Proiect PCMAI Anul 2 MAC [PDF]

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Calculul Termic al unui motor cu aprindere prin comprimare

1) Date de proiectare Pn =

:

56

kW

n=

4200

rot/min

i=

4

cilindri

2) Alegerea parametrilor initiali

:

a) temperatura initiala

To =

293

K

b) presiunea initiala

po =

1.02

*10^5 N/m2 102000

c) temperatura gazelor reziduale

Tr =

900

K

d) presiunea gazelor reziduale

pr =

1.1

*10^5 N/m2 110000

e) coeficientul de exces de aer

λ=

1.25

f) raportul de comprimare

ε=

20

3) Parametrii procesului de schimbare de gaze Se adopta urmatoarele marimi din tabelul 4: a) presiunea la sfarsitul admisiei b) preincalzirea amestecului

pa = 0.9 ΔT = 15

c) coeficientul de post umplere

νp = 1.14

Se calculeaza coeficientul gazelor reziduale:

γr =

0.0192

Temperatura la sfarsitul admisie va fi:

Ta = 319.15228

K

Coeficientul de umplere:

ην = 0.9537484

Valorile calculate se vor compara cu cele di tabelele 6 si 3.

*10^5 N/m2 90000

4) Parametri procesului de comprimare Se adopta coeficientul politropic de comprimare valoarea n1 =

1.4 10

Presiunea la sfarsitul comprimarii : pc =

5.966017 *10^6 N/m2

5966017.231

Temperatura la sfarsitul comprimarii: Tc =

1057.816 K

5) Parametrii procesului de ardere Conform cu tabelul 7 se adopta urmatoarea compozitie a motorinei: c=

0.875 kg

h=

0.133 kg

o=

0.01 kg

Puterea calorica inferioara Qinf =

41868 kJ/kg

Se mai adopta din tabelul 4 si 5 : a) coeficientul de utilizare a caldurii

ξ=

0.9

b) coeficientul de crestere a presiunii

π=

1.3

Cantitatea minima de aer necesara arderii: Lmin = 0.5040675

kmolaer/kgcomb

Cantitatea reala de aer necesara arderii: L = 0.6300843

kmolaer/kgcomb

Coeficientul teoretic de variatie molara a incarcaturi proaspete: μo =

1.0532667

Coeficientul real de variatie molara a incarcaturii proaspete: μf =

1.0522632

Caldura specifica molara medie a amestecului initial:

C'μν =

38.40599 kJ/kmol*K

Caldura specifica molara medie a gazelor de ardere pentru λ>1: C''μν =

27.36

+

0.002654 *Tz

Temperatura la sfarsitul arderii:

Rm =

8.314

Coeficietii ecuatiei: a=

0.0027927

b=

37.538438

c=

-110736.4

Δec =

2646.1511

x1 =Tz

2489.0396 K

x2 =

-15930.64

Presiunea la sfarsitul arderii: pz=pz'

77.558224 *10^5 N/m2

7755822.401

Valorile calculate se compara cu cele din tabelul 4 si 5. Gradul de destindere prealabila: ρ=

1.9045961

6) Destinderea Se adopta coeficientul politropic al destinderii n2 n2 =

1.18

Gradul de destindere: δ=

10.500914

Presiunea la sfarsitul destinderii: pb =

4.8370423 *10^5 N/m2

Temperatura la sfarsitul destinderii

483704.2264

Tb =

1630.0875 K

7) Parametrii principali ai motorului Se adopta urmatoarele valori: a) coeficientul de rotunjire a diagramei

μr =

b) randamentl mecanic

c

Presiunea medie a ciclului teoretic: p'i =

13.116306 *10^5 N/m2

1311630.634

Presiunea medie indicata: pi =

12.85398 *10^5 N/m2

1285398.022

Randamentul indicat al motorului: ηi =

0.4843928

Presiunea medie efectiva: pe =

10.540264 *10^5 N/m2

1054026.378

Randamentul efectiv al motorului: ηe =

0.3972021

Valorile calculate se compara cu cele din tabelele 5, 6, si 9. Consumul specificefectiv de combustibil: ge =

0.2164755 kg/kW*h

8) Dimensiuni fundamentale ale motorului Se adopta raportul cursa - alezaj Φ =S/D=

(tab. 9)

1.1

Capacitatea cilindrica necesara: Vh =

0.3794971 l

Vh =

379.49714 cm^3

Alezajul si cursa D=

0.7602949 dm =

76.0294864 mm

0.98 0.82 (tab. 9)

S=

83.632435 mm

Se adopta: S=

84 mm =

0.084 m

D=

76 mm

0.076 m

Viteza medie a pistonului: Wm =

11.708541 m/s

Cilindreea totala a motorului: Vt =

1.5179886 l

Puterea litrica a motorului: Pl =

36.890923 kW/l

9) Diagrama indicata

Volumul la sfarsitul cursei de admisie

Va=

Volumul la sfarsitul compresiei

0.0199735

Vc=Vz

0.0199735

α

X

[ºRAC]

[m] 0

Vx

  

V  p x  p z   z   Vx 

px

[N/m2]•105 0.0199735 1.1 [l]

