US2021362388A1PendingUtilityA1
Measuring apparatus of bulk viscosity of molding material
Est. expiryJan 13, 2040(~13.5 yrs left)· nominal 20-yr term from priority
B29C 45/77B29C 45/0046G06F 2113/22B29C 45/7693B29C 2945/76434B29C 2945/76006B29C 45/766B29C 45/7646B29C 2945/76053G01N 11/00G06F 30/28B29C 2945/76287B29C 2945/76859G01N 25/16B29C 2945/7604B29C 2945/76107
73
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Claims
Abstract
A measuring apparatus of bulk viscosity includes a temperature-controlling cylinder having a test chamber for holding a molding material and at least one piston configured to seal an opening of the temperature-controlling cylinder. The temperature-controlling cylinder and the at least one piston are configured for measuring pressures, specific volumes and temperatures (PVT) of the molding material by applying a plurality of cooling rates to the molding material inside the testing chamber under an isobaric environment, or applying a plurality of mechanical pressures to the molding material inside the testing chamber under an isothermal environment. The measuring apparatus further includes a process module configured for deriving a plurality of parameters in relation to the pressures, specific volumes and temperatures (PVT) of the molding material based on the measurement; deriving an equilibrium pressure based on the plurality of parameters obtained from a first slowest cooling rate among the plurality of cooling rates.
Claims
exact text as granted — not AI-modifiedWhat is claimed is:
1 . A measuring apparatus, comprising:
a temperature-controlling cylinder having a test chamber for holding a molding material; at least one piston, configured to seal an opening of the temperature-controlling cylinder; and wherein the temperature-controlling cylinder and the at least one piston are configured for measuring pressures, specific volumes and temperatures (PVT) of the molding material by applying a plurality of cooling rates to the molding material inside the testing chamber under an isobaric environment, or applying a plurality of mechanical pressures to the molding material inside the testing chamber under an isothermal environment; a process module configured for deriving a plurality of parameters in relation to the pressures, specific volumes and temperatures (PVT) of the molding material based on the measurement; deriving an equilibrium pressure based on the plurality of parameters obtained from a first slowest cooling rate among the plurality of cooling rates; deriving a rate of volume change of the molding material according to the specific volumes; and deriving a bulk viscosity of the molding material at least based on the rate of volume change and the equilibrium pressure.
2 . The measuring apparatus of claim 1 , wherein the at least one piston is configured to change a temperature in the testing chamber and change a pressure in the testing chamber so as to apply the plurality of cooling rates and the plurality of mechanical pressures to the molding material.
3 . The measuring apparatus of claim 1 , wherein the process module is configured to derive the equilibrium pressure by the following expression:
{circumflex over (ν)}(σ, T,Q ) PVTQ ={circumflex over (ν)}( p,T ) equilibrium PVT
wherein {circumflex over (ν)} represents the specific volumes, σ represents the mechanical pressures, T represents the temperatures, Q represents the cooling rates, p represents the equilibrium pressure.
4 . The measuring apparatus of claim 1 , wherein the process module is further configured to:
derive a plurality of control factors in relation to a pressure effecting on the molding material based on the first slowest cooling rate obtained from the plurality of parameters of the molding material; and derive a plurality of control factors in relation to a cooling rate effecting on the molding material.
