Tire having a model-based description enabling determination of road handling characteristics

• US 20010020386A1
• Filed: 04/26/2001
• Published: 09/13/2001
• Est. Priority Date: 04/07/1998
• Status: Active Grant

• Current Assignee: Pirelli Pneumatici S.P.A. (Pirelli & C SPA)
• Original Assignee: Pirelli Pneumatici S.P.A. (Pirelli & C SPA)
• Inventors: Mancosu, Federico, Sangalli, Roberto
• Granted Patent: US 6,761,060 B2
• Time in Patent Office: Days
• US Class Current: 73/146
• CPC Class Codes: B60C 99/003 Tyre heating arrangements
• CPC Class Codes: B60C 99/006 Computer aided tyre design or simulation
• CPC Class Codes: G01M 17/02 Tyres
• CPC Class Codes: G06F 30/15 Vehicle, aircraft or watercraft design

Abstract

A method for determining the road handling of a tire, comprising descriptions of the tire by means of a first, concentrated-parameter, physical model and by means of a second, finite-element model, a simulation on the second, finite-element model of a selected series of dynamic tests and an application to the first physical model of equations of motion suitable for representing the dynamic tests in order to obtain first and second frequency responses of selected quantities; a comparison between the first and second frequency responses of the selected quantities for determining the concentrated parameters of the first physical model and physical quantities indicative of the drift behavior of the tire.

Claims

1. Method for determining the road handling of a tire of a wheel for a vehicle, said tire being comprised by selected mixes of rubber and reinforcing materials, said method comprising:

a) a first description of said tire by means of a first, concentrated-parameter, physical model, said first physical model comprising a rigid ring which represents the tread band provided with inserts, a belting structure and corresponding carcass portion of said tire, a disk which represents a hub of said wheel and beading of said tire, principal springs and dampers connecting said rigid ring to said hub and representing sidewalls of said tire and air under pressure inside said tire, supplementary springs and dampers representing deformation phenomena of said belting structure through the effect of a specified vertical load and a brush model simulating physical phenomena in an area of contact between said tire and a road, said area of contact having a dynamic length 2a,

b) a definition of selected degrees of freedom of said first physical model, and

c) an identification of equations of motion suitable for describing the motion of said first physical model under selected dynamic conditions, characterized in that it comprises

d) the definition of said concentrated parameters, said concentrated parameters consisting of the mass M_c and a diametral moment of inertia J_c of said rigid ring, the mass M_m and a diametral moment of inertia J_m of said disk, structural stiffnesses K_c and structural dampings R_c respectively of said principal springs and dampers, and residual stiffnesses K_r and residual dampings R_r respectively of said supplementary springs and dampers, wherein

said structural stiffnesses K_c consist of lateral stiffness K_cy between said hub and said belt, camber torsional stiffness K<sub>cθ

x</sub> between said hub and said belt and yawing torsional stiffness K<sub>cθ

z</sub> between said hub and said belt,

said structural dampings R_c consist of lateral damping R_cy between said hub and said belt, camber torsional damping R<sub>cθ

x</sub> between said hub and said belt and yawing torsional damping R<sub>cθ

z</sub> between said hub and said belt,

said residual stiffnesses K_r consist of residual lateral stiffness K_ry, residual camber torsional stiffness K<sub>rθ

x</sub> and residual yawing torsional stiffness K<sub>rθ

z</sub>, and

said residual dampings R_r consist of residual lateral damping R_ry, residual camber torsional damping R<sub>rθ

x</sub> and residual yawing torsional damping R<sub>rθ

z</sub>,

e) a description of said tire by means of a second, finite-element model comprising first elements with a selected number of nodes, suitable for describing said mixes, and second elements suitable for describing said reinforcing materials, each first finite element being associated with a first stiffness matrix which is determined by means of a selected characterization of said mixes and each second element being associated with a second supplementary stiffness matrix which is determined by means of a selected characterization of said reinforcing materials,

