Pocdings of th 7th WSEAS Intnational Confnc on Simulation, Modlling and Optimization, Bijing, China, Sptmb 15-17, 7 331 Chaactization and Modling of Symmtic and Asymmtic Damping Poptis of a Magntohological Damp EN-RONG WANG WAN-JUN WANG HUI WANG School of Elctical & Automation Engining Nanjing Nomal Univsity No. 78 Ban-cang Stt, Nanjing 14, CHINA wang@njnu.du.cn http://d.njnu.du.cn/nwshtml/lishi/51161313.htm SUBHASH RAKHEJA CHUN-YI SU Dpatmnt of Mchanical & Industial Engining Concodia Univsity Montal, CANADA H3G 1M8 Abstact: - Fo alizing th intllignt vhicl suspnsion dsign with magnto-hological (MR fluids damps, xtnsiv laboatoy masumnts a pfomd to chaactiz th symmtic and asymmtic hystsis foc poptis of a MR-damp, und a wid ang of div cunt and hamonic xcitation conditions (fquncy and stok. Th poposd asymmtic damping foc gnation (ADFG algoithm is mployd to gnat th asymmtic damping foc in compssion and xtnsion fo th symmty MR-damp, and a gnalizd modl is poposd to chaactiz th symmtic and asymmtic hysttic foc-vlocity (f-v chaactistics of th contollabl MR-damp. Th masud data a usd to idntify th symmtic and asymmtic hysttic f-v modl paamts, and simulations a pfomd to assss th ffctivnss of th poposd modl synthsis by compaing th sults with thos obtaind fom th masud data und wid ang of opating conditions. Th sults show asonably good agmnts btwn th simulation sults and th masud data, ispctiv of th xcitation conditions and contol cunt, and vify that th poposd ADFG algoithm is ssntial to yild th asymmtic damping popty fom th symmty MR-damp. Ky-Wods: - Magnto-hological fluids damp Chaactistics Hadwa-in th-loop tst Chaactization Modling 1 Intoduction A wid ang of magnto-hological (MR fluid-basd damps a cuntly bing xplod fo thi potntial implmntation in vaious systms, such as vibation contol dvics and vhicl suspnsion. A numb of analytical and xpimntal studis hav claly stablishd supio potntial pfomanc bnfits of th MR-damp in vhicl applications in lation to convntional hydaulic damps[1-3]. Th MR damps off high viscous damping cosponding to low vlocitis in th p-yild condition, whil th post-yild satuation cosponding to high vlocitis can b chaactizd by a considably low viscous damping cofficint. Th quimnt of adquat id, oad-holding, handling and dictional contol stability pfomanc of oad vhicls ntails vaiabl damping, which could b achivd with MR damps with only minimal pow consumption, unlik a fully activ suspnsion which could add o mov ngy dpnding upon th dmand with th hlp of an laboat pow supply[4]. Th smi-activly contolld MR-fluid damps off apid vaiations in damping poptis in a liabl fail-saf mann, sinc thy continu to povid adquat damping in a passiv mann in th vnt of contol hadwa malfunction[5]. Although a vast numb of smi-activ vaiabl damping concpts basd upon hydaulic flows modulation and lcto-hological (ER fluids hav bn dvlopd, dfinit advantags of th MR-fluid damps hav bn claly stablishd, such as significantly high yild stss and wid opating tmpatu[3]. Owing to th hology of MR-fluid in tms of its sha stss-stain at bhavio, th damp xhibits highly nonlina vaiations in damping foc, attibutd to th hystsis and foc-limiting poptis of th fluid as functions of intnsity of applid magntic fild, and displacmnt and vlocity of th piston. Th dvlopmnt of an ffctiv contoll fo
