Identification of Characteristics of Hydraulic Shock Absorber

8/13/2019 Identification of Characteristics of Hydraulic Shock Absorber

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Paper: ASAT-13-HC-04

1 /13

13th

International Conference on

AEROSPACE SCIENCES & AVIATION TECHNOLOGY,

ASAT- 13, May 26 2!" 200#" $-Mail: a% a t& ' t c(e) * (e+ Military Technical Colle+e" ,ory $l.oah" Cairo" $+yptTel : 202 24022#2 2403613!" a: 202 22621#0!

Identification of Characteristics of Hydraulic Shock AbsorbersUsed in Light Weight Tracked

Vehicles

A( M( Sale'

" 5( alal7

Abstract: Shoc. a%orer% ha8e eco'e the 'o%t 9i)ely *%e) ter' in a*to'oti8e

%*%pen%ion%( They are *%e) for the opti'iation of )ri8in+ co'fort an) )ri8in+ %afety( Thi%

paper i% concernin+ 9ith i)entification of characteri%tic% an) )a'pin+ coefficient of

the hy)ra*lic %hoc. a%orer% of a li+ht 9ei+ht trac.e) 8ehicle *n)er real con)ition%(

;yna'ic eha8ior% of the a%orer are %t*)ie) y oth co'p*ter %i'*lation an)

eperi'ental te%tin+( In the eperi'ental te%tin+ the force an) 8elocity of the %hoc.

a%orer are 'ea%*re) on a %tan)ar) te%t ench 9hich allo9 %in*%oi)al ecitation 9ith

)ifferent fre<*encie% an) a'plit*)e% corre%pon)in+ to roa) con)ition%( The %i'*late) 'o)el

i% carrie) o*t for the %a'e ecitation con)ition% *%in+ A;AMS pro+ra'( The roa)

ro*+hne%% i% +enerate) in the 'o)el *%in+ a rotational =oint 'otion applie) to re8ol*te =oint

9hich i% connecte) to the 'o8ale en) of the %hoc. a%orer( The )a'pin+ coefficient of the

%hoc. a%orer i% al%o )eter'ine) accor)in+ to the re<*ire) rate of )a'pin+ of the 8ehicle(

The pre)icte) characteri%tic i% co'pare) 9ith the eperi'ental re%*lt% an) 9ith tho%e

otaine) fro' the co'p*ter %i'*late) 'o)el(

Keywords %hoc. a%orer" hy)ra*lic" 8i%co*% )a'pin+"

8iration

Introduction;*rin+ trac.e) 8ehicle 'otion" %hoc.% are +enerate) )*e to roa) ro*+hne%% an)tran%'itte)

thro*+h trac.% to the roa) 9heel% ca*%in+ )efor'ation of the ela%tic ele'ent% 9hich re%*lt%in h*ll 8iration( Thi% 8iration i% )a'pe) y the action of %hoc. a%orer% connecte) to%*ch 9heel%( In or)er to )e%i+n %hoc. a%orer% for re%i%tin+ i'pact an) atten*atin+

8iration" the acc*rate characteriation of the %hoc. a%orer ha% to e %t*)ie)( Theeffecti8ene%% of )a'pin+ )epen)% on the )a'pin+ coefficient an) n*'er an) locationof %hoc. a%orer% *%e) in the %*%pen%ion %y%te' of 8ehicle%(

In 'o)elin+ trac.e) 8ehicle )yna'ic%" the e<*ation of 'otion of it% h*ll ha% to e

)eri8e)> thi% 'o)elin+ can e carrie) o*t analytically 9ith a con%i)ere) n*'er of

a%%*'ption% or *%in+ %oft9are pac.a+e %*ch a% A*to'oti8e ;yna'ic Analy%i% of

Mechanical Sy%te' A;AMS( So'e phy%ical para'eter% in the e<*ation of 'otion can e

calc*late) )irectly 9hile other para'eter% '*%t e i)entifie) fro' eperi'ent% ?1@( ne of

the%e para'eter% i% that of )a'pin+ coefficient of the hy)ra*lic %hoc. a%orer% *%e) in

8ehicle %*%pen%ion %y%te'(

mailto:[email protected]





















2 /13

$+yptian Ar'e) orce%



3 /13


In 'o)elin+ 8ehicle %y%te'%" 'any re%earche% are relate) to the characteriation of %hoc.

