DYNAMIC ANALYSIS AND CONTROL OF ACTIVE ENGINE MOUNT SYSTEM

Transcription

1 To be submied o Jounal of Auomobile Engineeing DYNAMIC ANALYSIS AND CONTROL OF ACTIVE ENGINE MOUNT SYSTEM by Yong-Wook Lee and Chong-Won Lee Cene fo Noise and Vibaion Conol (NOVIC) Depamen of Mechanical Engineeing oea Advanced Insiue of Science and Technology Science Town, Taejon , oea July 7, 00 The numbe of figues : 15 The numbe of ables:

2 Posal Addess Pofesso Chong-Won Lee Addess : Cene fo Noise and Vibaion Conol (NOVIC) Depamen of Mechanical Engineeing oea Advanced Insiue of Science and Technology Science Town, Taejon Souh oea Phone : FAX : cwlee@novic.kais.ac.k Yong-Wook Lee Addess : NVH Team, Reseach & Developmen Division fo Hyundai Moo Company 77-1, Jangduk-Dong, Whasung-Si, Gyunggi-Do Souh oea Phone : FAX : ywlee@novic.kais.ac.k o newind@hyundai-moo.com

3 Absac Dynamic chaaceisics of a pooype AEM, designed based on a hydaulic engine moun, has been invesigaed and an adapive conolle fo he AEM has been designed. An equivalen mass-sping-dampe AEM model is poposed, and he ansfe funcion ha descibes dynamic chaaceisics of he AEM is deduced fom mahemaical analysis on he model. The damping coefficien of he model is deived by consideing nonlinea flow effec in he ineia ack. Expeimens confimed ha he model pecisely descibes dynamic chaaceisics of he AEM. An adapive conolle using he fileed-x LMS algoihm is designed o cancel he foce ansmied hough he AEM. The sabiliy of he LMS algoihm is guaaneed by using he seconday pah ansfe funcion deived based on he dynamic model of he AEM. The pefomance es in he laboaoy shows ha he AEM sysem is capable of significanly educing he foce ansmied hough he AEM. ey Wods acive engine moun (AEM), modeling, fileed-x LMS algoihm, sabiliy

4 NOMENCLATURE A A A d e A p A B C c D Dˆ D h F F 1 F F e F T f G g 0 I I, c I 0 i b c d i p y ε L L e l m m e m N P P 1 i c : ansfe funcion fo passive chaaceisics of acive engine moun : aea of decouple : equivalen coss-secional aea of uppe chambe : aea of he magneic pole : coss-secional aea of ineia ack : ansfe funcion fo acive chaaceisics of acive engine moun : ansfe funcion fo eleco-magneic acuao: cuen vs. displacemen : damping coefficien fo he flow in ineia ack : seconday pah ansfe funcion : esimaed seconday pah ansfe funcion : hydaulic diamee of ineia ack : foce fom eleco-magneic acuao : ansmied foce due o engine vibaion : ansmied foce due o acuao vibaion : engine exciaion foce : oal foce ansmied o chassis : ficion faco fo flow in ineia ack : ansfe funcion fo eleco-magneic acuao: volage vs. displacemen : nominal gap of eleco-magneic acuao : elecic cuen in he coil of eleco-magneic acuao : command cuen inpu o eleco-magneic acuao : bias elecic cuen in he coil of eleco-magneic acuao : conol cuen fo eleco-magneic acuao : bulge siffness of main ubbe : gain of cuen amplifie : deivaive gain of he feedback conolle : cuen siffness of eleco-magneic acuao : popoional gain of he feedback conolle : main siffness of main ubbe : posiion siffness of eleco-magneic acuao : compliance of lowe chambe : mino head loss a inle and oule of ineia ack : lengh of ineia ack : coodinae along ineia ack : mass of fluid in ineia ack : mass of engine : mass of he unne in eleco-magneic acuao : numbe of coil uns : pessue in fluid : pessue in uppe chambe

5 P R R u V e c W : pessue in lowe chambe : efeence signal fo fileed-x LMS algoihm : Reynolds numbe : flow velociy in ineia ack : conol signal inpu o cuen amplifie : coefficien veco fo adapive conolle k X, x : displacemen of engine d x d X, : displacemen of acuao x e : equivalen defomaion of bulge siffness X, x : displacemen of fluid in ineia ack Y, y : posiion of he unne in eleco-magneic acuao Z : veco of fileed efeence signal µ : convegence coefficien of fileed-x LMS algoihm µ 0 : absolue pemeabiliy ρ : densiy of fluid : low-pass fileing ime consan of cuen amplifie τ c

