Qualitative (Flow Pattern) and QuantitativeComputation of the Filling Process of a Mold(Simulation Models)

Producing a flow pattern during part or mold design is beneficial because it makes itpossible to recognize the location of weld lines and air trappings early on, that is beforethe mold i

quality problems for injection-molded parts because, on the one hand, a high fillingpressure causes pronounced orientation in the molded part that in this form - andespecially with filled materials - is often undesirable and troublesome On the otherhand, the maximum attainable flow-path lengths and the minimum part wall thicknessare restricted by this The gates and runners for molds that are intended for processinghighly-filled polymers should therefore, also for these thermodynamic reasons, have alarger cross-section than is usual for thermoplastic molds.

An alternative to large-dimensioned gates, that also serves to counteract freezingeffects, is hot-runner systems These permit much longer, more selective influence to beexerted on the molded-part-formation process in the holding-pressure phase [5.21].Since the formation of a frozen edge layer in the runner is suppressed, pressure lossesare reduced The disadvantage of this is the need for elaborate, thermal insulation of thehot-runner system toward the cavity with the risk of high orientation near the gate, wherethe material remains molten for a long time This problem has been successfullyeliminated in powder injection molding by using combinations of hot runners with short,freezing gates [5.22, 5.23] The effect is that the areas of high orientation are pushed intothe gate area to be later removed and therefore do not have any effect on the quality ofthe molded part

5 9 Q u a l i t a t i v e ( F l o w P a t t e r n ) a n d Q u a n t i t a t i v e

C o m p u t a t i o n o f t h e F i l l i n g P r o c e s s o f a M o l d ( S i m u l a t i o n M o d e l s ) [ 5 2 4 ]

5.9.1 Introduction

It is often necessary to study the filling process of a finished mold in advance, that isduring the conception of mold and molding Examinations of this kind are generallysummarized under the generic expression "rheological design" [5.25, 5.28] and make aqualitative and quantitative analysis of the later flow process possible Qualitativeanalysis here is the composition of a flow pattern, which provides informationconcerning

- effective kind and position of gates,

- ease of filling individual sections,

- location of weld lines,

- location of likely air traps and

- directions of principal orientation

Aids for theoretically composing a flow-pattern are the flow-pattern method [5.27 to5.29] and calculation software for computers capable of graphics [5.29, 5.30]

The second step is the quantitative analysis This is a series of calculations, whichinclude the behavior of the material and assumed processing parameters They determinemold filling data such as

With the help of these calculations the effect of planned design features can be estimated,e-g.

- properties of the molded part,

- strength of weld lines,

- surface quality,

- damage to material,

- selection of material and machine,

- suitable range of processing, etc

5.9.2 T h e Flow P a t t e r n a n d its Significance

A flow pattern pictures the courses of the flow fronts in different areas of the cavity atvarious stages of the mold-filling process The theoretical filling image corresponds withthe production of short shots in a finished mold Figures 5.35 to 5.37 demonstrate acomparison between a theoretical flow pattern and a series of short shots from a practicaltest

Producing a flow pattern during part or mold design is beneficial because it makes itpossible to recognize the location of weld lines and air trappings early on, that is beforethe mold is made

If such problems are recognized, one can examine how the mold filling can beimproved by

- a variation of position, kind and number of gates,

- a variation of the location of holes or different thicknesses of sections, which aredemanded by design,

- introduction of facilities or restraints for the melt flow

The production of a flow pattern is a pre-condition for the use of programs to computepressure and temperature during the filling stage Accurate computation requires amental break down of the molded part or cavity into computable basic segments, whichare established on the basis of the flow pattern.

5.9.3 Using t h e F l o w P a t t e r n for P r e p a r i n g a S i m u l a t i o n

of t h e Filling P r o c e s s

For producing a flow pattern one starts with a plane presentation of the part or itsdevelopment onto a plane

In essence, three geometrical operations are necessary for such a development:

- cutting open a surface along an edge,

- turning a face around a fixed axis,

- stretching a curved surface (flatten it onto the plane of the paper)

The following considerations and simplifications result in developments, which favorthe later production of a flow pattern:

- If possible, the actual part should be divided into subsections, which can be developed

in a simple way (making the cut along an existing edge) The correlation in the

Figure 5.37 Flow

pattern of a box-shaped molding [5.24]

Knit line Wall thickness

Figure 5.36 Series of short shots illustrating filling of box mold [5.24]

developed presentation is then done by identifying the common connecting lines(cutting edges) or points (Figure 5.38).