0

S   (1  cos )  (1  cos2 )  2 4 

V p x  p a   a  Vx

0.3994707 dm3

Vc=

X

10

1.423353 0.0264323

0.9

20

5.579057 0.0452895

0.9

30

12.13609 0.0750432

0.9

40

20.58155

0.113366

0.9

50

30.274

0.1573472

0.9

60

40.50946 0.2037925

0.9

70

50.59213 0.2495444

0.9

n1

n2

80

59.90197

0.2917895

0.9

90

67.95135

0.328315

0.9

74.42459 0.3576884

0.9

100 110

79.19611

0.3793401

0.9

120

82.32568

0.393541

0.9

130

84.03189

0.4012833

0.9

140

84.64771 0.4040777

0.9

150

84.56391 0.4036974

0.9

160

84.16784

0.4019002

0.9

170

83.78522

0.400164

0.9

180

83.63244 0.3994707

190

83.78522

0.400164

0.897818

200

84.16784

0.4019002

0.892393

210

84.56391 0.4036974

0.886835

220

84.64771 0.4040777

0.885667

230

84.03189

0.4012833

0.894314

240

82.32568

0.393541

0.919042

250

79.19611

0.3793401

0.967567

260

74.42459 0.3576884

1.050545

270

67.95135

0.328315

1.184444

280

59.90197

0.2917895

1.397089

290

50.59213 0.2495444

1.739059

300

40.50946 0.2037925

0.9

2.309181

310

30.274

0.1573472

3.316795

320

20.58155

0.113366

5.248625

325

16.16057

0.093305

6.89373

330

12.13609 0.0750432

9.351584

340

5.579057 0.0452895

18.96378

350

1.423353 0.0264323

40.30264

360

0.0199735

59.66017

370

1.423353 0.0264323

0

77.55822

380

5.579057 0.0452895

29.51804

390

12.13609 0.0750432

16.26661

400

20.58155

0.113366

9.997123

30.274

0.1573472

6.790018

420

410

40.50946 0.2037925

5.004062

430

50.59213 0.2495444

3.940308

440

59.90197

0.2917895

3.276291

450

67.95135

0.328315

2.850635

460

74.42459 0.3576884

2.576492

470

79.19611

0.3793401

480

82.32568

0.393541

2.403869 2.301847

490

84.03189

0.4012833

2.249533

500

84.64771 0.4040777

2.231188

510

84.56391 0.4036974

2.233668

520

84.16784

0.4019002

2.245459

530

83.78522

0.400164

2.25696

540

83.63244 0.3994707

1.1

550

83.78522

0.400164

1.1

560

84.16784

0.4019002

1.1

570

84.56391 0.4036974

1.1

580

84.64771 0.4040777

1.1

590

84.03189

0.4012833

1.1

600

82.32568

0.393541

1.1

610

79.19611

0.3793401

1.1

620

74.42459 0.3576884

1.1

630

67.95135

0.328315

1.1

640

59.90197

0.2917895

1.1

650

50.59213 0.2495444

1.1

660

40.50946 0.2037925

1.1

670

30.274

0.1573472

1.1

680

20.58155

0.113366

1.1

690

12.13609 0.0750432

1.1

700

5.579057 0.0452895

1.1

710 720

1.423353 0.0264323 0 0.0199735

1.1 1.1

Se adopta marimile pentru corectarea diagramei:αa=

35 grade RAC

0.610555556

unghiul de avans la aprindere

αev=

40 grade RAC

0.697777778

unghiul de avans la deschiderea evacuarii

λB=1/3.6

0.278 tabelul 6

raportul dintre raza manivelei si lungimea bielei

Poziţia punctului c’ se determină de cursa pistonului XS corespunzătoare unghiului de avans la aprindere

Xs=

9.4639718 mm

Poziţia punctului c’’ este determinată de presiunea în acest punct 715922.0677 N/m2 pc''=

7.1592207 *10^5N/m2

Poziţia punctului b’ este determinată cursa pistonului Xev corespunzatoare unghiului de avans la deschiderea evacuării

xev=Xb'

7.3760032 mm

Xa=

6.4901456 mm

Poziţia punctului a este determinată de presiunea in punctul a’ :

286852.1132 N/m2 pa'=

2.8685211 *10^5N/m2

Diagrama Indicata 100

90

80

70

P [N/m2]•10^5

60

50

px…

40

30

20

10

0 0

0.1

0.2

0.3

0.4

0.5

Presiunea in cilindru 110 100 90 80

px [N/m2]•105

70 60 px [N/m2]•105 50 40 30 20 10 0 0

90

180

270

360 α 0 RAC

450

540

630

720

Cinematica mecanismului biela-manivela n= α

unghiul de rotatie al manivelei

β

unghiul de inclinare al axei bielei

ω

viteza unghiulara de rotatie a arborelui cotit

S

cursa pistonului

R

raza manivelei

L

lungimea bielei

λ

raportul dintre raza manivelei si lungimea bielei

ω=

439.823 rad/sec

βmax=

15 grd

βmax=

12…180

λ=

1/3.2…1/3.8

λ=1/3.6=

0.278

R=S/2=

41.81622 mm

0.04182 m

L=R/λ=

150.5384 mm

0.15054 m

Ap- aria pistonului Ap=

0.00454 m2

α

xp

[ºRAC] 0

[m]