6 1. INTRODUCTION Auomobiles ae geing moe impoan as being no only a anspoaion means bu also a pa of moden life. Especially, passenge cas ae consideed as a pa of space fo eveyday life so ha comfo is one of he mos impoan cieia in he make. As a esul, he noise, vibaion and hashness (NVH) chaaceisics ae seiously aken ino accoun in designing an auomobile. On he ohe hand, hee is a song equiemen on fuel-efficien vehicles: cusomes wan o educe he expendiue on hei cas, and govenmens wan o conol he ai polluion fom cas. To impove fuel efficiency, makes ae ying o impove engine pefomance and cu down he weigh of auomobiles, bu in geneal he weigh educion is hamful o he NVH chaaceisics [1,]. Hence, acive noise/vibaion conol echnologies ae exensively developed o esolve his poblem. Engines ae one of he mos impoan souces of noise and vibaion in auomobiles, so he isolaion of engine vibaion is ciical o he impovemen of NVH chaaceisics. Engine mouns have o mee wo conadicoy funcional equiemens: effecive vibaion isolaion and fim engine suppo [3]. The pimay way o cu off pahs of noise and vibaion fom he engine is o use sof mouns. Howeve, engine mouns mus also consain o conol engine excusions caused by ough oads, fiing in cylindes, wheel oque eacions, ec. To limi engine moions, engine mouns should be siff and heavily damped. These conflicing demands on engine mouns have pomped auomoive indusies o seach fo a new engine mouning mehod. Hydaulic engine mouns [4-6] have been pomising alenaives o convenional ubbe mouns due o hei capabiliy of ceaing fequency dependen damping, bu hey had limiaions due o hei pe-deemined dynamic chaaceisics. To impove

7 he chaaceisics of hydaulic mouns, a numbe of adapive engine mouns wee poposed [7,8] bu hey sill had he limiaion ha hey could only educe he vibaion o some exen bu no cancel i ou. Recenly, AEMs [9-15] appeaed, which wee equipped wih high-powe, high-speed acuaos o geneae seconday vibaion so ha i desucively inefees wih he pimay vibaion fom he engine. Howeve, mos of he pevious wok on he AEMs concenaed on conol schemes so hee is lile maeial ha hooughly analyzes dynamic chaaceisics of AEMs. In his pape, we pesen a dynamic model of a pooype AEM and he influence of he model on he sabiliy of adapive conol algoihm. The dynamic behavio of he AEM is analyzed by using an equivalen mass-sping-dampe model, whee he damping coefficien is deived by consideing nonlinea flow effec in he ineia ack. An adapive conolle is designed by using he fileed-x LMS algoihm [16-1] o cancel ou disubance foces fom engines. The dynamic model of he AEM was expeimenally veified, and he AEM showed good pefomance in canceling he foce ansmied o he base of he AEM.

8 . STRUCTURE DESIGN AND MODELING OF AEM Two condiions ae usually imposed in designing an AEM: he AEM should wok as a passive moun unde abnomal siuaions such as acuao, conolle and/o senso malfuncioning, and he powe consumpion of he AEM should be easonably low so ha he powe o opeae he AEM can be supplied in he auomobile [10]. To educe powe consumpion, he engine weigh should be suppoed by a passive sping elemen, and o guaanee he pefomance as a passive moun, anohe sping elemen should be inseed beween he engine and acuao so ha he sping can alleviae shocks due o he malfuncioning of AEM componens. Figue 1 illusaes hese design conceps, inoducing wo spings: one suppos he engine weigh and he ohe connecs he engine and he acuao. Figue shows he sucue and equivalen model of a hydaulic engine moun [5,6]. Hydaulic engine mouns ae inended o inoduce siffness and damping ha ae dependen o he vibaion ampliude and fequency so ha he engine mouns would have diffeen siffness and damping fo diffeen opeaing condiions. The hydaulic engine moun is compised of a main ubbe, wo fluid chambes, an ineia ack, and a decouple as shown in Fig. (a), and Fig. (b) is is equivalen model. The main ubbe beas engine load in wo diffeen ways: one is due o he veical deflecion of he engine and he ohe is due o he volumeic change in he uppe chambe, hence i is modeled via wo siffness elemens and b. The main siffness elemen,, models he eacion due o he veical deflecion so ha i suppos he saic as well as dynamic load, and he bulge siffness elemen,, models he eacion due o volumeic change in he uppe chambe so ha i suppos he dynamic load only. The engine vibaion foces he fluid in he uppe chambe o flow beween he uppe and lowe chambes hough he ineia ack, whee he flow b