5 . The measuring apparatus of claim 4 , wherein the process module derives the plurality of control factors in relation to the pressure by the following expressions:
(
T
t
)
slow
=
a
T
t
P
+
b
T
t
(
α
m
)
slow
=
α
m
1
+
(
α
m
0
-
α
m
1
)
(
1
+
(
λ
m
P
)
2
)
n
m
-
1
2
(
α
s
)
slow
=
α
s
1
+
(
α
s
0
-
α
s
1
)
(
1
+
(
λ
s
P
)
2
)
n
s
-
1
2
(
v
^
t
)
slow
=
a
v
^
t
P
+
b
v
^
t
wherein (T t ) slow is a transition temperature under the first slowest cooling rate, (a Tt , b Tt ) are control factors in relation to the pressure under the transition temperature and the first slowest cooling rate, (α m ) slow is a volumetric coefficient of thermal expansion of the molding material in a molten state under the first slowest cooling rate, (α m0 , α m1 , λ m , n m ) are control factors in relation to the pressure effecting on the volumetric coefficient of thermal expansion in the molten state under the first slowest cooling rate, (α s ) slow is the volumetric coefficient of thermal expansion of the molding material in a solid state under the first slowest cooling rate, (α s0 , α s1 , λ s , n s ) are control factors in relation to the pressure effecting on the volumetric coefficient of thermal expansion in the solid state under the first slowest cooling rate, ({circumflex over (ν)} t ) slow is a specific volume at the transition temperature under the first slowest cooling rate, (a {circumflex over (ν)} t , b {circumflex over (ν)} t ) are control factors in relation to the pressure effecting on the specific volume at transition temperature under the first slowest cooling rate.
6 . The measuring apparatus of claim 4 , wherein the process module derives the plurality of control factors in relation to the cooling rate by the following expressions:
T t =q T t (ln( Q )−ln( Q slow ))+( T t ) slow
α m =q α m (ln( Q )−ln( Q slow ))+(α m ) slow
α s =q α s (ln( Q )−ln( Q slow ))+(α s ) slow
{circumflex over (ν)} t =({circumflex over (ν)} t ) slow exp(∫ T t T m (α m ) slow dT−∫ T t T m α m dT )
wherein q Tt is the control factor in relation to the cooling rate at a transition temperature, q αm is the control factor in relation to the cooling rate effecting on a volumetric coefficient of thermal expansion in a molten state of the molding material, q αs is the control factor in relation to the cooling rate effecting on the volumetric coefficient of thermal expansion in a solid state of the molding material, Q slow is the first slowest cooling rate, T m is an extreme high temperature that cooling rate effect can be neglected.
7 . The measuring apparatus of claim 4 , wherein the process module is further configured to select a second slowest cooling rate based on the first slowest cooling rate.
8 . The measuring apparatus of claim 7 , wherein the second slowest cooling rate is represented by the following expression:
N*Q slow wherein N is a number substantially smaller than 1.
9 . The measuring apparatus of claim 8 , wherein the number is equal to 0.1.
10 . The measuring apparatus of claim 1 , wherein the process module derives the bulk viscosity based on the following expression:
-
μ
d
=
σ
-
p
∇
·
u
wherein σ is a mechanical pressure applied to the molding material, p is a calculated equilibrium pressure, and ∇·u is the rate of volume change.
11 . The measuring apparatus of claim 1 , wherein the process module is further configured to derive a volumetric coefficient of thermal expansion of the molding material in a solid state and a volumetric coefficient of thermal expansion of the molding material in a molten state.
12 . The measuring apparatus of claim 1 , wherein the process module derives the specific volume of the molding material based on the following expression:
{circumflex over (ν)}={circumflex over (ν)} t exp(∫ T t T α ν ( T ) dT )
wherein {circumflex over (ν)} t is the specific volume of the molding material at a transition temperature, T is a temperature, T t is the transition temperature of the molding material, α v is a volumetric coefficient of thermal expansion of the molding material.
13 . The measuring apparatus of claim 12 , wherein the volumetric coefficient of thermal expansion of the molding material is represented by the following expression:
α
v
(
T
,
P
,
Q
)
=
{
α
m
,
if
T
>
T
t
+
Δ
T
α
s
+
α
m
-
α
s
2
Δ
T
(
T
-
(
T
t
-
Δ
T
)
)
,
if
T
t
-
Δ
T
<
T
<
T
t
+
Δ
T
α
s
,
if
T
<
T
t
-
Δ
T
wherein α v is the volumetric coefficient of thermal expansion, T is a temperature, P is a pressure, Q is a cooling rate, α m is the volumetric coefficient of thermal expansion in the molten state, α s is the volumetric coefficient of thermal expansion in the solid state, T t is the transition temperature, and ΔT is a control factor of the transition state.Cited by (0)
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