Upon Parametric Sensitivity Used in Damping Active Control for Human Body Protection Against Vibrations

Transcription

1 Poceedgs of he d WSEAS I. Cofeece o Appled d Theoecl Mechcs, Vece, Ily, Novebe 0-, Upo Pec Sesvy Used Dpg Acve Cool fo Hu Body Poeco Ags Vbos SIMONA LACHE Depe of Pecso Mechcs d Mechocs Uvesy Tslv of Bsov B-dul Eolo 9, Bsov ROMANIA Absc: - The opc of hu body poeco gs vbos s of hgh ees he scefc wold, due o he occupol dseses vbo duces. Ths ppe peses he wok pefoed hs feld Tslv Uvesy of Bsov, hvg s fl objecve o develop dvced odels of he vbo pheoeo d s fluece o he hu body, ode o fuhe popose cve cool syses fo poeco gs vbos. Dffee vbo solo echques e dscussed d he use of pec sesvy dpg cve cool s poposed. Key-Wods: - Hu body vbo, Acve vbo solo, Sesvy lyss, Mhecl odel, Pedco odel. Ioduco Udesdg d lyzg he dyc behvo of sucues d sucul copoes epese ssue of uos poce he desg pocess. Tkg o ccou he pese ke feues d he sog cocuece, he poducs ecooc d ecologc ssesse hs dvced o such exe h ove-desoed o pou pefoce pojecs e o oleed yoe. Oe seco h should gve poy o ehcg he vbo solo s he oe eled o hu body vbos. The esech he feld eveled hee fequecy evls wh egve fluece o he hu body: ge 0- Hz, wh he followg exposed occupos: eouc, e spo sff; ge -0 Hz, wh he followg exposed occupos: dves of ucks, vehcles fo fcoy spo), cos gculul, foes), escvos, bulldozes, cocee plfos, wokes oud fxed ches h s vbos hough he floo; ge 0-00 Hz, wh he followg exposed occupos: ll occupos h use vboy ches d ools, cg o he hd- syse: es peuc hes fo ock bog, hydo-elecc powe pls, lwys, ec., wokes fo che buldg veg, csed ps cleg, ec.), foesy wokes usg echcl sews), ods cosuco wokes, ec. The occupol dseses due o log e vbo exposue dvde hs poble wo dsc cegoes []: Whole Body Vbo kow by he coy WHB) wh effecs o he ee body; Hd A Vbos kow by he coy HAV) s sgfc cceleos d dsplcees oly o he hd- syse. A jo esech e fo Tslv Uvesy of Bsov, Ro, cossg of egees, physcs d copue scess s peoccuped o develop dvced odels of he vbo pheoeo d s fluece o he hu body, ode o fuhe popose cve cool syses fo poeco gs vbos. The Resech Appoch The esech ppoch, peseed Fg., s o develop syses fo educg vbos duced ucofog. The ew desg seges, by se d cb dpes chges, ogehe wh hoough udesdg of he opeo codo fo he ed vehcles o che ools, y led o dshg vbo effecs o hu opeos. The esech segy llused uses fou ppoches o cque foo. The ows coecg he ppoches depc he foo flows. The blck h ows coespod o vldos of he pedco odel of dscofo d he hck ows coespod o he odfco

