Congress Topic: Safety, Advanced Safety Title : Tire Road Friction Estimation Authors Dr Yves Delanne*, Director of Reseach [email protected]

Dr Minh-Tan Do*, Senior Researcher [email protected] Dr Nacer K. M’Sirdi**, Professor [email protected] * Laboratoire Central des Ponts et Chaussées, Centre de Nantes - France ** Laboratoire des Sciences de l’Information et des Système- UMR 6168, Domaine Universitaire Saint Jérome, Av. Escadrille Normandie-Niemen 13397 Marseille Cedex 20; Marseille - France

Abstract Two main approaches for tire road friction estimation: the “cause based” and the “effect based” are generally dealt with in the literature. The slip-based method seems to be the most promising and is, consequently, a very popular current subject. LCPC, a French research body in civil engineering has been working for several years on the relationship between road texture parameters and road surface condition (dry, damp, wet) and tire friction performance. In this framework the two methods were subject of dedicated programs. This paper briefly presents the two methods and the point of view of LCPC on them, based on its research, still under way. Introduction Driver assistance systems become more and more integrated in modern vehicles. When activated, these systems call for a reliable estimation of tire friction forces for the current dynamic state. This question is becoming the objective of many research programs throughout the world. In France, the Road and Bridges Central Laboratory (Laboratoire Central des Ponts et Chaussées LCPC), investigating since 1996 the relationships between road texture and condition (wetness) on tire road friction performance curves, can bring along new elements on this subject. Tire Road Friction Estimation Two main approaches for tire road friction estimation: the “cause based” and the “effect based” are generally dealt with in the literature [1] [2]. These approaches will be briefly described here after. Discussions about these methods will be based on investigations conducted at LCPC only on longitudinal forces. Ö Caused based estimation This approach is based firstly on the knowledge of a predictive model with knowledge of all the parameters that have influence onto the building up of friction forces and secondly on the possibility to measure or estimate these parameters on board. This approach is mainly conducted in Germany. Darmstadt University listed [3] [4] the main influencing parameters, which are: ¾ Vehicule - Wheel parameter: o Speed V, Tire, Camber, wheel load, torque applied, rotational speed, ¾ Tyre parameters : o Rubber type, Tire type, Tread pattern and depth, rubber temperature ¾ Lubricant o Type, thickness, temperature ¾ Road Mixes type, macrotexture, Microtexture, drainage capacity In [4], a µmax friction coefficient estimator (fig 1) has been proposed. The empirical model takes into account the following parameters: a low speed friction coefficient, the mean profile depth (MPD) [5], the tread depth (TD), the water depth (WD) and the load Fz. This model with 16 coefficients is applicable for a given tire but without including the effect of the driving speed a very influencing parameter.

Figure 1 : Fx/Fz longitudinal friction versus longitudinal slip Measured points and model fitted (ref LCPC) Notations: Kx longitudinal stiffness, µmax maximum value for Fx/Fz , µlocked value for Fx/Fz with 100% slip rate (wheel locked up). An other way to deal with this problem is to adapt a generic model, in general a Magic Formula (MF) tire model, taking into account parameters which can help modifying the tire characteristic curves. Paper [5], dealing with longitudinal friction (fig 1) is a good example of this procedure. Characteristics quantities needed to adapt key longitudinal parameters are: • wet friction values - low speed wet friction with a Skid Resistance Tester (Annex) - high speed wet friction with a tire/road measuring device called SRM (annex) • texture profile analysis o profile crest density (number per mm) - form and size of the roughness - percentage of profile area With these quantities known for the reference surface and for the new surface it is possible to estimate Kx, µmax and µlocked, values that have proved to be sufficient to fit a general parametric model [6] [7] inasmuch that the optimal longitudinal slipping rate (κ1opt for µmax) can be considered as invariant. A friction measurement (specific friction devices or instrumented vehicle [8]) is always needed for correction of tire characteristics curve, or estimator from pavement characteristics, consequently, this method is not actually an “on board estimator”. Is it possible to avoid this measure? Progress have been made on this question at LCPC. Research conducted since 1997 have shown that a low speed friction can be estimated from angular description of the fine scale micro-profile [9][10] and recently from parameter computed on high resolution digital image [11]. The first way uses a Kelvin solid running over a “mean profile motif” as exhibited in figure 2. An analytical solution taking into account the geometry of the motif and the stiffness and damping characteristics of the Kelvin solid has been developed [12]. This method, which needs a high-resolution texture profile measurement, cannot be applied in on board caused based estimation procedure. 1

