Numerical Computation for Thermal Designof Molded Parts

With progressing solidification more melt solidifies on the outside No parting line influence Temperature [0C] Parting line influence Temperature [0C] Melt temperature TM - 220 0CCoolant

The average temperature difference should not exceed a maximum of 3 to 5 0C to ensure

a uniform heat exchange over the whole length of the cooling line A required minimumflow rate V can be calculated from the permissible maximum temperature difference.However, the rate also depends on the arrangement of the cooling elements With anarrangement in series the permissible temperature difference applies to the sum of heatfluxes from all segments; with parallel arrangement it applies to each segment Parallelarrangement results in a lower flow rate and smaller pressure drop However, parallelarrangement calls for an adjustment of flow rates with throttles [8.1] and a constantmonitoring during production; for this reason it is not recommended

8.5.1.6.2 Pressure Drop

The flow through the heat-exchange system causes pressure drops, which are anadditional criterion for a controlled design of heat-exchange systems and a boundarycondition for the heat exchanger

If the pressure drop is higher than the capacity of the heat exchanger, then thenecessary flow rate and, with this, the permissible temperature difference betweencoolant entrance and exit, cannot be met The consequences are nonuniform cooling ofthe molding and heterogeneous properties and distortion of the molding For calculatingthe pressure drop, different causes have to be considered:

- pressure drop from the length of the cooling element,

- pressure drop from turnabouts, corners and elbows,

- pressure drop from spiral flow,

- pressure drop from changes in cross-sectional area,

- pressure drop in connectors,

- pressure drop from connecting lines

The total pressure drop is the sum of all items The equations used to compute thepressure drop [8.1, 8.15, 8.40, 8.41, 8.42] are too extensive to be listed here because ofall the effects they include However, with a bit of practical experience, they can readily

be estimated with sufficient accuracy

From the total pressure drop and the heat flux to the coolant one can conclude thecapacity of the heat exchanger:

(8.54)Where

= Pumping efficiency of the heating unit,

Numerical procedures are used for this, so that the Fourier differential equation for heatconduction can be solved without the simplifications presented in Section 8.1.

(8.55)

Differential methods and nowadays preferably finite element programs are used for this.Since there is a great deal of work involved in the compiling the computational net forthe three-dimensional calculation, two-dimensional programs are very widespread Theyusually supply enough information for the designer and so are also presented here

8.6.1 T w o - D i m e n s i o n a l C o m p u t a t i o n

In mold design, it is often necessary to optimize cooling at certain critical points, such

as corners or rib bases There is no need to perform a computation for the whole mold,and anyway, such a computation would unnecessarily extend the processing time It issufficient in this case to analyze the critical area Two-dimensional computation is wellsuited to this

In a two-dimensional computation, a section of the point under consideration is takenthrough the mold When selecting the section, it is important that as little heat as possible

is dissipated vertically to the section plane Because this heat flow is not allowed for, itwould reduce the accuracy and informativeness of the study

The mold section under consideration is then overlaid with a computational net withwhich the numerical computation is performed Various material combinations, startingtemperatures, thermal boundary conditions, and process settings can be taken intoaccount

The results of the computation are the temporal temperature curves in the sectionplane It sometimes makes sense therefore to perform the computation for several cycles

in order to be able to analyze start-up processes and to capture the temperature bution throughout the mold

distri-In this computational method, it is advantageous that the processing time is short andthe net generation is relatively simple For critical part areas, such as corners, rib basesand abrupt changes in wall thickness, results can be obtained relatively quickly

8.6.2 T h r e e - D i m e n s i o n a l C o m p u t a t i o n

If the temperature ranges for the entire mold and the quantities of heat to be dissipatedvia the cooling channels are to be analyzed, there is no getting round a three-dimensionalcomputation To this end, the entire mold along with all cooling channels must besimulated

There are two computational philosophies available for the computation There areprograms that see the mold as being infinitely large In them, the position and the number

of the cooling channels alone decide on the temperature conditions in the mold Heatflow to the environment is ignored [8.43] For the computation, only the molded part andthe cooling channels need to be modeled

If the influence of mold inserts and heat exchange with the environment is to beconsidered, this approach is unsuitable and the entire mold has to be simulated The

outlay on modeling and the processing time increase accordingly However, the resultsare then all the more precise.