a%orer% ?2" 3@( The principle of )a'pin+ in hy)ra*lic %hoc. a%orer% )epen)% on

tran%for'in+ the .inetic ener+y of the o%cillatin+ h*ll into heat ener+y thro*+ho*t

the )a'pin+ orifice%( In trac.e) 8ehicle%" the h*ll 8iration ha% a a) effect on cre9

co'fortaility" acc*racy of firin+ on 'o8e" an) 8ehicle an) *n)ercarria+e %y%te'%( 5hen

%hoc. a%orer% +et ol) an) lo%e fl*i)" the )a'pin+ coefficient )ecrea%e% an) the %*%pen%ion

%y%te' lo%t it% aility to re)*ce 8ehicle 8iration an) after the 8ehicle pa%%e% o8er a *'p" it

9ill o%cillate *p an) )o9n 'any ti'e% rather than =*%t once(

The paper i% concernin+ 9ith i)entification of )yna'ic characteri%tic an) )a'pin+

coefficient of the hy)ra*lic %hoc. a%orer *%e) in Ar'or Per%onnel Carrier APC M113

thro*+h three approache%( The fir%t one e%ti'ate% theoretically the )a'pin+ coefficient

of the %hoc. a%orer on the a%i% of the re<*ire) rate of )a'pin+ an) the 8ehicle

%pecification%( The 8ehicle %pecification% that affect the nee)e) )a'pin+ are tho%e of 'a%%

'o'ent of inertia" )i%tri*tion of roa) 9heel%" n*'er of %hoc. a%orer% that the 8ehiclee<*ippe)" an) the %tiffne%% of 8ehicle %*%pen%ion( The %econ) approach e8al*ate% the

)a'pin+ characteri%tic% an) the )a'pin+ coefficient eperi'entally *%in+ a %tan)ar) te%t

ench y 'ea%*rin+ the )a'pin+ force an) the 8elocity of the pi%ton of the %hoc. a%orer

*n)er )ifferent ecitation fre<*encie% an) a'plit*)e%( The thir) approach e%ti'ate% the

)a'pin+ characteri%tic% of the %hoc. a%orer y a )e8elope) %i'*late) 'o)el *%in+

A;AMS *n)er real operatin+ con)ition%( The operatin+ con)ition% are )eri8e) fro' the

nat*re of ecitation of the 8ehicle h*ll( Thi% ecitation i% )epen)in+ on confi+*ration of the

roa) that the 8ehicle i% 'o8in+ on an) on the 8ehicle 8elocity( In the follo9in+

in8e%ti+ation% the three approache% 9ill e )i%c*%%e) an) the final concl*%ion 9ill e

otaine)(

Theoretical In!estigationor li'itin+ the a'plit*)e an) other para'eter% of 8iration" the 8ehicle %*%pen%ioni%

e<*ippe) 9ith %hoc. a%orer% connecte) to etre'e roa) 9heel%( The %hoc. a%orerapplie% )a'pin+ re%i%tance force re%*ltin+ in a%orption of 8iration ener+y( The )a'pin+force can e f*nction of )i%place'ent" 8elocity or fre<*ency an) 'ay e linear or nonlinear9ith re%pect to the%e para'eter%( The %hoc. a%orer *%e) in APC M113 i% of 8i%co*% type(Thi% type of %hoc. a%orer i% the a%ic type *%e) in %*%pen%ion %y%te' of trac.e) 8ehicle%an) a*to'oile%( The i)eal 8i%co*% )a'per i% %*ch one in 9hich the )a'pin+ force i%

proportional to the fir%t po9er of 8elocity linear )a'pin+ ?4@( In APC M113 the )a'per%are connecte) to the fir%t" %econ) an) la%t roa) 9heel% in or)er to pro8i)e an effecti8e)a'pin+ 'o'ent(

The actin+ 'o'ent% on 8ehicle h*ll 9hen it i% %*=ecte) to an+*lar o%cillation " are

in)icate) in the follo9in+ i+( 1(



C l i i

4 /13


c(+ M sp

Md

"ig# $ Acting %o%ents on !ehicle hull in da%&ed !ibration

The e<*ation of 'otion of h*ll in thi% ca%e 9ill e a% follo9%:

