U.S. patent application number 16/897816 was filed with the patent office on 2021-02-18 for molding system for preparing injection-molded article.
The applicant listed for this patent is CORETECH SYSTEM CO., LTD.. Invention is credited to Rong-Yeu CHANG, Chia-Hsiang HSU, Huan-Chang TSENG.
Application Number | 20210046686 16/897816 |
Document ID | / |
Family ID | 1000005370919 |
Filed Date | 2021-02-18 |
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United States Patent
Application |
20210046686 |
Kind Code |
A1 |
TSENG; Huan-Chang ; et
al. |
February 18, 2021 |
MOLDING SYSTEM FOR PREPARING INJECTION-MOLDED ARTICLE
Abstract
The present disclosure provides a molding system for preparing
injection-molded articles. The molding system includes a molding
machine; a mold disposed on the molding machine and having a mold
cavity for being filled with a molding resin; a processing module
configured to generate an anisotropic viscosity distribution of the
molding resin in the mold cavity based on a molding condition for
the molding machine, wherein the anisotropic viscosity distribution
of the molding resin is generated based in part on an elastic
effect of the molding resin; and a controller operably
communicating with the processing module and configured to control
the molding machine with the molding condition using the generated
anisotropic viscosity distribution of the molding resin to perform
an actual molding process for preparing the injection-molded
article.
Inventors: |
TSENG; Huan-Chang; (CHUPEI
CITY, TW) ; CHANG; Rong-Yeu; (CHUPEI CITY, TW)
; HSU; Chia-Hsiang; (CHUPEI CITY, TW) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
CORETECH SYSTEM CO., LTD. |
Chupei City |
|
TW |
|
|
Family ID: |
1000005370919 |
Appl. No.: |
16/897816 |
Filed: |
June 10, 2020 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62886608 |
Aug 14, 2019 |
|
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
B29C 45/766 20130101;
B29C 45/7693 20130101; B29C 45/77 20130101 |
International
Class: |
B29C 45/76 20060101
B29C045/76 |
Claims
1. A molding system for preparing an injection-molded article,
comprising: a molding machine, including a barrel, a screw mounted
for moving within the barrel, a driving motor driving the screw to
move a molding resin; a mold disposed on the molding machine and
connected to the barrel of the molding machine to receive the
molding resin, and having a mold cavity for being filled with the
molding resin; a processing module configured to simulate an
anisotropic viscosity distribution of the molding resin in the mold
cavity based on a molding condition for the molding machine,
wherein the anisotropic viscosity distribution of the molding resin
is simulated based in part on an elastic effect of the molding
resin; and a controller operably communicating with the processing
module to receive the simulated anisotropic viscosity distribution
of the molding resin and with the molding machine to be configured
to control the driving motor of the molding machine with the
molding condition to move the screw to transfer the molding resin
at a desired flow rate according to the simulated anisotropic
viscosity distribution of the molding resin to perform an actual
molding process for preparing the injection-molded article.
2. The molding system of claim 1, wherein the processing module is
configured to simulate a velocity distribution of the molding resin
in the mold cavity, and the anisotropic viscosity distribution of
the molding resin is simulated based on the velocity
distribution.
3. The molding system of claim 1, wherein the processing module is
configured to simulate the anisotropic viscosity distribution based
in part on an anisotropic viscoelastic (VE) stress distribution of
the molding resin in the mold cavity.
4. The molding system of claim 3, wherein the anisotropic viscosity
distribution is represented using an expression: .eta. * = .tau. VE
: D 2 D : D ##EQU00012## where .eta.* represents an effective
viscosity scalar, .tau..sup.VE represents the anisotropic
viscoelastic stress distribution of the molding resin in the mold
cavity, and D represents a rate-of-strain tensor.
5. The molding system of claim 3, wherein the anisotropic
viscoelastic stress distribution is represented using an
expression: .lamda. 0 .tau. .gradient. + f ( I .tau. ) .tau. = 2
.eta. 0 D ##EQU00013## f ( I .tau. ) = 1 + .lamda. 0 .eta. 0 I
.tau. ##EQU00013.2## I .tau. = tr ( .tau. ) = .tau. 11 + .tau. 22 +
.tau. 33 ##EQU00013.3## where .lamda..sub.0 is the relaxation time
and .eta..sub.0 is the viscosity constant; is upper convected time
derivative of the extra stress tensor; .epsilon. is the adjustable
parameter; .tau..sub.11, .tau..sub.22, and .tau..sub.33 are normal
stress components.
6. The molding system of claim 3, wherein the anisotropic
viscoelastic stress distribution is represented using an
expression:
.tau.=.intg..sub.-.infin..sup.tM(t-t')[.PHI..sub.1(I.sub.B,II.sub.B)+.PHI-
..sub.2(I.sub.B,II.sub.B)B.sup.-1(t,t')]dt' where M(t-t') is a
time-memory function; h(I.sub.B,II.sub.B)is a damping function of
the two invariants (I.sub.B and II.sub.B) of the Finger strain
tensor B; t' and t are the past and present times, respectively.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This patent application claims priority under 35 U.S.C.
