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

Previous Page quality problems for injection-molded parts because, on the one hand, a high filling pressure causes pronounced orientation in the molded part that in this form - and especially with filled materials - is often undesirable and troublesome On the other hand, the maximum attainable flow-path lengths and the minimum part wall thickness are restricted by this The gates and runners for molds that are intended for processing highly-filled polymers should therefore, also for these thermodynamic reasons, have a larger cross-section than is usual for thermoplastic molds An alternative to large-dimensioned gates, that also serves to counteract freezing effects, is hot-runner systems These permit much longer, more selective influence to be exerted 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 losses are reduced The disadvantage of this is the need for elaborate, thermal insulation of the hot-runner system toward the cavity with the risk of high orientation near the gate, where the material remains molten for a long time This problem has been successfully eliminated 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 into the gate area to be later removed and therefore not have any effect on the quality of the molded part 5.9 Qualitative (Flow Pattern) and Quantitative C o m p u t a t i o n of t h e Filling P r o c e s s of a M o l d ( S i m u l a t i o n M o d e l s ) [5.24] 5.9.1 Introduction It is often necessary to study the filling process of a finished mold in advance, that is during the conception of mold and molding Examinations of this kind are generally summarized under the generic expression "rheological design" [5.25, 5.28] and make a qualitative and quantitative analysis of the later flow process possible Qualitative analysis here is the composition of a flow pattern, which provides information concerning - 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 to 5.29] 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, which include the behavior of the material and assumed processing parameters They determine mold filling data such as - pressures, temperatures, shear rate, shear stresses, etc 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 at various stages of the mold-filling process The theoretical filling image corresponds with the production of short shots in a finished mold Figures 5.35 to 5.37 demonstrate a comparison between a theoretical flow pattern and a series of short shots from a practical test Producing a flow pattern during part or mold design is beneficial because it makes it possible to recognize the location of weld lines and air trappings early on, that is before the mold is made If such problems are recognized, one can examine how the mold filling can be improved by - a variation of position, kind and number of gates, - a variation of the location of holes or different thicknesses of sections, which are demanded by design, - introduction of facilities or restraints for the melt flow Trapped air Change in wall thickness Before Figure 5.35 After Comparison of theoretical flow pattern and injection trial Figure 5.36 Series of short shots illustrating filling of box mold [5.24] Wall thickness Knit line Figure 5.37 Flow pattern of a box-shaped molding [5.24] The production of a flow pattern is a pre-condition for the use of programs to compute pressure and temperature during the filling stage Accurate computation requires a mental break down of the molded part or cavity into computable basic segments, which are established on the basis of the flow pattern 5.9.3 Using t h e Flow P a t t e r n for Preparing a Simulation of t h e Filling Process For producing a flow pattern one starts with a plane presentation of the part or its development 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 favor the 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 - 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 the longest 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 be clearly identified (Figure 5.38) Another way of developing complex parts begins with a paper model, which is subsequently cut open Conversely, a flow pattern can give a clear idea by cutting out the individual sections and joining the parts Figure 5.38 Examples for development on a plane [5.24] 5.9.4 Theoretical Basis for Producing a Flow P a t t e r n According to Hagen-Poiseuille the pressure demand to counter the resistance to flow in plate-like channels (W > H) is [5.31]: (5.1) Wherein Ap Pressure consumption, (p Factor for real molds, For molds with W » H -^ H1 [5.24] Step 5.9.7.3 Elongational Viscosity Aside from undergoing shear, the material is also subject to elongation, particularly where extreme cross-sectional changes occur, such as between the runner and the gate Like the behavior of viscous materials under shear, viscous elongational flow can be described mathematically with the aid of a viscosity