U.S. patent application number 15/920953 was filed with the patent office on 2018-11-08 for system and method for measuring a flowing property in a resin transfer molding system.
The applicant listed for this patent is CORETECH SYSTEM CO., LTD, NATIONAL TSING HUA UNIVERSITY. Invention is credited to Rong-Yeu CHANG, Tzu-Heng CHIU, Chia-Hsiang HSU, Sung-Wei HUANG, Shih-Po SUN, Tsai-Heng TSAI, Chih-Wei WANG, Hsun YANG, Yuan YAO.
Application Number | 20180319107 15/920953 |
Document ID | / |
Family ID | 64013534 |
Filed Date | 2018-11-08 |
United States Patent
Application |
20180319107 |
Kind Code |
A1 |
YAO; Yuan ; et al. |
November 8, 2018 |
SYSTEM AND METHOD FOR MEASURING A FLOWING PROPERTY IN A RESIN
TRANSFER MOLDING SYSTEM
Abstract
The present disclosure provides a system for measuring a
permeability/porosity ratio of a fiber preform in a molding system.
In some embodiments of the present disclosure, the system includes
a mold, a detection device, a resin-supplying source, and a
computing device. The mold includes an upper mold and a lower mold
forming a mold cavity. The resin-supplying source is configured to
input a molding resin into a preform in the mold cavity. The
detection device is configured to detect a flow front of the
molding resin at a first position and a second position in the mold
cavity. The computing device is configured to calculate a flowing
property of the molding resin into the preform based on the first
position, the second position, a travelling time of the flow front
from the first position to the second position, and a pressure
difference driving the flow front to travel from the first position
to the second position.
Inventors: |
YAO; Yuan; (HSINCHU, TW)
; CHIU; Tzu-Heng; (HSINCHU, TW) ; CHANG;
Rong-Yeu; (CHUPEI CITY, TW) ; HSU; Chia-Hsiang;
(CHUPEI CITY, TW) ; WANG; Chih-Wei; (CHUPEI CITY,
TW) ; SUN; Shih-Po; (CHUPEI CITY, TW) ; HUANG;
Sung-Wei; (CHUPEI CITY, TW) ; YANG; Hsun;
(CHUPEI CITY, TW) ; TSAI; Tsai-Heng; (CHUPEI CITY,
TW) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
CORETECH SYSTEM CO., LTD
NATIONAL TSING HUA UNIVERSITY |
Chupei City
Hsinchu |
|
TW
TW |
|
|
Family ID: |
64013534 |
Appl. No.: |
15/920953 |
Filed: |
March 14, 2018 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62502150 |
May 5, 2017 |
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
B29K 2995/0026 20130101;
B29C 70/54 20130101; B29C 70/546 20130101; G01N 11/06 20130101;
G01N 15/0826 20130101; B29C 70/48 20130101 |
International
Class: |
B29C 70/54 20060101
B29C070/54; B29C 70/48 20060101 B29C070/48; G01N 15/08 20060101
G01N015/08 |
Claims
1. A measurement system, the measurement system comprising: an
upper mold and a lower mold, the upper mode and the lower mode
forming a mold cavity; a resin-supplying source configured to input
a molding resin into a preform in the mold cavity; a detection
device configured to detect a flow front of the molding resin at a
first position and a second position in the mold cavity; and a
computing device configured to calculate a flowing property of the
molding resin into the preform based on the first position, the
second position, a travelling time of the flow front from the first
position to the second position, and a pressure difference driving
the flow front to travel from the first position to the second
position.
2. The measurement system of claim 1, wherein the detection device
is an image-capturing device configured to capture a first image
and a second image of the flow front at the first position and the
second position, respectively.
3. The measurement system of claim 2, wherein the upper mold is
transparent, the image-capturing device is disposed over the upper
mold, and the first image and the second image are captured through
the upper mold.
4. The measurement system of claim 1, further comprising a vacuum
pump coupled to an outlet port of the mold cavity.
5. The measurement system of claim 1, further comprising a front
pressure sensor coupled to an inlet port of the mold cavity.
6. The measurement system of claim 1, further comprising a rear
pressure sensor coupled to an outlet port of the mold cavity.
