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A study of the eect of rear suspension auxiliary rolldamping on vehicle-handling dynamicsE Uzunsoy and O A Olatunbosun*Department of Mechanical Engineering, The University of Birmingham, Birmingham, UK

The manuscript was received on 21 April 2004 and was accepted after revision for publication on 24 August 2004.

DOI: 10.1243/095440705X6523

Abstract: The handling dynamics of a University of Birmingham Racing Formula Student racing car,incorporating a novel rear suspension load transfer system which provides auxiliary roll damping, ismodelled using a simulation tool, HANDSIM, developed for vehicle-handling studies, and the eectof the system on the vehicles handling performance is discussed by considering the results obtainedfrom the simulation. The aim of implementing this suspension load transfer system is to improve thehandling characteristics of the vehicle in severe cornering manoeuvres.

Keywords: vehicle-handling dynamics, suspension system, simulation, fuzzy logic control, drivermodel

1 INTRODUCTION 2 TYRE AND VEHICLE MODEL

A four-degree-of-freedom vehiclemodel is used in thisThis paper discusses the eects of a rear suspensionstudy. The model takes into account lateral, yaw, roll,load transfer mechanism, featuring a pair of auxiliaryand longitudinal motions, enabling the inclusion ofdampers which provide roll damping only, on thetraction and braking forces on handling manoeuvres.general handling dynamics of a Formula StudentThe model considers the vehicle as travelling atracing car. The handling responses of the vehicle withconstant speed with small corrective braking andthe modied suspension system (including rear sus-tractive force inputs provided under the control ofpension auxiliary roll dampers) are compared witha fuzzy logic controller [1]. In accordance with thisthose with the normal suspension system (i.e. with-act, a fuzzy path planning method representing anout the auxiliary dampers). Both the front and theintelligent driver model [2] is used to create therear suspension systems are modelled to determinevehicle simulation path. The fuzzy controller consiststhe complete eect of the suspension system on theof three inputs related to the vehicle orientation fromvehicle-handling dynamics. While the front suspen-the drivers point of view and six outputs represent-sion system is an application of the double-wishboneing the steering angle, braking pressure applied todesign, the rear suspension is a combination of aeach wheel, and throttle position. A very general owconventional double wishbone and two diagonallydiagram of the vehicle model and fuzzy pilot inter-mounted additional damper units, referred to as theaction is shown in Fig. 1. The outputs provided byrear load transfer mechanism. The kinematics ofthe vehicle model block (heading, yaw, roll, etc.) areboth systems are analysed using the velocity diagramprocessed in the fuzzy inputs block and then sentapproach. Then, a four-degree-of-freedom vehicleto the fuzzy logic controller block. The controller ismodel, including the roll motion, is used to analyseintended to react as a real driver; so it determinesthe eects of the suspension system in terms of thethe direction in which to turn the steering wheel,handling dynamics.and by how much, by considering the membershipfunctions of the relevant inputs. It also determinesany application of braking pressures or the throttle

* Corresponding author: Department of Mechanical Engineering, as appropriate. The vehicle model block is replace-Vehicle Dynamics Research Group, Birmingham University, able by any vehicle model regardless of its complexity.Edgbaston, Birmingham, B15 2TT, UK. email: o.a.olatunbosun@ The path that the vehicle is supposed to follow is

pre-mapped on the Earth xed coordinates [13].bham.ac.uk

D08004 IMechE 2005 Proc. IMechE. Vol. 219 Part D: J. Automobile Engineering

22 E Uzunsoy and O A Olatunbosun

Fig. 2 Forces acting on the vehicle: top view

Fig. 1 General ow diagram of the vehicle path vehicle during roll motion is represented by Fig. 3.planning

The force distribution at each wheel is derived fromboth Fig. 2 and Fig. 3 as shown by the equations

The pitching eects of the small corrective braking Fvof=0.5mfgand tractive forces and the longitudinal load transferare ignored. The basic equations are +