9 velociy in he ack is much fase han ha in he wo chambes because of he small coss-secional aea of he ineia ack. Hence hee exis consideable ineia and damping which wee modeled as m and c. Remakable similaiies exis beween he concepual model of AEM in Fig. 1 and he equivalen mass-sping-dampe model of hydaulic engine mouns in Fig. (b). Boh have wo sping elemens, and one sping in each model suppos he engine weigh. Moeove, he second sping in Fig. (b) is no diecly conneced o he chassis bu o he decouple, jus as he second sping in Fig. 1 is conneced o he acuao. These facs songly imply ha he sucue in Fig. 1 can be ealized by insalling an acuao in he lowe chambe of he sucue in Fig. and connecing i o he decouple as shown in Fig. 3. Figue 3(a) shows he sucue of he AEM, which is an amalgamaion of he basic sucue of he hydaulic engine moun and an acuao sysem. Bu, due o he acuao, he ole of he decouple is changed o a pison so ha i ansmis he foce fom he acuao o he engine and chassis hough he uppe chambe. The ole of he ineia ack is also changed: in hydaulic engine mouns, he ineia ack geneaes fequency dependen siffness and damping [6], bu in he acive engine moun, i jus elieves he saic pessue in he uppe chambe. Accodingly, he model fo descibing he dynamic behavio in he uppe chambe is changed fom he link wih cleaance as in Fig. (b) o he pison-cylinde sucue as in Fig. 3(b). In Fig. 3(b), A e is he equivalen coss-secional aea of he uppe chambe (see Appendix A), Ad is he decouple aea and A is he coss-secional aea of he ineia ack. The compliance of he lowe chambe is modeled as ε. The compliance of he lowe chambe is usually much smalle han o b so i is fequenly negleced in many hydaulic engine moun models, bu we included i fo bee accuacy. The

10 equivalen model of he AEM in Fig. 3(b) shows ha hee ae wo pahs fo foce ansmission in he AEM: one is hough he main siffness elemen and he ohe is hough he bulge siffness elemen b and he acuao. The foce ansmied hough each pah is designaed as and, especively. F 1 Figue 4 shows fee body diagam of he engine-aem sysem of which equaion of moion is given as F mex( && ) = F e () FT ( ) (1) whee m is mass of he engine, x ( ) is displacemen of he engine, F e () is e engine exciaion foce coming fom gas pessue in cylindes and ecipocaing pas of he engine [], and F T () is he foce ansmied o he chassis ha is he sum of F ( ) and F ( ), i.e. 1 F T () = F 1 () F ( ). () Since he main siffness ansmis he engine vibaion o he chassis, as F 1( ) is given F1 ( ) = x( ). (3) The acuao vibaion affecs he pessue P( ) in he uppe chambe ha exes foce on he chassis as F ( ) = P( ). (4) A e Since he bulge siffness elemen defoms in popoion o he pessue in he uppe chambe, we have A e P() = { ( ) x( (5) b x e )}

11 whee x e () is he defomaion of he bulge siffness elemen. The pessue also foces he fluid in he ineia ack o flow, which is expessed as A P( ) = mx & ( ) cx& ( ) ε x ( ) (6) whee () x is he displacemen of he fluid in he ineia ack. Hee, he damping coefficien c is a vaiable depending on he flow velociy & (), and deailed analysis on he equivalen damping coefficien and mass will be given in he nex secion. The fluid can be consideed as incompessible, hus he coninuiy equaion becomes x A x ( ) A x ( ) A x ( ). (7) e e = d d Fom Eqs. () o (7) expessed in Laplace domain, we can expess he ansmied foce in ems of he engine and acuao displacemens as F ( s) = A( s) X ( s) B( s) X ( s) (8) T d whee A( s) = A A B( s) = Ae Ae b ( ms cs ) e ( ms cs ε ) A b e Ad b ( ms cs ) ( ms cs ε ) A b ε (8-a) ε (8-b) and F T (s), X (s) and X d (s) ae he Laplace ansfoms of F T (), x() and x d (), especively. By subsiuing X (s) in Eq. (8) ino Eq. (1) in Laplace domain we ge he mahemaical model ha descibes he ansmied foce in ems of engine exciaion foce and acuao moion as F T A( s) m s B( s) ( s) = F ( s) e X ( s) e d. (9) m s A( s) m s A( s) e e

12 3. MODELING OF FLOW IN THE INERTIA TRAC Figue 5 shows he flow beween he uppe and lowe chambes hough he ineia ack. The fluid in he ineia ack is foced o flow beween he uppe and lowe chambes due o he pessue diffeence in hose chambes. The flow is expessed by he momenum equaion as [3, 4] P u f ρ = ρ u u (10) l D h whee P is he pessue in he ineia ack, l is he coodinae along he ineia ack, u is he aveage flow speed a a coss-secion in he ineia ack, f is he ficion faco, and ρ is he densiy of he fluid. Povided ha u = u() and P = P( l,), Eq. (10) can be ewien as L L P P L u f e ρ 1 = ρ & u u (11) D h whee and P ae he pessues in uppe and lowe chambes, especively, and P1 L is he lengh of he ineia ack, and L e is he equivalen lengh fo mino head loss a inle and oule. Hee, he ficion faco numbe given as [4] f is he funcion of Reynolds 64 Re < 300 Re 1 5 f = { 96( R 300) } 300 < < 400 e Re (1) Re R > e Re Fo x = X sin ω, he second em in he igh hand side of Eq. (11) can be appoximaed by using he descibing funcion as