function The pressure losses that arise due to elongation are generally determined separately from those due to shear and are then superposed on these to form an overall pressure loss [5.46, 5.47] Models for calculating the volumetric flow rate-pressure characteristic at changes in cross-section in flow channels have been developed by [5.48] Formulas for calculating the additional pressure loss due to elongation in transfer molds are presented in [5.49] for the following mold areas: pressure losses in the transfer chamber and in the transition area from the transfer chamber to the gate nozzles, pressure losses in the conical nozzles and in the gates The elongational viscosity is described by a power law and the relation between the elongational and shear viscosity for biaxial loading of the compound at low elongation rates is given by TID = % (5.20) The derived relations for the various mold areas are discussed in detail in [5.50, 5.51] In [5.52] they are also used for designing elastomer injection molds with cold-runner systems To determine the elongational viscosity function is very time-consuming, a fact that explains why this material property has not yet been taken into account when injection molds are being designed 5.9.7.4 Simple Equations for Calculating Loss of Pressure in Gates and Runners Tables 5.1 and 5.2 list the equations for calculating the pressure drop as a function of length as well as the shear rates for various geometries of the intended runner and gate, both for Newtonian and pseudoplastic material behavior These relations are based on the following suppositions: - isothermal flow (all flowing mass particles at the same temperature), stationary flow (no temporal change in flow profile), laminar flow (Re < 2100), incompressible liquid (constant density), no allowance for flow-in and flow-out effects, wall adhesion By way of example, let us assume that the simple hot-runner system shown in Figure 5.80 has to be designed The gate diameter DG2 of part is to be adapted such that the two parts are filled under the same conditions (simultaneous entry by the melt into the mold halves; end of flow paths reached simultaneously) The material to be used is characterized by the following data: Power law: consistency factor: k = 1.14 • 104 kg/(ms2~n); flow exponent: n = 0.6 (5.21) Table 5.1 Pressure drop Ap/L [5.34] Newtonian (Approximation!) Intrinsic viscosity Intrinsic viscosity, repres quantities (Approximation!) (r| not defined with general validity) Table 5.2 Shear rates Shear rate or the mold wall7 w [5.32] Newtonian Geometry Non-Newtonian Circular (tube) Annular aperture Rectangular aperture Conical aperture Irregular cross-section (Approximation) Hot runner Molded part Figure 5.80 Molded part Simple hot runner system Dimensions of the hot-runner system: Hot runner as far as molded part 2: LHR2 = 50 mm; DHR = 10 mm; L 02 = mm; D 02 = ? Hot runner as far as molded part 1: LHR1 = 120 mm; DHR =10 mm; L01 = 5mm; D 01 = mm For simultaneous filling of the parts, the pressure on both flow paths must be equal: (5.22) For the various viscosities, the following applies: (5.23) Given the representative shear rate: (5.24) equation 5.22 becomes: (5.25) This is substituted into equation (5.21) to solve for DG2 When the numerical values have been inserted, DG2 computes to 2.61 mm This is a plausible result since the much greater resistance generated in this gate, which has a smaller diameter than gate 1, compensates the shorter flow path to molded part 5.10 Special Phenomena Associated with Multiple Gating To discover particular phenomena of materials, a mold was developed [5.52] based on the theoretical considerations above that would demonstrate dependency on an operating level The runner system shown in Figure 5.81 was chosen It has equal flow paths and equal gate cross-sections that would guarantee simultaneous onset of filling and a uniform filling pattern Trials on various materials (HDPE, LDPE, POM) confirmed the assumptions again Very different pictures of the filling process were obtained with PA and even more so with glass-reinforced nylon 12 A difference in the onset of filling could not be noticed but the throughput through the outside gates was considerably larger than through the inside gates (Figure 5.81) This phenomenon was more pronounced at lower material temperatures (< 250 C) and at high injection speeds However, at high material temperatures (approx 300 0C) and extremely low injection speeds, no advancing in the sense just described was noticeable This effect is best illustrated by a change of colors during molding to observe the origin of the melt in the individual cavities It can be clearly seen, as the low Reynolds numbers (Re < 20) would suggest, that completely laminar flow is maintained even in the gate This means that, above all, a flow path close to the wall remains there At the point of branching, the core material penetrates against the opposite wall and