1

tf[muf(V+rU )hu+(Kwf+KwAroll)w+Cww]

Fx=m(U+rV) (1)

(9) F

y=m(V+rU ) (2)

Fvif=0.5mfgMz=I

zzr (3)

1

tf[muf(V+rU )hu+(Kwf+KwAroll)w+Cww]Mx=Ixx p (4)

Equations (1), (2), (3) and (4) can be written in a (10)more detailed form from Fig. 1 as

Fvor=0.5mrgm(UrV)=FxrL+FxrR+(FxfL+FxfR) cos dFbrLFbrR(FbfL+FbfR) cos d, +

1

tr[mur(V+rU )hu+Kwrw+(Cw+CwAux)w]

(FyfL+FyfR) sin d (5) (11)

m(V+rU )=FyrL+FyrR+(FyfL+FyfR) cos d

Fvir=0.5mrg+(FxfL+FxfR) sin d,(FbfL+FbfR) sin d (6)

1

tr[mur(V+rU )hu+Kwrw+(Cw+CwAux)w]

Ixxp=ms(V+rU )(hcghrc)+msg(hcghrc)w (12)C

wwK

ww (7)

and

Izzr=a(F

yfL+FyfR) cos d+tf2(F

yfLFyfR) sin d+,

+a(FxfL+FxfR) sin d

+tr2(FbrLFbrRFxrL+FxrR),

b(FyrL+FyrR)

tf2(F

xfL+FbfRFxfRFbfL)

cos da(FbfR+FbfL) sin d (8)

respectively.Figure 2 shows the forces acting on a vehicle

Fig. 3 Force analysis of a vehicle during roll motionduring yaw motion while the force analysis of a

D08004 IMechE 2005Proc. IMechE. Vol. 219 Part D: J. Automobile Engineering

23Rear suspension auxiliary roll damping

Fig. 4 Tyre characteristics for a Goodyear 20.06.5-13 tyre [4] for Formula SAE racing cars

The tyre-cornering characteristics are providedby interpolation of measured data. Tyre data wereobtained from Goodyear Tyres [4] (Fig. 4) for aGoodyear 20.06.5-13 tyre which is specicallyproduced for Formula SAE racing cars.

3 VEHICLE SUSPENSION SYSTEM ANDANALYSIS

The Formula Student car (Car 201) (Fig. 5) suspen-sion system is of a double-wishbone design at boththe front and the rear. While the front suspensionsystem also includes an anti-roll bar, the rear design,which is the main subject of this study, includestwo diagonally mounted dampers (Fig. 6) aimed at

Fig. 6 Rear suspension (diagonal damper) load transferimproving the handling properties of the vehicle bymechanism: front viewproviding auxiliary damping in roll only.

The main objective for modifying the rear sus-pension system is instantaneously to produce highroll stiness at the rear of the vehicle by the actionof the diagonal dampers at the beginning of a turn.This instantaneously results in oversteer character-istics, which enables the car to turn into the cornerquickly. As the extra roll stiness due to the diagonaldampers is removed, the handling characteristicsrevert to understeer, giving the driver the condenceto accelerate out of the corner.

The velocity diagram approach is used to analysethe kinematics of both front and rear suspensionsystems. The velocity diagram to provide the ratiobetween the wheel and springdamper motions wasderived from the drawings of the suspension systemsusing the computer aided design software Solidworks

Fig. 5 Car 201 2003A . In the classical double-wishbone suspension



system, the springdamper system is assumed to bein the same vertical axis as the tyres for simplicity.All suspensions are functionally equivalent to a pairof springs and dampers, as shown in Fig. 3. Thelateral separation of the springs causes them todevelop a roll resisting moment proportional to thedierence in roll angle between the body and axle.The stiness is given by

Kw= 1

2Kss2 (13)

