Automatic control method, usable in particular for maintaining the slip of a tire at an optimum level

• US 6,923,050 B2
• Filed: 06/12/2003
• Issued: 08/02/2005
• Est. Priority Date: 06/13/2002
• Status: Expired due to Fees

• Current Assignee: Michelin Recherche et Technique SA (Compagnie Generale DES Etablissements Michelin SCA)
• Original Assignee: Michelin Recherche et Technique SA (Compagnie Generale DES Etablissements Michelin SCA)
• Inventors: Levy, Georges, Fangeat, Nicolas
• Primary Examiner(s): Cygan, Micheal
• Assistant Examiner(s): ALLEN, ANDRE J
• Application Number:
  US10/460,007
• Publication Number:
  US 20040024514A1
• Time in Patent Office: 782 Days
• Field of Search: 731/46, 731/462, 731/463, 731/464, 731/465, 731/468, 73/9, 701/74, 303/150, 303/149, 303/148
• US Class Current: 73/146
• CPC Class Codes: B60T 2210/12 Friction
• CPC Class Codes: B60T 8/172 Determining control parameters used in the regulation, e.g. by calculations involving measured or detected parameters B60T8/17551 takes precedence
• CPC Class Codes: G05B 13/024 in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

An automatic control method is provided for a phenomenon in which a parameter Y varies as a function of a parameter X according to a course exhibiting a rise, an extremum and a fall, in which the value of the parameter X is automatically controlled to maintain the value of a parameter Y at an optimum value, including the following steps. Estimations or measurements (X_i, Y_i) are determined for at least one pair of values in a coordinate system having an origin. Corresponding values are determined for the slope α_i of the straight line passing through the origin and through (X_i, Y_i). Coefficients A_p are calculated by direct calculation or by a regression from a sufficient number of pairs with (α_i, X_i) so as to model a variation curve α_i=f(X_i, A_p). A target value X_Target is calculated by using a predetermined Invariant “Invt”. In addition, applications relating to the testing and the functioning of the tires on a vehicle are provided, for example for controlling the grip on braking, with Y being the coefficient of friction and X being the slip of the tire under torque.

Claims

1. A method for testing a tire in terms of slip comprising the following steps:

(a) causing the tire to roll on a selected ground;

(b) applying a predetermined load F_Z1 to the tire;

(c) applying a predetermined slip to the tire;

(d) measuring or estimating the longitudinal force F_X1 of the tire;

(e) calculating a value of the coefficient of friction μ

₁=F_X1/F_Z1;

(f) repeating the previous steps for calculating at least one other value “

i”

of the coefficient of friction μ

_i for at least one other pair “

i”

of stresses F_Xi/F_Zi and measuring the associated slip G_i;

(g) determining for each of the calculated values of the coefficient of friction the slope α

_i of the straight line passing through the origin and through (G_i, μ

_i);

(h) calculating coefficients A_p by direct calculation or by an appropriate regression from a sufficient number of pairs with (α

_i, G_i) so as to model a variation curve α

_i=f(G_i, A_p); and

(i) calculating an optimum slip enabling a predetermined value of the coefficient of friction G^Opt to be attained, by using a predetermined Invariant “

Invt”

.

2. A test method according to claim 1, in which the Invariant is determined as follows:

$\mathrm{Invt}=\frac{\frac{\mathrm{\mu <br><br>}}{G}<br><br>\left(G_{\max }\right)}{\frac{\mathrm{\mu <br><br>}}{G}<br><br>\left(p·<br><br>G_{\max }\right)},$

with p having a positive value less than 1.

3. A test method according to claim 1, in which the Invariant “

Invt”

is used as an adjustment parameter to refine the method.

7. A test method according to claim 1, 2,3,4, or 5, in which the coefficients A_p are calculated by a regression chosen from the group consisting of a linear regression and an exponential regression.

8. A test method according to claim 1, 2,3,4, or 5, for automatically controlling the drift angle δ

of a tire, in which the value of p is between 0.25 and 0.75.

9. A test method according to claim 2, or 5, for automatically controlling the drift angle δ

of a tire in which p is 0.5.

