Modern Plastics Handbook 2011 Part 9 pps

To model such an effect requires a viscoelastic constitutive equation.6 There is a lack of appropriate models for which data is readily able and this has hindered the use of computer sim

The chief disadvantage of mobile drying is

■ Floor space Space around the processing machine must be available

for the dryer However, the mobility of these units means that theycan be stored out of the way when not in use

7.18.3 Central drying systems

For a processor that uses a lot of hygroscopic material, a central tem (Fig 7.48) may offer significant advantages In fact, it is easy tosee how a large-volume, continuous run processor could justify a cen-tral system Generally, these processors have the need to handle largeamounts of similar materials, fed to machines that may make thesame product day after day for long periods of time Custom proces-sors, however, usually make frequent material changes and are lesslikely to need a central drying system And yet, even these short-runprocessors tend to specialize, running lots of similar parts using simi-lar materials Even if they cannot standardize production plantwide,

sys-it may be possible to create discrete manufacturing cells wsys-ithin theirplant and centralize drying with each cell Thus almost any processorcan achieve the following:

Figure 7.48 A central material drying-distribution system includes one or more dryers, serving multiple hoppers, dedicated to drying different materials A manifold system allows dried material to be conveyed wherever it is needed.

■ Energy efficiency One large dryer can efficiently serve multiple

hop-pers Booster heaters located at the inlet to each hopper make it possible to exactly match the temperature requirements of eachresin and avoid heat losses between the dryer and the hopper

■ Safety Drying takes place in one area, away from the processing

machine

■ Easy material changes Switching from one material to another may

be as simple as switching conveying tubes at a central materials tribution manifold New materials can be loaded and predried with-out affecting on-going production

dis-■ Floor space and manpower No machine-side floor space is required.

A central system requires less floor space per machine because onedryer can serve several hoppers and one hopper can serve severalmachines

■ Material control With a well-organized, well-controlled central

sys-tem there is less chance of contamination and improper blending.Pocket conveying meters material into the distribution box underthe drying hopper so that only small amounts of material are con-veyed and no extra material remains in the conveying lines to absorbmoisture or contaminate subsequent material lots

The only real disadvantages to a central system are

■ Capital cost A central system will always require more up-front

expenditures and costs associated with central material conveyingsystems required to get material from the dryers to the processingmachines System expansion can be expensive too

■ Material control This is both an advantage and a disadvantage An

error or miscalculation in material control can be extremely costlybecause of the amount of material involved and the number of pro-cessing machines served by a central system

7.19 Gas or Electric?

Plastics processors, historically, have been very dependent on electricpower for most of their processing needs And, because of its depen-dence on heat, the resin drying process can be a heavy consumer ofelectrical power It’s not surprising, then, that processors are showingincreasing interest in natural gas as an alternative energy source fordrying In fact, a gas dryer can provide energy cost savings of up to70% (see Fig 7.49)

Today’s gas dryers incorporate the most advanced gas burners able, featuring a ceramic-metal fiber matrix firing surface that pro-vides flameless, efficient radiant gas heat, with low emissions.Gas-fired dryers are available in both large central systems andmachine-side portable units In addition, process air heaters are avail-able to convert installed dryers from electrical heating to gas (Fig.7.50).

avail-As an alternate heat source, natural gas has these advantages:

1 The cost per btu is approximately one-quarter of the cost of electricper Btu

2 Natural gas appliances have a long and proven track record as asafe heat source

3 By reducing electric consumption during peak hours, companieswhose rates are determined by peak usage can qualify for a loweroverall electric rate

4 Retrofitting existing dryers with a gas process air heater can free

up existing electric switch gear for use on other new machinery

5 Gas process heaters require less maintenance than comparableelectrical units

7.20 Handling Dried Material

Once plastic materials have been properly dried, it is imperative thatthey be protected from moisture regain prior to molding As noted inSec 7.18, each drying system will approach the problem in a slightlydifferent way

A drying hopper that is mounted directly to the machine throat, forinstance, will require no special accommodations because the resin

Figure 7.49 Bar chart illustrates the savings that

are possible when using gas instead of electricity

for drying.

goes directly from the hot, dry environment of the hopper to the processing machine, eliminating the possibility of moisture regain.When dried material needs to be conveyed from hopper to machine,however, precautions need to be taken.

The key is to prevent material from coming into contact with ture-laden ambient air for any appreciable length of time Some mate-rials regain moisture slowly and will stay dry enough to process for 2

mois-or 3 h after exposure to ambient air, while others will regain an ceptable amount of moisture in a matter of minutes

unac-Many processors choose to use a dry air generator to produce veying air, thus avoiding exposing dried resin to ambient air

con-However, the cost associated with adding another piece of ment to the system may be completely avoidable if precautions can betaken to limit the amount of time the material is exposed to ambientair A better approach is to keep material out of the conveying lines as

equip-Figure 7.50 Here, a gas-fire process air heater has been used to convert an existing tric dryer to clean, economical, and safe natural gas.

elec-much as possible That calls for pocket conveying, a technique in which

a discrete amount of dried material is dispensed into a closed chamber(see Fig 7.51) under the drying hopper That small “pocket” of mater-ial is then vacuum conveyed, using ambient air, to a small hopperloader (Fig 7.52) on the processing machine The quantities being con-veyed are so small that they can be processed within minutes of leav-ing the drying hopper In addition, the supply lines are constantlypurged of material, so nothing is left behind to become separated or topick up moisture

For the ultimate protection against moisture regain, processors cancombine pocket conveying with dry-air conveying

Figure 7.51 A “pocket” conveying valve avoids moisture regain problems by moving only small amounts of dried material and preventing material from remaining in conveying lines.

Figure 7.52 To minimize the time dried material is outside the drying hopper before molding, and thus prevent moisture regain, mini hoppers, like the one in the foreground, are used.

