METHOD FOR ESTIMATING THE PRESSURE OF THE TYRES OF A VEHICLE

Abstract

A method estimates tire pressure of vehicle. For each tire, signals or data indicative of angular velocity of the wheel with which the tire is associated are acquired. A subset of detected signals or data acquired in rectilinear vehicle travel condition is selected. Pressure relationship between tires of each pair of wheels of the same axle is determined by comparing the rolling radius of the wheel on which a first tire is mounted and the rolling radius of the wheel on which a second tire is mounted. A pressure relationship between tire pairs is determined for comparison between the mean value of the rolling radii of wheels of a first axle and the mean value of the rolling radii of wheels of a second axle. Ratios are calculated based on signals or data indicative of angular velocity of the wheels and on slippage of the drive wheels.

Claims

1. A method for estimating the pressure of tyres of a vehicle, the method comprising: for each tyre, acquiring signals or data indicative of an angular velocity of a wheel with which said tyre is associated; selecting a subset of acquired signals or data, wherein said subset includes signals or data acquired in a rectilinear vehicle travel condition; determining a pressure relationship between tyres of each pair of wheels belonging to a same axle of the vehicle by comparing between a value of a quantity correlated to tyre pressure for a first tyre and the value of said quantity correlated to tyre pressure for a second tyre, wherein a ratio between said quantity correlated to the tyre pressure of the first tyre and said quantity correlated to the tyre pressure of the second tyre is calculated based on the signals or data indicative of the angular velocity of the wheels with which said first tyre and said second tyre are associated; and determining a pressure relationship between pairs of tyres of a pair of axles of the vehicle by comparing between an average value of said quantity correlated to tyre pressure of the first tyre and the second tyre for a first pair of tyres belonging to a first axle of the vehicle and the average value of said quantity correlated to the tyre pressure of the first tyre and the second tyre for a second pair of tyres belonging to a second axle of the vehicle, wherein a ratio between the average value of said quantity correlated to the tyre pressure of the first tyre and the second tyre for said first pair of tyres belonging to the first axle of the vehicle and the average value of said quantity correlated to the tyre pressure of the first tyre and the second tyre for said second pair of tyres belonging to the second axle of the vehicle is calculated based on signals or data indicative of an average angular velocity of the wheels of the axles of the vehicle with which said pairs of tyres are associated and based on a quantity indicative of slippage of the pair of tyres of driving wheels on the ground, and wherein said quantity correlated to the tyre pressure is a rolling radius of the wheel on which the tyre is mounted, calculated from an acquired angular velocity of the wheel.

2. The method of claim 1, wherein said quantity indicative of the slippage of the pair of tyres of the driving wheels on the ground is a function of a grip index of the driving wheels on the ground and of a longitudinal acceleration of the vehicle.

3. The method of claim 2, wherein the ratio between an average value of the rolling radius of rear wheels of the vehicle and the average value of the rolling radius of front wheels of the vehicle is calculated according to the relationship $\frac{{\omega }_f}{{\omega }_r}=\frac{R_r}{R_f}+\tilde{k}\left(a_{x_{meas}}+\frac{c}{M}{V}_x^2+\frac{F_{\mathrm{roll}}}{M}\right)$ where: ω.sub.ƒ is the average angular velocity of the front wheels; ω.sub.r is the average angular velocity of the rear wheels; R.sub.f is the average rolling radius of the front wheels; R.sub.r is the average rolling radius of the rear wheels; $\tilde{k}=\frac{R_{r}L}{R_f{l}_{f}g{\mu }_1}$ with L being the wheelbase of the vehicle, l.sub.f the front half-wheelbase of the vehicle, ${\mu }_1=\frac{\partial \mu \left({\lambda }_r\right)}{\partial {\lambda }_r}$ μ being the longitudinal friction coefficient;
a.sub.x.sub.meas=a.sub.x+g sin(α) with α.sub.x being the longitudinal acceleration of the vehicle, α the inclination of the vehicle with respect to a horizontal travel plane; cV.sup.2.sub.x being the aerodynamic force; M being the mass of the vehicle; and F.sub.roll being the rolling force.

4. The method of claim 1, wherein the ratio between the value of the rolling radius, R.sub.1, of the wheel with which the first tyre is associated and the value of the rolling radius, R.sub.2, of the wheel with which the second tyre is associated is calculated according to the relationship: $\frac{{\omega }_2}{{\omega }_1}=\frac{R_1}{R_2}$ where ω.sub.1 is the angular velocity of the wheel with which the first tyre is associated and ω.sub.2 is the angular velocity of the wheel with which the second tyre is associated, assuming wheel slippage is zero or the same and steering angle of the vehicle is zero.

5. The method of claim 1, comprising a learning step in which a real tyre pressure value and a corresponding nominal value of the rolling radius of wheels with which the tyres are associated are acquired as a function of at least one parameter among: tyre model and tyre wear state.

