Measuring and testing – Tire – tread or roadway
Reexamination Certificate
1999-12-22
2003-04-01
Oen, William (Department: 2855)
Measuring and testing
Tire, tread or roadway
Reexamination Certificate
active
06539788
ABSTRACT:
This invention relates to a method for determining preselected performance characteristics of the tread of a tyre, comprising ride comfort, noise and handling, and to a tyre provided with a tread having optimal characteristics with reference to said performance characteristics.
The subject of this inventions a method which allows to determine a set of performance characteristics of the tread of a tyre by means of a single criterion which refers to all the performance characteristics taken into account.
An initial aspect of the invention is a method for determining preselected performance characteristics of the tread of a tyre—comprising ride comfort, noise and handling—where a longitudinal direction (x), a transversal direction (y) and a vertical direction (z) are associated with said tread, where said tread has a preselected thickness and a preselected circumferential development and is made from a preselected rubber compound and comprises blocks and grooves having at least a preselected pitch, each portion of said tread in contact with a road surface having a contact area, said method comprising the following phases:
a) dividing said tread into a 3-D grid of full cells and empty cells of preselected dimensions (dxdydz);
b) identifying piles of said cells in said grid, each pile of cells having a base area equal to that of one cell (dxdy) and a height equal to said thickness of the tread, said piles of cells being full, empty or partially full;
c) identifying a group of said piles of cells present under a contact area;
d) determining a stiffness value in the longitudinal direction c
xj
and a stiffness value in the transversal direction c
yj
for each pile of cells in said contact area;
e) identifying families of discrete areas in said contact area, each discrete area of each family having preselected dimensions in said longitudinal direction (x) and in said transversal direction (y);
f) dividing said contact area in transversal strips with a preselected length in said longitudinal direction (x), each transversal strip comprising a set of said piles of cells;
g) determining a stiffness value per unit of length in the longitudinal direction c
px
and a stiffness value per unit of length in the transversal direction c
py
for each of said transversal strips (
30
), by summing said stiffness values in the longitudinal direction c
xj
and said stiffness values in the transversal direction c
yj
of said piles of cells of said set, respectively;
h) assigning a preselected deformation state to each of said transversal strips;
i) determining at least one force per unit of length associated with each transversal strip by means of a preselected function linking one of said stiffness values c
px
and c
py
and said deformation state
j) summing preselected forces per unit of length of all the transversal strips associated with a discrete area to attain at least one preselected single force acting in one of said longitudinal (x) and transversal (y) directions;
k) determining at least one total force associated with said contact area by means of a suitable summation of preselected single forces associated with all the discrete areas of said contact area, said total force being representative of at least one of said performance characteristics;
l) repeating the steps from c) to k) for all the portions of said tread which are arranged in succession on said circumferential development and come in contact with said road surface in an entire revolution of said tyre by means of respective contact areas to attain a plurality of total forces associated with all the contact areas of said tread and
m) evaluating the pattern of said plurality of total forces to establish whether the arrangement of said full cells and empty cells in said 3-D grid is substantially uniform along said circumferential development and generates total forces with substantially equal and constant values, so as to optimize at least one preselected performance characteristic of said tread.
Preferably said stiffness values c
xj
and c
yj
are given by the following relationships:
c
xj
=&eegr;
x
GA
p
/h
c
yj
=&eegr;
y
GA
p
/h
where G is a preselected value for the modulus of elasticity in shear of said compound, A
p
is the area of said pile of cells, h is said height of said pile of cells, &eegr;
x
is a coefficient of efficiency in said longitudinal direction (x) and &eegr;
y
is a coefficient of efficiency in said transversal direction (y), where said coefficients of efficiency &eegr;
x
and &eegr;
y
depend on the respective slenderness ratios &lgr;
jx
and &lgr;
jy
—which, in turn, respectively depend on the ratio between the length of said pile of cells (dx) in said longitudinal direction and the height of said pile of cells and between the width of said pile of cells (dy) in said transversal direction and the height of said pile of cells—and on a shape coefficient which is a function of the position of said pile of cells in said grid.
Advantageously, each aforesaid discrete area has a length in said longitudinal direction (x) which is equal to said pitch of said tread.
Preferably, said length of each transversal strip is equal to a unit of length of said stiffness values c
px
and c
py
.
According to a preferred embodiment, in the aforesaid phases from i) to l), total longitudinal forces are determined by means of said stiffness values per unit of length in the longitudinal direction c
px
of said strips and by means of a triangular longitudinal shearing deformation state of said tread, where said longitudinal deformation is null at the start of the contact area and maximum at the end of the contact area.
According to another preferred embodiment, in the aforesaid phases from i) to l), total transversal forces are determined by means of said stiffness values per unit of length in the transversal direction c
py
of said strips and by means of a triangular transversal shearing deformation state of said tread, where the transversal deformation is null at the start of the contact area and maximum at the end of the contact area.
Preferably, total longitudinal stiffness values K
x
associated with said contact areas of said tread are determined. Total transversal stiffness values K
y
associated with said contact areas of said tread are also determined.
According to an additional preferred embodiment, total torsional stiffness values K
t
associated with said contact areas of said tread are determined by means of the following phases:
n) identifying plane elements (dxdy) of said piles of cells under said contact area;
o) imposing a rotation on said contact area with respect to its centre of gravity;
p) determining the slip of each plane element (dxdy) in said contact area;
q) splitting said slip into a longitudinal component and a transversal component;
r) multiplying said longitudinal slip component by said longitudinal stiffness c
xj
and said transversal slip component by said transversal stiffness c
yj
to obtain elementary forces which, multiplied by the offset of said plane element (dxdy) with respect to said centre of gravity generate torque values and
s) summing said torque values to obtain a total torsional moment which, linked with said rotation, results in said total torsional stiffness K
t
for each contact area.
Preferably, said stiffness values K
x
, K
y
and K
t
have the following values:
K
x
=2,300-2,500 N/mm
K
y
=2,400—2,600 N/mm
K
t
=80-88 N*m/degree
Preferably, the ratio between said stiffness values K
y
and K
x
has the following values:
K
y
/K
x
=0.98-1.05.
Advantageously, said piles of cells in said 3-D grid form a histogram in which a preselected character is associated with each pile of cells, said histogram being included in an optimal field delimited by a preselected lower surface and by a preselected upper surface.
Preferably, said histogram optimizes said total longitudinal stiffness values K
x
, making said total longitudinal forces assume a mean value which is lower than a preselected limit to thus minimize the noise output by said tread and optimizing r
Devizzi Andrea
Mancosu Federico
Matrascia Giuseppe
Oen William
Pirelli Pneumatici S.p.A.
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