13 ( ) ( ) bx X b X x x u u ω ω = ω ω ω ω ω = = cos cos cos cos & & (13) whee ( ). 3 8 cos cos 0 π = ω ω π ω = ω π d b Subsiuing Eq. (13) ino Eq. (11) we obain h e x X D L L f x L P & & & ω π ρ = ρ 3 8. (14) Finally, muliplying o Eq. (14) by A, we ge h e cx mx x X A D L L f x A L P A & && & && ω ρ π = ρ 3 4 (15) whee m ρa L = (15-a) ω ρ π = h e X A D L L f c 3 4. (15-b) These ae he equivalen mass and damping coefficien fo he flow in he ineia ack descibed in Eq. (6).

14 4. DESIGN OF ELECTRO-MAGNETIC ACTUATOR The engine exciaion foce is a esulan of gas pessue in cylindes and ineia foces geneaed in moving pas such as pisons o cankshafs. This mechanism was fully analyzed in [4], bu o calculae he engine exciaion foce, we have o know deailed daa on he engine: mass, oaional ineias and dimensions of moving pas, and gas pessue in cylindes, ec. Howeve, wha is needed in designing an AEM is he ouline, o he maximum values, of he equied foce, soke, and dynamic ange, bu he exac descipion of hem. Hence, if we can esimae he maximum foce and soke by simple measuemens, hen we don have o go hough deailed analysis on he engine. The foce ansmied o he chassis can be simply esimaed, wihou deailed daa on engine, by muliplying he ampliude of he engine vibaion wih he siffness of he engine moun. The ampliude of he engine vibaion is lages in idling sae, and i ges smalle as he oaing speed ges highe. Hence, he ansmied foce is lages in idling sae. The ampliude of he engine vibaion in idling sae was measued o be 0.mm in he es vehicle, and he foce ansmied o he chassis was calculaed o be abou 70N. The acuao foce affecs he pessue in he uppe chambe and, in un, he pessuized fluid exes foce o he chassis and engine as descibed in Eq. (4). This pocess amplifies he acuao foce by he aio of Ae Ad, which is abou 1.5 fo ypical commecial hydaulic engine mouns. Hence he minimum foce equiemen on he acuao o conol he ansmied foce of 70N is abou 50N. The opeaing fequency ange of AEM was seleced as 0-50Hz which coesponds o he fiing fequency fo engine speed of pm fo 4-cylinde 4- cycle in-line engines of which he ypical idling speed is abou 750pm.

15 The acuao soke equied o isolae engine vibaion can be deived fom Eq. (9) by leing he ansmied foce F T equal o zeo. In his fomulaion, we have o know he engine exciaion foce, which is difficul o ge boh analyically and expeimenally: i is had o diecly measue he exciaion foce acing on he mass cene of he engine, and i is a buden o ge ineias and dimensions of he moving pas necessay o calculae he exciaion foce. Howeve, if we deive he acuao soke fom Eq. (8), we can use engine displacemen which can be easily measued. By leing he ansmied foce F T in Eq. (8) equal o zeo, we ge A( s ) A A X ( s ) X( s ) e d = = X( s ) B( s ) 1. (16) b A d Ae Ad ( ms cs ε ) Figue 6 shows ha he acuao soke should be 0.7mm o lage ove he fequency ange of 0-50Hz in ode o cancel he engine vibaion of 0.mm in ampliude. The ypical size of hydaulic engine mouns is abou 100mm in diamee and 80mm in heigh, so he size of he acuao should be smalle han his. In sho, he acuao should be able o poduce foce lage han 50N and soke lage han 0.7mm ove 0-50Hz, and i should be smalle han 100mm in diamee and 80mm in heigh. Based on hese specificaions, we compaed he chaaceisics of sacked piezoacuaos, hydaulic acuaos, eleco-dynamic acuaos and eleco-magneic acuaos. Among he fou ypes of acuaos, eleco-magneic acuaos showed he bes chaaceisics: sacked piezo-acuaos have vey limied soke; hydaulic acuaos ae usually lage and expensive; eleco-dynamic acuaos could no poduce sufficien foce wih easonable size. Figue 7(a) shows he schemaic of an eleco-magne, of which he magneic foce is given as