J

y

M sp

M d 1

J y: 'a%% 'o'ent of inertia of 8ehicle ao*t it% lateral ae%

M sp : 'o'ent of %prin+% force%

M d : 'o'ent of )a'pin+ force%

M sp

k

2 F

i l i

1

" F i C

i f

i

" f i

l i

2

Fi: force of the ith

%prin+ fi : )eflection of the i

th%prin+

C i: %tiffne%% of %*%pen%ion %y%te' at the ith

roa) 9heel

l i: )i%tance of the ith

roa) 9heel fro' 8ehicle center of +ra8ity

. : n*'er of roa) 9heel% on one %i)e of 8ehicle for M113 .Ban) hence:

M sp

k

2 2

1

3

k d

M d 2 M

d i1

4

M di : 'o'ent of )a'pin+ force of the ith )a'per K d : n*'er of )a'per% on one %i)e of 8ehicle for M113 . ) B 3



/13

Paper: ASAT-13-HC-04 M

di Ri

l i

" Ri V

i

" V i l

i

Ri : )a'pin+ force of the ith

)a'per



l

2

2

2

i

: coefficient of %hoc. a%orer

V i : 8ertical 8elocity of )a'per 'o8ale part

Hence"

Md

k d

2 2

1

6

S*%tit*tin+ for M%p an) M) in e<*ation 1" 9e +et:

k kd

J 2C l2 2 l

2 y i i i

1 1

Intro)*cin+:

k d

l

i

1 n

J y

)a'pin+ con%tant !

k

2C i

l i

1

J y

%<*are of nat*ral fre<*ency #

Then the e<*ation of 'otion 9ill e:

2n 2 0 10

It i% a ho'o+eno*% %econ) or)er linear )ifferential e<*ation in 9hich it% +eneral %ol*tion i%:

Be

nt

cos( d t

) 11

9here:

2 2d

n fre<*ency of )a'pe) o%cillation

T 2d

perio) of )a'pe) o%cillationd

The co'plete %ol*tion i% otaine) y )eter'inin+ the con%tant% D an) fro' the

initial con)ition%" %o that:



d

o

cos o

e nt

cos( t o ) 12

o: initial an+*lar )i%place'ent of 8ehicle h*ll



i i

i

o

y

n tan 1 d

The +raph of co'plete %ol*tion i% interprete) on the follo9in+ fi+*re:

t

t1 Td

t2 = t1 + Td

"ig# ' (es&onse of !ehicle hull of free da%&ed !ibration

The 'ean 8al*e of %hoc. a%orer coefficient i% )eter'ine) fro' the re<*ire) rate of

a'plit*)e of )a'pin+ repre%ente) y the ratio of a'plit*)e% of t9o %*cce%%i8e

cycle%

1 ( Dy )i8i)in+ the re%pon%e at t9o )ifferent perio)% t1" t2" the follo9in+relation

2

of )a'pin+ con%tant i% otaine):

n ln

4 2 ln 213

Dy e<*aliin+ the ao8e e<*ation y e<*ation " the 'ean 8al*e of %hoc.

a%orer coefficient i% fo*n):

k

J C l2

1(41ln

1 14

kd

l2

4 2 ln 2

1

In trac.e) 8ehicle% an) a*to'oile%" the )a'per coefficient i% not con%tant 9hen the roa)9heel 'o8e% *p9ar)% to9ar)% the h*ll an) )*rin+ 9heel 'otion )o9n9ar)% a9ay fro' h*ll(The coefficient i% %'aller 9hen the 9heel 'o8e% *p9ar)% )a'per co'pre%%ion than 9hen9heel 'o8e% )o9n9ar)% )a'per reo*n)( Therefore the )a'per ha% t9o coefficient%:



1 for co'pre%%ion an) 2 for reo*n)" 9here 1 E 2 %o"



2

kd

l ikd 1

1 l i

kd 2

l i2

2 2

n 1 1 1

1 J

y J

y

k d1 : n*'er of %hoc. a%orer% %*=ecte) to co'pre%%ion front a%orer%

k d2 : n*'er of %hoc. a%orer% %*=ecte) to reo*n) rear a%orer%

The ratio of coefficient% 1 an) 2 are interrelate) a%

0(4 an) 0( a% 'entione) in ?@" hence:

1 r " the ratio r ha% a ran+e

et9een

2

2

kd 1

nJ y

kd 216

r l

2

l

2

i i1 1

,no9in+ 2 " 1 i% calc*late) a% 1 r

2

or trac.e) 8ehicle% the rate of )a'pin+ i% con%i)ere) to e in the ran+e et9een 12 an) 1