7.21 Introduction

We begin with some definitions of the acronyms used in this section The

term computer-aided drafting (CAD) is part of common language today

and refers to the use of computers for drafting and modeling of productdesigns In a sense, CAD is the technological backbone that providesopportunities for concurrent engineering and for the subsequent use ofCAE and CAM The CAD industry has seen tremendous growth since itsinception in the 1970s and continues to grow with advances in both tech-nology and integration of CAE and CAM products We will not discussCAD specifically in this section but will mention how trends in the CADindustry are impacting plastics CAE CAD has been embraced by manycompanies and plays a central role in CAM and CAE Using a CAD sys-tem, the designer creates a representation of the part to be manufactured

An application is a component to be made from plastic or the mold to duce the part The CAD system creates a representation of the compo-nent’s geometry This representation may be used for a variety ofdownstream operations including rapid prototyping, CAE analysis,numerical machining, mold building, or tolerance and assembly checking

pro-Computer-aided manufacturing (CAM) refers to the production or

alteration of control data for manufacturing Often the term is used tospecifically refer to computer numerically controlled (CNC) machinetooling With regard to the plastics industry, CAM generally refers tothe generation of CNC cutter paths for the production of molds anddies More recently, plastics CAM has been extended by the availabil-ity of “smart” controllers for injection-molding machines This is animportant development and will be discussed in detail subsequently

The term computer-aided engineering (CAE) describes the use of

computers for analysis of a particular design Often the design is a newproduct, but in the context of plastics it could be a cooling circuit lay-out for an injection mold or even the mold itself Frequently, the termCAE is used to embrace both CAM and CAD though, strictly speaking,

it refers to the analysis stage only There are many types of analysesavailable these days Typical examples include

■ Structural analysis for determination of deflections and stresses in

a design subject to applied load

■ Thermal analysis in which the temperature distribution is calculated

CAD, CAM, and CAE

Peter Kennedy

Moldflow Corporation, Lexington, Massachusetts

■ Flow analysis in which the flow of a material through a definedregion is calculated.

■ Mechanical analysis where motion of a linkage or mechanical tem is determined

sys-Regardless of the type of analysis, all CAE involves the use of amathematical model that simulates the physical process or conditions

to which the design is exposed.1The mathematical model is typically aset of equations, usually involving partial derivatives and suitableboundary conditions to ensure a unique solution In order to imple-ment the mathematical model in computer software, we need to useappropriate numerical methods for the solutions of the equationsforming the mathematical model One of the features of all numericalmethods is that the problem must be discretized For CAE this means

creating a set of points, which are called nodes, at which the

quanti-ties (e.g., temperature, pressure, stress) of interest will be calculated.One of the most popular methods is the finite element method.2 Inaddition to the generation of points, the finite element methodrequires that the points be arranged to form geometrical entities called

elements The combination of nodes and elements is called a mesh For

two-dimensional problems, the mesh generally consists of triangular

or quadrilateral elements In three dimensions, the elements are ally tetrahedral or hexahedral in shape Thus, the discretization step

usu-in fusu-inite element analysis usu-involves the generation of a mesh which resents the region in which a solution to the problem will be sought.These ideas are illustrated in Fig 7.53 It is common to refer tomeshed objects as models for analysis These models, not to be con-fused with the mathematical model mentioned earlier, are abstrac-tions of the component under consideration and provide informationfor the analysis in a form understood by the computer In the plasticsindustry, and for the purposes of this section, CAE describes the sim-ulation of a particular process, e.g., extrusion, injection molding, filmblowing, etc Generally, this will involve use of a computer code, input

rep-of material properties, definition rep-of the region in which calculationsare to be carried out, and input of processing conditions We will seelater that generation of a mesh is an important part of the process andcan represent a significant part of the total time involved in CAE

In this section we focus on injection molding For us, CAE willinvolve the simulation of the injection-molding process Injectionmolding is the most mature area of the plastics industry with respect

to utilization of CAD/CAM and CAE Moreover, developments in theinjection-molding field represent the state of the art Of course, many

of the general ideas of simulation of injection molding may also beapplied to other plastic part production methods

7.22 Simulation and Polymer Processing

All major manufacturing processes for plastic products have a commonfeature, namely, the melting and subsequent solidification of the mate-rial The notion that processing has a dramatic effect on the properties

of the manufactured article has been known since plastic processingbegan In practice, the relationship between process variables andarticle quality is extremely complex It is very difficult to gain anunderstanding of the relationship between processing and part quali-

ty by experience alone It is for this reason that simulation was born,but it is interesting to note that CAE has been much more successful

in injection molding than in other areas In this section we review whythis is the case and discuss some aspects of simulation for otherprocesses

The major processes encountered today are

Work on designing profile extrusion dies is complicated by the effect

known as die swell In capillary flow, elastic effects cause the diameter

of the extrudate to be greater than the capillary diameter This effectdepends on the length of the capillary as well as the processing condi-tions and must be taken into account when designing extrusion dies

To model such an effect requires a viscoelastic constitutive equation.6

There is a lack of appropriate models for which data is readily able and this has hindered the use of computer simulation in this field.Nevertheless, a great deal of literature exists on simulation.7

avail-Much work has been done on flat die extrusion, usually withNewtonian or generalized Newtonian material models.8 When flatextrusion dies are operated at high pressure, the deflection of the dieitself can be significant and may need to be accounted for.9

7.22.2 Blown film extrusion

This process has been studied for some time10 and the effect of coelasticity on bubble shape, velocity, and stress are still beingexplored.11Some simulation of the flow in the spiral mandrel has alsobeen performed.8

vis-7.22.3 Blow molding

Blow molding is complicated by the complex stress field set up in thematerials when the parison is inflated This amounts to a biaxialstretching of the molten polymer and it is difficult to obtain materialdata under these conditions so that simulation may be performed.Despite this, much work on the inflation stage has been done, mostlywith the aim of determining the final thickness distribution.12