The velocity diagram approach reduces any typeof springdamper placement to the classical systemby providing the motion ratios. In this graphicalanalysis method [57] of the suspension behaviour,roll characteristics are determined about an arbitrarypoint, which does not move as the body rotates.In the classical velocity diagram approach, the dia-gram starts from the roll centre. However, for eachincrement in the roll angle, it is necessary to updatethe diagram. This need could be eliminated byselecting an arbitrary point analysis instead. There-fore, the analysis presented here starts with theclassical approach rst (Fig. 7) to provide a referencevelocity to be used in the creation of the velocitydiagram as a result of the arbitrary point analysis

Fig. 8 Complete velocity diagram of the rear suspen-(Fig. 8). In Fig. 9, O is at the intersection of the vehicle sion systemcentre-line with the ground plane. XC is the linkwhich transfers the tyre forces to the main springdamper system (YZ) and the auxiliary damper (KL

2),

via the rocker. The rocker is expressed by its edgepoints: TLYKX. It rotates about the pivot point T.The inboard points of attachment of the suspensionlinks are A and B. The wheel contact point is O. Theposition of the roll centre is determined by extendingan imaginary axis from the suspension links AD andBC until a point of intersection is obtained.

A line from the intersection point through thepoint O cuts the centre line of the body at O, whichis the roll centre. The formation of the velocity dia-

Fig. 9 Rear suspension links and springdamper place-ment

gram (Fig. 8) starts from O with vectors ob and oain Fig. 7 perpendicular to OB and OA respectivelyin Figure 9, and also equal in length to these dis-tances by the assumption of a rotational velocity of1 rad/s. Similarly, ad is perpendicular to AD, and odis perpendicular to OD. In Fig. 7, only the signifi-cant vectors are shown for the analysis. In fact, thearbitrary point analysis is the rst step to obtain

Fig. 7 Velocity diagram (classical approach) the initially unknown vector measures [5]. By using



the measures from Fig. 7, then Fig. 8 can be obtained If it is assumed that positive and negative suspensionmovements are symmetrical, then the expressionto give the ratio of the spring to the wheel motions.

Considering the suspension shown in Fig. 9, an may be simplied [6] toarbitrary angular velocity is applied to the link BC.bc is perpendicular to BC, and ad is perpendicular qM

qw=2Kn2

w(21)

to AD (see Figs 8 and 9). Both a and b are points ofzero velocity and therefore coincident with o. Since

Since the springs and dampers are mounted concen-the length bc in Fig. 7 is known from the applicationtrically and have the same displacement, the sameof the arbitrary angular velocity to BC in Fig. 9,coecients are valid for the eective damping sti-similarly d is located since cd is perpendicular to CD;ness. Addition of the roll damping provided by theo is located since oc is perpendicular to OC, andauxiliary dampers results inod is perpendicular to OD.

By considering Figs 8 and 9, let [5] qMqw=2Cn2

w+2CAuxn2Aux (22)oy

oo=n (14)

Using the same approach outlined above, a similaranalysis is carried out on the front suspensionTherefore, the vertical force F

vcan be shown to be

geometry. If the numerical values obtained from theproportional to the spring force Fsaccording to

analyses are applied to equations (21) and (22), theFv=Fsn (15) resulting eective roll stiness K

wand roll damping

Cwfor both rear and front suspensions are presentedand

in Table 1. nw

is a constructive constant that isdetermined in the initial design studies (function ofqFv

qv=Fs

qnqvnqFsqv

(16)suspension geometry). Spring and damper rates arethe variable design parameters that can be modiedwhere v is the vertical displacement at o.after the initial design.Therefore,

Kv=qFvqv=AFs qnqv+Kn2B (17) 4 THE EFFECT OF ROCKER SHAPE ON LOAD

TRANSFERSince both suspension springs are involved, thesubscripts L and R are used and M is the moment