?@( or M113" the follo9in+ para'eter% are con%i)ere) ?6@:

Fy B 24 .G('(%2

" . )1 B 2 " . )2 B 1 " Ci B 12 .G/'

So y *%in+ e<*ation 14" the 'ean 8al*e of )a'pin+ coefficient " i% fo*n) to e in the

ran+e et9een 1( an) 16( .G(%/'(

or an a8era+e 8al*e of r=0!" the )a'pin+ coefficient in co'pre%%ion 1 B 11( .G(%/' an)

in reo*n) 2 B 23 .G(%/'

)*&eri%ental work The %hoc. a%orer of APC M113 i% te%te) on a %tan)ar) te%t ri+ MTS!0 )a'per te%t

%y%te'( The MTS!0 )a'per te%t %y%te' i% *%e) to 'ea%*re the perfor'ancecharacteri%tic% of %hoc. a%orer% y otainin+ the relation et9een the )e8elope)force in the %hoc. a%orer 9ith the pi%ton )i%place'ent an) 8elocity at )ifferenta'plit*)e% an) )ifferent fre<*encie%(

The loa)in+ *nit i% the 'ain part of the MTS!0( It con%i%t% of loa) fra'e" cro%%hea) lift

an) loc." force tran%)*cer" act*ator" three %ta+e %er8o 8al8e" hy)ra*lic 'anifol)" an)

acc*'*lator% a% %ho9n in i+( 3#

The te%t% perfor'e) 9ith the hy)ra*lic te%t ri+ 9ere con)*cte) y ecitin+ the %hoc.

a%orer y a %in*%oi)al inp*t fre<*encie% e<*al to 0( an) 0( H 9ith an a'plit*)e e<*al

to 0 ''( ;ata repre%entin+ force" )i%place'ent" te'perat*re an) 8elocity are collecte)

fro' %e8eral in%talle) %en%or% on the te%t ri+( Thi% infor'ation i% fe) into in%tr*'entation

%oft9are to +enerate +raph% that re8eal )a'per perfor'ance( The force of the %hoc. a%oreran) the 8elocity of the pi%ton 8er%*% ti'e 9ere otaine) an) recor)e)( The )a'pin+

coefficient of the te%te) %hoc. a%orer i% otaine) fro' the relation%hip et9een the



applie) force an) the 8elocity of the %hoc. a%orer pi%ton(



Te%te) %hoc. a %orer

orce tran%)*cer

Control panel

Act*ator 9ith ;T

"ig# + ,hotogra&hy of da%&er test syste%

The rotary 'otion of the )ri8e 'otor of the te%t ri+ i% tran%late) into linear 'otion of

the te%te) %hoc. a%orer( 5ith each co'pre%%ion/reo*n) cycle" the )a'per %haft i%

%tro.e) thro*+h a pre%et )i%place'ent ran+e( The inear ariale )ifferential Tran%)*cer

;T follo9% thi% 'o8e'ent an) yiel)% a ;C %i+nal that relate% to %pee)( In%i'ple linear 'o)elin+" the 8elocity rea)in+% are critical eca*%e the )a'pin+ force% that

are pro)*ce) are )irectly proportional to the )a'per %haft %pee)( i+( 4 %ho9% the 'ain

ele'ent% of %hoc. a%orer of APC M113(

"ig# - Tested shock absorber of A,C .$$+



0 0" 1 1" 2 2" 3 3" 40 0" 1 1" 2 2" 3 3" 4

0 0,5 1 1,5 2 2,5 3

0 0, 5 1 1,5 2 2,5 3

3 o r c e ? . G @

F o r c e [ k N ]

V e l o c i t y

[ m / s ]

I e l o c i t y ? ' / % @

i+( "i+( 6 repre%ent the 'ea%*re) force an) 8elocity 8er%*% the ti'e at fre<*encie% 0(

an)

0( H re%pecti8ely 9ith a'plit*)e 0 ''( ro' the%e fi+*re% it i% clear that yincrea%in+

the fre<*ency of ecitation> the applie) force increa%e% at the co'pre%%ion an)

reo*n) %tro.e%( Thi% increa%e in the force i% )*e to increa%e of the ela%tic ener+y

%tore) in the a%orer(

Dy increa%in+ the ecitation fre<*ency" the pi%ton 8elocity of a%orer i% al%o increa%e% at

the co'pre%%ion an) reo*n) %tro.e% an) hence the area of the cycle increa%e% an) the

