paper hydrodynamic bearing

8/12/2019 paper hydrodynamic bearing

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128

. 34, N . 3 (2012) 128 137

. . .

.P. S , R.S. G , .K. K

A & , , . ., , , . .,

K :

A B S R A C

& ( )

.

,

( ,

7.0

.

2012 P F E

C :

A & , , . .,

: 4 @ .

1.

I ,

N

P , E .

. F ,

.

I ,

N P L C S

J , S, A E P

. N

, R

.

R E S E A R C H


2/10

. . ., . 34, . 1 (2012) 128 137

129

I R F M ,

:

3 u xy xy

y

+ =

(1)

,

N P

. N = 0, D

< 0, P > 0.

J H

1

N . A ,

N B G 2

J , H S 3 ,H 4

, 5 S H 6

.

. S

P 7 . S

S . 8 , S . 9 S

. 10 , . H ,

, ,

R .

I , N

R F M . S ,

, , , ,

M 7.0.

. 1. S .

2.

F . 1.

, , . ,

F . 1, .

N R . .

D 11 ,

N R H 1

:

0u v

x y

+ =

(2)

xy p x y

=

(3)

0 p

y

=

(4)

:

u U = , 0v = 0 y = (5)

0u = y h= (6)


3/10

. . ., . 34, . 1 (2012) 128 137

130

hv V

t

= =

y h= (7)

0 p = 0, x B= (8)

.

3.

I (3) :

1 p

y c xy x

= +

(9)

F 9 1 :

31

1 1u p p

y c y c y x x

= + + +

(10)

I (10) (5,6), :

{

}

1 1 1 1 34 3 2 2( )

2 4 2 8

23 33 2 2

1 2 431 28 1 2

14

p pu y y h y hy h y

x x

p y y hy h y

xh y U

ph h

x

= + +

+ +

+

(11)

I (2) (5,7)

(11), R :

333 5 6 1220

h h p ph h U

x x x x t

+ = + (12)

:

( , ) ( ) ( )s mh h x t h x h t = + (13)

( ) :

( )21

( ) 4 1 1 1 112 x x

h x H h r bs c B B

= + + (14)

A 12 K13 , ( )

,

= 2 / 1

( . . ) .

I :

1

c H h =

_ x

x B= ,

R :

33 53 6 12

20sh hm

x x p ph h x x

+ = +

(15)

( )( )2

1

24 1 1 1 1s bh x r x

= + + (16)

A =B/ ,= 2 2/ 12 P

N . F = 0 (15)

R N .

F ,mh

:i

mh e = (17)

1i

o p p p e = + (18)

14 ( . .

) po

.

R :

3353

620

so os s

d p d pd d hh h

dx dxd x d x + =

(19)

R :

293 2 11 12

20

352 2

3 20

d d p d poh h is sd x d xd x

d d p d po oh hs sd x d xd x

+ =

+

(20)


4/10

. . ., . 34, . 1 (2012) 128 137

131

4.

I (20) :

0o p = 0,1 x =

,

( )

6( ) 0 3

361 3

0 01 73 20

C h x oo s p x dxohs

C hoo s x xC dx dxohh ss

+=

++

(21)

1 11 16 0 02 3C dx dxooh hs s

= (22)

( )363 11 10 01 7 320

C hoo sC dx dxoh hs s

+= (23)

5.

:

1

0 oW p dx= (24)

I ,

(G Q )

M 7.0. G Q

R , M R S .

.

I S C DS

D C DC , 1 / dp dx

(20) (21) :

2 5 2 312 3 ( ) ( )1 201293 2

1 ( )

20

C ix h f x h f xs sdp

dxh h f xss

+ +

=

+

(25)

F , :

( ) ( ) ( )1 11 12 p x p x i p x = + (26)

(26) :

01 p = 0,1 x =

( ) odp

f x dx= ,

1( )11 11 9 20 3 21 ( )

20

5 2 2( ) 1 ( )203

9 20 21 ( )20

x p x C dxh h f xss

f x h f xs x dxh h f xss

= { + }

{ + }

{ + }

(27)

12( )12 12 9 20 3 21 ( )

20

129 20 3 21 ( )

20

x p x C dxh h f xss

x x dxh h f xss

= { + }

+ { + }

(28)

