Automatic control method, usable in particular for maintaining the slip of a tire at an optimum level
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.
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:
Invt
=
μ
G
(
G
max
)
μ
G
(
p
·
G
max
)
,
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.
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:
Invt
=
F
δ
(
δ
Opt
)
F
δ
(
p
·
δ
Opt
)
,
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.
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
Lin
=
n
·
∑
G
·
α
-
∑
G
·
∑
α
n
·
∑
G
2
-
(
∑
G
)
2
,
B
Lin
=
∑
α
·
∑
G
2
-
∑
G
·
α
·
∑
G
n
·
∑
G
2
-
(
∑
G
)
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 ):
A
Exp
=
n
·
∑
G
·
Ln
(
α
)
-
∑
G
·
∑
Ln
(
α
)
n
·
∑
G
2
-
(
∑
G
)
2
,
B
Exp
=
∑
Ln
(
α
)
·
∑
G
2
-
∑
G
·
Ln
(
α
)
·
∑
G
n
·
∑
G
2
-
(
∑
G
)
2
.
12. A test method according to claim 10 , in which G Opt is calculated as follows:
G
Opt
=
-
B
Lin
A
Lin
·
1
-
Invt
1
-
p
·
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
Opt
=
Ln
(
Invt
)
p
·
A
Exp
,
with
α
=
ⅇ
A
Exp
·
G
+
B
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 Coeff — lin ·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 Coeff — exp ·G Opt ·e A Exp ·G Opt +A Exp
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
Lin
=
n
·
∑
δ
·
α
-
∑
δ
·
∑
α
n
·
∑
δ
2
-
(
∑
δ
)
2
,
B
Lin
=
∑
α
·
∑
δ
2
-
∑
δ
·
α
·
∑
δ
n
·
∑
δ
2
-
(
∑
δ
)
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 ):
A
Exp
=
n
·
∑
δ
·
Ln
(
α
)
-
∑
δ
·
∑
Ln
(
α
)
n
·
∑
δ
2
-
(
∑
δ
)
2
,
B
Exp
=
∑
Ln
(
α
)
-
∑
δ
2
-
∑
δ
·
Ln
(
α
)
·
∑
δ
n
·
∑
δ
2
-
(
∑
δ
)
2
.
18. A test method according to claim 16 , which δ Opt is calculated as follows:
δ
Opt
=
-
B
Lin
A
Lin
·
1
-
Invt
1
-
p
·
Invt
,
with α= A Lin ·δ+B Lin
19. A test method according to claim 17 , in which δ Opt is calculated as follows:
δ
Opt
=
Ln
(
Invt
)
p
·
A
Exp
,
with
α
=
ⅇ
A
Exp
·
δ
+
B
Exp
.
20. A test method according to claim 18 , in which in addition F Target is determined as follows:
F Target =F Coeff — lin ·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 Coeff — exp ·δ Opt ·e A Exp ·δ Opt +B Exp