)a'pin+ force otaine) at 'ai'*' relati8e 8elocity )ecrea%e% a% %o9n in i+( ( The rate%

of increa%e of the applie) force an) the a%orer 8elocity )eter'ine the a'o*nt of

linearity of the )a'pin+ coefficient of the te%te) %hoc. a%orer(

The ratio of )a'pin+ coefficient in co'pre%%ion an) reo*n) for t9o fre<*encie% can e

o%er8e) for' the fi+*re% to e aro*n) 0(6( Thi% 8al*e i% correlate) 9ith ratio r 'entione)

in the theoretical in8e%ti+ation(

4 0"2

0"1

20"1

0"0

0

0

-2 -0"0

-0"1

-4-0"1

-6Ti'e ?%@

-0"2

Ti'e ?%@

"ig# / Variation of force and !elocity with ti%e at 0#/ H1 and /0 %% a%&litude

6 0,25

0,24

0,15

20,1

00,05

0

-2-0,05

-4 -0,1

-6

-8

Time [s]

-0,15

-0,2

-0,25

Time [s]

"ig# 2 Variation of force and !elocity with ti%e at 0#3 H1 and /0 %% a%&litude

ro' the pre8io*% re%*lt% of 8ariation of force an) 8elocity 9ith ti'e" the 8ariation of force

9ith 8elocity 9a% con)*cte)( i+( re8eal% the 8ariation of the applie) force on the %hoc.

a%orer 9ith ti'e at fre<*encie% e<*al to 0( an) 0( H an) 9ith a'plit*)e e<*al to 0 ''(



F o

r c e

[ k N ]

F o r c e

[ k N ]

3

0" H:

2

6

0" H

4

2

0

-0,2 -0,15 -0,1 -0,05 0 0,05 0,1 0,15 0,2

-1

-2

0

-0,25 -0,2 -0,15 -0,1 -0,05 0 0,05 0,1 0,15 0,2 0,25

-2

-3

-4 -6

-5

Velocity [m/s]

-8

Velocity [m/s]

"ig# 3 Shock absorber characteristics at 0#/4 0#3 H1 and /0 %% a%&litude

ro' the )ata 'ea%*re) for the force an) 8elocity" the )a'pin+ coefficient of the %hoc.

a%orer can e otaine) y )i8i)in+ the 8al*e% of the 'ea%*re) force for co'pre%%ion an)

reo*n) y the corre%pon)in+ 8al*e% of 8elocity( Tale 1 repre%ent% the 8al*e of the

)a'pin+ coefficient of the %hoc. a%orer of APC M113 in co'pre%%ion an) reo*n)

%tro.e at ecitation fre<*encie% 0( an) 0( H an) at ecitation a'plit*)e 0 ''(

Table $ 5a%&ing coefficient obtained by hydraulic test rig

re<*ency H

;a'pin+ coefficient .G(%/'

Jeo*n) 2

Co'pre%%ion 1 A8era+e 8al*e

0( 1#(! 11(# 1(#

0(C 20(# 13(6 1C(2

Si%ulation In!estigationIn thi% part" the %i'*lation of the )yna'ic eha8ior of %hoc. a%orer of APC M113 i%acco'pli%he) thro*+h A*to'oti8e ;yna'ic Analy%i% of Mechanical Sy%te'

A;AMS

pro+ra'(

i+( ! %ho9% the %tep% of 'o)elin+ an) %i'*lation of a 'echanical %y%te' ( ;*rin+ trac.e)

8ehicle 'otion" it pa%%e% y roa) *ne8enne%% 9hich act% on the h*ll thro*+h the

trac.% repre%entin+ an eternal ecitation ca*%in+ the h*ll to *n)er+o force) 8iration%( A%a re%*lt of thi% e8ent" the %hoc. a%orer i% %*=ecte) to an ecitation force( Characteri%tic%of %*ch ecitation )epen) on the %hape of *ne8enne%% an) the 8ehicle 8elocity( Thi%ecitation repre%entin+ the ca%e of force) )a'pe) 8iration of 8ehicle h*ll(



"ig# 6 Ste&s of %odeling and si%ulation of %echanical syste%s

The roa) profile i% *lti'ately chan+e) an) it i% i'po%%ile to %i'*late eactly thi% profile(There ei%t %e8eral 'o)el% for the roa) profile( ne of the 'o%t 9i)ely applie) roa)'o)el% for trac.e) 8ehicle%" i% the 'o)el in 9hich the roa) *ne8enne%% i% con%i)ere)to e of %in*%oi)al %hape of len+th a B ! ' an) hei+ht h B 0(1 0(2 '(

