TitleStudies on high pressure gaskets (Commemoration volumededicated to Prof. Shinkichi Horiba in celebration of hissixtieth birthday)

Author(s) Uchida, Shun-ichi; Suezawa, Yoshitada

Citation The Review of Physical Chemistry of Japan (1947), 20: 91-97

Issue Date 1947-09-15

URL http://hdl.handle.net/2433/46633

Right

Type Departmental Bulletin Paper

Textversion publisher

Kyoto University

f

The Review of PhysiEal Chemistry of Japan Vol.

STUDIES ON HIGH PRESSURE GASKETS.

Icy SHUN-ICHf Ucuma* and Yoserrnon Suszawa.* • . •

A A'

1. Introduction.

With regard to the design of high pressure. chemical plant, the prevention of

leal•age o[ the tvorldttg (iuid from joints is of the utmost importance. The tvoik

teas taken, up from this point of view.

2. Previous Works.

A glance over earlier works is not otit of place here before entering into

detailed description of our present .cork.

A gasket joint of simple design as shown.in Pig. t is chosen, because it is

fmtdamental and convenient to apply the results obt~ined therewith to high pressure joints of particular design in which we have particular interests.

Let Q~=working fluid pressure, t=thickness of gasket before tightening joints,

b =width of gasket before tightening joints, f

Pat=initial total bolts load caused by. tightening joint,

then, u-hen the working fluid is pcrdtitted to exert pressure tho force PA, will increase

by pPA and assume the value of P„,. The joint will ecpand at the same time axially, stretching;'each bolt by pl.

Hence,

Pee-Pat=SPA=AnEa~l~1 ...............:.................(t)

where. AA=total cross-sectional area of bolls, -

! =natural lehgth of each bolt,

EA=malulus of latgitudinal elasticity of bolt materials.

The process will make the gasket recover its thickness by p! whicL wit reduce

the contact force by pPD, making it to assume the new valst€ of P•, or

PAI-Pq-pP,=~pEDQI/t ............ ............... ......(2)

where AD=:r(Y-~-Yi )=contact area of gasket, E,=modulus of longitudinal elasticity of gasket materials.

• Afemher of Japao Society for the Promotion of Scientific Rexarch: r5th Special Commince.

20 (1946)

• • The Review of Physical Chemistry of Japan Vol.

9a 5. UCI{IDA ANll,Y. SL'P:ZAWA

furthermore, the following relation holds.:

where Pp is the axial force exerted by the fluid. pressure po, acting upon the area Ao as will be discussed in the next section. '

Pig, z illustrates the diagram of these relationsbetween loads andelongations.

Inan-ideal case, even if the residual contact {or gasket) force P9 reduced to nothiu~ under the fluid pressure, the prevention of leakage of the working fluid

from joints could be attained ; but actually it is noY the case unless the .force PQ or the so-cakled residual r~ncan gasket pressure p, (=Po~A,) assumes the value

somewhat larger than the limiting one'to be-found experimentally. Accordingly, in every actual case, it is necFssary to take an adequate value of

the initial total bolts load Ps, in, order to prevent the leakage of the working fluid from joints.

Table [, compiled from the data found in some recent literatures, gives the values of the residual nrean gasket .pressure-wt contact surface and the initial bolts

load necessary to prevent the leakage from joints.

3. The authors' theory and its.;application to design.

As shown in Table t, the values of t!ie initial total bolts load or the residual

menu gasket pressm•c on contact surface vary so. widely that the d~isigner finds it very diffictilt to choose proper ones. ,

The-fact stay certainly be~due to the diversities of experimental couditions,

especially of the manner of tightening- the tianges, the dimcnsion~ratio of gaskets to flanges (especially the diameter of pitch-circle of bolts) and the number of bolts. .

furthermore, the assuntptioq of the u(ective area on ivhich working ({aids act may come into :question.

In this connection, the authors are of the opinion that the effective diameter of We .circle in which working tluict5 act is the inner diameter of gasket, and that,

with regard to the critical leakage pressure,. the tact that the distribution of the initial gasket pressure on contact surface is not uniform must also be taken into consideration. Accordingly, the miniuwnt casket pressure p„~„ on contact sm'Eace

will be discussed, being based on the tvorl:ing tuid pressure p,,. These considerations lead to a set of ecjuations of more general applicability than

the usual ones, as follows :- Let:. Ite distribution of the initial gasket,pressure un cuntact sw'face, b

by [Ite: equation, _

•

• is

20 (1946)

~~ "

e expressed .

. .'