5 2 2( ) 1 ( )1 203

9 2 20 1 ( )20

11 9 23 21 1 1 ( )200

f x h f xsdx

h h f xss

C h h f x dxss

{ + }

{ + }

= { + }

293 21 12 1 ( )0 20

12 293 21 1 1 ( )0 20

x h h f x dxssC

h h f x dxss

{ + }

=

{ + }

D, :

0 1( ) D

BF L p x dx= (29)


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. . ., . 34, . 1 (2012) 128 137

132

I :

1

0 1( ) DF p x dx= (30)

14) :

( )11 D D Di i id F e S h e C h edt = (31)

I :

D D DF S i C = (32)

F (29) (31), D C C D

S C DS

( ) 1

110Re D DS F p dx= (33)

( ) 1

120Im D DC F p dx= (34)

.

:

1 1

0 0 x xpdx pdx= (35)

.

N N , , ,

S & D P

1,13 .

N P = 0, D

< 0 P > 0.

= 0. F ,

1.2 < < 3.7,

0 < < 0.83 13

P 0.1 < 1.5.

. 5.

DC .

F 5 D C DC

P . D

br . A ,

, D = 0.1 = 0 = 0.1, = 0.

, N, D


7/10

. . ., . 34, . 1 (2012) 128 137

134

D , ,

P D . A , N (P D )

> 1.5:

F . 4.

. .

DS br .

F 6 S C DS

P . S C

DS

2

. I , S

C DS 0.1 = (D )

N ( 0) = 0.1 = (P ),

N . F , S N(P D )

> 1.5. H , > 1.5, S

P D N

. , D

>1.5 P ,

.

. . ( , ) D DS C

= 2.

F 7 D C DC

S C DS

P

= 2. B D S

. F , , D S

= 0.1 (D ) N ( = 0) =

0.1 (P ), N .

D

P .F , D

D

S .

P

.


8/10

. . ., . 34, . 1 (2012) 128 137

135

. . ( ) x .

F 8 x

br (1.3 3.8)br < < = 0,

0.25, 0.5 P . I

br . A ,

C P .

F , , C P 0.1 = (D )

N ( 0) = 0.1 = (P ),

N . . N , C P

P C P

D .H , N N(P & D )

. ,

.

. .P .

F 9 x

br . I

,

br .

N N (P& D )

0.2 br 3

, P

D .I 0.3,

.

, > 0.2 2 < 0.2 2 < < 3,

N .

1 S. , H. H : ,

B JSME 14, . 69, . 279 286, 1971.

2 P. B , B. G :

, ASME J , . 106,

. 285 290, 1984.

3 . C. H , E. S : , ASLE .,

. 8, . 191 194, 1965.

4 H. H , S. : ,

ASME J , . 108, . 282287, 1986.

5 R. , P. ,

, ASME, . 122, . 872875, 2000.

6 C R. H :

, ES 97, . 87 97, 2009

7 R.K. S , R.K. P : A

, O , . 1, N . 1, . 19 24, 2006.

8 M.E. S , G.M. D :

: , I ,. 34, N . 2, . 57 67, 2012.

9 D. . S , K.K. C , A.C.K. R : ,

I , . 31, N . 3&4, . 23 28, 2009.

10 B.S. S , R. P : P


10/10

. . ., . 34, . 1 (2012) 128 137

137

, I , .31, N . 3&4, . 29 36, 2009.

11 D. D : , J B E ,

ASME (S D), . 83, N . 2,. 227 334, 1961.

12 S. A : : , J

F I , . 259, N . 3, .221 233, 1955.

13 .K. K : ,

J J A P , . 8, N .7, . 827 833, 1969.

14 N.B. N , G.B. M :

, J M S , . 16, N . 3,

. 182 190, 2008.

B : L ,

DC : D ,

DC :3 31 Dh C LB ,

,h h : F , 1h h h= ( )

mh t : ,

mh : 1mh h ,

, ssh h : S , 1s sh h h=

21,h h : O I ,

, D DF F : F ,

2 21 D DF h F ULB =

c H : H ,

L : ,

, p p : F , 21 p h p UB =

br : S 2 1h h ,

S D : D ,

S D :3 2

1h S ULB D

t : ,

,u v : ,

,W W : L , 2 21W W h ULB =

x : x B ,

: 2 2 21U h ,

: 1c H h ,

: S , : C P ,

: ,

: F ,

: t ,

xy : S ,

: B U .

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