METHOD FOR ESTIMATING POTENTIAL TIRE-TO-GROUND ADHESION

Abstract

The rolling parameters of a tire on a rolling surface are evaluated, and more specifically a tire's adhesion potential on a rolling surface is estimated. A method and a system enabling such estimation are disclosed.

Claims

1.-10. (canceled)

11. A method for estimating adhesion potential of a tire on a rolling surface, the tire being installed on a vehicle, and the method comprising the following steps: a first step of estimating a force experienced by the tire as a function of a vehicle model and a state observer; a second step of estimating a force experienced by the tire as a function of a thermomechanical model of the tire; a step of statistically comparing the forces determined during the first and second estimating steps, and a step of determining, as a function of a result of the comparing step, a value of the adhesion potential of the tire on the rolling surface.

12. The estimation method according to claim 11, wherein the vehicle model is a bicycle model, and wherein the state observer is a Kalman filter.

13. The estimation method according to claim 11, wherein the comparing step employs a Bayesian logic method.

14. The estimation method according to claim 11, wherein the comparing step employs a Monte-Carlo Markov Chain method.

15. The estimation method according to claim 11, wherein the thermomechanical model of the tire comprises a model of longitudinal forces, transverse forces, a self-aligning torque and a balance of elementary shearing and slipping forces of the tire at a transition point between adhering and sliding contact regions.

16. The estimation method according to claim 11, further comprising, at least before the second estimating step, a step of reducing the tire model.

17. The estimation method according to claim 11, wherein all of the steps are performed in real time.

18. A system for estimating a tire's adhesion potential on a rolling surface, the tire being installed on a vehicle, and the system comprising: means for estimating a force experienced by the tire as a function of a vehicle model and of a state observer; means for estimating a force experienced by the tire as a function of a thermomechanical model of the tire; means for statistically comparing the forces determined during the first and second estimating steps; and means for determining, as a function of a result of the comparing step, a value of the adhesion potential on the rolling surface.

19. The estimation system according to claim 18, wherein the means are installed on the vehicle.

20. The estimation system according to claim 18, further comprising sensors installed on the vehicle.

Description

[0038] FIG. 1, already described, shows a normalized longitudinal friction force curve as a function of slip rate,

[0039] FIG. 2 is a block diagram outlining a method according to the invention,

[0040] FIG. 3 and FIG. 4 are depictions of the forces acting on a vehicle in a model used in the present invention.

[0041] A method according to the invention includes several steps, employing various data, as illustrated in FIG. 2.

[0042] The table below indicates the meanings of the various parameters that appear in the figure, together with their units.

TABLE-US-00001 TABLE 1 Variable Units Description ?.sub.x m/s Longitudinal vehicle speed ?.sub.f, ?.sub.r rad/s Wheel speed (front and rear) {dot over (?)} rad/s Vehicle pitch speed T.sub.f, T.sub.r N .Math. m Engine and braking torque (front and rear) F.sub.xf, F.sub.xr N Longitudinal friction force (front and rear) F.sub.zf, F.sub.zr N Vertical load (front and rear) s.sub.r Slip rate ? rad Camber T.sub.g ? C. Ground temperature T.sub.air ? C. Air temperature T.sub.i.sub.ini ? C. Initial internal tire temperature T.sub.s.sub.ini ? C. Initial tire surface temperature ?.sub.max Adhesion potential

[0043] The tire considered is installed on a vehicle fitted with various sensors. On the basis of the vehicle's known engine and braking torque, and from data measured by the various sensors, a set of running parameters for the vehicle 11 is determined in block 1, including a longitudinal vehicle speed and a slip rate. Any disturbances 12 are also taken into consideration.

[0044] These data are then used to perform two steps of estimating the forces experienced by the tire. A first step, in block 2, consists in determining the forces experienced by the tire, according to a vehicle model 21 and to any disturbances 22.

[0045] A bicycle model, as shown in FIG. 3, is advantageously used that accounts for longitudinal dynamic changes and pitch variations. In order to take these pitch variations into account, it is also necessary to consider a suspension model, such as the one shown in FIG. 4.

[0046] The use of the bicycle model and the suspension model leads to the following state representation:

[00001]$\begin{array}{cc}\{\begin{array}{c}\stackrel{.}{x}=f\left(x,u,t\right)\\ y=h\left(x,t\right)\end{array}& \left[\mathrm{Math}1\right]\end{array}$$\mathrm{With}$$\begin{array}{cc}\{\begin{array}{c}x={\left[{?}_x,{?}_f,{?}_r,F_{\mathrm{xf}},F_{\mathrm{xr}},{\stackrel{.}{F}}_{\mathrm{xf}},{\stackrel{.}{F}}_{\mathrm{xr}},?,\stackrel{.}{?}\right]}^T\\ u={\left[T_f,T_r\right]}^T\\ y={\left[{?}_x,{?}_f,{?}_r,\stackrel{.}{?}\right]}^T\end{array}& \left[\mathrm{Math}2\right]\end{array}$$\mathrm{And}$$\begin{array}{cc}f=\left[\begin{array}{c}{\stackrel{.}{?}}_x\\ {\stackrel{.}{?}}_f\\ {\stackrel{.}{?}}_r\\ {\stackrel{.}{F}}_{\mathrm{xf}}\\ {\stackrel{.}{F}}_{\mathrm{xr}}\\ {\stackrel{.Math.}{F}}_{\mathrm{xf}}\\ {\stackrel{.Math.}{F}}_{\mathrm{xr}}\\ \stackrel{.}{?}\\ \stackrel{.Math.}{?}\end{array}\right]=\left[\begin{array}{c}\frac{1}{m}\left[F_{\mathrm{xf}}+F_{\mathrm{xr}}-\frac{1}{2}{?}_a{S}_a{C}_x{?}_x^2-f_{\mathrm{RR}}\left(F_{\mathrm{zf}}+F_{\mathrm{zr}}\right)\right]\\ \frac{1}{2I_{\mathrm{wf}}}\left[T_f-\left(R+\mathrm{??}{F}_z\right)F_{\mathrm{xf}}\right]\\ \frac{1}{2I_{\mathrm{wr}}}\left[T_r-\left(R-\mathrm{??}{F}_z\right)F_{\mathrm{xr}}\right]\\ {\stackrel{.}{F}}_{\mathrm{xf}}\\ {\stackrel{.}{F}}_{\mathrm{xr}}\\ 0\\ 0\\ \stackrel{.}{?}\\ \frac{1}{I_y}\left[\left(F_{\mathrm{xf}}+F_{\mathrm{xr}}-F_{\mathrm{RR}}\right)h_G-F_{\mathrm{zf}}{L}_f+F_{\mathrm{zr}}{L}_r\right]\end{array}\right]\mathrm{and}h=\left[\begin{array}{c}{\stackrel{.}{?}}_x\\ {\stackrel{.}{?}}_f\\ {\stackrel{.}{?}}_r\\ \stackrel{.}{?}\end{array}\right]& \left[\mathrm{Math}3\right]\end{array}$

[0047] The state observer used is an extended Kalman filter.

[0048] The main assumptions of the bicycle model are as follows: [0049] front-left steering angles=front-right steering angles, [0050] rear steering angles are zero, [0051] vehicle moving on level ground (no banking).

[0052] Furthermore, in this model, the effects of pitching and rolling are often neglected. In the present example, the roll dynamics are indeed neglected but the pitch dynamics are not since a suspension system is being considered.

[0053] A second step, in block 3, estimates the forces experienced based upon a thermomechanical model 4. This model is determined from a set of parameters, notably temperature. Using this model, it is possible to calculate the values of mu as a function of slip rate under the tire operating conditions encountered (at the pressure, load, temperature, etc. encountered at the time of calculation) in order to determine the max adhesion potential for the mu.sub.0 value supplied to the model. By repeating this procedure for different settings of mu.sub.0, a list of mu.sub.max values corresponding to different possible levels of ground adhesion is obtained.

[0054] In an advantageous embodiment, the initial model is reduced to enable less resource-intensive calculations and therefore easier to embed directly in a vehicle. The results of blocks 2 and 3 are then compared, in a step 5, to determine an adhesion potential.

[0055] The comparison between the forces estimated in the preceding two parts is performed here using a Bayesian logic approach. This type of approach has the advantage of providing an associated probability in addition to the value sought. In order to implement it, it is first necessary to make an assumption regarding the probability density of the estimated forces knowing the adhesion potential. Because the Kalman filter works by considering Gaussian noise, the selected probability density has the form of a Gaussian distribution. Therefore one has:

[00002]$\begin{array}{cc}pr\left[\stackrel{?}{F}|{?}_{\max }\right]=\frac{1}{{\left(2?\right)}^{n/2}{.Math.S.Math.}^{1/2}}\exp \left(\frac{1}{2}{\left(\stackrel{?}{F}-F_{tire}\right)}^T{S^{-1}\left(\stackrel{?}{F}-F_{tire}\right)}^T\right)& \left[\mathrm{Math}4\right]\end{array}$

[0056] The Bayes formula is then used to determine the probability of the adhesion potential knowing the friction force, which gives:

[00003]$\begin{array}{cc}\mathrm{Pr}\left[{?}_j.Math.{\hat{F}}_k\right]=\frac{\mathrm{Pr}\left[{\hat{F}}_k.Math.{?}_j\right]\mathrm{Pr}\left[{?}_j.Math.{\hat{F}}_{k-1}\right]}{{.Math.}_{i=1}^J\mathrm{Pr}\left[{\hat{F}}_k.Math.{?}_i\right]\mathrm{Pr}\left[{?}_i.Math.{\hat{F}}_{k-1}\right]}& \left[\mathrm{Math}5\right]\end{array}$

[0057] The adhesion coefficient is thus obtained by calculating the weighted sum:

[00004]$\begin{array}{cc}{\widehat{?}}_k=\underset{i=1}{\overset{J}{.Math.}}\mathrm{Pr}\left[{?}_j.Math.{\hat{F}}_k\right]{?}_j& \left[\mathrm{Math}6\right]\end{array}$

[0058] The adhesion potential is therefore the maximum of this weighted sum.

[0059] In another example, use is made not of a Bayesian method but of a Monte-Carlo Markov Chain method, known as MCMC.

[0060] In a Bayesian method, ? is treated as a discrete random variable, so the denominator of the Bayes' formula is an easily calculated discrete sum. By using the MCMC method, it is possible to consider ? as a continuous random variable, thus achieving greater precision. However, in that case, the denominator of the Bayes' formula is no longer a discrete sum but an integral, which is more complicated to calculate. The MCMC method therefore proposes the calculation of probability density ratios in order to dispense with the need for the denominator. This method also has the advantage of working with low-load measurements. In this approach, these measurements are the forces estimated using the Kalman filter.

[0061] Thus, a method according to the invention provides a reliable estimate of adhesion potential. The invention has been described in detail for the longitudinal case.

[0062] Nevertheless, this description is not restrictive, and a similar approach could be envisioned for the lateral, or a combination of both.