f) a simulation on said second, finite-element model of a selected series of virtual dynamic tests for exciting said second model according to selected procedures and obtaining transfer functions and first frequency responses of selected quantities, measured at selected points of said second model,

g) a description of the behaviour of said first physical model by means of equations of motion suitable for representing the above dynamic tests for obtaining second frequency responses of said selected quantities, measured at selected points of said first physical model,

h) a comparison between said first and said second frequency responses of said selected quantities to determine errors that are a function of said concentrated parameters of said first physical model, and

i) the identification of values for said concentrated parameters that minimize said errors so that said concentrated parameters describe the dynamic behaviour of said tire,

j) the determination of selected physical quantities suitable for indicating the drift behaviour of said tire, and

k) the evaluation of the drift behaviour of said tire by means of said physical quantities.

2. Method according to

claim 1

, characterized in that said selected physical quantities are the total drift stiffness K_d of said tire, in turn comprising the structural stiffness K_c and the tread stiffness K_b, and the total camber stiffness K_γ

of said tire.

3. Method according to

claim 1

, characterized in that it also comprises

c) a definition of said brush model, said brush model having a stiffness per unit of length c_py and comprising at least one rigid plate, at least one deformable beam having a length equal to the length 2a of said area of contact and at least one microinsert associated with said beam, said microinsert consisting of at least one set of springs distributed over the entire length of said beam, said springs reproducing the uniformly distributed, lateral and torsional stiffness of said area of contact.

4. Method according to claims 1 and 3, characterized in that said degrees of freedom referred to at previous point b) are composed of:

absolute lateral displacement y_m of said hub, absolute yaw rotation σ

_m of said hub and absolute rolling rotation ρ

_m of said hub,

relative lateral displacement y_c of said belt with respect to said hub, relative yaw rotation σ

_c of said belt with respect to said hub and relative rolling rotation ρ

_c of said belt with respect to said hub,

absolute lateral displacement y_b of said plate, absolute yaw rotation σ

_b of said plate and absolute rolling rotation ρ

_b of said plate, and

absolute lateral displacement y_s of the bottom ends of said at least one microinsert.

5. Method according to the

claim 1

, characterized in that said selected series of virtual dynamic tests referred to at previous point f) comprises a first and a second test with said tire blown up and not pressed to the ground, said first test consisting in imposing a translation in the transverse direction y on the hub and in measuring the lateral displacement y_c of at least one selected cardinal point of said belt and the force created between said hub and said belt in order to identify said mass M_c, said lateral stiffness K_cy, and said lateral damping R_cy, said second test consisting in imposing a camber rotation θ

_x on said hub and in measuring the lateral displacement of at least one selected cardinal point of said belt y_c and the torque transmitted between said hub and said belt in order to identify said diametral moment of inertia J_c, said camber torsional stiffness K<sub>cθ

x</sub>, said camber torsional damping R<sub>cθ

x</sub>, said yawing torsional stiffness K<sub>cθ

z</sub> and said yawing torsional damping R<sub>cθ

z</sub>.

6. Method according to claims 1 and 5, characterized in that said selected series of virtual dynamic tests referred to at previous point f) also comprises a third and a fourth test with said tire blown up, pressed to the ground and bereft of said tread at least in said area of contact, said third test consisting in applying to said hub a sideward force in the transverse direction F_y and in measuring the lateral displacement y_c of said hub and of at least two selected cardinal points of said belt in order to identify said residual lateral stiffness K_ry, said residual lateral damping R_ry,said camber residual stiffness K_rθ

x, and said camber residual damping R<sub>rθ

x</sub>, said fourth test consisting in applying to said hub a yawing torque C<sub>θ

z</sub> and in measuring the yaw rotation of said hub and the lateral displacement y_c of at least one selected cardinal point of said belt in order to identify said residual yawing stiffness K<sub>rθ

z</sub> and said residual yawing damping R<sub>rθ

z</sub>.

