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 sprężarkę |
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N [kW] = |
16 |
rotacyjną. |
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Przełożenie: |
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Wykonać: |
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i =1: |
18 |
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]= |
7200 |
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: |
3 |
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iI = 1: |
3 |
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iII = 1: |
3 |
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iII = 1: |
3 |
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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: |
18 |
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ic = 1: |
18 |
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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= |
54 |
koło A z= |
18 |
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koło C z= |
19 |
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koło D z= |
57 |
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= |
54 |
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ir = 1: |
18 |
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koło D z= |
57 |
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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: |
18 |
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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]= |
7200 |
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koło B z= |
54 |
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nII[1/min]= |
2400 |
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nII[1/min]= |
2400 |
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koło D z= |
57 |
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nIII[1/min]= |
800 |
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nIII[1/min]= |
800 |
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koło F z= |
38 |
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nIV[1/min]= |
400 |
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nIV[1/min]= |
400 |
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Korzystając ze wzoru : |
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nI[1/min]= |
7200 |
obliczam prędkości kątowe wałków: |
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nII[1/min]= |
2400 |
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wI[1/s]= |
753,98 |
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nIII[1/min]= |
800 |
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wII[1/s]= |
251,33 |
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wII[1/s]= |
251,33 |
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nIV[1/min]= |
400 |
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wIII[1/s]= |
83,78 |
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wIII[1/s]= |
83,78 |
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wIV[1/s]= |
41,89 |
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wIV[1/s]= |
41,89 |
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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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71,34 |
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71,57 |
dB[o]= |
71,34 |
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Dla koła małego dA= |
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18,26 |
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18,43 |
dA[o]= |
18,26 |
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Na podstawie wzoru IV/36 obliczam zastępcze liczby |
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zębów: |
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dB= |
71,34 |
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18,97 |
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ZvA= |
18,97 |
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dA= |
18,26 |
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#DIV/0! |
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170,81 |
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ZvB= |
170,81 |
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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] = |
16 |
Mając wszystkie dane obliczam moduł koła małego w/g |
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dA= |
18,26 |
wzoru XI-10 dla zębów prostych: |
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bm= |
0 |
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Cb= |
1 |
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1,256 |
mnm= |
1,256 |
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lzast= |
0,387 |
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ZvA= |
18,97 |
Dobieram znormalizowany czołowy moduł zewnętrzny |
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nI[1/min]= |
7200 |
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= |
54 |
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]= |
2,5 |
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71,17 |
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Re= |
71,17 |
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dA= |
18,26 |
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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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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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ham= |
2,5 |
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2,5 |
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hfm= |
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Średnice wierzchołkowe [IV-32]: |
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deA= |
45 |
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49,74 |
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daeA= |
49,74 |
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deB= |
135 |
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136,58 |
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daeB= |
136,58 |
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ham= |
2,5 |
Wysokości stożków wierzchołkowych [IV-33] |
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hfm= |
3 |
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dB[o]= |
71,34 |
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66,71 |
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BB= |
20,13 |
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dA[o]= |
18,26 |
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20,13 |
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BA= |
66,71 |
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Kąty wysokości głowy zęba [IV-25]: |
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0,03512716032036 |
[o] |
2,01 |
Qa[o]= |
2,01 |
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Re= |
71,17 |
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2,01 |
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oraz stopy zęba [IV-26]: |
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0,042152592384432 |
[o] |
2,25 |
Qf[o]= |
2,25 |
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2,42 |
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Kąty stożków wierzchołkowych [IV-27]: |
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tgQa[o]= |
2,01 |
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tgQf[o]= |
