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mecanisme

MECANISME

Capitolul Nr I

Analiza structurala

Elementele mecanizmului sunt de rangul

J=3

Cuple cinematice:

--rotatie

--rotatie + tranzlatie

Mobilitatea se calculeaza cu formula lui Dobrovolsky

M=(G-f).n-S (n-f).C_n

Mecanizmul are patru cuple de clasa 5

M= 3n-C₄-2C₅=9-0-2.4 =9-8 =1

M= 1

f=3

Mecanizmul este format din motoelementul OA si diada RRT

I= (0,15+0,05.8+0,01.1+0,035.42).0,7

I=(0,15+0,4+0,01+1,47).0,7

I=1,421

OA=I . 0,06=1,421.0,06

OA=0,08526 m

AB=I . 0,30=1,421.0,30

=0,4263 m AB

AC=I . 0,08=1,421.0,08

AC=0,11368 m

BC=I . 0,24=1,421.0,24

BC=0,34104

Q=I . 30=1,421.30

Q=42,63

w=I . 50=1,421.50

K=AB/[AB]=0,4263/100

K=0,004263[m/mm]

[AB]=100[mm]

[OA]=OA/Kl=0,08526/0,004263

[OA]=20[mm]

[AC]=AC/Kl=0,11368/0,004263=0,11368/0,004263

[AC]=26,6[mm]

[BC]=BC/Kl=0,34104/0,004263

[BC]=80[mm]

Viteze j

V_A=OA . w

V_A=6,057723m/s

K_V=V_A/[V_A]=0,06057723 [m.s^-1/mm]

V_B/110x=V_A+V_BA/ AB

V_B=ib.Kv=80.Kv

V_B=4,8461784[m/s]

V_BA=ab.Kv=73.Kv

V_BA=4,42213779[m/s]

V_BA=AB.w

w=V_BA/AB

V_BA=10,3733rad/s

DABC Dabc

AB/ab=BC/bc

BC/AB . ab

bc=0,34104/0,4263 . 73

AB/ab=58,4[mm]

AB/ab=AC/ac=AC/AB . ab

ac=0,11368/0,4263 . 73

ac=19,4[mm]

V_C1=V_A/2

V_C1=3,0288615[m/s]

V_C2=ic₂.Kv=82.Kv

V_C2=4,96733286[m/s]

V_C=ic .Kv=82.Kv

V_C=4,96733286[m/s]

Acceleratii j

a_A=a^v.A+a^tA

aA=oA . w

aA=430,401219[m/s²]

Ka=aA/[aA]=430,401219/100

Ka=4,30401219[m/s²]

a^vBA=AB . w

a^vBA=45,872162[m/s²]

[a^vBA]=a^vBA/Ka=10,658[m/s²]

aB/110Y= aA+a^vBA/ AB+a^tBA/ AB

B A

a^tBA=m b . Ka

a^tBA=288,36817[m/s²]

a^tBA=AB.e

e=a^tBA/AB

e=676,445735[rad/s]

aB=jb . Ka=79 . Ka

aB=340,016963

DABC Da b c

AB/ab=AC/ac

ac=AC/AB . ab=0,11368/0,4263 . 70

ac=18,6[mm]

AB/ab=BC/bc

bc=BC/AB . ab=0,34104/0,4263 . 70

bc=56[mm]

ac=jc.Ka=100 . Ka

ac=430,401219[m/s²]

ac₁=aA/2=215,200609[m/s²]

ac₁=215,200609[m/s²]

ac₂=jc₂.Ka=90 . Ka

ac₂=387,361097[m/s²]

Viteze j

V_A=OA . w

V_A=6,057723[m/s]

K_V=0,06057723[m.s^-1/mm]

V_B=V_A+V_BA

oy AB

V_B=ib . KV=82 . KV

V_B=4,96733286[m/s]

V_BA=ab . KV=70 . KV

V_BA=4,2404061[m/s]

V_BA=AB . w

w=V_BA/AB

w=9,947[rad/s]

DABC Dabc

AB/ab=AC/ac

ac=AC/AB . ab=0,11368/0,4263 . 70

ac=18,6[mm]

AB/ab.BC/bc

bc=BC/AB . ab=0,34104/0,4263

bc=56[mm]

V_C1=3,0288615[m/s]

V_C2=ic₂.KV=92 . KV

V_C2=5,57310516[m/s]

V_C=ic.KV=103 . KV

V_C=6,23945469[m/s]

Acceleratii j

aA=OA . w

aA=430,401219[m/s²]

Ka=aA/[aA]

Ka=4,30401219[m/s²

a^vBA=AB.w

a^vBA=42,1962828[m/s²]