4;.:•:.:

-r~~W UiY.~ _ 1'

The Review of Physical Chemistry of Japan Vol. 20 (1946)

9351'Ul)IF.S ON FIIG[i PRESSURE GASKtiTS

(~. ~ L O o m V'~C~ •p

c

=I?` u t. ~~ Ci~"'

v ~ p~3 J

y ~(e ~'s Ga = - ~ p u u.. -Fr v'LY i

e

~1 S

C' O

~_ ~~ F{X 4 Vc e~U~ °~

~ e', ~ v ~ 2

~ IH~CVI~CY/6.°~ C N O e J LV'~ V :O ~ L r-i_mo=lGy>>~ E e E Ou K^~.1X

i C1 7E IFd=u ;~ ~ ~ a f5d °= d o '~' oa `c u`~

^ L a Y C O s. > ' c a.ry ~~ ~ is u3 x ~ 7 ~

V1 V

e~ ea i-u8

y~ `off

V a '= r. ~;

x . ° e - u di

I p 0 I n!fv I ~ IO~~Y.M ~a~~D W 9 M °.~"." . N~ I ~N

V .~

V

.'] V N~ ~9 Y

~0.~1s̀ ul

O

*a

wM

I I

,I I I <~ ~~

~~I I

U C

9

.~. \ p A

Q it

p „ 9 Y v C e ~m

i I I fn _ e o o~~c°~ N I I ,~ I I

I

N b

i~ vj ~2 ~ CV [(j

N NI~~~:~iz~

i N

_i x

C

$889;88$ M N ~:~ I , I ~a. t7 .f ~ N M <

O < M N ON n N N-M

~~ E _4` ga w S °~

°o ~~

i~~$ W ~ NN Od ~L.V v

~$ ~~~ ~~~ ~PV tH:

v'Yi~PIPV '~N .N

w S n ti =~~

>'~ ~. I c v. °' - ~ a== " I ~v~

T j C V ~~

~ 1. V~.~ v 'JN N Uv.X. ~

~ C C? ~ j Gb w .., u u ~ ~ 1~ .N.. ~_ ~ V ~'~

e ~ Irav ~ .9 ~,~ c ~3w

'O ~ Y 4 C '

~ I f_ . ~5

i ~du es

~ I Nz4

N M

O I .. u

z

wv ° ~, y M ~, H _

M

N

. V

L J N 3 ~_+

O 7 Iy A`_M

h • '+^ o I I s

T O O O p .pi a N

0, ivy

y

N

~ 9 `l O~ C ~ Y NU . N N

H ~~'~ v NNb

N'

M

!0G

i^^X °~. C tl

i,Vd„ v`i ~'C(J u ~'~~ M~=N 3

C

~C N

N W

[:

N

.Ui '~v M

O

N a

N

N

0C

0

G~n~, PH

~D C ~

d.~

M

_u

l7 i

Y

eO

y

L~ ~ ~C y

O

N

c Y

C A

~_

a~~ ~< u

My

~~ a a ~ b ai

I I 'I I , ~ I/ i

L

p N h ~~ N ~q N1 e.l y~ h r CIin

M I P

a

~' .V. S N v I N N Y r ~

.n 8O

M

i . y

O

N I P I O ~ I y p

• T n w ~ ~ )

w

Y.. 1~ V C ~ N

1t : c _~ ~_ ~ a L ~

CL c .~.

N °L c

;C u~GC ~ w y Y

~ ~` I N I r7 i~ C N I v> I 1~

z

. ,

~:::~b.r.~~,.a ! l1~~.-

,:.

~Lt~tie. ~ a pi. u

x

where p is

e]ementary

namely,

in which c

and the latt

Prom

S. UC[tIDA AvtJ

The Review of Physical Chemistry of Japan Vol.

Y. SUELAWA

20 (1946)

N

the distance hehveen the centre of any bolt and any point on the

coirespbnding area A, B, I7n AS of contact surface as shown in Pig. 3,

and a arc constants, the former being determined by boundary- conditions er experimentally. ~

E4• (4) ~ (5), it follows that- •

. P: h-- Pb,-~Pb,

P '_ 9_`eg nPA

'W

dYd

\'

Pn,a

1 1n

,

0„f,tr_. frs.~„~c

~~ P,b 2 Y, b ~~

- P Yi

•- 2Y

- 2R

Pig. i. Nlg. 1,

J

A,6:

A

2` ~~ZR _

R\ $ a rz BI

\\

r~

ti

x~•' z.:

res. ;.

~~z

~~

,~,

-_

t , ~~ ` ~ The Review of Physical Chemistry of JaparrVol .:

i '

STUDIES UN tIIGH.PRESSURE GASKETS gg

t ' p- .................................(6) r -2RY cos d+I~)„

The equation of equilibrium of forces acting upon the area A3 BI B~ A2, i. e.,

6o Ta Bo Pa3=J f pYdY~ z2

OTa ~

and the above equation (6) leads to the following equation,

Bo Ta

P Zn~ ~ ~ r~r~ (7)

. dl--- 4 -~,, ................~.

~~ ~u it ~(Y 2r.d COS ~+~)~~

From this equation (y) the constant c is detertirined and so Eq. (6) gives the

initial gasket pressLVC at any point For examlile, at the poiht B3 where flte

pressure is minimum,

- ~o Pin ............(3)

in which Do P ,~ ~ 1 ~ Y"I [~~ I - ...........................(9)

Table 2 gives some values of the iirtegmtion of 1„.