Recently parison inflation has been simulated using

three-dimension-al finite elements13and with remeshing of the parison as it inflates tominimize error from element distortion.14

7.22.4 Thermoforming

In principle, thermoforming is quite similar to the parison inflationstage of blow molding.12A complication is the use of plugs to assistforming The physics of the interaction between the molten materialand the plug is not well understood and is difficult to simulate As aresult, there are some limitations on what can be simulated today

7.22.5 Injection molding

Injection molding and its variants have been by far the most ful area of simulation and many codes are available Reasons for this

success-were mentioned in the introduction but may be reduced to three keyfacts:

1 The process may be represented by a relatively simple materialmodel, namely, the generalized Newtonian fluid which allows theviscosity of the fluid to be a function of the rate of deformation

2 The governing equations may be reduced to a simple form that issuitable for solution on ordinary computers

3 Injection-molding simulation has a high return on investment.The last point requires some explanation Previously in this section

we considered a number of common production processes for mers Of these, the majority were continuous processes For theseprocesses, although the process physics may be complex, the die isgenerally quite simple and inexpensive to make Moreover, theprocesses allow considerable flexibility in changing process condi-tions Of the two noncontinuous processes mentioned earlier, namely,blow molding and thermoforming, the cost of tooling in these indus-tries is also relatively inexpensive In fact, the cost of a blow-moldingmold can be as low as one-tenth that of an injection mold for a simi-lar article.15 Moreover, blow-molding machines provide the operatorwith enormous control so problems can generally be solved on the fac-tory floor In contrast, in injection molding, problems experienced inproduction may not be fixed by varying process conditions as with oth-

poly-er processes While thpoly-ere is scope to adjust process conditions to solveone problem, often the change introduces another For example,increasing the melt temperature and so decreasing the viscosity of themelt may cure a mold that is difficult to fill and which is flashingslightly The increase in temperature may, however, cause gassing ordegradation of the material possibly resulting in unsightly marks onthe product The fix may be to increase the number of gates or moldthe part on a larger machine Both of these are economically unfavor-able—the first, involving significant retooling—is also costly in terms

of time and the second will erode profit margins as quotes for the jobwere based on the original machine which would be cheaper to oper-ate Simulation, on the other hand, can be performed relatively cheap-

ly in the early stages of part and mold design and offers the ability toevaluate different design options in terms of both part and molddesign

In short, compared to other production processes, injection moldingdemands more of part and mold designers—experimentation after themold is built is expensive in terms of time and money Injection-moldingsimulation is relatively inexpensive in terms of project cost and offersgreat benefits to those using it early in the manufacturing process

7.23 The Injection-Molding Process

Injection molding is a seemingly simple process A mold is created toform the shape of the component to be made and molten plastic isinjected into it and then ejected when sufficiently cool Despite thisapparent simplicity, there are factors which complicate the processsignificantly They are

■ Nature of injection molding, in particular the basic physics of theprocess

■ Material properties

■ Geometric complexity of the mold

■ Process optimization/stability

7.23.1 Physics of injection molding

In injection molding there are two major heat transfer mechanisms—convection and conduction

During mold filling, the molten material enters the mold and heattransfer, due to convection of the melt, is the dominant mechanism.Due to the rapid speed of injection, heat may also be generated by vis-cous dissipation Viscous dissipation depends on the viscosity and rate

of deformation of the material It most often occurs in the runner tem and gates where flow rates are highest, however, it can also occur

sys-in the cavity if flow rates are sufficiently high or the material is veryviscous Finally, the mold acts as a heat sink and heat is removed fromthe melt by conduction through the mold wall and out to the coolingsystem As a result of these heat-transfer mechanisms, a thin layer ofsolidified material is formed as the melt contacts the mold wall.Depending on the local flow rate of the melt, this “frozen layer” mayrapidly reach equilibrium thickness or continue to grow, therebyrestricting the flow of the incoming melt This has a significant bear-ing on the pressure required to fill the mold When filling is complete,pressure is maintained on the melt and the packing phase begins Thepurpose of the packing stage is to add further material to compensatefor the shrinkage of material as it cools in the cavity Since the cavity

is full, mass flow rate into the cavity is much smaller than during ing and, consequently, both convection and viscous dissipation areminor effects During packing, conduction becomes the major heat-transfer mechanism and the frozen layer continues to increase inthickness until such time as the component has sufficient mechanicalstiffness to be ejected from the mold

fill-7.23.2 Material complexity

Polymers for injection molding generally can be classified as talline or amorphous Both have complex thermorheological behaviorthat has an enormous bearing on the molding process Thermoplasticstypically have viscous behavior that exhibits shear thinning and adependence on pressure and temperature (Fig 7.54) In addition, theirthermal properties are temperature dependent and, for the case ofsemicrystalline materials, many properties also depend on the rate oftemperature change An extra complexity in injection-molding simula-tion is the need to incorporate an equation of state to calculate densi-

semicrys-ty variation as a function of temperature and pressure The equation

of state relates the material’s specific volume (inverse of density),

pres-sure, and temperature This is referred to as the material’s pvT

char-acteristic It, too, is complex and varies depending on the type ofmaterial (Fig 7.55)

7.23.3 Geometric complexity

Injection-molded parts are generally thin-walled structures and may

be extremely complex in shape The combination of thin walls andrapid injection speeds leads to significant flow rates and shear ratesand these, coupled with the material’s complex viscosity characteris-tics, lead to large variations in material viscosity and so variation in

fill patterns The mold has two main functions in injection molding.The first is to form the shape of the part to be manufactured and thesecond is to remove heat from the mold as quickly as possible.Frequently the injection mold is a complex mechanism with provisionfor moving cores and ejection systems This complexity influences theposition of cooling channels which, in turn, can lead to variations inmold temperature These variations, in turn, affect the material vis-cosity and so the final flow characteristics of the material.