7. (canceled)
8. The measurement system of claim 1, wherein the mold cavity does
not contain a pressure sensor and the lower mold is free of having
pressure sensors mounted therein.
9. The measurement system of claim 1, wherein the computing device
is configured to calculate the flowing property of the molding
resin based on the following expression: K % .phi. % = .mu. G P 0 (
t n - t n - 1 ) .intg. X n - 1 X n x 2 - X n - 1 x ( Gx - 1 ) dx
##EQU00034## where K % .phi. % ##EQU00035## represents local ratios
of permeability to porosity of the preform, t.sub.n-1 and t.sub.n
represent a first timing and a second timing, x.sub.n and X.sub.n-1
represent the first position and the second position, P.sub.0
represents the pressure difference, .mu. represents the viscosity
of the molding resin, K n .phi. n and K n - 1 .phi. n - 1
##EQU00036## represent global ratios of permeability to porosity of
the preform, K.sup.0/1 represents the permeability and
.PHI..sup.0/1 represents the porosity, wherein the local ratios
refer to a ratio of permeability to porosity of a portion of the
preform, and wherein G represents a constant term.
10-17. (canceled)
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application claims the benefit of U.S. Provisional
Patent Application No. 62/502,150 filed May 5, 2017, which is
incorporated herein by reference in its entirety.
TECHNICAL FIELD
[0002] The present disclosure relates to a system and method for
measuring a flowing property in a resin transfer molding system,
and more particularly, to a system and method for measuring a
permeability/porosity ratio of a fiber preform in a resin transfer
molding system.
DISCUSSION OF THE BACKGROUND
[0003] Resin transfer molding (RTM) is one of the most promising
techniques for manufacturing high-performance fiber-reinforced
plastic (FRP). In RTM, the permeability/porosity ratio of the fiber
preform inside the mold is a critical process parameter, which
varies with the geometric formation of the fiber reinforcement.
This parameter affects the characteristic of resin flow and hence
influences the final product quality. Various measurement systems
have been developed for permeability estimation. However, most of
the existing measurement systems assume that the material porosity
is a constant and estimate the permeability of the entire fiber
preform as a single value, while the local variations are often
ignored.
[0004] 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
[0005] One embodiment of the present disclosure provides a system
for measuring a permeability/porosity ratio of a fiber preform in a
molding system. In some embodiments of the present disclosure, the
system comprises: an upper mold and a lower mold forming a mold
cavity; a resin-supplying source configured to input a molding
resin into a preform in the mold cavity; a detection device
configured to detect a flow front of the molding resin at a first
position and a second position in the mold cavity; and a computing
device configured to calculate a flowing property of the molding
resin flowing into the preform based on the first position, the
second position, a travelling time of the flow front from the first
position to the second position, and a pressure difference driving
the flow front to travel from the first position to the second
position.
[0006] In some embodiments of the present disclosure, the detection
device is an image-capturing device configured to capture a first
image and a second image of the flow front at the first position
and the second position.
[0007] In some embodiments of the present disclosure, the upper
mold is transparent, and the image-capturing device is disposed
over the upper mold, and the first image and the second image are
captured through the upper mold.
[0008] In some embodiments of the present disclosure, the system
comprises a vacuum pump coupled to an outlet port of the mold
cavity.
[0009] In some embodiments of the present disclosure, the system
comprises a front pressure sensor coupled to an inlet port of the
mold cavity.
[0010] In some embodiments of the present disclosure, the system
comprises a rear pressure sensor coupled to an outlet port of the
mold cavity.
[0011] In some embodiments of the present disclosure, the system
comprises a pressure sensor disposed outside the mold cavity and
configured to detect an internal pressure of the mold cavity.
[0012] In some embodiments of the present disclosure, the mold
cavity does not contain an internal pressure sensor configured to
detect an internal pressure of the mold cavity.