- That face is the starting surface, on which the gate(s) is (are) placed or on which thelongest flow paths can be expected

- Areas, which cannot be directly included in the development of connected part sections(e.g ribs), are folded separately onto the paper plane

- Connection points of areas (ribs), which are presented in subdevelopments, have to beclearly identified (Figure 5.38)

- Another way of developing complex parts begins with a paper model, which is sequently cut open

sub Conversely, a flow pattern can give a clear idea by cutting out the individual sectionsand joining the parts

Figure 5.38 Examples for development on a plane [5.24]

(p Factor for real molds,

For molds with W » H -^ <p = 1.5,

vF Velocity of advancing flow front,

L Length of flow path,

W Width of segment,

H Height of a segment,

q Viscosity of fluid

Since only the flow front is considered, it is permissible to assume that

a) all factors everywhere along the flow front are equal This is the case as long as thewhole range has the shape of a plate with uniform thickness;

b) the pressure is uniform, which automatically follows for the flow front;

c) the viscosity along the flow front is the same This is the case as long as the melt alongthe flow front is of equal temperature and no larger differences in height exist, whichwould change the intrinsic viscosity, that is H1 / H2 < 5

Always equally wide segments of the flow front are considered, that is W1 = W2 Thus,for two points of the flow front with different thickness H follows

The advance of the flow front in equal time intervals corresponds with the ratio ofthicknesses at the points considered.

Present experience demonstrates a very good agreement between flow pattern andpractical results as long as one can assume that the flow front is uniformly supplied withmelt This holds true in all cases even for very different materials from very fluidreactive polyurethanes or caprolactams to elastomers and filled thermosets If,however, narrow cross-sections, such as a living hinge, restrict the filling, then adeviation from the location of weld lines in the following area can be noticed This,however, has never really interfered with the qualitative prediction of the location ofweld lines If this method, however, should serve to compute pressure and temperature

in a simulation program (CADMOULD or MOLDFLOW) then the result has aconsiderable error in such cases

5.9.5 Practical P r o c e d u r e for Graphically P r o d u c i n g

a Flow P a t t e r n

5.9.5.1 Drawing the Flow Fronts

The model on which the method of the flow pattern is based, relies on the theory of wavepropagation according to Huygens It implies that every point of an "old" wave front(flow front) can be considered the starting point (center) of a so-called elementarywavelet (circular wave) The envelope of the new elementary wavelets is the new (next)wave front (flow front) The "new" flow front is the envelope of the new elementarywavelets, which expand in circular form from every point of the last flow front Theradius of every elementary wavelet is equal to the advance of the flow front Al (Figures5.39 and 5.40)

5.9.5.2 Radius Vectors for the Presentation of Shadow Regions

Areas of a part which are located in the "shadow" of openings cannot be directly reached

by parallel or swelling flow from the gate They are filled beginning from a flow front(Figure 5.41)

Vectors starting at the gate indicate these regions and offer points of support forproducing the flow front (Figure 5.42)

The points P, where the vectors are tangent to the opening, are, as points of an "old"flow front, the origins of new elementary wavelets They start the filling of the shadowregions (Figure 5.43 to 5.45)

With complex shapes of openings or barriers to flow it may be necessary to introducemore vectors during the process to completely cover the flow around them (Figure 5.46)

(5.4)

New flow front

Old flow front

Elementary wavelets New flow frontNew flow front

Old flow front

Figure 5.39 Methodology of designing a flow pattern [5.24]

Swelling flow Parallel flow

Figure 5.40 Application with pinpoint gate

(left) and edge gate (right) [5.24]

Areas not directly accessible

Edge gate Pinpoint gate

Figure 5.42 Vectors outline areas which

are not directly accessible [5.24]