16 Hee, µ 0N I Ap F = (17) 4g 0 7 µ 0 is he absolue pemeabiliy ( 4 π 10 Wb A m), N is he numbe of coil uns, I is he cuen in he coil, A p is he aea of magneic pole face, and g 0 coesponds o he maximum soke which is pe-deemined fom he specificaions. Because he magnes can poduce aacive foce only, he elecomagneic acuao is composed of a pai of eleco-magnes o poduce bi-diecional moions as shown in Fig. 7(b). The ne foce acing on he unne is he diffeence beween he foces fom he wo eleco-magnes given as Ap ( I0 i) ( g y) Ap ( I0 i) ( g ) µ 0N µ 0N F = (18) y whee I 0 is he offse cuen, i is he conol cuen, and y is he displacemen of he unne fom is nominal posiion. We can lineaize Eq. (18) by using he Taylo seies expansion as F ( i, y) F( 0,0) F i ii y y F i y i= 0, y= 0 y i= 0, y= 0 (19) whee i and y ae he cuen and posiion siffnesses, especively, given as i N = µ 0 A I p 0 g0 and y N = µ 0 ApI0 g0 3. The equaion of moion fo he unne in Fig. 6(b) hen becomes my && = F= i y (0) i y o

17 i y y m i y = & & (1) In his equaion, he siffness em has negaive sign, implying ha he sysem is unsable. This insabiliy can be compensaed by applying he popoional-deivaive (PD) feedback conol as ( ) y y i d p & =. () This conol scheme modifies Eq. (1) as ( ) 0 = y y y m y p i d i & & &. (3) Hence, we can make he sysem sable by selecing pope and values. If we add command em in Eq. () such as p d ( ) c d p i y y i = & () hen Eq. (1) becomes ( ) c i y p i d i i y y y m = & & & (3) o we can ge he ansfe funcion as. ) ( ) ( ) ( ) ( y p i d i i c s s m s I s Y s C = = (4) We used a cuen amplifie ha dives elecic cuen accoding o conol signal in volage of which ansfe funcion is s S V S I c c c c = 1 τ ) ( ) ( (5) whee is he conol signal in volage, is he gain of he amplifie, and c V c c τ is he ime consan fo low pass fileing deemined by he gain of he amplifie and

18 inducance of he coil. The ansfe funcion of he eleco-magneic acuao is given as { ( ) }. 1 ) ( ) ( ) ( ) ( s s s m s V s Y s G c y p i d i i c c τ = = (6) The eleco-magneic acuao was designed o poduce 100N of foce and 1.0mm of soke ove he fequency ange of 0-60Hz. The paamees of he elcomagneic acuao ae lised in Table 1, and Fig. 8 shows ha he uppe limi of he acuao bandwidh is highe han 60Hz.

19 5. DESIGN OF ADATPIVE CONTROLLER The conol schemes fo acive vibaion isolaion can be classified ino wo caegoies: feedback and feed fowad conolles. Beween hem, he feed fowad conolles ae geneally acceped o be moe advanageous in acive vibaion conol. Howeve, he feed fowad conolles equie pecise modeling of dynamic chaaceisics of he sysems o be conolled, which may vay fom sysem o sysem and change accoding o he aging of he sysem. Adapive naue is inoduced o feed fowad conolles o esolve his poblem because i enables he feed fowad conolles o adjus hemselves accoding o such vaiaions. The fileed-x LMS algoihm [16] is widely adoped fo is simple sucue and good pefomance. The sysem model o be povided o he adapive conolle can be deived fom Eq. (9) and Eq. (6). Since he acuao displacemen Y in Eq. (6) is he same as X d in Eq. (9), we can subsiue Eq. (6) ino Eq. (9) o ge A( s) m s B( s) G( s) F ( s) F ( s) e T = V ( s) e c. (7) mes A( s) mes A( s) Fom his equaion, we can see ha he seconday pah ansfe funcion o be used in fileed-x LMS algoihm should be m s B( s) G( s) D( s) = e (8) mes A( s) Accodingly, we can obain he conolle updae fomula as W 1 = W ( n) Z (9) k k µ F T whee W k is he conolle weigh veco, µ is he sep size, F T (n) is sampled daa of he ansmied foce, and Z is he veco of he sampled efeence signal

20 fileed hough he ansfe funcion D(z), he discee-ime domain expession fo D(s). Figue 9 shows he block diagam of he AEM sysem using he fileed-x LMS algoihm, whee D ˆ ( z ) is he esimaed D(z) and Ẑ is he efeence signal veco fileed hough D ˆ ( z ). Noe ha he ansfe funcion D(s) in Eq. (8) becomes vey small a vey low fequencies. This implies ha he AEM is ineffecive in conolling low fequency disubances.