Pocdings of th 7th WSEAS Intnational Confnc on Simulation, Modlling and Optimization, Bijing, China, Sptmb 15-17, 7 33 alizing dsiabl vaiations in damping quis accuat chaactization of hysttic foc-vlocity (f-v chaactistics of th MR-damp in th p-yild condition and foc satuation in th post-yild condition. Spnc, t al[], poposd a damp modl on th basis of th Bouc-Wn hystsis modl. Th modl, howv, poss inhnt difficultis in pdicting ssntial paamts and in alizing contol systms fo dsid tacking contol pfomanc. Bingham plastic modl has bn poposd assuming igid matial bhavio in th p-yild, whil th sha flow in th post-yild is chaactizd by a viscous damping cofficint. Assuming th matial to b plastic in both p- and post-yild conditions, Stanway, t al[1], poposd a nonlina modl, wh th p-yild foc is chaactizd by considably high viscous damping. On th basis of this modl, Wly, t al[3], poposd a nonlina hysttic bilina modl by fitting th f-v chaactistics using fou paamts: p- and post-yild viscous damping cofficints, yild foc and zo-foc vlocity intcpt. Th abov modls, howv, do not includ th ffcts of continually vaying contol cunt. Moov, hysttic damping foc gnatd by a MR-damp not only dpnds upon th intnsity of th magntic fild but also upon th xcitation fquncy and amplitud, and can only yild th symmtic damping popty in compssion and bound. In this study, xtnsiv laboatoy tsts a pfomd to chaactiz th dpndnc of hysttic damping foc of a candidat MR-damp und a wid ang of div cunt and xcitation conditions (fquncy and stok, so as to synthsiz an optimal smi-activ contoll fo implmnting intllignt vhicl suspnsion with th symmty MR-damp[6-8]. Th poposd asymmtic damping foc gnation (ADFG algoithm[9] is mployd to modulat th div cunt in asymmtic mod to gnat th asymmtic damping foc in compssion and bound fo th symmty MR-damp, and th poposd gnalizd MR-damp modl[1] is poposd to chaactiz th hysttic f-v chaactistics of th contollabl symmty and asymmty MR damps. Th gnalizd modl synthsis in conjunction with th masud data fo th symmtic and asymmtic damping chaactistics a usd to idntify th modl paamts. Simulations a pfomd to assss th ffctivnss of th poposd modl synthsis, and sults obtaind und wid ang of simulation conditions a compad with thos obtaind fom th masud data[11]. Chaactization of Symmtic Hysttic F-V Chaactistics A MR-damp, dvlopd by CARRERA[1] and pictoially shown in Fig.1, is considd fo chaactizing its damping poptis in th laboatoy and applying in psnt studis[6-8]. Th considd damp, dsignd fo automotiv applications, could povid a total stok of mm. Th damp is a mono-tub dsign and compiss floating piston, which spaats th MR-fluid and th gas mdia. Th piston is dsignd with annula oifics, and it compiss lcto-magntic coils to gnat magntic fild in spons to an applid lctic cunt. Th vaiations in viscous and sha poptis of th fluid, causd by th applid magntic fild, yild vaiations in th damping foc dvlopd by th damp. Fo this paticula damp, a dict cunt limitd to.5 A at 1 V svs as th command signal fo th coils. Fig.1 A pictoial viw of a candidat MR-damp.1 Tst appaatus and mthodology Th foc-vlocity (f-v and foc-displacmnt (f-d chaactistics of th candidat MR-damp a masud in th laboatoy ov a wid ang of applid cunts and xcitations. A voltag-to-cunt cicuit is dsignd to aliz diffnt constant lvls of cunt xcitations fo th coil. Owing to th symmtic dsign of th damp, th voltag-to-cunt cicuit is initially applid to obtain symmtic f-v chaactistics in compssion and bound und a fixd div cunt and symmtic xcitation. A Hadwa-in-th-loop (HIL tst platfom, as shown in Fig., is dvlopd in th laboatoy[8, 1]. Th candidat MR-damp is installd on an MTS lcto-hydaulic vibation xcit btwn th xcit and a fixd intial fam though a foc tansduc. Position (LVDT and vlocity (LVT snsos a also installd on th xcit to masu th instantanous position and vlocity of th damp piston. Th damp is subjct to hamonic displacmnt xcitations of diffnt constant amplituds at slctd disct fquncis to chaactiz its poptis ov a wid ang of xcitations. Th foc, vlocity and displacmnt
