L 1

A. PRORAČUN REZERVOARA ZA KOMPRIMIRANI VAZDUH

Pritisak vazduha….…..p=15⋅ 105 Pa = 1,5 N/mm2 Usvojeni materijal…..Č 0371Prečnik rezervoara…...D=780 mm Granica tečenja….…..Re=235 N/mm2

Dužina rezervoara……L=3800 mm Faktor slabljenja…….ϕ =0,7Radijus danceta……....R=0,8⋅ D=625mm Stepen sigurnosti……S=1,5 Širina otvora cjevi……d1=0,15⋅ D=117 mm

Proračun debljine limova:

σdoz= ==5,1

/235 2mmN

S

Re 157 N/mm2

Debljina lima : δ= =+⋅⋅

⋅=+⋅

⋅1

/1577,02

/5,17801

2 2

2

mmN

mmNmmkorozijuzamm

pD

dozϕσ 6,3 mm

Debljina danceta : δd= =⋅⋅

⋅=+⋅⋅⋅

2

2

/1577,02

/5,16251

2 mmN

mmNmmpR

dozσϕ 5,3 mm

Debljina cjevi : δ c= =+⋅⋅⋅=+

⋅⋅⋅

1/1577,02

/5,11171

2 2

21

mmN

mmNmmpd

dozσϕ 1,8 ≈ 2 mm

Spoljašnji prečnik cjevi : d2=d1+2δc=117mm+2⋅ 2mm=121 mm

Proračun zavarenih sastavaka :Detalj A: τ s=Fs/As < τ s doz ; Fs=p⋅ d2

2⋅π /4 ; As=d2⋅π ⋅ a ; a(debljina vara)=0,7⋅δ d

τ s= ≈⋅⋅

⋅=⋅⋅

⋅=

⋅⋅⋅⋅⋅

mm

mmmmNdp

ad

dp

d 3,57,04

121/5,1

7,044

22

2

22

δππ

12,23 N/mm2

Detalj B: σz=Fz/Az < σz doz ; Fz=[D+2(δ-δd)]2⋅π ⋅ p/4 ; Az=[D+2(δ-δd)]⋅πδ d

σz= ≈⋅

⋅−+=⋅

++=

−+−+

mm

mmNmmmmpD

D

pD

d

d

dd

d

3,54

/5,1])3,53,6(2780[

4

)](2[

)](2[4

)](2[ 22

δδδ

πδδδπδδ

55,3N/mm2

Detalj C: σz=Fz/Az < σz doz ; Fz=p⋅ D2⋅π /4 ; Az=D⋅π ⋅δ

σz = =⋅

⋅=⋅⋅=

⋅⋅⋅⋅⋅

mm

mmmmNDp

D

Dp

3,64

780/5,1

44

22

δδππ

46,42 N/mm2

B.1 ZAVARENI SPOJ RUČICE I VRATILA (sl.2_)

Prečnik vratila………….….d=110 mmSila ručice……………….…F=± 9900 NKrak ručice………………....R=145 mmRačunska debljina vara.…….a=5 mmZavarivanje………………….NMaterijal…………………….Č 0545Dozvoljeni τ napon………….τD(-1)=140 N/mm2

L 2

Radni napon uvijanja : τ t=Mt/W0 ; Mt= F⋅ R , W0=)2(16

])2[( 44

ad

dad

+⋅−+ π

τ t= =⋅−⋅+

⋅+⋅⋅⋅=⋅−+

+⋅⋅14,3])110()52110[(

)52110(161459900

])2[(

)2(164444 mmmmmm

mmmmmmN

dad

adRF

π 14,4 N/mm

Radni napon smicanja : τ s=Fs/As ; As= π⋅−+4

)2( 22 dad

τ s= =⋅−⋅+

⋅=⋅−+ 14,3])110()52110[(

99004

])2[(

42222 mmmmmm

N

dad

Fsπ 5,48 N/mm2

Ukupna amplituda napona (oba napona tangencijalna) : τa= ± (τs+τt)= ± (14,4+5,48)= ± 19,88 N/mm2

