OPTIMIZATION OF THE VERTICAL COMFORT AND SAFETY OF A GROUND VEHICLE

Transcription

1 Proceeding of COE 7 Copyright 7 by AC 19th International Congre of echanical Engineering November 5-9, 7, raília, DF OPTIIZATION OF THE VERTICAL COFORT AND SAFETY OF A GROUND VEHICLE Walter Je Pacar Caa, walter.pacar.caa@g.br arício atti, maricio.matti@g.br Venâncio Láaro atalhone Neto, batalhone-@bol.com.br Univeridade Federal do Rio Grande do Sl, Departamento de Engenharia ecânica, Ra Sarmento Leite 45, CEP 95-17, Porto Alegre RS, rail Abtract. A nonlinear optimiation methodology i applied to improve the vertical dynamic involving comfort and afety of grond vehicle implemented with paive penion. The methodology take advantage of the fmincon algorithm of ATLA to find the minimm of a contrained nonlinear mltivariable fnction and the vehicle model i developed throgh the dynamic of mltibody ytem. The deign variable inclde penion parameter ch a the tiffne and the damping coefficient. Some inpt are conidered fixed throghot the optimiation, ch a the random profile of a econdary road of very low qality. The obtained relt how that the nonlinear optimiation algorithm i an adeqate tool for improving the vertical comfort and afety of grond vehicle. eyword: vehicle dynamic, vertical comfort and afety, nonlinear optimiation, paive penion. 1. INTRODUCTION The behavior of the vertical dynamic of a vehicle relt from a variety of interaction variable: the condctor, the type of vehicle, the involved load and the road where the vehicle tranit. The optimiation of the vertical dynamic of a vehicle i directly involved with the improvement of the comfort and the afety, and indirectly with the redction of the damage to the road. The determination of the parameter that inflence the dynamic of the vehicle are baed on relt of laboratory, field tet and till in comptational imlation. Thi work look for the optimal vertical dynamic behavior, where the variable of the problem are the coefficient of damping and tiffne of the penion. For doing that, a complete vehicle i modeled and bmitted to a random excitation of the road. To decribe the dynamic of the vehicle, one model with even degree of freedom i conidered, where the penion are independent between them.. VEHICLE ODEL For the mathematical analyi of the problem, a complete model of the vehicle with even degree of freedom i adopted, baed on the propoal of Ikenaga et al. () and ed by otta and Zampieri (5). The model conit in a prng ma (body of the vehicle) linked to for nprng mae (axle of the vehicle), a hown in Fig. 1 and conidering the definition of variable according to Tab...1. Dynamic eqation The dynamic eqation of the model are, Ikenaga et al. (): Vertical movement of the body: && g ( ( a a b b ) ( ) θ ( a a b b )θ& ) (1) Pitch movement of the body: I yy ( a && θ = ( a a a a a b b a b b a ) ( a ) θ ( a b a a b b b b b b ) ) & θ b ()

2 Roll movement of the body: I xx && ϕ =,5w,5w,5w ( (,5w,5w ) & ϕ,5w ) ϕ,5w,5w,5w,5w (3) Vertical movement of the left front axle: ( && ) g a rfl θ a & θ,5w ϕ,5w (4) Vertical movement of the right front axle: ( && ) g a rfr θ a & θ,5w ϕ,5w (5) Vertical movement of the left rear axle: ( && ) g b rrl θ b & θ,5w ϕ,5w (6) Vertical movement of the right rear axle: ( && ) g b rrr θ b & θ,5w ϕ,5w (7) Z rear right Z Z Zrrr Z Z roll ϕ X front Z Zrfr Centro de Gravidade Z pitch θ Y left Z Zrrl Z Zrfl Figre 1. Vehicle model with even degree of freedom, Ikenaga et al. ().