Pocdings of th 7th WSEAS Intnational Confnc on Simulation, Modlling and Optimization, Bijing, China, Sptmb 15-17, 7 333 data, acquid though a data acquisition boad, a dictly impotd into an Excl woksht using Dynamic Data Exchang to obtain an on-lin display of th hysttic f-v chaactistics. A dual gulatd DC pow supply is usd to supply th command cunt to th damp. A thmocoupl is also mountd on th damp body to monito th damp tmpatu. Th xpimntal data und ach condition w acquid in th vicinity of a dfind tmpatu ang (4±1 C, so as to suppss th thmal ffcts in th chaactization task. 3 1 Fig. A pictoial viw of MR-damp tst systm (1-Svo-contoll, -Data acquisition, 3-DC pow supply, 4-Tmpatu monito, 5-Foc tansduc; 6-MR-damp, 7-Hydaulic actuato Th hysttic f-v chaactistics of th candidat damp, symmtic in compssion and bound, a masud und sinusoidal displacmnt xcitations at sval disct fquncis in th to 15 Hz ang, which is considd to psnt th ang of pdominant vhicula motions along th vtical axis. Th tsts a pfomd und diffnt constant magnituds a m of displacmnt, anging fom.5 to 75 mm, and command cunt i d in th to.4 A ang. A total of 165 tsts a pfomd cosponding to diffnt combinations of fquncy, stok and div cunt, as summaizd in Tabl 1. Th amplituds of displacmnt xcitations at high fquncis a limitd to low valus to nsu damp opation within saf vlocity limits. Th masumnts a initially pfomd und low amplitud xcitation at a fquncy of.1 Hz. Th masud foc is considd to psnt th sal fiction, assuming ngligibl contibutions du to MR-fluid damping at xtmly low vlocitis[5]. Th damp is thn subjctd to a slctd xcitation condition and cunt using th svo-contoll and th voltag-cunt cicuit, spctivly. Th foc, vlocity and displacmnt signals a acquid in th dynamic stat as th body tmpatu appoachs 4 C. Th masud signals a displayd in th fom of tim-histois and Lissajuous cuvs in f-v and f-d cosponding to ach tst condition. Th acquid data a subsquntly analyzd to chaactiz impotant poptis of th MR-fluid damp[11]. 4 5 6 7 Amplitud (a m / mm Tabl 1 Tst matix of th MR-damp Cunt (i d / A Fquncy ( f / Hz.1.5.5 5. 7.5 1 1.5 15.5.1..3.4 1.5.1..3.4 5.1..3.4 5.1..3.4 75.1..3.4. Symmtic hysttic f-v chaactistics Th foc-vlocity (f-v chaactistics masud und a fw slctd xcitation conditions a initially analyzd to build an undstanding th dynamic bhaviou of th MR-damp. Figs.3 to 5 illustats a goup of typical hysttic f-v chaactistics masud und slctd hamonic xcitations and div cunts. Th sults show that th damping foc stongly dpnds on both th div cunt (i d and th damp vlocity ( v = xɺ, and bhavios naly lina is at low vlocitis in th p-yild and foc satuation at high vlocitis in th post-yild, as vidnt in Fig.3. Th tansition btwn p- and post-yild stags occus aound th vlocity v =.5 m/s fo th candidat damp considd. Th nonlina damping poptis a futh dpndnt upon xcitation fquncy and amplitud, as illustatd in Figs.4 and 5, spctivly. Fig.4 illustats that th hystsis loop incass with incasing fquncy in a naly lina mann fo fquncis blow 1 Hz, and xhibits stong hystsis at high fquncis. In th passiv mod (i d =, th damping foc vais naly linaly with vlocity, paticulaly at fquncis abov 5. Hz, and th chang in th damping cofficint obsvd at th onst of post-yild tnds to diminish und high xcitation. Application of a high cunt (i d.3 A and xcitation fquncy (f 1 Hz causs a slight asymmty in th hystsis loop, whil