Definition given in the next paragraph

Compléter/modifier par Tan

Figure 2 : Kelvin solid running over a mean profile motif High resolution image processing, still in laboratory development, could be in the long run a possible on board solution, until then, friction measurement remain necessary for caused based prediction methods. Ö Slip based method: Longitudinal friction slip based estimator uses data from traction, braking. The idea of this method is to use data from low wheel slip and low friction (µ) manoeuvres to predict the maximum µmax of the slip curve. The idea is based on the assumption that when looking at the slip curve the slope at the beginning of the curve contains sufficient information to give a value at the maximum friction This means that tire longitudinal stiffness, for low values, indicates the peak value of the µx (V, κ) curve. Basic wheel model

Notations: .

θ angular position and θ = d θ /dt wheel angular speed Tb/d braking/driving torque Reff effective rolling radius rayon - Vx longitudinal velocity Fx longitudinale friction force Jw wheel inertia µb friction coefficient of braking disc τ braking efficiency time delay µx friction coefficient m quarter vehicle mass Definition : -

κ (kappa) longitudinal sleep rate during braking = (Vx(t) - w(t) Reff)/ Vx(t)

Dynamic model, braking Equation 1 :

Jw(d θ (t)/dt) = Reff Fx – Tbr (t-τ) µb(w(t)), with Fx = Fz µx (,Vx(t))

Equation 2

m × dVx/dt = Fx = Fz µx ( θ ,Vx)

.

The following quantities have to be estimated: • wheel angular speed from angular encoders • Reff • Fx from equation 1 Many papers deal with the estimation of the wheel longitudinal slip. Different procedures have been compared: recursive least square, kalman filtering, sliding mode observers. Figure 3 exhibits an example of results obtained. Completer par Nacer How consistent is the assumptions that longitudinal stiffness is correlated to µmax? Th. Dieckmann published in 1992 one of the first study on the assessment of road grip by way of measuring variable [13]. Test runs under different conditions on different roads including dry, wet and snowy surfaces were carried out. “The results proved a decrease in the tire’s longitudinal stiffness on slippery road”. Many other papers refer to this conclusion and consider that longitudinal stiffness estimation can take apart dry/wet/snowy/icy road surfaces. An investigation has been recently conducted at LCPC to see how far the longitudinal stiffness estimation can be exploited to classify slipperiness of different road surfaces. Many measuring campaigns were carried out during our research program on test track and recently, on trafficked roads with various mixes. The Michelin’s C35, a special measuring vehicle, was used to get steady state longitudinal friction curves (Fx vs κ for Fz =450 daN). On test tracks measurements were generally done for 3 speeds, three water thickness and 3 wheel loads. These data were “summarised” by a Magic Formula model, based from which our analysis was carried out. 1. Can we distinguish dry /slightly wet(>0.5mm)/wet? The analysis was conducted on different pavements. As shown on figure 3, it is almost impossible to separate dry from wet (0.5/1mm water thickness) for a brand new tire.

Figure 3: comparison of Fx/Fz versus slip rate in dry and wet condition

This example clearly shows that estimation of µmax from low slip rate values is erroneous: lower values are obtained for dry from 0 to 7% slip rate. Figures 4 and 5 illustrate typical results obtained with different water thickness on the same track section.

