 |
N |
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|
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Fwy= |
48623,6363636364 |
N |
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|
Obliczam długości wpustów z nacisków powierzchniowych |
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|
27 |
dobieram |
30 |
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lB= |
37 |
dobieram |
2x20 |
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lC= |
35 |
dobieram |
62 |
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N[kW]= |
14 |
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lD= |
60 |
dobieram |
62 |
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ir2= |
0,5 |
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lE= |
52 |
dobieram |
76 |
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ir3= |
0,5 |
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lF= |
108 |
dobieram |
2x76 |
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lwy= |
74 |
dobieram |
76 |
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zC= |
19 |
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zE= |
19 |
V. Obliczam przekładnię na zagrzanie |
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Wyznaczam moc tarcia dla kół stożkowych wg [XI-17] |
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0,1196 |
[kW] |
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0,1579 |
[kW] |
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0,1579 |
[kW] |
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0,4354 |
[kW] |
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Zatem współczynnik pewności na zagrzanie: |
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1,307 |
>1 |
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