2,25 |
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20,44 |
setne |
20,26 |
daA[o]= |
20,26 |
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daB[o]= |
73,35 |
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73,58 |
setne |
73,35 |
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dB[o]= |
71,34 |
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dA[o]= |
18,26 |
i dna wrębów [IV-28]: |
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16,02 |
setne |
16,01 |
dfA[o]= |
16,01 |
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dfB[o]= |
69,1 |
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69,16 |
setne |
69,1 |
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Dobieram szerokość wieńca około b=1/3,5 Re: |
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b[mm]= |
20 |
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b[mm]= |
20 |
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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= |
38,6771111423353 |
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40,77 |
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dvmnA= |
40,77 |
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dA[o]= |
18,26 |
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oraz przełożenie czołowe [IV-9]: |
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ZA= |
18 |
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ZB= |
54 |
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0,111111111111111 |
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iv= |
0,111111111111111 |
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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 |
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1322 |
MPa |
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kH[Mpa]= |
1322 |
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ZHj[MPa]= |
1600 |
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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= |
1,53 |
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eA= |
1,53 |
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eB= |
1,88 |
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eB= |
1,88 |
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eA= |
1,53 |
Zatem ze wzoru I-55: |
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eB= |
1,88 |
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Cm,a= |
478,2 |
1,71 |
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ea= |
1,71 |
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nI[1/min]= |
7200 |
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kH[Mpa]= |
1322 |
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ea= |
1,71 |
154,41 |
N[kW]= |
154,41 |
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b[mm]= |
20 |
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dvmnA= |
40,77 |
Warunek Hertza jest spełniony. |
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bm= |
0 |
Prędkość obwodowa dla ustalenia nadwyżki dynamicznej: |
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iv= |
0,111111111111111 |
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dC= |
1,88 |
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15,37 |
m/s |
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n= |
15,37 |
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nII= |
1 |
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Wartość współczynnika nadwyżek dynamicznych Cd |
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1,39 |
IX/13-V |
Cd= |
1,39 |
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n= |
15,37 |
Z tablicy IX/11 odczytuję współczynnik przeciążenia Cp |
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Cp= |
1,25 |
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Cp= |
1,25 |
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Ze wzoru IX-9 wyznaczam siłę statyczną: |
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N[kW]= |
16 |
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1040,99 |
[N] |
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Pstat= |
1040,99 |
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1808,72 |
[N] |
Pzast= |
1808,72 |
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Siła obliczeniowa [IX-13]: |
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Pzast= |
1808,72 |
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ea= |
1,71 |
1096,19 |
N |
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Pobl= |
1096,19 |
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Sprawdzam naprężenia: |
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Pobl= |
1096,19 |
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l= |
0,387 |
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56,65 |
<kgj[MPa]= |
310 |
sgzast[MPa]= |
56,65 |
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b[mm]= |
20 |
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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. |
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kgj [MPa]= |
310 |
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Przyjmuję szerokość wieńca y= |
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22 |
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y= |
22 |
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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]= |
16 |
Obliczam minimalny moduł [X-4]: |
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y= |
22 |
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l= |
0,387 |
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1,36 |
mm |
mo= |
1,36 |
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nII= |
2400 |
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ZC= |
19 |
Dobieram moduł czołowy m= |
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2 |
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m= |
2 |
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Średnice podziałowe kół : |
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38 |
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dC= |
38 |
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ZD= |
57 |
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114 |
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dD= |
114 |
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m= |
2 |
Średnice głów zębów: |
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dC= |
38 |
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42 |
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dD= |
114 |
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daC= |
42 |
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y= |
1 |
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118 |
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daD= |
118 |
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Średnice stóp zębów: |
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c=0,2m |
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33,2 |
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dfC= |
33,2 |
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109,2 |
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dfD= |
109,2 |
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y= |
22 |
Szerokość wieńca: |
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m= |
2 |
|
44 |
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b[mm]= |
44 |
