Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Mechanical measurement system
Reexamination Certificate
2000-03-28
2003-02-11
Hilten, John S. (Department: 2863)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Mechanical measurement system
C702S041000, C702S043000, C703S002000, C703S009000
Reexamination Certificate
active
06519536
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method for determining the behaviour of a viscoelastic material.
It also relates to a method for improving the storage of experimental curves, a method for determining at least one viscoelastic material having predetermined characteristics and apparatus useful for this purpose.
2. Description of the Related Art
Among the properties of viscoelastic materials, those which are mainly associated with their use are the dynamic properties, or the responses to the application of deformations.
At present, in order to be able to select, at the time of use, the material which best satisfies the final dynamic requirements of a desired product, it is necessary to know the dynamic properties of a large number of materials and, therefore, to have first carried out numerous experimental measurements in order to characterize them.
These dynamic properties, however, depend on the temperature and, in the case of some materials, such as for example polymers containing reinforcing fillers or asphalts, also on the deformation applied. Consequently, the characterization of each material requires the acquisition of a large number of experimental values according to variation in the temperature and the deformation applied.
For example, in order to determine the dynamic properties of these materials, generally experimental measurements of the force following deformation cycles in a predetermined temperature range are performed.
Moreover, the storage of the abovementioned data requires a large amount of space or memory depending on whether it is stored on a paper medium or electronic medium. In the case of storage on a paper medium, moreover, a very long time is needed in order to check whether, with the stored experimental data, it is possible to identify a product having the required characteristics, at a certain temperature.
Another drawback inherent in the known methods is that it is possible to identify the product having the required characteristics only if experimental measurements have been performed at the temperature concerned at the moment when said identification is performed.
SUMMARY OF THE INVENTION
The inventors of the present invention, therefore, have considered the problem of simplifying the characterization, storage and selection processes which are currently used.
More precisely, considering the experimental curves of a dynamic parameter P as a function of a deformation q applied to a generic test piece of viscoelastic material at a temperature T, the inventors of the present invention have surprisingly discovered that these experimental curves are referable to a summation of exponentials of the type:
P
(
q
,
T
)
=
a
*
T
2
+
b
*
T
+
c
+
∑
i
=
1
∞
(
d
i
*
T
2
+
e
i
*
T
+
f
i
)
*
e
-
q
q
i
(
I
)
where
q is the deformation expressed in %;
T is the temperature expressed in Kelvin;
P(q,T) is a dynamic parameter preferably selected from the group comprising the elastic modulus, the viscous modulus, the complex modulus and the loss factor;
a, b, c are characteristic constants which depend on the type of viscoelastic material and the type of dynamic parameter considered;
d
i
, e
i
, f
i
are characteristic constants which depend on the effect of the temperature on the dynamic parameter P and on the ith characteristic deformation;
q
i
is the characteristic deformation at the ith exponential.
The inventors, moreover, have realized that, in order to obtain good approximation of said experimental curves, it is sufficient to perform the abovementioned summation (I) as far as the second term. In such a case, therefore, there are only 11 parameters to be determined for each dynamic parameter P of each viscoelastic material, namely, a, b, c, q
1
, q
2
, d
1
, e
1
, f
1
, d
2
, e
2
and f
2
.
In the case where, on the other hand, it is desired to obtain a greater accuracy, it is sufficient to perform the abovementioned summation (I) as far as the higher term, which ensures the desired accuracy. Obviously, in this case, the number of parameters which must be determined will gradually increase.
Therefore, even though the description which follows is mainly based on carrying out the summation as far as the second term, the person skilled in the art will not have any difficulty in determining the required parameters and in carrying out the abovementioned summation (I) up to any term higher than the second term which ensures the desired accuracy.
For example, in the case of the experimental curves for the elastic modulus G′, measured at different temperature values T, as a function of a torsion &ggr; applied to a cylindrical test piece consisting of a compound for a tyre containing a reinforcing filler, the inventors have found that these experimental curves are referable, according to the present invention, to the relation:
G
′
(
γ
,
T
)
=
a
*
T
2
+
b
*
T
+
c
+
(
d
1
*
T
2
+
e
1
*
T
+
f
1
)
*
e
-
γ
γ
1
+
(
d
2
*
T
2
+
e
2
*
T
+
f
2
)
*
e
-
γ
γ
2
Furthermore, investigating also the experimental curves of the complex modulus G*, viscous modulus G″
(where |
G
*|={square root over ((
G
′)
2
+(
G
″)
2
)})
and the loss factor tan &dgr; (where tan &dgr;=G″/G′) as a function of the torsion &ggr;, applied to the test piece, and of the temperature T, the inventors have surprisingly found that they may also be represented by the abovementioned summation of exponentials and that in order to obtain a good approximation, for each of the abovementioned experimental curves, 11 parameters are sufficient, as illustrated above.
Finally, the inventors have even more surprisingly found that the values of the parameters a, b, c, q
1
, q
2
, d
1
, e
1
, f
1
, d
2
, e
2
and f
2
, which have been determined on the basis of at least 5 experimental measurements, carried out at each of at least three temperatures T
x
, T
y
, T
z
, of a dynamic parameter P of a viscoelastic material as a function of a deformation q, may be used to determine the progression of said dynamic parameter P as a function of said deformation q also at a temperature T
w
different from T
x
, T
y
and T
z
. Thus, with this method the progression of said dynamic parameter P is determined as a function of said deformation q at a temperature T
w
for which no experimental determination was performed.
According to a first aspect thereof, the present invention therefore relates to a method for determining the behaviour of a viscoelastic material at a temperature T
w
characterized in that
a) N experimental measurements, where N≧5, of a dynamic parameter P as a function of a deformation q at each of at least three temperatures T
x
, T
y
, T
z
different from T
w
are performed;
b) for each of said at least three temperatures T
x
, T
y
, T
z
, the experimental curve which passes through all the points which represent the N values determined experimentally in said step a) is plotted;
c) at least 11 values of said dynamic parameter P and of the associated deformation q distributed along the experimental curves plotted in said step b) at said at least three temperatures T
x
, T
y
, T
z
are chosen;
d) said at least 11 values are inserted in the relation (A):
P
(
q
,
T
)
=
a
*
T
2
+
b
*
T
+
c
+
(
d
1
*
T
2
+
e
1
*
T
+
f
1
)
*
e
-
q
q
1
+
(
d
2
*
T
2
+
e
2
*
T
+
f
2
)
*
e
-
q
q
2
so as to determine, for subsequent approximations, values of parameters a, b, c, q
1
, q
2
, d
1
, e
1
, f
1
, d
2
, e
2
, f
2
of said relation (A) which generate the curves which best approximates said experimental curves plotted in step b); and
e) the temperature T
w
and the values of said parameters a, b, c, q
1
, q
2
, d
1
, e
1
, f
1
, d
2
, e
2
, f
2
obtained in the previous step d) are inserted in said relation (A) in order to determine the progression of said dynamic parameter P as a function of the deformation q at the temperature T
w
.
More particularly
Brunacci Antonio
Nahmias Nanni Marco
Serra Antonio
Cherry Stephen J.
Finnegan Henderson Farabow Garrett & Dunner L.L.P.
Hilten John S.
Pirelli Pneumatici S.p.A.
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