Methods for estimation of tire wear
A method for controlling the functioning of a tire includes the steps of determining estimations or measurements of the slip G i and the coefficient of friction μ i prevailing at such slip for at least one pair “i” of values (G i , μ i ); determining the corresponding values of the slope α i of the straight line passing through the origin and through each pair (G i , μ i ); calculating a coefficient B by direct calculation or by a regression from a sufficient number of pairs of (α i , G i ) so as to estimate the value of slope α 0 at the origin; and using α 0 in an indicator of the longitudinal stiffness of the tread pattern.
1. A method for controlling the functioning of a tire, comprising the step of:
(a) determining estimations or measurements of the slip G i and the coefficient of friction μ i prevailing at said slip, for at least one pair “i” of values (G i , μ i ) in a coordinate system having an axis G, an axis μ and an origin;
(b) determining the value of the slope α i of the straight line passing through the origin and through each pair of values (G i , μ i );
(c) calculating a coefficient B by direct calculation or by a regression from a sufficient number of pairs of (α i , G i ) so as to estimate the value of slope α 0 at the origin; and
(d) using α 0 in an indicator of the longitudinal stiffness of the tread pattern.
2. A method for controlling the functioning of a tire according to claim 1 , in which the slope α i is determined by direct calculation α i =μ i /G i .
3. A method for controlling the functioning of a tire according to claim 1 , in which the slope α i is determined by carrying out a suitable regression.
4. A method for controlling the functioning of a tire according to claim 1 , in which the following linear regression is carried out:
∑
GG
=
∑
G
j
2
,
∑
G
μ
=
∑
G
j
·
μ
j
,
α
i
=
∑
G
μ
∑
GG
.
5. A method for controlling the functioning of a tire according to claim 1 , in which a coefficient B, representative of the longitudinal stiffness, is calculated by the following linear regression, applied to “n” measured or estimated points:
B
Lin
=
∑
α
·
∑
G
2
-
∑
G
·
α
·
∑
G
n
·
∑
G
2
-
(
∑
G
)
2
.
6. A method for controlling the functioning of a tire according to claim 1 , in which the coefficient B, representative of the longitudinal stiffness, is calculated by the following exponential regression, applied to “n” measured or estimated points:
B
E
xp
=
∑
L
n
(
α
)
·
∑
G
2
-
∑
G
·
L
n
(
α
)
·
∑
G
n
·
∑
G
2
-
(
∑
G
)
2
.
7. A method for controlling the functioning of a tire according to claim 1 , in which an average value of α 0 is determined and a comparison with reference values for the tire subject to processing is made, in order to estimate the wear rate.
8. A method for controlling the functioning of a tire according to claim 7 , wherein an estimation of the remaining height H of the tread pattern is made as follows:
H
=
H
0
·
Stiffness
Stiffness
0
.
9. A method for controlling the functioning of a tire according to claim 7 or 8 , in which an average value of α 0 is determined on the basis of a predetermined number of brakings or accelerations.
10. A method for controlling the functioning of a tire according to claim 7 or 8 , in which an average value of α 0 is determined on the basis of a predetermined distance.