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Prędkość obwodowa dla ustalenia nadwyżki dynamicznej: |
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dC= |
38 |
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4,78 |
m/s |
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n= |
4,78 |
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nII= |
2400 |
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Wartość współczynnika nadwyżek dynamicznych Cd |
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1,22 |
IX/13-V |
Cd= |
1,22 |
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n= |
4,78 |
Z tablicy IX/11 odczytuję współczynnik przeciążenia Cp |
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Cp= |
1,25 |
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Cp= |
1,25 |
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Ze wzoru IX-9 wyznaczam siłę statyczną: |
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N[kW]= |
16 |
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3347,28 |
[N] |
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Pstat= |
3347,28 |
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5104,6 |
[N] |
Pzast= |
5104,6 |
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eC= |
1,53 |
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eC= |
1,53 |
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eD= |
1,78 |
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eD= |
1,78 |
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Zatem ze wzoru I-55: |
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eC= |
1,53 |
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eD= |
1,78 |
1,66 |
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ea= |
1,66 |
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Siła obliczeniowa [IX-13]: |
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Pzast= |
5104,6 |
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ea= |
1,66 |
3075,06 |
N |
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Pobl= |
3075,06 |
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Sprawdzam naprężenia: |
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Pobl= |
3075,06 |
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l= |
0,387 |
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90,29 |
<kgj[MPa]= |
310 |
sgzast[MPa]= |
90,29 |
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b[mm]= |
44 |
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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= |
38 |
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dD= |
114 |
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47,94 |
kW |
N= |
47,94 |
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kH[Mpa]= |
1322 |
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b[mm]= |
44 |
Warunek Hertza jest spełniony. |
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nII= |
2400 |
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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. |
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kgj [MPa]= |
310 |
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Przyjmuję szerokość wieńca y= |
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|
20 |
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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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l= |
0,387 |
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l= |
0,387 |
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N[kW]= |
16 |
Obliczam minimalny moduł [X-4]: |
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y= |
20 |
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l= |
0,387 |
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2,03 |
mm |
mo= |
2,03 |
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kgj [MPa]= |
310 |
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nIII[1/min]= |
800 |
Dobieram moduł czołowy m= |
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3 |
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m= |
3 |
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ZE= |
19 |
Średnice podziałowe kół : |
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ZF= |
38 |
|
57 |
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dE= |
57 |
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|
114 |
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dF= |
114 |
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m= |
3 |
Średnice głów zębów: |
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dE= |
57 |
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63 |
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dF= |
114 |
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daE= |
63 |
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y= |
1 |
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daF= |
120 |
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Średnice stóp zębów: |
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c=0,2m |
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49,8 |
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dfE= |
49,8 |
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106,8 |
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dfF= |
106,8 |
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y= |
20 |
Szerokość wieńca: |
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|
60 |
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b= |
60 |
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|
Prędkość obwodowa dla ustalenia nadwyżki dynamicznej: |
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2,39 |
m/s |
|
n= |
2,39 |
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Wartość współczynnika nadwyżek dynamicznych Cd |
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n= |
2,39 |
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|
1,39 |
IX/13-V |
Cd= |
1,39 |
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|
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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N= |
16 |
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|
6694,56 |
[N] |
|
Pstat= |
6694,56 |
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|
11631,8 |
[N] |
Pzast= |
11631,8 |
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eE= |
1,53 |
|
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eE= |
1,53 |
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|
|
eF= |
1,7 |
|
|
eF= |
1,7 |
|
|
|
|
|
eE= |
1,53 |
Zatem ze wzoru I-55: |
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|
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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= |
11631,8 |
Siła obliczeniowa [IX-13]: |
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ea= |
1,62 |
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7180,12 |
N |
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Pobl= |
7180,12 |
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Pobl= |
7180,12 |
Sprawdzam naprężenia: |
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l= |
0,387 |
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|
103,07 |
<kgj[MPa]= |
310 |
sgzast[MPa]= |
103,07 |
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b[mm]= |
60 |
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m= |
3 |
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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43,58 |
kW |
N= |
43,58 |