Figure 5.41 Design of a flow front with

elementary wavelets behind an opening [5.24]

Opening

Figure 5.43 Design of a flow

front behind flow barriers [5.24] right: Edge gate,

left: Pinpoint gate

Figure 5.44 Design of flow

front behind a rectangular opening [5.24]

right: Edge gate,

left: Pinpoint gate

+ gate

weld line

Figure 5.45 Design of flow

front behind circular opening [5.24]

right: Edge gate,

left: Pinpoint gate

5.9.5.3 Areas with Differences in Thickness

A special benefit of the flow pattern method is the correct determination of the fillingprocess even if there are differences in thickness (height) For a one-time step there isthe relation

Al

— = const (5.5)H

This means that the ratio of advancement of the flow front Al and its height H is the same

in different regions of the cavity during the same time intervals At

This relation becomes evident with center-gated plates, one with constant thickness,the other one with twice the thickness in one half (Figure 5.47)

The tangential design as an aid for producing a flow pattern is used if a continuousflow front is drawn in adjacent areas with different section thickness The flow from aregion with a thicker section into one with a thinner one is approximated by linearinterpolation between known points of the "new" front This method is an approximation

of the central design, which will be discussed later

Figure 5.47 Flow front with

varying wall thickness [5.24]

Figure 5.46 Design of flow front with several vectors

[5.24] (pinpoint gate)Vector 1

Vector 2

Various steps of this method:

1 The last flow front just touches the border of the region with a thicker section (II) atthe point P (Figure 5.48)

2 First the continuation Al1 in the old region is drawn This results in the known points

A and B of the new front, at the border of the region II Starting at the point P of theold flow front the circle of an elementary wavelet is outlined in the region II Theradius results from the rule Aln = Al1 Hn/Hj (Figure 5.49)

Figure 5.48 Tangential design,

4 This generates the complete sequel of the new front (Figure 5.51)

Figure 5.50 Tangential design, step

Area Il Area I

Figure 5.52 Tangential design, H > H [5.24]

The central design, another aid to produce a flow pattern, is a refinement of thetangential design.

Instead of a linear interpolation between known points, an interpolation of a circulararc is carried out It should be primarily applied for

- large step sizes, or

- large differences in section thickness between adjacent regions

Various steps of this method:

1 The last flow front just touches the border of a region with a different section ness in the point P (Figure 5.53)

thick-2 The new front is drawn with the advance Al1, in the old region This results in knownpoints A and B of the new flow front in the region II Starting with point P of the oldfront the advance Aln is outlined in region II It results from the rule Aln = Al1 • HnZH1.Thus another point C of the new flow front has been determined (Figure 5.54)

3 There are now three points of the new flow front A, B and C The points A and C aswell as B and C are connected by a straight line and their median verticals erected.Their intersection is the center M (Figure 5.55)

4 A circular arc through the points A, B and C represents the new flow front in theregion II (Figure 5.56)

As a comparison the flow front according to the tangential design for the same example

is shown (Figure 5.57)

Some more examples for both methods are presented in Figures 5.58 to 5.60 Acombination of tangential and central design is also possible (Figure 5.61) The centraldesign pictures the flow into region I and II and the tangential design the overflow from

I to II (Figure 5.62)

Figure 5.53 Central design, step 1 [5.24] Figure 5.54 Central design, step 2[5.24]

Figure 5.55 Central design, step 3 [5.24] Figure 5.56 Central design, step 4

[5.24]

Area Il

Area I

Here, tangential and central design can also be combined (Figure 5.63) The first onepictures the overflow from region II to I and the second one the flow into regions I andII.