[0013] In some embodiments of the present disclosure, the computing
device is configured to calculate the flowing property of the
molding resin based on the following expression:
K ~ .phi. ~ = .mu. G P 0 ( t n - t n - 1 ) .intg. X n - 1 X n x 2 -
X n - 1 x ( Gx - 1 ) dx ##EQU00001##
where
K ~ .phi. ~ ##EQU00002##
represents a local ratio of permeability to porosity of the
preform, t.sub.n-1 and t.sub.n represent the first timing and the
second timing, X.sub.n and X.sub.n-1 represent the first position
and the second position, (t.sub.n-i.sub.n-1) represents the
travelling time, P represents the pressure difference, .mu.
represents the viscosity of the molding resin, and
K n .phi. n and K n - 1 .phi. n - 1 ##EQU00003##
represent global ratio of permeability to porosity.
[0014] Another embodiment of the present disclosure provides a
method for measuring a permeability/porosity ratio of a fiber
preform in a molding system, which comprises an upper mold and a
lower mold forming a mold cavity. In some embodiments of the
present disclosure, the method comprises steps of: applying a
pressure difference to a molding resin for driving the molding
resin to flow into a preform in the mold cavity; detecting a flow
front of the molding resin at a first position and a second
position in the mold cavity; and calculating a flowing property of
the molding resin based on the first position, the second position,
a travelling time of the flow front from the first position to the
second position, and the pressure difference.
[0015] In some embodiments of the present disclosure, the step of
detecting a flow front of the molding resin is performed by an
image-capturing device configured to capture a first image and a
second image of the flow front at the first position and the second
position.
[0016] In some embodiments of the present disclosure, the upper
mold is transparent, and the image-capturing device is disposed
over the upper mold, and the first image and the second image are
captured through the upper mold.
[0017] In some embodiments of the present disclosure, the pressure
difference is constant when the flow front travels from the first
position to the second position.
[0018] In some embodiments of the present disclosure, the step of
calculating a flowing property of the molding resin is performed
based on the following expression:
K ~ .phi. ~ = .mu. G P 0 ( t n - t n - 1 ) .intg. X n - 1 X n x 2 -
X n - 1 x ( Gx - 1 ) dx ##EQU00004##
where
K ~ .phi. ~ ##EQU00005##
represents a local ratio of permeability to porosity of the
preform, t.sub.n-1 and t.sub.n represent the first timing and the
second timing, X.sub.n and X.sub.n-1 represent the first position
and the second position, (t.sub.n-i.sub.n-1) represents the
travelling time, P.sub.0 represents the pressure difference, .mu.
represents the viscosity of the molding resin, and
K n .phi. n and K n - 1 .phi. n - 1 ##EQU00006##
represent global ratio of permeability to porosity.
[0019] In some embodiments of the present disclosure, the step of
applying a pressure difference to a molding resin comprises
detecting a front pressure of the mold cavity by a front pressure
sensor coupled to an inlet port of the mold cavity.
[0020] In some embodiments of the present disclosure, the step of
applying a pressure difference to a molding resin comprises
detecting a rear pressure of the mold cavity by a rear pressure
sensor coupled to an outlet port of the mold cavity.
[0021] In some embodiments of the present disclosure, the step of
applying a pressure difference to a molding resin is performed in
an absence of an internal pressure sensor in the mold cavity.
[0022] The present disclosure provides a measurement system and a
method to measure the local values of the permeability/porosity
ratio of a fiber preform in RTM reinforcements, which does not
require a large number of pressure sensors to be mounted in the
mold to obtain the local pressure gradients. In some embodiments of
the present disclosure, at each sampling time point, the overall
(global) permeability/porosity ratio of the fiber preform between a
pressure-sensing site (e.g., the injection gate) and the flow front
of the molding resin is calculated using a formula presented in
Darcy's law. In the formula, the pressure difference along the flow
path is known when the constant-pressure injection is employed,
while the position of the flow front is acquired by a detecting
device such as a visualization system (image-capturing device).
Subsequently, the local ratio can be derived based on the
relationship between the overall values and the local ratios.
[0023] 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
[0024] Aspects of the present disclosure are best understood from
the following detailed description when read with the accompanying
figures. It is emphasized that, in accordance with the standard
practice in the industry, various features are not drawn to scale.
In fact, the dimensions of the various features may be arbitrarily
increased or reduced for clarity of discussion.
[0025] FIG. 1 shows a new measurement system for measuring the
permeability/porosity ratio in the resin transfer molding in
accordance with one embodiment of the present disclosure.