.sctn.119(e) from Provisional Patent Application No. 62/886,608,
filed on Aug. 14, 2019, the disclosure of which is incorporated by
reference herein in its entirety, including all exhibits appended
to Provisional Patent Application No. 62/886,608.
TECHNICAL FIELD
[0002] The present disclosure relates to a molding system for
preparing an injection-molded article, and more particularly, to an
injection-molding system for preparing an injection-molded article
using a computer-aided engineering (CAE) simulation. DISCUSSION OF
THE BACKGROUND
[0003] In plastics manufacturing, the actual flow of polymer melts
is transient, non-Newtonian and non-isothermal, with frozen layers
building up as the complex mixture flows through the mold cavity.
Characteristics of a finished product are determined by many
complex factors, such as changes in the direction of flow,
inclusion of ribs, and changes in thickness and holes. To control
the quality of the products, a deep understanding of complicated
flow fields is critical. Nowadays, CAE (computer-aided engineering)
software provides realistic simulation and predictive analysis for
complex flows of complex fluids.
[0004] According to results of academic research of fluid mechanics
and rheology, a strain rate that indicates a rate of deformation of
a material with respect to time plays an essential role in the
physics of fluids. Strain includes both shear and extension
deformations. As a rule, both have been investigated
separately.
[0005] In practice, a complex geometric channel flow is a
combination of shear flow and extension flow. For the complex flow,
a generalized strain rate that can be determined with certainty is
widely applied in the CAE tool. Flows in injection molding are
dominated by shear flows, but extension flows are encountered, such
as the contraction flow at gate and nozzle regions, and the
fountain flow of a melt front in the cavity. However, the
generalized strain rate is not decomposed into individual rates of
shear and extension. To resolve such significant issue, the present
invention proposes the principal shear rate and the principal
extension rate to be obtained from the generalized strain rate. In
addition, a new quantity is defined to show the degree of shear and
extension variance with respect to flow geometric features. This is
based on extensive research of complicated flow phenomena related
to shear and extension.
[0006] This Discussion of the Background section is provided for
background information only. The statements in this Discussion of
the Background are not an admission that the subject matter
disclosed in this section constitutes prior art to the present
disclosure, and no part of this Discussion of the Background
section may be used as an admission that any part of this
application, including this Discussion of the Background section,
constitutes prior art to the present disclosure.
SUMMARY
[0007] The present disclosure provides a molding system for
preparing an injection-molded article, comprising: a molding
machine; a mold disposed on the molding machine and having a mold
cavity for being filled with a molding resin; a processing module
configured to generate an anisotropic viscosity distribution of the
molding resin in the mold cavity based on a molding condition for
the molding machine, wherein the anisotropic viscosity distribution
of the molding resin is generated based in part on an elastic
effect of the molding resin; and a controller operably
communicating with the processing module and configured to control
the molding machine with the molding condition using the generated
anisotropic viscosity distribution of the molding resin to perform
an actual molding process for preparing the injection-molded
article.
[0008] In some embodiments, the processing module is configured to
generate a velocity distribution of the molding resin in the mold
cavity, and the anisotropic viscosity distribution of the molding
resin is generated based on the velocity distribution.
[0009] In some embodiments, the processing module is configured to
generate the anisotropic viscosity distribution based in part on an
anisotropic viscoelastic (VE) stress distribution of the molding
resin in the mold cavity.
[0010] In some embodiments, the anisotropic viscosity distribution
is represented using an expression:
.eta. * = .tau. VE : D 2 D : D ##EQU00001##
[0011] where .eta.* represents an effective viscosity scalar,
.tau..sup.VE represents the anisotropic viscoelastic stress
distribution of the molding resin in the mold cavity, and D
represents a rate-of-strain tensor.
[0012] In some embodiments, the anisotropic viscoelastic stress
distribution is represented using an expression:
.lamda. 0 .tau. + f ( I .tau. ) .tau. = 2 .eta. 0 D ##EQU00002## f
( I .tau. ) = 1 + .lamda. 0 .eta. 0 I .tau. ##EQU00002.2## I .tau.
= tr ( .tau. ) = .tau. 11 + .tau. 22 + .tau. 33 ##EQU00002.3##
[0013] where .lamda..sub.0 is the relaxation time and .eta..sub.0
is the viscosity constant; is upper convected time derivative of
the extra stress tensor; .epsilon. is the adjustable parameter;
.tau..sub.11, .tau..sub.22, and .tau..sub.33 are normal stress
components.
