9 Computer-Aided Analysis

Nevertheless, a skilled computer operator can arrive at fill rates, filling and cooling times, shrinkage and warpage values, fill pressures, and pressure distributions that are more accu

Computer-aided analysis (CAA) of a variety of

plastic processes is available For the purposes of this

book, CAA includes a finite-element analysis of what

may be happening in an injection mold during the

mold-ing cycle In spite of the use of a computer for the

analysis, this is not an exact science Many

assump-tions are involved in the computer algorithms The

pro-gram operator must make yet more assumptions Thus,

the end result of the analysis can follow the well-known

computer admonition: garbage in, garbage out

Nevertheless, a skilled computer operator can arrive

at fill rates, filling and cooling times, shrinkage and

warpage values, fill pressures, and pressure distributions

that are more accurate than those that can be estimated

by the most experienced mold designer or builder

There are only a few programs on the market that

qualify as good analyzing programs.[64] Among the

longer term players are Plastics & Computer’s

TMconcept® family of software tools and Moldflow’s

Flow Analysis family of programs There are other

companies that offer analysis packages If the intent of

the end user is to check a box that says the analysis

was performed without using the analysis to optimize

the process, any program will do

Any good analysis software should yield results

that are in line with what you expect when you model a

very simple part without using “fudge factors.” If you

have to use fudge factors to make the analysis work

out as expected, how can you trust the analysis when

the part is complicated?

Giorgio Bertacchi of Plastics & Computer, Inc.,

says, “We contend that no computer program can

com-pensate for a user’s inexperience In the hands of

non-professionals, even the best models, based on process

fundamentals and using transparent, automatic

mod-eling, carry the inherent risk of producing erroneous

results and causing costly mistakes.”

For any analysis, someone with a lot of experience

should review the results If the results appear to be

out of line, then a careful review of all assumptions

and inputs to the program are appropriate Before

ac-cepting the results, a logical reason for the unexpected

results should be found

Injection molding is an art of compromise What

are the objectives that you are trying to achieve? If a

fast cycle is the objective, then better cooling may be the purpose of the analysis If holding tighter toler-ances is the objective, then longer cycles or a different resin may be indicated

If the molding project has a small window of moldability, some changes might be advisable to avoid excessive mold maintenance such as repairing gate wear

or cleaning minerals out of the water lines

For example, how do you clean out the water lines

of a mold that is built with “conforming” water lines? Conforming water lines are water channels that are formed into a mold insert by one of several processes whereby the water lines follow the molded part profile

at a constant distance from the mold surface These water lines are not straight and are not drilled They may have any number of twists, turns, or other convo-lutions that defy mechanical cleaning

The premiere analysis systems that use finite-element methods consist of a number of modules Each module simulates a different portion or aspect of the process For example, one module will take a CAD (computer-aided design) model and mesh it for analysis Coupled with that module are modules that analyze the filling and the packing/holding phases of the process Other modules predict the resulting shrinkage/warpage or final shape of the part, or re-move some simplifying assumptions about the cooling capabilities of the mold In addition, there may be modules to analyze special subsets of injection mold-ing like gas-assisted moldmold-ing or injection compression molding

Decision support modules may also be available that offer quick approximations to help guide the de-tailed analysis process and identify the hurdles and chal-lenges presented by a particular application Some of these modules can be used even before a detailed CAD drawing is completed and can be used to help guide design decisions to ensure a robust process and part quality These modules offer estimations regarding the difficulty of filling the part, attainable tolerances, shrink rate, machine capability determination, etc In addition, these programs typically look at the eco-nomic impact of various design decisions and present

a detailed engineering cost estimation The costing portion should help with decisions on mold features such as recommending the number of cavities and run-ner type, as well as molding machine capability re-quirements, and production planning issues

