masinski elementi

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A. PRORAČUN REZERVOARA ZA KOMPRIMIRANI VAZDUH Pritisak vazduha….…..p=15⋅ 105 Pa = 1,5 N/mm2 Prečnik rezervoara…...D=780 mm Dužina rezervoara……L=3800 mm Radijus danceta……....R=0,8⋅ D=625mm Širina otvora cjevi……d1=0,15⋅ D=117 mm

Usvojeni materijal…..Č 0371 Granica tečenja….…..Re=235 N/mm2 Faktor slabljenja…….ϕ =0,7 Stepen sigurnosti……S=1,5

Proračun debljine limova: Re 235 N / mm 2 = = 157 N/mm2 S 1,5 D⋅ p 780mm ⋅ 1,5 N / mm 2 + 1mm za koroziju = + 1 = 6,3 mm Debljina lima : δ= 2 ⋅ ϕ σ doz 2 ⋅ 0,7 ⋅ 157 N / mm 2 σdoz=

Debljina danceta : Debljina cjevi : Spoljašnji prečnik cjevi :

R⋅ p 625mm ⋅ 1,5 N / mm 2 +1 = = 5,3 mm δ d= 2 ⋅ ϕ ⋅ σ doz 2 ⋅ 0,7 ⋅ 157 N / mm 2 d1 ⋅ p 117 mm ⋅ 1,5 N / mm 2 +1 = + 1 = 1,8 ≈ 2 mm δ c= 2 ⋅ ϕ ⋅ σ doz 2 ⋅ 0,7 ⋅ 157 N / mm 2 d2=d1+2δ c=117mm+2⋅ 2mm=121 mm

Proračun zavarenih sastavaka : Detalj A: τ s=Fs/As < τ s doz ; Fs=p⋅ d22⋅π /4 ; As=d2⋅π ⋅ a ; a(debljina vara)=0,7⋅δ d 2 p ⋅ d2 ⋅π p ⋅ d2 1,5 N / mm 2 ⋅ 121mm = = ≈ 12,23 N/mm2 τ s= 4 ⋅ d 2 ⋅ π ⋅ a 4 ⋅ δ d ⋅ 0,7 4 ⋅ 0,7 ⋅ 5,3mm Detalj B: σz=Fz/Az < σz doz ; Fz=[D+2(δ-δ d)]2⋅π ⋅ p/4 ; Az=[D+2(δ-δ d)]⋅πδ d [ D + 2(δ − δ d )]2 πp [ D + 2(δ + δ d )] p [780mm + 2(6,3 − 5,3)mm] ⋅ 1,5 N / mm 2 = = ≈ 55,3N/mm2 σz= 4[ D + 2(δ − δ d )]πδ d 4 ⋅δ d 4 ⋅ 5,3mm Detalj C: σz=Fz/Az < σz doz ; Fz=p⋅ D2⋅π /4 ; Az=D⋅π ⋅ δ p ⋅ D2 ⋅π p ⋅ D 1,5 N / mm 2 ⋅ 780mm = = = 46,42 N/mm2 σz = 4 ⋅ D ⋅π ⋅δ 4 ⋅δ 4 ⋅ 6,3mm B.1

ZAVARENI SPOJ RUČICE I VRATILA (sl.2_)

Prečnik vratila………….….d=110 mm Sila ručice……………….…F=± 9900 N Krak ručice………………....R=145 mm Računska debljina vara.…….a=5 mm Zavarivanje………………….N Materijal…………………….Č 0545 Dozvoljeni τ napon………….τ D(-1)=140 N/mm2

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[(d + 2a) − d ] ⋅ π 16(d + 2a) F ⋅ R ⋅ 16(d + 2a) 9900 N ⋅ 145mm ⋅ 16 ⋅ (110mm + 2 ⋅ 5mm) = = 14,4 N/mm τ t= 4 4 [(d + 2a) − d ] ⋅ π [(110mm + 2 ⋅ 5mm) 4 − (110mm) 4 ] ⋅ 3,14 4

Radni napon uvijanja :

τ t=Mt/W0

;

4

Mt= F⋅ R , W0=

( d + 2a ) 2 − d 2 ⋅π 4 4 Fs 4 ⋅ 9900 N = = 5,48 N/mm2 τ s= 2 2 [(d + 2a) − d ] ⋅ π [(110mm + 2 ⋅ 5mm) 2 − (110mm) 2 ] ⋅ 3,14 Ukupna amplituda napona (oba napona tangencijalna) : τ a= ± (τs+τt)= ± (14,4+5,48)= ± 19,88 N/mm2 ξ1=0,9 τ naponi i ugaoni sastavak ξ2=0,5 Normalno zavarivanje ξ3=0,8 Ugaoni sastavak bez zavarenog korena ξ 1 ⋅ ξ 2 ⋅ ξ 3 ⋅ τ d 0,9 ⋅ 0,5 ⋅ 0,5 ⋅ 0,8 ⋅ 140 N / mm 2 = = 1,268 Dinamički stepen sigurnosti : Sd= τa 19,88 N / mm 2 B.2 ROTOR SA ZAVARENIM RUKAVCEM (sl.4_) Radni napon smicanja :

