System and method for predicting warping behavior in a product
A method for predicting warping behavior in a product involves: 1) acquiring experimental warping data from a specimen under predetermined molding conditions, 2) generating simulated warping data using a digital twin, 3) calculating strain/stress components of both experimental and simulated data, 4) performing regression analysis to establish conversion relationships between experimental and simulated strains in transverse/parallel directions, and 5) generating calibrated simulation predictions using the derived relationships.
1 . A system for predicting warping behavior in a product, comprising:
an injection-molding apparatus configured to carry out a molding process of a product and monitor operating conditions during molding of the product;
and a computer coupled with the injection-molding apparatus, and carrying a simulation software,
wherein the simulation software is configured for, when being executed by the computer, simulating the molding conditions of the product according to the operating conditions of the injection-molding apparatus, predetermined molding conditions, and/or given molding conditions;
wherein simulating the molding conditions comprises:
acquiring, via the injection-molding apparatus, experiment warping behavior data of a specimen of the product;
generating simulated warping behavior data of the specimen via the simulation software;
determining an experimental strain and a characteristic strain from the experiment warping behavior data of the specimen of the product and the simulated warping behavior data of the specimen, respectively, in an in-processing state, of a principal coordinate system;
deriving an experimental stress and a characteristic stress from the experimental strain and the characteristic strain, respectively, in the in-processing state;
converting the experimental stress and the characteristic stress from the in-processing state to a fully-aligned orientation state to obtain orientation-calibrated stresses at a transverse direction and a parallel direction of a pseudo coordinate system;
generating additional-simulated warping behavior data of the specimen under a given molding condition based on the conversion relationship derived from the orientation-calibrated stresses; and
wherein the injection-molding apparatus is further configured to conduct an actual molding of the product according to the additional-simulated warping behavior data.
2 . The system of claim 1 , wherein the simulation software simulating the molding conditions of the product further comprises:
generating, via the simulation software, additional-simulated warping behavior data of the specimen under a given molding condition according to the conversion relationship; and
conducting, via the injection-molding apparatus, an actual molding of the product according to the given molding condition,
wherein a first molding thickness of the specimen described in the predetermined molding condition and a second molding thickness of the specimen described in the given molding condition are different from each other.
3 . The system of claim 1 , wherein the predetermined molding condition comprises at least one selected from the group consisting of a material for molding the specimen, an estimated cooling time of the material, a temperature of a mold for molding the specimen, an injection flow rate for injecting the material into the mold, an injection pressure for injecting the material into the mold, a packing pressure for molding the specimen, a packing time for molding the specimen, and a molding thickness of the specimen.
4 . The system of claim 1 , wherein the principal coordinate system defines at least one principal directions selected from the group consisting of: a flow direction of an injection mold for molding the specimen, a cross direction of the flow direction, and a normal direction of the injection mold.
5 . The system of claim 1 , wherein:
the characteristic strain and the characteristic stress correspond to at least one characteristic effect selected from the group consisting of mechanical-induced effect, thermal-induced effect, pressure-induced effect, crystalline-induced effect and flow-induced effect; and
the at least one characteristic effect is imposed on the specimen during an injection-molding process.
6 . The system of claim 1 , wherein deriving, via the simulation software, the experimental stress in the principal coordinate system from the experimental strain is based on a material constitutive equation expressed as:
σ
i
j
experiment
=
c
i
j
k
l
(
a
overall
)
ε
k
l
experiment
(
a
overall
)
where i, j, k, l represent index of principal directions in the principal coordinate system,
σ
ij
experiment
represents the experimental stress, ε kl represents the experimental strain, c ijkl (a overall ) represents a weakly-oriented overall stiffness coefficient tensor, and a overall represents an overall effective orientation tensor under comprehensive influences of warpage.
7 . The system of claim 6 , wherein determining, via the simulation software, the orientation-calibrated experimental strain at the transverse direction and the orientation-calibrated experimental strain at the parallel direction according to the orientation-calibrated experimental stress at the transverse direction and the orientation-calibrated experimental stress at the parallel direction, respectively, is based on a fully-oriented material constitutive equation expressed as:
ε
IJ
experiement
=
s
IJKL
σ
KL
experiement
where I, J, K, L represent index of principal directions in the pseudo principal coordinate system in the fully-aligned orientation state, s IJKL represents a fully-aligned overall compliance coefficient tensor.
8 . The system of claim 1 , wherein deriving, via the simulation software, the characteristic stress in the principal coordinate system from the characteristic strain is based on a material constitutive equation expressed as:
σ
i
j
Π
=
c
i
j
k
l
(
a
overall
)
ε
k
l
Π
(
a
Π
)
where i, j, k, l represent index of principal directions in the principal coordinate system,
σ
ij
Π
represents the characteristic stress,
ε
k
l
Π
represents the characteristic strain, c ijkl (a overall ) represents a weakly-oriented overall stiffness coefficient tensor, and a overall represents an overall effective orientation tensor under comprehensive influences of warpage.
9 . The system of claim 8 , wherein determining, via the simulation software, the orientation-calibrated characteristic strain at the transverse direction and the orientation-calibrated characteristic strain at the parallel direction according to the orientation-calibrated characteristic stress at the transverse direction and the orientation-calibrated characteristic stress at the parallel direction, respectively, is based on a fully-oriented material constitutive equation expressed as:
ε
IJ
Π
=
s
IJKL
σ
KL
Π
where I, J, K, L represent index of principal directions in the pseudo principal coordinate system in the fully-aligned orientation state, s IJKL represents a fully-aligned overall compliance coefficient tensor.
10 . The system of claim 1 , wherein:
the calibrated-simulated warping behavior data comprises a calibrated-simulated strain at the transverse direction and a calibrated-simulated strain at the parallel direction of the specimen under the predetermined molding condition; and
the conversion relationship defines a regression parameter of a characteristic effect constituting the calibrated-simulated strain at the transverse direction and/or the calibrated-simulated strain at the parallel direction.
11 . The system of claim 10 , wherein:
when the characteristic effect is a thermal-induced effect, the regression parameter corresponds to a calibrated thermal property of a material of the specimen;
when the characteristic effect is a pressure-induced effect, the regression parameter corresponds to a calibrated pressure distribution of a material of the specimen;
when the characteristic effect is a crystalline-induced effect, the regression parameter corresponds to a calibrated crystalline shrinkage of a material of the specimen; and/or
when the characteristic effect is a flow-induced effect, the regression parameter corresponds to a calibrated flow-induced residual stress of a material of the specimen.
12 . The system of claim 1 for predicting warping behavior in a product, wherein the specimen comprises at least one material selected from the group consisting of polypropylene, polyethylene, high-density polyethylene, low-density polyethylene, polystyrene, polyvinyl chloride, acrylonitrile-butadiene-styrene copolymer resin, polyoxymethylene, polycarbonate, polyamine, thermoplastic elastomer, epoxy resin, phenolic resin, unsaturated polyester, silicone, nitrile rubber, polyethyleneimine, polyethylene terephthalate, polylactic acid, and polyhydroxyalkanoate, Polyetherketone, liquid crystal polymer, modified polyphenylene ether, polyphenylene sulfide, nylon resin, and acrylic resin.