' Table z.

r, re I, 7

qa q.3 0.0734 o.or63 .~ 43 oa54 0.0350 47 o.zgt o.o56z „ q.9 0.336 0.0805 .

When the working fluids act, tfie minimum initial gaslcet pressure on contact

surface caused by tightening .joints reduces to the value:

where a is defined by

OPa=aPo .....' .....................................(10) or ~Po=(I-a)Po

Hence. remembering the relations expressed in Eq. (t) & (2), it follows that

i

r. rs i, r.

q.[ 4.3 o.o73q o.oI63

4~5 ' O.IgQ OA35a

4.7 o.zgl o.o56z

q~9 0.336 oASoS

20 (1946)

.. ..

t The Review of Pfiysical Chemistrypf Japan Vol. 20•(1946)

r

• -

qb ~ -S. L•CHIDA ANllY. SliHZAtvA ~ ~ ~.

' a A~F,t

i-a = A~~ A,E,t or- a= A

D&al~-AoEQI ..........................................(ti) ' -

• - _ To prevent entirely the leakage of the lvorking fluid from joints, the next equation must hold, i. e., ,

pmz~-(t-a ~ JO ~ -. .. 9 ............ . ..........................(i 2) - Po or p.~a~(i-a~

P

On the other hand, from various experiments and ezpericnces as described in

the former section, it is apparent -That flie initial tightening force Pn, should be

_ ' _ greater than the hyYlraulic forec Po ; henc@; we can. put in general

++•here x is the coefficient of additional force.

Lt~eailicr works the coeflicieui_a' +vas regarded as independent of t11e dimension - ratio of joints. But, tlie'theoretical considerations based upon non-iiiuform distri-

~. bution, of initial gasket pressure lead to the conclusion that x depends upon the . dimension ratio of joints.

' -Let the ratio A~/A, be denoted by a, then from Eroin I:y. (~3) ive obtain

On the other hand,

Hence, from Eq. (t¢) & (i5) we have ~

P« p. Fina t F~ p~A Fa

' To lirevent entirely the eakage of the. working fluid from joie+.ts, it must hold at least as the postulate of'Ey. (i2) that

r --

9

~' _ 1 pn • ~'

pwiu -

,:, •~... ,-lecoi•dingly. fmm F;y,(t61 dk (tyl we bhtain following equation, -

,- 1 ~ ~ •

N' _ ~- i ;~7e...a-. ~ti3v_3_:!/ ~~•,ais~lc•Gs.7c r_.~e ..~. ~ ~ ~ ..-.. / j F

o

t_

- - -,_ , The Review of Physical Chemistry of Japan Vol. 21

-~ STUDIES oN IiIGFI PRESSURE GASKETS gy

r

=l(I-a)~mta--IJ[L ......(18) 5

. ` n

For the special case. of a=o,

4

, ~ 3 `/ m _

- - \ ~'rrnn n-

or, remembering Eq. (ty)

i

po o ~ n:

Fig. (q) shows how the vahle of x varies, v ~ ~ 3 ~ _ with the dimensioq ratio of bfr, and the- ex- ~ n~a• 4•

peritnedtal constant n in flee case of P./y,=2.oq, lh=.-./3 S a=o ; by. which• we can readily recognize the facts mentioned above.

With a set of equations thus obtained, we can now easily design the gasket.

joint of simple type in the following way. First assume the main dimensions of joints. and the number of bolts, as tlje

inside and outside diameter of vessels aiul the waking fluid pressure p„ arc given and also the constant n is known*"*. t

Then we find the value of ~i„~p,q;n from Eq. (S) ~ (I5), calculating the value. of 1,, by Eq. (9). The coefficient of additional force, x, will also lie determined by

v

Eq. (t8) rvith the value of a computed from Eq. ([ [). The miniinutn value of the

initial tightening force. 1'L, will be thus obtained. ~If the value of Pb, thus found is not appropriate in view of the strength of bolt materials, the first assumption. should

be modified and. the calculation be repeated. In t1tis way the can finally decide the adequate main dimensions of joints and-the corresponding initial tightening force.

4. Conclusions.

As above mentioned, theoretical considerations based upon non-uniform distri-

bution of initial- gasket ,pressure have led to a set of equations of more .general applicability than the usual ones. With the aid of these equations we can fiud the

mlmerical values rcgttisite in the design of the gasket joint of simple type.

The present paper is the contribution by a member of the Committee to the Sexsginhof llr..S. Horiba tvho is the Head of the t 5th Special Committee of Japan

Society fur the Yromotioil of Scientific Ttesearch.

- %'hB !'okyo .Gu~till<le 4( 2'echatoZoyy. .

zz/ In nur prdimioary experiments where R(Y,=2.o7. 1+/Y==os45~o.t95. 9n=U/8 and a=o.o5, the ra]ne ~f ihi• ̂mtaN o: fell near tS.

1 1

~__

i

n:

ro

~~~i

(1946)20