vp

aI

aII

ap

0

[m/s] 0.00

[m/s2] 8089.11

[m/s2] [m/s2] 2246.97 10336

10 0.0014234

4.07

7966.21

2111.46

10078

20 0.0055791

7.93

7601.27

1721.28

9322.6

30

0.0121361

11.41

7005.37

1123.49

8128.9

40 0.0205815

14.34

6196.62

390.18

6586.8

50

16.60

5199.58

-390.18

4809.4

60 0.0405095

18.14

4044.55

-1123.49

2921.1

70 0.0505921

18.92

2766.64

-1721.28

1045.4

80

18.99

1404.66

-2111.46

-706.8

0.030274

0.059902

4200 rot/min

S=

84 mm

0.084 m

D=

76 mm

0.076 m

90 0.0679514

18.39

100 0.0744246

17.24

-1404.66

0.00 -2246.97 -2111.46

-2247 -3516

110

0.0791961

15.64

-2766.64

-1721.28

-4488

120 0.0823257

13.72

-4044.55

-1123.49

-5168

130 0.0840319

11.57

-5199.58

-390.18

-5590

140 0.0846477

9.31

-6196.62

390.18

-5806

150 0.0845639

6.98

-7005.37

1123.49

-5882

160 0.0841678

4.65

-7601.27

1721.28

-5880

170 0.0837852

2.32

-7966.21

2111.46

-5855

180 0.0836324

0.00

-8089.11

2246.97

-5842

190 0.0837852

-2.32

-7966.21

2111.46

-5855

200 0.0841678

-4.65

-7601.27

1721.28

-5880

210 0.0845639

-6.98

-7005.37

1123.49

-5882

220 0.0846477

-9.31

-6196.62

390.18

-5806

230 0.0840319

-11.57

-5199.58

-390.18

-5590

240 0.0823257

-13.72

-4044.55

-1123.49

-5168

250

0.0791961

-15.64

-2766.64

-1721.28

-4488

260 0.0744246

-17.24

-1404.66

-2111.46

-3516

270 0.0679514

-18.39

0.00 -2246.97

-2247

280

0.059902

-18.99

1404.66

-2111.46

-706.8

290 0.0505921

-18.92

2766.64

-1721.28

1045.4

300 0.0405095

-18.14

4044.55

-1123.49

2921.1

310

0.030274

-16.60

5199.58

-390.18

4809.4

320 0.0205815

-14.34

6196.62

390.18

6586.8

330

0.0121361

-11.41

7005.37

1123.49

8128.9

340 0.0055791

-7.93

7601.27

1721.28

9322.6

350 0.0014234

-4.07

7966.21

2111.46

10078

0

0.00

8089.11

2246.97

10336

370 0.0014234

4.07

7966.21

2111.46

10078

380 0.0055791

7.93

7601.27

1721.28

9322.6

390

0.0121361

11.41

7005.37

1123.49

8128.9

400 0.0205815

14.34

6196.62

390.18

6586.8

410

16.60

5199.58

-390.18

4809.4

420 0.0405095

18.14

4044.55

-1123.49

2921.1

430 0.0505921

18.92

2766.64

-1721.28

1045.4

440

1404.66

-2111.46

-706.8

0.00 -2246.97

-2247

360

0.030274

0.059902

18.99

450 0.0679514

18.39

460 0.0744246

17.24

-1404.66

-2111.46

-3516

470

0.0791961

15.64

-2766.64

-1721.28

-4488

480 0.0823257

13.72

-4044.55

-1123.49

-5168

490 0.0840319

11.57

-5199.58

-390.18

-5590

500 0.0846477

9.31

-6196.62

390.18

-5806

510 0.0845639

6.98

-7005.37

1123.49

-5882

520 0.0841678

4.65

-7601.27

1721.28

-5880

530 0.0837852

2.32

-7966.21

2111.46

-5855

540 0.0836324

0.00

-8089.11

2246.97

-5842

550 0.0837852

-2.32

-7966.21

2111.46

-5855

560 0.0841678

-4.65

-7601.27

1721.28

-5880

570 0.0845639

-6.98

-7005.37

1123.49

-5882

580 0.0846477

-9.31

-6196.62

390.18

-5806

590 0.0840319

-11.57

-5199.58

-390.18

-5590

600 0.0823257

-13.72

-4044.55

-1123.49

-5168

610

0.0791961

-15.64

-2766.64

-1721.28

-4488

620 0.0744246

-17.24

-1404.66

-2111.46

-3516

630 0.0679514

-18.39

640

0.059902

-18.99

1404.66

-2111.46

-706.8

650 0.0505921

-18.92

2766.64

-1721.28

1045.4

660 0.0405095

-18.14

4044.55

-1123.49

2921.1

670

0.030274

-16.60

5199.58

-390.18

4809.4

680 0.0205815

0.00 -2246.97

-2247

-14.34

6196.62

390.18

6586.8

0.0121361

-11.41

7005.37

1123.49

8128.9

700 0.0055791

-7.93

7601.27

1721.28

9322.6

710 0.0014234

-4.07

7966.21

2111.46

10078

0.00

8089.11

2246.97

10336

690

720

0

Deplasarea pistonului, xp 0.09

0.08

0.07

0.06

0.05 xp [m] 0.04

0.03

0.02

0.01

0 0

60

120

180

240

300

360 α 0 RAC

420

480

540

600

660

Viteza pistonului, vp

vp [m/s]

25.00

20.00

15.00

10.00

vp [m/s]

5.00

0.00 0

60

120

180

240

300

360

-5.00

-10.00

-15.00

-20.00

-25.00

α 0 RAC

420

480

540

600

660

720

aI, aII, ap 15000

10000

5000

aI, aII, ap

0 0

60

120

180

240

300

360

420

480

540

600

660

-5000 series1 Series2 Series3 -10000 α 0 RAC

720

Forţele care acţioneaza in mecanismul bielă - manivelă

1 Forta de presiune a gazelor, Fg

Fg  ( p g  p 0 )  A p unde:

Ap aria suprafetei capului pisstonului pg presiunea gazelor in cilindru dupa diagrama indicata p0 presiunea mediului ambiant

2 Fortele de inertie

F  m  a m – masa elementelor in miscare , in a - acceleratia maselor , in

m / s 

N  Kg 

2

2.1 Fortele de inertie ale maselor in miscare de translatie,

Fj  m j  R   2  (cos   cos2 )

ml  m p  m1b unde:

mj - masele piselor în mişcare de translaţie mp - masa pistonului asamblat , in kg

Fj

2.2.Fortele de inertie ale maselor in miscare de rotatie Aceste forte sunt produse de o parte din masa bielei si masa neechilibrata al arborelui cotit (masa manetonului si masele reduse ale celor doua brate ). Fortele de inertie ale maselor in miscare de rotatie se determina cu relatiile :

Fr   m r  R   2 N  forta centrifuga

Ft   mr  R 

d dt

N 

forta tangentiala

mr -masa se miscare de rotatie , R - raza manivelei, în [m] ω - viteza unghiulară a arborelui

d  dt



0

Masele pieselor in miscare ale mecanismului biela – manivela Pentru majoritatea motoarelor de autovehicule , repartizarea masei bielei pe cele doua componente este :

m1b  0,2......0,3  mb

m2b  0,7.....0,8  mb

sau cu suficienta aproximatie :

m1b  0,275  mb

m2b  0,725  mb

In aceste conditii , masa elementelor aflate in miscare de translatie alternativa se poate determina cu relatia :

m j  m p  m1b  m p  0,275  mb mp - masa pistonului asamblat mb - masa bielei Masele rotitoare mr, sunt constituite din masa fusului maneton mm, masa bratului de manivela redusa la raza R si componenta m2b a bielei , adica:

mr  mm  2  mbr R  m2b Masa bratelor manivelei avand centrul de masa la raza r fata de axa arborelui cotit , se poate reduce la raza R a manivelei pornind de la egalitatea :

mbr R  R   2

 mbr     2

,

mbr R  R   2

 mbr     2

de unde se obtine :

mbr R

 mbr 



Kg 

R

ρ - reprezintă distanţa de la axa arborelui cotit la centrul de greutate al bratului

Masele constructive ale pistonului şi bielei Tipul motorului

Masa pistonului din aliaje de Al, ( kg/m2 ; g/cm2)

Masa bielei ( kg/m2 ; g/cm2)

M.A.C cu D=80 … 120 mm

200 - 300 ( 20 - 30 )

250 - 350 ( 25 - 35 )

3.Forţele rezultate din mecanismul bielă – manivelă

F  Fg  F j N  Calculul fortei F se face tabelar si se construeste curba F=f(α) Forta F aplicata in axa boltului se descompune in doua componente, una de sprijin, normala pe axa cilindrului (N) si una dupa axa bielei (B):

N.  F  tg N 

B 

F cos 

N 

In axa fusului maneton, forta B se descompune in doua componente, una radiala Z si una tangentiala T:

Z  S  cos     N  T  S  sin    

po=

N 

2 2 1.02 *10^5 N/m 102000 N/m

Ap=

2 0.0045 m

mp=

1.135 kg

2 250 kg/m

mb=

1.362 kg

2 300 kg/m

m1b=

0.3745 kg

2 82.5 kg/m

m2b=

0.9874 kg

2 217.5 kg/m

m1b  0,275  mb

m2b  0,725  mb

mj=

1.5095 kg

R=

0.0418 m

ω= λ=1/3.6=

m j  m p  m1b  m p  0,275  mb

440 rad/sec 0.278

α

px

[ºRAC]

2

0

[N/m ] 110000

Fg

FI

[N]

[N]

36.32 -12210.86

FII

Fj

F

β

N

[N]

[N]

[N]

[grade]

[N]

-3391.91 -15602.76 -15566.44

0.000

0.00

10

90000

-54.48 -12025.35

-3187.35 -15212.70 -15267.18

0.048

-737.28

20

90000

-54.48 -11474.45

-2598.35 -14072.80 -14127.28

0.095

-1348.27

30

90000

-54.48 -10574.91

-1695.95 -12270.87 -12325.35

0.139

-1728.61

40

90000

-54.48

-9354.06

-589.00

-9943.06

-9997.54

0.180

-1814.24

50

90000

-54.48

-7848.99

589.00

-7259.99

-7314.47

0.214

-1592.93

60

90000

-54.48

-6105.43

1695.95

-4409.48

-4463.96

0.243

-1106.35

70

90000

-54.48

-4176.36

2598.35

-1578.01

-1632.49

0.264

-441.43

80

90000

-54.48

-2120.39

3187.35

1066.95

1012.48

0.277

287.95

90

90000

-54.48

0.00

3391.91

3391.91

3337.43

0.281

965.04

100

90000

-54.48

2120.39

3187.35

5307.74

5253.26

0.277

1494.06

110

90000

-54.48

4176.36

2598.35

6774.71

6720.23

0.264

1817.15

120

90000

-54.48

6105.43

1695.95

7801.38

7746.90

0.243

1920.00

130

90000

-54.48

7848.99

589.00

8437.99

8383.51

0.214

1825.74

140

90000

-54.48

9354.06

-589.00

8765.06

8710.58

0.180

1580.69

150

90000

-54.48

10574.91

-1695.95

8878.96

8824.48

0.139

1237.62

160

90000

-54.48

11474.45

-2598.35

8876.10

8821.62

0.095

841.91

170

90000

-54.48

12025.35

-3187.35

8838.00

8783.52

0.048

424.17

180

90000

-54.48

12210.86

-3391.91

8818.95

8764.47

0.000

0.00

190

89781.8

-55.47

12025.35

-3187.35

8838.00

8782.53

-0.048

-424.12

200

89239.3

-57.93

11474.45

-2598.35

8876.10

8818.17

-0.095

-841.58

210

88683.5

-60.46

10574.91

-1695.95

8878.96

8818.50

-0.139

-1236.78

220

88566.7

-60.99

9354.06

-589.00

8765.06

8704.08

-0.180

-1579.51

230

89431.4

-57.06

7848.99

589.00

8437.99

8380.93

-0.214

-1825.18

240

91904.2

-45.83

6105.43

1695.95

7801.38

7755.55

-0.243

-1922.14

250

96756.7

-23.80

4176.36

2598.35

6774.71

6750.91

-0.264

-1825.44

260

105054

13.87

2120.39

3187.35

5307.74

5321.61

-0.277

-1513.50

270

118444

74.66

0.00

3391.91

3391.91

3466.56

-0.281

-1002.38

280

139709

171.20

-2120.39

3187.35

1066.95

1238.15

-0.277

-352.14

290

173906

326.45

-4176.36

2598.35

-1578.01

-1251.56

-0.264

338.42

300

230918

585.29

-6105.43

1695.95

-4409.48

-3824.19

-0.243

947.79

310

331680

1042.74

-7848.99

589.00

-7259.99

-6217.25

-0.214

1353.98

320

524862

1919.79

-9354.06

-589.00

-9943.06

-8023.27

-0.180

1455.97

330

935158

3782.52 -10574.91

-1695.95 -12270.87

-8488.34

-0.139

1190.47

340 1896378

8146.44 -11474.45

-2598.35 -14072.80

-5926.36

-0.095

565.60

350 4030264 17834.24 -12025.35

-3187.35 -15212.70

2621.55

-0.048

-126.60

360 5966017 26622.52 -12210.86

-3391.91 -15602.76

11019.76

0.000

0.00

370 7755822 34748.21 -12025.35

-3187.35 -15212.70

19535.51

0.048

943.41

380 2951804 12938.06 -11474.45

-2598.35 -14072.80

-1134.75

0.095

-108.30

390

1626661

-1695.95 -12270.87

-5348.94

0.139

-750.18

400

999712

4075.60

-9354.06

-5867.46

0.180

-1064.76

6921.93 -10574.91

-589.00

-9943.06

410

679002

2619.58

-7848.99

589.00

-7259.99

-4640.41

0.214

-1010.58

420

500406

1808.76

-6105.43

1695.95

-4409.48

-2600.72

0.243

-644.56

430

394031

1325.81

-4176.36

2598.35

-1578.01

-252.20

0.264

-68.19

440

327629

1024.35

-2120.39

3187.35

1066.95

2091.31

0.277

594.78

450

285064

831.10

0.00

3391.91

3391.91

4223.01

0.281

1221.11

460

257649

706.64

2120.39

3187.35

5307.74

6014.39

0.277

1710.53

470

240387

628.27

4176.36

2598.35

6774.71

7402.98

0.264

2001.77

480

230185

581.96

6105.43

1695.95

7801.38

8383.34

0.243

2077.73

490

224953

558.21

7848.99

589.00

8437.99

8996.19

0.214

1959.17

500

223119

549.88

9354.06

-589.00

8765.06

9314.94

0.180

1690.37

510

223367

551.00

10574.91

-1695.95

8878.96

9429.96

0.139

1322.54

520

224546

556.36

11474.45

-2598.35

8876.10

9432.46

0.095

900.21

530

225696

561.58

12025.35

-3187.35

8838.00

9399.58

0.048

453.92

540

110000

36.32

12210.86

-3391.91

8818.95

8855.27

0.000

0.00

550

110000

36.32

12025.35

-3187.35

8838.00

8874.32

-0.048

-428.56

560

110000

36.32

11474.45

-2598.35

8876.10

8912.42

-0.095

-850.58

570

110000

36.32

10574.91

-1695.95

8878.96

8915.28

-0.139

-1250.35

580

110000

36.32

9354.06

-589.00

8765.06

8801.38

-0.180

-1597.17

590

110000

36.32

7848.99

589.00

8437.99

8474.31

-0.214

-1845.51

600

110000

36.32

6105.43

1695.95

7801.38

7837.70

-0.243

-1942.50

610

110000

36.32

4176.36

2598.35

6774.71

6811.03

-0.264

-1841.70

620

110000

36.32

2120.39

3187.35

5307.74

5344.06

-0.277

-1519.88

630

110000

36.32

0.00

3391.91

3391.91

3428.23

-0.281

-991.30

640

110000

36.32

-2120.39

3187.35

1066.95

1103.27

-0.277

-313.78

650

110000

36.32

-4176.36

2598.35

-1578.01

-1541.69

-0.264

416.87

660

110000

36.32

-6105.43

1695.95

-4409.48

-4373.16

-0.243

1083.85

670

110000

36.32

-7848.99

589.00

-7259.99

-7223.67

-0.214

1573.15

680

110000

36.32

-9354.06

-589.00

-9943.06

-9906.74

-0.180

1797.76

690

110000

36.32 -10574.91

-1695.95 -12270.87 -12234.55

-0.139

1715.87

700

110000

36.32 -11474.45

-2598.35 -14072.80 -14036.48

-0.095

1339.60

710

110000

36.32 -12025.35

-3187.35 -15212.70 -15176.38

-0.048

732.89

720

110000

36.32 -12210.86

-3391.91 -15602.76 -15566.44

0.000

0.00

Ordinea de lucru a cilindrilor 1-3-4-2-1 alfa 0

Cil Admisie

Compresie Destindere Evacuare

180

Compresie DestindereEvacuare

540

Evacuare

360

DestindereEvacuare

ψ=

Admisie

Admisie

1 2

Compresie Destindere

3

Admisie

4

Compresie

180 ψ= unghiul de decalaj intre manivele

Momentul motor M=T·R α

M1

M2

M3

M4

Mt

Mmed

T1

T2

[ºRAC] 0

[Nm]

[Nm]

[Nm]

[Nm]

[Nm]

[Nm]

[N]

[N]