" B 0"0 '

a = 6 m

"ig# 7 characteristics of a ty&ical road

i+( # %ho9% a typical type of roa) 9ay 9ith a'plit*)e 0 '' an) len+th 6 '( The

a'plit*)e of ecitation i% repre%ente) y the hei+ht of the roa) " 9hile the fre<*ency of

ecitation i% )epen)in+ on the %hape of the roa) an) 8ehicle 8elocity # %o that it can ecalc*late) a% follo9%:

2#1e

aor a re+*lar 8ehicle 8elocity of 12 .'/hr an) for the +i8en roa)" the ecitation fre<*ency

i%

fo*n) to e 0( H( Hence" the %hoc. a%orer i% ecite) y t9o fre<*encie% 0(" 0( H

9ith a'plit*)e 0 ''( In thi% 'o)el" the %hoc. a%orer i% ecite) a% it 9a% te%te) in the

eperi'ental in8e%ti+ation a% %ho9n in i+( 10(



"ig# $0 Si%ulated %odel of shock absorber

The a'plit*)e an) fre<*ency of ecitation i% repre%ente) y an i'po%e)

)i%place'ent epre%%e) y the follo9in+ f*nction:

y yo

cos t

yo: a'plit*)e of ecitation)i%place'ent

: ecitation fre<*ency

1!

"ig# $$ I%&osed dis&lace%ent on the si%ulated shock absorber



F o r c e

[ k N ]

F o r c e

[ k N ]

v e l o c i t y

[ m / s ]

V e l o c i t y

[ m / s ]

The a'plit*)e of ecitation yo i% epre%%e) y the roa) hei+ht 0 '' 9hile the fre<*encyof ecitation ha% t9o 8al*e% corre%pon)in+ to 0( an) 0( H a% 'entione) in the

eperi'ental part %*ch that ha% 3(14" 4(4 %-1

re%pecti8ely(

The re%*lt% otaine) fro' the 'o)el are repre%ente) in i+( 12"i+( 13( i+( 12 ill*%trate%the 8ariation of applie) force an) 8elocity 9ith ti'e at 0( H an) 0 '' a'plit*)e 9hile

i+(13 )e'on%trate% the%e 8ariation% at 0( H an) 0 '' a'plit*)e( Dy co'parin+ the%ere%*lt%

9ith tho%e otaine) fro' eperi'ental in8e%ti+ation" it can e %een that 8ariation of applie)

force an) 8elocity 9ith ti'e ha% +oo) a+ree'ent% 9ith the re%*lt% otaine) eperi'entally

for oth fre<*encie%( ariation of the applie) force 9ith 8elocity i% otaine) y )i8i)in+ the

applie) force y the 8elocity at each ti'e inter8al( Thi% 8ariation repre%ent% the )a'pin+

coefficient of the %hoc. a%orer in oth co'pre%%ion an) reo*n)( A% 'entione) in the

theoretical part" the )a'pin+ coefficient of %hoc. a%orer% *%e) in tac.e) 8ehicle% an)

a*to'oile% i% %'aller in co'pre%%ion than in reo*n)( Thi% )ifference can e %een fro' thefi+*re%( The po%iti8e 8al*e% of the force an) 8elocity in i+( 12 an) i+( 13 %ho9% the

action of %hoc. a%orer% in co'pre%%ion 9hile the ne+ati8e 8al*e% %ho9 it% action in

reo*n)( ro' oth action%" the 8al*e% of )a'pin+ coefficient in oth co'pre%%ion an)

reo*n) are fo*n) an) co'pare) 9ith the 8al*e% otaine) fro' eperi'ental re%*lt%( The

ratio of the )a'pin+ coefficient% of %hoc. a%orer in co'pre%%ion an) reo*n) +i8e%

the pre)icte) 8al*e 'entione) in the theoretical part 9hich i% 0(6( Thi% 'ean% that the

)a'pin+ coefficient of the hy)ra*lic %hoc. a%orer can e pre)icte) 9ith hi+h acc*racy