6. The method of claim 5, wherein a comparison between the value of the rolling radius of the wheel with which the first tyre is associated and the value of the rolling radius of the wheel with which the second tyre is associated is compared with the nominal value of the rolling radius of the wheel with which the first tyre is associated and the nominal value of the rolling radius of the wheel with which the second tyre is associated, and a comparison between the average value of the rolling radius of the wheels belonging to the first axle of the vehicle and the average value of the rolling radius of the wheels belonging to the second axle of the vehicle is compared with a nominal average value of the rolling radius of the wheels belonging to the first axle of the vehicle and a nominal average value of the rolling radius of the wheels belonging to the second axle of the vehicle.

7. The method of claim 6, further comprising determining a deflation condition of a tyre if at an end of said comparison a difference between compared values is greater than a predetermined threshold.

8. The method of claim 6, further comprising determining a deflation condition of a pair of tyres associated with wheels of the same axle if at an end of said comparison the difference between the compared values is greater than a predetermined threshold.

9. The method of claim 8, wherein said predetermined threshold is variable as a function of a grip index of the driving wheels on the ground, of longitudinal velocity of the vehicle or of both.

10. The method of claim 1, wherein said rectilinear vehicle travel condition is determined by acquiring during traveling of the vehicle, signals or data indicative of operation of a vehicle braking system or of a variation of a torque to the driving wheels of the vehicle, or signals or data indicative of the steering angle of the vehicle or rotation angle of a steering wheel.

11. The method of claim 1, further comprising acquiring a pressure measurement of at least one tyre of the vehicle.

12. A processing system for evaluating tyre pressure of a vehicle, the processing system being programmed to carry out the method of claim 1.

13. A non-transitory computer readable medium storing a computer program or program group executable by a processing system, comprising one or more code modules for implementing the method for estimating pressure of the tyres of a vehicle according to claim 1.

Description

[0016] Further characteristics and advantages of the invention will be described in greater detail in the following detailed description of an embodiment thereof, provided by way of non-limiting example, with reference to the accompanying drawings wherein:

[0017] FIG. 1 is a general block representation of a system for estimating the tyre pressure of a vehicle, which is the subject-matter of the invention;

[0018] FIG. 2 is a block diagram of a three-index system for estimating the tyre pressure of a vehicle, according to the invention;

[0019] FIG. 3 is a kinematic vehicle model used in the method of the invention;

[0020] FIGS. 4a and 4b are graphs indicative of the detection of a deflation condition of a tyre, respectively of a front axle and a rear axle of the vehicle;

[0021] FIG. 5 is a further kinematic vehicle model used in the method of the invention;

[0022] FIG. 6 is an indication of the physical quantities underlying the method according to the invention;

[0023] FIG. 7 is a graph showing the trend of parameters affecting the longitudinal acceleration of a vehicle under experimental conditions;

[0024] FIG. 8 is a graphical representation of a regression analysis technique;

[0025] FIG. 9 shows graphs indicating the detection of a relative deflation condition of the rear axle tyres with respect to the front axle tyres;

[0026] FIG. 10 is a graph showing the variation of a relative deflation index as a function of the grip conditions;

[0027] FIG. 11 is a graph showing the trend of thresholds for detecting the deflation of a tyre as a function of the variation of the relative deflation index represented in FIG. 10;

[0028] FIG. 12 shows the trend of deflation indices in different grip conditions; and

[0029] FIG. 13 shows the trend over time of the deflation indices of all tyres on a four-wheeled vehicle and the represented grip conditions, together with the trend over time of the threshold curves for detecting a deflation condition.

[0030] With reference to FIG. 1, a vehicle V is shown in its essential lines with four wheels W1-W4 and an associated pressure estimation system of the tyres, respectively indicated as T1-T4. It comprises sensor devices S1-S4, respectively associated to the wheels W1-W4, including angular velocity sensors to detect the angular velocity of the aforesaid wheels, an optional pressure sensor device SP associated with a wheel and a processing unit P connected at its respective inputs with the sensor devices S1-S4 and possibly with the sensor device SP, if present.

[0031] At least one display device D is connected to the processing unit P and is adapted to give an indication to a user of the vehicle of an inflation anomaly of at least one tyre.

[0032] The processing unit P is programmed to implement a method for estimating the tyre pressure of a vehicle as better described hereinafter.

[0033] It is known to use signals or data available on board the vehicle, for example from sensors S1-S4, to measure at least one quantity representing an indirect index of the inflation pressure of one or more tyres, which may be identified generically according to the following relationship

I=ƒ(P)

[0034] where I is the inflation pressure index quantity and P is the inflation pressure.

[0035] If the function ƒ is fully known, from the index I it is possible to derive directly the pressure P as

P=ƒ.sup.−1(I)

[0036] This ideal condition is never met because the relationship ƒ is affected by many unknown variable factors, such as the tyre model, the state of wear of the tyre, the load condition of the vehicle.