0.000

0.000

0.000

0.000

0.000

-111.519

-63.542

-64.206

142.697

20 -203.892

10

34.191

0.00

0.00

-96.570

34.191 -2666.88

-1519.55

-126.112

-127.460

-16.377

-473.842

34.191 -4875.91

-3015.87

30

-261.317 -185.398

-187.433

-113.406

-747.554

34.191 -6249.18

-4433.64

40

-274.131 -236.888

-239.537

-160.885

-911.440

34.191 -6555.60

-5664.99

50 -240.548 -273.895

-276.946

-152.608

-943.997

34.191 -5752.51

-6549.96

60 -166.954 -288.645

-291.703

-97.268

-844.571

34.191 -3992.58

-6902.71

70

-66.562 -274.336

-276.779

-10.283

-627.959

34.191 -1591.78

-6560.51

80

43.385 -227.643

-228.603

89.613

-323.249

34.191

1037.51

-5443.89

90

145.274 -150.895

-149.226

183.822

28.975

34.191

3474.11

-3608.53

100

224.719

-53.055

-47.275

257.278

381.666

34.191

5373.97

-1268.76

110

273.089

51.030

62.860

300.834

687.813

34.191

6530.70

1220.35

120

288.323

143.027

163.558

312.010

906.919

34.191

6895.01

3420.37

130

273.979

204.464

237.562

294.002

1010.008

34.191

6551.98

4889.59

140

237.065

219.997

271.641

253.513

982.216

34.191

5669.22

5261.03

150

185.524

179.966

259.392

198.253

823.135

34.191

4436.64

4303.75

160

126.162

85.532

202.582

134.897

549.173

34.191

3017.05

2045.43

170

63.549

-19.149

110.856

68.006

223.262

34.191

1519.73

-457.93

34.191

180

0.000

0.000

0.000

0.000

0.000

0.00

0.00

190

-63.542

142.697

-111.519

-64.206

-96.570

34.191 -1519.55

3412.48

200

-126.112

-16.377

-203.892

-127.460

-473.842

34.191 -3015.87

-391.65

210 -185.398 -113.406

-261.317

-187.433

-747.554

34.191 -4433.64

-2712.01

220 -236.888 -160.885

-274.131

230 -273.895 -152.608

-240.548

-239.537

-911.440

34.191 -5664.99

-3847.42

-276.946

-943.997

34.191 -6549.96

-3649.48

240 -288.645

-97.268

-166.954

250 -274.336

-10.283

-66.562

-291.703

-844.571

34.191 -6902.71

-2326.09

-276.779

-627.959

34.191 -6560.51

-245.91

260 -227.643

89.613

43.385

-228.603

-323.249

34.191 -5443.89

2143.01

270 -150.895

183.822

145.274

280

-53.055

257.278

224.719

-149.226

28.975

34.191 -3608.53

4395.96

-47.275

381.666

34.191 -1268.76

6152.58

290

51.030

300.834

273.089

62.860

687.813

34.191

1220.35

7194.19

300

143.027

312.010

288.323

163.558

906.919

34.191

3420.37

7461.46

310

204.464

294.002

273.979

237.562

1010.008

34.191

4889.59

7030.81

320

219.997

253.513

237.065

271.641

982.216

34.191

5261.03

6062.56

330

179.966

198.253

185.524

259.392

823.135

34.191

4303.75

4741.06

340

85.532

134.897

126.162

202.582

549.173

34.191

2045.43

3225.96

350

-19.149

68.006

63.549

110.856

223.262

34.191

-457.93

1626.32

360

0.000

0.000

0.000

0.000

0.000

34.191

0.00

0.00

370

142.697

-64.206

-63.542

-111.519

-96.570

34.191

3412.48

-1535.44

380

-16.377 -127.460

-126.112

-203.892

-473.842

34.191

-391.65

-3048.10

390

-113.406 -187.433

-185.398

-261.317

-747.554

34.191 -2712.01

-4482.29

400 -160.885 -239.537

-236.888

-274.131

-911.440

34.191 -3847.42

-5728.32

410 -152.608 -276.946

-273.895

-240.548

-943.997

34.191 -3649.48

-6622.94

420

-97.268 -291.703

-288.645

-166.954

-844.571

34.191 -2326.09

-6975.83

430

-10.283 -276.779

-274.336

-66.562

-627.959

34.191

-245.91

-6618.94

440

89.613 -228.603

-227.643

43.385

-323.249

34.191

2143.01

-5466.85

450

183.822 -149.226

-150.895

145.274

28.975

34.191

4395.96

-3568.63

460

257.278

-47.275

-53.055

224.719

381.666

34.191

6152.58

-1130.55

470

300.834

62.860

51.030

273.089

687.813

34.191

7194.19

1503.24

480

312.010

163.558

143.027

288.323

906.919

34.191

7461.46

3911.37

490

294.002

237.562

204.464

273.979

1010.008

34.191

7030.81

5681.10

500

253.513

271.641

219.997

237.065

982.216

34.191

6062.56

6496.06

510

198.253

259.392

179.966

185.524

823.135

34.191

4741.06

6203.14

520

134.897

202.582

85.532

126.162

549.173

34.191

3225.96

4844.57

530

68.006

110.856

-19.149

63.549

223.262

34.191

1626.32

2651.02

34.191