21 6. EXPERIMENTS Pio o invesigaing he vibaion isolaion pefomance of he AEM, we ied o veify he analyical model in Eq. (8) by expeimen. If Eq. (8) is veified, hen Eq. (9) is deived by a naual consequence. Equaion (8) has no coupling em beween he engine vibaion X ( s) and he acuao vibaion Xd ( s), we can ge he ansfe funcions As ( ) and B( s) sepaaely: As ( ) by exciing he fee op side of he AEM and measuing he foce a he fixed boom while he acuao unne is fixed, and B( s) by exciing he acuao and measuing he foce while he op and boom sides of he AEM ae fixed. Figue 10 depics he es seup, whee he AEM is insalled upside down in a commecial hydaulic shake. Duing he model veificaion ess, a poximiy pobe and a foce ansduce measued x( ) and F T ( ), especively, and x d ( ) is measued fom he unne posiion feedback sysem by a buil-in poximiy pobe. Figues 11 and 1 compae he expeimenal and analyical esuls of As ( ) and B( s), especively. The paamees in Eq. (8) wee measued fom he pooype AEM and lised in Table. Noe ha he analyical esuls based on Eqs. (8-a) and (8-b) agee well wih he expeimenal esuls, confiming ha he model in Eq. (8) accuaely descibes he dynamic behavio of he AEM. Figue 11 shows he ypical behavio of a hydaulic engine moun because he AEM was designed o funcion as a hydaulic engine moun when he acuao is ou of ode. In Fig. 1, he small dynamic siffness below 10Hz implies ha he saic pessue acing on he acuao is vey small. This allows he acuao o conol he dynamic loads only as inended in designing he sucue. The vibaion isolaion pefomance of he AEM incopoaed wih he fileed- X LMS algoihm is expeimenally invesigaed in he laboaoy. The algoihm is

22 pogammed on a TMS30C30 digial signal pocesso and implemened o he AEM. In he expeimen, he seconday pah ansfe funcion D(z) is esimaed as an FIR file, which is designaed as D ˆ ( z ) in Fig. 9. The adapive conolle W and he k seconday pah ansfe funcion D ˆ ( z ) have 150 aps each, and he sampling fequency is 4kHz which is consideed fas enough. The sep size µ in Eq. (9) is se o be Figue 13 shows he laboaoy es seup. The funcion geneao poduces hamonic signal which is fed o he excie o exe disubance foce on he AEM. Meanwhile, he squae wave signal, having he same fequency as he hamonic signal, is geneaed o simulae he achomee signal fom he engine. A mass block, insead of he engine, is aached on he op side of he AEM o imiae he eal engine-mouning sysem. The foce ansduce a he boom of he AEM measues he ansmied foce and feeds i o he DSP. An addiional foce ansduce is inseed on he opside of he mass block o monio he exciaion foce. The DSP compues he conol command accoding o he fileed-x LMS algoihm by using he achomee and foce signals. The PD conolle sabilizes he acuao and he cuen amplifie dives elecic cuen o he acuao o poduce conol foce. Figue 14 shows he ypical pefomance of he AEM sysem wih he exciaion of 5Hz which coesponds o he ypical exciaion fequency of he 4-cylinde 4-cycle in-line engine a idling sae. Noe ha he ansmied foce was almos compleely eliminaed. Figue 15 shows he effecive dynamic siffness of he AEM ove he fequency ange of 10 o 70Hz. Owing o he conol effo, he dynamic siffness was significanly educed ove he fequency ange of 15 o 60Hz. The sligh incease in he dynamic siffness beyond 60Hz is due o he limiaion of he acuao bandwidh, and he siffness incease below 15Hz is due o he low fequency chaaceisics of he seconday pah ansfe funcion commened a he end of secion 5.

23 7. CONCLUSIONS An equivalen mass-sping-dampe model was poposed o descibe he dynamic chaaceisics of he AEM. The mahemaical analysis on he equivalen model, accouning fo he nonlinea flow effec in damping, povided he ansfe funcion of he AEM ha agees well wih he expeimenal esuls. The equiemens on he acuao fo foce, soke, bandwidh, and size wee deduced fom engine vibaion chaaceisics as well as he dynamic model of he AEM, and he elecomagneic ype acuao was designed o fulfill he equiemens. The adapive conolle using he fileed-x LMS algoihm was employed o cancel ou he disubance foce due o he engine vibaion. The sabiliy of he LMS algoihm was guaaneed by deiving pope seconday pah ansfe funcion ha ake ino accoun he influence of he conol foce on he engine vibaion. The laboaoy expeimens confimed ha he AEM combined wih he adapive conolle is able o significanly educe he vibaion ansmission.

24 ACNOWLEDGEMENT The auhos ae gaeful fo he suppo fom Hyundai Moo Co., Ld., Hyundai Eleconics Indusies Co., Ld. and Pyonghwa Indusial Co., Ld. duing he poducion and esing of he AEM pooype.