[0037] However, it is possible to learn the nominal value of the index I at an actual pressure value of a tyre acquired by a known method, for example by means of an on-board pressure sensor SP or by measuring the pressure at a garage, and to determine a deflation of the tyre if the measured value of said index differs from the nominal value for a quantity greater than a predetermined threshold for the detection of a deflation condition.

[0038] A three-index system for estimating the tyre pressure of a vehicle according to the invention is represented in FIG. 2.

[0039] Therein, at least one signal, and preferably a plurality of signals or data carried on an on-board CAN network is indicated collectively at 10. A data selection module is indicated at 12 and arranged to select the signals or data 10 provided by the CAN network by generating a subset of said signals or data, which includes—in a currently preferred embodiment—the signals or data detected in a rectilinear travel condition of the vehicle. An index calculation module 14 is located downstream of the selection module 12 and is configured to calculate the value of predefined indexes of the pressure value on the basis of the selected signals or data, as will be described below. In parallel with the module 14, a module 16 is arranged to detect a quantity indicative of the slippage on the ground of the pair of tyres of the drive wheels of the vehicle, on the basis of the signals or data selected. Downstream of the index calculation module 14 and the module 16 for measuring an indicative slippage quantity, a pressure estimation module 18 is provided to obtain estimate data of the tyre pressure on the basis of the data received from the index calculation module 14 according to the slippage on the ground of the pair of tyres of the vehicle's drive wheels measured by the module 16.

[0040] The pressure estimation module 18 controls said at least one display device D to represent, at least visually, an indicative signal of an inflation anomaly of at least one tyre.

[0041] It is known that the rolling radius of a wheel depends on the pressure of the tyre, according to the general relationship

R=R(P)

[0042] where R indicates the rolling radius of the wheel.

[0043] Comparing the angular velocity of two wheels together, the relative radii may be calculated, that is, the ratio between the radii, which is the index of a relative deflation of one tyre with respect to another, according to the relationship

[00001]$R_{\mathrm{ij}}=\frac{R_i}{R_j}=f\left(\frac{{\omega }_j}{{\omega }_i}\right)$

where ω.sub.i and ω.sub.j are respectively the angular velocity of the i-th wheel and the j-th wheel, R.sub.i and R.sub.j are respectively the rolling radii of the i-th wheel and the j-th wheel, and R.sub.ij is an indicative index of the ratio of said rolling radii, which assumes a unitary value in the condition wherein the rolling radii are equal, i.e. the inflation levels of the respective tyres, thus their pressure values, are equal, independently of the absolute pressure value that is not known.

[0044] The preceding considerations make it possible to create a system that, on the basis of three indices, allows the deflation of one, two or three tyres to be detected, but not of all four tyres at the same time.

[0045] With

[00002]${\hat{R}}_{12}=f_1\left(\frac{{\omega }_2}{{\omega }_1}\right)\sim \frac{R_1}{R_2}$

[0046] an estimate of the ratio between the rolling radii of a first wheel W1 and a second wheel W2 belonging to the same axle of the vehicle is indicated, in the example case the front axle, which provides information about the deflation of a wheel of said axle.

[0047] With

[00003]${\hat{R}}_{34}=f_2\left(\frac{{\omega }_4}{{\omega }_3}\right)\sim \frac{R_3}{R_4}$

[0048] an estimate of the ratio between the rolling radii of a first wheel W3 and a second wheel W4 belonging to the same axle of the vehicle is indicated, in the example case the rear axle, which provides information about the deflation of a wheel of said axle.

[0049] With

[00004]${\hat{R}}_{\mathrm{rf}}=f_3\left(\frac{{\omega }_1+{\omega }_2}{{\omega }_3+{\omega }_4}\right)\sim \frac{R_r}{R_f}$

[0050] an estimate of the ratio between the average rolling radius of the rear wheels W3, W4 belonging to the rear axle of the vehicle and the average rolling radius of the front wheels W1, W2 belonging to the front axle of the vehicle is indicated, which provides information about the simultaneous deflation of both wheels on the same axle.

[0051] For example, in the case of the ratio between the rolling radii of a first wheel W1 and a second wheel W2, respectively indicated as R.sub.1 and R.sub.2 in the preceding formula, the following three ideal cases may occur:

R.sub.12<1

R.sub.12˜1

R.sub.12>1

[0052] corresponding to the relative deflation of the tyre of the left front wheel W1 with respect to the tyre of the right front wheel W2, to no relative deflation between the tyres of the front wheels, or to relative deflation of the tyre of the right front wheel W2 with respect to the tyre of the left front wheel W1.