3 Proceeding of COE 7 Copyright 7 by AC 19th International Congre of echanical Engineering November 5-9, 7, raília, DF.. Vehicle excitement For achievement of the road roghne profile to be ed in the dynamic analyi it i applied the Power Spectral Denity (PSD) Fnction method, given by the Eq. (8) in m 3 /cycle, according to Dodd and Robon (1973). Thi method e experimental crve of pectral denity for the characteriation of typical road roghne profile. In thi cae, it wa ed the claification of road and parameter a propoed by Dodd and Robon (1973). Seeing that the vehicle in analyi mt pport any cla of road, it wa adopted the profile of econdary road in order to impoe the mot evere condition. The characteritic vale of the econdary road ed to determine the road profile are hown in Tab. 1. Table 1. Characteritic parameter of econdary road. Road cla Qality c x 1-8 (m³/cycle) w 1 w Secondary road edim 18 Low 51 Very low where the experimental roghne index c i aociated to the road qality, n i the wave nmber, and w 1 and w are mean vale of the road qality. In thi work, the PSD fnction i a implified adaptation where w 1 and w are amed both eqal to another variable w, taken a.5. w G ( n) = c n (8) One random road profile i applied to the left tire and another one to the right tire. Alo, the front and the rear tire are expoed to the ame road profile, bt the fnction of the rear tire i delayed relative to the front ignal. The vehicle move with a velocity of 6 km/h and the power pectral denity crve i compoed by 1 component. The ditance between the front tire and the rear one of the vehicle i eqal to.5654 m. The road roghne profile or vertical excitation for each tire can be oberved in Fig. and 3. Figre. Roghne profile for a econdary road of very low qality acting at the front tire.

4 Figre 3. Roghne profile for a econdary road of very low qality acting at the rear tire. 3. PARAETERS OPTIIZATION OF THE PASSIVE SUSPENSION In order to perform the optimiation of the vertical dynamic of the vehicle, Rill (4) propoe one merit fnction combining comfort and afety part a expreed by the Eq. (9), where the gravitational acceleration g and the tire preload F T were ed to weight the comfort and afety part. inimie & g t n & G = c t i g FT dt (9) The firt two term of the Eq. (9) are aociated with the comfort and the lat one with the afety. Then, the adopted objective fnction to optimie i given by the Eq. (1). inimie n {, } R bject to : Gc ( ) ( ) ( ) = tn ti min min min && g < < ( ) < < < ( ) < ( ) max max max g FT dt (1) where, & : acceleration of the prng ma, (m/ ), : tiffne coefficient of the penion, (N/m), : vertical diplacement of the prng ma, (m), : prng ma, (kg), : damping coefficient of the penion, (N/(m/)), : vertical diplacement of the nprng ma, (m), : nprng ma, (kg); : vertical tire tiffne, (N/m); F : tire preload eqal to ( )g, (kg); T In thi work, the optimiation variable are the tiffne and the damping coefficient of the penion, tarting with the initial vale from He (3) and conidering the bond given by the Tab.. The minimiation i realied throgh the fmincon atlab fnction, which attempt to find a contrained minimm of a calar fnction of everal variable tarting at an initial etimate. The problem i referred to a contrained nonlinear optimiation or nonlinear programming. 4. RESULTS ANALYSIS For the objective fnction given by the Eq. (1), the Tab. 3 how the coefficient of tiffne and damping for the penion before and after the optimiation. It i oberved that the optimied vale of the damping coefficient are