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b[mm]= |
60 |
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nIII= |
800 |
Warunek Hertza jest spełniony. |
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Cm,a= |
478,2 |
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dE= |
57 |
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]= |
16 |
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wI[1/s]= |
753,98 |
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943 |
N |
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PAo= |
943 |
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deA= |
45 |
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Siłę poosiową koła napędzającego [XV-11]: |
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dA= |
18,26 |
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N |
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PoA= |
109 |
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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= |
943 |
Koła napędzanego: |
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dB= |
71,34 |
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326 |
N |
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PoB= |
326 |
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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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326 |
N |
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PrA= |
326 |
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PAo= |
943 |
Koła napędzanego: |
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N |
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PrB= |
109 |
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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= |
18,26 |
Obliczeniowa szerokość koła A: |
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b= |
20 |
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e= |
19 |
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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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22,5 |
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a= |
22,5 |
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b= |
39 |
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a= |
22,5 |
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PrA= |
326 |
Reakcje w płaszczyźnie poziomej H: |
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PAo= |
943 |
Z równania momentów: |
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deA= |
45 |
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R2H= |
125 |
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125 |
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-451 |
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R1H= |
-451 |
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Momenty gnące w płaszczyźnie poziomej H: |
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Dla koła A: |
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PoA= |
109 |
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2,4525 |
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Mk= |
2,4525 |
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Dla łożyska ł1: |
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b= |
39 |
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a= |
22,5 |
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-4,8825 |
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Mk= |
2,4525 |
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R1H= |
-451 |
Dla łożyska ł2: |
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Mł1H= |
-4,8825 |
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PrA= |
326 |
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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= |
943 |
|
-1487,03846153846 |
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R1V= |
-1487,03846153846 |
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544,038461538462 |
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R2V= |
544,038461538462 |
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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= |
21,2175 |
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21,2175 |
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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]= |
16 |
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wI[1/s]= |
753,98 |
21 |
Nm |
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Ms= |
21 |
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Momenty zastępcze do obliczeń średnic wałków: |
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Dla koła: |
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Mk= |
2,4525 |
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18,4 |
Nm |
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MZk= |
18,4 |
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Ms= |
21 |
Dla łożyska ł1: |
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MZł1= |
28,4 |
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Mgł1V= |
21,2175 |
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28,4 |
Nm |
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Mł1H= |
-4,8825 |
Dla łożyska ł2 moment zastępczy jest równy momentowi |
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skręcającemu: |
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21 |
Nm |
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MZł2= |
21 |
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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= |
18,4 |
Pod koło zębate z warunku na skręcanie: |
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dla stali |
16HG |
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Kt[MPa]= |
200 |
12,3 |
dobieram |
20 |
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kgj[MPa]= |
310 |
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Dk[mm]= |
20 |
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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= |
28,4 |
9,7 |
|
20 |
Dł1= |
9,7 |
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Pod łozysko ł2 z warunku na skręcanie: |
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12,8 |
|
20 |
Dł2= |
12,8 |
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1. Obliczenie wałka II |
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Siły pochodzące od koła B: |
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POB= |
326 |
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PrB= |
109 |
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PBo= |
943 |
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Siła obwodowa koła C: |
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N[kW]= |
16 |
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wII[1/s]= |
251,33 |
3351 |
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PCo= |
3351 |
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dpC= |
38 |
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an[o]= |
20 |
Siła promieniowa: |
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PCo= |
3351 |
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|
1220 |
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PrC= |
1220 |
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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]= |
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]= |
72,5 |