The advantages of 3D computation over analytical computations lie [8.43]

- in solving in several directions, even for complex geometries and heat flow,

- in more accurate simulation of the cooling conditions,

- in intelligible results (color plots),

- in rapid "playing through" of variants (processing conditions, cooling channel ments),

arrange in good coupling to computation modules for the filling and holding phase as well as

to shrinkage and distortion programs

A further effect that can only be taken into account with a 3D computation is theinfluence of the parting line on the mold wall temperature distribution This will beexplained below with an example At the parting line, heat conduction is much poorerrelative to the bulk material This exerts an effect, particularly in the case of differentlycooled mold halves, on the exchanged heat flux q Figure 8.45 shows the results obtainedwith and without parting line influence It may be clearly seen that the colder, lowermold half without parting line influence is heated in the edge zone At the cavity edgethere is a temperature minimum If the slight insulating effect of the parting line is takeninto account, there will be a temperature maximum taken instead at this point

The computation shows that in critical cases - molds that are operated at hightemperatures - large, non-permissible temperature differences may establish themselves

It is often, therefore, expedient to carry out such computational analyses

8.6.3 S i m p l e E s t i m a t i o n of t h e H e a t F l o w a t Critical Points

Corners of moldings, especially with their differences in surface, areas, have highcooling rates on the outside and a low rate inside the corner (Figure 8.46) Immediatelyafter injection, the melt solidifies on the surface and the temperature maximum is in thecenter of a section With progressing solidification more melt solidifies on the outside

No parting line influence Temperature [0C] Parting line influence Temperature [0C]

Melt temperature TM - 220 0CCoolant temperature Tc * 20 0C Cooling time t( * 90 s

Figure 8.45 Influence of parting line on the mold wall temperature

A material deficit during solidification of the last melt is generated because the shrinkagecannot be compensated by melt supplied by the holding pressure Tensile stresses arecreated accordingly These stresses are counterbalanced by the rigidity of the mold Afterdemolding, the external forces have ceased and the formation of a stress equilibrium inthe part causes warpage or deformation Besides this, voids and sink marks and evenspontaneous cracking may occur Deformation can be eliminated, however, if theremaining melt, and with it the forces of shrinkage, are kept in the plane of symmetry.Then an equilibrium of forces through-out the cross section is generated if the lastmaterial solidifies in the center.

8.6.4 Empirical C o r r e c t i o n for C o o l i n g a C o r n e r

One draws the corner of the part and the planned cooling channels on an enlarged scale.Then the cross section of the corner is divided into rectangles of equal size with one sideequal to half the thickness of the section (s/2); the other one equal to the distancebetween two cooling channels Thus, the area is pictured, which is cooled by one coolingchannel (cooling segment) By comparing areas and adjustment, one hole at the corner

is either eliminated or the holes are shifted in such a way that equal cooling surfaces(ratio of holes to rectangles) are generated (Figure 8.46)

Figure 8.46 Freezing of melt in a corner

[8.1]

The drawing at the top shows that the farthest

square a on the convex side is affected by

two cooling channels d On the concave side

three squares b are affected by only one

cooling channel c Consequently melt close

to the concave side will solidify last

Last melt Cooling channels

than on the inside of the corner because the heat-exchange areas are of different size andmore heat is dissipated on the outside than on the inside Figure 8.46 demonstrates thatthe remaining melt moves from the center towards the inside At the end of the coolingtime, the melt which solidifies last is close to the internal surface

of the mold level out to a constant value (The basic correlations for describing thedynamics are presented in [8.44 to 8.46].)