540

0.000

0.000

0.000

0.000

0.000

0.00

0.00

550

-64.206

-111.519

142.697

-63.542

-96.570

34.191 -1535.44

-2666.88

560 -127.460 -203.892

-16.377

-126.112

-473.842

34.191 -3048.10

-4875.91

570 -187.433 -261.317

-113.406

-185.398

-747.554

34.191 -4482.29

-6249.18

580 -239.537 -274.131

-160.885

-236.888

-911.440

34.191 -5728.32

-6555.60

590 -276.946 -240.548

-152.608

-273.895

-943.997

34.191 -6622.94

-5752.51

600 -291.703 -166.954

-97.268

-288.645

-844.571

34.191 -6975.83

-3992.58

610 -276.779

-10.283

-274.336

-627.959

34.191 -6618.94

-1591.78

-66.562

620 -228.603

43.385

89.613

-227.643

-323.249

34.191 -5466.85

1037.51

630 -149.226

145.274

183.822

-150.895

28.975

34.191 -3568.63

3474.11

640

224.719

257.278

-53.055

381.666

34.191 -1130.55

5373.97

-47.275

650

62.860

273.089

300.834

660

163.558

288.323

312.010

670

237.562

273.979

294.002

680

271.641

237.065

253.513

690

259.392

185.524

198.253

700

202.582

126.162

710

110.856

720

0.000

51.030

687.813

34.191

1503.24

6530.70

143.027

906.919

34.191

3911.37

6895.01

204.464

1010.008

34.191

5681.10

6551.98

219.997

982.216

34.191

6496.06

5669.22

179.966

823.135

34.191

6203.14

4436.64

134.897

85.532

549.173

34.191

4844.57

3017.05

63.549

68.006

-19.149

223.262

34.191

2651.02

1519.73

0.000

0.000

0.000

0.000

34.191

0.00

0.00

S

T

[N]

[N]

-15566.4

0.00

Z

M

[N]

[N•m]

-15566.44

0.00

-15285

-2666.88

-15050.51

-111.52

-14191.5

-4875.91

-13327.55

-203.89

-12446

-6249.18

-10763.36

-261.32

-10160.8

-6555.60

-7763.14

-274.13

-7485.91

-5752.51

-4790.36

-240.55

-4599.01

-3992.58

-2282.60

-166.95

-1691.12

-1591.78

-571.07

-66.56

1052.63

1037.51

177.77

43.38

3474.15

3474.11

-17.07

145.27

5461.59

5373.97

-974.40

224.72

6961.57

6530.70

-2411.13

273.09

7981.28

6895.01

-4019.91

288.32

8580.01

6551.98

-5539.68

273.98

8852.84

5669.22

-6799.47

237.07

8910.85

4436.64

-7727.83

185.52

8861.71

3017.05

-8332.30

126.16

8793.76

1519.73

-8661.44

63.55

8764.47

0.00

-8764.47

0.00

8792.76

-1519.55

-8660.47

-63.54

8858.24

-3015.87

-8329.04

-126.11

8904.81

-4433.64

-7722.60

-185.40

8846.23

-5664.99

-6794.39

-236.89

8577.36

-6549.96

-5537.98

-273.89

7990.19

-6902.71

-4024.40

-288.65

6993.35

-6560.51

-2422.13

-274.34

5532.65

-5443.89

-987.07

-227.64

3608.58

-3608.53

-17.73

-150.90

1287.25

-1268.76

217.40

-53.05

-1296.51

1220.35

-437.81

51.03

-3939.89

3420.37

-1955.46

143.03

-6362.98

4889.59

-4071.77

204.46

-8154.31

5261.03

-6230.11

220.00

-8571.42

4303.75

-7412.62

179.97

-5953.29

2045.43

-5590.88

85.53

2624.6

-457.93

2584.34

-19.15

11019.8

0.00

11019.76

0.00

19558.3

3412.48

19258.27

142.70

-1139.9

-391.65

-1070.51

-16.38

-5401.29

-2712.01

-4671.07

-113.41

-5963.29

-3847.42

-4556.11

-160.88

-4749.18

-3649.48

-3039.08

-152.61

-2679.4

-2326.09

-1329.85

-97.27

-261.252

-245.91

-88.22

-10.28

2174.24

2143.01

367.19

89.61

4396.01

4395.96

-21.60

183.82

6252.9

6152.58

-1115.57

257.28

7668.85

7194.19

-2656.09

300.83

8636.97

7461.46

-4350.16

312.01

9207.05

7030.81

-5944.53

294.00

9467.07

6062.56

-7271.23

253.51

9522.25

4741.06

-8258.07

198.25

9475.32

3225.96

-8909.26

134.90

9410.53

1626.32

-9268.94

68.01

8855.27

0.00

-8855.27

0.00

8884.66

-1535.44

-8750.98

-64.21

8952.92

-3048.10

-8418.07

-127.46

9002.53

-4482.29

-7807.35

-187.43

8945.13

-5728.32

-6870.35

-239.54

8672.93

-6622.94

-5599.68

-276.95

8074.83

-6975.83

-4067.03

-291.70

7055.64

-6618.94

-2443.70

-276.78

5555.99

-5466.85

-991.24

-228.60

3568.67

-3568.63

-17.53

-149.23

1147.03

-1130.55

193.71

-47.28

-1597.06

1503.24

-539.30

62.86

-4505.47

3911.37

-2236.17

163.56

-7392.99

5681.10

-4730.89

237.56

-10068.5

6496.06

-7692.63

271.64

-12354.3

6203.14

-10684.07

259.39

-14100.3

4844.57

-13241.89

202.58

-15194.1

2651.02

-14961.00

110.86

-15566.4

0.00

-15566.44

0.00

Z1

Z2

T'