An analysis may result in the use of a smaller

mold-ing machine for large parts by optimizmold-ing the gate

lo-cation to lower injection pressures An analysis can

help size runners and gates in family molds to ensure

that all cavities fill at the same time It can help

ar-range gates and flow patterns to minimize the tendency

for cores to shift under injection pressure It can help a

mold designer position and time sequential gates (see

Fig 9.1), so that as the flow-front passes a new gate, it

opens, thus avoiding weld lines and minimizing flow

distance and cavity-pressure differential Gas-assist

injection molding simulations (see Fig 9.2) help

deter-mine the correct size of the gas channel, the shot size

to be used, and the process conditions to ensure the

desired size of the voids left when the gas displaces the

plastic in the heavier sections such as rib intersections

Each of these CAA programs requires good

knowl-edge of the molding process and of the assumptions

made in the computer analysis programs in order to

obtain reasonably accurate results Probably the most

basic assumptions deal with the relationship between

pressure, temperature, and volume These relationships

are well known and documented for relatively slow

cooling rates, say five degrees per minute The

rela-tionships between these variables at cooling rates of

perhaps hundreds of degrees per minute are not

com-monly available Therefore, certain assumptions are

made about these relationships when analyzing mold

filling, cooling, and shrinkage These three variables are the most prominent of the variables to be consid-ered, but there are approximately thirty total variables Most finite-element–based analysis programs use

what are called midplane analysis techniques

Mid-plane analysis involves making a model of the mid-plane of part That midmid-plane surface model is then meshed with either triangular or quad plate/shell ele-ments The appropriate thickness property is then as-signed to each element Once the mesh is generated and the thicknesses defined, the gates and runners are typically added and defined The gates and runners are normally one-dimensional elements with length and diameter or size properties In some programs, gate and runner elements may have special element types to better define their flow and heat-transfer properties (for example, hot runner, cold runner, or insulated runner) Calculation times will vary by program and will depend on the part-flow configuration Most analysis output consists of pictures and graphic data that indi-cate the flow-front at any time during the filling pro-cess, and the temperature, shear stress, shear rate, fro-zen skin, and pressure distribution at any instant dur-ing the process Fully dynamic programs, like Plastics

& Computer’s TMconcept® programs, recompute all the field variables in each element back to the origin of flow at each interval of time; other programs assume that once an element is filled, the conditions in that element only change on a time-dependent basis (that

is, the shear stress stays the same, but the temperature drops due to time-dependent heat transfer) Due to the latter assumption and the assumption of “fountain

Figure 9.1 The injection pressure and flow-line distribution

that result from the use of sequential gating [61] (Courtesy

of Plastics & Computer.)

Figure 9.2 An analysis of thick-walled parts where

high-pressure gas is used to fill out the mold The gas creates voids in the heaviest sections so that the parts are hollow This minimizes the amount of plastic required, creates hollow parts, and minimizes sink marks [61] (Courtesy of Plastics & Computer.)

flow,” some programs can erroneously identify the

ar-eas far from the gate to be hotter than the arar-eas near

the gate

The metric system is preferred in CAA for

mold-ing plastic Round-off errors can result in

division-by-zero errors more often with inch units than with

milli-meters (A millimeter is about 1/25th the size of an inch.)

This is primarily a problem in small parts

Shrinkage can vary widely It is influenced by many

factors already discussed, but the shape of the part and

its constraints while in the mold are significant Some

of the simplified decision support programs, like

Plas-tics & Computer’s MCO (Moldability and Cost

Opti-mization) programs, do not generally consider such

restraints to shrinkage They assume that the parts are

allowed to shrink to the extent that molding conditions

predispose them In other words, molded parts that are

constrained may appear to shrink much less (or more)