Pocdings of th 7th WSEAS Intnational Confnc on Simulation, Modlling and Optimization, Bijing, China, Sptmb 15-17, 7 334 lag hystsis width in compssion could b attibutd to possibl mixing of gas in th MR-fluid, as shown in Fig.4b. Th sults shown in Fig.5 futh illustat that th incas of xcitation amplitud sults in lag incas of hystsis width in th damping foc. 1..5 -.5-1. -. -.1.1. (a f=.5 Hz a m =5 mm (b f=.5 Hz a m =1.5 mm Fig.3 Masud f-v chaactistics of MR-damp und diffnt div cunts and xcitations. 1-1 -.6.4. -. -.4 -.6 1..5 -.5-1. -. -.1.1. -. (a i d = A.4 A.3 A. A.1 A A -.1.1. -. -.1.1..4 A.3. A.1 A A 15 Hz 1.5Hz 1 Hz 7.5 Hz 5.Hz.5Hz 15 Hz 1.5Hz 1 Hz 7.5 Hz 5. Hz.5 Hz (b i d =. A Fig.4 Masud f-v chaactistics of MR-damp und diffnt xcitation fquncis and div cunt (a m =.5 mm. 1..5 -.5-1. -.. 1..5 -.5-1. -. -. -. -.1.1 (a i d =. A -.1.1 (b i d=.4 A Fig.5 Masud f-v chaactistics of MR-damp und diffnt xcitation amplituds and div cunt (f=.5 Hz Th abov xpimntal sults vals that th damping poptis of th candidat damp stongly dpnd on th magnituds of div cunt, and xcitation fquncy and amplitud, and futh vals th ssntial dynamic bhavio of th candidat MR-damp such as th contollabl popty, passiv bhavio, hysttic phnomnon, which foms th basis fo th gnalizd hysttic f-v modl synthsis poposd by th authos[5, 1]. 3 Chaactization of Asymmtic Hysttic F-V Chaactistics Th candidat MR-damp is dsignd to povid symmtic damping foc in compssion (v > and bound (v <. Th vhicl suspnsion, howv, a dsignd to aliz asymmtic damping to achiv compomis among th conflicting id, oad-holding and dictional contol pfomancs. It has bn suggstd that th atio of bound damping foc to that in compssion should b in th 3 to 5 ang to aliz btt suspnsion pfomanc. Fo this pupos, an asymmtic damping foc gnation (ADFG algoithm[9] has bn initially poposd by th authos and applid to xpimntal chaactization of th asymmtic f-v chaactistics fom th symmty MR-damp dsign, by intgating th algoithm within th cunt div cicuit. Th poposd ADFG algoithm illustats that th asymmtic damping poptis of th symmtic candidat damp can b alizd by limiting th div cunt i d to a low valu i L duing.. 75 mm 5 mm 5 mm 1.5mm 75 mm 5 mm 5 mm 1.5mm
Pocdings of th 7th WSEAS Intnational Confnc on Simulation, Modlling and Optimization, Bijing, China, Sptmb 15-17, 7 335 compssion, whn th lativ vlocity of th piston is positiv. Th cunt is switchd to a high valu i H duing bound motion. Such an appoach, howv, would caus tansint sponss du to switching discontinuitis aound v =, and an algbaic filting tchniqu without phas dlay is intgatd in th algoithm to suppss th cunt discontinuity. Th asymmtic div cunt of th MR-damp i d is fomulatd as i = M ( p, ξ, v i (1 d p c p M p ( p, ξ, v = + [p( v > ( v π p 1 ξv ] tan ( v m ( wh M p is th multipli of th poposd ADFG algoithm, v m is th pak lativ vlocity, p is asymmty facto of div cunt ( p 1 and ξ is smoothing facto dfining th slop of th actan function (ξ>. By implmnting th poposd ADFG