10. A test method according to claim 2, in which two particular coefficients A_p, the coefficients A and B, are calculated by the following linear regression, applied to “

n”

measured or estimated points (G_i, μ

_i);

$A^{\mathrm{Lin}}=\frac{n·<br><br>\sum <br><br>G·<br><br>\mathrm{\alpha <br><br>}-\sum <br><br>G·<br><br>\sum <br><br>\mathrm{\alpha <br><br>}}{n·<br><br>\sum <br><br>G^2-{\left(\sum <br><br>G\right)}^2},<br><br>B^{\mathrm{Lin}}=\frac{\sum <br><br>\mathrm{\alpha <br><br>}·<br><br>\sum <br><br>G^2-\sum <br><br>G·<br><br>\mathrm{\alpha <br><br>}·<br><br>\sum <br><br>G}{n·<br><br>\sum <br><br>G^2-{\left(\sum <br><br>G\right)}^2}.$

11. A test method according to claim 2, in which two particular coefficients A_p, the coefficients A and B, are calculated by the following exponential regression, applied to “

n”

measured or estimated points (G_i, μ

_i);

$\begin{array}{c}{A}^{\mathrm{Exp}}=\frac{n·<br><br>\sum <br><br>G·<br><br>\mathrm{Ln}<br><br>\left(\mathrm{\alpha <br><br>}\right)-\sum <br><br>G·<br><br>\sum <br><br>\mathrm{Ln}<br><br>\left(\mathrm{\alpha <br><br>}\right)}{n·<br><br>\sum <br><br>G^2-{\left(\sum <br><br>G\right)}^2},\\ B^{\mathrm{Exp}}=\frac{\sum <br><br>\mathrm{Ln}<br><br>\left(\mathrm{\alpha <br><br>}\right)·<br><br>\sum <br><br>G^2-\sum <br><br>G·<br><br>\mathrm{Ln}<br><br>\left(\mathrm{\alpha <br><br>}\right)·<br><br>\sum <br><br>G}{n·<br><br>\sum <br><br>G^2-{\left(\sum <br><br>G\right)}^2}.\end{array}$

12. A test method according to claim 10, in which G^Opt is calculated as follows:

$G^{\mathrm{Opt}}=-\frac{B^{\mathrm{Lin}}}{A^{\mathrm{Lin}}}·<br><br>\frac{1-\mathrm{Invt}}{1-p·<br><br>\mathrm{Invt}},$

with α

=A^Lin·

G+B^Lin

13. A test method according to claim 11, in which G^Opt is calculated as follows:

$G^{\mathrm{Opt}}=\frac{\mathrm{Ln}<br><br>\left(\mathrm{Invt}\right)}{p·<br><br>A^{\mathrm{Exp}}},\mathrm{with}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\alpha <br><br>}={\mathrm{e<br><br>}}^{A^{\mathrm{Exp}}·<br><br>G+B^{\mathrm{Exp}}}.$

14. A test method according to claim 10, in which in addition the value of μ

corresponding to G^Opt is determined as follows;

μ

=μ

<sup>Coeff—

lin</sup>·

G^Opt·

(A^Lin·

G^Opt+B^Lin)

15. A test method according to claim 11, in which in addition μ

_max is determined as follows;

μ

_max=μ

<sup>Coeff—

exp</sup>·

G^Opt·

e<sup>AExp·

GOpt+AExp</sup>

4. A method for testing a tire in terms of drift comprising the following steps:

(a) causing the tire to roll on the ground;

(b) applying a predetermined load F_Z1 to the tire;

(c) applying a predetermined drift angle δ

_i to the tire, such that the tire remains below the grip limit, and measuring or estimating the drift thrust F_i corresponding to said drift angle δ

_i;

(d) repeating the previous steps for calculating at least one other pair “

i of values (δ

_i, F_i);

(e) determining the corresponding values of the slope α

_i of the straight line passing through the origin and through (δ

_i, F_i);

(f) calculating coefficients A_p by direct calculation or by an appropriate regression from a sufficient number of pairs (α

_i, δ

_i) so as to model a variation curve α

_i=f(δ

_i, A_p ); and

(g) calculating a value of the drift angle δ

^Opt by using a predetermined Invariant “

Invt”

.

5. A test method according to claim 4, in which the Invariant is determined as follows:

$\mathrm{Invt}=\frac{\frac{F}{\mathrm{\delta <br><br>}}<br><br>\left({\mathrm{\delta <br><br>}}^{\mathrm{Opt}}\right)}{\frac{F}{\mathrm{\delta <br><br>}}<br><br>\left(p·<br><br>{\mathrm{\delta <br><br>}}^{\mathrm{Opt}}\right)},$

with p having a positive value less than 1.