than the analysis indicates due to warpage caused by

differential shrinkage and physical constraints Unlike

finite-element based shrinkage/warpage programs,

MCO can consider shot-to-shot and cavity-to-cavity

variabilities to come up with an anticipated range of

shrinkage so that attainable tolerances can be more

effectively considered

Finite-element shrinkage/warpage is a simulation

and cannot consider the shot-to-shot and

cavity-to-cav-ity variations However, it does consider warpage and

the user can apply constraints To consider the impact

of variations in the process, multiple analyses under

different conditions need to be run This process can

be very time-consuming and will not account for the

cavity-dimension tolerances due to toolmaking

Most analysis programs today assume that there

is adequate venting, so no backpressure is considered

during the filling stage As all molders know, inadequate

venting can significantly affect the moldability of a part,

and the filling pattern

None of the current analysis programs have

spe-cific result displays to addresses surface finish

imper-fections Some programs provide displays indicating

weld-line location, but these should be used with

cau-tion and verified by looking at the flow-front

develop-ment since there are frequent reports of incorrect

indi-cation, and the analyses do not offer any indication

regarding the potential severity of the resulting surface

or structural problems It is generally recommended

that weld-line formation and integrity can be

evalu-ated by interpreting the flow pattern and melt

condi-tions at the time that the flow fronts meet Other

phe-nomena like surface roughness from inadequate

vent-ing, moisture, or stick-slip skin folding are not

ana-lyzed, although users with extensive molding experi-ence may be able to anticipate some of these by inter-preting changes in the field variables (temperature, stress, pressure, etc.) during the molding process Some programs claim to predict the depth of visible sink marks (see Fig 9.3)

There is a tendency for people to accept the output

of a computer program as an error-free fact, forgetting that an imperfect human wrote the program and the operating system The computer analysis of plastic flow, cooling, and shrinkage within a mold requires consid-eration of many variables, some of which change from moment to moment during the molding process and cannot be predicted in advance Other parameters vary with the age and condition of the mold and molding machine

Therefore all analysis programs must make as-sumptions What these are and how they are addressed

in the computer program affect the end results The CAA results should not be based on faith but rather be subjected to intense scrutiny Before selecting a pro-gram or accepting the results of an analysis, there are certain questions that will help determine its accuracy and validity

First of all, the user should be aware of the as-sumptions that are built into the analysis program Carefully determine what these assumptions are and how they will affect the analysis results

Figure 9.3 Filling pressure distribution and potential sink

marks [61] (Courtesy of Plastics & Computer.)

Consider how the program handles branching flow

into the mold Even a single-cavity mold has flow

branching as the flow moves away from the sprue or

gate through one finite element and spreads out into

two or more other elements Does the program assume

a constant flow rate? Does the flow rate change in each

element as the flow diverges from the gate? Does the

program consider a modern molding machine’s ability

to vary the flow rate as the molding cycle progresses?

Do the analysis results show that flow advances faster

in thick sections when compared to thinner sections?

To put it another way, does the flow-front advance

in-versely when compared to the resistance to flow?

Con-sider a simple mold containing two cavities of vastly

different volumes but with a common runner, gate, and

cavity thickness Does the program predict that they

will fill at a different time, as it should? (See Fig 9.4.)

How about a mold with two cavities, each with the

same flow length but with different cavity thicknesses?

Does the program predict that the cavities will fill at a

different rate and pressure?

How does the program handle shear rates? Shear

rates will vary depending on skin thickness as the mold

fills Some programs have assumed that no solid skin

develops as the mold fills so that the maximum shear

rate occurs at the mold surface The analysis program

should predict the different skin thicknesses and

tem-peratures that result from very long, slow injection

cycles, and short, rapid injection cycles

How can you verify temperatures calculated and

how does the program deal with crystalline materials?

One simple test is to determine actual no-flow

condi-tions within a test mold by increasing packing or hold-ing time until the part-weight stops increashold-ing, while carefully documenting all parameters Determine one set of conditions for an amorphous material and an-other set of conditions for crystalline materials Com-pare the results with the analysis program If the analy-sis program fails to accurately predict the no-flow tem-perature, its other results are suspect

Are cross-section temperature predictions reason-able? (See Fig 9.5.) It has been established that tem-perature profiles through the thickness of a part vary widely depending on flow rates At high flow rates, a shear-heating temperature peak occurs near each wall

of the cavity At low flow rates, the temperature peak near the wall fails to develop because there is little shear heating Testing the analysis program’s temperature-profile predictions at high and low flow-rates should show a peak near the wall at high flow-rates and no apparent peak at low flow-rates

Does the program consider and recalculate condi-tions in each element based on the influence of other elements as time progresses? As resistance to flow in-creases in one area, is the flow shifted to other areas that are experiencing lower resistance to flow? Does the program predict plastic temperature rise based on increasing shear rates?

