FRICTION POTENTIAL AND SAFETY : PREDICTION OF

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1 BRITE EURAM PROJECT BRPR CT FRICTION POTENTIAL AND SAFETY : PREDICTION OF HANDLING BEHAVIOR FLORENCE, FEBRUARY 23 d 2001 Title : Guide Lines fo vehicle design Authos: P.I. Umbeto Delcao, CRF D.Ing. Thomas Maulick, Posche D. Ing. Leonado Pascali, CRF D. Ing. Patizio Tuco, CRF ABSTRACT Vehicle design fom vehicle dynamics point of view is eally had because vehicle is a complex system made of a lot of complex subsystems. Futhe difficulties come fom the necessity to individuate the ight taget behaviou not only fo safety easons, but also to meet maket equiements. Fo this eason assume a paticula impotance the taget definition expessed in tems of manoeuve specification and objective paametes to be evaluate in both modelling and expeimental appoach. This aticle gives an oveview with some examples of how some simple design paametes can influence vehicle handling and how it's possible to synthesise such a kind of infomation towad vehicle design guide line. Floence Febuay 23 d 2001 Pape pag. 1

2 INTRODUCTION Due to the high level of complexity of vehicle handling design, one of the fist think to be done to simplify the poblem is individuation of the dynamics behaviou classes to be individually analysed within vehicle design. In the following a list of six dynamics behaviou is showed: 1. Longitudinal pefomance 2. Lateal pefomance 3. Stability 4. Steeability 5. Diectional stability 6. Roll ove To each items is possible to associate a set of manoeuves with an appopiate set of objective paametes to disciminate vehicle behaviou. Manoeuves and objective paametes definition is an had and continuously upgaded pocess as it equie a lot of simulations and also a lot of expeimental tests to veify the validity of vitually hypothesis with espect to the eal dives peception. To obtain an affodable taget definition it's necessay: 1. To undestand which vehicle behaviou has to be defined. 2. To make simulations in ode to undestand which manoeuves and which objective paametes could identify the behaviou defined in point 1 and which ae vehicle design paametes that influence this behaviou. 3. Testing the most significant diffeent vehicle configuations using a multi subjective appoach, evaluate if the objective paametes ae able to disciminate investigated behaviou and if they ae elevant and coelate with subjective judgement. The table 1 show a list of suitable manoeuves to descibe vehicle dynamics behaviou. They ae all open loop manoeuves then with a focus on how vehicle-tye-oad system is behave. Including also closed loop manoeuves it's possible to intoduce also the diffeent eaction due to dives skill, veifying ca "fiendliness" to diffeent dives cluste. Floence Febuay 23 d 2001 Pape pag. 2

3 MANOEUVRE Manoeuve desciption Steeing pad at Radius R = 40 m, with low speed inceasing R=40 [m] Slow amp stee speed = 100 [Km/h] amp stee = 180 [degees] in 6 [s] Step stee input speed = 120 [Km/h] nea the limit step stee = +/-15%, +/-30% the steeing angle coesponding to the max lateal acceleation in the slow amp stee Baking in staight initial speed = 100 Km/h line on a m -slip longitudinal deceleation = 0.3 g (without EBD inteaction) suface µ = 0.5 Baking in a tun adius = 100 m lateal acceleation = 0.5 [g] longitudinal deceleation = (0.1;0.2;0.3;0.4[g]) Taction in a cuve adius = 10 [m] lateal acceleation befoe thottle actuation = 0.1;0.2;0.3;0.4;0.5;0.6 [g] gea = 1 st Slow stee-angle initial adius = staight line amp while longitudinal acceleation = max possible inceasing thottle amp stee = 180 [degees] in 6 [s] speed to begin stee = (speed coesponding to max toque on 2 nd gea) gea = 2 nd Slow ste e-angle initial adius = staight line amp while baking longitudinal deceleation (0.1;0.2;0.3;0.4[g]) amp stee = 180 [degees] in 6 [s] speed = 100[Km/h] gea = 4 th Mu-change in a speed = 100 [Km/h] tun adius =150[m] µ = seconds at low fiction Fishhook speed = 100 [Km/h] stee=0*[0:1]-100*[1.2:1.7]+600*[3.1:6] gea =4 th Acceleation on initial speed = 10 [km/h] staight line gea = 1 st step thottle = 100% Baking on staight line initial speed = 100 Km/h high mu-conditions (µ=1) max longitudinal deceleation Table 1 Floence Febuay 23 d 2001 Pape pag. 3