[a^vBA]=a^vBA/Ka=9,80394128[m/s²]

aB= aA + aBA + a^tBA

oy AB AB

B A

a^tBA=m b .Ka=70 . Ka

a^tBA=301,280853[m/s²]

a^tBA=AB.e

e=a^tBA/AB

e=706,734349[rad/s]

aB=j b . Ka=80 . Ka

aB=344,320975[m/s²]

DABC Da b c

AB/ab=AC/ac

ac=AC/AB . ab=0,11368/0,4263 . 73

ac=19,4[mm]

AB/ab=BC/bc

Bc=BC/AB . ab=0,34104/0,4263 . 73

bc=58,4[mm]

ac=jc . Ka=80 . Ka

ac=344,320975[m/s²]

ac₁=aA/2

ac₁=215.200609[m/s²]

ac₂=jc₂.k_a.

ac₂=80.k_a

ac₂=344,320975[m/s²]

Viteze j

VA=OA.w

VA=6,057723[m/s]

K_V=0,06057723[m.s^-1/mm]

VB=VA+VBA

//oy AB

VB=ib.K_V

VB=60.K_V

VB=3,6346338[m/s]

VBA=AB.w

w=VBA/AB

w=8,526[rad/s]

DABC Dabc

AB/ab=AC/ac

ac=AC/AB.ab

ac=0,11368/0,4263.70

ac=18,6[mm]

AB/ab=BC/bc

Bc=BC/AB.ab

bc=0,34104/0,4263.70

bc=56[mm]

V_C1=3,0288615[m/s]

V_C2=ic₂.K_V=73.K_V

V_C2=4,42213779[m/s]

V_C=ic.K_V=80.K_V

V_C=4,8461784[m/s]

Acceleratii j

aA=430,401219[m/s²]

K_a=aA/[aA]

K_a=4,30401219[m/s²]

a^vBA=AB.w

a^vBA=30,9888878[m/s²]

[a^vBA]=a^vBA/K_a

[a^vBA]=7,20[m/s]

aB = aA + aBA + a^tBA

//oy //AB AB

B A

a^tBA=m b .K_a=69.K_a

a^tBA=296,976841[m/s²]

a^tBA=AB.e

e=a^tBA/AB

e=696,638144[m/s²]

aB=j .b .K_a=60.K_a

aB=258,240731[m/s²]

DABC Da b c

AB/ab=AC/ac

ac=AC/AB.ab=0,11368/0,4263.70

ac=18,6[mm]

AB/ab=BC/bc

bc=BC/AB.ab=0,34104/0,4263.70

bc=56[mm]

ac=jc .K_a=93.K_a

ac=400,273134[m/s²]

ac₁=aA/2

ac₁=215,200609[m/s²]

ac₂=jc₂.K_a=76.K_a

ac₂=327,104926[m/s²]

Capitolul Nr.2

Metoda Analitica

l₁=OA=0,08526

l₂=AB=0,4263

AC=0,11368

BC=0,34104

OA .cosj+AB . cosj T l₁cosj+l₂cosj Tl₂cosj=-l₁cosj

l₁l₂

OA.cosj+AB.sinj= S Tcosj=-l₁cosj/l₂ T

T S=0,08526 . sin45⁰+0,4263.sin98,13⁰=0,4821T

Ta=arc cos(-l₁.cosj/l₂) = arc cos(-0,08526.cos45⁰/0,4263)

XA=-OA.w.cosj=-0,08526.71,05.cos45⁰TXA=-4,2834m

YA=OA.w.sinj=0,08526 . 71,05 . sin45⁰TYA=4,2834m

XA=OA.cosj=0,08526 . cos45⁰TXA=0,06028m

YA=OA.sinj=0,08526 . sin45⁰TYA=0,06028m

VA X²A+Y²A = 6,0577[m/s]

cosa=AB²+AC²-BC²/2AB.AC

cosa

cosa

a=arc cos 0,807651=84,43

-l₂.sinj w-l₁.sinjw

l₂ . cosjw+l₁.cosjw=s

w=l₁.sinj/l₂sinj w=0,08526.sin45⁰/0,4263.sin82,12 . 71,05

w=10,1436rad

s=VB=l₁.cosj w+l₂.cosj w

s=0,08526.cos45⁰.71,05+0,4263.cos82,12⁰.10,1436

s=4,8461784[m/s]

