Method for determining the temperature of an internal part of the materials of a tire

1. A method for evaluating thermal stresses associated with use of a tire mounted on a rim, the method comprising steps of:

measuring a temperature of a gaseous fluid contained in an internal cavity of the tire at regular time intervals, in order to obtain a fluid temperature (T AI );

measuring a temperature at location on the rim at regular time intervals, in order to obtain a rim temperature (T j );

determining an estimated temperature (T ZI ) at at least one internal zone of materials of which the tire is made using a pre-established law connecting the estimated temperature (T ZI ) to the fluid temperature (T AI ) and the rim temperature (T j ).

2. The method according to claim 1 , wherein the pre-established law connecting the estimated temperature (T ZI ) to the fluid temperature (T AI ) and the rim temperature (T J ) has a formula of:

T ZI =α T AI T ZI ·T AI +α T j T ZI ·T j +T ZI0

in which, for a given internal zone of a given type of the tire, α T AI T ZI , α T j T ZI , T ZI0 are coefficients that are determined experimentally.

3. The method according to claim 1 , wherein the step of measuring the temperature of the gaseous fluid contained in the internal cavity of the tire at the regular time intervals is performed over a given time period, and

wherein a smoothed temperature (T AIsmoothed ) determined from a weighted mean of the measured temperatures obtained over the given time period is used to determine the estimated temperature (T ZI ).

4. The method according to claim 3 , wherein the smoothed temperature (T AIsmoothed ) is determined using a pre-established law having a formula of:

T

AI

⁢

⁢

smoothed

⁡

(

t

)

=

∑

i

=

1

n

-

1

⁢

1

/

2

⁢

(

T

AI

i

·

p

i

+

T

AI

i

+

1

·

p

i

+

1

)

·

(

t

i

+

1

-

t

i

)

∑

i

=

1

n

-

1

⁢

·

1

/

2

⁢

(

p

i

+

p

i

+

1

)

·

(

t

i

+

1

-

t

i

)

,

in which:

T Al i represents a value of a temperature of the gaseous fluid contained in the internal cavity of the tire, measured at a time t i ,

p i represents a weighting coefficient having a formula of:

(

p

i

=

1

-

(

t

-

t

i

T

INT

)

)

,

and

T INT represents a time interval during which at least two measurements of the temperature of the gaseous fluid contained in the internal cavity of the tire are taken.

5. The method according to claim 1 , wherein the fluid temperature (T AI ) used for determining the estimated temperature (T ZI ) is a delay-adjusted temperature (T AIdelay ), which is readjusted according to an evaluation of an increase or a decrease in a value of the temperature of the gaseous fluid contained in the internal cavity of the tire over a given time period, so as to take into account a delay-related temperature change of the gaseous fluid contained in the internal cavity of the tire with respect to the estimated temperature (T ZI ).

6. The method according to claim 5 , wherein, at a given time value (t), the delay-adjusted temperature (T AIdelay ) has a formula of:

T AIdelay ( t )= T AI ( t )+τ· T AI ′( t )·(1− e Δt/τ )

in which

T AI ′ represents, at a time instant t, a value of a derivative of T AI (t),

for a given internal zone of a given type of the tire, τ represents a period of heat transfer, τ have a value that is adjusted according to whether a value of T AI (t) is increasing or decreasing, and

Δt represents an amount of time between two measurements.

7. The method according to claim 1 , further comprising steps of:

measuring a pressure of the gaseous fluid contained inside the internal cavity of the tire at regular time intervals, in order to obtain a gas pressure (P) in the internal cavity of the tire;

measuring a load borne by the tire at regular intervals, in order to obtain a tire load (Z); and

correcting the estimated temperature (T ZI ) based on the gas pressure (P) and the tire load (Z).

8. The method according to claim 7 , wherein, at a given time value (t), the pre-established law connecting the estimated temperature (T ZI ) to the fluid temperature (T AI ) and the rim temperature (T J ) takes into account the gas pressure (P) and the tire load (Z), and has a formula of:

T ZI =α T AI T ZI ·T AI +α T j T ZI ·T j +α P T ZI ·P+α Z T ZI ·Z+T ZI0

in which, for a given internal zone of a given type of the tire, α T AI T ZI , α P T ZI , α Z T ZI , T ZI0 are coefficients that are determined experimentally.

9. The method according to claim 1 , where the estimated temperature (T ZI ) at at least one internal zone of the materials of which the tire is made is an internal temperature of materials situated at at least one of:

a zone at an end region (N) of a working ply of the tire,

a zone at a bead region (B) of the tire,

a zone at a tread region (C) of the tire.

10. The method according to claim 7 , wherein, at each time value (t), values of the fluid temperature (T AI ), the rim temperature (T J ), the gas pressure (P), and the tire load (Z) are transmitted to a remote operator.

11. The method according to claim 1 , wherein the estimated temperature (T ZI ) at at least one internal zone of materials of which the tire is made is transmitted to a remote operator.

12. The method according to claim 1 , further comprising a step of emitting an alert when the estimated temperature (T ZI ) at at least one internal zone of materials of which the tire is made exceeds a given threshold during a given time period.

13. A system for evaluating thermal stresses associated with use of a tire mounted on a rim, the system comprising:

(A) a computer; and

(B) a memory storing executable code that, when executed by a processing unit of the computer, causes the computer to perform a method that includes:

(1) utilizing temperatures of a gaseous fluid contained in an internal cavity of the tire measured at regular time intervals to determine a fluid temperature (T AI ) in the internal cavity of the tire,

(2) utilizing temperatures at a location on the rim measured at regular time intervals to determine a rim temperature (T j ),

(3) calculating an estimated temperature (T ZI ) at at least one internal zone of materials of which the tire is made using a pre-established law connecting the estimated temperature (T ZI ) to the fluid temperature (T AI ) in the internal cavity of the tire and the rim temperature (T j ),

wherein the temperatures of the gaseous fluid contained in the internal cavity of the tire, and the temperatures at the location on the rim are transmitted from the tire to the computer.

14. A computer for evaluating thermal stresses associated with use of a tire mounted on a rim, the computer comprising a processing unit programmed with code for at least:

calculating a fluid temperature (T AI ) in an internal cavity of the tire using temperatures of a gaseous fluid contained in the internal cavity of the tire measured at regular time intervals;

calculating a rim temperature (T j ) using temperatures at a location on the rim measured at regular time intervals; and

calculating an estimated temperature (T ZI ) at at least one internal zone of materials of which the tire is made using a pre-established law connecting the estimated temperature (T ZI ) to the fluid temperature (T AI ) in the internal cavity of the tire and the rim temperature (T j ).

15. A non-transitory computer-readable storage medium storing code that, when executed by a computer processor, causes the computer processor to perform a method for evaluating thermal stresses associated with use of a tire mounted on a rim, the method comprising steps of:

calculating a fluid temperature (T AI ) in an internal cavity of the tire using temperatures of a gaseous fluid contained in the internal cavity of the tire measured at regular time intervals;

calculating a rim temperature (T j ) using temperatures at a location on the rim measured at regular time intervals; and

calculating an estimated temperature (T ZI ) at at least one internal zone of materials of which the tire is made using a pre-established law connecting the estimated temperature (T ZI ) to the fluid temperature (T AI ) in the internal cavity of the tire and the rim temperature (T j ).