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Obliczeniowa szerokość koła B e: |
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b[mm]= |
20 |
|
6 |
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e[mm]= |
6 |
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Zakładam rozstaw między łożyskiem B1 a kołem B: |
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30 |
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L1[mm]= |
20 |
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Zakładam rozstaw między kołami B i C: |
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a[mm]= |
30 |
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L2[mm]= |
10 |
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35 |
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b[mm]= |
35 |
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Odległość między łożyskiem B2, a osią koła C: |
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c[mm]= |
101,5 |
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L3[mm]= |
72,5 |
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101,5 |
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Długość wałka między osiami łożysk: |
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a[mm]= |
30 |
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166,5 |
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Lc[mm]= |
166,5 |
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b[mm]= |
35 |
Reakcje w płaszczyźnie poziomej H: |
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c[mm]= |
101,5 |
Z równania momentów: |
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PrC= |
1220 |
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PrB= |
109 |
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589 |
N |
R2H= |
589 |
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deB= |
135 |
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Lc[mm]= |
166,5 |
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POB= |
326 |
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Przemysłw Kowalak:
siła skierowana w dół jest
dodatnia
522 |
N |
R1H= |
522 |
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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= |
589 |
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R1H= |
522 |
-38 |
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MKB= |
-38 |
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Dla koła C: |
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-60 |
MKC= |
-60 |
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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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2816 |
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R1V= |
2816 |
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R2V= |
1478 |
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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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84,48 |
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MKB= |
84,48 |
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Dla koła C: |
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150,035 |
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MKC= |
150,035 |
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Dla łożyska ł2: |
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0 |
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Moment skręcający na wałku: |
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63,7 |
Nm |
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MsII= |
63,7 |
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Momenty zastępcze do obliczeń średnic wałków: |
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Dla łożyska ł1: |
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MKBV= |
84,48 |
Mzł1= |
0 |
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Mzł1= |
0 |
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MKBH= |
-38 |
Dla koła B: |
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MsII= |
63,7 |
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MzB= |
107,8 |
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107,8 |
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Dla koła C: |
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MKCH= |
-60 |
170,7 |
MzC= |
170,7 |
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MKCV= |
150,035 |
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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= |
107,8 |
Pod koło zębate B: |
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MzC= |
170,7 |
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dla stali |
15 |
19,7 |
dobieram |
28 |
DB[mm]= |
28 |
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Kt[MPa]= |
90 |
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kgj[MPa]= |
140 |
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23 |
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]= |
16 |
-obwodową |
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wIII[1/s]= |
83,78 |
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3350,46257323902 |
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PDo= |
3350,46257323902 |
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dD= |
114 |
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-promieniową |
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PDo= |
3350,46257323902 |
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1219 |
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PDr= |
1219 |
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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= |
57 |
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6701 |
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PEo= |
6701 |
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-promieniową |
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PEo= |
6701 |
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2439 |
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PEr= |
2439 |
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Obliczam długość wałka |
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-szerokość łożyska A |
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58 |
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BA= |
14 |
[mm] |
48,5 |
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-odstęp pomiędzy łożyskiem A a kołem zębatym D |
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L1= |
36 |
[mm] |
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-szerokość wieńca zębatego koła D |
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bD= |
44 |
[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= |
60 |
[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= |
24 |
[mm] |
58 |
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Zakładam rozstaw między łożyskiem A a kołem D: |
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65 |
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Zakładam rozstaw między kołami D i E: |
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a[mm]= |
65 |
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L1= |
36 |
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b[mm]= |
58 |
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58 |
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Odległość między łożyskiem B2, a osią koła C: |
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L2= |
6 |