algoithm into th diving cunt cicuit of th xpimntal stup shown in Fig., th xpimnts a pfomd to chaactiz th asymmtic damping foc und th tst conditions summaizd in Tabl 1, and using p= and ξ= in th modulation function[11]. This would yild i L = and i H =i d. As an xampl, Fig.6 illustats th masud asymmtic hysttic f-v chaactistics cosponding to th slctd xcitation conditions and i d anging fom to.3 A. Th sults show that th sam candidat damp can povid asymmtic damping foc in compssion and bound in continuous mann. Th chosn paamts of th modulation function yild asymmtic damping foc atio (γ in th od of 4, fo low vlocitis. Th atio γ, howv, diminishs und high vlocitis as obsvd in Fig.6d. A γ valu of appoximatly is attaind und i d =.3 A, which is patly attibutd to th foc limitd bhavio of th MR-damp..4. -. -.4 -.6 -.8-1. A.1 A. A.3 A -.4 -...4 (a f=.5 Hz a m =1.5 mm.4. -. -.4 -.6 -.8-1. -1..4. -. -.4 -.6 -.8. A -1..3 A -1. -.15-1. 1..5 -.5 A.1 A. A.3 A -.8 A.1 A (b f=.5 Hz (c f= Hz -.4.4.8 (d f=.5 Hz a m =5 mm -.5.5 1..15 a m =1.5 mm -1. A.1 A. A -..3 A -.5 -.4 -...4 a m =5 mm Fig.6 Masud asymmtic f-v chaactistics of th candidat MR-damp und diffnt contol conditions 5 Gnnalizd Hysttic F-V Modl Th availabl tst damp povidd only symmtic damping foc in bound and compssion du to th symmtic natu of th applid cunt. Futhmo, th potd modls of th MR-damp, invaiably, chaactiz th symmtic chaactistics as a function of th piston vlocity, whil th cunt dpndnc is mostly ignod[1-4]. Th vhicl suspnsion systms, howv, a gnally dsignd with asymmtic damping chaactistic to achiv a btt compomis among diffnt conflicting pfomanc masus. Th convntional suspnsion damps povid high bound damping to suppss whl vlocity in th upwad diction whn compad to that in th downwad diction. Th modl synthsis of th symmtic damp[5] can b asily xtndd to chaactiz th asymmtic
Pocdings of th 7th WSEAS Intnational Confnc on Simulation, Modlling and Optimization, Bijing, China, Sptmb 15-17, 7 336 hysttic damp poptis[1]. Th gnalizd hysttic f-v modl is fomulatd as a( v+ vh+ vb 1 Ci ( Ft F + + + b (1 kvc v v a( v vh v (3 b F (, = d v id a( v+ vh+ vb 1 C ( F ( < i t F ( + + b kv v v a v vh vb Th fomulation can chaactiz both symmtic and asymmtic hysttic f-v chaactistics of th MR-damp, psntd in Figs.3-6. Th modl involvs fatu paamts (F t, F b, v h, v b, α, k vc, k v that a dpndnt not only on th natu of xcitation v m, but also on th div cunt i d. Th tansition foc F t, th cunt dpndnt function C i, th constant α, th zo-foc vlocity intcpt v h, th foc offst F b, th vlocity offst v b, th high vlocity lina is cofficints k v and k vc a xpssd as 1vm F t = F ( (4 k k C ( i d, Ci ( id 1 i a ( id+ I I a (5 a = a /( kvm (6 k 3 k 3 vh = sgn( ɺ x k 4 vm ( a3 ( id+ I1 a3 I1 (7 F b = k5 ci Ft v b = k6 vmt (8 a4vm a4vm k v = k 1 k vc = k 1c (9 v = ( xɺ ɺxɺ x (1 m Th poposd hysttic f-v modl can b usd to dscib both symmtic and asymmtic hysttic f-v chaactistics of th MR damps as a function of th applid cunt and xcitation condition. Th modl quis idntification of a total of 16 paamts (F, I, I 1, a, a 1, a, a 3, a 4, k, k 1c, k 1, k, k 3, k 4, k 5, k 6 fom th masud data fo th asymmtic chaactistics, and can b simplifid to chaactiz th symmtic f-v chaactistics by ltting k 5 =k 6 = and k 1c = k 1. Th damping foc chaactistics in th passiv hysttic mod can also b divd by ltting k =, k 3 =, a =, α 3 =, I = and I 1 =, and th poposd modl can b futh simplifid to yild th man f-v chaactistics of th MR-damp by ltting k 4 = (v h =. It should b notd that th poposd gnaliad hysttic f-v modl has a littl diffnc fom that in th foc offst paamt fomulation F b in[1]. 