Any flow analysis program should give results that are consistent with an experienced molder’s observa-tion of the real world If the predicted results are in-consistent with expected trends, then the analysis should

be suspect

Figure 9.4 The effects of adjusting runner size to ensure

that both cavities of a two-cavity mold complete the filling

sequence at the same time [61] (Courtesy of Plastics &

Computer.)

Figure 9.5 Temperature distribution and temperature

cross-sections in a mold [61] (Courtesy of Plastics & Computer.)

9.4 Customer Requirements

The hardest job for the person making the analysis

may be to get the person requesting the analysis to

pre-cisely define his goals If a “complete analysis” of a

part would cost $10,000, the actual requirement might

be much less if the exact purpose of the analysis is

defined

For bids on analysis, include a rendering or

draw-ing of the part and a careful description of exactly what

analysis is desired and what your goals are

What are the purposes of the filling analysis? Is it

to size runners and gates? Perhaps it is to determine if

the part will fill? Is the shrinkage of the part of

pri-mary concern? Is distortion due to warpage a pripri-mary

concern? How can the cooling and cycle time be

im-proved? Can the quality of the part be imim-proved? (See

Figs 9.6–9.8.) What can be done to minimize size

variations? What can be done to minimize or eliminate

sink marks? By moving the gates, can the part be filled

on a smaller machine? Is the available machine

ad-equate from the standpoint of shot size and clamp

ca-pacity? Can you hold the tolerances requested? Do you

need to consider a different resin? Do you need to

con-sider all available manufacturers and grades or can you

limit yourself to a single manufacturer’s specific resin

and grade? What are the operating conditions of the

finished molded part? Is it going to be used in Alaska

or Saudi Arabia? Widely differing end-use

tempera-tures can cause parts to be out of tolerance due to the

coefficient of thermal expansion differences in mating

parts of dissimilar materials How are the parts

in-spected, and at what temperature? The customer should

carefully consider these questions and others, and de-fine carefully what he expects of the analysis

Even though a resin may meet a set of specifica-tions, variations in flow and shrinkage between differ-ent manufacturers can throw a part out of tolerance What are the manufacturing issues? One example is that of a medical tray of Ultem which was analyzed The original question was “Can the tray be molded with two gates?” The analysis showed the tray could

be molded, but at a pressure near 20,000 psi Most machines are capable of this pressure, but what of the clamp force required to keep the mold closed? The in-jection pressure times the projected area of the part indicated the need for a clamp pressure of more than twice that available to the molder Redesign of the gat-ing allowed the part to fill with three gates and within the clamping capacity of the molder’s machine

Figure 9.6 A separate gate at the root of each fan blade,

fiber orientation, and distortion in a shrouded fan [61]

(Courtesy of Plastics & Computer.)

Figure 9.7 An analysis of a molded tray showing improved

distortion and pressure distribution using two gates instead

of one [61] (Courtesy of Plastics & Computer.)

Figure 9.8 Distortion improvement that results from using

two center gates instead of two edge gates [61] (Courtesy of Plastics & Computer.)