[0014] In some embodiments, the anisotropic viscoelastic stress
distribution is represented using an expression:
.tau.=.intg..sub.-.infin..sup.tM(t-t')[.PHI..sub.1(I.sub.B,II.sub.B)+.PH-
I..sub.2(I.sub.B,II.sub.B)B.sup.-1(t,t')]dt'
[0015] where M(t-t') is a time-memory function; h(I.sub.B,
II.sub.B) is a damping function of the two invariants (I.sub.B,
II.sub.B)of the Finger strain tensor B; t' and t are the past and
present times, respectively.
[0016] The foregoing has outlined rather broadly the features and
technical advantages of the present disclosure in order that the
detailed description of the disclosure that follows may be better
understood. Additional features and advantages of the disclosure
will be described hereinafter, and form the subject of the claims
of the disclosure. It should be appreciated by those skilled in the
art that the conception and specific embodiment disclosed may be
readily utilized as a basis for modifying or designing other
structures or processes for carrying out the same purposes of the
present disclosure. It should also be realized by those skilled in
the art that such equivalent constructions do not depart from the
spirit and scope of the disclosure as set forth in the appended
claims.
BRIEF DESCRIPTION OF THE DRAWINGS
[0017] A more complete understanding of the present disclosure may
be derived by referring to the detailed description and claims when
considered in connection with the Figures, where like reference
numbers refer to similar elements throughout the Figures, and:
[0018] FIG. 1 and FIG. 2 show the flow lines in 4:1 planar
contraction flow patterns with a corner vortex. For polymer fluids,
the vortex size is increased with increasing flow rate because of
the Viscoelastic (VE) property;
[0019] FIG. 3 is a flowchart illustrating an injection-molding
simulation operation in accordance with some embodiments of the
present disclosure;
[0020] FIG. 4 is a schematic view of an injection-molding apparatus
in accordance with some embodiments of the present disclosure;
[0021] FIG. 5 is a functional block diagram of the computer in FIG.
4;
[0022] FIG. 6 is a plot showing the stress distribution of the
molding resin in the mold cavity with respect to the shear rate,
using different models.
[0023] FIG. 7 is a plot showing the viscosity distribution of the
molding resin in the mold cavity with respect to the shear rate,
using different models.
[0024] FIG. 8 is a schematic diagram showing a fluid driven from a
reservoir (L.sub.1=3.0 mm size) through a planar abrupt contraction
channel (L.sub.2=0.75 mm size) with a 4:1 contraction ratio
(L.sub.1/L.sub.2).
[0025] FIGS. 9-12 show the increase of the vortex size with respect
to the flow rates in accordance with some comparative embodiments
of the present disclosure.
[0026] FIGS. 13-16 show the increase of the vortex size with
respect to the flow rates in accordance with some embodiments of
the present disclosure.
DETAILED DESCRIPTION
[0027] The following description of the disclosure accompanies
drawings, which are incorporated in and constitute a part of this
specification, and illustrate embodiments of the disclosure, but
the disclosure is not limited to the embodiments. In addition, the
following embodiments can be properly integrated to complete
another embodiment.
[0028] References to "one embodiment," "an embodiment," "exemplary
embodiment," "other embodiments," "another embodiment," etc.
indicate that the embodiment(s) of the disclosure so described may
include a particular feature, structure, or characteristic, but not
every embodiment necessarily includes the particular feature,
structure, or characteristic. Further, repeated use of the phrase
"in the embodiment" does not necessarily refer to the same
embodiment, although it may.
[0029] The present disclosure is directed to a molding system for
preparing an injection-molded article using a computer-aided
engineering (CAE) simulation. In order to make the present
disclosure completely comprehensible, detailed steps and structures
are provided in the following description. Obviously,
implementation of the present disclosure does not limit special
details known by persons skilled in the art. In addition, known
structures and steps are not described in detail, so as not to
limit the present disclosure unnecessarily. Preferred embodiments
of the present disclosure will be described below in detail.
However, in addition to the detailed description, the present
disclosure may also be widely implemented in other embodiments. The
scope of the present disclosure is not limited to the detailed
description, and is defined by the claims.
[0030] Polymers/Plastics applications can be found in almost all
areas of everyday living due to their versatility as an
economically attractive option in the manufacturing industry.
Viscoelasticity (VE) is a primary property of polymer materials
that exhibit both "viscous" and "elastic" characteristics. Polymer
materials can be processed by fast, highly-automated methods, such
as injection molding. Thickness-variation or contraction channels
are widely used in production of injection-molding products. An
obvious and significant vortex is found in the corner of the
thicker upstream channel FIG. 1 (slower flow rate) and FIG. 2
(faster flow rate) show the flow lines in 4:1 planar contraction
flow patterns with a corner vortex. For polymer fluids, the vortex
size is increased with increasing flow rate because of the VE
property (see, Bird, R. B., R. C. Armstrong, and O. Hassager,
Dynamics of Polymeric Liquids: Fluid Mechanics (Wiley-Interscience,
New York, 1987)).
