Optimal Design for Molded Composite Products and Processes

Douglas E. SmithUniversity of Missouri at Columbia

NSF/DOE/APC Workshop Future of Modeling in Composites Molding Processes

Design and Optimization GroupJune 9-10, 2004

MISSOURI

Design and Optimization ResearchNumerical optimization in polymer processingNumerical optimization in polymer processing• Employ mathematical programming methodsEmploy mathematical programming methods• Easily interfaced with finite element methodsEasily interfaced with finite element methods• Process/product metrics enter cost function Process/product metrics enter cost function

and constraintsand constraints• Efficiency gained with analytical gradients Efficiency gained with analytical gradients

Design Sensitivity AnalysisDesign Sensitivity Analysis• Quantify relationship between design Quantify relationship between design

variables and performance measuresvariables and performance measures• Finite difference methods often employedFinite difference methods often employed

• Analytical approaches provide greater accuracy and efficiencyAnalytical approaches provide greater accuracy and efficiency

E.g., E.g.,

i

i

i b

FF

db

dF

)()( bbb

0bbuRbR

bbub

)),(()(

)),(()( FF

iii db

dF

b

F

db

dF u

u

ii bdb

dR

Ru

uwhere and

increasing F

b1

b2

b1

b2

b1

F

F(b)

b2

MISSOURI

Design and Optimization ResearchInjection molding process designInjection molding process design

Sheet extrusion die cavity designSheet extrusion die cavity design

gate 1(b1=0.5)

gate 2(b2=0.5)

time (sec)4.643.983.312.651.991.330.660.00

2.822.412.011.611.210.810.400.00

initial design optimal design

gate 1(b1=0.412)

gate 2(b2=0.733)fill time (sec)

4.75 2.90 (-39%)

find:to min:

subject to:

gate locations, gate pressuresfill timeinjection rateclamp forceflow front uniformity

find:to min:

subject to:

die cavity geometry, inlet pressureinlet pressureexit velocity uniformityprescribed exit flow rate

initialinitialdesigndesign

optimaloptimaldesigndesign

230

240

250

260

0 100 200 300 400 500

distance along die exit (mm)

die

ex

it v

elo

cit

y (

mm

/s)

LDPE @ 473K

LDPE @ 453K

LDPE @ 433K

half-gap(mm)

MISSOURI

State of the Art• Numerous software / algorithms available for numerical optimization

– VDoc/DOT, ISight, Hyperopt, LMS Optimus, Dakota, IMSL, Excel, Matlab, IMSL, Minpack, etc….

• Structural optimization well established– Sizing, Shape, and Topology

• Multidisciplinary Design Optimization (MDO) developed for niche applications, e.g., aeroelasticity, automotive body structure, etc…

• Non-Deterministic Approaches (NDA) address uncertainty in design– Reliability Analysis Methods, Robust Design, Reliability-Based

Design, etc…• Design Sensitivity Analysis methods developed for numerous

manufacturing applications– Polymer injection molding and extrusion, forging, casting, metal

extrusion, etc…• Optimal design applied to polymer composites

– IM, Sheet extrusion, RTM

MISSOURI

Vision

drops (8x)

gates (13x)

sprue

manufacturing

materialsdesign

The development and implementation of a comprehensive composites design environmentthat generates the geometric configuration, component materials, and processing schedule for industrial products. Designtool to be based on validated simulations, and address uncertainty in the product’s use, its processing, and models used to assess each, and provide desirable performance over its entire life cycle.

Composite Design AttributesComposite Design AttributesUsability

ExtendibilityDurability

Dimensional stabilityReliability

ManufacturabilityServiceabilityRecycle abilityDisposability

etc…

MISSOURI

Vision (cont)Integrated product and process design for short fiber reinforced Integrated product and process design for short fiber reinforced

polymer compositespolymer composites• Stiffness and strength defined by fiber direction during manufacturingStiffness and strength defined by fiber direction during manufacturing

• Integrated product and process design yields improved performanceIntegrated product and process design yields improved performance

• IPPD enabling technologiesIPPD enabling technologies

integrated non-integrated

mold fillingfiber orientation

material propertiesproduct performance

polymermelt flowanalysis

staticstress

analysis

modalanalysis

thermalstress

analysis

moldfilling

simulation

fiberorientationprediction

materialproperty

calculation

mold coolinganalysis

warpagesimulation

numericaloptimization

designsensitivityanalysis

multidisciplinarydesign

methodologies

structuraloptimization

MISSOURI

Perceived Gaps• Validated models needed for all aspects of composites processing

– E.g., strength and stiffness prediction from flow simulation• Design sensitivities not developed to level of analyses

– Fiber orientation– Mechanical properties from process models– Non-isothermal flow, reactive flow

• Optimal Design / DSA not available to end user– Design parameterization process appropriate

• Optimal design applications are task or discipline focused– I.e., Multidisciplinary design methods rarely not applied to composite

molding problems• Nondeterministic approaches not applied to composite molding problems

MISSOURI

Future Research

• Further develop/validate composite molding process/product models

• Development and application of DSA method for composites molding

• Development of a user-oriented composites molding design environment– Incorporate multidisciplinary design methodologies– Incorporate design under uncertainty tools– Include process control in optimal process design

• Application / Validation on industrial scale problems