The ratio of the velocity vector of the auxiliaryabout the centre O and considering Fig. 9, let [5]damper to that of the tyre is the key element for the

n OO=nw

(18) amount of additional roll damping obtainable fromthe vehicles suspension [see equation (22) and the

From equation (15),velocity diagram in Fig. 8]. The higher the ratioobtained, the higher is the roll damping that can beM=FsL(nw)+FsR(+nw) (19)provided by the load transfer mechanism. Higher roll

Dierentiating equation (19) with respect to the roll damping leads to a higher transient load transfer atangle w gives the rear and this can result in an increased oversteer

characteristic and, as a result, an improved corneringqMqw=FsL

q(nw)

qw+FsR

q(+nw)

qw+(n

w)qFsLqw performance. A very simple design change to the

rockers is suggested to obtain higher roll dampingfrom the system, which did not seem to be eective+(+n

w)qFsRqw

(20)with the original design parameters. The rocker is

Table 1 Stiness and damping values obtained by the velocity diagram approach

Roll stiness Auxiliary stiness Roll damping Auxiliary damping(N m/rad) (N m/rad) (N m s/rad) (N m s/rad)

Front suspension 0.991Kf

3000 0.991Cf

Rear suspension 1.362K

r 1.362C

r0.188C

Aux



provided to transfer the vertical motion of the tyre extended points of the rocker instead of K and Xrespectively (Fig. 11a). The new shape of the rockerto the struts, which are expected to absorb the dis-

turbing force caused by the tyreroad interaction and is proposed as TLYKX instead of TLYKX.From equation (18) and the velocity diagram givento keep the tyre in contact with the road. In doing

this, a load transfer is also developed from the inner in Fig. 11b, the ratio nw=0.716. This ratio provides

4.096 times the auxiliary damping stiness of thetyre to the outer tyre of a vehicle in a corneringmanoeuvre. Therefore, from the given geometry of original design. The new coecients used in the cal-

culation of roll stiness and damping are presentedthe vehicles suspension system, rockers are importantin terms of providing the motion ratio between the in Table 2.

From the new resulting coecients, the newtyre and struts.The modied rear axle and rocker design are shown damper rates required in the modied suspension

system to provide the same damper stiness valuein Figs 10 and 11. Figure 11a shows the original andproposed rocker geometries while Fig. 11b presents as the original design are shown in Table 3. This table

provides much lower damper rates to be used insteadthe modied form of the velocity diagram which wasoriginally presented in Fig. 8. K and X show the new of those provided in the original design.

Fig. 10 Modied rear axle design for Car 201

Fig. 11 (a) Final modication for the rocker; (b) the resulting velocity diagram of the new rearsuspension system



Table 2 Stiness and damping values obtained by the velocity diagram approach

Roll stiness Auxiliary stiness Roll damping Auxiliary damping(N m/rad) (N m/rad) (N m s/rad) (N m s/rad)

Front suspension 0.991Kf

3000 0.991Cf

Rear suspension 1.704K

r 1.704C

r1.0253C

Aux

Table 3 Equivalent damper rates provided by thedesign modications

Auxiliary damper rates Equivalent damper rates(original design) (modied rear axle and rocker)(N s/m) (N s/m)

750 1831500 3663000 7326000 1464

10 000 2441

5 SIMULATION RESULTS AND DISCUSSION

Simulation of vehicle response was carried outusing a vehicle-handling dynamics simulation tool,

Fig. 13 Roll rate response of Car 201 at 43 km/hnamely HANDSIM, which was developed by theVehicle Technology Research Centre, Universityof Birmingham, using the MATLABASIMULINKAenvironment [8]. The simulation was carried out ata vehicle speed close to themaximum speed at whichthe vehicle can traverse the given path without lossof control. Vehicle speed is kept constant during themanoeuvre by a fuzzy logic controller. Figures 12 to16 show the vehicle responses of Car 201 with andwithout the rear suspension auxiliary damper loadtransfer mechanism. Car 201 has a front biasedweight distribution of 55 per cent front and 45 percent rear.

