Roberto Spinola Barbosa. Introduction 1. Vehicle Modeling. = θ, (1)

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1 Roeo Spnola Baoa Roeo Spnola Baoa Mee, ABCM Unvey o São Palo Polyehn Shool Mehanal Engneeng Depaen São Palo, SP, Bal Vehle Dyna Repone De o Paveen Roghne The goal o he peen dy he developen o a peal ehod o oan he eeny epone o he hal-vehle jeed o a eaed paveen oghne n he eeny doan. Fo h ppoe, a hal-vehle dyna odel wh a wo-pon delayed ae exaon wa developed o oelae wh he peal deny non o he paveen oghne, o oan he ye peal ane non, n he eeny doan. The veal paveen pole wa eaed along wo oad eon. The ae oghne wa hee expeed n e o he peal deny non o he eaed veal paveen pole wh epe o he evenne wave ne o he paveen oghne. A eeny epone analy wa appled o oan he veal and angla odal vehle dyna epone wh he exaon o he powe peal deny PSD o he paveen oghne. The el how ha a low peed, he vehle penon ode agned de o he npaved a gnae. A /h n an ndlaed aphaled oad, he vehle vaon ode ha a gnan oon aplaon, whh ay ae paenge doo. Keywod: vehle, dyna, paveen, oghne, ando Inodon In geneal, dng he vehle poje and degn developen phae, he aoove ndy le a onaon o degn ool h a vehle odal epone o neal laon Coa, 99, laoaoy e wh hae g Bogg, 9 and he el o expeenal eld oad e, o ne ne vehle penon Vlela and Taa, 5. Depe he eeny o he neal laon, laoaoy and expeenal e ae ll n e, even hogh eng e-onng, expenve and led o he pe oad ondon o he e a. Qae a vehle odel wh ngle ando np adonally ed o peal de Baoa, ; Sn, 998; Ceon, 999; Slva, 999. The oplee vehle odel eployed o odal and onol ppoe Vlela, ; Coa 99. The ovaon o he peen wo o exend he powe o he analy ool o he degn o vehle penon wh he applaon o he eeny doan epone ehne o deal wh ando np o he paveen oghne. One o he onon o he peen dy he developen o a hal-vehle odel wh delayed wo-pon ae exaon oelaed wh he peal deny non o a eaed paveen oghne, n ode o geneae he ye peal ane non n he eeny doan. The veal paveen pole wa eaed along wo oad eon. The ae oghne expeed wh he peal deny non o he eaed veal paveen pole wh epe o he evenne wave ne o he paveen oghne. Th ehod allow he denaon o he vehle dyna epone de o he noaled oghne deny don o a eaed paveen oghne o adde he paenge oo and vehle aey de o he paveen/ye ona load. Vehle Modelng The dyna vehle ehavo wa aoplhed wh he adonal hal-a vehle epeenaon Sn, 7. The odegee o eedo lped paaee odel deng elevan oon wa adoped a hown a Fg.. The vehle ody ee o ove veally n he deon and o ae an angla oon aoaed wh a and oen o nea J G, epevely. The on and ea penon onneon ae deed y pngdape popee,, and. Hee and ae he vehle npng a wh he oeponden ye ne and dapng ae deed y,, and vale. The odel exed y he oad evenne and, whh nde o-o-phae on and ea penon oveen, epevely, wh a e delay. A JG λ F G M Fge. Hal-a odel. The eaon o oon ae oaned ng he agange ehod appled o he lped gd ode. The ne, poenal and he genealed enegy dpaon non ae epevely gven y he ollowng eaon: T J G, V l l, l l R Sng he paal devave o he aove eaon o he agange expeon gven y Vx x Pape eeved 6 Ag 9. Pape aeped 9 Janay. Tehnal Edo: Dongo Rade / Vol. XXXIII, No., Jly-Sepee ABCM