[0053] In practice, at a nominal pressure of both tyres, the condition R.sub.12=1 could not occur because different vertical loads act on the wheels or the tyres have different wear conditions or manufacturing tolerances. In this more general case, it is appropriate to refer to the following conditions:

R.sub.12<R.sub.12.sub.nominal

R.sub.12<R.sub.12.sub.nominal

R.sub.12<R.sub.12.sub.nominal

[0054] where the ratio of the rolling radii of the aforesaid wheels is compared with a nominal value of this ratio acquired in a preliminary learning stage, under known inflation conditions.

[0055] Defining

∈.sub.12=R.sub.12−R.sub.12.sub.nominal

∈.sub.34=R.sub.34−R.sub.34.sub.nominal

∈.sub.rf=R.sub.rf−R.sub.rf.sub.nominal

[0056] and δ the threshold for detecting a deflation condition, the following conditions are given: (1)

ε.sub.12<−δ

|ε.sub.12|<δ & |ε.sub.rf|<δ

∈.sub.12>δ

[0057] which represent a condition of relative deflation of the front left tyre of the wheel W1 with respect to the front right tyre of the wheel W2, a condition of no relative deflation between the front wheel tyres and a condition of relative deflation of the front right tyre of the wheel W2 with respect to the rear left tyre of the wheel W1, respectively; (2)

ε.sub.34<−δ

|ε.sub.34|<δ & |ε.sub.rf|<δ

∈.sub.34>δ

[0058] which represent a condition of relative deflation of the rear left tyre of the wheel W3 with respect to the rear right tyre of the wheel W4, a condition of no relative deflation between the rear wheel tyres and a condition of relative deflation of the rear right tyre of the wheel W4 with respect to the rear left tyre of the wheel W4, respectively; (3)

|∈.sub.rf|>δ & |∈.sub.12|<δ

∈.sub.rf|<−δ & |∈.sub.12<δ

which represent a condition of relative deflation of the front tyres of the wheels W1 and W2 with respect to the rear tyres of the wheels W3 and W4 and a condition of relative deflation of the rear tyres of the wheels W3 and W4 with respect to the front tyres of the wheels W1 and W2, respectively; (4)

∈.sub.12<−δ & ∈.sub.rf<0

∈.sub.12>δ & ∈.sub.rf>0

which represent a condition of relative deflation of the tyres of the wheels W1, W3 and W4 with respect to the front tyre of the wheel W2 and a condition of relative deflation of the tyres of the wheels W2, W3 and W4 with respect to the front tyre of the wheel W1, respectively; and (5)

∈.sub.34<−δ& ∈.sub.rf<0

∈.sub.34>δ& ∈.sub.rf>0

[0059] which represent a condition of relative deflation of the tyres of the wheels W1, W2 and W3 with respect to the rear tyre of the wheel W4 and a condition of relative deflation of the tyres of the wheels W1, W2 and W4 with respect to the rear tyre of the wheel W3, respectively.

[0060] The calculation of the aforementioned indices refers to the travel parameters of the vehicle and to measurable quantities, such as the angular velocity of the wheels, according to the following relationships defined with reference to the vehicle kinematic model shown in FIG. 3:

[00005]$\{\begin{array}{c}{R}_1{\omega }_1\left(1-{\lambda }_1\right)=\left(V_x-\frac{L_f}{2}\psi \right)\cos \delta -\left(V_y-l_f\psi \right)\sin \delta \\ R_2{\omega }_2\left(1-{\lambda }_2\right)=\left(V_x-\frac{L_f}{2}\psi \right)\cos \delta -\left(V_y-l_f\psi \right)\sin \delta \\ R_3{\omega }_3\left(1-{\lambda }_3\right)=\left(V_x-\frac{L_r}{2}\psi \right)\\ R_4{\omega }_4\left(1-{\lambda }_4\right)=\left(V_x-\frac{L_r}{2}\psi \right)\end{array}\mathrm{and}\{\begin{array}{c}\frac{{\omega }_2}{{\omega }_1}=\frac{R_1\left(1-{\lambda }_1\right)}{R_2\left(1-{\lambda }_2\right)}+\frac{L_f}{R_2\left(1-{\lambda }_2\right)}\left(\cos \delta *\frac{\psi }{{\omega }_1}\right)\\ \frac{{\omega }_4}{{\omega }_3}=\frac{R_3\left(1-{\lambda }_3\right)}{R_4\left(1-{\lambda }_4\right)}+\frac{L_f}{R_4\left(1-{\lambda }_4\right)}\left(\frac{\psi }{{\omega }_3}\right)\end{array}$

where ω.sub.i are the angular velocities of each wheel W1-W4, with i=1, 2, 3, 4, λ.sub.i are the slippages of each wheel W1-W4, with i=1, 2, 3, 4, V.sub.x and V.sub.y are respectively the longitudinal and transverse velocity components applied to the center of mass of the vehicle, L.sub.f and L.sub.r are respectively the front and rear track widths of the vehicle axles, l.sub.f and l.sub.r are respectively the front and rear half-wheelbase of the vehicle, ψ is the derivative in time of the direction of travel of the vehicle and δ is the steering angle of the steering wheels of the vehicle.