ξ1=0,9 τ naponi i ugaoni sastavakξ2=0,5 Normalno zavarivanjeξ3=0,8 Ugaoni sastavak bez zavarenog korena

Dinamički stepen sigurnosti : Sd= =⋅⋅⋅⋅=⋅⋅⋅

2

2321

/88,19

/1408,05,05,09,0

mmN

mmN

a

d

ττξξξ

1,268

B.2 ROTOR SA ZAVARENIM RUKAVCEM (sl.4_)

Sila savijanja………………..F=1580 N Materijal……………………..Č. 0545 Računska debljina vara……...a=7 mmPrerčnik osovine…………….d=115 mmKrak sile……………………..L=1,5⋅ d=172,5 mmMoment uvijanja…………….Mu=0,28 kNm=0,28⋅ 106NmmMoment savijanja…………….Mf=F⋅ L=272550 NmmSpoljašni prečnik zavara….…dz=d+2a=129 mm

Površina preseka zavara…….A= ≈⋅+ πz

z

d

dd 22

2680 mm2

Polarni otporni moment ……..W0= =⋅−

16

44 πz

z

d

dd174103,2 mm3

Otporni moment za osu………Wx= =⋅−

32

44 πz

z

d

dd87051,6 mm3

Napon savijanja na zavaru……σ= ==3

0 6,87051

272550

mm

Nmm

W

M f3,131 N/mm2

Napon uvijanja u zavaru………τ t= =⋅=3

6

0 2,174103

1028,0

mm

Nmm

W

M u1,61 N/mm2

Napon smicanja zavara………..τ s= ==22680

1580

mm

N

A

F

s

s0,59 N/mm2

Sabiranje tangencijalnih napona……….τmin=τt=1,61 N/mm2

τmax=τt+τs=1,61N/mm2+0,59N/mm2=2,2 N/mm2

τ sr=(τmin+τmax)/2=1,905 N/mm2

Trajna dinamička izdržljivost…………..τd=140 N/mm2 Koeficijenti otpornosti za τ napone….. . ξ1=0,4 , ξ2=1 , ξ3=0,5 , ξ4=0,75

Din.stepen sigurnosti za τ napone..Sτ= =⋅⋅⋅⋅=⋅⋅⋅⋅

2,2

/14075,05,014,0 24321 mmN

a

d

ττξξξξ

9,5

L 3

Koeficijenti otpornosti za savijanje……ξ1=0,2 , ξ2=1 , ξ3=0,5 , ξ4=0,75

Din. stepen sigurnosti za savijanje…….Sf= =⋅⋅⋅⋅=⋅⋅⋅⋅

2

24321

/131,3

/24075,05,012,0

mmN

mmN

a

d

σσξξξξ

5,7

Ukupni stepen sigurnosti………….Sd= 22τσ

τσ

SS

SS

+

⋅=4,89

B.3 DINAMIČKI STEPEN SIGURNOSTI ZAVARENOG SPOJA (sl.3)

-Napomena : Radi zadovoljavanja stepena sigurnosti dimenzije R i l su dva puta umanjene u odnosu na zadate .F=5200 N R=105 mm l=50 mmd=48 mm D=64 mm a=3 mm

Otporni moment za osu……………..…Wx= =⋅−−32

)2( 44 πD

aDD5603,14 mm3

Površina poprčnog preseka vara………..As= =⋅−−4

])2([ 22 πaDD1407 mm2

Polarni otporni moment…………………W0= =⋅−−16

)2( 44 πD

aDD11206,28 mm3

Moment savijanja u zavaru……………....Mf=F⋅ l=5200 N⋅ 50 mm=260 000 NmmMoment torzije u zavaru……………..…..Mt=F⋅ R=5200 N⋅ 105 mm=546 000 Nmm