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c[mm]= |
48,5 |
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L3= |
6,5 |
48,5 |
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a[mm]= |
65 |
Długość wałka między osiami łożysk: |
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b[mm]= |
58 |
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171,5 |
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Lc= |
171,5 |
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c[mm]= |
48,5 |
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bD= |
44 |
Obliczam reakcję łożysk w płaszczyźnie |
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bE= |
60 |
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PDo= |
3350,46257323902 |
-6076 |
R2V= |
-6076 |
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PEo= |
6701 |
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6076 |
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R2V= |
-6076 |
-3975 |
R1V= |
-3975 |
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3975 |
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PDr= |
1219 |
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1287 |
R2H= |
1287 |
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PEr= |
2439 |
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R2H= |
1287 |
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67 |
R1H= |
67 |
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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= |
-3975 |
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258,4 |
MgDV= |
258,4 |
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683,3 |
MgEV= |
683,3 |
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0 |
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- w płaszczyźnie poziomej |
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Mg1H= |
0 |
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4,355 |
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MgDH= |
4,355 |
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R1H= |
67 |
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-62,46 |
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MgEH= |
-62,46 |
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0 |
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Obliczam moment skręcający na wałku |
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N[kW]= |
16 |
Ms1= |
0 |
Ms2= |
0 |
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wIII[1/s]= |
83,78 |
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MsE=MsD= |
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191 |
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Ms= |
191 |
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MgDV= |
258,4 |
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MgEV= |
683,3 |
Obliczam rzeczywisty moment zginający wałki |
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258,4 |
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MgD= |
258,4 |
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MgDH= |
4,355 |
686,1 |
MgE= |
686,1 |
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MgEH= |
-62,46 |
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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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MgD= |
258,4 |
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MgE= |
686,1 |
|
306,8 |
MZD= |
306,8 |
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Ms= |
191 |
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MZE= |
686,1 |
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686,1 |
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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= |
306,8 |
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MZE= |
686,1 |
21,5 |
dobieram |
30 |
DD= |
30 |
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kgj[MPa]= |
310 |
Pod koło C: |
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28,1 |
dobieram |
36 |
DE= |
36 |
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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= |
6700,9 |
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N[kW]= |
16 |
|
6700,9 |
[N] |
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wIV[1/s]= |
41,89 |
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dpF= |
114 |
-promieniową |
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2438,9281427944 |
[N] |
PFr= |
2438,9281427944 |
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PFo= |
6700,9 |
Obliczam długość wałka |
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an[o]= |
20 |
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-szerokość łożyska 1 |
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B1= |
24 |
[mm] |
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-odstęp pomiędzy łożyskiem 1 a kołem zębatym F |
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L1= |
86 |
[mm] |
128 |
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-szerokość wieńca zębatego koła F |
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43,5 |
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bF= |
60 |
[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= |
14 |
[mm] |
0 |
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-długość wałka pod sprzęgło |
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128 |
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L3= |
50 |
[mm] |
171,5 |
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L1= |
86 |
Zakładam rozstaw między łożyskiem 1 a kołem F: |
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L2= |
6,5 |
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|
128 |
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a[mm]= |
128 |
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L3= |
50 |
Odległość między łożyskiem 2, a osią koła F: |
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b[mm]= |
43,5 |
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43,5 |
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Długość wałka między osiami łożysk: |
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171,5 |
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Lc= |
171,5 |
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Obliczam reakcję łożysk w płaszczyźnie |
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a[mm]= |
128 |
-pionowej |
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b[mm]= |
43,5 |
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5001,3 |
[N] |
R2V= |
5001,3 |
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R2V= |
5001,3 |
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R1V= |
1699,6 |
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R1V= |
1699,6 |
1699,6 |
[N] |
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PFo= |
6700,9 |
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-poziomej |
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1820,3 |
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R2H= |
1820,3 |
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R1H= |
618,628142794395 |
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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= |
1699,6 |
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|
233 |
MgFV= |
233 |
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a[mm]= |
128 |
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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= |
