Method for evaluating the firmness of a ground

Abstract

A method for evaluating the firmness of the ground on which is running a vehicle equipped with at least one mounted assembly having a radial stiffness k.sub.radial comprising a tyre casing having a crown, two sidewalls and two beads, equipped with a sensor sensitive to the circumferential curvature and positioned in line with the crown, comprises the following steps: Estimating a value of the curvature ρ.sub.A of the tire casing corresponding to first steady-state conditions of the tire casing in contact with the ground; and Evaluating the relative firmness of the ground with respect to the radial stiffness k.sub.radial of the mounted assembly as being a function of the value of the curvature ρ.sub.A of the tire casing.

Claims

1. A method for evaluating firmness of a ground on which is running a vehicle equipped with at least one mounted assembly having a radial stiffness k.sub.radial comprising a tire casing having a crown, two sidewalls and two beads, equipped with at least one sensor sensitive to a circumferential curvature and positioned in line with the crown, comprising the following steps: estimating a value of a curvature p A of the tire casing corresponding to first steady-state conditions of the tire casing in contact with the ground; and evaluating a relative firmness of the ground with respect to the radial stiffness k.sub.radial of the at least one mounted assembly as being a function of the value of the curvature ρ.sub.A of the tire casing.

2. The method according to claim 1 further comprising: estimating a value of a curvature ρ.sub.B of the tire casing corresponding to second steady-state conditions of the tire casing not in contact with the ground; and evaluating the relative firmness of the ground with respect to the radial stiffness k.sub.radial of the at least one mounted assembly as being a function of the values of the curvature ρ.sub.A and ρ.sub.B of the tire casing.

3. The method according to claim 2 further comprising: establishing a relative curvature C as being a ratio ρ.sub.A/ρ.sub.B of the curvatures of the tire casing in contact or not in contact with the ground; and evaluating the relative firmness of the ground with respect to the radial stiffness k.sub.radial of the at least one mounted assembly as being a function of the relative curvature C.

4. The method according to claim 3 further comprising: evaluating the relative firmness of the ground with respect to the radial stiffness k.sub.radial of the at least one mounted assembly by applying the following formula in which the parameters α, β1 and β2 are coefficients dependent on the at least one mounted assembly and P is the inflation pressure of the mounted assembly: $\frac{k_{\mathrm{ground}}}{k_{\mathrm{radial}}}=\frac{.Math.1+\alpha *C-\left(1+\alpha \right)*C^2.Math.}{{\beta }_1*P^{{\beta }_2}*C}.$

5. The method according to claim 1, wherein, with the tire casing defining a contact patch, by applying nominal conditions of use of the at least one mounted assembly, the contact patch having a dimension Ladc in an axial direction of the at least one mounted assembly, the at least one sensor, upon each measurement, evaluates the mean circumferential curvature over a length comprised between 10% and 80% of the dimension Ladc.

6. The method according to claim 5, wherein, with the tire casing defining a contact patch having a dimension ladc in a transverse direction of the at least one mounted assembly, the at least one sensor, upon each measurement, evaluates a mean circumferential curvature over a width comprised between 10% and 80% of the width ladc.

7. The method according to claim 1, wherein the at least one sensor measures a mean curvature of a zone of the crown of the tire casing in contact with the ground that is homogeneous in terms of radial stiffness.

8. The method according to claim 1, wherein the at least one sensor measures a mean curvature of a zone of the crown in line with a tread pattern element of the tire casing.