[0061] The angular velocities of each wheel W1-W4 are measured by wheel revolution sensors of the phonic wheel type, e.g. sensors of a vehicle ABS system, the slippages of each wheel W1-W4 are calculated from the measured wheel velocities, the longitudinal velocity is calculated as an average of the wheel velocities, the front and rear track widths of the vehicle axles and the front and rear half-wheelbase of the vehicle are known and the steering angle of the vehicle's steering wheels is measured by an encoder. The signals or data of angular velocity, slippage, longitudinal and transverse velocity, yaw and steering are collectively indicated at 10 in FIG. 2 and acquired by the on-board CAN network.

[0062] Assuming the assumptions of a rear-wheel drive vehicle, whereby there is no slippage of the front wheel W1 e W2, i.e. λ.sub.1=λ.sub.2=0, and rectilinear travel, whereby {dot over (ψ)}=δ=0, where there is a uniform assumption of rear-wheel drive slippage, i.e. λ.sub.3=λ.sub.4, the preceding equations are simplified as follows

[00006]$\{\begin{array}{c}\frac{{\omega }_2}{{\omega }_1}=+\\ \frac{{\omega }_4}{{\omega }_3}=+\end{array}\mathrm{obtaining}\{\begin{array}{c}\frac{{\omega }_2}{{\omega }_1}=\frac{R_1}{R_2}\\ \frac{{\omega }_4}{{\omega }_3}=\frac{R_3}{R_4}\end{array}$

[0063] The assumptions referred to here are achieved by selecting the signals or data acquired through the selection module 12 and, advantageously, the ratios between the rolling radii of the front and rear wheels

[00007]${\hat{R}}_{12}=f_1\left(\frac{{\omega }_2}{{\omega }_1}\right)\sim \frac{R_1}{R_2}$$\mathrm{and}$${\hat{R}}_{34}=f_2\left(\frac{{\omega }_4}{{\omega }_3}\right)\sim \frac{R_3}{R_4}$

[0064] are filtered, for example, at 0.1 Hz. i.e.

[00008]$\hspace{1em}\{\begin{array}{c}{\hat{R}}_{12}={\mathrm{filt}}_{0.1\mathrm{Hz}}\left(\frac{{\omega }_2}{{\omega }_1}\right)\\ {\hat{R}}_{34}={\mathrm{filt}}_{0.1\mathrm{Hz}}\left(\frac{{\omega }_4}{{\omega }_3}\right)\end{array}$

[0065] to remove high-frequency noise due to quantization of the measurement and to the dynamics of the sensor.

[0066] In FIGS. 4a and 4b three graphs are reproduced, by way of example, showing respectively—from top to bottom—the trend over time of the ratio between the rolling radii of the front wheels R.sub.12, the trend over time of the ratio between the rolling radii of the rear wheels R.sub.34 and the trend over time of the digital anomaly signals D1-D4, indicative of a deflation condition of the tyres associated respectively with the wheels W1-W4 (the notation R indicates the true radius, while notation {circumflex over (R)} indicates an estimate of R; since the value R of the radius is not available, each time it is referred to in the course of the description, it is to be understood as a value {circumflex over (R)}). FIG. 4a shows the case wherein at the time to a variation of 0.2% (corresponding to 0.7 mm) of the rolling radius of the wheel W1 is detected with respect to the rolling radius of the wheel W2, interpreted as a condition of deflation of the tyre associated with the wheel W1, and indicated by the switching of the anomaly signal D1 from a low logic level to a high logic level. FIG. 4b shows the case wherein at the time to a variation of 0.2% (corresponding to 0.7 mm) of the rolling radius of the wheel W3 with respect to the rolling radius of the wheel W4 is detected, interpreted as a condition of deflation of the tyre associated with the wheel W3, and signaled by the switching of the anomaly signal D3 from a low logic level to a high logic level, by comparison with a threshold δ for the detection of a deflation condition the default value of which is—in the case of predetermined tyre models −δ=0.0012.

[0067] With reference to the kinematic vehicle model illustrated in FIG. 5, the following relationships between the average rolling radii of the front wheels and the average rolling radii of the rear wheels are defined.

[00009]$\hspace{1em}\{\begin{array}{c}{R}_f{\omega }_f(1-=V_x-\\ R_r{\omega }_r\left(1-{\lambda }_r\right)=V_x\end{array}$

[0068] where R.sub.f is the average rolling radius of the front wheels W1 and W2, R.sub.r is the average rolling radius of the rear wheels W3 and W4,

[00010]${\omega }_f=\frac{{\omega }_1+{\omega }_2}{2}$$\mathrm{and}$${\omega }_r=\frac{{\omega }_3+{\omega }_4}{2}.$

[0069] With the assumptions—similar to those above—that the vehicle is a rear-wheel drive vehicle, whereby there is no slippage of the front wheel W1 and W2, i.e. λ.sub.f=0, and with rectilinear travel, whereby {dot over (ψ)}=6=0, where there is a uniform assumption of drive-wheel slippage, i.e. λ.sub.3=λ.sub.4, the preceding equations are simplified as follows

[00011]$\frac{{\omega }_f}{{\omega }_r}=\frac{R_r}{R_f}-\frac{R_r}{R_f}{\lambda }_r$

[0070] and it is necessary to estimate the longitudinal slippage component of the rear wheels λ.sub.r.