7.23.4 Process stability

Finally, in production, the process conditions to produce parts ofacceptable quality may be unstable That is, slight deviations fromthese conditions can dramatically affect product quality

7.23.5 Value of simulation

The preceding factors bring a level of complexity to injection moldingthat is not present in other plastic forming processes Moreover, thecost of tooling for injection molds is very high, significantly more thanfor blow molding or extrusion dies All these aspects combine to makeinjection molding an ideal focus for simulation Simulation of injectionmolding has a higher return on investment than simulation of otherplastic forming processes For this reason we will focus on injectionmolding in this section

7.24 History of Injection-Molding Simulation

Injection molding was practiced a long time prior to the advent of ulation While the observation that part quality was affected by pro-cessing was well known, due to the complex interplay of the factorsmentioned earlier, injection molding was something of an art

T, °C

P(MPa)

100 200

T, °C

P(MPa)

1.041.101.201.301.40

3/g

0 20 40 60 100 160

Figure 7.55 Graphs of pvT data for amorphous (left) and semicystalline (right) polymer.

Experience was the only means of dealing with problems encountered

in the process An overview of this approach is given in Ref 16 Thebibliography of Ref 16 cites hundreds of empirical studies, each con-tributing to the relationship between processing and part quality.Demand for increased quality of molded parts in the 1970s saw anincreased interest in mathematical modeling of the injection-moldingprocess During this time, many pioneering studies were published(see, for example, Refs 17 to 23) These focused on rather simplegeometries and, while of academic interest, offered little assistance toengineers involved with injection molding Nevertheless, these studiesprovided a scientific base for simulation

7.24.1 Early simulation of filling

In 1978, Moldflow introduced commercial software on a worldwidecomputer time-sharing system This software enabled users to deter-mine process conditions (melt temperature, mold temperature, andinjection time) and to balance flow in cavities and runner systems.Although accepted at the time, this software was difficult to use as itrequired the user to produce a “layflat.”24

The layflat was a representation of the part under considerationthat reduced the problem of flow in a three-dimensional geometry toflow in a plane For example, consider an open box with a thickened lip

at the open end If the box is to be injected at the center of its base, apotential problem could arise from polymer flowing around the rim ofthe box and forming an airtrap (Fig 7.56) The layflat of the box isshown in Fig 7.57 As can be seen, the box has been “folded out” toform the layflat Analysis could now be done on the various flow paths

on the layflat For example, the results of such analysis could be used

to thicken the sections shown to promote flow and so prevent the flow

of material around the thickened rim While this type of analysis wasundoubtedly useful, it did require considerable skill on the part of theuser to produce the layflat and optimize the various flow paths.Hieber and Shen25made a significant breakthrough with the intro-duction of finite element analysis to the injection-molding process.Despite the fact that computing technology was not up to the demands

of finite element analysis for injection molding, their use of the nique indicated the advantage of the approach, namely, that the mod-

tech-el for analysis was created in a form that resembled the part geometryand that results could be shown on the part representation In 1983,Moldflow introduced a finite element filling analysis program thatfound ready acceptance in the market For the first time, analystscould model the part under consideration in a form that resembled thecomponent and display the results of analysis on the part

Since finite element was introduced, the CAE industry has oped rapidly By 1987 there were no less than six companies involved

devel-in the development of software to simulate devel-injection molddevel-ing.26

7.24.2 Simulation of packing, cooling, and

variations of injection molding

Over the past decade, development has been rapid with simulationnow available for the packing and cooling phases of the injection-mold-ing process Also, in the 1990s some variants of injection molding havebeen introduced These include

■ Co-injection, in which a charge of material is first injected and thenfollowed by a second charge This results in the second materialforming the core of the part which is encapsulated with the firstmaterial

■ Gas injection, in which after introduction of some polymer into themold, a charge of inert gas is introduced to force the polymer to theextremities of the mold and so produce a hollow component in theareas penetrated by the gas

■ Injection compression molding in which the mold is initially openand is then closed after the polymer is injected or closed while poly-mer is being injected

We will not discuss the details of simulation for these processes, asmany of the fundamental ideas are common to injection-molding sim-ulation

Figure 7.56 Box with thick edge gated at top center

may have gas trap (dark region) and weld line due to

flow “race tracking” around thick edge.

7.24.3 Simulation of warpage

Moldflow introduced software for prediction of shrinkage and warpage

in 1990 Since this time, analysis of fiber-reinforced materials hasbeen introduced in which the orientation of the fibers in the moldingare calculated With the distribution of fibers known, it is possible tocalculate mechanical properties of the composite material in principaldirections This data can then be used in warpage calculations or usedfor structural analysis of the resulting part

7.25 Current Technology for

Injection-Molding Simulation

In this section we review the current state of technology for simulation

of injection molding In particular, we consider analysis of

■ Filling and packing phases

■ Automatic midplane generation

■ Dual domain finite element analysis (DD/FEA)*

■ Full three-dimensional analysis

7.25.1 Filling and packing analysis

Earlier we mentioned that a model exists for injection-molding lation that allows simulation to be carried out in reasonable time onrelatively inexpensive computers This model is based on the fact that

simu-in a thsimu-in-walled part we may neglect any pressure variation simu-in the mal direction This assumption underlies the basis of most commercialplastic CAE analysis

nor-The approximation arises in the study of flow between parallelplates and is sometimes known as the Hele-Shaw approximation Asmost injection-molded parts are thin walled, it turns out that thismodel is also applicable to the injection-molding process