Because of the already mentioned increase in cycle time, an uncooled core can result

in parts of inferior quality and even fully interrupt a production This becomesparticularly apparent with cores having a square or rectangular cross section Withuncooled cores, sink marks or distorted sides can hardly be avoided Therefore,provisions for cooling of cores should always be made To do so, the following optionsare available dependent on the diameter or width of the core (Figure 8.47)

If diameter or width are minor, only air cooling is feasible most of the time Air isblown from the outside during mold opening or flows through a central hole from theinside This procedure, of course, does not permit maintaining exact mold temperatures(Figure 8.47a)

A better cooling of slender cores is accomplished by using inserts made of materialswith high thermal conductivity, such as copper, beryllium-copper, or high-strengthsintered copper-tungsten materials (Figure 8.47b) Such inserts are press-fitted into thecore and extend with their base, which has a cross section as large as it is feasible, into

a cooling channel

The most effective cooling of slender cores is achieved with bubblers An inlet tubeconveys the coolant into a blind hole in the core The diameters of both have to beadjusted in such a way that the resistance to flow in both cross sections is equal Thecondition for this is ID/OD = 0.5 The smallest realizable tubing so far are hypodermicneedles with an OD of 1.5 mm To guarantee flawless operation in this case, the purity

of the coolant has to meet special demands Bubblers are commercially available and areusually screwed into the core (Figure 8.47d) Up to a diameter of 4 mm the tubing should

be beveled at the end to enlarge the cross section of the outlet (Figure 8.47c)

Bubblers can be used not only for core cooling but also for flat mold sections, whichcannot be equipped with drilled or milled channels

A special bubbler has been developed for cooling rotating cores in unscrewing molds(Figure 8.47e)

It is frequently suggested to separate inlet and return flow in a core hole with a baffle(Figure 8.47f) This method provides maximum cross sections for the coolant but it is

difficult to mount the divider exactly in the center The cooling effect and with it thetemperature distribution on one side may differ from those of the other side This dis-advantage of an otherwise economical solution, as far as manufacturing is concerned,can be eliminated if the metal sheet forming the baffle is twisted This "cooling coil" isself-centering It conveys the coolant to the tip and back in the form of a helix and makes

for a very uniform temperature distribution (Figure SAIg).

Further logical developments of baffles are one or double-flighted spiral cores(Figure 8.47h)

A more recent, elegant solution uses a so-called heat pipe (Figure 8.47i) This is aclosed cylindrical pipe filled with a liquid heat conductor, the composition of whichdepends on the temperature of use It has an evaporation zone where the liquid evapo-rates through heat and a condensation zone where the vapor is condensed again Thecenter zone serves the adiabatic heat transfer Heat pipes have to be fitted very accurately

to keep the resistance between pipe and mold to a minimum They have to be cooled attheir base as described for inserts of highly conductive metals (Figure 8.47b) Heat pipesare commercially available from 3 mm upward They can be nickel-coated and thenimmediately employed as cores

For core diameters of 40 mm and larger a positive transport of coolant has to beensured This can be done with inserts in which the coolant reaches the tip of the corethrough a central hole and is led through a spiral to its circumference, and between coreand insert helically to the outlet (Figure 8.47j) This design weakens the core onlyinsignificantly

Cooling of cylindrical cores and other circular parts should be done with a doublehelix (Figure 8.47k) The coolant flows to the tip in one helix and returns in the otherone For design reasons, the wall thickness of the core should be at least 3 mm in thiscase For thinner walls another solution is offered with Figure 8.471 The heat is removedhere by a beryllium-copper cylinder intensely cooled at its base

Another way of cooling poorly accessible mold areas (narrow cores) is not to useconventional mold steels for the cavity but rather to use instead a microporous material(TOOLVAC®), through which liquid gas, usually CO2, flows (Figure 8.47m) The gasexpands in the special material, thereby absorbing heat energy via the pore surface andtransports it via the evacuation channels out of the mold [8.53, 8.54]