[0071] To do this, the following considerations are used, referring to physical quantities associated with a vehicle V represented, for ease of understanding, in FIG. 6.

[0072] Assuming to operate in the linear zone of the Pacejka curve, the forward longitudinal force F.sub.x is given by the formula

F.sub.x=F.sub.zr*μ(λr)˜F.sub.zrμ.sub.1λ.sub.r

[0073] where F.sub.zr is the force acting vertically on the rear wheels given by:

[00012]$F_{\mathrm{zr}}=\frac{l_f}{L}Mg+\frac{M{a}_{x}h}{L}$

[0074] where the second term is negligible because the effect of load transfer over long periods of travel is statistically negligible, and

[00013]${\mu }_1=\frac{\partial \mu \left({\lambda }_r\right)}{\partial {\lambda }_r}$

[0075] μ being the longitudinal friction coefficient which corresponds to the ratio of the longitudinal force and the normal force.

[0076] Indicating with F.sub.drag, F.sub.slope and F.sub.roll respectively the aerodynamic force, the slope force related to the case of the vehicle running on a non-horizontal surface, and the rolling force, all ideally applied to the center of mass of the vehicle in the direction opposite to the longitudinal forward force F.sub.x, where

F.sub.slope=Mg sin(α)

F.sub.drag=cV.sub.x.sup.2

[0077] it is recognized that

Ma.sub.x=F.sub.x−F.sub.drag−F.sub.slope−F.sub.roll

[0078] where M is the mass of the vehicle and a.sub.x its longitudinal acceleration, given by

a.sub.x.sub.meas=a.sub.x+g sin(α)

[0079] the longitudinal acceleration signal not being compensated due to the inclination of the vehicle by an angle α with respect to a horizontal plane of travel.

[0080] From the above one may deduce

[00014]$\{\begin{array}{c}{\lambda }_r=\frac{L}{l_{f}g{\mu }_1}{a}_{x_{\mathrm{meas}}}+\frac{L}{l_{f}g{\mu }_1}*V_x^2+\frac{L}{l_{f}g{\mu }_1}*\frac{F_{\mathrm{roll}}}{M}\\ \frac{{\omega }_f}{{\omega }_r}=\frac{R_r}{R_f}-\frac{R_r}{R_f}{\lambda }_r\end{array}\mathrm{and}\frac{{\omega }_f}{{\omega }_r}=\frac{R_r}{R_f}-\frac{R_{r}L}{R_f{l}_{f}g{\mu }_1}{a}_{x_{\mathrm{meas}}}-\frac{R_{r}L}{R_f{l}_{f}g{\mu }_1}*\frac{c}{M}*V_x^2-\frac{R_{r}L}{R_f{l}_{f}g{\mu }_1}*\frac{F_{\mathrm{roll}}}{M}$

[0081] where, considering

[00015]$\tilde{k}=\frac{R_{r}L}{R_f{l}_{f}g{\mu }_1}$

[0082] one obtains

[00016]$\frac{{\omega }_f}{{\omega }_r}=\frac{R_r}{R_f}+\tilde{k}\left(a_{x_{meas}}+\frac{c}{M}{V}_{\chi }^2+\frac{F_{\mathrm{roll}}}{M}\right)$

[0083] wherein R.sub.r/R.sub.f is the index to be estimated and {tilde over (k)} is the grip index of the vehicle, proportional to 1/μ.sub.1 and where it is still possible to write

[00017]$a_{x_{corrected}}=a_{x_{meas}}+\frac{c}{M}{V}_x^2+\frac{F_{\mathrm{roll}}}{M}$

where the parameters c/M and F.sub.roll/M depend on uncertain factors such as vehicle mass, wheel type (e.g. tyre compound and wheel size, which determine the interaction with the road), the road profile, the wind velocity, any change in the aerodynamic profile of the vehicle due to the presence of cargo carriers or bars on the roof of the vehicle, are not known a priori but may be determined at a calibration stage or statistically estimated on the basis of preliminary test results.

