MODELING OF DYNAMIC FORCES OF A TRACTOR AND THREE-POINT HITCHED IMPLEMENT IN THE MATLAB-SIMULINK PROGRAM ENVIRONMENT 1

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1 TEKA Kom. Mo. Energ. Roln., 006, 6, 9 33 MODELING OF DYNAMIC FORCES OF A TRACTOR AND THREE-POINT HITCHED IMPLEMENT IN THE MATLAB-SIMULINK PROGRAM ENVIRONMENT Konny Juiucuk, Zbigniew Kmińki Dermen of Auomoive Vehicle, Biłyok Univeriy of Technology Summmry. The yem of rcor wih hiched imlemen (THI) h been modeled in he MATLAB-SIMULINK rogrm wih he hel of mhemicl yem model. The exemlry reul of imulive exlorion of dynmic lod of he ggrege wheel re reened. Key word: rcor, biliy, eerbiliy INTRODUCTION Sfe uge of uni, eecilly hoe wih hree-oin hiched imlemen (THI) on he bck i condiioned fir of ll by: muul fiing of he rcor nd ool from he oin of view of he lif cciy, he rcor biliy minennce fer he ool rie, biliy nd conrollbiliy minennce of rcor-imlemen ggrege while mneuvering on he field nd rnorion croing. The execuion of he ler condiion h riculr imornce for he fey of rod rffic nd he roviding of he fe condiion of work for he inrumen oeror. The bic crierion of biliy ued in rcice i he requiremen of minennce of defined vlue of ic lod R of rcor ggrege fron wheel, for in. R ( )G [Kucewki 968], R (G c L u )/L [Meyer 956], R (G c L c k)/l [Merin nd Ulrich 978], where: G c weigh of rcor; G weigh of rcor ggrege; L u condiioned dince of m cener from bck xel wheel of rcor, L u = 0.5 m; L xel be of rcor; L c dince of m cener from bck xel wheel of rcor; k = ( ) emiric coefficien, i vlue reened bove re ued for rcor exloied on mounin ie. Since he k of he definiion of ic lod of fron wheel of ggrege i imly olved on he bi of ic, he eimion of he conneced dynmic lod require he licion of numeric imulion mehod. Uing clicl mhemicl model of rcor uenion, i block cheme h been conruced in he rogrm Mlb-Simulink. The dynmic yem obined in hi wy h i inu. Through he inu he mooring eed nd he funcion which decribe he rod roughne under he wheel re e. The ouu i defined in he form of liner nd ngle dilcemen of ggrege nd rod groundwork recion on he wheel. The work w onored by Recor rojec W/WM/7/03

2 30 Konny Juiucuk, Zbigniew Kmińki A MATHEMATICAL MODEL OF TRACTOR OSCILLATION For he decriion of dynmic lod he clic fl mechnicl yem w ued [Chodkowki 98]. I w umed, h he vehicle move recilinerly on he rod wih he me rod roughne under he wheel of boh lef nd righ ide of he ggrege, nd he ggrege m i diribued ymmericlly concerning i cenrl lne. Beide, i w umed h he join of he rcor nd hiched imlemen on (THI) i inflexible. Therefore, he ggrege i regrded he iff body. The model of ggrege comoed from ringing m m wih he cener in S oin nd ineri momen I i hown in Fig.. Fig.. The hyicl model of he iff join of he ggrege: rcor-hiched-imlemen A he me ime i i umed h in he comoiion of he ringing m he me of vehicle wheel re included. I er from he bence of he clic mouning of he vehicle wheel. The ringing m i conneced wih weighle ire which i chrceried by boh iffne coefficien of ire of fron nd bck wheel k nd k nd coefficien of ire dming c nd c. The model locion in coordine x, define: roion ngle ϕ, vericl dilcemen of m m cener, vericl dilcemen nd in he lne of fron nd bck xel. We cn obin he following differenil equion from he equilibrium condiion of force rojecion on 0 xi nd from he equilibrium condiion of momen of force concerning he xi which goe hrough he m cener S nd orhogonl o 0x lne: m && I ϕ& & = R = R + R G L + R L where: L, L re he dince of m cener from he wheel of fron nd bck xel correondenly; G force of grviy of he ggrege. ()