2 Vehle Dyna Repone De o Paveen Roghne J. o he Ba. So. o Meh. S. Eng. Copygh y ABCM Jly-Sepee, Vol. XXXIII, No. / Q R V T T d d 4 one oan he ollowng o deenal eaon:, 5, 6 F, 7 M J 8 Tale how he adoped vale o he vehle nea, penon elay and dpaon. Thee vale ae ypal o a ed ed paenge a Baoa,. Tale. Hal-a popee. Eleen/Chaa. Vehle Body Spenon H/Tye A Ma 75 g g Inea oen 6 g Rgdy B N/ 5 N/ Dapng N/ ---- O.: A ndvdal popee; B gdy depend on he ye pee. The odal ye popee ae deed y o opled vaon ode de o he non-dagonal onon o he ye ax. The vehle odal epone ha o naal daped eene aond.~. and H, epevely. Fo he ody ode on and ea end one, a hown n Fg., dapng ao ae.4 and.6, epevely, a peened n Tale. Fo he penon ode, aoaed wh he npng a o h and ye elay, dapng ao ae aond. a peened n Tale. on end one ea end one Fge. Vehle opled ode on and ea end one. I hold e noed ha he penon eeny ao one deade aove hoe o he vehle ode. The noaled odal Egen-veo oaned o he dyna ax ae hown n he ollowng ale. Tale. Vehle odal popee. Mode Ne Mode vehle on end one Mode vehle ea end one Daped Naal Fe. H.88 H Dapng Fao.44.6 D. Feedo Mag. Phae Mag. Phae Tale. Spenon odal popee. Mode Ne Mode n phae wheel/h Mode 4 o o phae wheel/h Daped Naal Fe.7 H.86 H Dapng Fao.6.7 D. Feedo Mag. Phae Mag. Phae By ang he aplae ano o he ye eaon and ang eo nal ondon Felío, 7, one oan he o ollowng eaon: ] U, ] U, F ] ], M J G ] 9 One o he onon o he peen wo he nodon o he delayed o-o-phae np no he vehle on and ea wheel. Condeng ha he ea wheel n on he ae a gh ae he on wheel, he ae elevaon ha pode he vehle veal penon dplaeen gven y he ae non whh dee he exaon o he on wheel delayed n e. Tang a haon non a he poed veal dplaeen o he on wheel, hen he ea wheel delayed np an e expeed a: T, whee An ω In he aove eaon ω he angla eeny gven y λ π ω / x V and T he e delay gven y x V T /, whee he ne-ax dane, V x he vehle peed and λ he wavelengh, ee Fg..

3 Roeo Spnola Baoa The aplae anoaon o he on wheel and he ea wheel np non, ondeng he anoaon o he delayed non ae epevely gven y: U ] and U ] whee U U and T U U e Upon he on o U no E. and he elnaon o and o hee wo eaon, and ae oe algea anplaon o ge he veal and angla oon o he vehle ody ove dplaeen exaon U elaonhp, he ollowng ane non o he veal and angla dplaeen an e oaned: H and H U U The dplaeen eeny epone non FRF nown a eepane H. Howeve, ondeng a peod np, hee a ple elaonhp eween aeleaon and dplaeen, ne Aω n ω. The aeleaon eeny epone non nown a neane I an e oaned. Analyng he ye veal and angla oed oveen n he eeny doan epone, eplang wh ω and ang he vehle popee peened n Tale, he eeny epone neane non Iω an e oaned a: I ω ω H ω and I ω ω H ω The veal I and angla I vehle odal ane non depend on T ha a peed non T / Vx. The neane non o he opled veal and angla vehle ody oon hown n Fg.. Theeoe, he FRF hape wll e peeddependen a an e oeved n Fg. o 5.6 /h 7. / and Fg. 4 o /h. /. In oh ae,.4. Feeny Repone Speed 5.6 /h Veal Angla ea end one a.88 H, wheel a.7 H. Fo he angla ode, he pea o a.9, 7.8 H e. ee Fg. 4. Magnde Feeny Repone Speed /h Veal Angla - Feeny H Fge 4. Vehle neane eeny epone a /h. I hold e poned o ha o a peed o 86 /h 4 / and an ne-axle dane o.4, T eal o. and, heeoe, he nex veal hp one deade aove he eeny o he ode. Paveen Roghne Meaeen Two eon o oad ae eglae wee aally eaed n he peen wo. The eon wa a.4 long oad o ol oveed wh gavel npaved oad. The eond eon wa a. long o