Plastic and nonmetallic article shaping or treating: processes – With measuring – testing – or inspecting
Reexamination Certificate
2000-07-14
2002-11-12
Vargot, Mathieu D. (Department: 1732)
Plastic and nonmetallic article shaping or treating: processes
With measuring, testing, or inspecting
C264S040600, C264S326000, 36
Reexamination Certificate
active
06478991
ABSTRACT:
The present invention relates to a method for vulcanizing a tire by predetermining its degree (level) of vulcanization.
In the field of tire production, models of vulcanization kinetics have been developed in order to improve the vulcanization cycles. A history of the temperature of the vulcanization cycle is generally used in the attempt to improve the vulcanization according to the model. These models, however, have proved to be either complicated or of low reliability.
The object of the present invention is to avoid the problems and overcome the limitations of the known methods.
In one aspect, the invention relates to a method for vulcanizing a tire by predetermining the change of its state of vulcanization in time by means of a parameter consisting of its degree of vulcanization, the said tire comprising specified vulcanizable mixtures and specified fabrics, the said vulcanization being carried out by means of a vulcanization mould heated by heat-supply fluids and by subjecting the said tire to cooling by means of a specified cooling fluid, the said method comprising the steps of:
a) determining specified structural and dimensional parameters (geometry) of the said tire and the said mould,
b) determining the change over a time t of specified thermodynamic parameters, comprising the temperature T(t) and diffusivity &agr; of the said tire, mould, heat-supply fluid and cooling fluid,
c) determining a parameter consisting of an equivalent vulcanization time t
0
which, at a specified constant reference temperature T
0
, makes it possible to obtain an equivalent degree of vulcanization X(t
0
) equal to the degree of vulcanization X(t) obtained at a specified instant t and at a specified temperature T(t) variable in time, the said equivalent vulcanization time t
0
being obtained by means of a specified function of the said reference temperature T
0
, of the said temperature T(t) and of the said time t,
d) determining the said equivalent degree of vulcanization X(t
0
) at specified points within the said tire when the said equivalent vulcanization time t
0
varies, the said degree of vulcanization X(t
0
) being obtained by means of an equivalent isothermal rheometric curve, at the said reference temperature T
0
, comprising three consecutive sections having the following equations:
X
(
t
o
)
=
{
k
t
o
n
1
+
k
t
o
n
k
x
t
o
n
x
1
+
k
x
t
o
n
x
+
f
(
t
o
-
t
xx
)
1
-
C
k
R
(
t
o
-
t
100
)
n
R
1
+
k
R
(
t
o
-
t
100
)
n
R
where the aforesaid first equation is valid for a t
0
less than or equal to a first specified equivalent time value (t
0
≦t
60
) at which there is a first specified equivalent degree of vulcanization (X(t
60
)=60%), the aforesaid third equation is valid for a t
0
greater than or equal to a second specified equivalent time value (t
0
≧t
100
) at which there is a second specified value of the equivalent degree of vulcanization (X(t
100
)=100% or 1), and the aforesaid second equation is valid for a t
0
lying between the said first and second values of the said equivalent time (t
60
≦t
0
≦t
100
),
where t
xx
is a third specified equivalent time value, intermediate between the said first (t
60
) and second (t
100
) equivalent time value, at which there is a third specified value of the equivalent degree of vulcanization (X(t
xx
)=90%),
where f(t
0
−t
xx
) is a cubic interpolation function which, for a t
0
less than or equal to the said third equivalent time value (t
0
≦t
xx
), is equal to 0, while, for a t
0
lying between the said third equivalent time value and the said second equivalent time value (t
xx
≦t
0
≦t
100
), it is such that the function X(t
0
) passes through an intermediate point consisting of the said intermediate value of the equivalent degree of vulcanization (X(t
xx
)) and terminates with a horizontal tangent at a point consisting of the said second value of equivalent degree of vulcanization X(t
100
),
where C is equal to 1 −X
∞
, X
∞
being a fourth, asymptotic value of the equivalent degree of vulcanization which is present for the equivalent time value tending towards infinity, and where each pair of the aforesaid parameters (n, k; n
x
, k
x
; n
R
, k
R
) is determined by setting a corresponding pair of values of equivalent degree of vulcanization (X
1
, X
2
), determining the corresponding equivalent vulcanization times (t
1
, t
2
) by the procedure described in point c), and obtaining from each of the aforesaid three equations a system of two equations with three unknowns.