9. The method according to claim 2, wherein the estimation of the curvature values corresponding to the first and second steady-state conditions in terms of boundary conditions of the tire casing comprises the following steps: obtaining a recorded signal from the at least one sensor sensitive to curvature corresponding to N revolutions of the wheel of the mounted assembly, N being an integer strictly greater than 1; identifying in the recorded signal the 2N local maxima Y.sub.2N, and corresponding abscissa values X.sub.2N; for any j, being an integer strictly greater than 1 and strictly less than 2N, if (X.sub.j−X.sub.j−1)<(X.sub.j+1−X.sub.j), (a) isolating a first signal in the recorded signal between the central maximum (X.sub.j, Y.sub.j) and a previous maximum (X.sub.j−1, Y.sub.j−1); (b) identifying the steady-state conditions curvature value denoted ρ.sub.j in the first signal; (c) isolating a second signal in the recorded signal between the central maximum (X.sub.j, Y.sub.j) and the next maximum (X.sub.j+1, Y.sub.j+1); and (d) identifying the steady-state conditions curvature value denoted ρ.sub.j+1 in the second signal; and if (X.sub.j−X.sub.j−1) is not less than (X.sub.j+1−X.sub.j), (a) isolating a first signal in the recorded signal between the central maximum (X.sub.j, Y.sub.j) and the next maximum (X.sub.j+1, Y.sub.j+1); (b) identifying the steady-state conditions curvature value denoted ρ.sub.j in the first signal; (c) isolating a second signal in the recorded signal between the central maximum (X.sub.j, Y.sub.j) and the previous maximum (X.sub.j−1, Y.sub.j−1); and (d) identifying the steady-state conditions curvature value denoted ρ.sub.j+1 in the second signal; and establishing the curvature of the tire casing under conditions of contact with the ground ρ.sub.A as being the mean of the at least one curvature value ρ.sub.j and the curvature of the tire casing under conditions not in contact with the ground ρ.sub.B as being the mean of the at least one curvature value ρ.sub.j+1.

10. The method according to claim 9, wherein the obtaining of the recorded signal from the at last one sensor sensitive to the curvature corresponding to N revolutions of the wheel of the mounted assembly comprises the following steps: recording a signal emitted by the at least one sensor sensitive to the curvature corresponding to one revolution of the wheel of the mounted assembly; and periodizing the signal emitted over N periods, N being an integer greater than 1.

11. The method according to claim 9, wherein, with the at least one sensor outputting an indirect parameter for the circumferential curvature of the tire casing involving at least one parameter that is variable, the method further comprises: correcting the indirect parameter on the signal recorded using the at least one variable parameter.

12. The method according to claim 9, wherein the curvature of the tire casing under conditions of contact with the ground ρ.sub.j is evaluated on a signal reduced from the first signal.

13. The method according to claim 12, wherein the signal reduced from the first signal corresponds to the first half of the first signal.

14. The method according to claim 12, wherein the signal reduced from the first signal corresponds to the second half of the first signal.

15. The method according to claim 13, wherein the identification of the values for curvature under conditions of contact with the ground ρ.sub.j comprises making the reduced signal symmetrical over an interval corresponding to the reduced signal in order to obtain a new signal in the form of a square wave.

16. The method according to claim 14, wherein the identification of the values for curvature under conditions of contact with the ground ρ.sub.j comprises making the reduced signal symmetrical over an interval corresponding to the reduced signal in order to obtain a new signal in the form of a square wave.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention will be better understood upon reading the following description, given solely by way of example and with reference to the appended figures, throughout which the same reference numerals denote identical parts, and in which:

(2) FIG. 1 shows a flowchart of the steps in the method for evaluating the firmness of the ground according to the invention;

(3) FIG. 2 shows the signals recorded by two sensors sensitive to circumferential curvature which are positioned either in line with a tread pattern element according to the invention, or in the space between two tread pattern elements;

(4) FIGS. 3a and 3b show the steps in the processing of a signal outputting the direct quantity for circumferential curvature.

DETAILED DESCRIPTION OF EMBODIMENTS

(5) FIG. 1 shows a flowchart of the various compulsory and optional steps regarding the method for evaluating the firmness of the ground. The starting point lies in a signal 102 emitted by a sensor sensitive to circumferential curvature. The spatial discretization of this signal needs to be sufficient to suitably describe the passage through the contact patch. A minimum of six measurement points in the contact patch is needed. This signal may be a direct measurement of the circumferential curvature via a bending sensor or an indirect measurement via, for example, a mono-axis accelerometer positioned radially with respect to the tyre casing or else a piezoelectric sensor the main direction of which is positioned circumferentially with respect to the tyre casing.

(6) This signal may be supplemented by other signals 101 and 103 useful in exploiting the curvature signal 102. In particular, in instances in which the curvature signal 102 is influenced by variable parameters, it is necessary, in order to correct the curvature signal 102, also to record the variation of these variable parameters. In addition, a signal 103 of the encoder type or a revolution marker pulse is also needed in order to isolate the response of the signals over the revolution of the wheel of the mounted assembly. Of course, the synchronization 104 of all these signals is a prerequisite to any information-processing method. At the end of this first process, the method generates curvature signals 108 corresponding to a finite number N of revolutions of the wheel which have, if necessary, been corrected for the fluctuations in the variable parameters.