lingers there afterwards (Figure 5.82) [5.53] Figure 5.81 Runner system [5.25] The reason for the advancing of melt could therefore be due to the dependency of melt viscosity on shearing time in the various zones Those portions of melt which are close to the runner wall during the filling process (melt for the outside cavities) have experienced a larger shearing time integral than the melt which fills the inside cavities This is confirmed by the simultaneous onset of filling already mentioned because the gate-filling phase differs from the mold-filling phase A considerable part of the melt which is sheared in the runner during gate filling remains in the runner to fill the gate next to the runner wall As a result, the design of a runner system demands that: - The flow of melt must be divided up symmetrically (Figure 5.82) - Two branches must not be placed in the same plane From this example (glass-reinforced nylon 12), it is evident that the initially derived methods of estimation are sufficient if the consequences of the flow path study are taken into consideration Figure 5.82 Melt distribution in a runner system [5.25] It is, however, more practical today to employ one of the commercial simulation programs (CADMOULD, MOLDFLOW, C-MOLD, etc.) to balance a runner system This subject is treated in Chapter 14 5.11 D e s i g n of G a t e s a n d for Crosslinking 5.11.1 Runners Compounds Elastomers 5.11.1.1 Calculation of Filling Process The design of gates and runners, as in thermoplastics processing, is performed under rheological and thermal aspects In addition, however, allowance must be made for the reaction kinetics of the material as a function of prevailing temperatures Rheological mold design has long been based on simulation programs such as CADMOULD [5.54], RUBBERSOFT [5.55] and FILCALC [5.56] The flow behavior is described by the Carreau or power laws (see also Chapter 14) To guarantee dependable mold filling, scorching must not occur during the injection phase The injection time available to the processor for filling the mold and during which scorching has not occurred is called the incubation time It is material and temperature dependent The occurrence of scorching is described mathematically by the scorch index This is the ratio of elapsed (injection) time and incubation time and can assume values from "O" to " " As soon as the value " " is attained, the incubation period has elapsed and actual crosslinking begins Consequently, scorch indices below " " are required for dependable mold filling Figure 5.83 shows the scorch index distribution for Figure 5.83 Scorch index distribution at the end of the filling phase a 3-cavity mold for a medium-voltage bushing at the end of the filling phase Scorching can therefore be expected during the injection phase for the chosen parameter setting It is suggested in [5.57] that so-called processing windows be established for frequently used materials These windows are based on tests performed on plate molds and results from rheometers and plastometers With this, scorch is also registered, which plays an important part in the case of elastomers However, creating them involves a relatively high input The following section explains how different materials and mold geometries influence processing window qualitatively After this, several calculated processing windows are discussed 5.11.1.2 Effect of Processing Characteristics on the Basis of Processing Windows The processing properties of an elastomer may be characterized by its - viscosity, - incubation time (t{ time) and - curing velocity (difference between t90 and t{) Of greatest interest during processing is the question of how different material types or different lots in the process behave and how potential processing problems can be eliminated These questions can be discussed with the aid of a processing window Figure 5.84 demonstrates how the position of the - injection-time line, injection limit, holding-time line, and heating-time line vary according to material (or lot) Higher viscosity causes higher pressure losses in the mold Higher pressure losses lead to very different effects [5.58] depending on the injection-speed control of the injectionmolding machine With a closed-loop control, the injection speed is decreased continuously With an open-loop control, in contrast, the speed is decreased more or less irregularly How low the speed may become depends on the dimension of the hydraulic drive If the machine reaches its pressure limit (maximum injection pressure) an injection speed results which corresponds with the equilibrium between injection pressure and pressure loss [5.58] Therefore higher pressure losses (due to a higher viscosity) have a very different effect If there is still an adequate pressure reserve, the injection time remains constant (closedloop control) or becomes a little longer (open-loop control) At this time, however, the injection pressure rises This means another, higher