Fig. 14 Resulting vehicle trajectory at 48 km/h with2250 N s/m damper rate

5.1 Simulation results with the original vehicledesign parameters

The parameters used in the vehicle simulation aregiven in Table 4. The method is to run the simulationboth with and without the rear load transfer mech-anism. The auxiliary damper rate is set to variousvalues to observe the handling response of the carwith the mechanism. The vehicle has an intrinsicundersteer characteristic due to the weight distri-Fig. 12 Resulting vehicle trajectory for Car 201 at

43 km/h bution, which is 55 per cent front and 45 per cent



Table 4 Vehicle control and simulation parameters

Vehicle speed (constant) (km/h) 40Steer angle for constant-steer test (deg) 3

Path coordinates (m)X 0, 30, 60, 90, 120,

105, 70, 40Y 0, 8, 0, 12, 25, 70,

50, 80

Wheelbase (m)Front 0.742Rear 0.908

Track (m)Front 1.342Rear 1.28

Mass of vehicle (including driver) (kg) 300Roll inertia (kg m2) 20Yaw inertia (kg m2) 200

Fig. 15 Front lateral load transfer of the vehicle with Damper rate (N s/m)Front 750and without the auxiliary dampersRear 750

Auxiliary damper rate (N s/m) Variable

Spring rate (N/m)Front 22 000Rear 22 000

Anti-roll bar rate (N m/rad) 3000Height of centre of gravity (m) 0.285

Roll centre (m)Front 0.0093Rear 0.02325

Modied roll centre (m)Rear 0.01602

however, the positive eect of the system can onlybe obtained by using extremely high damper rates forCar 201 with its original design parameters. On theother hand, the need for these extreme damper rates

Fig. 16 Rear lateral load transfer of the vehicle with can be eliminated by modication of the motionand without the auxiliary dampersratio of the tyre to the struts. For this reason, therocker which is responsible for transferring the tyremotion to the struts and auxiliary dampers isrear. However, the longitudinal velocity of the vehicle

and lateral load transfer and also the resultant tyre redesigned to improve the motion ratio.slip angles determine the actual characteristics.

5.2 Results for the modied suspension system atconstant speed and variable path5.1.1 Vehicle-handling simulation at constant speed

and steer angleA simulation of the car traversing a winding circuitis carried out with the original and modied suspen-Figure 12 shows the resulting paths for a constant-

speed constant-steer-angle turn without the rear sion systems, respectively. Some of the results areshown in Figs 14 and 15. A slight path improvementload transfer mechanism and with it, using various

damping rates. The reductions in path radius pro- was achieved with the modied suspension systemin Fig. 14. A sample part from the lateral load transfervided by dierent auxiliary damper rates are shown

in the gure. The roll rate response of the vehicle is history of the vehicle (Figs 15 and 16) conrms theinitial increase in load transfer at the rear axleshown in Fig. 13.

The simulation results provided by constant steer (decreased load transfer at the front) with auxiliarydampers compared with the original suspension.angle and constant vehicle speed reveal important

information about Car 201. Firstly, even though the This produces a transient increase in the oversteertendency of the vehicle, which disappears once theeects due to the rear auxiliary dampers are small,

the theoretical basis explained is correct. Secondly, roll velocity reduces to a small value.



2 Uzunsoy, E. and Olatunbosun, O. A. A generic6 CONCLUSIONSfuzzy pilot and path planning for vehicle handlingdynamics simulation studies. In Proceedings of theCar 201 was designed to get round the twistingSAE International Conference on Future TransportationFormula SAEFormula Student circuits as quickly asTechnology, Costa Mesa, California, 2003, SAE paper

possible and safely. The load transfer mechanism 2003-01-2263.was designed for the rear suspension system to help 3 Uzunsoy, E. Application of fuzzy control in vehicleachieve this objective. The simulation results of handling simulation and path planning. PhD Dis-the original Car 201 discussed above show that the sertation, University of Birmingham, Birmingham,