5 Proceeding of COE 7 Copyright 7 by AC 19th International Congre of echanical Engineering November 5-9, 7, raília, DF cloe to the lower bond of the variable, indicating that the fnction i directly proportional to thee coefficient. The initial vale of the objective fnction i and after the optimiation i eqal to Table. Vehicle parameter. Variable Decription Unit Vale ond Stiffne of the left front penion N/m Stiffne of the right front tiffne N/m Stiffne of the left rear penion N/m Stiffne of the right rear penion N/m Damping of the left front penion N/(m/) Damping of the right front penion N/(m/) Damping of the left rear penion N/(m/) Damping of the right rear penion N/(m/) Front or rear tire tiffne N/m Sprng or body ma kg Left front nprng ma kg Right front nprng ma kg Left rear nprng ma kg Right rear nprng ma kg Vertical diplacement of the nprng ma m e-6 Table 3. Spenion coefficient. Coefficient Decription Initial vale Optimied vale, Damping of the front penion 17 N/(m/) 8 N/(m/), Damping of the rear penion 141 N/(m/) 8 N/(m/), Stiffne of the front penion 998 N/m 9885 N/m, Stiffne of the rear penion 1195 N/m 11 N/m Some comparative relt are hown in Fig. 4 to 6. Figre 4 how the comparative in body acceleration before and after the optimiation. Althogh the crve of acceleration eem imilar, the RS vale before optimiation i eqal to 6.71 and after optimiation i eqal to 6.36, indicating 5.% of redction in 3 econd of imlation. Figre 5 how the comparative in body velocity before and after the optimiation. Althogh for the firt econd of imlation the modle of the optimied velocity grow de to the eqilibrim tabiliation, it poterior behavior how a redction in ocillation if compared with the non-optimied vale. Figre 6 how the comparative in body diplacement before and after the optimiation. Althogh the optimied vale initially how the diplacement larger than the non-optimied cae becae of the le rigid penion, it poterior behavior how a redction in the amplitde of ocillation if compared with the non optimied vale. Finally, it i oberved that thi work look for the ame et of coefficient for the front penion and another for the rear one, with the practical prpoe of dipoing with two type of penion.

6 Acceleration (m/^) ,5 1 1,5,5 3 3,5 Time () Not optimied Optimied Figre 4. Comparative of body acceleration. Velocity (m/),6,4, -, -,4 -,6 -,8-1 -1,,5 1 1,5,5 3 3,5 Time () Not optimied Optimied Figre 5. Comparative of body velocity. -,5 Diplacement (m) -,1 -,15 -, -,5,5 1 1,5,5 3 3,5 Time () Not optimied Optimied Figre 6. Comparative of body diplacement.

7 Proceeding of COE 7 Copyright 7 by AC 19th International Congre of echanical Engineering November 5-9, 7, raília, DF 5. CONCLUSIONS The vehicle comfort aociated with the vertical dynamic i optimied modifying the coefficient of tiffne and damping of the penion. It i oberved that the optimied vale of the damping coefficient are cloe to the lower bond of the variable, indicating that the objective fnction i proportional to thee coefficient. Incorporating one retriction aociated with the penion pring travel mt modify thi condition. Althogh the crve of body acceleration eem imilar, the RS vale before optimiation i eqal to 6.71 and after optimiation i eqal to 6.4, indicating 7% of redction dring 3 econd of imlation. The comparative in body velocity before and after the optimiation how that for the firt econd of imlation the abolte vale of the optimied velocity grow becae of the eqilibrim tabiliation, bt it poterior behavior how a redction in the ocillation if compared with the non optimied vale. The comparative in body diplacement before and after the optimiation how that for the firt econd of imlation the optimied vale i larger than the non optimied cae becae of the le rigid penion. Alo, it poterior behavior how a redction in the amplitde of the ocillation if compared with the non optimied vale. 6. ACNOWLEDGEENTS The accomplihment of thi work conted with one cientific reearch cholarhip, PIIC CNPq-UFRGS (.) and IC/FAPERGS (V.L..N.). 7. REFERENCES Dodd, C.J. and Robon, J.D., 1973, The Decription of Road Srface Roghne, Jornal of Sond and Vibration, Vol. 31, pp He, Y., 3, Deign of Rail Vehicle with Paive and Active Spenion Uing ltidiciplinary Optimiation, ltibody Dynamic, and Genetic Algorithm, Ph.D. Thei in echanical Engineering, Univerity of Waterloo, Ontario, Canada. Ikenaga, S., Lewi, F.L., Campo, J. and Davi, L.,, Active Spenion Control of Grond Vehicle aed on a Fll-Vehicle odel, Proceeding of the American Control Conference, Chicago, Illinoi, pp otta, D.D.S. and Zampieri, D.E., 5, odeling of a Vehicle Spenion with Non Linear Element and Performance Comparion to a Semi-Active odel, Proceeding of the 18 th International Congre of echanical Engineering, Oro Preto, G, rail. Rill, G., 4, Vehicle Dynamic. Lectre Note, Fachhochchle Regenbrg Univerity of Applied Science. 8. RESPONSIILITY NOTICE The athor are the only reponible for the printed material inclded in thi paper.