8. Method according to

claim 1

, characterized in that it also comprises

i) a simulation of the behaviour of said first physical model in the drift transient state by means of equations of motion reproducing selected experimental drift tests, and

ii) the determination, with a selected input of a steering angle imposed on said hub, of the pattern with time of the selected free degrees of freedom of said first physical model, of the sideward force and of the self-aligning torque in said area of contact in order to determine the length of relaxation of said tire.

9. Method according to

claim 1

, characterized in that said first elements of said second, finite-element model have linear form functions and their stiffness matrix is determined by means of selected static and dynamic tests conducted on specimens of said mixes, whereas the stiffness matrix of said second elements is determined by means of selected static tests on specimens of said reinforcing materials.

7. Method according to claims I and 3, characterized in that it also comprises

m)an application to said first physical model of a drift angle α

, starting from a condition in which said at least one beam is in a non-deformed configuration and said brush model has a null snaking σ

_b,

n) the determination of the sideward force and the self-aligning torque that act on said hub through the effect of said drift and which depend on the difference α

-σ

_b and on the deformation of said at least one beam,

o) the determination of the deformation curve of said at least one beam,

p) an application of said sideward force and said self-aligning torque to said second, finite-element model in order to obtain a pressure distribution on said area of contact and

q) the determination of the sideward force and the self-aligning torque that act on said hub through the effect of said drift α

on said first physical model, that depend on the pressure distribution calculated in the previous step p),

r) a check, by means of said pressure distribution obtained in the previous step p), that said sideward force and said self-aligning torque are substantially similar to those calculated in previous step q),

s) a determination of the sideward force and of the self-aligning torque for said angle of drift, and

t) repetition of the procedure from step m) to step s) for different values of the drift angle α

to obtain drift, force and self-alignment torque curves, suitable for indicating the drift behaviour under steady state conditions of said tire, and

u) the evaluation of the steady state drift behaviour of said tire.

10. Tire for a wheel of a vehicle, said tire being made from selected mixes of rubber and reinforcing materials and comprising a carcass, a belting structure, a tread band provided with inserts, shoulders, sidewalls, beads provided with bead wires and bead fillings, said tire being representable by means of a first, concentrated-parameter, physical model and a brush model with a road, characterized in that said concentrated parameters comprise structural stiffnesses K_c consisting of lateral stiffness K_cy, camber torsional stiffness K_cθ

x and yawing torsional stiffness K<sub>cθ

z</sub>, structural dampings R_c consisting of lateral damping R_cy, camber torsional damping R<sub>cθ

x</sub> and yawing torsional damping R<sub>cθ

z</sub>, residual stiffnesses K_r consisting of residual lateral stiffness K_ry, residual camber torsional stiffness K<sub>rθ

x</sub> and residual yawing torsional stiffness K<sub>rθ

z</sub>, and residual dampings R_r consisting of residual lateral damping R_ry, residual camber torsional damping R<sub>rθ

x</sub> and residual yawing torsional damping R<sub>rθ

z</sub>,

said tire also being representable by means of a second, finite-element model comprising first elements with a selected number of nodes, suitable for describing said mixes, and second elements suitable for describing said reinforcing materials, said concentrated parameters being identified by means of a selected series of dynamic tests on said second, finite-element model and represented by equations of motion applied to said first physical model, said tire having construction characteristics substantially equivalent to said concentrated parameters which describe the dynamic behaviour of said tire and enabling the determination of selected physical quantities suitable for indicating the drift behaviour of said tire for evaluation of said tire in relation to its road handling.

11. Tire according to

claim 10

, characterized in that said selected physical quantities are the total drift stiffness K_d of said tire, in turn comprising the structural stiffness K_c and the tread stiffness K_b, and the total camber stiffness K_γ

of said tire.

12. Tire according to

claim 11

, characterized in that the total drift stiffness K_d and the total camber stiffness K_γ

are within the following value ranges;

K_d=500-2,000 [N/g]

K_γ

=40-3,500 [N/g]

where g=degree.

13. Tire according to

claim 11

, characterized in that the structural stiffness K_c and the tread stiffness K_b are within the following value ranges:

K_c=8,000-30,000 [N/g]

K_b=150-400 [N/g]

where g=degree.