All fluid flow problems involve solution of the equations that expressconservation of mass, momentum, and energy In what follows we give abrief summary of the governing equations and simplification of them.Details may be found in Ref 27 The conservation equations take the form

Energy: c p   T T   p 2   (kT)

(7.3)where  is the material density, t is time, is the velocity of the melt,

Adopting a cartesian coordinate system and assuming the cavitythickness is small compared to the other dimensions, the mass andmomentum equations may be reduced to the single equation

h and hare, respectively, the upper and lower z coordinates of the

frozen layer position,  is the coefficient of compressibility, and H is

half the wall thickness

With the additional assumption that convection in the z direction

may be ignored, the energy equation takes the form

The left-hand side of the energy equation represents the rate ofchange of temperature and convection, while the terms on the right-hand side account for heat of expansion/compression, viscous dissipa-tion, and conduction to the mold, respectively

These equations, and their respective boundary conditions, are erally solved with a hybrid approach introduced in Ref 25 The pres-sure solution is found from Eq (7.4) using finite elements and thetemperature field is obtained from Eq (7.5) using the finite differencemethod.28

gen-7.25.2 Cooling analysis

The cooling of the mold is a key factor in efficient production and ity Generally, cooling systems are given too little priority in the molddesign process This is unfortunate as careful attention to cooling sys-tem design can reduce cycle time and so increase the productivity ofthe mold/machine combination

qual-Injection-molding cooling systems can be analyzed quite readilytoday Generally, two analyses are done The first concerns the flow ofthe coolant in the cooling system; the second concerns the heat trans-fer from the part, through the mold, and into the coolant

The flow of the coolant can be handled using conventionalhydraulics theory Results include the flow rates, required pressure,

and the Reynold’s number for the coolant The latter is a measure ofthe degree of turbulence achieved In general, a turbulent flow increas-

es the heat transfer from the mold to the coolant Beyond a certainReynold’s number, however, the heat transfer increases only margin-ally while the power required to pump the fluid increases significant-

ly So while it is desirable to achieve turbulence, it is inefficient to usetoo high a pump capacity

Heat transfer from the plastic to the mold can be calculated usingfinite difference schemes for thin-walled, shell-like parts or finite ele-ment methods for true three-dimensional analysis Heat transferthrough the mold is generally performed using the boundary elementmethod (BEM) As the mold is three-dimensional, use of the BEM per-mits a heat-transfer analysis through the mold using only a surfacemesh.29 This is far easier than meshing the mold steel internally aswould be required for a finite element analysis and accounts for thepopularity of the method for this application Results from the coolinganalysis provide the temperature distribution on the surface of themold at particular points of time during the cycle These temperaturedistributions enable mold designers to position cooling lines so as tominimize temperature variations over the mold surface and, in partic-ular, from one side of the mold to the other Temperature variationsfrom side to side are a frequent cause of part warpage and should beavoided if possible

The temperature field calculated by the cooling analysis, while ofinterest in its own right, may also be used as a boundary condition forthe flow analysis That is, the cooling analysis is used to define themold temperature for the flow analysis This type of coupling betweenflow and cooling analysis most accurately describes the real process

7.25.3 Fiber orientation analysis

In many engineering applications short glass fiber reinforcement isadded to the material This has the advantage of increasing the strengthand modulus of the material As the material flows into the mold, thefluid deformation and interaction with other fibers alters the orienta-tion of the fibers The final orientation state will depend on the process-ing history of the material and may lead to highly anisotropic materialproperties

In simplest terms, fibers tend to align in the flow direction when theflow is converging and align transverse to flow where the flow diverges(Fig 7.58) With multiple injection points and complicated geometry,the final orientation distribution can be extremely complex.Simulation can assist here by first calculating the final orientationstate and then using this information to derive the thermomechanical

properties of the material such as elastic moduli, Poisson’s ratio, andlinear coefficients of expansion These derived properties may be usedfor subsequent structural analysis of the part They may also be usedfor determining shrinkage and warpage of the component.

Predicting fiber orientation. Isotropic constitutive models are not validfor injection-molded fiber-reinforced composites Unless the embeddedfibers are randomly oriented, they introduce anisotropy in the ther-momechanical properties of the material The fiber orientation distri-bution is induced by kinematics of the flow during filling and, to alesser extent, packing An extensive literature deals with flow-inducedfiber orientation while much other work has been devoted to micro-mechanical models which estimate anisotropic elastic and thermalproperties of the fiber-matrix system from the properties of the con-stituent fiber and matrix materials based on given microstructures.Comprehensive reviews of both research areas have been given in tworecent books edited, respectively, by Advani30 and by Papathanasiouand Guell31where many references can be found

Analysis of the final properties of injection-molded short-fiber posite parts requires accurate prediction of flow-induced fiber orienta-tion Several different fiber suspension theories and numericalmethods are available for the calculation of the motion of fibers duringflow Only the works of Folgar and Tucker32 and Fan33 are brieflyreviewed here since they are the most relevant The reader is referred

com-to Phan-Thien and Zheng34for additional information for other tutive theories of fiber suspensions In what follows we assume thefibers are rigid rods of circular cross section

consti-Figure 7.58 Fibers tend to align in the flow direction in

con-verging flow and transverse to the flow in dicon-verging flow.