-l₂.sinj w-l₂ . sinj e=l₁cosj w

-l₂ . sinj w+l₂ . cosj e=s+l₁sinj w

e=l₁.cosjw+l₂.cosj w/l₂.sinj

e=0,08526.cos45⁰.71,05+0,4263.cos82,12.10,14²/0,4263.sin82,12⁰

e=674,4357[rad/s]

s= -l₂sinj w+l₂.cosj e-l₁.sinjw

s=0,4263.sin82,12.10,14²+0,08526.cos82,12.674,4357-0,08526.sin45⁰.71,05

s=281,3688

XC=OA.cosj+AC.cos(j a

XC=0,08526.cos45⁰+0,11368.(cos82,12⁰-10,14⁰)

XC=1,003[m/s]

YC=OA.sinj+AC.sin(j a

YC=0,08526.sin45⁰+0,11368.sin(82,12⁰-10,14⁰)

YC=1,0039[m/s]

XC CX=-OA.w.cos45⁰+AC.sina w=3,12084[m/s]

YC=OA.w.sin45⁰+AC.cosa w=4,91741[m/s]

VC XC²+YC²=4,967312[m/s]

Capitolul Nr 3

Calculul fortelor si cuplurilor ce actioneaza pe elementul mecanizmului

F_i=-m.a-forta de inertie

M_i= - K_c-momentul fortelor de inertie

Fortele de greutate

OA=0,08526.mTdOA=OA/10=0,008526

mOA=jOL.V bara

jOL=7800Kg/m³

V bara=V cil=pd²/4.lOA=p.0,008526²/4 .0,08526=6,8.10^-8m³

mOA=7800.6,8.10^-8=0,000485Kg

V placi=A bazei.d placi

h placi=0,11368/10=0,011368m

Ab= p(p-a).(p-b).(p-c)

p=a+b+c/2=0,4269+0,11368+0,34104/2=0,44081m

Ab=

Ab=0,015129

V placi=0,015129.0,011368=2,612.10^-6m³

m placa jOL.V placa=0,0212Kg

G₁=m₁.g=0,000485Kg.9,81=0,004757

G₂=m2.g=0,0212 . 9,81=0,207972

ac₁=215,2006[m/s²]

ac₂=387,361[m/s²]

F_i1=-mOA.a_c1=0,000485.215,2006=0,10437

M_i1=j₁.e

I₀=m.l²₁/3=4,2.10^-8

F_i2=m₂.ac₂=0,0212.387,361=8,2120

M_i2=j_c.e

I_c=m(l²₁+l²₂+l²₃)/36=9,817.10^-6

G₁=m₁.g=0,004757

G2=m₂.g=0,207972

ac₁=215,2006[m/s²]

ac₂=344,3209[m/s²]

F_i1=mOA.ac₁=0,10437

M_i1=0=e.j₀

w=ctTe

J₀=m₁.l₁²/3=4,2.10^-8

F_i2=m₂.ac₂=8,2120

M_i2=j_c.e

J_c=m₂(l²₁+l²₂+l²₃)/36=9,718.10^-6

G₁=m₁.g=0,004757

G₂=m₂.g=0,207972

ac₁=215,2006[m/s²]

ac₂=327,104[m/s²]

F_i1=mOA.ac₁

M_i1=0=e.j₀

w=ctTe

J₀=ml₁/3=4,2.10^-8

F_i2=m₂.ac₂=8,2120

M_i2=j_c.e

j_c=m₂(l²₁+l²₂+l²₃)/36=9,818.10^-6

Capitolul Nr.4

Calculul reactiunilor din cuple

Calculul reactiunilor din cuple prin metoda grafo-analitica

S_MB TN.X=0TX=0

S_MA TM_i2+Q.d₅-F_i2.d₇+G₂.d₂+Q.d₆-N.d₈=0

N=M_i2+Q.d₅.K_L-F_i2.d₇.K_L-G₂.d₂.K_L+Q.d₆.K_L/d₈.K_L

N=0,5522+42,63.14.0,004263-8,2120.20.0,004263-0,2079.2.0,004263+42,63.23.0,004263/0,4263

N=10,31[N]

S_MA TM_i2+Q.d₅-G₂.d₂-F_i2.d₇-R^t_B.AB=0

R^t_B=M_i2+Q.d₅.K_L-G₂.d₂.K_L-F_i2.d₇.K_L/AB

R^t_B=0,5522+42,63.14.0,004263-0,2079.2.0,004263.20.0,004263/0,4263

R^t_B=10,121[N]

S_MB TF_i2.d₃+M_i2-Q.d₄-G₂.d₉+R^t_A.AB=0

R^t_A=-F_i2.d₃-M_i2+Q.d₄.K_L-G₂.d₉.K_L/AB

R^t_A=8,2120-41-0,5522+42,63.76.0,004263-0,2079.12.0,004263/0,4263

R^t_A=9,21[N]

S_F T R^t_B+N+Q+Rⁿ_B=0

K_f=Q/[Q]=42,63/100=0,4263[N/mm]