In the CONTURA® system [8.54, 8.55], the mold core is separated such that at acertain distance close to the mold wall cooling channels may be milled so as, on the onehand, to increase the surface area available for heat exchange and, on the other, to allowthe cooling channel system to follow the mold wall contour at a close distance (8.47n)

In this case, a more uniform temperature distribution in the core ensures better moldreproduction of the part as well as shorter cooling times The use of a suitable joiningmethod (high-temperature soldering under vacuum) joins all section lines together again

If there are several cores in a mold to be cooled simultaneously, solutions are strated with Figure 8.48 and 8.49 They represent a cooling layout in series or parallel.With cooling in series the individual cores are supplied with coolant one after theother Since the temperature of the coolant increases and the temperature differentialbetween molding and coolant decreases with the increasing flow length of the coolant, auniform cooling of cores and thus of moldings is not provided With such a system in amulti-cavity mold the quality of all parts will not be the same To avoid this shortcoming,parallel cooling is employed

demon-With parallel cooling the individual cores are supplied with coolant from a mainchannel Another collecting channel removes the coolant Thus, each core is fed with

Base of insert should be enlarged

Bubbler with beveled tip(4 mm)

OutIn

Water in

Figure 8.47 Core cooling techniques [8.47 to 8.55] (continued on next page)

Air

Cu

Thermal pin (heat pipe) from

3 mm dia, installation withtamp rings or silver orcopper compound

Helical cooling channel

Double helix and bubbler

Molding; b+ Be-Cu sleeve,

thickness £ 3 mm; b Steel,

thickness > 3 mm; c Helicalcooling channel, d Weldedstainless steel part

a Microporous material

b Capillary tube for CO2 feed

Slicing of coreMilling of modified heating channelsJoining of core

Figure 8.47 (continued) Core cooling techniques [8.47 to 8.55]

Design

Capillary action Shell

coolant of the same temperature This provides for a uniform cooling [8.56] if, inaddition, one sees to it that the coolant volume is equally divided.

As a more elegant, although more costly way of cooling, each core could be equipped

with a bubbler (Figure SAId) separately supplied with coolant.

All these cooling systems are well suited for cooling parts with circular cross section.The helical design in single- or double-flighted form can be used equally well forcores or for cavities

8.7.2 Cooling S y s t e m s for Flat P a r t s

One has to distinguish between circular and angular parts here For circular parts thesystem presented with Figure 8.50 has been successfully used in practice The coolantflows from the center (opposite the gate) to the edge of the part in a spiral pattern Thisoffers the advantage of the largest temperature differential between molding and coolant

at the hottest spot The temperature of the coolant increases as it flows through the spiral,while the melt has already cooled down to some degree because of the length of its flow.Thus the temperature differential is getting smaller, and less heat is removed This results

in a rather uniform cooling The uniformity is improved even more if a second spiral ismachined into the mold, parallel to the first one, for the return flow of the coolant Thissystem is expensive to make but produces high-quality and particularly distortion-freeparts It has been used for molding precision gears and compact discs [8.57]

Of course both mold halves must be equipped with this cooling system for moldinghigh-quality parts

Figure 8.51 Straight cooling channels Poor design for circular parts [8.58]

Straight cooling lines should only be used, at best, in molds for rectangular parts.Drilling straight through the mold plate is most cost effective [8.51] The ends areplugged and the coolant is positively directed into cross bores by diverting plugs androds (Figure 8.53)

Figure 8.50 Cooling line in spiral

design [8.56]

For economic reasons, molds for circular parts have frequently straight, through-goingcooling channels This cannot, of course, produce a uniform temperature distribution(Figures 8.51 and 8.47) Consequently distortion of the part may occur

Considerably more expensive is the cooling system presented in Figure 8.52 Thecooling channel is milled into the plate conveying the coolant in form of a spiral fromthe center towards the edge This system is justified only for central gating because of itscosts Another cooling system for centrally gated, rectangular parts is equally effectivebut less costly (Figure 8.53) The system consists of blind holes drilled into the moldplate.