Usually, fiber suspensions are classified into three concentrationregimes according to the fiber volume fraction, , and the fiber aspect

ratio a R (defined by the length-to-diameter ratio, L/d) The volume

frac-tion satisfies   nd2L/4 for rodlike fibers where n is the number

den-sity of the fibers A suspension is called dilute if the volume fraction

satisfies a R21 In dilute suspensions, each fiber can freely rotate Theregion in which 1a R

2

a R is called semiconcentrated, where each fiber

has only two rotating degrees-of-freedom Finally, the suspension with

a R 1 is called concentrated, where the average distance between fibers

is less than a fiber diameter, and, therefore, fibers cannot rotate pendently except around their symmetry axes Any motion of the fibermust necessarily involve a cooperative motion of surrounding fibers.Most commercial composites commonly used in injection molding fallinto the semi- or highly concentrated regimes

inde-There are several choices available to model the motion of the fibers.One is to track a large number of fibers and explicitly determine theirinteraction and motion This can be done by attaching a unit vector p

along the axis of each fiber and track its evolution with time Whilepossible, this method is not really practical for complex models Analternative is to use a probability distribution function, (p)  (, ),

whose value represents the probability of finding a fiber between theangles  and   d and  and   d (see Fig 7.59) Given such a dis-

tribution, we assume that one end of the fiber is indistinguishablefrom the other and so, (, )(, ) Also, the integral of thedistribution over all possible directions must be one That is,

For an individual fiber, with a unit vector, p, directed along its

length, Jeffery’s equation for the time evolution of the fiber is as follows:

iis the fluid velocity, and  is a constant that depends on the shape ofthe particle and is approximately 1 for slender rods

Jeffery’s equation was extended to concentrated solutions by Folgarand Tucker who added a diffusion term to account for the fiber-fiberinteraction In terms of the orientation tensor, the Tucker-Folgar equa-tion has the form

D D

a t

An empirical constant called the interaction coefficient C I is

intro-duced in the diffusion term The constant C Ifor a given suspension isassumed to be isotropic and independent of the orientation state, as afirst approximation The Folgar-Tucker model has extended the fiberorientation simulations into nondilute regimes It is widely used todetermine the orientation of fibers in injection molding

The main uncertainty in using this model is the chosen value for the

coefficient C I Some progress has been made in this area recently Fan

et al.33have recently presented a direct numerical simulation of fiber interactions Short-range interaction is modeled by lubricationforces Long-range interaction was calculated using a boundary ele-ment method The hydrodynamic force and torque on each fiber werecalculated to determine the motion of the fiber Although the directsimulation method is currently limited to a simple shear flow, thenumerical results can be used to produce macroscopic properties of the

fiber-suspension, including the Folgar-Tucker constant C I This may then be

used in finite element simulations for more complex flows This sents the current state of the art with regard to fiber orientation, anddetails may be found in Ref 37

repre-After determining the resulting distribution of fiber orientation in aninjection-molded part, it is possible to predict mechanical properties forthe composite Moduli and Poisson’s ratios may be determined using avariety of mechanical theories for composite materials These propertiesmay then be used in structural analysis or warpage analysis

7.25.4 Warpage analysis

Warpage is a common problem in injection molding It is evidenced bydeformation of the part such that assembly is difficult or the part isnot fit for its purpose Warpage is a complex phenomenon and a directconsequence of processing effects on the material Warpage is caused

by variations in shrinkage of the material These variations are ofthree types:

■ Variation from point to point on a part This type of variation is

fre-quently caused by variation in the density distribution which iscaused by variation in the pressure/temperature history experienced

by the material

■ Variation of shrinkage in different directions This type of variation,

which also varies from point to point in the molding, is due toanisotropic shrinkage This, in turn, arises from anisotropy in thethermomechanical properties of the material due to molecular ori-entation and the morphology of semicrystalline materials

Shrinkage anisotropy is a common problem when using fiber-filledmaterials as the orientation of the fibers leads to quite extremeanisotropy in thermomechanical properties.

■ Variation of shrinkage from one side of the molding to the other This

type of variation arises from asymmetry in the flow and temperaturefields of the molding It is mostly due to temperature variation fromone side of the mold to the other

There are two main approaches to analysis of based methods and residual stress methods Strain-based methods areamong the earliest and owe their existence to the difficulty of accu-rately determining residual stresses Essentially, the idea is to predictthe shrinkage strain experienced by the material.38These strains arethen input to a structural analysis program that determines the over-all part shrinkage and the deformation of the part Residual stressmethods are more directly linked to the physics of the process butrequire accurate material characterization to perform well The idea is

warpage—strain-to predict the residual stress distribution in the injection-moldedmaterial while it is in the mold This stress distribution is then used

as input to a structural analysis that determines the shrinkage anddeformation of the part Early calculations considered only thermallyinduced stresses39 caused by the material cooling while in the mold.This was later extended to models incorporating both thermallyinduced stress and the stress induced in solidified material by thepressure exerted on it by the melt.40 Regardless of the method used,the prediction of warpage requires accurate prediction of the filling,packing, and cooling phases of the injection-molding process

Results from warpage simulation include the deformed shape of the

part; part shrinkage; deflections in the x, y, and z directions; and

residual stresses and strains The deformed shape and its nying stress distribution may be subsequently used for structuralanalysis

run, usually subject to the constraint that the cavities all fill at thesame time Runner dimensions are defined to lie in a range and theoptimization algorithm varies the diameters of the runners subject tothe constraints until a satisfactory solution is obtained.

More recently, there has been interest in optimizing the turing conditions used to mold the part Much of the motivation forthis work stems from the possibility of using these results to provideinformation to the injection-molding machine We return to the topic

manufac-of machine interaction in a later section For now, we consider thescope of optimization of processing conditions For this purpose it isconvenient to consider the molding process as consisting of the fillingphase in which the velocity of the ram is controlled as a function ofposition and the packing phase in which pressure as a function of time

is the main variable

For the filling phase it is known that many surface defects may becaused by sudden changes in the flow front velocity Hence a commonconstraint is that the flow front velocity be constant Of course inattempting to achieve this, one must be careful to ensure that thematerial shear stress limits are not exceeded and that the tempera-ture of the material is within permissible limits

By considering these factors, optimization algorithms can define aram profile that meets these conditions that can be entered on themolding machine directly The advantage of simulation here is that iteffectively allows you to view the plastic in the mold—something thatmachine setters cannot do