25 REFERENCES 1. Fod, D.M. An analysis and applicaion of a decoupled engine moun sysem fo idle isolaion. SAE pape , Haa, H. and Tanaka, H. Expeimenal mehod o deive opimum engine moun sysem fo ilde shake. SAE pape , Choi, S.H. e al. Pefomance analysis of an engine moun feauing ER fluid and piezoacuaos. Inenaional Jounal of Moden Physics B, 1996, 10(3), Clak, M. Hydaulic engine moun isolaion. SAE pape , im, C.S. Dynamic Analysis of Hydaulic Engine Moun. MS Thesis of AIST, Seo,., e al. Opimum design mehod fo hydaulic engine moun. Tansacions of JSME, seies C, 1991, 57(534) (in Japanese) 7. Duclos, T. An exenally unable hydaulic moun which uses eleco-heological fluid. SAE pape , im, J.H., Lee, C.W. and Lee, S.. Modeling of magneo-heological fluid based semi-acive moun. Poceedings of he Thid Inenaional Confeence on Moion and Vibaion Conol, 1996, 3, Haldenwange, H. and lose, P. Isolaion and compensaion of vibaion by means of acive piezo-ceamic mouns. Poceedings of AVEC '9, 199, Gennesseaux, A. Reseach fo new vibaion echniques: fom hydo-mouns o acive mouns. SAE Poceedings of he 1993 Noise and Vibaion Confeence, 1993, Ushijima, S. and Jumakawa, S. Acive engine moun wih Piezo-acuao fo vibaion conol. SAE pape 93001, 1993.

26 1. Rahman, Z. and Spanos, J. Acive engine moun echnology fo auomobiles. Poceedings of he Thid Inenaional Confeence on Moion and Vibaion Conol, 1996, 3, Lee, Y.W., Lee, C.W., Jeong, G.S. and Lee, H.S. Modeling and dynamic analysis of acive engine moun using eleco-magneic acuao. Poceedings of AVEC '96, 1996,, Lee, Y.W., Lee, C.W., Jeong, G.S. and Moon, H.S. Design of acive engine moun and evaluaion of vibaion conol pefomance using nomalized fileed-x LMS algoihm. Poceedings of he Fouh Inenaional Confeence on Moion and Vibaion Conol, 1998,, Nakaji, Y. e al. Developmen of an acive conol engine moun sysem. Vehicle Sysem Dynamics, 1999, 3, Widow, B. and Sens, S. Adapive Signal Pocessing. Englewood Cliffs, NJ; Penice-Hall, Haykin, S. Adapive File Theoy. Uppe Saddle Rive, NJ; Penice-Hall, Na, H.S. and Pak, Y. An adapive feedfowad conolle fo ejecion of peiodic disubances. Jounal of Sound and Vibaion, 1997, 01(4), Fukumoo, M., uboa, H. and Tsujii, J. Impovemen in sabiliy and convegence speed on nomalized LMS algoihm. Poceedings of he IEEE Inenaional Symposium on Cicuis and Sysems, 1995,, Tokhi, M.O. and Leich, R.R. Acive Noise Conol. Oxfod Univesiy Pess, Ellio, S.J. Adapive mehods in acive conol. Poceedings of MOVIC 98, 1998, 1, Whie, F.M. Fluid Mechanics. McGaw-Hill, Fox, R. and McDonald, A. Inoducion o Fluid Mechanics (3 d ediion). John Wiley & Sons, 1985.

27 4. Taylo, C.F. The Inenal combusion Engine in Theoy and Pacice. MIT Pess, Wang, A.. and Ren, W. Convegence analysis of he muli-vaiable fileed-x LMS algoihm wih applicaion o acive noise conol. IEEE Tansacions on Signal Pocessing, 1999, Apil, 47(4),

28 APPENDIX A. Equivalen coss-secional aea of uppe chambe Figue A.1 shows he shape of he uppe chambe. The volume of he fluid conained in he main ubbe is ( ) H V π =. (A-1) When he main ubbe is veically defomed, hen volume change of he uppe chambe is given as ( ) ( )( ) ( ) x x H H V π = π π = (A-) Hence, he equivalen pison aea is defined as he volume change due o veical deflecion divided by he veical deflecion iself as ( ) x V A e π =. (A-3) 1 x H Figue A.1 Volume change of uppe chambe due o veical deflecion.