[0031] In the academic community, the polymer rheology has
completely developed numerous mathematical models of the VE
constitutive equations. The constitutive equations qualitatively
and phenomenologically describe complicated changes in stress
tensor with respect to time, involving both differential and
integral forms (See, Bird, R. B., R. C. Armstrong, and O. Hassager,
Dynamics of Polymeric Liquids: Fluid Mechanics (Wiley-Interscience,
New York, 1987)). Note that the differential constitutive equation
is famous to apply in the VE flow simulations. Over the last two
decade, the 3D computational fluid dynamics (3D-CFD) has been
essential for commercial software of injection molding in the
plastic manufacturing. So far, the development of reliable routines
for 3D-VE simulations of the four-to-one contraction flow with
corner vortex has been the difficult object of much research
efforts, due to easily yielding divergent numerical problems
practically in high flow rates. However, a precise 3D-numerical
simulation of VE flow in complex industrial geometries is still a
largely unresolved challenge for the CAE (Computer-Aided
Engineering) society (See, Bird, R. B., R. C. Armstrong, and O.
Hassager, Dynamics of Polymeric Liquids: Fluid Mechanics
(Wiley-Interscience, New York, 1987)); Ray, S., "Three-Dimensional
Flow Simulation Using a Viscoelastic Constitutive Equation and a
Segregated Finite Element Scheme," Ph.D. Thesis, Swinburne
University of Technology (2000)).
[0032] More recently, for "fiber-filled" polymer materials the
inventors of Favaloro et al. and Tseng et. al. (See, Favaloro, A.
J., H.-C. Tseng, and R. B. Pipes, "A New Anisotropic Viscous
Constitutive Model for Composites Molding Simulation," Composites
Part A: Applied Science and Manufacturing 115 112-122 (2018);
Tseng, H.-C. and A. J. Favaloro, "The Use of Informed Isotropic
Constitutive Equation to Simulate Anisotropic Rheological Behaviors
in Fiber Suspensions," J Rheol 63 263-274 (2019); Favaloro, A. J.,
R. B. Pipes, and H.-C. Tseng, "Molding System for Preparing
Fiber-Reinforced Thermoplastic Composite Article," US Patent No.
10201918 (2019); Tseng, H.-C., R.-Y. Chang, and C.-H. Hsu, "Molding
System for Preparing Fiber-Reinforced Thermoplastic Composite
Article," U.S. Pat. No. 10,201,921 (2019)) have developed the
so-called informed isotropic (IISO) viscosity model in order to
overcome the previous numerical convergent issue in the flow
simulation. Before the IISO computation, the fiber orientation
states are necessary to be determined. It is an important IISO
conception that the steady-state stress tenor, which is related to
the anisotropic viscosity tensor and the fiber orientation tensor,
is transferred to obtain the viscosity scalar. Nowadays,
state-of-the-art CAE tools do not provide satisfactory simulations
of VE flow behaviors for polymer fluids. Based on the IISO
conception, is the present invention is proposed in which the
stress tensor evolved from the VE constitutive equations is
transfer to an effective VE viscosity. Therefore, the objective of
the invention is to effectively improve the numerical convergent
issue in high flow rates for the contraction channel, and
successfully simulate the 3D corner vortex.
[0033] The actual flow of polymer melts is transient, non-Newtonian
and non-isothermal, with frozen layers building up as the complex
mixture flows through the mold cavity. The governing equations of
the fluid mechanics (See Bird, R. B., R. C. Armstrong, and O.
Hassager, Dynamics of Polymeric Liquids: Fluid Mechanics
(Wiley-Interscience, New York, 1987)) include the equation of
continuity, the equation of motion, and the equation of energy to
describe the transient and non-isothermal flow motion are as
follows:
.differential. .rho. .differential. t + .gradient. .rho. u = 0 ( 1
) .differential. .differential. t ( .rho. u ) + .gradient. ( .rho.
uu ) = - .gradient. P + .gradient. .tau. + .rho. g ( 2 ) .rho. C P
( .differential. T .differential. t + u .gradient. T ) = .gradient.
( k .gradient. T ) + .tau. : D ( 3 ) ##EQU00003##
where .rho. is the density; u the velocity vector; t the time;
.tau. the extra stress tensor; .gradient.u the velocity gradient
tensor; D the rare-of-deformation tensor (i.e., symmetric tensor of
.gradient.u); g the acceleration vector of gravity; P the
pressure;; C.sub.p the specific heat; T the temperature; k the
thermal conductivity.
[0034] The viscoelastic properties of polymer fluids are related to
the extra stress tensor .tau. [see Eq. (2)]. For the multi-mode
applications of linear viscoelastic spectrum (relaxation time and
viscosity constant), the stress .tau. can be expressed as the sum
of a discrete set (See Peters, G. W. M., J. F. M. Schoonen, F. P.