The packing phase is known to have a dramatic affect on part ity—particularly part weight, dimensional tolerance, and warpage Inthe packing phase, material is subjected to high pressure while it cools

qual-in the mold The pressure temperature history determqual-ines the mate density of the molded material A common goal of the optimiza-tion is, therefore, to minimize density variation throughout the part.Alternatively, it is possible to minimize variation in linear shrinkage

ulti-in directions along, and transverse to, the flow direction The result ofthese operations is a pressure profile with pressure varying as a func-tion of time Figure 7.60 gives an example of the variables and the type

of output that can be achieved today Here the optimization algorithm

determines the initial pack pressure, P c , the time of application t c , the

level to which pressure should decay P d and the time to do this, t cl1, the

time to decay to zero pressure t cl2 , and the cooling time tcool Such a file is capable of improving part quality dramatically It is almostimpossible for a molder to define an optimum profile such as this sincethere is no way of quantifying the effect of changing pressures andrates of pressure decay

pro-7.25.6 Modeling for CAE analysis

Of particular importance is the assumption of thin-walled geometry

From Eq (7.3) we see that the pressure is independent of the z

coordi-nate Consequently, the finite element utilized for pressure calculationneed have no thickness That is, the element is a plane shell—gener-ally a triangle or quadrilateral This has great implications for users

of plastics CAE It means that a finite element model of the component

is required that has no thickness In the past this was not a problem.Almost all common CAD systems were using surface or wireframemodeling and thickness was never shown explicitly The path from theCAD model to the FEA model was clear and direct

In recent years, tremendous development has occurred in CAD usingsolid models With solid modeling the component is represented faith-fully All details are shown and the model is photo-realistic Initially, sol-

id modelers were not so popular for plastic designers This was becauseinjection-molded parts were thin walled Advances in modeling technol-ogy in the area of “shelling” now mean that the designer can producethin-walled models very easily Solid modeling is fast becoming thenorm, due to the realization that the solid model can be the master fordesign as well as all downstream operations such as rapid prototyping,assembly analysis, tolerancing analysis, and mold making Theincreased interest in solid modeling is evidenced by the number of prod-ucts available now and the reduction in price due to competition.41

The adoption of solid modeling introduced a problem for many users

of plastics CAE Due to the requirement of having an FEA model of nothickness, solid models had to be “midplaned” to generate an appro-priate model To overcome this problem, plastic CAE suppliers havedeveloped three recent technologies:

■ Midplane generation

■ Dual domain finite element analysis

■ Three-dimensional finite element analysis

7.25.7 Midplane generation

This is the direct approach in which a solid model is read into a gram and an automatic midplane mesh is generated (Fig 7.61).Details of such a system were given in Ref 42 and will not be discussedhere In practice, the fully automatic generation of a midplane model

pro-is difficult In many cases there pro-is some need to clean up the resultingmodel before analysis Nevertheless, midplane generation can save anenormous amount of time for many types of part

7.25.8 Dual domain finite element analysis

Dual domain finite element analysis (DD/FEA) is a method that enablesanalysis on the solid model It uses a surface mesh on the solid geometry

Figure 7.61 Automatic midplane generation seeks to transform three-dimensional solid geometry (left) to midplane shell representation (right).

and then inserts extra elements to ensure that the filling pattern is ically sensible Figure 7.62 gives the idea Imagine injecting a polymerinto a rectangular plate as shown If we simply used the surface mesh onthe plate with a conventional FEA, the flow pattern would be physicallyincorrect The material would flow out from the injection point across the top of the plate and then down the edges and finally along the bot-tom surface However, by inserting an extra element from the injectionpoint though the thickness to the other side, we can obtain a satisfacto-

phys-ry result using a conventional solver based on the Hele-Shaw mation For more complex geometry, it is necessary to insert more

approxi-(a)

(b)

(c)

(d)

Figure 7.62 Flow in a center-gated plate If normal FEA were performed using a surface

mesh, the flow would run along top surface only (c) and not match the physical reality (a) and (b) Dual domain finite element analysis uses a connector element to synchronize flows on opposite surfaces (d).

connector elements In particular, at any rib a connector element must

be introduced (Fig 7.63) This technique is called DD/FEA The namederives from the fact that you are, in fact, doing two FEA analyses—one

on each side of the component DD/FEA has had a striking impact onplastics CAE since its introduction by Moldflow in 1997 We return tothis in a later section

7.25.9 Three-dimensional FEA

All technology discussed here is based on the assumption that theplastic part is thin walled and makes use of the Hele-Shaw approxi-mation Three-dimensional finite element analysis (3D/FEA) elimi-nates this requirement In so doing, it introduces a new class ofcomponents to simulation With 3D/FEA it is possible to simulate themolding of parts for which a midplane is not available Typically, suchparts are chunky—some examples are given in Fig 7.64 Many parts

(a)

(b)

Figure 7.63 For ribs, additional connector elements must be inserted Without connector

elements (a) the flow is unrealistic Connector elements (b) are introduced to ensure the

flow is physically realistic.

contain inserts, either metal or some other material, and it can be ficult to analyze these using conventional shell-based analysis Theseparts are also amenable to 3D/FEA.

dif-In addition to broadening the range of parts that can be simulated,3D/FEA also couples well with solid modeling A particular advantage

is that the model for analysis is an unambiguous representation of thereal part geometry Sometimes it is difficult to achieve this with shell-based modeling

Three-dimensional FEA solves the conservation equations, Eqs.(7.1) to (7.3), discussed earlier with fewer assumptions Generally,inertial and gravitational terms are omitted, as viscous forces aredominant Importantly, 3D/FEA has a pressure gradient in the thick-ness direction and so there is explicit calculation of convection of themelt from the midstream to the wall at the flow front The phenome-

na of “fountain flow” is thus accounted for in 3D/FEA

Another advantage in three-dimensional calculations is that themodel for analysis unambiguously represents the part For example,the modeling of the gate regions of some parts is quite complex and isbetter handled in three dimensions Figure 7.65 shows a gate regioncomprising a runner of circular cross section, a conical feed to the partgate that is of square cross section This feed configuration would beimpossible to model accurately with shells and beams

7.26 The Changing Face of CAE

In an earlier section we mentioned the dramatic effect of dual domainfinite element analysis on the CAE industry In this section we elabo-rate on this

Figure 7.64 Parts such as these do not possess a midplane and so cannot be analyzed with conventional CAE Such parts require full 3D FEA analyses.