[0026] FIG. 2 shows a comparative measurement system for measuring
the permeability/porosity ratio in the resin transfer molding in
accordance with a comparative embodiment of the present
disclosure.
[0027] FIG. 3 and FIG. 4 show the pressure sensor array in FIG.
2.
[0028] FIG. 5 shows a piece of fiber mat serving as the fiber
preform.
[0029] FIG. 6 and FIG. 7 show the images captured by the detection
device in accordance with a comparative embodiment of the present
disclosure.
[0030] FIG. 8 is a flow chart of a method for measuring the
permeability/porosity ratio in the resin transfer molding in
accordance with a comparative embodiment of the present
disclosure.
[0031] FIG. 9 shows experimental results of a nearly-uniform fiber
preform.
[0032] FIG. 10 shows experimental results of a uniform fiber
preform.
DETAILED DESCRIPTION
[0033] 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.
[0034] 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.
[0035] The present disclosure is directed to a system and method
for measuring a flowing property in a resin transfer molding
system, and more particularly, to a system and method for measuring
a permeability/porosity ratio of a fiber preform in a resin
transfer molding system. 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.
[0036] The present disclosure provides a measurement system to
measure the local values of the permeability/porosity ratio of a
fiber preform in RTM reinforcements, which does not require a large
number of pressure sensors to be mounted in the mold to obtain the
local pressure gradients. In some embodiments of the present
disclosure, at each sampling time point, the overall (global)
permeability/porosity ratio of the fiber preform between a
pressure-sensing site (e.g., the injection gate) and the flow front
of the molding resin is calculated using a formula presented in
Darcy's law. In the formula, the pressure difference along the flow
path is known when the constant-pressure injection is employed,
while the position of the flow front is acquired by a detecting
device such as a visualization system (image-capturing device).
Subsequently, the local ratio can be derived based on the
relationship between the overall values and the local ratios. The
feasibility of the proposed method is illustrated with the
experimental results.
[0037] Instrumentation and Equipment
[0038] FIG. 1 shows a new measurement system 10 for measuring the
permeability/porosity ratio in the resin transfer molding in
accordance with a one embodiment of the present disclosure. In some
embodiments, the measurement system 10 comprises a mold 21, a
resin-supplying source 30, a detection device 40, and a computing
device 50. The mold 21 includes an upper mold 21A and a lower mold
21B forming a mold cavity 23. The resin-supplying source 30 is
configured to input a molding resin into a preform in the mold
cavity 23. The detection device 40 is configured to detect a flow
front of the molding resin at a first position and a second
position in the mold cavity. The computing device 50 is configured
to calculate a flowing property of the molding resin into the
preform based on the first position, the second position, a
travelling time of the flow front from the first position to the
second position, and a pressure difference driving the flow front
to travel from the first position to the second position.
[0039] In some embodiments, the molding resin is stored in the
resin-supplying source 30 (resin bucket) linked to the inlet port
25A of the mold 21, while the outlet port 25B of the mold 21 is
connected to a vacuum pump 60. During the vacuum-assisted infusion,
the molding resin is driven by the pressure difference and injected
into the mold 21 to impregnate the preform. In some embodiments,
the upper mold 21A is transparent, facilitating the flow
visualization, while the lower mold 21B is made of metal alloy,
with the mold cavity 23 configured to contain the preform. In some
embodiments, the dimension of the mold cavity 23 is 30 cm.times.12
cm.times.0.3 cm. During experiments, the flow front information was
captured through the upper mold 23A in real time by the detection
device 40 such as an image-capturing device (CCD camera) disposed
over the upper mold 21A and stored in a National Instruments (NI)
IMAQ frame grabber card.
[0040] In some embodiments, the measurement system 10 comprises a
front pressure sensor 61A coupled to the inlet port 25A of the mold
21 and a rear pressure sensor 61B coupled to the outlet port 25B of
the mold 21, while the pressure difference is generated based on
the measurements of the front pressure sensor 61A and the rear
pressure sensor 61B outside the mold 21. In other words, the
measurement system 10 uses the pressure sensors disposed outside
the mold cavity 23 to detect an internal pressure of the mold
cavity 23, while the mold cavity 23 does not contain a pressure
sensor.