injection pressure counts for the injection-time line Because of the higher pressure loss, more energy is dissipated during injection and the temperature of the material increases The curing process proceeds more rapidly and the incubation phase is shortened This shifts the injection limit to smaller time periods (Figure 5.84, effect a) Consequently, increasing viscosity narrows the possible filling-time range (distance between injection-time line and injection limit) If the machine is operated at its pressure limit, the injection time is increased by a material with higher viscosity This means that the injection-time line is shifted to the Mold temperature Tw Viscosityn t(a,b,c) Incubation period tf ^(d) Reaction period t9Oj(e) Injection time Injection limit Holding pressure timfi Heating time Processing time Figure 5.84 Effect of material properties in a processing window (qualitative response) a-e effect (see text) [5.53] right (Figure 5.84, effect b, arrow in parentheses) Then the injection-time line always represents the maximum injection pressure of the machine Although the same amount of energy is dissipated during injection (equal pressure loss), filling lasts longer and the material is heated up, therefore, by thermal conduction The higher melt temperature may again result in shorter incubation time and a narrowing of the possible filling range The effects described here also cause the holding-pressure and heating phases to start with higher material temperatures, of course The higher melt temperature at the onset of the holding-pressure phase has almost no effect in the gate area The material rapidly attains the mold temperature in the (usually) small cross-section of the gate anyway and, with this, the maximum curing velocity possible The holding-pressure time (distance between injection line and holding-pressure time) is hardly shortened at all as a result In heavy sections, however, the higher material temperature (at the end of the injection process) shortens the curing time, that is, the distance between the injection-time and heating-time lines (Figure 5.84, effect c) The decisive factors for this are faster equalization of temperature and, therefore, higher curing velocity In contrast, a shorter incubation time only shifts the injection limit to the left (Figure 5.84, effect d) Storage of a material mixture increases the viscosity and shortens the incubation period at the same time These two effects reinforce each other and reduce the maximum filling time Higher vulcanization rates of a material shorten only the holding-pressure and heating time (Figure 5.84, effect e) The corresponding lines also move to the left However, the processes that occur in the injection phase are not affected Certain processing problems can often be attributed to different causes or resolved by different measures A processing window can help to choose the most effective measure 5.11.1.3 Criticism and Examples Concerning the Processing-Window Model The calculation of a processing window does not consider the feeding process, although it can affect the course of the process if the conditions are unfavorable Such conditions are - a feeding time longer than the heating time, and - attaining high material temperature during feeding In the first case, the processing time or the cycle, respectively, is increased and the calculated window pictures a processing time that is too short In the case of extreme feeding conditions, the material temperature can become so high that part of the incubation phase is already used up before injection The assumption for the calculation of the processing window that injection starts with a scorch index of zero becomes erroneous From processing windows, as shown in Figure 5.85 for two molds and two different gates, one can pick up the changes of processing conditions and obtain help in designing molds and, above all, gates The complete processing window for molds C and D is presented in Figure 5.85 For the two graphs, top and center, holding-pressure and heating times are calculated from the 50 MPa-injection-time line One can recognize that the flat runner shifts the heating-time line slightly towards shorter time periods With an injection limit for a scorch index of 10%, mold D allows a maximum mold temperature of only 164 C This results in a significantly increased minimum processing time for mold D compared to C The latter allows a mold temperature of 200 C because of the longer distance between injection-time line and injection limit Thus the processing time in mold C can be reduced to almost half of that of mold D (78 s against 138 s) Only a higher injection pressure of 70 MPa increases the distance from the injection-time line to the injection limit in mold D to the extent that a temperature of 200 C is also possible (Figure 5.85, bottom) With this step, minimum processing time can be reduced to 68 s Figure 5.86 demonstrates the effect of different heights of