Figure 4: comparison of Fx/Fz versus slip rate in dry and different wet condition

Figure 5: comparison of Fx/Fz versus slip rate in different wet condition For both figure 4 and figure 5 wheel load is fixed, respectively 300 daN and 500 daN On figure 4, for a speed of 50 km/h dry/wet condition can be made out only for slip rate higher than 5%. On figure 5, at higher speed and for a higher load, slightly wet and wet (1.5mm and 3mm water thickness) can be separate even at low slip rates. 2. How different road surfaces behave with for a same water condition? Figure 6 exhibits the different Fx/Fz curves obtained on three different sections (T1, T2, T3) on a test track. The mobile watering system gave roughly similar water thicknesses. Coefficients µmax for section T1 and T3 cannot be correctly estimated (relative level order) from values at low slip rates. Difference between high friction sections and a low friction section is clearly visible on figure 6.

Figure 6: comparison of Fx/Fz versus slip rate for a similar t wet condition on three sections on a test track (T1,T2,T3) and two wheel loads 3. What is the effect of mixes type? In October 2004, a C35 measurement campaign was conducted on 12 road sections with different friction courses types. Measurement were done with a worn tire (tread pattern depth : 4 mm) and a new brand tire on 6 sections amongst these 12 sections (“N” first column table1). Water thicknesses are considered as similar for all sections. A Pacejka’s Model type fitted for the 12 sections is: phi = (1-E) × (G + SH) + E/B × arctg (B × (G + SH)) FX/FZ= D × sin( C × arctg(B × phi)) Parameters of the model fitted are given on table 1. Table 1: Pacejka’s model parameter A C D F N Q S V Y1 Y2 Z1 Z2 AN VN Y1N Y2N Z1N Z2N

BCD 39.4098 24.80126 29.09916 26.12968 33.14533 24.52482 26.14308 37.46013 32.39853 39.69777 23.20031 23.62358 31.92 35.51139 29.29782 30.17817 23.19841 25.91373

D 0.9935 0.7871 0.7609 0.9104 1.0190 0.9987 0.9223 1.0452 0.9810 1.0108 0.8166 0.8303 1.0244 1.0626 0.9924 1.0015 0.7701 0.7848

C 1.7728 1.8397 1.8660 1.7322 2.0013 1.8737 1.9997 1.9567 2.0021 1.9548 2.0080 1.8851 1.9358 1.9553 1.9666 1.9443 1.9657 1.9657

E 0.8269 0.7474 0.8115 0.5735 0.9163 0.8912 0.8884 0.9264 0.9264 0.9137 0.8809 0.8215 0.8859 0.8988 0.8989 0.8853 0.8765 0.7580

Figure 7 exhibits the computed points with these different parameters for the worn tire.

Figure 7: Fx/Fz versus Kappa% from fitted Pacejka’s models Table 2 gives computed values for κ = 2% and 4% and µmax. Table 2 Sections A C D F N Q S1 V Y1 Y2 Z1 Z2

Kappa = 2% Kappa = 4% 0.709 0.924 0.458 0.642 0.427 0.676 0.640 0.821 0.593 0.890 0.484 0.767 0.588 0.801 0.637 0.936 0.499 0.814 0.544 0.842 0.552 0.704 0.509 0.699

µ4% - µ2% 0.216 0.184 0.249 0.181 0.297 0.282 0.213 0.299 0.315 0.298 0.152 0.190

µmax 0.993 0.733 0.761 0.853 1.018 0.998 0.942 1.045 0.992 1.001 0.770 0.784

Figure 8 shows that stiffness estimation from Fx/Fz at two low slip rate values (2%and 4%) is roughly correlated to µmax (R² = 0.6). This correlation improves if stiffness is estimated from higher rate values (from 6%) but in this case, values can be good estimators of µmax (R²>0.95 for µ6%).