T. Baaijens, and H. E. H. Meijer, "On the Performance of Enhanced
Constitutive Models for Polymer Melts in a Cross-Slot Flow." J
Non-Newtonian Fluid Mech 82 387-427 (1999).), hence,
.tau. = i = 1 M .tau. i ( 4 ) ##EQU00004##
where M denotes the total number of the discrete set.
[0035] The differential constitutive equation can describe a
time-evolution equation of the stress tensor, including both
differential and integral forms. The differential constitutive
equation is famous to apply in the VE flow simulations, and its
general form (See Peters, G. W. M., J. F. M. Schoonen, F. P. T.
Baaijens, and H. E. H. Meijer, "On the Performance of Enhanced
Constitutive Models for Polymer Melts in a Cross-Slot Flow." J
Non-Newtonian Fluid Mech 82 387-427 (1999).) of one individual mode
can be defined:
.lamda. 0 [ .tau. .gradient. + f c ( .tau. , D ) + f d ( .tau. ) ]
+ .tau. = 2 .eta. 0 D ( 5 ) .tau. .gradient. = .differential. .tau.
.differential. t + u .gradient. .tau. - .gradient. u .tau. - .tau.
.gradient. u T ( 6 ) ##EQU00005##
where .lamda..sub.0 is the relaxation time and .eta..sub.0 is the
viscosity constant; is upper convected time derivative of the extra
stress tensor; both tensor functions f.sub.c(.tau.,D) and
f.sub.d(.tau.) that are related to the tensors .tau. and D depend
upon the chosen constitutive model.
[0036] The Phan-Thien & Tanner (PTT) model is the famous
differential constitutive equation,
.lamda..sub.0+f(I.sub..tau.).tau.=2.eta..sub.0D (7)
[0037] The function f(I.sub..tau.) is related to the first
invariant of the extra stress tensor I.sub..tau.,
f ( I .tau. ) = 1 + .lamda. 0 .eta. 0 I .tau. ( 8 ) I .tau. = tr (
.tau. ) = .tau. 11 + .tau. 22 + .tau. 33 ( 9 ) ##EQU00006##
where .epsilon. is the adjustable parameter; .tau..sub.11,
.tau..sub.22, and .tau..sub.33 are normal stress components. The
PTT model has been achieved in the 3D flow computation to simulate
the VE behaviors. However, there is a numerical convergent issue
especially in high flow rates, due to the numerical
singularity.
[0038] In addition, the K-BKZ (Kaye-Bernstein-Kearsley-Zapas) model
(See Bird, R. B., R. C. Armstrong, and O. Hassager, Dynamics of
Polymeric Liquids: Fluid Mechanics (Wiley-Interscience, New York,
1987)) is the well-known "integral" constitutive equation:
.tau.=.intg..sub.-.infin..sup.tM(t-t')h(I.sub.B,II.sub.B)B(t,t')dt'
(10)
where M(t-t') is a time-memory function; h(I.sub.B, II.sub.B) is a
damping term of the two invariants (I.sub.B, II.sub.B) of the
Finger strain tensor B; t' and t are the past and present times,
respectively.
[0039] The integral equation of the stress tensor above is
complicated and so are not repeated here. In the "2D" flow
computation, such a model can be used in high flow rates.
Unfortunately, it is difficult for the 3D computation, due to the
streamline integration scheme. Therefore, the objective of the
invention is to effectively improve the numerical convergent issue
of the "differential" constitutive equations in the 3D flow
simulation. Details of the constitutive equations are available
elsewhere (See Bird, R. B., R. C. Armstrong, and O. Hassager,
Dynamics of Polymeric Liquids: Fluid Mechanics (Wiley-Interscience,
New York, 1987)). Therefore, the objective of the invention is to
effectively improve the numerical convergent issue of the
"differential" constitutive equations in the 3D flow
simulation.
[0040] For the anisotropic "fiber-filled" materials, Favaloro et
al. and Tseng et. al. (See, Favaloro, A. J., H.-C. Tseng, and R. B.
Pipes, "A New Anisotropic Viscous Constitutive Model for Composites
Molding Simulation," Composites Part A: Applied Science and
Manufacturing 115 112-122 (2018); Tseng, H.-C. and A. J. Favaloro,
"The Use of Informed Isotropic Constitutive Equation to Simulate
Anisotropic Rheological Behaviors in Fiber Suspensions," J Rheol 63
263-274 (2019); Favaloro, A. J., R. B. Pipes, and H.-C. Tseng,
"Molding System for Preparing Fiber-Reinforced Thermoplastic
Composite Article," US Patent No. 10201918 (2019); Tseng, H.-C.,
R.-Y. Chang, and C.-H. Hsu, "Molding System for Preparing
Fiber-Reinforced Thermoplastic Composite Article," U.S. Pat. No.