4 1. LONGITUDINAL PERFORMANCE Longitudinal pefomance depends upon: Tyes; Bake system; Dive line which include powe tain, clutch, geabox and diffeential; Weight distibution; Bake system must be design in ode to waant high longitudinal deceleation level. A good value, fo a poduction ca, could be about 1[g] in high adheence in each load condition, without consideing aeodynamics effects. This equiement have to deal with tye peak facto as longitudinal pefomances ae popotional to its value. Than in ode to obtain the bette longitudinal pefomances compomise it s necessay to define bake distibution, font and ea, able to guaantee the highest bake efficiency and stability in baking in a tun, taking in account wheel load distibution and wheel load tansfe. It s clea that an high bake efficiency means less stability in baking in a tun and vice vesa. These consideations must be epeated fo each condition of adheence educing the taget of longitudinal deceleation popotional to available fiction. A simila analysis, fom tye point of view, must be epeated fo dive line in ode to waant longitudinal acceleation taget. Often this aim fo poduction cas, supe cas not included, is coveed by bake taget because the longitudinal acceleation is not so high such as deceleation. In this case it s necessay to impove taction in a cuve. In case of fee diffeential the best thing to do is to educe ba stiffness in ode to educe wheel load tansfe between intenal and extenal wheel. A ba stiffness eduction impoves stability in case of ea taction but educe it in case of font taction vehicle. MANOEUVRE Paamete Baking in a tun Path deviation at 3 [s] Table 2 Path deviation compaed with 2 Vel Re ff = at 3 [s] ay Max longitudinal acceleation in the tansient phase Mean longitudinal acceleation afte 2 seconds el Floence Febuay 23 d 2001 Pape pag. 4

5 Example on wheel base Baking in tun A wheel base eduction inceases vetical load tansfes at the same longitudinal deceleation: M Fz = H g a x. l This moe weight tansfe, in paticula duing the tansient phase taking into account even the inetia effects, causes moe instability (incease of max side slip angle BETA an max yaw ate PSIP) even if the path vaiation at 3 [s] is eally low and it s coelated to the diffeent toe angle due to pitch changes. Simulations have been done until 0.4[g]. Unde this value the vehicle ty to close moe the path. But if we continued to incease bake toque we would each the condition to anticipate lateal font tye foce satuation and the vehicle wouldn t be able to follow the desied path. Max side slip angle in figue 1consides even the kinematics effect. MAX PSIP [deg/s] PSIPmis / PSIPcalc % 10% % DEVIATION % DEVIATION Ax [g] Ax [g] MAX BETA [deg] PATH DEVIATION AT 3[S] [m] % DEVIATION] % DEVIATION Ax [g] Ax [g] Figue 1: Baking in a tun of R=100m stating fom a lateal acceleation of 0.5g Floence Febuay 23 d 2001 Pape pag. 5