[0084] The parameters c/M and F.sub.roll/M may be obtained during the preliminary calibration experimentally, for a given vehicle, by measuring the acceleration of the vehicle by means of calibrated accelerometers and the longitudinal velocity of the vehicle by means of encoders coupled to the wheels of the vehicle and by applying known methods of regression analysis. For example, the inventors have estimated the parameters c/M and F.sub.roll/M for a prototype vehicle used in tests as

[00018]$\frac{M}{}=0.1086$$\frac{\hat{c}}{M}=3.92e-4$

[0085] minimizing the maximum error between the different tests conducted, the results of which are shown in the graph in FIG. 7, in which the four curves drawn represent coasting down tests where the vehicle starts up from a standstill and then decelerates, the coasting down tests being known to a person skilled in the art to determine the friction parameters and resistance for a specific vehicle.

[0086] The synthetic expression of the previous relationship is:

[00019]$\frac{{\omega }_f}{{\omega }_r}=R_{\mathrm{rf}}+\tilde{k}{a}_{x_{\mathrm{corrected}}}$

[0087] where ω.sub.ƒ/ω.sub.r and a.sub.x_corrected are measured or measurable signals or even data that may be calculated on the basis of the results of some measurements, while R.sub.rf and {tilde over (k)} are parameters to be estimated, for example by applying known methods of regression analysis such as a technique of recursive least squares, represented as an example in FIG. 8.

[0088] FIG. 9 shows, by way of example, two graphs showing respectively—from top to bottom—the trend over time of the ratio between the average rolling radii of the rear wheels and the average rolling radii of the front wheels, indicated collectively at R.sub.rf, and the trend over time of the digital signals of anomaly D1-D4, indicative of a condition of deflation of the tyres associated respectively with the wheels W1-W4. FIG. 9 shows the case wherein at the time to a variation of 0.3% (corresponding to about 1 mm) of the average rolling radius of the rear wheels W3 and W4 is detected with respect to the rolling radius of the front wheels W1 and W2, interpreted as a condition of deflation of the tyres associated with the rear wheels W3 and W4, and signaled by the switching of the anomaly signal D3, D4 from a low logic level to a high logic level, by comparison with a threshold δ.sub.rf for the detection of a deflation condition the predetermined value of which is a function of the tyre model.

[0089] It is important to note that a.sub.x_corrected, being based on the parameters c/M and F.sub.roll/M which are preliminarily identifiable and constant, but influenced in their current value by multiple factors such as vehicle mass, wheel type, road profile, wind velocity, modification of the aerodynamic profile of the vehicle, is potentially affected by an error depending on the current velocity of the vehicle, which introduces an estimation error of R.sub.rf. Assuming a learning stage is conducted in a condition of high grip (ideal), the estimation error on R.sub.rf due to the compensation uncertainties of the acceleration may be expressed as:

δR.sub.rf=|R.sub.rf.sub.learning−R.sub.rf.sub.online|=(|{tilde over (k)}.sub.high|+|{tilde over (k)}.sub.online|)*∈.sub.F.sub.resMAX(V.sub.x)

[0090] where

[0091] |{tilde over (k)}.sub.high| is the grip index in conditions of high grip in the learning stage;

[0092] |{tilde over (k)}.sub.online| is the grip index in the current execution conditions of the estimation process; and

[0093] ∈.sub.F.sub.resMAX(V.sub.x) is the error on the value of A.sub.x in the worst case.

[0094] Considering experimental conditions, the inventors have found that the sensitivity of R.sub.rf to the uncertainties of the parameters c/M and F.sub.roll/M is amplified in conditions of low grip, as shown in the graph in FIG. 10, in which the curve L indicates the trend of the variation R.sub.rf as a function of the longitudinal velocity of the vehicle in a condition of low grip and the curve H indicates the trend of the variation of R.sub.rf as a function of the longitudinal velocity of the vehicle in a condition of high grip.

[0095] It is therefore expedient to increase the tolerances on the pressure values, i.e. to relax the detection tolerances, in conditions of low grip and high velocity, and this condition may be advantageously implemented by the module 18 estimating the pressure on the basis of the data indicative of the slippage on the ground of the pair of tyres of the vehicle's drive wheels provided by the module 16 and on the basis of the current longitudinal velocity data of the vehicle provided by the CAN 10 network.

[0096] In FIG. 11 the trend of the curves L, H of variation of R.sub.rf as a function of the longitudinal velocity of the vehicle and of the grip conditions is shown superimposed on two curves δ.sub.20 and δ.sub.40 representing the development of the threshold δ for the detection of a deflation condition, adapted to the grip conditions and to the current velocity of the vehicle to ensure the detection of a deflation condition of at least 20% in conditions of high grip and for speeds up to 130 km/h, the detection of a deflation condition of at least 40% in conditions of low grip and for speeds up to 100 km/h and the absence of false positives due to the uncertainties considered (excluding uncertainties related to wind velocity, road conditions and variations in aerodynamics).