aphaled oad o hgh aly. The paveen oghne wa eaed wh he -pon-ddle-hod eang deve. Th ye opoed o hee wheel and a dplaeen eno. The wo exenal wheel ae eeed and he enal one alaed wh egad o he ohe. A onvenonal a pll he eang ye along he oad eang he a evenne. The enal wheel veal oon apled evey enee y an analog o dgal aple oad nalled n a poale ope. The daa aed ae oed n agne eda o po poeng ppoe Paveo, 9. The eaed daa ae eaed wh he deve ye ane non, o oan he opogaph veal elevaon o he oad ae oghne, a hown n Fg. 5 o he npaved oad. In h ae, en pon pe ee wee apled one aple a evey. ee. Wavelengh p o wee ondeed. Magnde 5 Road Elevaon Paveo R - Feeny H Fge. Vehle neane eeny epone a 5.6 /h. Elevaon 5-5 Hp an e noed n he PSD ve hown n Fg. de o he ne-axle dane.4 ee a a vehle peed o 5.6 /h 7. /. Fo he veal ode, hee hp o a evey nege, elng n pea a aond,, 6, 9 H. The odal eene ae dened wh a le n he ge on end one a. H, - : po/ T: ada: Dane Fge 5. Road elevaon npaved. 4 / Vol. XXXIII, No., Jly-Sepee ABCM

4 Vehle Dyna Repone De o Paveen Roghne The el o he veal elevaon o he oad ae oghne o he aphaled oad ae hown n Fg. 6. In h ae, wo pon pe ee wee apled. Wavelengh p o 5 wee ondeed n he an-alang poee. The el o he aphaled oad evenne aally epeened y he oghne ndex n Inenaonal Roghne Index IRI. The ean IRI vale o h oad eon.9, laed a level A y he ISO ea. - - H - G Powe Speal Deny Hghway Paveo R 5 IRI.9 Road Elevaon Paveo R PSD F -4 E -5 D C -6 B 5-7 A Elevaon -5-8 ISO Cla Wave engh Fge 8. PSD o he aphal paveen. - : po/ T: 5 ada: Dane Fge 6. Hghway elevaon aphal. The daa eaen wa peoed p o 48 pon a a aple ae down o -. Th ange allow analyng wavelengh a long a and down o.. Th wde ange npeedened n h aea ondeng ha adonal eang deve have a eed oevale and. The npaved and he aphaled a elevaon eaeen wee he eaed o geneae don wavelengh o he peod eglae. The peal deny non PSD n he ange o wavelengh eween. o o he npaved oad veal elevaon peened n Fg. 7. Th eaed oad eon pe ha pala gnae wh nened wavelengh onen eween.4 and.9. PSD Powe Speal Deny Sol - Wave engh Fge 7. PSD o he npaved a. Paveo R The peal deny non o wavelengh eween and ee o he aphaled veal elevaon oad peened n Fg. 8, whee he level o oad oghne neny ae alo peened. The pe o h oad eon ha nened wavelengh onen eween and 4 ee. Thee eaed pea o veal elevaon o oad ae oghne wll e ed o allae he vehle veal and angla peal epone. The neny o he eaed paveen oghne laed, aodng o he agnde o he powe peal paen o he eglae n an exponenal ahon wh a pala lope ISO nenaonal andad, 995. Dplaeen powe peal deny PSD o a oad oghne la oaned y a logah expeon n n o : n ϖ Sd n Sd no / n o 4 whee he lope n he log-log ve ϖ xed a 4 db pe deade. The paal eeny dependene e Sd a n o oaned o:. Sd n 4 n o 5 whee n he la ne vayng o o 8 o A o H o deen lae o oad, aodng o ISO. The. exponen n E. 5 apple o he ean geoe oghne o n o a. yle/, a hown n Tale 4. I hold e poned o ha he hgh aly o he aphaled oad eon eaed laed a ISO la A, wh a Sd n wave-lengh vale o ee, gven a 6 8 o he geoe ean and a IRI Inenaonal Roghne Index o.9. Thee vale wee ed a vehle exaon n he eeny doan. Cla ne n Road Cla Tale 4. Road Cla Roghne. Sd n A -6 S RMSn B - S RMSn A B C D E F G H O.: A : Geoe Mean; B : vale; n ee, o ISO 868. Condeng he paveen eglae a an egod aonay ando poe, deed y he noal don, he evenne deny an e expeed y he oghne oo ean J. o he Ba. So. o Meh. S. Eng. Copygh y ABCM Jly-Sepee, Vol. XXXIII, No. / 5