Dozvoleni dinamički napon savijanja za jednosmerna opterećenja …………..…..σd(0)=180 N/mm2

Dozvoljeni dinamički napon uvijanja za jednosmerna opterećenja…………..……τd(0)=120 N/mm2

Napon savijanja………….σf = ==314,5603

260000

mm

Nmm

W

M

x

f46,6 N/mm2

Napon uvijanja………….τ t= ==328,11206

546000

mm

Nmm

W

M

x

t48,7 N/mm2

Naponi smicanja………..τ s= ==21407

5200

mm

N

A

F

s3,7 N/mm2

Normalni naponi………..σf=46,4 N/mm2

σfa=46,4 N/mm2

Tangencijalni naponi……τ= τt+τs= 48,7 N/mm2 +3,7 N/mm2 =52,4 N/mm2

Koeficijenti otpornosti za normalne napone…..ξ1=0,9 , ξ2=1 , ξ3=0,7 , ξ4=0,9

Stepen sigurnosti za σ napone…..Sσ= =⋅⋅⋅⋅=⋅⋅⋅⋅

4,46

/1809,07,019,0 24321 mmN

f

d

τσσξξξξ

2,2 N/mm2

Koeficijenti otpornosti za tangecijalne napone…..ξ1=0,9 , ξ2=1 , ξ3=0,7 , ξ4=0,9

Stepen sigurnosti za τ napone…..Sτ= =⋅⋅⋅⋅=⋅⋅⋅⋅

4,52

/1209,07,019,0 24321 mmN

a

d

ττξξξξ

1,3 N/mm2

Ukupni stepen sigurnosti………….Sd= 22τσ

τσ

SS

SS

+

⋅=1,12

L4

B.4 STEPEN SIGURNOSTI ZAVARENOG I NE ZAVARENOG DJELA (sl.5a. i sl.5b.) Proračun ne zavarenog djela:

B=70 mm b=40 mm a=3 mm δ=8 mmF=8040 N ρ=6 mm Ms max=0,056 kNmm

Otporni moment za osu⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ Wx= =⋅=⋅6

408

6

22bδ2133 mm2

Kritični pop.presjek⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ A=b⋅δ =40⋅ 8=320 mm2

⇒

=

=

=

1

085,0

57,0

ρ

ρ

tB

B

b

za zatezanje αk=1,75 ,za savijanje αk=1,5

Nominalni naponi zatezanja⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ σnz=F/A=8040N/320mm2=25,125 N/mm2

Stvarni naponi zatezanja⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ σz=αk⋅σ nz=1,75⋅ 25,125 N/mm2=44 N/mm2

Nominalni naponi savijanja⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ σnf= Mf max/Wx =0,056 kNmm /2133 mm2=0,03 NStvarni naponi sanijanja⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ σf=αk⋅σ nf=1,5⋅ 0,03 N/mm2=0,045 N/mm2

Maksimalni napon⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ σmax=σf max+σz=0,045+44 N/mm2 =44,045 N/mm2

Minimalni napon⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ σmin= σz =44 N/mm2

Srednji napon⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ σsr= =+2

minmax σσ44,0225 N/mm2

Dinamički stepen sigurnosti :ηk=0,7 ; βk=(αk -1)⋅η k+1=(1,75-1)⋅ 0,7+1=1,525 ; σd=250 N/mm2

ξ1=0,8 ; ξ2=0,9 ; ξ3=1,2

Sd= =⋅

⋅⋅⋅=⋅

⋅⋅⋅045,44525,1

2502,19,08,0

max

321

σησξξξ d

3,22

Proračun stepena sigurnosti za slučaj zavarenog spoja :ξ1=1 ; ξ2=0,5 ; ξ3=1 ; ξ4=0,8