6. A test method according to claim 4, in which the Invariant “

Invt”

is used as an adjustment parameter to refine the method.

16. A test method according to claim 4, in which two particular coefficients A_p, the coefficients A and B, are calculated by the following linear regression, applied to “

n”

measured or estimated points (δ

_i, F_i);

$A^{\mathrm{Lin}}=\frac{n·<br><br>\sum <br><br>\mathrm{\delta <br><br>}·<br><br>\mathrm{\alpha <br><br>}-\sum <br><br>\mathrm{\delta <br><br>}·<br><br>\sum <br><br>\mathrm{\alpha <br><br>}}{n·<br><br>\sum <br><br>{\mathrm{\delta <br><br>}}^2-{\left(\sum <br><br>\mathrm{\delta <br><br>}\right)}^2},<br><br>B^{\mathrm{Lin}}=\frac{\sum <br><br>\mathrm{\alpha <br><br>}·<br><br>\sum <br><br>{\mathrm{\delta <br><br>}}^2-\sum <br><br>\mathrm{\delta <br><br>}·<br><br>\mathrm{\alpha <br><br>}·<br><br>\sum <br><br>\mathrm{\delta <br><br>}}{n·<br><br>\sum <br><br>{\mathrm{\delta <br><br>}}^2-{\left(\sum <br><br>\mathrm{\delta <br><br>}\right)}^2}.$

17. A test method according to claim 4, in which two particular coefficients A_p, the coefficients A and B, are calculated by the following exponential regression, applied to “

n”

measured or estimated points (δ

_i, F_i);

$\begin{array}{c}{A}^{\mathrm{Exp}}=\frac{n·<br><br>\sum <br><br>\mathrm{\delta <br><br>}·<br><br>\mathrm{Ln}<br><br>\left(\mathrm{\alpha <br><br>}\right)-\sum <br><br>\mathrm{\delta <br><br>}·<br><br>\sum <br><br>\mathrm{Ln}<br><br>\left(\mathrm{\alpha <br><br>}\right)}{n·<br><br>\sum <br><br>{\mathrm{\delta <br><br>}}^2-{\left(\sum <br><br>\mathrm{\delta <br><br>}\right)}^2},\\ B^{\mathrm{Exp}}=\frac{\sum <br><br>\mathrm{Ln}<br><br>\left(\mathrm{\alpha <br><br>}\right)-\sum <br><br>{\mathrm{\delta <br><br>}}^2-\sum <br><br>\mathrm{\delta <br><br>}·<br><br>\mathrm{Ln}<br><br>\left(\mathrm{\alpha <br><br>}\right)·<br><br>\sum <br><br>\mathrm{\delta <br><br>}}{n·<br><br>\sum <br><br>{\mathrm{\delta <br><br>}}^2-{\left(\sum <br><br>\mathrm{\delta <br><br>}\right)}^2}.\end{array}$

18. A test method according to claim 16, which δ

^Opt is calculated as follows;

${\mathrm{\delta <br><br>}}^{\mathrm{Opt}}=-\frac{B^{\mathrm{Lin}}}{A^{\mathrm{Lin}}}·<br><br>\frac{1-\mathrm{Invt}}{1-p·<br><br>\mathrm{Invt}},$

with α

=A^Lin·

δ

+B^Lin

19. A test method according to claim 17, in which δ

^Opt is calculated as follows;

${\mathrm{\delta <br><br>}}^{\mathrm{Opt}}=\frac{\mathrm{Ln}<br><br>\left(\mathrm{Invt}\right)}{p·<br><br>A^{\mathrm{Exp}}},\mathrm{with}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\alpha <br><br>}={\mathrm{e<br><br>}}^{A^{\mathrm{Exp}}·<br><br>\mathrm{\delta <br><br>}+B^{\mathrm{Exp}}}.$

20. A test method according to claim 18, in which in addition F^Target is determined as follows:

F^Target=F<sup>Coeff—

lin</sup>·

δ

^Opt·

(A^Lin·

δ

^Opt+B^Lin)

21. A test method according to claim 19, in which in addition F^Target is determined as follows:

F^Target=F<sup>Coeff—

exp</sup>·

δ

^Opt·

e<sup>AExp·

δ

Opt+BExp</sup>