Who normally requests an analysis? It could be

anyone involved in the design and production process

The designer, the engineer, the molder, the moldmaker,

and the end user each has an interest in producing a

satisfactory part The best arrangement is for all of

these people to be on the same team, working together

and using the analysis software to optimize the design

of the part, the design of the mold, and the molding

conditions to maximize production and profit That way,

the expertise of all the team members is utilized to find

the best set of compromises available When used

cor-rectly, the analysis serves as a virtual mold trial, where

trying different options is relatively cheap, easy, and

fast It helps improve communication between the team

members and, therefore, can make design review

meet-ings more productive and allow the team to push the

limits of the standard practices

Anne Bernhardt, of Plastics & Computer, Inc.,

(who sell the TMconcept® line of software), suggests

that the least experienced designer or engineer with

CAD knowledge run the programs and “punch the

keys,” with the more experienced team members

deter-mining the issues, desired results, alternatives to try,

and helping in the interpretation of the results This

helps less-experienced members of the team rapidly

learn the molding process and problems that occur in

real-world production while still being a valuable

mem-ber of the team Through the way their menus are

writ-ten and some of the results are presented, most

pro-grams have some tools to help guide the options that

are considered

The part designer is the member of the team that

can usually answer questions about part modifications

He learns from the analysis which features cause

prob-lems, and that improves his future designs The

moldmaker and molder better understand the designer’s

intent and requirements, and also gain valuable insight

about each other’s strengths and constraints

Manage-ment gains a valuable tool to understand how to

maxi-mize production and profit

Simplified programs that offer very fast

calcula-tions, simplified inputs, and consider economics are

important tools for decision support and project

man-agement These programs should let you evaluate the

viability of a project at the initial concept stage and

refine the inputs and analysis as decisions are made

Ideally, you should also be able to use these tools to

evaluate improvement options of existing production

Unlike standard simulation programs, these tools cal-culate costs, do not require detailed CAD drawings, and some consider process variability and machine capabilities

These programs use a lot of simplifying assump-tions As a result, many believe them to be inferior to detailed simulation programs; however, in many cases they offer more “bang for the buck.” Because decision support programs are very fast, and require very few inputs, they make it possible for the product develop-ment team to consider many more options than with-out them The economic impact of changing resin and manufacturing constraints can be considered, as well

as the economic incentive to overcome limitations (mold size and thickness problems, excess tonnage or shot size or residence time, clamp stroke for deep-draw parts, recovery time, etc.) or change part or quality require-ments

Decision support programs are not meant to re-place simulation programs, rather they help guide the design process by helping the team select the best op-tions and focus engineering resources on the aspects that are likely to cause problems in production Some programs are limited to estimating the ability to fill the part, the associated clamp requirements, and an esti-mate of mold-closed cycle time Others also let you evaluate economics and costs, the total cycle, includ-ing machine actuation time, tool size and cost, general cooling requirements, attainable tolerances, and other factors

An important additional benefit to decision sup-port programs is that they provide the basis for estab-lishing a methodology that ensures that all aspects of the application are considered early in the project The early identification of features that are difficult or costly

to achieve enables the team to focus on design alterna-tives in these areas while changes are relatively inex-pensive to make

Decision support programs like Plastics & Computer’s TMconcept® MCO (Moldability & Cost Optimization) programs estimate cycle time, process-ing conditions, and required gate size based on the resin,

a simplified description of the part geometry, and tol-erance requirements Economic factors such as opti-mum numbers of cavities, machine selection, and batch size can be optimized based on machine availability and capability, production requirements, part quality requirements, and costs The program also determines the resultant yields, production-planning data, and the finished part cost A plant database with hourly rates and machine capabilities reduces data entry The gram also helps identify factors that could limit

pro-ductivity and/or increase costs MCO also has the

ca-pability to add markups, as well as the cost of inserts,

secondary operations, and transportation costs, to come

up with a sale price for the finished part

A filling analysis simulates the filling phase of the

injection-molding process In other words, it covers the

time from the initial introduction of melt into the mold

until the instant that the entire mold is filled with resin

Filling analysis requires a definition of the part or mold

geometry, a resin database, and molding conditions

Based on the way the geometry is defined, there are

four major categories of filling analysis on the market

today See Fig 9.9

Lay Flat or User Defined The oldest form of flow

analysis, this method is sometimes called a 2D

(two-dimensional) method The part is defined in segments

that approximate how you expect the part to fill

Vari-ous segment geometries (radial, rectangular, round, etc.)

are available to describe the filling pattern in the part

and runner system This method requires a lot of user

knowledge and understanding of what the most likely

filling pattern will be In recent years, this method has

been most commonly used for runner sizing and

bal-ancing This method is particularly good in small,

single-gated parts Mold Masters offers a program of

this type called FillPlus™ This program starts with

an expert system to help the user select the correct

com-ponents from their product line, and then completes the flow analysis for verification It can also check for the number of shots required for a color change

Midplane FEA The most common flow analysis

is the midplane FEA (finite-element analysis) method, which is sometimes called a 2½ D method The part is described as 3- (triangles) or 4- (quads) noded elements

on a midplane of the part These elements are then as-signed thickness properties to define the part volume Examples of this type are Plastics & Computer’s faBest® programs and Moldflow’s MPI (Moldflow Plastic Insight) programs This type of program is the most thoroughly tested and widely used Although ex-cellent for most injection-molded parts, it is difficult to use in modeling parts with very thick wall sections where it is hard to determine a midplane, and in very small parts, or parts with a lot of detail