6 2. LATERAL PERFORMANCE Lateal pefomance depends upon: tye; suspensions; weight distibution; symmetic and asymmetic stiffness. Fist of all it s necessay to define unde stee gadient (Kus) and side slip gadient (Kβ) taget. In a steeing pad at constant speed, taking into account kinematics effects and knowing the total weight distibution on font and ea axles: l M b M a Kus = + 2 v l Cf l C b m a Kβ = 2 v C l These two tagets specify font and ea tye cone stiffness. Afte this it s necessay to define max lateal acceleation. This taget specifies peak factos fo tyes: F ya + F yp > m a t yt This taget is also influenced by asymmetic stiffness distibution. Inceasing font stiffness potion max lateal acceleation deceases because font axle inceases weight tansfe and extenal font lateal foce eaches satuation befoe. The intoduction of suspension chaacteistics modifies gadients and max values. In paticula toe chaacteistics influence gadients while cambe ones influence maximum values. Table 3 shows manoeuves and paametes used to define lateal pefomance. MANOEUVRE Steeing pad at R=40 [m] Table 3 Paamete Unde-stee gadient Side slip angle gadient Max lateal acceleation... Floence Febuay 23 d 2001 Pape pag. 6

7 Floence Febuay 23 d 2001 Pape pag. 7 Example on wheel base Steeing pad R=40m Wheel base vaiation influences only the kinematics side slip angle and the kinematics stee value. The definition of the side slip angle is: y y a C M R b a l C a M R b = = β whee a and b ae font and ea wheel base. While the definition of stee angle is: + = + = ay K R l ay C M C M R l us f f τ τ δ The othe paametes have vaiations less than 1%. In this case wheel base is not elevant towad these paametes.

8 3. STABILITY Stability depends upon: tye; weight distibution; symmetic stiffness; suspensions; dampes; bake system. Stability in tems of tyes means specifies peak facto and shape facto. Peak factos must be defined in ode to avoid max lateal acceleation befoe vetical side slip asymptot in slow amp stee. Shape facto must be defined in ode to limit max side slip angle in slow amp stee. In this case asymmetic stiffness distibution plays a eally impotant ole. Inceasing font asymmetic stiffness stability inceases, educing yaw ate and side slip velocity oscillations while inceasing ea one stability deceases. The eason of this is that changing asymmetic stiffness distibution wheel load tansfes change on the font and ea axle anticipating o delaying lateal foce satuation on font axle. Tye sensibility to the cambe may change vehicle behaviou nea the limit, even if the effect is less impotant. In this tem suspension design must be oiented in ode to impove stability. That means that ea extenal wheel cambe must be negative while font one must be positive in suspension efeence. A positive cambe on font extenal wheel, howeve educes max lateal acceleation. About bake system, font and ea bake distibution, must be designed in ode to incease bake efficiency and stability in baking in a tun. That means high longitudinal deceleation and low value of yaw ate and side slip oveshot. MANOEUVRE Paamete Slow amp stee max lateal acceleation befoe vetical side slip asymptot max side slip Mu-change in a Side slip velocity oveshot tun Side slip oveshot Total side slip velocity RMS Fist change side slip velocity RMS Second change side slip velocity RMS Table 4... Floence Febuay 23 d 2001 Pape pag. 8

9 Example on wheel base Slow amp stee The wheel base vaiation, in this case, influences side slip and unde stee gadient. The definition of the side slip angle is: β b M a b = ay = R C l 2 v M C a y While the stee angle is: δ l τ v = 2 + K us a y The othe paametes ae stictly coelated do these gadients. Floence Febuay 23 d 2001 Pape pag. 9

10 µ change in a tun In this case a lage wheel base, passing fom high to low adheence condition, educes side slip angle oscillations, side slip oveshot elative to steady state in low adheence and yaw ate fequency. On the othe hand, passing fom low to high adheence condition, a lage wheel base induces highe yaw ate oveshoot. In the fist change thee s a stable tansition phase, when font wheel is in low adheence and ea wheel is in high adheence. This phase outlasts moe and stability moment is highe when the wheel base is lage. In the second change thee s an unstable tansition phase, when font wheel is in high adheence and ea wheel is in low adheence. This phase outlasts moe and instability moment is highe when the wheel base is lage. RELATIVE SIDE SLIP 0.25 beta-beta0 [deg] time[s] YAW RATE PSIP[deg/s] % 10% time[s] Figue 4: Relative side slip angle and yaw ate in a tun of R=150m with m change Floence Febuay 23 d 2001 Pape pag. 10