Sd= =⋅⋅⋅⋅045,44

2508,015,012,27

B.5. NOSIVOST SKLOPA GLAVČINA-ZUPČANIK ZA SLUČAJ ZAVARENOG I PRESOVANOG SPOJA (sl.6)

Dimenzije:D=290 mm Materijal Č.0545 Presovani sklopD1=70 mm Stepen sigurnosti S=3 φ 70 H8/za9d=60 mm Normalno zavarivanje he=hi=5 µmb=20 mm Jednosmerno opterećenjea=10 mm

Polarni otporni moment vara⋅ ⋅ ⋅ ⋅ ⋅ ⋅ W0=( )

=⋅+

−+162

2

1

41

41 π

aD

DaD90711 mm3

τd=170 M/mm2 (jednosm. opterećenje) ; ξ1=0,7 ; ξ2=0,5 ; ξ3=0,6 ; ξ4=0,8τ t max=ξ1⋅ξ 2⋅ξ 3⋅ξ ⋅τ d/S =0,7⋅ 0,5⋅ 0,6⋅ 0,8⋅ 170 / 3 =9,52 N/mm2 Mt max=W0⋅τ t max =9,52 N/mm2 ⋅ 90711 mm3 =863568,72 Nmm Fobod.=2⋅ Mt max /D=2⋅ 863568,72 Nmm/290 mm =5956 N (za slučaj zavarenog sklopa)

L 5

φ 70 H8 : φ 70 za9 :Tr=Ag=0,046 mm T0=0,074 mm Ad=0 ad=0,274 mm Dg=D1+Ag=70+0,046=70,046 mm ag=ad+T0=0,274+0,074 = 0,348 mm Dd=D1+Ad=70 +0 =70 mm dg=D1+ag=70 + 0,348 = 70,348 mm dd=D1+ad =70 + 0,274= 70,274 mm

Zg=Dg – dd=70,046 – 70,274 = -0,228 mm = Pg

Zd=Dd - dg =70 – 70,348 = -0,348 mm = Pd

Pd’ =Pd – 1,2(he+hi)=0,348 – 1,2⋅ (0,005+0,005) =0,336 mmPg’ =Pd – 1,2(he+hi)=0,228 – 1,2⋅ (0,005+0,005) =0,216 mmFaktori deformacije :ψ s=D1/D= 70/290 = 0,241 -za rupu ms= mu= 0,3 ; Es=Eu=2,06⋅ 10-5 mm2/Nψu= d/D =60/70 = 0,857 - za osovinu (za Č.0545)

ξs=( ) ( )

( )( ) =

−⋅⋅⋅⋅−++=

−⋅⋅−++

)241,01(1006,23,0

241,0)13,0(13,0

1

1125

2

2

2

ψψ

ss

sss

Em

mm2,16⋅ 10-5 mm2/N

ξu=( ) ( )

( )( ) =

−⋅⋅⋅⋅++−=

−⋅⋅++−

)857,01(1006,23,0

857,0)13,0(13,0

1

1125

2

2

2

ψψ

uu

uuu

Em

mm1,55⋅ 10-5 mm2/N

Najmanji dodirni pritisak :

Pmin= ( ) ( ) =⋅⋅⋅+

=⋅⋅+

−−−−− NmmD

hhP

su

iea

/10701055,116,2

336,0

10

)(2,1'2555

1ξξ 1,2938⋅ 107 N/mm2

Koeficijent trenja za Č.0545⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ µ=0,1Dodirna površina⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ A=D1⋅π ⋅ b = 70⋅ 3,14⋅ 20= 4396 mm2

Sila trenja :Fµ=Pmin⋅ A⋅µ =1,2938 N/mm2 ⋅ 4396 mm2 ⋅ 0,1 = 5,688⋅ 10 9 N

Obodna sila : Fobod. = Fµ ⋅ D1/D = 5,688⋅ 10 9 N ⋅ 70 mm/290 mm = 1,373 ⋅ 109 N (za slučaj presovanog spoja)