τ s=Fs/As

;

As=

Sila savijanja………………..F=1580 N Materijal……………………..Č. 0545 Računska debljina vara……...a=7 mm Prerčnik osovine…………….d=115 mm Krak sile……………………..L=1,5⋅ d=172,5 mm Moment uvijanja…………….Mu=0,28 kNm=0,28⋅ 106Nmm Moment savijanja…………….Mf=F⋅ L=272550 Nmm Spoljašni prečnik zavara….…dz=d+2a=129 mm 2 d +d2 ⋅ π ≈ 2680 mm2 Površina preseka zavara…….A= z dz 4

Polarni otporni moment ……..W0=

dz − d 4 π ⋅ = 174103,2 mm3 dz 16 4

dz − d 4 π ⋅ = 87051,6 mm3 Otporni moment za osu………Wx= dz 32 Napon savijanja na zavaru……σ=

Mf W0

=

272550 Nmm = 3,131 N/mm2 87051,6mm 3

M u 0,28 ⋅ 10 6 Nmm = = 1,61 N/mm2 W0 174103,2mm 3 Fs 1580 N = = 0,59 N/mm2 Napon smicanja zavara………..τ s= As 2680mm 2 Sabiranje tangencijalnih napona……….τ min=τt=1,61 N/mm2 τ max=τt+τs=1,61N/mm2+0,59N/mm2=2,2 N/mm2 τ sr=(τmin+τmax)/2=1,905 N/mm2 Trajna dinamička izdržljivost…………..τ d=140 N/mm2 Koeficijenti otpornosti za τ napone….. . ξ1=0,4 , ξ2=1 , ξ3=0,5 , ξ4=0,75 Napon uvijanja u zavaru………τ t=

Din.stepen sigurnosti za τ napone..Sτ =

ξ 1 ⋅ ξ 2 ⋅ ξ 3 ⋅ ξ 4 ⋅ τ d 0,4 ⋅ 1 ⋅ 0,5 ⋅ 0,75 ⋅ 140 N / mm 2 = = 9,5 τa 2,2

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Koeficijenti otpornosti za savijanje……ξ1=0,2 , ξ2=1 , ξ3=0,5 , ξ4=0,75 ξ 1 ⋅ ξ 2 ⋅ ξ 3 ⋅ ξ 4 ⋅ σ d 0,2 ⋅ 1 ⋅ 0,5 ⋅ 0,75 ⋅ 240 N / mm 2 = = 5,7 Din. stepen sigurnosti za savijanje…….Sf= σa 3,131N / mm 2 Sσ ⋅ Sτ Ukupni stepen sigurnosti………….Sd= =4,89 S σ2 + Sτ2 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 mm d=48 mm D=64 mm a=3 mm 4 D − ( D − 2a ) 4 π Otporni moment za osu……………..…Wx= ⋅ = 5603,14 mm3 D 32 2 2 [ D − ( D − 2a ) ] ⋅ π Površina poprčnog preseka vara………..As= = 1407 mm2 4 4 D − ( D − 2a ) 4 π Polarni otporni moment…………………W0= ⋅ = 11206,28 mm3 D 16 Moment savijanja u zavaru……………....Mf=F⋅ l=5200 N⋅ 50 mm=260 000 Nmm Moment 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…………..……τ d(0)=120 N/mm2 Mf 260000 Nmm = = 46,6 N/mm2 Napon savijanja………….σf = Wx 5603,14mm 3 Mt 546000 Nmm = = 48,7 N/mm2 Napon uvijanja………….τ t= W x 11206,28mm 3 F 5200 N = = 3,7 N/mm2 Naponi smicanja………..τ s= As 1407 mm 2 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 ξ 1 ⋅ ξ 2 ⋅ ξ 3 ⋅ ξ 4 ⋅ σ d 0,9 ⋅ 1 ⋅ 0,7 ⋅ 0,9 ⋅ 180 N / mm 2 = = 2,2 N/mm2 Stepen sigurnosti za σ napone…..Sσ= τσ f 46,4 Koeficijenti otpornosti za tangecijalne napone…..ξ1=0,9 , ξ2=1 , ξ3=0,7 , ξ4=0,9 ξ 1 ⋅ ξ 2 ⋅ ξ 3 ⋅ ξ 4 ⋅ τ d 0,9 ⋅ 1 ⋅ 0,7 ⋅ 0,9 ⋅ 120 N / mm 2 = = 1,3 N/mm2 Stepen sigurnosti za τ napone…..Sτ = τa 52,4 Sσ ⋅ Sτ Ukupni stepen sigurnosti………….Sd= =1,12 S σ2 + Sτ2