5.9.5.4 Flow Patterns of Ribs

First, ribs are looked at which are thinner than the base (Figure 5.64) They are filledfrom the base and do not affect the flow pattern of the main body

In Figure 5.64 venting should be provided in the corner C; the rib should not bemachined as a closed pocket

Figure 5.60 Determination of flow

pattern with tangential design [5.24]

Figure 5.61

Determination of flow pattern with tangential and central design [5.24]

•Weld line Direction of flow

Figure 5.58 Determination of flow

pattern with central design [5.24]

Figure 5.59 Determination of flow

pattern with tangential design [5.24]

Figure 5.57 Flow front based on

tangential design [5.24]

Another example is shown with Figure 5.65 Here provisions should be made for venting

at the points A and B

The filling of ribs which are thicker than the base is demonstrated with Figure 5.66.The advancement of melt in a thick rib affects the flow pattern of the base area Ventingshould be provided in the corner C and at the ends of both weld lines

5.9.5.5 Flow Pattern of Box-Shaped Moldings

In the development, connecting lines (cutting lines) of continuous regions are presented

as curves, in special cases as straight lines For the determination of a filling image theadvances of the flow have to be picked off from one connecting line and transferred tothe proper "opposite" connecting line to correctly determine an advance of flow or anoverflow (Figure 5.67)

5.9.5.6 Analysis of Critical Areas

Knit lines are created by several merging melt flows They occur, in any case, behindopenings

In a flow pattern, points of a knit line are recognized as "breaks" in the course of theflow front Then the knit line results from a connecting line of these points

Figure 5.64 Rib thinner than base [5.24]

Central design

Tangential design

Figure 5.62 Determination of flow

pattern with tangential design [5.24]

Figure 5.63

Determination of flow pattern with tangential and central design [5.24]

Weld line Direction of flow Area I

Area Il

Figure 5.65 Ribs thinner than base

Figure 5.67 Junction in a box-shaped molding [5.24]

The smaller the angle of two merging flow fronts becomes, the more pronounced the knitline (and the reduction in quality) is (Figure 5.68)

Weld lines close to the gate are less critical than those far from it because they arecreated at relatively high temperatures and are possibly passed through by followingmelt Weld lines far from the gate may present weak points because of cool melt and poorwelding

Air trapping occurs if flow fronts merge and the air cannot escape through a partingline or any other way (Figure 5.69) Besides incomplete filling, burned spots may be theconsequence

The faces at the parting lines should be carefully ground (grain size 240, but notfiner)

Figure 5.68 Weld lines [5.24]

left: Pronounced right: Insignificant

Figure 5.69 Air trapping

[5.24]

left: Crucial right: Not crucial Parting line

If the air cannot escape through an existing parting line, the problem can be redressedby:

- use of an additional parting line,

- relocation of ejector pins into areas of air trapping (air escapes through holes),

- The design with elementary wavelets is well suited for the continuation of a flow front

in regions of equal section thickness It is always applicable and should be employed

if difficulties arise with a different design

- The central design is suggested if a region of different section thickness has to be

filled It is more accurate than the tangential design but also more work

- The tangential design should be used if an overflow from a heavier section into a

region with a thinner section perpendicular to the direction of flow takes place.Although the central design can be employed here, too, it takes much more time, inparticular if for every flow front a new center has to be found

- The maximum "step width" should be selected so long that a "problem point" is just

reached

Problem points are

- reaching of a region of different thickness,

- filling of a "shadow area" (radius vector),

- overflow from a region with heavier into one with thinner section (perpendicular to thedirection of flow in the heavier section),

- merging of flow fronts (weld lines, air trapping)

5.9.6 Quantitative Analysis of Filling

A quantitative analysis is based on the concepts of fluid dynamics (rheology) andthermodynamics It has to solve the fundamental equations for continuity, momentum,and energy This is a matter of an interactive system of differential equations(Figure 5.70) For such a complex geometry as the cavity of an injection mold, no exactsolution can be found, of course, so that some method of approximation has to be used.There are two possibilities:

a) The geometry is subdivided by a set of a finite number of nodal points equally spaced

by small time intervals Each point represents a finite difference approximation Withthe resulting set of difference equations a final solution can be found [5.26, 5.27].b) The geometry is divided into subregions called finite elements An approximationwith small time intervals is defined within each element according to knownprocedures and appropriate continuity conditions imposed on the inter-elementboundaries (Figure 5.71) [5.9]

Figure 5.70 Computation of the flow process (basic equations) [5.26, 5.27]