Determining the midplane can be time consuming Many CAD programs and some plastics analysis pro-grams have midplane generators; however, many us-ers report that they work very poorly For most me-dium- to large-size parts, using either outside surface generally works fine if there are no significant features

on the other side One of the most important aspects of the meshing is to ensure that there is “connectivity” between the elements Without connectivity, the mate-rial can not flow between the elements Most mesh generators have utilities to check and repair connec-tivity

Solid FEA Also called 3D, this is the newest type

of analysis An example is shown in Fig 9.10 These are true 3D solid element programs where the solid CAD model is broken into bricks, hexahedrons, or tetrahedrons These programs are excellent for very thick-walled parts, small parts, and fiber reinforced parts One of the major drawbacks of these programs

is the excessively long calculation times required by some Current commercial programs in this category include Plastics & Computer ’s faSolid™, and Moldflow’s MPI/3D

Figure 9.9 Several filling-analysis program results Notice

the flow hesitation in the upper left corner where a “living

hinge” is creating an impediment to flow [61] (Courtesy of

Plastics & Computer.)

Figure 9.10 A representation of a solid FEA analysis during

the filling operation [61] (Courtesy of Plastics & Computer.)

Dual Domain FEA This method is patented by

Moldflow and used exclusively by them Their MPI/

Fusion product line uses this method It is a clever way

to automate the process of meshing a solid model in

STL format, but it creates new problems Initially, this

meshing technique resulted in physically incorrect flow

patterns in the presence of simple ribs on flat surfaces

Some solutions have been added to help resolve these

problems, but they increase the meshing and

calcula-tion times, and the quality of results seems to be more

sensitive to the mesh than those of the midplane meshes

The resin database for all filling analysis programs

includes thermal and rheological properties Some

pro-grams, like Plastics & Computer’s faBest® and faSolid®

also require the latent heat of crystallization for

crys-talline and semicryscrys-talline materials Many software

suppliers include menu-driven programs that allow the

user to enter her or his own materials into the database

since it is impossible and impractical to include every

grade available on the market

Processing conditions are generally entered through

menus when an analysis is set up These inputs include

selecting the melt entry location, the resin, the fill time

or injection rate, the injection profile, melt

tempera-ture, mold temperatempera-ture, and the V/P changeover point

(switch from volumetric control to pressure controls)

In most cases, the analyses will use the assumption of

a uniform, assigned mold-surface temperature Some

programs allow specific mold temperatures to be

as-signed to the “a” and “b” side of certain elements, or

for the mold temperature to be refined by integration

with the cooling analysis, discussed below, Sec 9.9,

and in Ch 6

The results of a filling analysis include the

pres-sure required to fill the cavity, opening forces

gener-ated by the injection pressure on the projected area of

the mold, and animated views of the progress of filling

the part, as well as the distribution of field variables

during the process Field variables typically include

temperature, pressure, shear stress, shear rate, frozen

skin, and flow orientation Plots of the flow rate and

injection pressure at the melt entry-point and of the

progression of the field variables can also be displayed

In addition, each supplier offers a variety of displays

aimed at helping the user evaluate the results or

iden-tify things like the location of weld lines

Evaluation of the advancing flow-front shows the

filling pattern and makes it possible to predict

weld-line location, the last point to fill, and other locations

of potential air entrapment where vents will be needed

The quality of weld lines can be evaluated by looking

at the melt temperature, shear rate, and frozen skin as the weld line is formed

The following are general guidelines for evaluat-ing the various fillevaluat-ing-analysis result displays

Cooling Time This is the time required for the

center of the element to reach the freezing temperature

of the resin (as specified in the database) starting at the end of the filling of the part This time is used as a reference to set the cooling time It normally repre-sents the maximum cooling time since some parts can

be ejected with a partially hot core

Frozen Skin The frozen skin is the percentage of

material frozen during the filling of the part For ex-ample, 10% frozen skin on a 3-mm thick part means that the frozen layer in each side is 0.15 mm This vari-able is essential to optimize the molding conditions and

is a very interesting index to use for judging the

qual-ity of the part because it measures the frozen

orienta-tion The allowable amount depends on the type of material

The frozen skin is very important for parts with very thin wall thicknesses molded with crystalline ma-terials