10,201,921 (2019)) recently derive that fourth-order viscosity
tensor .eta..sub.4=[.eta..sub.ijkl] transferred to obtain an
informed isotropic (IISO) viscosity scalar .eta..sup.HSO in the
steady-state stress tensor .tau.,
.tau. = .eta. 4 : D = 2 .eta. IISO D ( 11 ) .eta. IISO = .tau. : D
2 D : D ( 12 ) ##EQU00007##
where .eta..sub.4=[.eta..sub.ijkl] is the fourth-order viscosity
tensor. They have demonstrated that the IISO viscosity scalar can
improve the previous numerical convergent issue.
[0041] However, for the "un-filled" polymers solving the
differential VE constitutive equations easily yield a numerical
divergent issue at high flow rates, as well. Such a problem has
been largely unresolved. Thus, the present inventors are inspired
by the IISO conception: the VE stress tensor .tau..sup.VE evolved
from the differential/integral constitutive equations are
transferred to get an effective viscosity scalar .eta.*,
.eta. * = .tau. VE : D 2 D : D ( 13 ) ##EQU00008##
[0042] The same as the fiber orientation tensor, .tau..sup.VE also
is a "directional" tensor, involving the off-diagonal components of
shear viscous stresses and the diagonal components of extension
elastic stresses. It is critical that the elastic stress tensor
contribution is transferred to an effective viscosity scalar. Then,
this effective viscosity with the VE effect is given into the
equation of motion and energy based on the viscosity, as below:
.differential. .differential. t ( .rho. u ) + .gradient. ( .rho. uu
) = - .gradient. P + .eta. * .gradient. 2 u + .rho. g ( 14 ) .rho.
C P ( .differential. T .differential. t + u .gradient. T ) =
.gradient. ( k .gradient. T ) + .eta. * .gamma. . 2 ( 15 )
##EQU00009##
[0043] For solving the governing equations, the VE constitutive
equation and the effective viscosity and stress, the flowchart is
drawn below. In addition, this flowchart will be verified to
improve the numerical divergent issue for the 3D contraction flow
simulation.
[0044] FIG. 3 is a flowchart showing an injection-molding
simulation operation in accordance with some embodiments of the
present disclosure. Referring to FIG. 3, in injection-molding
simulation operations, the governing equations of fluid mechanics
that describe the transient flow behaviors are as follows:
.differential. .rho. .differential. t + .gradient. .rho. u = 0 ( 16
) .differential. .differential. t ( .rho. u ) + .gradient. ( .rho.
uu ) = .gradient. .sigma. + .rho. g ( 17 ) .sigma. = - PI + .tau.
.tau. = 2 .eta. D ( 18 ) .rho. C P ( .differential. T
.differential. t + v .gradient. T ) = .gradient. ( k .gradient. T )
+ .eta. .gamma. . 2 ( 19 ) ##EQU00010##
where .rho. represents density; u represents the velocity vector; t
represents time; .sigma. represents the total stress tensor; .tau.
represents the extra stress tensor; .gradient.u represents the
velocity gradient tensor; D the rare-of-deformation tensor (i.e.,
symmetric tensor of .gradient.u) g represents the acceleration
vector of gravity; P represents pressure; C.sub.p represents
specific heat; T represents temperature; k represents thermal
conductivity; .eta. represents shear viscosity; and {dot over
(.gamma.)} represents the total strain rate.
[0045] Solving the governing equations (16)-(19) requires a
transient state analysis, which can be performed numerically using
a computer (See Rong-Yeu Chang and Wen-hsien Yang, "Numerical
simulation of mold filling in injection molding using a
three-dimensional finite volume approach," International Journal
for Numerical Methods in Fluids Volume 37, Issue 2, pages 125-148,
Sep. 30, 2001; the entirety of the above-mentioned publication is
hereby incorporated by reference herein and made a part of this
specification). During the transient state analysis, the process
variables that change with time are not zero; i.e., the partial
derivatives
( .differential. .differential. t ) ##EQU00011##
in the governing equations (16)-(19) are not considered zero.
[0046] The true 3D Finite Volume Method (FVM) is employed due to
its robustness and efficiency to solve the transient flow fields in
a complex 3D geometrical article. In some embodiments of the
present disclosure, the simulation flow in FIG. 3 can be
implemented using commercial injection-molding simulation software,
Moldex3D (CoreTech System Co. of Taiwan), to facilitate the
orientation predictions of the molding resin.
[0047] FIG. 4 is a schematic view of an injection-molding apparatus
10 in accordance with some embodiments of the present disclosure.
Referring to FIG. 4, the injection-molding apparatus 10 that can be
used to carry out molding includes a molding machine 20, a mold 30,
a clamping assembly 40 and a computer 50. The molding machine 20
includes a barrel 210 having a downstream end 212 connected to the
mold 30. The mold 30 includes mold halves 310 and 320 to define a
mold cavity 330 and a runner 340 in communication with the mold
cavity 330.