2 Poceedgs of he d WSEAS I. Cofeece o Appled d Theoecl Mechcs, Vece, Ily, Novebe 0-, pocedue fo vehcle desgs whe usg he pedco odel of dscofo []. Fg. The esech ppoch fo lyzg d dshg he dscofo duced by hu body vbo yelds o he followg obsevos: - fo <, ll he cuves e lge h d becoe slle h fo > ; he ccl fequecy dels he solo euo d plfco dos; - fo 0, he hgh fequecy decy e s /s, whle vey lge pludes occu e he ul fequecy of he spg-ss syse); - he dpg educes he plude esoce d eds o educe he effecveess hgh fequecy; he hgh fequecy decy e becoes 3 Acve Vbo Isolo Sg fo he luped pee odel poposed by Rose d Ac [3], sudy egdg cve vbo solo hs bee pefoed, ode o develop cve cool syses fo poeco gs vbos. Thee e ube of dffee dpg solo echques o use such s pssve d cve dpg. Acve dpg solos e usully expesve d hve hgh eegy cosupo []. Theefoe hey e les fvoed by os vehcle desges, fo exples. Pssve dpg syses e ofe cegozed s le d o-le e.g. pogessve dpg solos. Spekg g bou vehcles vbos, he leue le dpg solo wh low dpg o ws foud o offe he bes vbo poeco o sooh sufces d hghe dpg o ws foud o pefeble o ough ck. The pogessve dpg syses e pefeble o ough ods d foklfs e os ofe dve o sooh sufces, excep fo occsol ses. I geel, dpg o bewee 0. d.0 s used e.g. []) 3. Pssve Isolo Cosdeg he odel of dy body/cle body solo poble [4] peseed Fg., x d deoes he dy body oo h epeses he dsubces d x c s he cle body dsplcee d epeses he syse oupu. The pssve solo syse volves spg d dpe, he syse sssbly beg defed s: X s) / c s ) X s) / s / d S As s peseed Fg., he plude dg /s Fg. FRF of pssve solo sssbly fo dffee vlues of he dpg [4] The bove obsevos led o he cocluso h he desg of pssve solo volves de-off bewee he esoce plfco d he hgh fequecy euo. The del solo should hve fequecy depede dpg, whch s hgh fo vlues below ccl fequecy - o educe he plfco pek, d low fo vlues bove - o pove he decy e. As cosequece, he objecve of he cve solo syse c be fouled: o cheve o plfco below d ppope decy e hgh fequecy Fg. ). 3. The sky-hook dpe Cosdeg he sgle xs solo peseed Fg. 3, cosss of spg k cg pllel wh he foce cuo F wh o dpg he solo). The bsolue cceleo of he cle body & x& c s esued wh cceleoee d egl coolle s used so h: F g s ) X c

3 Poceedgs of he d WSEAS I. Cofeece o Appled d Theoecl Mechcs, Vece, Ily, Novebe 0-, I yelds he esulg foce cool s popool o he cle body bsolue velocy hs s he eso why hs ype of cool s clled sky-hook dpe Fg. 3b). Fg. 3 ) Isolo wh cceleo feed-bck; b) equvle sky-hook dpe [4] The closed-loop sssbly s gve by he followg elo: X c s) M g ) s s. 3) X s K K d Fo hs elo y be obseved h he coe fequecy s K / M, he hgh fequecy decy e s /s d he cool g g c be chose so h he solo s cclly dped ): g KM. Ths sssbly fulfls he objecve of he cve solo Fg. ). 3.3 Foce Feedbck If he cle body s gd, he cceleo s popool o he ol foce sed by he efce: FF F k. Theefoe, he sky-hook dpe c be obed fo he cool cofguo peseed Fg. 4. Fg. 4 Foce feedbck solo [4] I hs cse, he cceleo seso fo Fg. 3 hs bee subsued wh he foce seso. The cool ehods bsed o cceleo feedbck d o foce feedbck sees o be equvle fo he solo of gd bodes. The leue ephszes wo dvges of foce feedbck [4]: - Sesvy: foce sesos wh sesvy of 0-3 N e coo d coeclly vlble; cceleoees wh sesvy eeded fo ou esech puposes e oe dffcul o fd. - Sbly whe he cle body s flexble: he skyhook dpe sees o be sble oly fo sll g codolly sble) whe he cle body becoes flexble, so h he coe fequecy of he solo ovelps wh he ul fequecy of he cle body. The ol foce sed by he solo s he su of he cool foce F d he spg foce K x, whee x s he elve dsplcee of he wo sucues log he solo xs: F K x F, 4) F s) X s) o K 5) F s) F s) Fo elo 5) yelds he ope-loop sfe fuco F/F s he su of K x / F d egve u feedhough. The sfe fuco gve by he o bewee he oupu d he pu, x / F, hs ll s esdues posve d s poles d zeos lee log he gy xs. The FRF F ) / F ) obed fo s j, whch s puely el whe he syse s udped) yelds fo he FRF, by ovg log he ode xs by he ou of feedhough; hs chges he loco of zeos, whou chgg he elcg popey. 4 Sesvy Alyss Sesvy lyss epeses elvely ew cocep whch hs bee oduced sucul dycs; cosss of deeo of odl pees chge s esul of he chge of he syse ss, sffess o dpg [5]. The hecl bss e Tylo s sees develope, so he ehod s ppoxe oe: jus oe o wo sel es e used fo eso of pees chge. Ths ppoch s poposed o be used he dpg solos desg pocess, fo ehcg he hu body poeco gs vbos. 4. The Mhecl Model Le us cosde uldesol le vscous dpg syse [6], wh degees of feedo, descbed by equo 6): [ M ]{ & x [ C]{ x& [ K]{ x { F. 6) By pplyg he Lplce sfo fo ull l codos, he equo 6) becoes: p [ M ] p[ C] [ K] ){ X p) { F p) 7) Ths ls equo c be sfoed geel egevlue poble [6]:

4 Poceedgs of he d WSEAS I. Cofeece o Appled d Theoecl Mechcs, Vece, Ily, Novebe 0-, p [ A] [ B] ){ Y { F' 8) [ 0] [ M ] whee [ ] [ ] [ ] A, [ B] M C p{ X { { 0 Y, { F'. { X { F [ M ] [ ] [] 0 [ K] 0, The egevlue equo coespodg o equo 8), especvely elo 7): [A] [B] 0, 9) esuls N egevlues he syse poles) j d he coplex cojuges, ssebled he dgol x [ \ ] \, ogehe wh he coespodg egevecos {, ssebled he odl vecos { x []. Cosdeg he egevlue poble fo ce egevlue : [ A] [ B] ) { 0 0) ode o sses he fluece of oe odl pee u o he syse dyc behvo, s ecessy o deee he egevlues d coespodg egevecos pl devves wh espec o h pee u: s. By ulplyg equo 0) lef wh he spose of he egeveco coespodg o egevlue, yelds: { [ ] [ B] ) 0 A ) The devve of hs equo wh espec o odl pee u s he followg: [ ] [ ] [ A] [ B] ) A B ). [ A] [ B] ) 0 ) Tkg o ccou elo 0), equo ) becoes: [ ] [ ] { ) A B { 0, 3) o: { [ ] [ A] [ B] & A 0. 4) ' If he ohogoly codos e cosdeed [6], he sesvy of pole wh espec o he odl pee u chge s gve by he followg elo: & ' [ A] [ B]. 5) Sce he egevecos se-up bse fo he N N veco spce, he pl devve of egeveco wh espec o he pee u s le cobo of hese egevecos: N * g, 6) whee: g e coeffces d he ls N egevecos epese he coplex cojuges of he fs N egevecos. The defco of he g coeffces llows us o fuhe clcule he odl shpes sesvy. By clculg he devve of elo 0) d cobg wh elo 6), yelds: [ A] [ B] ) & g 0 N * ' [ ] [ ] ) A B { 7) By ulplyg lef equo 7) d kg o ccou he ohogoly codos, esul he expesso of g coeffces, whee : g g [ A] [ B] ) [ A] [ B] ) { ) & [ A] ', 8) [ A] [ B] [ A] [ B], 9) g & ) ' { 0) By devo of he ohogoly codo bsed o x [A] [6], he g e obed: [ ] { { [ A] { { [ ] 0 A A ) By oducg elo 6) he bove equo yelds: N { [ ] { { [ A] A * g { ) By pplyg he ohogoly codos, elo ) becoes:

5 Poceedgs of he d WSEAS I. Cofeece o Appled d Theoecl Mechcs, Vece, Ily, Novebe 0-, [ A] { g. 3) By cobg equos 6), 0) d 3), flly esuls he odl shpes sesvy, gve by he elo: [ A] { { N *, [ A] [ B] & ' 4) By expessg elos 5) d 4) es of l ode shpes vecos uexpeded see elo ), of ss, sffess d dpg ces, hese equos becoe: { & u ' d, especvely, { N { [ M ] [ C] [ K] { { *, [ M ] [ C] [ K ] & ' [ M ] [ C] { 5) { & { { ' 6) If sucul chges e kg plce he syse, such s locl chge of ss, sffess swch bewee wo degees of feedo of ce le elsc elees, o le vscous dpg swch bewee wo degees of feedo, s po o kow he ss, sffess o dpg ces, especvely. f u pee s locl ss wh espec o k d.o.f.: j k k k j k k N *, 7) f u s le vscous dpg bewee wo d.o.f.s de k d l: ckl ) k l k j j ) k j k N k l ) j k l ) *, 8) f u s le sffess bewee wo d.o.f.s de k d l: k kl j k kl ) ) k k l l N * l, ) k l j 9) 4. Iepeo of Pec Sesvy Alyzg he sesvy expessos fo he syse poles d he syse ode shpes, especvely, soe obsevos yeld, whch e fuhe peseed [7]. I s vey po he ek h, ode o clcule he syse pole sesvy s suffce o kow he coespodg odl veco elo ). O he ohe hd, he clculo of odl shpes sesvy eeds kowledge bou ll he ode shpes elo ). Geelly, he odl odel cosss of led ube of odes, whch egvely fluece he ccucy of odl shpes sesvy clculus. Sce he sesvy lyss gves fs ode ppoxos, he esuls c be cosdeed s ccue oly fo lle chge of he odl pees. Pobles bou ccucy could lso be geeed by he exsece of vey close esoce fequeces. Aohe po ssue egdg sesvy lyss ccucy s h he esuls e sogly flueced by he eso ccucy of he odl pees. They e fuhe oduced he sesvy elos, fo clculus. The quly of pee eso s led, o oe hd, by he ube of esued odes, he possbly of esug he ool d.o.f.s, he esuee pecso, he ppoxe feue of he eso ehods; ll hese pobles occu whe he expeel d e used. O he ohe hd, whe lycl d e used, ohe ssues y occu d l he quly of pee eso: ube of copued odes, led odel d.o.f.s, ccuces egdg he odelg ehods, egleced dpg.

6 Poceedgs of he d WSEAS I. Cofeece o Appled d Theoecl Mechcs, Vece, Ily, Novebe 0-, Cocluso Hu body vbos due o dffee cegoes of cuses epese owdys po esech ssue fo he scess. A wy fo he dshg d cool cosss developg cve dpg syses o be dped o he vbo souces. Soe leves egdg he syses solo gs hu body vbo evl 0- Hz - exposed occupos: eouc,e spo sff; evl -0 Hz - dves of ucks, vehcles, cos, escvos, bulldozes, cocee plfos, wokes oud fxed ches h s vbos hough he floo; evl 0-00 Hz - exposed occupos: ll occupos h use vboy ches d ools, cg o he hd syse: es, wokes fo che buldg) hve bee dscussed d he use of pec sesvy dpg cve cool hs bee poposed. [6] Ss P., Heyle W., Modl lyss - heoy d pcce. Couse lecues, Ieol Se o Modl Alyss, Leuve, Belgu, 995. [7] Les, S., Fequecy Respose Bsed Vldo of Dyc Sucul Fe Elee Models, Ph.D. Dsseo, Kholeke Uvese Leuve, Belgu, 995. Ackowledgee Ths wok ws suppoed by he Ro Nol Coucl fo Scefc Resech fo Hghe Educo fcl suppo ckowledge goes hee). Refeeces: [] Abbe, C. e. Al, Affecve Coeles of Occupol Exposue o Whole-Body Vbos, Psychohe Psychoso, 004, No. 73, pp , DOI:0.59/ , Kge Pess. [] Jösso. P., Pocedue fo he Reduco of he Effec of Tse Whole Body Vbos, Ph.D. Thess 005, Lule Uvesy of Techology. [3] Rose, J., Ac, M., Modelg he Hu Body/Se Syse Vbo Evoe, Joul of Boechcl Egeeg, ASME Ts., Apl 003, vol. 5, pp. 3-3, DOI: 0.5/ SUA. [4] Peuo, A., A Ioduco o Acve Vbo Cool, Resposve Syses fo Acve Vbo Cool, NATO Scece Sees II. Mhecs, Physcs d Chesy vol. 85, Kluwe Acdec Publshes, 00. [5] Heez, F. M., Fh, C., Loco d Idefyg Sucul Dge Usg Sesvy-Bsed Updg Mehodology, Poceedgs of he 34 h Sucues, Dycs d Mels Cofeece, L Joll, Clfo, 993.