618,628142794395 |
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79,2 |
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MgFH= |
79,2 |
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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]= |
16 |
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wIV[1/s]= |
41,89 |
|
MsF= |
|
382 |
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Ms= |
382 |
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|
382 |
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Ms2= |
382 |
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Obliczam rzeczywisty moment zginający wałki |
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MgFV= |
233 |
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MgFH= |
79,2 |
246,1 |
MgF= |
246,1 |
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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= |
246,1 |
|
412,3 |
MZF= |
412,3 |
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Ms= |
382 |
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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|
382 |
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|
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Minimalne średnice wałka dla obciążeń złożonych: |
|
|
|
|
Ms= |
382 |
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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= |
412,3 |
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Ms= |
382 |
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|
23,7 |
dobieram |
35 |
Df= |
35 |
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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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|
33,7 |
dobieram |
35 |
Dł2= |
35 |
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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= |
1553,92547636451 |
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RI2= |
558,213980148416 |
19145,8790481198 |
N |
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RII1= |
2863,97276523364 |
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RII2= |
1591,03896872453 |
|
|
CI2= |
6877,74124914606 |
N |
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RIII1= |
3975,56461398881 |
|
|
CII1= |
25379,1826551383 |
N |
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RIII2= |
6210,80872350775 |
|
|
CII2= |
14099,0407062787 |
N |
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RIV1= |
1808,68486449609 |
|
|
CIII1= |
25337,9332411765 |
N |
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RIV2= |
5322,26397128139 |
|
|
CIII2= |
39584,077254391 |
N |
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|
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nI[1/min]= |
7200 |
|
|
CIV1= |
9363,24261743363 |
N |
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|
7200 |
|
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CIV2= |
27552,4221025742 |
N |
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nII[1/min]= |
2400 |
Z katalogu łożysk na podstawie dopuszczalnych obciążeń |
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|
2400 |
dynamicznych dobieram łożyska: |
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nIII[1/min]= |
800 |
|
wymiary: |
d[mm] |
D[mm] |
B[mm] |
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|
800 |
łI1= |
30204A |
20 |
47 |
14 |
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nIV[1/min]= |
400 |
łI2= |
30204A |
20 |
47 |
14 |
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|
400 |
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= |
NU2306 |
25 |
62 |
24 |
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łIV1= |
NU204 |
20 |
47 |
14 |
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łIV2= |
NJ2207 |
35 |
72 |
23 |
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|
Odległości między osiami kół: |
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|
łożysk 1 |
łożysk 2 |
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II-III= |
76 |
54,5 |
54,5 |
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III-IV= |
85,5 |
54,5 |
67 |
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Pod koła i sprzęgła dobieram następujące średnice: |
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wymiary: |
t1 |
b |
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MI[Nm]= |
21,22 |
sprzęgło wejściowe= |
|
20 |
3,5 |
6 |
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MII[Nm]= |
63,66 |
|
koło B= |
28 |
4 |
8 |
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koło C= |
34 |
5 |
10 |
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koło D= |
30 |
5 |
10 |
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|
63,66 |
|
koło E= |
36 |
5 |
10 |
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|
|
MIII[Nm]= |
190,98 |
|
koło F= |
35 |
5 |
10 |
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|
190,98 |
sprzęgło wyjściowe= |
|
35 |
5 |
10 |
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|
|
MIV[Nm]= |
381,95 |
~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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|
2122 |
N |
|
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|
|
Pdop[MPa]= |
140 |
|
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|
|
FB= |
4547,14285714286 |
N |
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|
|
FC= |
3744,70588235294 |
N |
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|
|
FD= |
12732 |
N |
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FE= |
10610 |
N |
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|
|
FF= |
21825,7142857143 |
N |
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|
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Fwy= |
21825,7142857143 |
N |
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|
Obliczam długości wpustów z nacisków powierzchniowych |
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|
10 |
dobieram |
20 |
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lB= |
16 |
dobieram |
20 |
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|
lC= |
15 |
dobieram |
40 |
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N[kW]= |
16 |
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lD= |
28 |
dobieram |
40 |
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ir2= |
0,333333333333333 |
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lE= |
25 |
dobieram |
46 |
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ir3= |
0,5 |
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lF= |
41 |
dobieram |
46 |
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lwy= |
41 |
dobieram |
46 |
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V. Obliczam przekładnię na zagrzanie |
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Wyznaczam moc tarcia dla kół stożkowych wg [XI-17] |
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zC= |
19 |
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zE= |
19 |
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0,1339 |
[kW] |
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0,1604 |
[kW] |
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0,1805 |
[kW] |
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0,4748 |
[kW] |
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Zatem współczynnik pewności na zagrzanie: |
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0,935 |
<1 |
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