Throughout its relatively short history, plastics CAE has been seen

as a specialist activity Analysis was typically performed by dedicatedstaff who were expert users of software and had a good understanding

of injection-molding theory While it has always been recognized thatsimulation performed early in the design stage provides more benefit,the lack of direct interfaces between the CAD systems on which partswere designed and CAE software meant analysis was outside thedesign environment DD/FEA provides a solution to this problem Forthe first time, it is possible to closely couple plastics CAE with solidmodeling In doing this, the use of CAE by plastic designers ratherthan dedicated analysts is possible

Several solids-based CAD systems now offer products with DD/FEAtechnology to facilitate analysis at an early stage This type of tech-nology redefines the use of plastic CAE analysis by enabling nonspe-cialists to perform analysis very early in the design stage Accordingly,special attention was paid to results presentation Whereas the tradi-tional outputs have been pressure and temperature distributions, newdisplay technology has been introduced in response to the fact that thedesigner may have little previous experience in plastics CAE Forexample, in order to choose the number of gates, wall thickness, andresin type, a key variable is the pressure required to fill the part This,

in turn, depends on the temperature of the material which, in turn,depends on the processing conditions, locations of gates, and the partgeometry Determination of the pressure required to fill is therefore a

Figure 7.65 True three-dimensional analysis allows users to accurately describe the geometry at complex gate regions This provides greater accuracy in fluid and heat- transfer calculation.

multidimensional task that requires simultaneous interpretation ofpressure and temperature distributions To simplify the interpretation

of results, the pressure and temperature distributions are processed toproduce a single plot called “confidence of fill.” This is displayed byoverlaying the colors red, yellow, and green over the part geometry inareas that have low, medium, and high probabilities of filling, respec-tively Figure 7.66 gives an example of such a plot (red shows here asblack, yellow as light gray, and green as gray The gate position is atthe end of the part Most of the part has a high confidence of fill.However regions far from the gate are shown in yellow, while areas atthe end of the part are shown in red Such a plot is far easier to under-stand than the simultaneous pressure and temperature distributions.DD/FEA enables plastic designers to begin analysis very early in thedesign phase The information gleaned here is valuable only in so far

as it can be rapidly communicated to other people involved in theprocess For example, material suppliers, mold designers, and themolder can all benefit from this early knowledge of how the part willfill The rapid development of the Internet has been adopted by CAEsuppliers as the way to facilitate communication among team mem-bers Latest products are now offering report writers in which analy-sis images and notes can be linked together into a format that can beviewed on a browser or sent as a message on the Internet

DD/FEA provides the means to take analysis into the design stage

As well as its appearance in CAD systems, DD/FEA-based advanced

Figure 7.66 Simplified results interpretation in DD/FEA technology Regions that are unlikely to fill have low confidence of fill shown here as black, regions of medium confi- dence are in light gray while regions with high confidence are in gray.

analysis modules are also available This means that designers whoencounter problems can send their models to analysts armed withadvanced products for detailed analysis In this way DD/FEA has pro-vided a link between the traditional CAE user and part designers Theresult is that more designs are subject to analysis and parts can bemodified, if necessary, at a stage where change is least expensive.

7.27 Machine Control

While simulation is of great benefit, it is aimed at the part design andmold design areas of injection molding Of course the actual process-ing of the material has a dramatic effect on the quality of the compo-nent, and much effort has been devoted to controlling theinjection-molding machine Much of this effort has been focused onensuring that the molding machine is capable of repeating a particu-lar cycle While this is certainly important, the part quality is affected

by the polymer flow Much of the focus in machine control has been onmaking the machine respond rather than concern for the melt.Moreover, injection-molding machine controllers do not provide sys-tematic tools for optimization of the molding cycle

Advances in simulation technology have led to several attempts tolink the results of simulation to the injection-molding machine One ofthe difficulties in doing this is that injection-molding machines havecharacteristics that are not easily accounted for in simulation Forexample, the ability of the machine to respond to a desired change inprocess conditions is not known nor is the performance of the flowcheck valve Nevertheless, simulation can be used to get somewherenear an optimum set of process conditions The setup can then be fine-tuned to optimum performance

It is a fact of life that many plastic components are designed out the benefit of simulation For such a mold, how does one determinethe optimal set of processing conditions so as to maximize part quali-

with-ty and minimize production time? In general, the task falls to highlyskilled machine setters who are, unfortunately, in short supply What’smore, there is only so much a machine setter can do without some lev-

el of instrumentation on the mold, for example, a pressure transducer.Use of in-mold sensors while providing some information brings somedisadvantages:

■ Additional cost of the pressure transducers

■ Damage to the transducer, wiring, or connectors in a productionenvironment due to mishandling

■ Need for an operator to interpret the information from the ducer and adjust the machine control

7.25 .9 Three-dimensional FEA

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The adoption of solid modeling introduced a problem for many users

of plastics CAE Due to the requirement... thatmachine setters cannot

The packing phase is known to have a dramatic affect on part ity—particularly part weight, dimensional tolerance, and warpage Inthe packing phase, material is subjected