dengeleme_ornek

n100A 150

I

200 150250

II

100B

z

x

Problem 2:

2m 3m 2m 3m

1m 1m

d/d 1200 kgm, 4.1 kgm, 0.8 kgm, 2.1 332211 nmmm

a) A ve B yatak kuvvetlerini bulunuz?

b) Tam dengelemeyi gerekletiriniz? (Dengeleme byklklerini ve alarn bulunuz?)

zm:

a)

1 1 2 2 3 3

1 1 2 2 3 3

0.848, 0.4, 1.21

0.848, 0.69, 0.7

, w 40

XX X

Z Z Z

m m m

m m m

X Ekseni ZEkseni

0XF

2 2 2

3 3 1 1 2 2X X X X XA m w m w m w B

NBA XX 600)40(038.02

0XMA

2 2 2

1 1 2 2 3 3150 500 850 950 0X X X Xm w m w m w B

NA

NB

X

X

35.12257

35.11657

0ZF

2 2 2

3 3 1 1 2 2Z Z Z Z ZA m w m w m w B

NAB ZZ 9.9558)40(542.02

0ZMA

2 2 2

1 1 2 2 3 3150 500 850 950 0Z Z Z Zm w m w m w B

NA

NB

Z

Z

56.4951

76.13510

NAAAZX

8.1321922 NBBB ZX 73.17844

22

b) X Ekseni Z Ekseni

0XF

IIXXXXIX mmmmm )()( 221133

038.0)()( IIXIX mm

0XMI

0600450)(250100 332211 XIIZXX mmmm

0600450)(250100 332211 ZIIZZZ mmmm

kgm 617.1)(

kgm 58.1)(

IX

IIX

m

m

0ZF

ZZIZIIZIZ mmmmm 33221 )()(

542.0)()( IZIIZ mm

0ZMI

0600450)(250100 332211 ZIIZZZ mmmm

kgm 963.0)(

kgm 5.1)(

IZ

IIZ

m

m

I nolu dengeleme dzlemi

kgm 882.1)()()(22 IZIXI mmm

o

IX

IZI

m

mArctg 77.30

)(

)(

1. Blge

II nolu dengeleme dzlemi

kgm 178.2)()()(22 IIZIIXII mmm

o

IIX

IIZII

m

mArctg 5.43

)(

)(

3. Blge

ooo

II 5.2235.43180

Problem1

nA 100 150 200 150 250

I IIz

m1

xB

D2D1z

x

y

m2D1

r2

m2D2

m3

xr1

d/d 1500 m, 3.0 m, 2.0 kg, 1.5 kg, 3 kg, 0.5 kg, 1 214321 nrrmmmm

a) Dengelenmemi durumda, A ve B yatak kuvvetlerini bulunuz?

b) Bu sistemde ideal dengelemeyi gerekletirerek, I ve II nolu dengeleme dzlemlerine konacak

dengeleme byklklerini ve alarn bulunuz?

zm:

a)

kgmm

kgmm

Z

X

5.15.0360cos

6.2866.0330cos

33

33

rd/s 5030

1500.

D2Z ekseninde

05.15.134 Zmm

m3x

m4

z

m3zm3

x

Z Ekseni X Ekseni

Az Bz

m2

350 250250 r1

Az

m3x

Bz

m1

r1

200 150 250250 r2

NrmBA ZZ 4.24672

12 06002500 212 zz BrmMA

NBz 1028600

275.616850 NAz 3.1439

2

11

2

23 rmBxrmA xx 8.49347.19245 xx BA

NAB xx 8.14310 060045025002

23

2

11 xx BrmrmMA

NBx 13.12378600

8.7426877 NAx 77.1932

NAAAZX

8.240922

NBBB ZX 74.1242022

b)

Z Ekseni X Ekseni

Z Ekseni

IIZIZz mmrmF )()(0 12

IIZIZ mm )()(1.0

0750)(1500 12 IIZz mrmMI

kgm 08.0)(m

kgm 02.0)(

IZ

IIZm

X Ekseni

2311 .)()(0 rmmrmmF XIIXIXX

0750)(350150.0 2311 IIXXX mrmrmMI

58.0)()(

78.0)(2,0)(

IIXIX

IIXIX

mm

mm

kgm 256.0)(m

kgm 323,0)(

IX

IIXm

I nolu dengeleme dzlemi

kgm 268.0)()()(22 IZIXI mmm


zx

I II

x

z

o

IX

IZI

m

mArctg 35.17

)(

)(

3. Blgede

ooo

I 35.19735.17180

2.)( IdenI mF

NFdenI 93.6605

II nolu dengeleme dzlemi


o

IIX

IIZII

m

mArctg 53.3

)(

)(

3. Blgede

oooII 53.18353.3180

2.)( IIdenII mF

8001denIIF N

256,01 xm 323,01 xm

1 2

08,01 zm 02,011 zm

268,01 m 324,011 m

yx

z

Problem 3:

n=1848 dev/dak

a) Dinamik yatak kuvvetlerini hesaplaynz?

b) Bu sistemi dinamik olarak dengeleyiniz?

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