29 Lis of Tables Table 1. Paamees of eleco-magneic acuao. Table. Paamees of pooype AEM. Lis of Figues Figue 1. Desied achiecue of acive engine moun. Figue. Hydaulic engine moun: (a) sucue; (b) equivalen model. Figue 3. Acive engine moun: (a) sucue; (b) equivalen model. Figue 4. Fee body diagam of AEM sysem. Figue 5. Flow beween uppe and lowe chambes hough ineia ack. Figue 6. Requied acuao soke fo suppessing engine vibaion of 0.mm. Figue 7. Sucue of eleco-magneic acuao: (a) schemaic diagam of an elecomagne; (b) dual eleco-magne sucue. Figue 8. Bandwidh of he eleco-magneic acuao. Figue 9. Block diagam of fileed-x LMS algoihm. Figue 10. Tes seup fo model veificaion. Figue 11. Passive ansfe funcion of acive engine moun, A(s). Figue 1. Acive ansfe funcion of acive engine moun, B(s). Figue 13. Laboaoy es seup fo vibaion isolaion pefomance. Figue 14. Typical laboaoy pefomance esul of AEM sysem a 5Hz. Figue 15.Vibaion isolaion pefomance of AEM.

30 Table 1. Paamees of eleco-magneic acuao. Paamee coil uns, N offse cuen, I0 pole face aea, Ap nominal gap (o maximum soke), g0 Value 480 uns 1.5A 16mm 1.0mm

31 Table. Paamees of pooype AEM. Paamee main ubbe siffness, bulge siffness of main ubbe, compliance of lowe chambe, b ε Value N / m N / m.0n / m he equivalen coss-secional aea of he uppe chambe, A e 413mm decouple aea, Ad 166mm coss-secional aea of ineia ack, fluid mass in ineia ack, m A 50mm 1.5g damping coefficien in ineia ack, c 0.08 N s m

32 Engine Weigh suppoing sping Acuao Shock alleviaing sping Chassis Figue 1. Desied achiecue of acive engine moun.

33 Engine Main Rubbe Uppe Chambe Lowe Chambe Decouple Ineia Tack (a) Engine b A : A e m c (b) Figue. Hydaulic engine moun: (a) sucue; (b) equivalen model.

34 Engine Main Rubbe Uppe Chambe Pison (decouple) Ineia Tack Lowe Chambe Bellow Acuao (a) F e Engine, m e x x e b A e A A d x m x d ε c F 1 F (b) Figue 3. Acive engine moun: (a) sucue; (b) equivalen model.

35 Engine, F e me x F T F T AEM F T F T Figue 4. Fee body diagam of AEM sysem.

36 l u() Uppe Lowe chambe P( l, ) chambe P1 P Ineia ack L Figue 5. Flow beween uppe and lowe chambes hough ineia ack.

37 1.5 Acuao soke (mm) Fequency (Hz) Figue 6. Requied acuao soke fo suppessing engine vibaion of 0.mm.

38 Cuen, I N-uns g 0 F Pole face, A p (a) Magne Coe y Coil ( I0 i ) Runne Coil ( I0 i ) (b) Figue 7. Sucue of eleco-magneic acuao: (a) schemaic diagam of an elecomagne; (b) dual elecomagne sucue.

39 Magniude (db) dB Fequency (Hz) 100 Figue 8. Bandwidh of he eleco-magneic acuao.

40 Coelaed signal (achomee) F e () R () A( s) me s A( s) A/D W D/A D(s) F T ( ) R(n) Engine-AEM W k 1 = W k µ F T ( n) Z A/D F T ( n ) D ˆ ( z ) Z Figue 9. Block diagam of fileed-x LMS algoihm.

41 cossba foce ansduce poximiy senso hydaulic excie Figue 10. Tes seup fo model veificaion.

42 10 7 expeimen simulaion Siffness (N/m) Fequency (Hz) (a) siffness Phase (deg.) Fequency (Hz) 100 (b) phase Figue 11. Passive ansfe funcion of acive engine moun, A(s).

43 Siffness (N/m) expeimen simulaion Fequency (Hz) 100 (a) siffness 0-40 Phase (deg.) Fequency (Hz) (b) phase Figue 1. Acive ansfe funcion of acive engine moun, B(s).

44 funcion geneao achomee PC wih DSP excie exciaion foce PD conolle unne posiion mass Block poximiy senso powe amp. conol cuen foce ansduce AEM (a) schemaic diagam of expeimenal seup mass block foce ansduce foce ansduce unne posiion senso (b) close-up view of AEM Figue 13. Laboaoy es seup fo vibaion isolaion pefomance.

45 Tansmied foce (N) conolled unconolled Time (sec.) Figue 14. Typical laboaoy pefomance esul of AEM sysem a 5Hz.

46 conolled unconolled Siffness (kn/m) Fequency (Hz) (a) siffness 0.8 Ampliude (mm) conolled unconolled Fequency (Hz) (b) vibaion ampliude Figue 15.Vibaion isolaion pefomance of AEM.