Method for simulating a deflection radius of a motor vehicle tire

1. A method for determining a behaviour of a tire to be produced for a motor vehicle, the method comprising steps of:

(i) implementing within a software program of a simulation computer-processing tool a formula for estimating a laden radius R l of the tire, the formula having a form of:

R

l

=

R

0

-

Fz

Kzz

+

R

V

×

V

2

-

(

R

Y

⁢

⁢

1

Pg

+

R

Y

⁢

⁢

2

)

×



Fy



+

R

γ

×



γ



,

where:

K ZZ has a form of: K ZZ =K ZZ 0 +K ZZp ×Pg,

K ZZ0 and K ZZp are numerical values,

Pg is an inflation pressure of the tire,

V is a speed of the vehicle,

F Z is a load applied to the tire,

F Y is a transverse thrust force exerted on the tire,

γ is a camber angle of the vehicle,

R 0 is a free radius value of the tire at rest,

R V is a coefficient of influence of the speed of the vehicle on the laden radius,

R Y1 is a coefficient of influence of an inflation pressure on the laden radius via a value of a transverse load,

R Y 2 is a coefficient of influence of the transverse load on the laden radius without the part of the transverse load associated with the inflation pressure, and

R γ is a coefficient of influence of a camber angle value of the vehicle on the laden radius;

(ii) determining values for Pg, V, F Z , F Y , γ, R 0 , R V , R Y1 , R Y 2 , and R γ to be used in the formula for estimating the laden radius R l ;

(iii) estimating the laden radius R l of the tire by executing the software program in the simulation computer-processing tool using the values determined in the step (ii);

(iv) determining a predicted behaviour of the tire based on the laden radius R l of the tire estimated in the step (iii); and

(v) utilizing the predicted behaviour determined in the step (iv) to produce a tire having a predictable rolling behaviour.

2. The method according to claim 1 , wherein, in the step (ii), the values for the coefficients R 0 , R V , R Y1 , R Y 2 , and R γ are determined by physical tests on a tire representative of the tire to be produced.

3. The method according to claim 2 , wherein the physical tests are carried out using a roller of a flat ground type.

4. The method according to claim 1 , further comprising a step of, before the step (iv), using the software program to simulate force dynamics at a wheel center.

5. The method according to claim 4 , wherein the values for the coefficients R 0 , R V , R Y1 , R Y 2 , and R γ are used in the software program to simulate the force dynamics at the wheel center.

6. The method according to claim 1 , wherein, in the step (ii), the value for the transverse thrust force (F Y ) is determined by inputting into the simulation computer-processing tool a plurality of physical parameters that are indicative of physical stresses to which the tire to be produced would be subjected.

7. The method according to claim 6 , wherein the value for the transverse thrust force (F Y ) is determined by taking into account an internal temperature and a surface temperature of the tire to be produced.

8. The method according to claim 6 , further comprising a step of, before the step (iv), using the software program to simulate force dynamics at a wheel center, wherein the simulation computer-processing tool is a processor that executes the software program to simulate the force dynamics at the wheel center.

9. The method according to claim 7 , further comprising a step of, before the step (iv), using the software program to simulate force dynamics at a wheel center, wherein the simulation computer-processing tool is a processor that executes the software program to simulate the force dynamics at the wheel center.

10. A processor for determining a behaviour of a tire to be produced for a motor vehicle, the processor comprising:

(i) programmed instructions for a formula for estimating a laden radius R l of the tire by using a formula having a form of:

R

l

=

R

0

-

Fz

Kzz

+

R

V

×

V

2

-

(

R

Y

⁢

⁢

1

Pg

+

R

Y

⁢

⁢

2

)

×



Fy



+

R

γ

×



γ



,

where:

K ZZ has a form of: K ZZ =K ZZ 0 +K ZZp ×Pg,

K ZZ0 and K ZZp are numerical values,

Pg is an inflation pressure of the tire,

V is a speed of the vehicle,

F Z is a load applied to the tire,

F Y is a transverse thrust force exerted on the tire,

γ is a camber angle of the vehicle,

R 0 is a free radius value of the tire at rest,

R V is a coefficient of influence of the speed of the vehicle on the laden radius,

R Y1 is a coefficient of influence of an inflation pressure on the laden radius via a value of a transverse load,

R Y 2 is a coefficient of influence of the transverse load on the laden radius without the part of the transverse load associated with the inflation pressure, and

R γ is a coefficient of influence of a camber angle value of the vehicle on the laden radius;

(ii) programmed instructions for estimating the laden radius R l of the tire by executing the programmed instructions of (i) using calculated or inputted values for Pg, V, F Z , F Y , γ, R 0 , R V , R Y1 , R Y 2 , and R γ ; and

(iii) programmed instructions for determining a predicted behaviour of the tire based on the laden radius R l of the tire estimated using the programmed instructions of (ii),

wherein the predicted behaviour determined using the programmed instructions of (iii) is used to produce a tire having a predictable rolling behaviour.

11. A tire for a motor vehicle, the tire being produced according to a design that takes into account results of a simulation method for determining a behaviour of the tire, the method comprising:

(i) implementing within a software program of a simulation computer-processing tool a formula for estimating a laden radius R l of the tire, the formula having a form of:

R

l

=

R

0

-

Fz

Kzz

+

R

V

×

V

2

-

(

R

Y

⁢

⁢

1

Pg

+

R

Y

⁢

⁢

2

)

×



Fy



+

R

γ

×



γ



,

where:

K ZZ has a form of: K ZZ =K ZZ 0 +K ZZp ×Pg,

K ZZ0 and K ZZp are numerical values,

Pg is an inflation pressure of the tire,

V is a speed of the vehicle,

F Z is a load applied to the tire,

F Y is a transverse thrust force exerted on the tire,

γ is a camber angle of the vehicle,

R 0 is a free radius value of the tire at rest,

R V is a coefficient of influence of the speed of the vehicle on the laden radius,

R y1 is a coefficient of influence of an inflation pressure on the laden radius via a value of a transverse load,

R Y 2 is a coefficient of influence of the transverse load on the laden radius without the part of the transverse load associated with the inflation pressure, and

R γ is a coefficient of influence of a camber angle value of the vehicle on the laden radius;

(ii) determining values for Pg, V, F Z , F Y , γ, R 0 , R V , R Y1 , R Y 2 , and R γ to be used in the formula for estimating the laden radius R l ;

(iii) estimating the laden radius R l of the tire by executing the software program using the values determined in the step (ii);

(iv) determining a predicted behaviour of the tire based on the laden radius R l of the tire estimated in the step (iii); and

(v) utilizing the predicted behaviour determined in the step (iv) in the design so that the tire has a predictable rolling behaviour.