2003.original design of the vehicle is not suitable enough4 Goodyear Tyres, Formula SAE tyre data: 20.06.5-13.for this purpose. Car 201 is an understeering vehicle

http://www.goodyear.com.which is not ideal in a racing car. However, this car5 Fenton, J. Handbook of Automotive Design Analysis,has been designed for the students who have little

1976 (Butterworth, London).opportunity to experience driving the car on the6 Ellis, J. R. Vehicle Dynamics, 1969 (London Business

track. Therefore, an understeering car which is easier Books Limited, London).to control at the limit of traction may be the best 7 Ellis, J. R. Vehicle Handling Dynamics, 1994 (Mech-choice in the circumstances. The design of the sus- anical Engineering Publications Limited, London).pension system very much aects the ride and hand- 8 Uzunsoy, E. and Olatunbosun, O. A. A new vehicle

handling dynamics simulation tool: HANDSIM. Inling properties of the vehicle. While a well-designedProceedings of the 7th Annual Research Symposiumrear load transfer mechanism can build an oversteer-of Postgraduate Research, University of Birmingham,ing tendency on an understeering vehicle, the rearMay 2001, pp. 2630.suspension geometry of Car 201 with its long sus-

pension links and narrow dierential box has beenshown not to be a good base for the rear load trans-fer mechanism. However, while keeping most of theexisting design, it has been possible to nd a cost APPENDIXeective solution through the redesign of the loadtransfer rocker to provide a more suitable wheel-to- Notationdamper velocity ratio. It has been shown that the

a distance from the front axle to therocker geometry is very important in load transfercentre of gravity (m)and the velocity diagram can be used to obtain a

b distance from the rear axle to thesuitable design.centre of gravity (m)Although a design change can also be made for

Cw

roll damping of the suspensionthe front suspension geometry, possible changesmay(N s/m)be limited due to the initially designed leg placement

d distance between the roll centre andof the driver. Also, this study was especially focusedthe centre of gravity (m)on the rear suspension system.

Fb

braking force (N)Under these conditions, the rear load transferFx

tractive force (N)mechanism is analysed and by a proper modicationF

sspring force (N)of the rockers and axle, the benets of the system

Fv

vertical force (N)are shown. As a result, it is shown that the rear loadFy

lateral force (N)transfer mechanism can be used in future models ofW F

x, W F

yforces applied about the x and y axesthe Formula Student cars and, indeed, in road-goingrespectively (N)cars, with a proper optimization of the struts and

hcg

height of the centre of gravity of theanti-roll bar rates and the design of the links andvehicle (m)rockers, to improve the handling performance.

hrc

height of the roll centre of thevehicle (m)

Ixx

moment of inertia about the x axisREFERENCES I

zzmoment of inertia about the z axis

K actual spring stiness (N/m)1 Uzunsoy, E. and Olatunbosun, O. A. A fuzzy logic

Ks

vertical rate of each of the left andapplication on vehicle path planning and yaw con-right springs (N/m)trol. In Proceedings of the 9th Annual Research

Kv

eective spring stiness at wheelSymposium of Postgraduate Research, University ofBirmingham, 7 May 2003, pp. 5054. (N/m)



V, V vehicle lateral acceleration (m/s2)Kw

roll stiness of the suspensionm total vehicle mass (kg) and velocity (m/s) respectivelym

ssprung mass (kg)

d steer angle (rad)Mx

total moment about the x axis (N m)w roll angle (deg)M

ytotal moment about the y axis (N m)

p, p roll acceleration and velocityrespectively of the vehicle

r, r yaw acceleration and velocitySubscripts

respectively of the vehicles lateral separation of the springs (m) f front

L leftt track (m)U, U vehicle longitudinal acceleration r rear

R right(m/s2) and velocity (m/s) respectively


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