(7) The second process consists in determining the values representative of the circumferential curvature in each of the steady-state conditions of the mounted assembly. What is meant here by “steady-state conditions” is that the boundary conditions applied to the crown zone of the tyre casing which is situated in line with the sensor are identical, namely either in contact with the ground or not in contact with the ground.

(8) To this end, the great variations in curvature on entering and leaving the contact patch are put to good use to distinguish the zones of steady-state conditions in the signal from the sensor sensitive to curvature. In this way it is easy to determine the local maxima 110 on the curvature signal 108 corresponding to a finite number of revolutions of the wheel. Pairwise comparison of the ordinate values of these local maxima makes it possible easily to identify those parts of the signal 108 that correspond to one or other of the sets of steady-state conditions. Specifically, the size of the contact patch is necessarily small on the scale of the perimeter of the mounted assembly because of the toroidal shape of the tyre casing. Thus, comparing the distances between the ordinate values of the previous and next local maxima clearly indicates those zones of the tyre casing that are in contact or not in contact with the ground.

(9) The curvature signal 108 corresponding to each of these zones delimited by the local maxima can be likened to a square-wave having two fronts with steep variation in curvature, separated by a plateau having a near-constant level of curvature. The isolated fronts correspond to the transition zones marking the transitions between the zones of steady-state conditions. The plateau corresponds to the zone that is stable in terms of boundary conditions applied to the crown of the tyre casing at which the measurement sensor is located. It is this part of the signal that will be subsequently exploited.

(10) For each of these parts of the signal a value representative of curvature associated with the mounted assembly will be determined. This representative value is determined using mathematical methods of the minimum-value, median-value type, least-squares method, or using any other algorithm. The first representative value 111 or 113, denoted ρ.sub.j corresponds to the mean curvature under steady-state conditions of boundary conditions of the type reflecting contact with the ground. The second representative value 112 or 114, denoted ρ.sub.j+1 denotes the mean curvature under steady-state conditions reflecting no contact with the ground. Finally, by averaging the representative values for each of the sets of steady-state conditions across the entire curvature signal 108, there are evaluated, on the one hand, a value for the curvature of the tyre casing under conditions of the type reflecting no contact with the ground 115, denoted ρ.sub.B and, on the other hand, a value for the curvature of the tyre casing of the type reflecting contact with the ground 116, denoted ρ.sub.A.

(11) This last process consists in evaluating the relative firmness of the ground 120 with respect to the radial stiffness of the mounted assembly from the values of curvature of the mounted assembly 115 and 116 considered individually or in combination. If the parameter associated with the circumferential curvature 116 under steady-state conditions of the type reflecting contact with the ground ρ.sub.A taking the stiffness of the ground into consideration is the most relevant, taking the circumferential curvature 115 with no contact with the ground ρ.sub.B into consideration quantitatively improves the determination of the firmness of the ground.

(12) Optionally, it is possible to evaluate the firmness of the ground as the tyre casing sinks into the ground by focusing on the first half of the plateau of the square-wave signal in the direction of travel of the mounted assembly. This measurement is an intrinsic characteristic of the ground. It is also possible to measure the firmness of the ground over the second half of the contact patch, which provides access to the firmness of the ground that may have been modified by the passage of the mounted assembly. The discrepancy between these two distinctive ground-firmness characteristics makes it possible to work back to a parameter that can be likened to the compaction of the ground after the passage of the mounted assembly.

(13) FIG. 2 includes the responses of sensors of piezoelectric type which are sensitive to the circumferential curvature when these sensors are installed on a tyre casing of the Michelin Multibib make, size 650/60 R38 run on a Fendt Turbomatik Favorit 614 LSA tractor. This tyre casing has two series of lugs positioned on the lateral parts of the tread with an angular offset of one series with respect to the other. Specifically, each lug starts from the centre of the crown and extends in a direction that makes an angle of approximately 30 degrees alternately in the clockwise direction and in the anticlockwise direction with respect to the axis X toward the outside.

(14) A first piezoelectric sensor is positioned on the inner liner of the tyre casing with the active part of the sensor fixed in line with a lug. In order to optimize the response of the signal, this sensor is situated as close as possible to the middle of the tread. A second sensor is positioned in line with an inter-lug zone, namely between two lugs. This sensor is also centred as best possible with respect to the width of the crown.