*%in+ the relation% 'entione) efore(

3,00 0,20

2,00 0,15

1,00 0,10

0,00

0,00 0,50 1,00 1,50 2,00 2,50 3,00 3,50 4,00

-1,00

-2,00

0,05

0,00

0,00 0,50 1,00 1,50 2,00 2,50 3,00 3,50 4,00

-0,05

-3,00 -0,10

-4,00 -0,15

-5,00

Time [s]

-0,20

Time [s]

"ig# $' Variation of force and !elocity with ti%e at 0#/ H1 and /0 %% a%&litude

6,000,25

4,00

2,00

0,20

0,15

0,10

0,00

0,00 0,50 1,00 1,50 2,00 2,50 3,00

-2,00

-4,00

-6,00

0,05

0,00

-0,05

-0,10

-0,15

-0,20

-8,00

Time [s]

-0,25

Time [s]

"ig# $+ Variation of force and !elocity with ti%e at 0#3 H1 and /0 %% a%&litude



ConclusionThe theoretical in8e%ti+ation of the )a'pin+ coefficient of %hoc. a%orer *%e) intrac.e)8ehicle% pro8i)e% a +oo) approach to pre)ict it% 8al*e in oth co'pre%%ion an)

reo*n)%tro.e%(

The )a'pin+ coefficient in oth co'pre%%ion an) reo*n) %tro.e% can e e%ti'ate) *%in+ a

'ea%*re) force an) 8elocity otaine) fro' the hy)ra*lic te%t ri+ of 'o)el MTS !0

The a8era+e 8al*e of )a'pin+ coefficient of hy)ra*lic %hoc. a%orer% of APC M113 at lo9

ecitation fre<*encie% i% fo*n) to e 12( .G(%/' in co'pre%%ion %tro.e an) 20( .G(%/'

in

reo*n) %tro.e(

A n*'erical 'o)el *%in+ A;AMS ha% een )e8elope) in or)er to %i'*late the )yna'ic

eha8ior of the %hoc. a%orer an) to )e%crie an) e8al*ate it% )a'pin+ coefficientin co'pre%%ion an) reo*n) cycle%(

$8al*ation of %o'e para'eter% li.e a'plit*)e an) fre<*ency of ecitation y *%in+the %i'*late) 'o)el i% )i%c*%%e)( The %t*)y %ho9% that the%e para'eter% e%i)e the )a'pin+coefficient are the .ey factor% that affect the perfor'ance characteri%tic% of the %hoc.a%orer(

The )e8elope) n*'erical 'o)el can e *%e) a% a *nit of %*%pen%ion %y%te' of

trac.e) 8ehicle% )*rin+ 'o)elin+ of )yna'ic eha8ior of %*ch 8ehicle%(

(eferences?1@ 5( Schiehlen" D(H*" KSpectral Si'*lation an) Shoc. A%orerI)entificationK"

International Fo*rnal of Gon-inear Mechanic% 3!" 2003" pp( 161-11?2@ J( Da%%o" K$peri'ental Characteriation of ;a'pin+ orce in Shoc. A%orer%

9ith

Con%tant elocity $citationK" ehicle Sy%te' ;yna'ic% 30" 1##!" pp( 431-

442(?3@ S( Cafferty" ,( 5or)en" ( To'lin%on" KCharacteriation of A*to'oti8e

Shoc. A%orer% L%in+ Jan)o' $citationK" Proc( In%t( Mech( $n+( Part ; 20#" 1##" pp(23#-24!

?4@ S( A)hi.ari an) F( 5oo)ho*%e" KI)entification of ;a'pin+: Part 1" i%co*%

;a'pin+K" Fo*rnal of So*n) an) iration" 2001" 2431" pp( 43-61

?@ Printe) lect*re% of tan.% )epart'ent" KTheory of S*%pen%ionK" Chair of tan.%"

Military

Technical Colle+e" Cairo" $+ypt" 1#4(

?6@ A(M Sale'" T( Salah*)ien" K$8al*ation of Characteri%tic% of Trac.e) ehicle%

Tor%ion Dar%K" 13th

international conference on Applie) Mechanic% an) Mechanicalen+ineerin+" Military Technical Colle+e" Cairo" $+ypt" 2-2# May 200!

?@ Stefaan 5(J( ;*y'" KSi'*lation Tool%" Mo)elin+ an) I)entification" foran A*to'oti8e Shoc. A%orer in the Contet of ehicle ;yna'ic%K" ehicle Sy%te'

;yna'ic%" 33" 2000" pp( 261-2!

Identification of Characteristics of Hydraulic Shock Absorber

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