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B.4 STEPEN SIGURNOSTI ZAVARENOG I NE ZAVARENOG DJELA (sl.5a. i sl.5b.) Proračun ne zavarenog djela: a=3 mm δ=8 mm Ms max=0,056 kNmm δ ⋅ b 2 8 ⋅ 40 2 = = 2133 mm2 Otporni moment za osu⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ Wx= 6 6 Kritični pop.presjek⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ A=b⋅ δ =40⋅ 8=320 mm2  b = 0,57  B  ρ  = 0,085 ⇒ za zatezanje αk=1,75 ,za savijanje αk=1,5 B  t  =1  ρ  B=70 mm F=8040 N

b=40 mm ρ=6 mm

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 N Stvarni 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 σ + σ min = 44,0225 N/mm2 Srednji napon⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ σsr= max 2 Dinamički stepen sigurnosti : ηk=0,7 ; β k=(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 ξ 1 ⋅ ⋅ξ 2ξ 3 ⋅ σ d 0,8 ⋅ 0,9 ⋅ 1,2 ⋅ 250 = = 3,22 S d= η ⋅ σ max 1,525 ⋅ 44,045 Proračun stepena sigurnosti za slučaj zavarenog spoja : ξ1=1 ; ξ2=0,5 ; ξ3=1 ; ξ4=0,8 1 ⋅ 0,5 ⋅ 1 ⋅ 0,8 ⋅ 250 = 2,27 S d= 44,045 B.5. NOSIVOST SKLOPA GLAVČINA-ZUPČANIK ZA SLUČAJ ZAVARENOG I PRESOVANOG SPOJA (sl.6) Dimenzije: D=290 mm Materijal Č.0545 Presovani sklop D1=70 mm Stepen sigurnosti S=3 φ 70 H8/za9 d=60 mm Normalno zavarivanje he=hi=5 µm b=20 mm Jednosmerno opterećenje a=10 mm ( D1 + 2a ) 4 − D1 4 π ⋅ = 90711 mm3 Polarni otporni moment vara⋅ ⋅ ⋅ ⋅ ⋅ ⋅ W0= D1 + 2a 16 2 τ d=170 M/mm (jednosm. opterećenje) ; ξ1=0,7 ; ξ2=0,5 ; ξ3=0,6 ; ξ4=0,8 τ 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)

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φ 70 H8 : Tr=Ag=0,046 mm Ad=0 Dg=D1+Ag=70+0,046=70,046 mm Dd=D1+Ad=70 +0 =70 mm

φ 70 za9 : T0=0,074 mm ad=0,274 mm ag=ad+T0=0,274+0,074 = 0,348 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 mm Pg’ =Pd – 1,2(he+hi)=0,228 – 1,2⋅ (0,005+0,005) =0,216 mm Faktori deformacije : ψ s=D1/D= 70/290 = 0,241 -za rupu ms= mu= 0,3 ; Es=Eu=2,06⋅ 10-5 mm2/N ψ u= d/D =60/70 = 0,857 - za osovinu (za Č.0545) ξs=

( ms + 1) + ( ms − 1) ⋅ψ s2

(

ms ⋅ E s 1 − ψ

2

)

( mu − 1) + ( mu + 1) ⋅ψ u2

=

0,3 ⋅ 2,06 ⋅ 10 ⋅ (1 − 0,241 ) 5

2

= 2,16⋅ 10-5 mm2/N

( 0,3 − 1) + (0,3 + 1) ⋅ 0,857 2

= 1,55⋅ 10-5 mm2/N mu ⋅ E u 1 − ψ 2 0,3 ⋅ 2,06 ⋅ 10 5 ⋅ (1 − 0,857 2 ) Najmanji dodirni pritisak : Pa '−1,2( he − hi ) 0,336 = = 1,2938⋅ 107 N/mm2 Pmin= −5 −5 −5 2 (ξ u + ξ s ) ⋅ D1 ⋅ 10 ( 2,16 + 1,55) ⋅ 10 ⋅ 70 ⋅ 10 mm / N Koeficijent trenja za Č.0545⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ µ=0,1 Dodirna 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 ξu=

(

)

=

( 0,3 + 1) + (0,3 − 1) ⋅ 0,2412

Obodna sila : Fobod. = Fµ ⋅ D1/D = 5,688⋅ 10 9 N ⋅ 70 mm/290 mm = 1,373 ⋅ 109 N

(za slučaj presovanog spoja)