[0041] FIG. 2 shows a comparative measurement system 100 for
measuring the permeability/porosity ratio in the resin transfer
molding in accordance with a comparative embodiment of the present
disclosure. The comparative measurement system 100 in FIG. 2 is
substantially the same as the present measurement system 10 in FIG.
1, except the comparative measurement system 100 uses a mold 120
having an upper mold 121A and a lower mold 121B with a pressure
sensor array 127 embedded in the lower mold 121B to record the
pressure distributions during infusion.
[0042] FIG. 3 and FIG. 4 show the pressure sensor array in FIG. 2.
The pressure sensor array is a 3.times.8 pressure sensor array
embedded in the lower mold 121B. It should be noted that these
sensors are not needed by the present measurement system 10 in FIG.
1. The pressure sensor array are utilized to get the information
necessary for conducting the method developed in the publication
(see B. J. Wei, Y. S. Chang, Y. Yao, and J. Fang, "Online
estimation and monitoring of local permeability in resin transfer
molding," Polymer Composites, vol. 37, pp. 1249-1258, 2016). After
the information is gathered, the feasibility of the proposed scheme
in FIG. 1 can be verified through the comparison with the gathered
information in FIG. 2. In the present disclosure, LabVIEW is used
to integrate the hardware devices in FIG. 1 and FIG. 2. The
positions of the pressure sensors can be observed through the
transparent upper mold 121A.
[0043] FIG. 5 shows a piece of fiber mat serving as the fiber
preform. The epoxy resin is adopted as the raw material in the
experiments, wherein the epoxy resin has a viscosity of about 550
cp at room temperature. The preform is composed of glass fibers,
which are commonly used as a reinforcing material for polymer
composites.
[0044] FIG. 6 and FIG. 7 show the images captured by the detection
device 40 in accordance with a comparative embodiment of the
present disclosure. The detection device 40 is an image-capturing
device (CCD) configured to capture a first image, shown in FIG. 6,
and a second image, shown in FIG. 7, showing the flow front of the
molding resin at the first position and the second position,
respectively.
[0045] FIG. 8 is a flow chart of a method 200 for measuring the
permeability/porosity ratio in the resin transfer molding in
accordance with a comparative embodiment of the present disclosure.
In some embodiments, the method 200 comprises an operation 201 of
applying a pressure difference to a molding resin for driving the
molding resin to flow into a preform in the mold cavity; an
operation 203 of detecting a flow front of the molding resin at a
first position and a second position in the mold cavity; and an
operation 205 of calculating a flowing property of the molding
resin based on the first position, the second position, a
travelling time of the flow front from the first position to the
second position, and the pressure difference.
[0046] Measurement of Local Permeability/Porosity Ratio
[0047] In this section, an in situ measurement system and a method
are proposed for measuring the local values of the
permeability/porosity ratio of the fiber preform used as
reinforcement in RTM. The basic idea is as follows. At each
sampling time point after the infusion begins, the overall value of
the ratio of permeability to porosity between the injection gate
and the current flow front position is calculated. Next, the local
value between two consecutive flow front positions can be derived
from the relationship between the values of the overall ratio and
the local ratios. The details are presented below.
[0048] The motion of incompressible fluids flowing through porous
fiber structure is governed by the well-known Darcy's law (1) and
the continuity equation (2) as follows:
u = - 1 .mu. K P ( 1 ) u = 0 ( 2 ) ##EQU00007## [0049] where u is
the vector of Darcy velocity, K is the permeability tensor, .mu. is
the viscosity of the resin, and .gradient.P denotes the
pore-average pressure gradient inside the mold. These equations
describe the macroscopic relationship between Darcy velocity and
pressure drop. Therefore, they are often used in permeability
estimation.
[0050] In this study, linear flow experiments were conducted in a
rectangular mold. Therefore, it is reasonable to make the following
assumptions (see S. G. Advani and E. M. Sozer, Process Modeling in
Composites Manufacturing. New York: Marcel Dekker, 2002): flow
coordinate is along the principle direction of fiber; resin flows
along a one-dimensional direction, i.e., the x-axis; and the z-axis
scale is ignored. The behavior of the resin flow is then described
with the following simplified equation which is in one
dimension:
u = - K .mu. ( .differential. P .differential. x ) ( 3 )
##EQU00008## [0051] where u, K and
[0051] .differential. P .differential. x ##EQU00009##
are the Darcy velocity, permeability and pressure gradient along
the flow coordinate, respectively.