(15) The mounted assembly will run over two types of ground with different firmnesses. The first ground is a road with a bitumen pavement with high stiffness. The second ground is an agricultural field without crops and which has not been ploughed for several days. Thus, the deformation experienced by the tyre casing between the two zones is different, and the sensor sensitive to the circumferential curvature is expected to be able to reflect these phenomena.

(16) The mounted assembly is inflated to a pressure of 1.6 bar and the tractor runs at a constant speed of 10 km/h both on the road and in the agricultural field. The curves 201 and 203 depicted in bold line indicate the response of the first piezoelectric sensor the active part of which lies in line with a lug of the tread. The curves 202 and 204 depicted in fine line are the responses from the second sensor situated in the inter-lug zone. The curves 201 and 202 indicated in continuous line correspond to the running on the road, while the curves 203 and indicated in broken line correspond to the running in the agricultural field.

(17) The signals observed are the mean, over 10 revolutions of the wheel, of the raw outputs from the piezoelectric sensor in volts over a complete revolution of the wheel. The origin for the angles is situated in the vertical direction, with Z positive in the Galilean frame of reference. The sharp change situated in the region of 180 degrees corresponds to the response of the sensor as it passes through the contact patch.

(18) It may be seen fairly clearly that the response of the first sensor is correct according to expectation. A sharp change in its response can also be visualized by comparing the plateaus of the square waves of the curves 201 and 203 corresponding to the passage through the contact patch, which change is proportional to the stiffness of the ground and therefore to the curvature of the tyre casing.

(19) By contrast, the response of the second sensor is not sufficiently discriminating. First of all, the amplitude of the response of the second sensor is markedly lower than that of the first sensor, particularly at the plateau of the square wave, compare curves 202 and 201 or 203 and 204. In addition, the amplitude of the response of the second sensor is similar, and this is true regardless of the nature of the ground, compare curves 202 and 204. As a result, it is indeed found that positioning the sensor in line with a tread pattern element in contact with the ground is a prerequisite for a quality evaluation of the firmness of the ground.

(20) Thus, the sensor sensitive to the circumferential curvature of the tyre casing makes it possible, for the same conditions of use of the mounted assembly, namely for the same inflation pressure, the same applied load and the same running speed, to qualify ground in relative terms according to its firmness.

(21) FIG. 3a shows, on the one hand, a recording with respect to time of an electrical signal emitted by the sensor sensitive to the circumferential curvature, denoted 400 and, on the other hand, pulses from a revolutions marker encoder, denoted 401. The signals are synchronized and discretized at a sampling frequency of 2400 Hz.

(22) The curvature sensor, of piezoelectric type, is installed on a tyre casing of the Michelin Multibib make, size 650/60 R38 run on a Fendt Turbomatik Favorit 614 LSA tractor. The tractor runs over ground of a certain stiffness at a constant speed of 10 km/h. The mounted assembly here is inflated to a pressure of 1.6 bar. The conversion for converting the output voltage of the sensor into curvature is provided. It would also have been possible to use the output signal of an accelerometer positioned in line with the tread pattern element delivering the radial acceleration of the tyre casing, having low-frequency filtered said signal and corrected it for the rotational speed of the mounted assembly. This rotational speed is determined, for example, using the wheel revolutions marker pulse.

(23) Using a revolutions marker mounted on the axle of the tractor comprising the casing that is to be measured and generating Dirac pulses for each revolution of the wheel, a recorded signal corresponding to 5 revolutions of the wheel will be extracted. This recorded signal is the one contained inside the box 1000 drawn in dotted line.

(24) It may be seen that this recorded signal contains 10 local maxima numbered from 501 onwards, namely two per revolution of the wheel. These local maxima correspond to the moment at which the sensor sensitive to the circumferential curvature enters or leaves the contact patch. The spatial separation between two adjacent local maxima differs greatly. Thus, considering one local maximum 506, the preceding and next local maxima 505 and 507 respectively are respectively close to, and distant from, the maximum 506. The circumferential length of the tyre casing in the contact patch being markedly smaller than the remaining circumferential length of the tyre casing, it is obvious that the maximum 505 corresponds to the entering of the contact patch and the maximum 506 to the leaving of the contact patch in the same revolution of the wheel. Finally, the maximum 507 is the entering of the contact patch in the next revolution of the wheel.