[0048] The clamping assembly 40 is in operative connection with the
mold 30 for clamping the mold halves 310 and 320. In some
embodiments, the clamping assembly 40 includes a fixed plate 410, a
plurality of tie bars 420 mounted on the fixed plate 410, and a
moving plate 430 slidably engaged with the tie bars 420 and guided
by a driving cylinder 440. The mold half 310 proximal to the barrel
210 is secured on the fixed plate 410, and the mold half 320 distal
to the barrel 210 is secured on the moving plate 430 in any
suitable manner, wherein the driving cylinder 440 drives the moving
plate 430 to open or close the mold 30. In some embodiments, the
barrel 210 includes a nozzle 2102 adapted to engage a sprue 450 in
the fixed plate 410. In some embodiments, the sprue 450 is in
communication with the runner 340 as the mold half 310 is assembled
with the fixed plate 410. In some embodiments, the fixed plate 410
may be equipped with a sprue bushing 452 including the sprue 450
and receiving the nozzle 2102 during an injection time. A molding
material 100 under pressure is delivered to the sprue bush 452 from
the nozzle 2102 pressed tightly against the sprue bush 452 in order
to deliver the molding material 100 to the sprue 450 during a
filling stage of the injection time.
[0049] In some embodiments, the clamping assembly 40 further
includes an ejector plate 460 mounted with at least one ejector pin
(not shown), wherein the moving plate 430 is disposed between the
fixed plate 410 and the ejector plate 460. In some embodiments, the
ejector plate 460 is fixed on one of the plurality of tie bars 420.
In some embodiments, the driving cylinder 440 penetrates the
ejector plate 460 and directly connects to the moving plate 430 to
open or close the mold 30. After the mold halves 310 and 320 are
separated (i.e., the mold 30 is opened), a distance between the
moving plate 430 and the ejector plate 460 is reduced, so the
ejector pin can penetrate through the ejector plate 460 to push a
molded product out of the mold 30.
[0050] A screw 220 is mounted for moving within the barrel and is
operably connected, at an upstream end 214 opposite to the
downstream end 212 of the barrel 210, to a driving motor 230. The
molding machine 20 processes material, such as plastic granules
102, by feeding the material through a hopper 240 to the barrel 210
in order to make the material soft and force the molding material
100 into the mold 30 by the use of the screw 220, wherein the phase
of the plastic granules 102 is changed from solid to liquid by at
least one heater band 250 surrounding the barrel 210. In some
embodiments, the molding machine 20 further includes a check valve
260 mounted on the screw 220, wherein the check valve 260 is in
tight contact with the barrel 210 during the filling stage, and the
check valve 260 is open for allowing the liquid material to flow to
the downstream end 212 of the barrel 210 during a packing stage. In
some embodiments, if the mold cavity 330 is almost filled with the
molding material 100, a packing process proceeds. In some
embodiments, the screw 220 rotates and moves toward the upstream
end 214 of the barrel 210 during the packing stage.
[0051] The injection-molding apparatus 10 further includes a
controller 270 for controlling and monitoring the real-time
functions of the molding machine 20, and a display 280 for
displaying data related to the performance and operation of the
molding machine 20 to on-site technicians. In some embodiments, the
display 280 is further configured to accept input data from the
on-site technicians. In other words, the display 280 is provided
with a communications link directly with the controller 270 to
provide real-time control of the molding machine 20 by the on-site
technicians particularly where the on-site technicians'
intervention is required.
[0052] In some embodiments, the injection-molding apparatus 10 can
further include operation interface communication links among the
controller 270, the display 280 and peripheral devices, and a
program sequence of operation which allows the operation interface
to monitor diagnostic functions of the controller 270 and the
molding machine 20, trigger sound and/or light alarms regarding
conditions of the molding machine 20, receive performance data from
the molding machine 20, and receive input data from the display
280.
[0053] The computer 50 is associated with the molding machine 20
and is configured to execute CAE simulation software and transmit
at least one simulation result to the controller 270 through a
connection such as a hard wire connection or a wireless coupling.
In some embodiments, the computer 50 includes a standardized
operation system capable of running general-purpose application
software for assisting with the analysis of process performance
data and for communicating with the controller 270 and the display
280 via communication ports of each.
[0054] FIG. 5 is a functional block diagram of the computer 50 in
FIG. 4. Referring to FIG. 5, the computer 50 includes a processing
module 510 such as a processor adapted to perform a
computer-implemented simulation method for use in injection
molding, an input/output (I/O) interface 520 electrically coupled
to the processing module 510, and memories, which may include a
read-only memory (ROM) 530, a random access memory (RAM) 540 and a
storage device 550. The ROM 530, the RANI 540 and the storage
device 550 are communicatively coupled to the processing module
510.