5 Paamt Idntification and Modl Validation A sis of laboatoy tsts hav bn pfomd to chaactiz th dpndnc of hysttic damping foc of a MR-damp on th xcitation fquncy and stok, and th div cunt. Th masud data a usd to idntify th paamts of th gnalizd symmtic and asymmtic hysttic f-v modl of th MR-damp, so as to dmonstat th ffctivnss of th poposd modl by compaing th simulation sults with th masud data ov a wid ang of xcitation paamts and magnituds of div cunt. 5.1 Modl Paamt Idntifications Th gnalizd hysttic f-v modl synthsis in conjunction with th masud data fo th symmtic and asymmtic damping chaactistics a usd to idntify th modl paamts. In od to chaactiz th damping poptis ov wid angs of applid cunt and xcitation condition, a cost function U is fomulatd to incopoat th squad os cosponding to diffnt tst conditions[11]. L K J U = F ( i, v F ( i, v (11 [ l= 1 k= 1 j= 1 d j, k, l d d j, k, l ] wh F (j,k,l is th magnitud of masud damping foc cosponding to j th coodinat of th hyston loop, k th cunt and l th fquncy. F d(j,k,l is th cosponding damping foc computd fom th modl. J, K and L dfin th lvls of data points, cunts and fquncis considd in th squad sum o function U. Th o function is divd upon considing th stady-stat sponss ov a singl cycl. A total of 36 data points a considd within ach hystsis loop divd fo 5 diffnt lvls of cunt (K=5:,.1,.,.3, and.4 A and diffnt xcitation fquncis, fo th symmtic f-v modl paamt idntification. Th considation of ths fquncis fo a givn xcitation magnitud povids a asonabl ang of th piston vlocity. Th optimization function availabl within th MATLAB optimization toolbox (fminunc is usd to solv th minimization poblm dfind in Eq.(11. A numb of inquality constaints fo th modl paamts a dfind to nsu fasibl solution: a i (i=1,,4, k i (i=1,,6, and F >, whil k 4, I and I 1 w abitay valus. Owing to th stong dpndnc of th hysttic focs in th symmtic and asymmtic mods on th pak vlocity and thus th xcitation fquncy, th o minimization is pfomd fo two diffnt angs of xcitation fquncis fo th symmtic f-v modl paamt idntification. Th diffnt modl paamts a thus idntifid fo th low and high fquncy angs in th.5 to 5. Hz and 5. to 15 Hz, spctivly. A total of 4 diffnt fquncis (J=4:.5,,.5 and 5. Hz a considd fo low fquncy xcitation, whil thos fo th high fquncy involvd 5 diffnt fquncis (J=5: 5, 7.5, 1, 1.5 and 15 Hz. Fo th asymmtic modl, th paamt idntification is limitd to th low fquncy only (J=:.5 and, and 4 diffnt lvls of cunt a considd (K=4:,.1,. and.3.
Pocdings of th 7th WSEAS Intnational Confnc on Simulation, Modlling and Optimization, Bijing, China, Sptmb 15-17, 7 337 Tabls and 3 summaiz th paamts of th symmtic and asymmtic modls idntifid fom th masud data. Th sults psntd fo th symmtic modl show that paamts latd to th cunt dpndnc of th damping foc (k, a, I, width of th hystsis loop (k 3, a 3, I 1, tansition foc (a 1 and high vlocity lina is (k 1, a 4 a stongly influncd by th xcitation fquncy ang. Th low vlocity bhavio is lativly insnsitiv to th xcitation fquncy. This is vidnt fom compaabl valus of th sal fiction foc (F and low vlocity is paamt (a und th two fquncy angs. Th sults psntd fo th asymmtic modl show that paamts latd to th low vlocity bhavio is almost th sam as thos of th symmtic modl at low fquncy ang, which a th sal fiction foc (F, low vlocity is paamt (a and hystsis width paamt (k 4. Tabl Idntifid symmtic modl paamts of th candidat MR-damp Paamt Fquncy (Hz Paamt.5-5 5-15.5-5 5-15 Fquncy (Hz a 99.985 988.967 k 15.987 177.49 a 1, s/m 5.197 4.477 k 1 11. 