[0052] The above equation cannot be used in permeability estimation
directly, because the flow front velocity captured by the CCD
camera is the seepage velocity instead of the Darcy velocity. The
relationship between these two types of velocity is
u=.nu..PHI. (4) [0053] where v is the seepage velocity and .PHI. is
the porosity of the fibers. By combing (3) and (4), it can be
derived that
[0053] v = dx dt = - K .phi. .mu. ( .differential. P .differential.
x ) ( 5 ) ##EQU00010##
[0054] In the interval between the injection gate and the flow
front along the x-axis, the overall permeability K and the overall
porosity .PHI. are represented by constants. When resin is injected
at constant pressure, the pressure gradient
.differential. P .differential. x ##EQU00011##
is approximated as
.differential. P .differential. x = - P 0 x ( 6 ) ##EQU00012##
[0055] where P.sub.0 is the injection pressure and x is the
distance the flow front has traveled. Substituting (6) into (5) and
performing integration with regard to the time, (7) is
obtained:
[0055] x 2 = 2 KP 0 .phi. .mu. t ( 7 ) ##EQU00013## [0056] where t
is the travelling time of the resin flow. Clearly, there is a
linear relationship between x.sup.2 and t, from whose slope S the
permeability/porosity ratio is obtained as
[0056] K .phi. = S .mu. 2 P 0 ( 8 ) ##EQU00014##
[0057] When the overall porosity .PHI. is a known constant, K can
be calculated.
[0058] The above equation only evaluates the value of the overall
permeability, while the local variations are ignored. In practice,
both the permeability and porosity may vary with location in an
arbitrary manner. Therefore, it is necessary to derive an algorithm
to extract the local information. Denoting the flow front position
at time t.sub.n as X.sub.n, the following equation can be obtained
from Darcy's law:
v = dx dt = - K ~ .phi. ~ .mu. ( - P n - 1 x - X n - 1 ) ( 9 )
##EQU00015## [0059] where {tilde over (K)} and {tilde over (.PHI.)}
are the local permeability and porosity between X.sub.n-1 and
X.sub.n, respectively, x is the flow front position at time t,
X.sub.n-1<x.ltoreq.X.sub.n, P.sub.n-1 denotes the pressure at
X.sub.n-1 at time t, and
[0059] - P n - 1 x - X n - 1 ##EQU00016##
is an approximation of
.differential. P .differential. x . ##EQU00017##
In (9), both x and P.sub.n-1 are functions of time t, so the
value
K ~ .phi. ~ ##EQU00018##
cannot be calculated directly. In order to extract more
information, the following equations are established:
v = K .phi. .mu. P 0 x ( 10 ) v = K n - 1 .phi. n - 1 .mu. ( P 0 -
P n - 1 ) X n - 1 ( 11 ) ##EQU00019## [0060] which are also based
on Darcy's law. Here, K and .PHI. are the overall permeability and
porosity between the injection gate and the flow front position at
time t, respectively. K.sub.n-1 and .PHI..sub.n-1 are defined in a
similar way, and are the overall permeability and porosity between
the injection gate and X.sub.n-1, respectively. Combining (10) and
(11),
[0060] K .phi. .mu. P 0 x = K n - 1 .phi. n - 1 .mu. ( P 0 - P n -
1 ) X n - 1 ( 12 ) ##EQU00020##
[0061] To simplify the calculation,
K .phi. ##EQU00021##
is approximated with a constant according to (13):
K .phi. = 1 2 ( K n .phi. n + K n - 1 .phi. n - 1 ) ( 13 )
##EQU00022##
[0062] It is noted that the values of both
K n .phi. n and K n - 1 .phi. n - 1 ##EQU00023##
can be obtained from (8). Therefore, the approximate value of
K .phi. ##EQU00024##
is also known. Denoting the constant term
K n .phi. K .phi. n X n ##EQU00025##
by G, i.e.