Z'

[N]

Rm

[N]

[N]

Rmmed [N]

Rp [N]

Rpmed

[N]

[N]

-15566.44

-8764.474

0.00

-3400.99

23554.00

14078.23

3400.99

2933.58

[N]

-15050.51

-8660.465

-573.66

-3195.02

23191.91

14078.23

3246.12

2933.58

-13327.55

-8329.041

-930.02

-2499.25

21865.68

14078.23

2666.68

2933.58

-10763.36

-7722.597

-907.77

-1520.38

19764.85

14078.23

1770.77

2933.58

-7763.14

-6794.388

-445.31

-484.37

17060.49

14078.23

657.96

2933.58

-4790.36

-5537.976

398.73

373.81

14013.08

14078.23

546.55

2933.58

-2282.60

-4024.4

1455.06

870.90

11018.92

14078.23

1695.78

2933.58

-571.07

-2422.131

2484.36

925.53

8705.39

14078.23

2651.16

2933.58

177.77

-987.0731

3240.70

582.42

7878.40

14078.23

3292.62

2933.58

-17.07

-17.72798

3541.32

0.33

8726.02

14078.23

3541.32

2933.58

-974.40

217.39596

3321.37

-595.90

10449.69

14078.23

3374.40

2933.58

-2411.13

-437.8109

2655.17

-986.66

12279.35

14078.23

2832.57

2933.58

-4019.91

-1955.46

1737.32

-1032.23

13846.32

14078.23

2020.84

2933.58

-5539.68

-4071.771

831.19

-733.96

15030.45

14078.23

1108.86

2933.58

-6799.47

-6230.109

204.09

-284.68

15836.54

14078.23

350.28

2933.58

-7727.83

-7412.621

66.45

-157.61

16329.64

14078.23

171.04

2933.58

-8332.30

-5590.876

485.81

-1370.71

16596.40

14078.23

1454.26

2933.58

-8661.44 2584.3432

988.83

-5622.89

16718.21

14078.23

5709.18

2933.58

-8764.47

11019.76

0.00

-9892.12

16752.03

14078.23

9892.12

2933.58

-8660.47

19258.273

-2466.02

-13959.37

16717.22

14078.23

14175.52

2933.58

-8329.04

-1070.511

-1312.11

-3629.27

16592.97

14078.23

3859.17

2933.58

-7722.60

-4671.069

-860.81

-1525.76

16323.79

14078.23

1751.84

2933.58

-6794.39

-4556.113

-908.78

-1119.14

15830.28

14078.23

1441.65

2933.58

-5537.98

-3039.077

-1450.24

-1249.45

15028.04

14078.23

1914.24

2933.58

-4024.40

-1329.851

-2288.31

-1347.27

13854.04

14078.23

2655.47

2933.58

-2422.13

-88.22108

-3157.30

-1166.96

12304.54

14078.23

3366.06

2933.58

-987.07

367.19362

-3793.45

-677.13

10496.66

14078.23

3853.41

2933.58

-17.73

-21.59645

-4002.25

1.93

8781.01

14078.23

4002.25

2933.58

217.40

-1115.572

-3710.67

666.48

7873.06

14078.23

3770.05

2933.58

-437.81

-2656.088

-2986.92

1109.14

8513.29

14078.23

3186.20

2933.58

-1955.46

-4350.164

-2020.55

1197.35

10514.87

14078.23

2348.67

2933.58

-4071.77

-5944.534

-1070.61

936.38

13012.90

14078.23

1422.33

2933.58

-6230.11

-7271.227

-400.77

520.56

15159.83

14078.23

656.96

2933.58

-7412.62

-8258.068

-218.65

422.72

15990.24

14078.23

475.93

2933.58

-5590.88

-8909.257

-590.26

1659.19

13731.63

14078.23

1761.06

2933.58

2584.34

-9268.937

-1042.12

5926.64

5422.58

14078.23

6017.57

2933.58

11019.76

-8855.273

0.00

9937.52

3032.21

14078.23

9937.52

2933.58

19258.27

-8750.98

2473.96

14004.63

11776.00

14078.23

14221.46

2933.58

-1070.51

-8418.066

1328.23

3673.78

9066.53

14078.23

3906.51

2933.58

-4671.07

-7807.347

885.14

1568.14

12945.88

14078.23

1800.70

2933.58

-4556.11

-6870.345

940.45

1157.12

13120.45

14078.23

1491.09

2933.58

-3039.08

-5599.681

1486.73

1280.30

11614.87

14078.23

1962.02

2933.58

-1329.85

-4067.031

2324.87

1368.59

9603.37

14078.23

2697.78

2933.58

-88.22

-2443.703

3186.51

1177.74

8079.52

14078.23

3397.20

2933.58

367.19

-991.2377

3804.93

679.22

7915.96

14078.23

3865.08

2933.58

-21.60

-17.53192

3982.29

-2.03

9136.24

14078.23

3982.29

2933.58

-1115.57

193.71402

3641.57

-654.64

10987.32

14078.23

3699.94

2933.58

-2656.09

-539.3026

2845.48

-1058.39

12846.93

14078.23

3035.94

2933.58

-4350.16

-2236.168

1775.05

-1057.00

14418.48

14078.23

2065.92

2933.58

-5944.53

-4730.891

674.86

-606.82

15605.62

14078.23

907.56

2933.58

-7271.23

-7692.631

-216.75

210.70

16419.05

14078.23

302.28

2933.58

-8258.07

-10684.07

-731.04

1213.00

16923.29

14078.23

1416.26

2933.58

-8909.26

-13241.89

-809.31

2166.31

17202.01

14078.23

2312.55

2933.58

-9268.94

-14961

-512.35

2846.03

17332.96

14078.23

2891.78

2933.58

-8855.27

-15566.44

0.00

3355.59

16842.83

14078.23

3355.59

2933.58

-8750.98

-15050.51

565.72

3149.77

16808.81

14078.23

3200.17

2933.58

-8418.07

-13327.55

913.90

2454.74

16686.38

14078.23

2619.34

2933.58

-7807.35

-10763.36

883.44

1478.01

16418.58

14078.23

1721.91

2933.58

-6870.35

-7763.137

413.64

446.40

15923.91

14078.23

608.58

2933.58

-5599.68

-4790.357

-435.22

-404.66

15115.43

14078.23

594.28

2933.58

-4067.03

-2282.598

-1491.62

-892.22

13927.50

14078.23

1738.10

2933.58

-2443.70

-571.0655

-2513.58

-936.32