If the part is gated at the side, the coolant can, of course, also be supplied from theside (Figure 8.54)

High-quality parts from multi-cavity molds can be produced if the same coolingconditions are ensured for each cavity, that is, each cavity has to be cooled separately.This can be done by arranging several cooling circuits parallel as shown in Figure 8.55,however, equal flow rates are not guaranteed by this design This always needsadditional control

All these systems presented so far for cooling flat parts can also be used for shaped parts after being appropriately modified The location of the gate determines themore practical layout of the cooling lines, either in series or parallel

box-As an example for a parallel layout the core cooling of a mold for refrigerator boxes

is presented with Figure 8.56 This system can only be made cost effectively by drillingblind or through-going holes Plugs or welding has to be used to achieve positive flow

of the coolant This may result in weakened or otherwise hazardous spots Plugs maycause marks in transparent parts Welding may distort the core to such an extent that even

a finishing machining cannot compensate for the dimensional deviation

It is suggested, therefore, to cool rectangular cores with the same systems as circularones in accordance with Figure 8.47 using parallel or series layouts (Figure 8.57)

8.7.3 Sealing of C o o l i n g S y s t e m s

Plugging and welding to close cooling-line ends as well as sealing the system with aplate on top of it (Figure 8.52) are problematic There is always the danger that a slightbending of the plates has already caused the channels not to be sealed any more against

Figure 8.52 Cooling line layout in spiral

form for rectangular parts [8.59]

Figure 8.53 Rectangular part with center

gating [8.59]

Figure 8.54 Straight cooling

channels for rectangular parts

gated laterally [8.56]

a Rod, b Diverting plug

Water supply

Figure 8.55 Parallel layout of several

cooling circuits for a large surface [8.60]

Figure 8.56 Parallel layout of core cooling

for box mold [8.59, 8.60]

Water supply Water out

Hose connections

1,2,3,4 and 5 Cooling circuits

out out

in in

one another or against the outside Even a "short-cut" between channels is already adefect because it creates uncooled regions where no coolant flows Thus, the plates have

to be bolted in adequately small intervals

Another problem are holes for ejector pins, etc They have to be carefully andindividually sealed, e.g., by O-rings or by applying pasty sealants Sealants are applied

to the cleaned surface with a roller, or continuously squeezed from a tube and curedbetween the matching faces at room temperature and under exclusion of air Suchproducts seal gaps up to 0.15 mm They are temperature resistant in the range from -55

to 200 0C

To facilitate disassembly, O-rings are used considerably more often for sealing thecooling systems Depending on the mold temperature, they can be made of synthetic ornatural rubber, and of silicone or fluoro rubber The groove which accommodates theO-ring, should be of such a size as to cause a deformation of 10% of the ring afterassembly Figure 8.58 shows O-rings for sealing a core cooling in parallel layout [8.56].One uses according to temperature

- below 20 0C: O-rings of synthetic rubber,

- above 20 0C: O-rings of silicone or fluoro rubber,

- above 120 0C: Copper-asbestos

8.7.4 D y n a m i c M o l d C o o l i n g

In the injection molding of thermoplastics there are specialty applications in whichthe requirements imposed on cooling not only concentrate on rapid cooling of thepart but also require brief or local heating In other words, the mold is heated to e.g thetemperature of the molten plastic prior to injection When the filling phase is finished,the part is cooled to the demolding temperature This is known as dynamic orvariothermal mold cooling

Examples of such applications are low-stress and low-oriented injection molding ofprecision optical parts [8.61] The hot cavity walls permit relaxation of internal stress inthe outer layers before demolding, so as to avoid distortion afterwards Furthermore,increasing the temperature of the cavity walls as closely as possible to the melttemperature can improve the flowability of the injected plastic It is thus possible toattain extreme flow-path/wall-thickness ratios [8.62, 8.63] as well as microstructuredparts that have areas with micrometer dimensions [8.64] Under certain circumstances,the heating time determines the cycle time in these applications

Figure 8.57 Cooling circuit for core

of a box mold [8.60]