3 MODELING OF DYNAMIC FORCES OF A TRACTOR... 3 Dynmic recion of he rod groundwork on he wheel of fron R nd bck R xel re decribed by he deendence: R = k R = k ( q ) + c ( q& & ) where: q, q kinemicl inu on he wheel of fron nd bck xel. ( q ) + c ( q& & ) () There re he following deendence beween dilcemen of m cener of ggrege, roion ngle φ nd dilcemen, of vehicle xel: = = L ϕ L L + L, = + L ϕ ϕ = L, (3) Afer he ubiuion of he exreion () nd (3) o () we obin he equion of he ggrege dynmic which re he be for elborion of Mlb-Simulink model (Fig. ). Ech equion i rereened by one of he wo min line in he ubyem uenion. The min line of he model correond o he wo degree of freedom of he ggrege nd re couled. Trnor Dely block relie he inu dely of bck xel ccording o driving velociy v nd xel be of rcor. The worked ou model llow for he choice of one of he hree inu ignl which rereen he obcle overcome by he ggrege. Thee re: inuoidl hum of he given heigh nd be widh, e he of given heigh nd irregulriy of ochic chrcer (coefficien k o i he meure of rod quliy, nd coefficien w o = 0/v deend on he driving velociy v). Rndom Number grb x g(x) v [m] x g(x) Schem modelu do ymulcji Wym. loowe ko wo.+ Clock krwęŝnik min wymueni Wyn min wymueni. Fi.. q(x) R R R R Zwieenie Mux Cier gregu G L 6 R 5 R 8 R L L L 7 R q(x) /(m) R R R R Podyem "Zwieenie" Rekcje-rod Rekcje-yl fi -/(J) q q 3. fi 4. Trnor Dely fi. L fi. L Fig.. The model cheme for imulion nd rucurl cheme of uenion ubyem

4 3 Konny Juiucuk, Zbigniew Kmińki The reul of imulion re obined on he ouu of uenion ubyem: ime run of vericl nd ngle dilcemen of ggrege body nd dynmic recion of rod groundwork. EXEMPLARY RESULTS OF SIMULATION EXPLORATIONS For imulion exlorion he rcor of 50 kw ower, xel be L =.5 m nd own m of m c = 800 kg w choen. The following rmeer of ire were cceed: k =. 0 5 N/m, k = N/m, c =. 0 3 N/m i c = N/m. The exlorion w bed on he definiion of ime run of longiudinl vibrion nd wheel lod of ggrege while driving wih vriou velociy hrough obcle. Runge Ku mehod w ued in he imulion cceing miniml inegrion e, 0.0 mximl inegrion e nd olernce equl o 0-6. Exemlry exlorion reul for unloded rcor nd ggrege rcor-mouning-ool re hown in Fig. 3. Fig. 3. Exemlry reul of ggrege exlorion while ing he inuoidl hum of 0.05 m heigh nd 0.5 m be widh wih he velociy of 0 km/h:, c, e for unloded rcor (m c = 800 kg, I = 800 kg m, L = 0.74 m); b,d,f for ggrege wih hihed imlemen (m c = 3740 kg, I = 080 kg m, L = 0.3 m)

5 MODELING OF DYNAMIC FORCES OF A TRACTOR In he ce of ing of unloded rcor hrough inuoidl obcle he vericl dilcemen of fron i bigger hn in he ce of ggrege ing. The obviou dechmen of fron xel wheel from rod urfce ke lce. Th men h he imely lo of rcor eerbiliy er. Reducion of vericl dilcemen come quicker wih relion o he ggrege ing ime. Recion vlue on fron xel wheel come under much more coniderble ocillion nd i chrceried by higher frequency hn in he ce of ggrege. CONCLUSIONS Sic mehod of he deecion of rod groundwork recion imc on he wheel of rcor fron xel re only of n exemlry chrcer. The mehod don ke ino ccoun he dynmic of he rcor nd i hiched imlemen hyicl yem. The moion biliy modeling in yem rcor-imlemen he yem wih differen conrucion wih elemen which work in differen condiion require o ke ino ccoun he ecrum of lod of rcor wih hree-oin mouning imlemen (THI). The lod re he reul of kinemicl inu which deend on rod rofile. The reened in he work exemlry reul of behviour imulion in rcor fron xel under n influence of inuoidl inu re o be regrded he conribuion o he following exlorion of widely underood biliy of he rcor-imlemen yem. Furher reerch on he defining of n influence of m rmeer of hiched imlemen nd fron bll on he wheel lod of he ggrege while ing hrough differen obcle will be conduced fer he verificion of he decribed mhemicl model. REFERENCES Chodkowki A.W. 98: Bdni modelowe ojdów gąienicowych i kołowych. WKiŁ, Wrw. Kucewki J. 968: Podwy eklocji gregów rolnicych. PWRiL, Wrw. Meyer H. 956: Zur Problemik de Selnhnger fur Ackerchleer. Lnd. Forchung Bd. 6, Von Merin K.H., A.Ulrich A. 978: Zur Frge der Lenkicherhei von Ackerchleern mi Anbugeren bei SrBenfhr. Grundl. Lndechnik Bd. 8, 3.