This variable may also be important for large parts (such as automobile bumpers) needing very long fill-ing times, and where the heat transfer to the mold can

be higher than the heat dissipation

Isochrone This view shows the evolution of the

filling phase since it is a multicolored picture of the advancing flow front Each color corresponds to a dif-ferent short shot with its time

No-Flow Time No-flow time is the time it takes

for all layers in an element to reach the no-flow tem-perature of the resin (as specified in the material data-base) starting at the end of the filling of the part It gives the first indication of the packing of the part (the theoretical maximum holding time for each element)

Opening Force The opening force is the force

act-ing on the mold that needs to be opposed by the mold-ing machine clampmold-ing force It is generated by the fill-ing pressure actfill-ing on the projected area of the model

It can be determined at various instants during the in-jection time In cases where the pressure for the subse-quent holding phase is higher than the pressure required for filling, the final view must be carefully evaluated

In fact, during the pre-holding phase after the V/P change, particularly if the melt compressibility calcu-lation has been activated, the final pressure distribu-tion might not be equalized in the whole part and give

an underestimation of the clamping force required in the holding phase It is recommended that a holding/ packing analysis be done in all cases where the

clamp-ing force durclamp-ing the holdclamp-ing phase is a critical

require-ment

Orientation Orientation is an indication of the

main flow-stream in each element As with the other

variables (e.g., temperature, stress), it is calculated at

each time-step during the filling phase Orientation is

used for a better understanding of the filling pattern in

order to judge potential causes of warpage The

ex-amination of the orientation’s velocity vectors becomes

very important for materials with anisotropic

shrink-age, like all the glass-reinforced resins

Pressure Distribution The pressure distribution

indicates areas of overpacking, which can cause

dif-ferential shrinkage and consequent warpage

Filling-analysis programs perform the calculation of the

ini-tial holding phase for all flow paths that are filled prior

to the end of filling the entire mold

Note that at 100% of filling, it is common to find

differently packed areas that are assumed to be

identi-cal It happens because of minor differences in the

math-ematics of the calculation due to geometry (for example,

the position of symmetrical nodes not being exactly

symmetrical), and the convergence of field variables

(local temperature, pressure, etc.) These “errors,”

which do not play any significant role in the evolution

of flow but cause minor distortions in the flow front,

seem much more evident in the pressure distribution

just near the completion of the filling phase Since this

situation lasts just for an infinitesimal time, it cannot

be considered as overpacking When in doubt, look at

the view saved just before the completion of flow (for

example, the V/P change point) Actually, this

phe-nomenon of unbalancing near the 100% filling occurs

also in practice, and it is the reason why a safety factor

in clamping force is usually required to avoid flashing

In injection molding, it is always possible that a minor

difference (in this case, of local temperature or cavity

thickness) can cause apparently identical areas to reach

pressurization at slightly different times

Shear Rate This is the gradient of the difference

in velocity between adjacent laminar layers within the

flow channel, divided by the distance between them

The maximum shear rate across the thickness of the

segment is shown See the shear-stress considerations

Shear Stress This is the ratio between the shear

force, which drives the flow, and the area resistant to

flow It is a function of the material viscosity and the

flow rate The stress displayed is the maximum

shear-stress across the thickness of the element at various

instants during filling During cooling, part of the stress

at the end of the filling relaxes, but a residual stress

remains frozen-in and will be one of the causes tending

to distort the part

The shear stress should not go above a specific limit that is a function of the type of plastic Typically,

in the part, it should not exceed 0.3 to 0.7 MPa This value is also a function of the temperature and frozen skin In fact, high stresses can be found either in situa-tions of high velocity and hot material, or low velocity and cool material The latter occurs due to high mate-rial viscosity Because the level of stress, which relates

to part quality, is basically the stress that can be frozen

in the part, it is evident that one can accept much higher values of stress in the first case, since it will have more time to relax thanks to the higher material tempera-ture, than in the second case