[R^t_B]=R^t_b/K_f=10,121/0,4263=23,7414[mm]

[N]=N/K_f=10,31/0,4263=24,1848[mm]

[Rⁿ_B]=[Rⁿ_B].K_f=96.0,4263=40,9248[N]

R_B= Rⁿ²_B+R^t2_B=9,1810[N]

S_F T R^t_A+F_i2+G₂+Q+Rⁿ_a=0

[R^t_A]=R^t_A/K_f=9,21/0,4263=21,604

[F_i2]=F_i2/K_f=8,2120/0,4263=19,2634[mm]

Q=100[mm]

G₂=G₂/K_f=0,2079/0,4263=0,487684[mm]

Rⁿ_A=[Rⁿ_A].K_j=25.0,4263=106575[N]

S_F TR_A+F_i1+G₁+R₀=0

F_i1=F_i1/K_f=0,1043/0,4263=0,2446[mm]

G₁=G₁/K_f=0,00475/0,4263=0,011142[mm]

R_o=[R_o].K_f=98.0,4263=41,774

S_Mo TR_a.d₁₀+G₁.d₁-M_c1=0

M_c1=R_a.d₁₀.K_L+G₁.d₁.K_L

M_c1=0,1816[N.m]

Capitolul Nr.5

Calculul reactiunilor din cuple

S_MB T N.X=0 TX=0

S_MA TN(XB-XA)-Q(XA-XB)-F_i2y(XA-XC₂)+F_i2x(y_C2-y_A)-G₂(XA-XC₂)-Q(YC-YA)

N=Q(XA-XB)+F_i2y(XA-XC₂)-F_i2x(YC2-YA)+G₂(XA-XC₂)+Q(YC-YA)/(XB-XA)

S_Fx TR_BX+N=0TR_BX=-N

S_Fy TR_BY-Q=0TR_BX=Q

S_Fx T-R_BX-F_i2x-Q-R_AX=0TR_AX=F_i2x-R_BX-Q

S_Fy T-R_BY+F_i2Y-G₂+R_AY=0TR_AY=R_BY-F_i2+G₂

S_FX TR_OX+F_i1x+R_AX=0TR_OX=-R_AX-F_i1x

S_Fy TR_OY+F_i1Y+R_OY=0TR_OY=-R_AY-F_i1Y

S_Mo TM_C1=G₁(X_C1-X₀)+F_i1x(Y_C1-Y₀)-F_i1Y(X_C1-X₀)+R_AY(X_A-X₀)-R_AX(Y_A-Y_O)

Momentul de inertie redus la elementul 1

J(red 1)

J_{red 1}=1/w S(j₁.w+mi.v_c²)

J_red=1/71,05(j₁.w+j₂.w+m₂.V_C2²)

J_red=1/71,05(4,2.10^-8.71,05²+9,187.10^-6.10,3733²+0,0212.4,9673²)=11,852.10^-8Kg.m²

Momentul de inertie redus la elementul 1 M_red1

M_red=1/wS(F_j.V_j.cosaj+M_j.w_j

M_red=1/w(Q.V_L.cosa+Q.V_s.cosa+G₁.V_C1.cosa+G₂.V_C2.cosa

M_red1=1/71,05(42,63.4,9673.cos220+42,63+4,8461.cos180+0,004757.3,0288.cos225⁰+0,2079.4,9673.cos210⁰)

M_red1=0,873N.m

Cuprins :

Capitolul Nr 1 . . . . . . . . . . . . . . . . Pag.3

Analiza structurala . . . . . . . . . . . . . . Pag.3

Capitolul Nr.2 . . . . . . . . . . . . . . . . Pag.15

Metoda analitica . . . . . . . . . . . . . . . Pag.15

Capitolul Nr.3 . . . . . . . . . . . . . . . . Pag.18

Calculul fortelor si cuplurilor ce actioneaza pe elementul

mecanizmului . . . . . . . . . . . . . . . .Pag.18

3.1 Fortele de greutate . . . . . . . . . . . . ..Pag.18

Capitolul Nr.4 . . . . . . . . . . . . . . . .Pag.21

Calculul reactiunilor din cuple . . . . . . . . .Pag.21

4.1 Calculul reactiunilor din cuple prin metoda

grafo-analitica . . . . . . . . . . . . . . . . Pag.21

Capitolul Nr.5 . . . . . . . . . . . . . . . ..Pag.23

Calculul reactiunilor din cuple . . . . . . . . . ..Pag.23

5.1 Momentul de inertie redus la elementul 1 . . . ..Pag.24

5.2 Momentul de inertie redus la elementul 1 Mred1..Pag24.

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