[0063] G = K n - 1 .phi. K .phi. n - 1 X n - 1 ( 14 ) ##EQU00026##
[0064] it is derived from (12) that
[0064] P n - 1 = P 0 ( Gx - 1 ) Gx ( 15 ) ##EQU00027##
[0065] Substituting (15) into (9) gives
dx dt = - K ~ P 0 .phi. ~ .mu. ( Gx - 1 ( x - X n - 1 ) Gx ) ( 16 )
##EQU00028##
[0066] By transposition of terms and integrating, (17) yields:
.intg. X n - 1 X n x 2 - X n - 1 x ( Gx - 1 ) dx = K ~ P 0 .phi. ~
.mu. G .intg. t n - 1 t n dt ( 17 ) ##EQU00029##
[0067] That is
K ~ .phi. ~ = .mu. G P 0 ( t n - t n - 1 ) .intg. X n - 1 X n x 2 -
X n - 1 x ( Gx - 1 ) dx ( 18 ) ##EQU00030##
[0068] From the above derivation, it is clear that the flowing
property (the local ratio of permeability to porosity),
K ~ .phi. ~ , ##EQU00031##
can be obtained with the values of t.sub.n, t.sub.n-1, X.sub.n-1,
X.sub.n, P.sub.0, .mu.,
K n .phi. n and K n - 1 .phi. n - 1 ##EQU00032##
known. Here, t.sub.n-1 and t.sub.n are sampling time points (the
first timing and the second timing), which are selected by the
operator. X.sub.n and X.sub.n-1 are positions (the first position
and the second position) measured by the visualization system
(detection device). The pressure difference .DELTA.P(P.sub.0-0) is
1.013 bar, i.e. 1 atm, in the experiments. The viscosity of the
resin, .mu., as measured before the experiments, ranged from 650 cp
to 1200 cp.
K n .phi. n and K n - 1 .phi. n - 1 ##EQU00033##
can be estimated during the experiments as explained previously. No
local information of pressure is needed. Therefore, it is not
necessary to mount pressure sensors inside the mold cavity as shown
in the comparative measurement system shown in FIG. 2.
[0069] Results and Discussions
[0070] In this section, two experiments are presented to
demonstrate the effectiveness of the proposed methods. In the first
experiment, the permeability and porosity of the preform were
nearly uniform; while in the second case, variations in the
material properties were significant. For the purpose of
comparison, two other methods were also used as reference,
including one method that can be used to measure the local
permeability/porosity ratio with the help of a pressure sensor
array (see B. J. Wei, Y. S. Chang, Y. Yao, and J. Fang, "Online
estimation and monitoring of local permeability in resin transfer
molding," Polymer Composites, vol. 37, pp. 1249-1258, 2016) and
another suited to overall permeability estimation (see Y. J. Lee,
J. H. Wu, Y. Hsu, and C. H. Chung, "A prediction method on in-plane
permeability of mat/roving fibers laminates in vacuum assisted
resin transfer molding," Polymer Composites, vol. 27, pp. 665-670,
2006).
[0071] Nearly-Uniform Fiber Preform
[0072] In the first experiment, the reinforcement preform was
constructed by stacking nine layers of fiber mats, while the
injection pressure was set to 1.013 bar. The total infusion time
was 374 seconds. The viscosity of the resin was measured to be 560
cp. In this case, the permeability was believed to be nearly
constant, because there was no irregular arrangement of fiber
mats.
[0073] FIG. 9 shows experimental results of a nearly-uniform fiber
preform. The measurement started eight seconds after the injection
began. The sampling time interval was set to six seconds. The
results of three different methods are shown in FIG. 9, where the
squares are the local permeability/porosity ratio values measured
by the proposed method of the present disclosure and the circles
are the measurements obtained by Reference Method 1 introduced in
the publication (see B. J. Wei, Y. S. Chang, Y. Yao, and J. Fang,
"Online estimation and monitoring of local permeability in resin
transfer molding," Polymer Composites, vol. 37, pp. 1249-1258,
2016). These two methods gave similar trends in the results,
indicating that there was no statistical change point in the local
permeability/porosity ratio of the preform. Such analysis confirms
the known fact. In addition, the statistical properties, such as
mean and standard deviation, can be estimated from these results.