Temperature Temperature displays represent the

average temperature of the material across the thick-ness of each element Temperature can be obtained at different time intervals and at the end of filling To obtain high-quality moldings, the temperature differ-ence in all elements describing the part should be in a narrow range It requires that the heat lost by conduc-tion to the cold mold-surface be compensated for by the heat generated by friction The maximum allow-able difference depends on the plastic See Fig 9.11

A temperature rule-of-thumb: at the end of flow, the material should not cool down more than 15° to 20°C when compared with its typical average value Whenever possible, it is desirable to heat the material about 10° to 15°C by friction in the runners In very difficult filling situations, one can even accept heating the material by 10° to 15°C due to friction in the part near the gate

Figure 9.11 Several possible outputs of an analysis

program, including temperature, in a molded part at a particular time [61] (Courtesy of Plastics & Computer.)

9.7 Packing and Holding Simulation

Holding and packing analysis programs extend the

filling analysis calculations through to part ejection The

inputs include the holding pressure (which may be

pro-filed), holding time, and the cooling time The output of

these programs include the distribution of pressure,

frozen skin, shear stress, temperature, density, and

volumetric shrinkage in the part during this phase of the

process Some programs also include estimations of

the risk of sink marks (Fig 9.3) throughout the part

One of the most important graph outputs in this

kind of analysis program is the plot of the entering

mass over time This helps ensure that gate freeze-off

is achieved prior to release of the holding pressure

This is also one of the few variables that is relatively

easy to verify

The hold (or pack) time is the duration of time that

melt pressure is maintained on the melt within the mold

cavity This portion of the cycle typically accounts for

less than 5% of the part weight but is critical in

deter-mining the final part density, part weight, and

there-fore the shrink rate This is especially critical in

semi-crystalline resins that go through a phase change that

results in a relatively significant change in density The

pressure can only be maintained as long as the gates

and runners remain unfrozen If the holding time is too

short, and the gate is still unfrozen, melt may flow back

out of the cavity, causing high shrink rates and more

shrinkage variability Similarly, if the runners have high

levels of frozen skin, the pressure loss in the runners

may limit the ability to pack the part

Holding/packing modules are typically

consider-ably less expensive than the filling analysis modules

They are strictly an add-on module and fundamentally

consist mostly of extending the filling calculations

Differential shrinkage, residual stresses, and residual

thermal stresses contribute to warpage The amount of

distortion is also affected by the overall rigidity or

in-herent mechanical constraints due to part geometry

Shrinkage/warpage modules are extensions to the

filling/packing/holding analysis that predict the final

shape of the part They are in fact a strain analysis,

where the stresses have been determined during the

previous analyses

Shrinkage/warpage modules predict the direction

and magnitude of warpage The program should be

able to predict the linear shrinkage between any two

(or more) points on the molded part and offer a variety

of displays to mimic a wide variety of dimensional evaluation methods such as flatness or deviation from

a defined plane, out-of-round conditions, etc Some in-clude special views to help find a nominal shrinkage rate for tool making

Shrinkage/warpage modules are generally quite ex-pensive and calculation times generally take longer than the calculation times of filling or packing analysis

Cooling analysis modules allow an accurate deter-mination of the effectiveness of the mold-cooling sys-tem at maintaining the desired mold sys-temperature, avoid-ing hot spots, and meetavoid-ing desired cycle time These programs are generally integrated with the filling and packing/holding modules They perform transient dy-namic heat transfer analysis aimed at either determin-ing the required cooldetermin-ing time for selected elements to reach a specified center-line temperature, and/or they predict the temperature distribution at the end of an assigned cooling time See Fig 9.12

These program modules should include the model

of the cavity or a means whereby the cavity and mold may be modeled, and methods for modeling cooling lines, fountains, baffles, or any other cooling configu-ration The program modules should also have options

to include a number of inserts with different heat-trans-fer properties In addition, identification of circuit loops should ideally be part of the calculation setup, which will also include the water temperature and flow rate

Figure 9.12 Cooling analysis, with cooling cross sections

in the upper right corner [61] (Courtesy of Plastics & Computer.)