[0055] The computer 50 further includes a communication port 560
associated with the controller 270 of the molding machine 20. The
computer 50 may further include one or more accompanying
input/output devices including a display 570, a keyboard 580 and
one or more other input devices 590. The input devices 590 may
include a card reader, an optical disk drive or any other device
that allows the computer 50 to receive input from the on-site
technicians. In some embodiments, the input devices 590 are
configured to input computer instructions (software algorithms)
stored in a non-transitory computer-readable medium 500, and the
processing module 510 is configured to execute operations for
performing a computer-implemented injection-molding simulation
method according to the computer instructions. In some embodiments,
the processing module 510 reads software algorithms from the other
input device 590 or the storage device 550, executes the
calculation steps, and stores the calculated result in the RAM
540.
[0056] FIG. 6 is a plot showing the stress distribution of the
molding resin in the mold cavity with respect to the shear rate,
using different models, and FIG. 7 is a plot showing the viscosity
distribution of the molding resin in the mold cavity with respect
to the shear rate, using different models. As clearly shown in FIG.
6, the stress distribution of the molding resin with respect to the
shear rate, using the conventional Newtonian model is isotropic; in
contrast, the stress distribution of the molding resin with respect
to the shear rate, using the present model considering the elastic
effect of the molding resin is anisotropic. Correspondingly, the
viscosity distribution of the molding resin with respect to the
shear rate, using the conventional Cross WLF model is different
from that using the present model considering the elastic effect of
the molding resin is anisotropic.
[0057] In our present work, a planar contraction flow simulation
was performed via Moldex3D. FIG. 8 is a schematic diagram showing a
fluid driven from a reservoir (L.sub.1=3.0 mm size) through a
planar abrupt contraction channel (L.sub.2=0.75 mm size) with a 4:1
contraction ratio (L.sub.1/L.sub.2). As clearly shown in FIG. 8,
the vertex occurs at the corner, wherein Lv represents the vortex
size. The material of interest was the well-known IUPAC-LDPE
(low-density polyethylene) used in the polymer rheology. For the
LEPD material at the isothermal temperature 150.degree. C., the PTT
model parameters and the linear viscoelastic spectrum (relaxation
time and viscosity constant) can be referred to elsewhere. As a
result, FIGS. 9-12 show the increase of the vortex size with
respect to the flow rates in accordance with some comparative
embodiments (using the conventional PTT differential model without
considering the elastic effect of the molding resin) of the present
disclosure; and FIGS. 13-16 show the increase of the vortex size
with respect to the flow rates in accordance with some embodiments
of the present disclosure. As shown in FIGS. 9-12, the vortex size
is increased from 0.13 mm.sup.3/s to 1.3 mm.sup.3/s. However, the
divergent results are found at high flow rates (130 and 1300
mm3/s). Such a numerical convergent issue is a long-running problem
requiring an urgent solution in the industrial application of
state-of-the-art predictive engineering tools for VE flow
simulation of polymer rheology. In contrast to the conventional PTT
differential model without considering the elastic effect of the
molding resin, considering the elastic effect of the molding resin
in the present disclosure, FIGS. 13-16 shows the vortex size is
increased with flow rates, while there are stable results
especially at high flow rates. Therefore, the present disclosure is
verified to be an effective method for resolving the numerical
convergent issue of VE constitutive equations.
[0058] The present disclosure provides a molding system for
preparing an injection-molded article, comprising: a molding
machine; a mold disposed on the molding machine and having a mold
cavity for being filled with a molding resin; a processing module
configured to generate an anisotropic viscosity distribution of the
molding resin in the mold cavity based on a molding condition for
the molding machine, wherein the anisotropic viscosity distribution
of the molding resin is generated based in part on an elastic
effect of the molding resin; and a controller operably
communicating with the processing module and configured to control
the molding machine with the molding condition using the generated
anisotropic viscosity distribution of the molding resin to perform
an actual molding process for preparing the injection-molded
article.
[0059] Although the present disclosure and its advantages have been
described in detail, it should be understood that various changes,
substitutions and alterations can be made herein without departing
from the spirit and scope of the disclosure as defined by the
appended claims. For example, many of the processes discussed above
can be implemented in different methodologies and replaced by other
processes, or a combination thereof.
[0060] Moreover, the scope of the present application is not
intended to be limited to the particular embodiments of the
process, machine, manufacture, composition of matter, means,
methods and steps described in the specification. As one of
ordinary skill in the art will readily appreciate from the
disclosure of the present disclosure, processes, machines,
manufacture, compositions of matter, means, methods, or steps,
presently existing or later to be developed, that perform
substantially the same function or achieve substantially the same
result as the corresponding embodiments described herein, may be
utilized according to the present disclosure. Accordingly, the
appended claims are intended to include within their scope such
processes, machines, manufacture, compositions of matter, means,
methods, and steps.
* * * * *