Preferably, in said step b) the said temperature (T) is determined by means of the following steps:
b1) finite element modelling of the said tire and the said mould by means of a lattice (mesh) formed from specified finite elements and nodes;
b2) assigning initial contour conditions by the association of specified initial temperatures with each of the aforesaid nodes,
b3) determining the variation in time of the temperature and convection coefficient of the said fluids for supplying heat to the said mould during the said vulcanization,
b4) determining the variation in time of the temperature and convection coefficient of the said cooling fluid during the cooling of the said tire,
b5) determining the change in time of the said temperature T(t) at specified points within the said tire and the said mould, by means of the Fourier equation for heat transmission, solved by the finite element method.
Advantageously, the said specified function by means of which the said equivalent vulcanization time t
0
is determined in step c) is expressed as follows:
t
0
(
t
)
=
∫
0
t
ⅇ
α
T
(
t
)
-
T
0
(
T
(
t
)
·
T
0
)
β
ⅆ
t
where T(t) is found in the preceding step b5), and &agr; and &bgr; are determined by means of three isothermal rheometric diagrams obtained from test specimens of each mixture at three specified temperatures (T
A
, T
B
, T
C
), each rheometric diagram representing the change of the torque S′ and of the corresponding degree of vulcanization (X
A
(t); X
B
(t); X
C
(t)) of the said mixture as a function of time, &bgr; being found by means of the aforesaid equation using the aforesaid three temperatures (T
A
, T
B
, T
C
) and three time increments (&Dgr;t
A
, &Dgr;t
B
, &Dgr;t
C
) which cause the degree of vulcanization to change from a first specified value X
11
to a second specified value X
21
in the aforesaid three rheometric diagrams, and &agr; is found by means of the aforesaid equation using two of the aforesaid temperatures (T
A
, T
B
) and two of the said time increments (&Dgr;t
A
, &Dgr;t
B
) of two of the aforesaid three rheometric diagrams.
Preferably, the method also comprises the following step:
e) determining a parameter consisting of a torque S′ at a specified temperature T, given the aforesaid degree of vulcanization X(t
0
), by means of the following function:
S
′(
T, X
)=
S′
min
(
T
)+
X
*(
S′
max
(
T
)−
S′
min
(
T
))
where
&AutoLeftMatch;
&AutoLeftMatch;
&AutoLeftMatch;
{
S
min
′
(
T
)
=
S
′
(
T
,
0
)
=
S
min
′
(
T
0
)
+
D
min
(
T
-
T
0
)
S
max
′
(
T
)
=
S
′
(
T
,
1
)
=
S
max
′
(
T
0
)
+
D
max
(
T
-
T
0
)
and where S′
min
(T
0
)=minimum torque at the said reference temperature T
0
; S′
max
(T
0
)=maximum torque at the said reference temperature T
0
; D
min
=derivative of S′
min
with respect to the said temperature T; D
max
=derivative of S′
max
with respect to the said temperature T.
Preferably, the aforesaid pair of values of the equivalent degree of vulcanization (X
1
, X
2
) consists of X
1
=30% and X
2
=60% for the aforesaid first equation.
In turn, the aforesaid pair of values of the equivalent degree of vulcanization (X
1
, X
2
) consists of X
1
=60% and X
2
=90% for the aforesaid second equation.
Preferably, t
Daminelli Giovanni
Mancosu Federico
Pinheiro Eduardo Goncalves
Finnegan Henderson Farabow Garrett & Dunner LLP
Pirelli Pneumatici S.p.A.
Vargot Mathieu D.
LandOfFree
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