# US 2021/0240879 A1 · Method for simulating the physical behavior of a tire and application to real-time simulation

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- Number: US 2021/0240879 A1
- Document ID: US20210240879A1
- Status: Published application
- Kind: A1
- Application number: 17/052,670
- Filed: 2019-05-03
- Published: 2021-08-05
- Earliest claimed: 2018-05-03
- Assignees: Compagnie Generale Des Etablissements Michelin
- Applicants: Compagnie Generale Des Etablissements Michelin
- Inventors: JEREMY VAYSSETTES
- Web page: https://patentgrep.com/patent/US20210240879A1

## CPC

- G06F 30/15: Vehicle, aircraft or watercraft design
- G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30)
- G06F 30/23: using finite element methods [FEM] or finite difference methods [FDM]
- G06F 2111/10: Numerical modelling
- G06F 2119/14: Force analysis or force optimisation, e.g. static or dynamic forces
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

A method for simulating the physical behavior of a tire comprises, to calculate a resultant force transmitted by the tire between the ground and the vehicle at a given instant: modelling (Ea) of the contact area in the form of a square surface, discretization (Eb) by a subdivision in slices orthogonal to the direction of travel of the tire, determination (Ec) of the nature of the contact, gripping or sliding, as a function of the steering lock angle, calculation (Ed) of the elementary force exerted on the slice by application of predetermined equations, tire, and calculation (Ee) of the resultant force by integration of the elementary forces over the entire square surface.

## Claims

### Claim at position 1

-14. (canceled)

### Claim 15

A method for simulating the physical behavior of a tire equipping a vehicle that is stationary or virtually stationary on a ground with which a tread of the tire has a contact area including a gripping contact zone and a sliding contact zone, the vehicle having a steering lock angle that varies during simulation, the method being implemented by a computer and comprising the following steps to calculate a resultant force transmitted by the tire between the ground and the vehicle at a given instant:
modelling the contact area in a form of a square surface;
discretizing the square surface by subdivision into slices orthogonal to a direction of travel of the tire;
for each slice, determining a nature of the contact, gripping or sliding, between the slice and the ground as a function of the steering lock angle;
for each slice, calculating an elementary force exerted on the slice by application of predetermined equations, specific according to the nature of the contact, gripping or sliding, and expressed as a function of dynamic parameters linked to conditions of use of the tire and as a function of physical parameter characteristics of the tire; and
calculating the resultant force by integration of the elementary forces over the entire square surface.

### Claim 16 (depends on 15)

The method according to claim 15, wherein, the contact area having a substantially rectangular form of length L and of width l, the square surface modelling the contact area has sides of dimension (L+l)/2 corresponding to an average of the length L and of the width l.

### Claim 17 (depends on 15)

The method according to claim 15, wherein the calculated resultant force models a self-alignment torque.

### Claim 18 (depends on 15)

The method according to claim 15, wherein the steering lock angle is the steering lock angle relative to an initial steering lock angle corresponding to the steering lock angle applied at a last incident of non-zero speed.

### Claim 19 (depends on 15)

The method according to claim 15, wherein determining the nature of the contact, gripping or sliding, between the slice and the ground, is performed as a function of an absolute value of the steering lock angle and of a direction of variation of the steering lock angle.

### Claim 20 (depends on 19)

The method according to claim 19, wherein the determining the nature of the contact, gripping or sliding, between the slice and the ground, comprises comparison of the absolute value of the steering lock angle to a threshold value calculated specifically for each slice.

### Claim 21 (depends on 20)

The method according to claim 20, wherein determining the nature of the contact, gripping or sliding, between the slice and the ground, determines that:
the contact is gripping if the absolute value of the steering lock angle is less than the threshold value, or if the absolute value of the steering lock angle is greater than the threshold value and the direction of variation of the steering lock angle is reversed; and
the contact is sliding if the absolute value of the steering lock angle is greater than the threshold value and the direction of variation of the steering lock angle is retained.

### Claim 22 (depends on 21)

The method according to claim 21, wherein the threshold value induces a slip of each of the slices for which the resultant overall of the slices generates an offset linked to the slip creating a hysteresis effect.

### Claim 23 (depends on 20)

The method according to claim 20, wherein the threshold value calculated specifically for each slice (T) is:
proportional to a grip coefficient between a rubber of the tire and the ground, to a local contact pressure, and to a thickness of the tread; and
inversely proportional to a shear modulus of the tread, to a softening coefficient of the tread, to a grooving rate of the tread, and to a distance of the slice relative to a central slice.

### Claim 24 (depends on 17)

The method according to claim 17, wherein, for a gripping contact, the elementary forces calculated for the modelling of the self-alignment torque are:
proportional to a shear modulus of the tread, to a softening coefficient of the tread, to a grooving rate of the tread, to a square of a distance from the slice relative to a central slice, to a width of the contact area ((L+l)/2), to the steering lock angle of the slice, and to a width of the slice; and
inversely proportional to a thickness of the tread.

### Claim 25 (depends on 17)

The method according to claim 17, wherein, for a sliding contact, the elementary forces calculated for the modelling of the self-alignment torque are:
proportional to a coefficient of adhesion between a rubber of the tire and the ground, to a local contact pressure, to a distance of the slice relative to a central slice, to a width of the contact area ((L+l)/2), and to a width of the slice.

### Claim 26 (depends on 15)

The method according to claim 15, wherein, in a transitional phase between the vehicle being stationary and running, the resultant force is calculated from a sum:
of a first term corresponding to a resultant force calculated in an assumption of the vehicle being stationary, the first term being weighted by a first coefficient that is variable between 0 and 1 and that decreases exponentially with the distance travelled from being stationary; and
of a second term corresponding to a resultant force calculated in an assumption of the vehicle rolling, the second term being weighted by a second coefficient that is variable between 0 and 1 and that increases exponentially with the distance travelled from being stationary,
the sum of the first coefficient and of the second coefficient being equal to 1.

### Claim 27 (depends on 15)

A method according to claim 15, wherein, in a transitional phase between the vehicle being stationary and rolling, the resultant force is calculated from a coefficient of adhesion obtained by a sum:
of a first term corresponding to a coefficient of adhesion μstationary in an assumption of the vehicle being stationary, the first term being weighted by a first coefficient that is variable between 0 and 1 and that decreases exponentially with the distance travelled from being stationary; and
of a second term corresponding to a coefficient of adhesion μrolling in an assumption of the vehicle rolling, the second term being weighted by a second coefficient that is variable between 0 and 1 and that increases exponentially with the distance travelled from being stationary,
the sum of the first coefficient and of the second coefficient being equal to 1.

### Claim 28 (depends on 15)

A method of real-time simulating dynamic behavior of a vehicle provided with at least one tire comprising performing the method according to claim 15.