Figure 8: correlation between Fx/Fz at low slip rate with µmax

Ö

Conclusion regarding the slip based method

Estimation of longitudinal stiffness from Fx/Fz and low slip rate estimates can give an order of the current friction level, distinguishing this level in 4/5 classes. This method is not capable to estimate reliably µmax. The method needs a calibration phase on a reference surface to which stiffness estimates will be compared. It is necessary to estimate as precisely as possible, recursively values of Fx, Fz, Reff,Vx, κ for a slip rate up to at least to 4%. Conclusion Estimation of friction potential is a challenging problem. Progress have been made on both alternative methods: ¾

Prediction from road parameters and water thickness measurement

¾

Estimation of longitudinal stiffness, implying recursive estimation of4/5 parameters from on board sensors during braking Further researches are needed to improve their reliability and to see whether a mixed solution would be efficient. References [1] [Michael Robert Utchanski. Road friction estimation for automobiles using digital signal processing methods - PhD thesis Fall 2001 University of California Berkeley [2] S. Müller, M. Uchanski, K. Hedrick Estimation of the Maximum Tire Road Friction Coefficient – Journal of Dynamics Systems, Measurement and control dec 2003 vol 125 pp607-617 [3] Bert Breuer, Ulrich Eichhorn, and Jurgen Roth. Measurement of tyre/road friction ahead of the car and inside the tyre. Proceedings of AVEC‘92 (International Symposium on Advanced Vehicle Control), pages 347–353, 1992. [4] F. Kelmpau Development of a friction prediction system 2nd International Colloquium on Vehicle Tyre Road Interaction “friction potential and safety : prediction of handling behaviour” Florence 23/02/2001. [5] ISO Standard 13473-1 « Characterisation of pavement texture by use of surface profiles - Part 1 : Determination of Mean Profile Depth » 2002 [6] H. Fischlein, R Gnadler, H-J; Unrau -The influence of the Track Surface Structure on the Frictional Force Behaviour of Passenger Car Tyres in Dry and Wet Track Surface Conditions. Der Einsfluss der Fahrbahn-oberflächenstruktur auf das Krasftschlussverhalten von Pkw-Reifen ATZ worlwide 10/2001 volume 103 [7] Y. Delanne, G. Beurier - Evaluation of tire/road friction performance models from on site measurements, SURF 2000 June Nantes France [8] G. Beurier, Y. Delanne - Méthode de recherche statistique de relations entre les paramètres de modèles en vue de l’identification de ces paramètres. - CIFA 2000 Juillet, Lille France. [9] P. Van Der Jagt, A.W. Parsons – Road Surface Correction of Tire Test Data – Vehicle System Dynamics , 25 (1196) pp 147-165 [10] M.-T. Do, H. Zahouani - Frottement Pneumatique/Chaussée : Influence de la Microtexture des Surfaces de Chaussée. Actes des Journées Internationales Francophones de Tribologie (JIFT), Association Française de Mécanique, SIRPE Editeur, 2002. [11] M.T. Do, P. Marsac, Y. Delanne - Prediction of tire / wet road friction from road surface microtexture and tire rubber properties, SURF, Juin 2004. [12] M.T. Do - Contribution des échelles de texture routière à l’adhérence des chaussées- rapport de la collection Etudes et Recherche des Laboratoires des Ponts et Chaussée décembre 2004 [13] Th. Dieckmann – « Assessment of road grip by way of measuring variable3 proceedings of FISITA 92 Congress London pp 75-81

Annex Skid Resistance Tester This apparatus is used to measure the frictional resistance between a rubber slider (mounted on the end of a pendulum arm) and the road surface. This method provide a measure of frictional property of surfaces, either in the field or in the laboratory.

Figure 9 : the Skid Resistance Tester

Stuttgarter Reibungsmesser (SRM) Device for road friction measurement at 18% slip rate and 60km/h with a bald AIPCR tire. See

http://www.ivt.ethz.ch/iv/measuring/srm/index