9.486 a, A -1 7.58 1.757 k 9.44 4.355 a 3, A -1 6.635 1.137 k 3 9.186 17.781 a 4, s/m 7.54 5.51 k 4 -.119 -.156 I, A.79 -.8 F, N68.56 7.91 I 1, A.67.165 Tabl 3 Idntifid asymmtic modl paamts of th candidat MR-damp Paamt Asymmty Paamt Asymmty a 995.499 k 1c 16.877 a 1, (m/s -1 1.417 k 1 4.673 a, A -1 5.5 k 1.61 a 3, A -1.441 k 3 1.666 a 4, (m/s -1.383 k 4 -.15 I, A.68 k 5.69 I 1, A 1.131 k 6.453 k 177.51 F, N 79.9 5. Validation of symmtic f-v modl Th poposd symmtic hysttic f-v modl is futh analyzd und a wid ang of xcitation conditions and magnituds of div cunt. Th simulation sults a compad with th masud data to valuat th ffctivnss of th poposd modl. Figs.7-9 shows compaisons of simulation sults in tms of f-v chaactistics with th masud data und a numb of th tst conditions, as xampls, to dmonstat th validity of th poposd modl. Fig.7 illustats th compaisons und diffnt div cunts (i d = to.4 A and two diffnt xcitation conditions (f= and.5 Hz; a m =1.5 mm. Fig.8 shows compaisons of sults und diffnt xcitation amplituds in th.5 to 5 mm ang, and fquncis in th.5 to.5 Hz ang, whil th applid cunt is hld fixd (i d =. A. Fig.9 futh illustats th compaison of th modl sponss cosponding to high fquncy xcitations with th masud data. Th figu illustats th modl validity ov th nti ang of applid cunt (i d = to.4 A and xcitation fquncis in th 5. to 15 Hz ang, whil th displacmnt amplitud is hld as.5 mm. Th modl sults follow tnds simila to thos obsvd in th masud data, colat asonably wll with th masud data und low cunts and xcitation fquncis. (a f= Hz (b f=.5 Hz Fig.7 Compaisons of symmtic modl sults with th masud data und diffnt applid cunts and xcitation fquncis (a m =1.5 mm 1..5 1..5 -.5-1. -.15 -.1 -.5.5.1. 1..5 -.5-1. -. -.5-1. -. -. -.1.1. -.1.1. (a Diffnt xcitation amplituds, f=.5 Hz.4 A.3 A. A.1 A A.15 5 mm 5 mm 1.5 mm.5 mm
Pocdings of th 7th WSEAS Intnational Confnc on Simulation, Modlling and Optimization, Bijing, China, Sptmb 15-17, 7 338 (b Diffnt fquncis, a m =1.5 mm Fig.8 Compaisons of symmtic modl sults with th masud data fo fixd cunt (i d =. A. 1..5 -.5-1.. 1..5 -.5-1. (a Applid cunt: f=1 Hz a m =.5 mm.8 1..6.4. -. -.4 -.6 -.8-1. -. -. -. -.1 -..1. -.1.1. 5. Hz.5 Hz Hz.5 Hz -.1.1..4 A.3 A. A.1 A A 15 Hz 1.5 1 Hz 7.5 Hz 5. Hz (b Excitation fquncy: i d =.1 A a m =.5 mm Fig.9 Compaisons of symmtic modl sults with th masud data und high fquncy xcitations Th abov sults gnally show asonably good agmnts btwn th symmtic modl sults and th tst data ov th nti ang of tst conditions considd, with th xcption of thos attaind at high fquncis. 5.3 Validation of asymmtic f-v modl Th poposd asymmtic hysttic f-v modl is futh analyzd und slctd angs of xcitations and div cunts. Th simulation sults a compad with th masud data to dmonstat th validity of th poposd modl. Fig.1 illustats th compaisons of th modl sults with th masud data und diffnt div cunts (i d = to.4 A and low fquncy xcitations (f=.5 and Hz; a m =1.5 and 5 mm. Th compaisons of modl sults with th masud data gnally show asonably good agmnts btwn th modl sults and th tst data ov th ang of tst conditions considd..4. -. -.4 -.6 -.8-1..3 A -1. -.8.4. -. -.4 -.6 -.8-1. -1..4. -. -.4 -.6 -.8.3 A -1. -.4 -. A.1 A. A A A.1 A. A.1 A. A.3 A -.1 (a f=.5 Hz a m =1.5 mm -.4 (b f=.5 Hz -.5..4.8 a m =5 mm.5.1.4 (c f= Hz a m =1.5 mm Fig.1 Compaisons of asymmtic modl sults with th masud data und low fquncy xcitations and applid cunt Th abov sults show asonably good agmnts btwn th masud data and th asymmtic modl sults, ispctiv of th applid cunt and xcitation conditions within th low fquncy ang. 6 Conclusion Extnsiv laboatoy masumnts a pfomd to chaactiz th symmtic and asymmtic hystsis foc poptis of a MR-damp und a wid ang of div cunt and xcitation conditions (fquncy and stok. Th poposd asymmtic damping foc gnation (ADFG algoithm is usd to gnat th asymmtic damping foc in compssion and xtnsion fo th symmtic MR-damp, and a gnalizd modl is poposd to
Pocdings of th 7th WSEAS Intnational Confnc on Simulation, Modlling and Optimization, Bijing, China, Sptmb 15-17, 7 339 chaactiz th hysttic f-v chaactistics of th contollabl symmtic and asymmtic MR damps. Simulations a pfomd to assss th ffctivnss of th poposd modl synthsis and sults obtaind und wid ang of simulation conditions a compad with thos obtaind fom th masud data. Th sults show asonably good agmnts btwn th simulation sults and th masud data, ispctiv of th xcitation conditions and contol cunt. It is thus concludd that th poposd modl can ffctivly dscib th nonlina symmtic and asymmtic hysttic dynamic poptis of th contollabl MR damps, and can thus b ffctivly usd to synthsiz th optimal smi-activ contoll fo implmntation in vhicl suspnsion. Rfncs: [1] Stanway R, Sposton J L, and EI-Wahd A K. Application of lcto-hological fluids in vibation contol: a suvy. J. of Smat Matials and Stuctus, 1996, 5(4: 464-48. [] Spnc B F, Dyk D J, Sain K M, and Calson J D. Phnomnological modl of a magnto-hological damp. J. of Eng. Mch., 1997, 13(3: 3-38. [3] Wly N M, Pang L. Nondimnsional analysis of smi-activ lcto-hological and magnto-hological damps using appoximat paalll plat modls. J. of Smat Matials and Stuctus,, 7: 73-743. [4] L H S and Choi S B. Contol and spons chaactistics of a magnto-hological fluid damp fo passng vhicls. J. of Intllignt Matial Systms and Stuctus,, 11(1: 8-87. [5] Wang E R, Ma X Q, Rakhja S, and Su C Y. Modling hysttic chaactistics of an MR-fluid damp. Pocs. of th Institution of Mchanical Engins, J. of Automobil Engining, 3, 17(D7: 537 55. [6] WANG E R, YING L, WANG W J, t al. Smi-activ contol of vhicl suspnsion with MR-damp: Pat I-Contoll synthsis and valuation [J]. Chins J. of Mchanical Engining, 7. (In pss [7] WANG E R, YING L, WANG W J, t al. Smi-activ contol of vhicl suspnsion with MR-damp: Pat II-Evaluation of suspnsion pfomanc [J]. Chins J. of Mchanical Engining, 7. (In pss [8] WANG E R, YING L, WANG W J, t al. Smi-activ contol of vhicl suspnsion with MR-damp: Pat III-Expimntal validation [J]. Chins J. of Mchanical Engining, 7.(In pss [9] WANG E R, YE B M, CHEN Y S, t al. Rsach on gnation of asymmtic f-v chaactistics fom symmtic MR-damp [J]. Chins J. of Mchanical Engining, 6, 19(: 39-44. [1] WANG E R, MA X Q, RAKHEJA S, t al. Gnalizd asymmtic hystsis modl of contollabl magnto-hological damp fo vhicl suspnsion attnuation. Chins J. of Mchanical Engining, 4,17( :31-35. [11]WANG E R. Synthss and analyss of smi-activ contol algoithms fo a magnto-hological damp fo vhicl suspnsions [D]. Montal, Canada, Concodia Univsity, 5. [1]Caa wb sit, http://www.caashocks.com,.