5 Roeo Spnola Baoa ae vale -vale. Aodng o he Peeval heoe Oppenhe, 975, he -vale o a noally ded ando veal dplaeen oghne eal o he ae oo o he powe peal deny. Theeoe, y ang he ae oo o he pevo expeon, one ge: n n / S RMS n Sd n Sd no / o 6 whee he logah lope hange o, whh hal o he nlnaon o Sd ϖ db pe deade. Vehle/Road Ineaon The vehle naal ehavo expeed y eeny doan epone non Baoa, 998. The paveen eglae ae expeed y paal eeny /pae. In he peen analy, he oad paveen ondeed a gd ae. The elaonhp eween e eeny ω and he paal eeny n he vehle peed V, ply gven y: ω V n 7 whee ω eeny n He, n /λ he nvee o he wavelengh n ee and V vehle peed n ee pe eond. By anong Sn no he eeny doan, one ge: ω / ω S ω S 8 n o o Aodng o he heoy o oha poe, he op o a lnea e-nvaan ye a aonay ando poe he np alo a aonay ando poe. In o ae, he paveen oghne old e deed a a eo ean Gaan egod ando poe Newland, 984. Hene, he epone o he hal-a ye alo a eo ean Gaan aonay ando poe. The elaonhp eween he PSD o he ye epone Hω and he PSD o he ye exaon Sω expeed y: G ω H ω S ω and G ω H ω S ω 9 whee G ω and G ω ae he powe peal dene o he vehle veal dplaeen epone and he angla epone o he png a, epevely. penon naal eeny ange. Th ee agne he expeed aeleaon ponene aond H, whh ay ae doo o paenge. Magnde Feeny Repone Speed 5.6 /h Veal Angla PSD Ta Feeny H Fge. Vehle neane non o npaved a. Fge how he agnde o he deny non o he veal and angla aeleaon o he vehle dng a /h on he aphaled oad. Magnde Feeny Repone Speed /h Veal Angla PSD Ta Feeny H Fge. Vehle neane non n aphal oad a /h. Sae Ieglae Sω np Vehle Reepane Hω op Fge 9. Blo daga non. Vehle Reepane Repone de o a Gω Hω Sω Applyng h anoaon o he vehle neane non I ω and I ω, he ollowng expeon an e oaned: GI ω ω I ω S ω and GI ω ω I ω S ω The agnde o he deny non o he veal and angla aeleaon o he vehle dng on he npaved a a 5 /h 7 /, hown n Fge. I an oeved n h ge ha he o evee wavelengh onen o he npaved a eon, whh eween.4 and.9 ee, onde wh he A vehle wll e vey epve o paveen oghne wh wavelengh onen n he ange ao.85 and 4 λ V / ω wheneve avelng a /h, whh wll e deenal o he vehle peoane. Theeoe, vehle penon nng poe an e oped agan vaon and a pealed anenane nevenon an pode he e o/ene ao eween oo and he aon o wo. Say and Conlon A ehodology wa peened o evalae vehle/ogh-oad dyna neaon. Th ehodology aed on he odal vehle eeny epone non and he aal depon o he geoey o he ogh. Fly, a hal-vehle dyna odel wh a wo-pon delayed ae exaon wa deved. Seondly, wo-oad eon ae elevaon wee eaed wh a peal eeened eang deve. The vehle neane non wa hen oaned. 6 / Vol. XXXIII, No., Jly-Sepee ABCM

6 Vehle Dyna Repone De o Paveen Roghne The neane non elaed o he paenge oo and an e ed o degn ppoe. The veal and angla vehle ody ane non wee allaed wh he ae eeny eglae non n he eeny doan a np. The eaed oad wa a.4 long eon o an npaved a and he eond wa a. long eon o good aly aphaled oad. The geoeal daa olleed wa hen poeed o oan a peal oadand don wh wavelengh eween and. n e o peod oghne wavelengh. The wde ange o wavelengh h oaned npeedened, ondeng ha he adonal eang deve have a eed oevale and. The eaed aphaled oad eon