the runner hr during the injection phase (mold A: hr = mm; mold B: hr = mm) The cavity depth is mm in both molds With equal injection pressure, the injection line shifts to double the time because of the increased pressure loss in the runner of mold B The position of the injection limit remains about the same in both molds Figure 5.87 compares the effect of different cavity depths h c during the injection phase (mold A: h c = mm; mold C: h c = 12 mm) The height of the runner hr is the same in both molds (hr = mm) MoIdC Initial material temperature °c Mold temperature Tw MoIdD °c MoIdD C Figure 5.85 Processing window for two runner heights hr Test molds C and D, plot of injection time L1, of injection limit LL (S1 = 10%), of holding pressure L N , (Xr = 30%) and of heating time LH (Xc = 80%); material: NBR [5.53] Processing time MoIdA Initial material temperature °c MoIdB 'C Figure 5.86 Processing window for two runner heights hr Test molds A and B, plot of injection time Lj for two injection pressures P1 and of injection limit LL for different scorch indices S1; material: NBR [5.53] Processing time t, Initial material temperature Mold temperature Tw C C Injection time tj Figure 5.87 Processing window for two cavity heights h c Test molds A and C, plot of injection time L1 for different injection pressures P1 and of injection limit LL for different scorch indices S1; material: NBR [5.53] 5,11.2 T h e r m o s e t s 5.11.2,1 Flow-Curing Behavior of Thermosets Calculating the pressure loss in the case of thermosets is difficult One reason for this is additional flow effects in the form of elongational flow losses and uncompacted flow front areas Another reason is, it is difficult to determine the viscosity function since the high filler content and the rapid crosslinking reaction make it almost impossible to conduct a measurement with the aid of a high-pressure capillary viscometer In practice, therefore, generally simple test procedures are used for characterizing the material For example, test specimens are compression molded with constant molding compound weight under defined molding pressure (rods, slabs, tumblers, etc.) The resultant thickness or length of the test specimen then acts as a measure of the complex flow behavior However, a low-viscosity but highly-reactive compound may lead to the same results as a high-pressure, less-reactive compound A separate description of the flow or curing behavior is possible however, in principle by recording different curves of flow resistance over time (e.g Brabender Plastograph or Kanavec viscometer) Admittedly, the demands on the material in these tests are not in the same order of magnitude as in injection molding, so it is difficult to translate the data obtained A method for estimating pressure losses is presented in [5.59] Starting from a mechanical analogy, formulas are developed for calculating pressure losses in straight channels, at cross-section transition and in turnarounds To be sure, the use of a trial mold to determine the material constants contained in the formulas is relatively laborious, but it pays off if the molding compound rarely changes The following formula is to be used for calculating the pressure loss: (5.26) Where R is the resistance to flow, specific to the material, vF is the medium flow velocity of cross-section, C is the circumference of the flow channel, L is the length of the flow channel, A is the cross-sectional area of the flow channel The experiments are now conducted with molds and the results recorded as shown in Figure 5.88 The evaluation of the test results with the help of Equation (5.25) can be presented in a double-logarithmic system of coordinates (Figure 5.88) R (5.27) Figure 5.88 Flow resistance in a phenolic resin [5.59] vF There is a clear connection with the resistance to flow R An effect of the channel geometry cannot be seen anymore It is completely included in the geometry coefficient CL/A The function R is a function of the velocity and invariant with respect to geometry According to these preconditions a computation of arbitrary channel geometries is possible The mathematical relations for different geometric shapes are summarized in Table 5.3 More detailed information is to be found in [5.26, 5.59-5.63] Table 5.3 Pressure calculation Geometry Straight channels Pressure drop Characteristics = m/s = tan a, Slope of the curves in the double-logarithmic plot R = f(vF) = f(V ) Elbows = rK/B, Geometry function =1 = tan p, Slope of the curves in the double-logarithmic plot RE = f W = fWo) Cross-sectional transitions = A1ZA2 -1, Cross-sectional ratio =1 = f(v0,0) = tan 7, Slope of the curves in the double-logarithmic plot ApA0 = f(v) = tan 8, Slope of the curves in the double-logarithmic plot References [5.1] [5.2] [5.3] Pye, R.G.E.: Injection Mould Design (for Thermoplastics) Ilitte Books Ltd., London, 1968 Szibalski, M.; Meier, E.: Entwicklung 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