11 4. STEERABILITY Steeability depends upon: tye; suspensions; weight distibution; asymmetic stiffness. Steeability is a ca behaviou in contast with stability. Having a good steeability often means not to have good stability. In ode to have a good steeability font tye lateal foces must not be satuated. Max steeing angle coesponding to max lateal acceleation must be high in slow amp stee. That means educe asymmetic stiffness distibution on font axle and changing shape facto in font tyes. Floence Febuay 23 d 2001 Pape pag. 11

12 5. DIRECTIONAL STABILITY Diectional stability depends upon; tack width; stee system, Inceasing tack width, unstable moment, caused by baking in split conditions, inceases and vehicle changes quickly its diection. A solution to this could be woking on king pin using asymmetic longitudinal foces in ode to move font wheels and having a stable moment. 6. R OLL OVER Rollove depends upon: Vehicle mass cente height; Tack width; tyes; Suspensions Asymmetic stiffness. Duing last yeas ca manufactues have lunched a lot of cas with high mass cente and naow tack. This ca layout can give ollove. In ode not to have such a poblem it s necessay to incease tack and educe mass cente height. If It s not possible to do this the best thing to do is to educe max lateal acceleation by changing asymmetic stiffness distibution, inceasing font one, o using less pefomance tyes on font axle in ode to anticipate font wheel lateal foce satuation compaed to the ea one. MANOEUVRE Paamete Fishhook Max speed at which thee s a contact between intenal, font and ea wheels and oad Vetical load on wheels Table 5... Floence Febuay 23 d 2001 Pape pag. 12

13 Example on tack width Fishhook A tack width eduction incease the intenal vetical wheel load eduction. A good citeia to define tack width looking at ollove poblems is to define an infeio limit fo intenal wheel vetical load not to be eached in a Fishhook manoeuves at a defined speed, 100 [km/h] fo example. INTERNAL WHEEL VERTICAL LOAD MIN INTERNAL WHEEL VERTICAL LOAD % 5% 0% 10 5 time[sec] % DEVIATION % 0 5% Fz [N] -10 TRACK WIDTH % DEVIATION Figue 2 Intenal Wheel load in a fishhook manoeuve CONCLUSION This document gives geneal infomation about vehicle dynamics design and defines a set of manoeuves and objective paametes in ode to evaluate how design paametes change vehicle behaviou in: lateal and longitudinal pefomance, stability, steeability, diectional stability and oll-ove. Moeove thee ae examples of how design paametes, like wheel base and tack width, can influence vehicle behaviou. Some design paametes modify only one vehicle behaviou and in this case the choose is clea. On the othe side thee ae othe design paametes, like asymmetic stiffness distibution, that wok in opposite diections in two diffeent vehicle behaviou, stability and steeability. In this case it s necessay to find a compomise but it s even possible to use design paametes to have a paticula vehicle behaviou. Floence Febuay 23 d 2001 Pape pag. 13

14 REFERENCES 1. Race Ca vehicle dynamics, William F. Milliken, Douglas L. Milliken, Automotive Handbook, Robet Bosch Gmbh, distibuited by Society of Automotive Enginees, Waendale, PA, Road vehicles-steady state cicula test methods, ISO (E), Intenational Oganization fo Standadization, Road vehicles-lateal tansient esponse test methods, ISO (E), Intenational Oganization fo Standadization, A New tie model with an application in Vehicle dynamics Studies, E. Bakke, L. Nybog, H.B. Pacejka, SAE Pape No , New Diections in Suspension Design, Robet Bentley, Inc., Cambidge, MA, Meccanica dell Autoveicolo, Giancalo Genta, Levotto & Bella-Toino,1993 Floence Febuay 23 d 2001 Pape pag. 14