Both methods call for the application of computers, which will be treated in detail inChapter 14 They are suitable for other material melts or reactive liquids (RIM) as well

5.9.7 Analytical D e s i g n of R u n n e r s a n d G a t e s

5.9,7,1 Rheological Principles [5.32]

A general flow is completely described by the conservation laws of mass, momentumand energy and by a rheological and thermodynamic equation of state The rheologicalequation of state, also called the law of materials, describes the relation between the flowrate field and the resultant stress field This accounts for all the flow properties of thepolymer concerned The describing, explaining and measuring of the flow properties ofmaterials is a key subject of the science of deformation and flow of matter, known as

rheology [5.33] The principles of rheology will be introduced in this chapter in as far as

they are necessary for the design of gates and runners from an engineer's point of view.Polymer melts do not exhibit purely viscous behavior, but possess a not inconsiderableamount of elasticity Their properties, therefore, lie between those of an ideal fluid and

an ideal (Hookean) solid They are said to exhibit viscoelastic behavior or

visco-Generating flow Established flow

Figure 5.71 Computation of the flow process (definitive equations) [5.26, 5.27]

elasticity It is therefore common to distinguish between material data pertaining to

purely viscous behavior and material data pertaining to elastic behavior when describingrheology

Viscous Melt Properties

In the flow processes of the kind that occur in injection molds, the melt is mainlysheared This so-called shear flow is due to adhesion of the polymer melts to the surfaces

of the mold halves shaping them (Stokes' adhesion) The result is a change in flow rateacross the channel cross-section that is described by the shear rate:

v Flow rate,

y Direction of shear

Under stationary shear flow, shear stress T occurs between the fluid layers In the

simplest case of a Newtonian fluid, the shear stress T is proportional to the shear rate 7,

yielding:

T = T] • 7 (5-7)

The proportionality factor is called the dynamic shear viscosity or simply viscosity.

It has the unit Pa s The viscosity is a measure of the internal flow resistance of asheared fluid

In general, polymer melts do not exhibit Newtonian behavior Their viscosity is notconstant but instead depends on the shear rate By analogy with the equation forNewtonian fluids, Equation (5.7), the flow law is as follows:

in the following discussion

Viscosity and Flow Function

A double logarithmic plot of viscosity as a function of shear rate (at constant ture) for polymers has the basic shape shown in Figure 5.72 It can be seen that theviscosity remains constant at low shear rates but declines as the shear rate increases.Behavior of the kind that the viscosity decreases with the shear rate is termed

tempera-structural viscosity or pseudoplasticity The constant viscosity for low shear rates is

called the Newtonian viscosity, lower Newtonian intrinsic viscosity or when 7 = 0 as

zero viscosity 0.

Not only can the viscosity be plotted as a function of the shear rate to yield a viscosity curve, but the shear stress can be plotted against the shear rate (also on a double logarithmic scale) to yield a flow curve (Figure 5.73).

In a Newtonian fluid, the shear rate is proportional to the shear stress A doublelogarithmic plot of the pairs of values yields a straight line with a slope of 1, i.e., theangle between the abscissa and the flow curve is 45° Any deviation by the flow curvefrom this slope is therefore a direct indicator of non-Newtonian flow behavior

A pseudoplastic fluid would have a slope greater than 1 on this plot, i.e., the shear rateincreases progressively with increase in shear stress

Mathematical Description of Pseudoplastic Melt Behavior

Various mathematical models have been developed to describe the viscosity and flowcurves; they differ in the amount of mathematics involved on the one hand and in theiradaptability to concrete experimental data and thus accuracy on the other Overviews areprovided in [5.33, 5.36] The models most commonly employed for thermoplastics andelastomers are briefly discussed below In the following chapters, reference will be madeexclusively to the models described here

Power Law ofOstwald and de Waele [5.37, 5.38]

When the flow curves of different polymers are plotted on a double logarithmic scale,the resultant curves have two approximately linear ranges separated by a transition range(Figure 5.74) In many cases, we are often only dealing with one of the two ranges and

so we only need one function, namely

non-Figure 5.73 Shear rate as a function of shear

stress in the form of a flow curve Shear stress log x