ha an IRI o.9 and an e laed aodng o ISO ea a level A. The eaed npaved oad eon ha a peal gnae don wh onenaon eween.4 and.9. A wo o-o-phae delayed vehle np wa ondeed oepondng o he on and ea wheel poon, y applyng he eaed a oghne deny non. The neane non wa oaned o he veal and angla vehle ody oon. Condeng he low peed 5.6 /h, he vehle penon ode agned de o he npaved a gnae. In he aphaled a, a hgh peed /h, he vehle vaon ode ha a gnan oon aplaon, whh ay ae doo o paenge. The developed ehodologe exend he eeny o vehle neal laon ool, wh he powe o povdng vehle eeny epone analy de o he paveen oghne aally deed. Rel allow he evalaon o paenge doo. A oe oplex odel o adde vehle-paveen neaon an e deved aed on a ple o degee o eedo ye ondeed y he peen dy. B,, loe, oplee vehle and ohe oplex penon ype wll e nvegaed n e eeahe. Fo hee ae, a wo-denonal paveen ao-oelaon oghne non wll e neeay. Alo, he han oo ehavo aodng o ISO 6 ay e nlded n h analy o he oplee yle o vaon popagaon. Anowledgeen The aho wold le o han he valale onon o Poeo Edlon Taa and Maelo Baa. The aho whe o anowledge he ppo o h eeah povded y he Mehanal Engneeng Depaen o he Polyehn Shool Unvey o São Palo. Reeene Baoa, R.S., 998, Ineação Veílo/Paveno, Conoo e Segança Vela, ª Renão Anal de Pavenação, Aoação Balea de Paveno ABPv. Vol., São Palo, Bal, pp Baoa, R.S., 999, Aplação de Sea Mlopo na Dnâa de Veílo Gado. PhD. Thee. Unvedade de São Palo USP, São Palo, Bal, 7 p. Baoa, R.S. and Coa, A.,, Saey Vehle Ta Speed, IX Inenaonal Sypo on Dyna Pole o Mehan, IX DINAME, Aoação Balea de Cêna Meâna ABCM, Floanópol, Sana Caana, Bal. Bogg, C., Sohwad, S. and Ahadan, M., 9, Applaon o Sye Idenaon o Een Spenon Tnng n Hgh-Peoane Vehle: Fll-Ca Model Sdy, SAE Doen Ne: 9--4 n he Boo Te and Wheel Tehnology and Vehle Dyna and Slaon, Pod Code: SP-, 44 p. Ceon, D., 999, Hand Boo o Vehle-Road Ineaon, Swe elnge Plhe, Neheland, 589 p. Coa, A. 99, Applaon o Mlody Sye MBS Modelng Tehne o Aoove Vehle Cha Slaon o Moon Conol Sde, Doo o Phloophy n Engneeng, Unvey o Waw, England. Felío,.C., 7 Modelage da Dnâa de Sea e Edo da Repoa, Edoa Ra, São Calo, São Palo, Bal, 55 p. ISO 866 Inenaonal Oganaon o Sandadaon, 995, Mehanal Vaon Road Sae Pole - Repong o Meaed Daa, Inenaonal Sandad ISO-868:995, p. Newland, D.E., 984, An nodon o ando vaon and peal analy, nd Edon, ongan Sen Tehnal, New Yo, 77 p. Oppenhe, A.V., Shae, R.W., 975, Dgal Sgnal Poeng, Pene-Hall Plhe, 556 p. Paveo, 9, The Paveen Roghne Meang Sye, e: nene ny on ay 9. Sn,., Deng, X., 998, Pedng Veal Dyna oad Caed y Vehle-Paveen Ineaon, Jonal o Tanpoaon Engneeng, Vol. 4, No. 5, pp Sn,., o, F., 7, Nonaonay Dyna Paveen oad Geneaed y Vehle Tavelng a Vayng Speed, Jonal o Tanpoaon Engneeng ASCE, Vol., pp Slva, J.G.S., Roehl, J..P., 999, Poal Folaon o he Analy o Hghway Bdge De wh Iegla paveen Sae, Jonal o he Balan Soey o Mehanal Sene and Engneeng ABCM, Vol. XXI, No., Bal, pp Vlela, D., Taa, E.H., 5, Opaon o Vehle Spenon Ung Ro Engneeng Mehod and Repone Sae Mehodology, Poeedng o The Inenaonal Sypo on Dyna Pole o Mehan DINAME. São Palo, Bal. Vlela, D.,, Aplação de Méodo Néo de Oação ao Polea Conjno da Dgldade e Conoo Vela, Tee de Dooado na Unvedade de São Palo, Bal, 5 p. J. o he Ba. So. o Meh. S. Eng. Copygh y ABCM Jly-Sepee, Vol. XXXIII, No. / 7