[0097] The inventors have acknowledged that low grip conditions, such as those encountered in off-road driving, also influence the trend of indices R.sub.12 and R.sub.34, as shown in FIGS. 12a and 12b, which respectively represent the trend of indices R.sub.12 and R.sub.34 over time in the passage between a high grip zone H and a low grip zone L and the distribution of the values assumed by the example index R.sub.12) in the different grip conditions. The graph in FIG. 12b shows, in particular, a first distribution H of the values assumed by the index R.sub.12 in the condition of high grip and a second distribution L of the values assumed by the index R.sub.12 in the condition of low grip, the distribution L presenting a greater standard deviation (indicative of a more “noisy” index R.sub.12) and an average value deviating from the average value of the distribution H and close to the threshold 320 represented by the vertical line T.

[0098] FIG. 13 shows the trend over time of the deflation indices R.sub.12, R.sub.34 and R.sub.rf and of the grip conditions represented by the curve G of the graph below, together with the trend over time of the threshold curves δ.sub.+ and δ.sub.− for the detection of a deflation condition, the step variation of which is determined by the detection of the variation of the grip conditions, and assumes, by way of example, values equal to:

[00020]${\delta }_{12}={\delta }_{34}=\{\begin{array}{cc}0.0012& \mathrm{HighGrip}\\ 0.0028& \mathrm{LowGrip}\end{array}$

[0099] For this reason, preferably, detection of the change in grip conditions should be as rapid as possible, for example by performing a regression analysis of the curve

[00021]$\frac{{\omega }_f}{{\omega }_r}=R_{\mathrm{rf}}+\tilde{k}{a}_{x_{\mathrm{corrected}}}$

[0100] for the application of the technique of recursive least squares with forgetting factor ƒ.sub.ƒ equal to 0.999 (instead of ƒ.sub.ƒ=0.9999 as for example adoptable in the regression analysis aimed to obtain the index R.sub.rf).

[0101] Naturally, since the implementation of a system for estimating the pressure of the tyres of a vehicle according to the three-index approach described in the previous section allows for the deflation of one, two or three tyres to be detected, but not of all four tyres at the same time, nor for the absolute values of the tyre pressure to be determined, a further refinement to the system of the invention may be made using the signals or measurement data of at least one actual pressure of a tyre provided by a sensor SP, shown in FIG. 1 as an option.

[0102] The knowledge of at least one actual pressure of a tyre allows a deflation condition of all four tyres of the vehicle to be estimated if the conditions of absence of anomaly found by the determination of the three indices (R.sub.12R.sub.34, R.sub.rf) and of pressure measured by the single sensor lower than a nominal reference pressure are met simultaneously.

[0103] Moreover, the knowledge of at least one real tyre pressure allows the absolute values of the pressures of the other tyres to be estimated, assuming a linear relationship between the pressure of a tyre and the rolling radius of the relative wheel according to the general relationship P.sub.i=K*R.sub.i+P.sub.0, assuming that in a nominal learning condition all the tyres have the same nominal pressure value P.sub.n, and the proportionality parameter K is constant for all tyre types or may be obtained from a table of K values for tyre models.

[0104] As a first approximation, it is therefore possible to estimate the absolute values of the pressures of all tyres according to the following relationships

[00022]$P_2=P_1-\tilde{K}\left(R_{12}-R_{{12}_{\mathrm{nominale}}}\right)$$P_3=P_1-\tilde{K}\left(R_{13}-R_{{14}_{\mathrm{nominale}}}\right)$$P_4=P_1-\tilde{K}\left(R_{14}-R_{{14}_{\mathrm{nominale}}}\right)$$\tilde{K}=\frac{R_{1_{\mathrm{nominale}}}}{K}$

[0105] where P.sub.1 is the directly measured actual pressure value of the tyre equipped with the pressure sensor SP (in the example, the tyre associated with the wheel W1), and the indexes R.sub.13 and R.sub.14 of relationship between the rolling radius of the wheel W1 and the rolling radius of the wheel W3, respectively W4 may be calculated from the indexes R.sub.12, R.sub.34, R.sub.rf calculated by the module 14 according to the relationships:

[00023]$R_{13}={\left(\frac{1+\frac{1}{R_{12}}}{1+\frac{1}{R_{34}}}*R_{\mathrm{rf}}\right)}^{-1}$$R_{14}={\left(\frac{1+\frac{1}{R_{12}}}{1+R_{34}}*R_{\mathrm{rf}}\right)}^{-1}$

[0106] It should be noted that the embodiment proposed for the present invention in the foregoing discussion is purely illustrative and non-limiting. A person skilled in the art may easily implement the present invention in different embodiments which however do not depart from the principles outlined herein and are therefore included in the present patent.

[0107] This applies in particular to the possibility of applying the method described by exchanging the rear-wheel drive axle with the front-wheel drive axle or in the case of a four-wheel-drive vehicle, and of extending the method described to vehicles having more than two wheels per axle or more than two axles.

[0108] Obviously, without prejudice to the principle of the invention, the embodiments and the details of implementation may be greatly modified with respect to those described and illustrated purely by way of non-limiting example, without thereby departing from the scope of protection of the invention as defined in the accompanying claims.