12354.00

14078.23

2682.31

2933.58

-991.24

177.77134

-3252.18

-584.50

10512.15

14078.23

3304.29

2933.58

-17.53

-17.06757

-3521.37

-0.23

8764.50

14078.23

3521.37

2933.58

193.71

-974.3958

-3252.26

584.05

7875.41

14078.23

3304.29

2933.58

-539.30

-2411.125

-2513.73

935.91

8658.35

14078.23

2682.30

2933.58

-2236.17

-4019.914

-1491.82

891.87

10946.38

14078.23

1738.09

2933.58

-4730.89

-5539.682

-435.44

404.40

13929.60

14078.23

594.26

2933.58

-7692.63

-6799.467

413.42

-446.58

16972.54

14078.23

608.57

2933.58

-10684.07

-7727.831

883.25

-1478.12

19675.07

14078.23

1721.91

2933.58

-13241.89

-8332.303

913.76

-2454.79

21775.19

14078.23

2619.34

2933.58

-14961.00

-8661.442

565.65

-3149.78

23101.17

14078.23

3200.17

2933.58

-15566.44

-8764.474

0.00

-3400.99

23554.00

14078.23

3400.99

2933.58

Variatia FI, FII , Fj functie de α [RAC] 15000

10000

5000

FI, FII , Fj

0 0

60

120

180

240

300

360

420

480

540

600

660

-5000

-10000

-15000 FI [N] FII [N] Fj [N]

-20000

RAC

720

Variatia F,Fg,Fj 40000

Fg [N] Fj [N] F [N] 30000

F,Fg,Fj [N]

20000

10000

0 0

90

180

270

360

-10000

-20000 α 0 RAC

450

540

630

N,S functie de α [RAC]

60000

N [N] S [N] 50000

40000

N,S [N]

30000

20000

10000

0 0

60

120

180

240

300

360

-10000

-20000 α 0 RAC

420

480

540

600

660

720

T,Z functie de α [RAC] 25000

20000

15000

10000

T,Z [N]

5000

0 0

60

120

180

240

300

360

-5000

-10000

-15000

-20000

α 0 RAC

420

480

540

600

660

Momentul motor instantaneu M M [N•m] 400

300

200

M [N•m]

100

0 0

60

120

180

240

300

360

-100

-200

-300

-400 α 0 RAC

420

480

540

600

660

Momentul total 1500 Mt [Nm] Mmed [Nm] 1000

Mt [Nm]

500

0 0

60

120

180

240

300

360

-500

-1000

-1500 α 0 RAC

420

480

540

600

660

720

T-Z Z [N] -20000

-10000

-8000

-6000

-4000

-2000

0

2000

0

Z [N]

10000

20000

30000

40000

50000

60000 T [N]

4000

6000

8000

10000

Diagrama fortei rezultante Rm pe fusul maneton 25000

Rm [N] Rmmed [N] 20000

Rm [N]

15000

10000

5000

0 0

60

120

180

240

300

360 RAC

420

480

540

600

660

720

T' - Z'

Z' [N]

-42000

-32000

-22000

Z' [N]

-12000

-5000

-4000

-3000

-2000

-2000 0 -1000

8000

18000

28000

38000

T' [N]

1000

2000

3000

4000

5000

Diagrama fortei rezultante Rp pe fusul palier 16000

14000

12000

Rp [N]

10000

Rp [N]

8000

Rpmed [N]

6000

4000

2000

0 0

60

120

180

240

300

360 RAC

420

480

540

600

660

720

Date de intrare

Pm

56 kW

nm

56000 W

4200 rot/min

2. Calculul dinamic al autovehiculului

2.1 Calculul caracteristicii externe a motorului cu ardere interna

Coeficientul de elasticitate al motorului c=(0.45…0.65) se adopta c=

0.6

Calculul coeficientilor α1,α2,α3 α1= 0.75 α2= 1.5 α3= -1.25 Verificare α1+α2+α3=

1

Turatia la moment maxim nM= 2520

Mom la putere max: Mm=

ωm = cmin= 300

127.324 N•m

439.82 g/kWh

rot/min

Pe

n

Me

ce

Ce

ce

1000

13.82

131.94

343.78

4.75

68.75547

1100

15.50

134.60

337.00

5.23

67.40046

1200

17.22

137.07

330.92

5.70

66.18483

1300

18.97

139.36

325.48

6.18

65.09647

1400

20.74

141.47

320.63

6.65

64.125

1500

22.53

143.40

316.31

7.13

63.26161

1600

24.32

145.15

312.49

7.60

62.49876

1700

26.12

146.72

309.15

8.08

61.83003

1800

27.92

148.11

306.25

8.55

61.25

1900

29.71

149.32

303.77

9.03

60.75408

2000

31.49

150.35

301.69

9.50

60.33845

2100

33.25

151.20

300.00

9.98

60

2200

34.99

151.86

298.68

10.45

59.73622

2300

36.69

152.35

297.73

10.93

59.54519

2400

38.37

152.66

297.13

11.40

59.42553

2500

40.00

152.79

296.88

11.88

59.3764

2520

40.32

152.79

296.88

11.97

59.375

2600

41.58

152.73

296.99

12.35

59.39745

2700

43.12

152.50

297.44

12.83

59.48882

2800

44.59

152.08

298.26

13.30

59.65116

2900

46.00

151.49

299.43

13.78

59.88565

3000

47.35

150.71

300.97

14.25

60.19397

3100

48.61

149.75

302.89

14.73

60.57838

3200

49.80

148.62

305.21

15.20

61.04177

3300

50.90

147.30

307.94

15.68

61.58765

3400

51.91

145.80

311.10

16.15

62.2203

3500

52.82

144.12

314.72

16.63

62.94479

3600

53.63

142.27

318.84

17.10

63.76712

3700

54.33

140.23

323.47

17.58

64.69438

3800

54.92

138.01

328.67

18.05

65.73483

3900

55.38

135.61

334.49

18.53

66.8982

4000

55.72

133.03

340.98

19.00

68.19588

4100

55.93

130.27

348.21

19.48

69.64122

4200

56.00

127.32

356.25

19.95

71.25

4300

0.00

0.00

900.00

13.00

180

350

1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000 4100 4200 4300

Diagrama caracteristiii externa Me ce

Pe Ce

300

50

0 80

70

60

250

50

200

40

150 30

100 20

10

0