(25) It is thus possible easily on the curve 400 to identify the response zones in which the sensor is in the contact patch or not in the contact patch. It will be noted that the response of the sensor exhibits a certain degree of stability whatever the geographical position of the mounted assembly within the field. The spatial discretization of the measurement is approximately five metres. This allows us to average the responses of the sensor over several revolutions of the wheel. If the reverse is true, then a revolution-by-revolution analysis is required. By coupling the wheel revolution information with the geographical position of the tractor in the field using, for example, a GPS (Global Positioning System), it is possible to obtain a map of the stiffness of a given surface with a more or less fine spatial discretization, by multiplying for example the ground firmness measurements. This multitude of measurements may be made up for example of a grid pattern produced with the aid of the movements of the tractor.

(26) FIG. 3b contains the averages, over 5 revolutions of the wheel, of the responses of the curvature sensor mounted on the tyre casing driving either over loose ground 500 or over firm ground 600. The conditions of use of the tyre casing, namely chiefly the inflation pressure, the applied load and the speed of travel are identical.

(27) It may be noted that the curvature of the tyre casing outside of the contact zone is near-constant with a curvature of approximately six degrees. Coherently, the curvature experienced by the tyre casing outside of the contact zone decreases if the mounted assembly is driving over loose ground by comparison with the curvature obtained on stiff ground.

(28) Finally, the curvature in the contact zone differs greatly according to the nature of the ground. On firm ground, the curvature is small because of the flattening of the tyre casing. By contrast, on loose ground, although a drop in curvature is observed by comparison with the condition of not being in contact with the ground, the resulting curvature is still, in this instance, of the order of 50% of the curvature when not in contact with the ground.

(29) In this case, the algorithm used for evaluating the curvature is the median value of the points across the entire plateau. Thus, for the curve 500 corresponding to the loose ground, a value of 3.2 degrees is identified for the curvature ρ.sub.A′ in contact with the ground, and a value of 5.9 degrees is identified for the curvature ρ.sub.B′ not in contact with the ground. Similarly, on the curve 600 for the firm type, a value of around 0.5 degrees is identified for the curvature p A in contact with the ground, and a value of around 6.1 degrees is identified for the curvature ρ.sub.B not in contact with the ground.

(30) A first value of relative curvature, denoted C, and of the order of 0.54, is determined on loose ground, and a second value of relative curvature, denoted C′ and of the order of 0.082 is determined on firm ground.

(31) Prior to this, complementary measurements were undertaken on the mounted assembly. First of all, a numerical simulation campaign, in order to identify how the vertical stiffness of the mounted assembly changes as a function of inflation pressure. Thus, for nominal conditions of use of the mounted assembly in terms of pressure and in terms of applied load, simulations of the vertical stiffness of the mounted assembly were performed following a calculation of squashing on slippery ground to apply the load. This results in the identification of a power law for inflation pressure, of the type (P).sup.γ.

(32) Next, an experimental calibration of the sensor sensitive to the circumferential curvature of the mounted assembly was performed, in order to identify the parameter α of the model. Thus, having previously set an inflation pressure for the mounted assembly that is within the range of service pressures of the mounted assembly, runnings at constant speed, at constant load and in a straight line were undertaken on three grounds of different firmness. Identification, using a least-squares method, allowed the coefficient α of the mounted assembly to be evaluated, namely in this instance, a value of 2.4.

(33) Finally, using the calibration performed previously, a value of the order of 5.95 is obtained for the firmness of the firm ground relative to that of the loose ground, and this is correct because of the differentiated nature of the grounds.

(34) In addition, with the inflation pressure of the same mounted assembly altered to 2.6 bar, curvature measurements for the same two grounds were undertaken.

(35) For the firm ground, the measurement protocol identifies a value of around 1 degree for the curvature ρ.sub.A′ in contact with the ground, and a value of around 6.1 degrees for the curvature ρ.sub.B′ not in contact with the ground. As a result, a value of the order of 0.16 is identified as the relative curvature value C′ for the firm ground.

(36) For the loose ground, a value of around 4.3 degrees is identified for the curvature ρ.sub.A in contact with the ground, and a value of around 6.0 degrees is identified for the curvature ρ.sub.B not in contact with the ground. Therefore, the relative curvature value C for loose ground is of the order of 0.72. And similarly, a value of the order of 6.04 is obtained for the value of the firmness of the firm ground relative to that of the loose ground.

(37) Finally, for this same mounted assembly, a value of the order of −0.4 is identified for coefficient β2 of the empirical law for a coefficient γ identified as being 0.79 describing the change in vertical stiffness of this mounted assembly with respect to inflation pressure.