The triangle in FIG. 9 represents the result of using Reference
Method 2 (see Y. J. Lee, J. H. Wu, Y. Hsu, and C. H. Chung, "A
prediction method on in-plane permeability of mat/roving fibers
laminates in vacuum assisted resin transfer molding," Polymer
Composites, vol. 27, pp. 665-670, 2006). The result was only
obtained at the end of the infusion, because this method only
provided the overall information of material properties and did not
reflect the local details.
[0074] Non-Uniform Fiber Preform
[0075] In the second experiment, the preform was non-uniform, half
of which was made of ten layers of fiber mats, while the other half
contained only nine layers. Because the volume of the mold cavity
was a constant, it was expected that a significant shift would be
observed in the measurement values of the local
permeability/porosity ratio. The resin viscosity was 550 cp in this
case, while the injection pressure was 1.013 bar. Similar to the
first case, the sampling interval was six seconds. The first
measurement was conducted eight seconds after the injection
began.
[0076] FIG. 10 shows experimental results of a uniform fiber
preform. It is clear that both the proposed method and Reference
Method 1 captured the shift around 13 cm, indicating the change in
material properties. The local permeability/porosity ratio before
the switching point was significantly smaller than that after the
shift. It is also observed that, in this case, the proposed method
produced a smoother trend than that given by Reference Method 1. A
possible reason is that the local pressure readings used by
Reference Method 1 suffered from measurement noise, making the
measurement results of the local permeability/porosity ratio prone
to noise-caused inaccuracies. In contrast, the proposed method only
utilizes the information of injection pressure, reducing the chance
of errors. Reference Method 2 was not suited to this case, because
it only gave an overall impression of the physical properties of
the materials under investigation and did not provide any details
of the local information.
CONCLUSIONS
[0077] In RTM manufacturing, resin flow behaviors are largely
determined by the permeability and porosity of the reinforcement
preform. Hence, the ratio of permeability to porosity is critically
important to both process simulation and flow control. Most of the
existing studies focus on global material properties and ignore
local variability, although the local characteristics often
determine product quality. In the present disclosure, an in-situ
measurement approach of local permeability/porosity ratio, which
does not require complex sensor design, is proposed. The
experimental results illustrate the feasibility of the proposed
method.
[0078] In Brief, the present disclosure provides a measurement
system and a method to measure the local values of the
permeability/porosity ratio of a fiber preform in RTM
reinforcements, which does not require a large number of pressure
sensors to be mounted in the mold to obtain the local pressure
gradients. In some embodiments of the present disclosure, at each
sampling time point, the overall (global) permeability/porosity
ratio of the fiber preform between a pressure-sensing site (e.g.,
the injection gate) and the flow front of the molding resin is
calculated using a formula presented in Darcy's law. In the
formula, the pressure difference along the flow path is known when
the constant-pressure injection is employed, while the position of
the flow front is acquired by a detecting device such as a
visualization system (image-capturing device). Subsequently, the
local ratio can be derived based on the relationship between the
overall values and the local ratios.
[0079] One aspect of the present disclosure provides a system for
measuring a permeability/porosity ratio of a fiber preform in a
molding system. In some embodiments of the present disclosure, the
system comprises: an upper mold and a lower mold forming a mold
cavity; a resin-supplying source configured to input a molding
resin into a preform in the mold cavity; a detection device
configured to detect a flow front of the molding resin at a first
position and a second position in the mold cavity; and a computing
device configured to calculate a flowing property of the molding
resin into the preform based on the first position, the second
position, a travelling time of the flow front from the first
position to the second position, and a pressure difference driving
the flow front to travel from the first position to the second
position.
[0080] Another aspect of the present disclosure provides a method
for measuring a permeability/porosity ratio of a fiber preform in a
molding system, which comprises an upper mold and a lower mold
forming a mold cavity. In some embodiments of the present
disclosure, the method comprises steps of: applying a pressure
difference to a molding resin for driving the molding resin to flow
into a preform in the mold cavity; detecting a flow front of the
molding resin at a first position and a second position in the mold
cavity; and calculating a flowing property of the molding resin
based on the first position, the second position, a travelling time
of the flow front from the first position to the second position,
and the pressure difference.
[0081] 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.
[0082] 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, or steps.
* * * * *