The Heat Exchange System

8 T h e H e a t E x c h a n g e S y s t e m [8.1, 8.2] The velocity of the heat exchange between the injected plastic and the mold is a decisive factor in the economical performance of an injection mold Heat has to be taken away from the thermoplastic material until a stable state has been reached, which permits demolding The time needed to accomplish this is called cooling time The amount of heat to be carried off depends on the temperature of the melt, the demolding temperature, and the specific heat of the plastic material For thermosets and elastomers, heat has to be supplied to the injected material to initiate curing Primarily, the cooling of thermoplastics will be discussed here in detail To remove the heat from the molding the mold is supplied with a system of cooling channels through which a coolant is pumped The quality of a molding depends very much on an always constant temperature profile, cycle after cycle The efficiency of production is very much affected by the mold as an effective heat exchanger (Figure 8.1) The mold Figure 8.1 Heat flow in an injection mold [8.1] a Region of cooling, b Region of cooling or heating, c Q E = Heat exchange with environment, d Qp = Heat exchange with molding, e Q c = Heat exchange through coolant has to be heated or cooled depending on the temperature of the outside mold surface and that of the environment Heat removal from the molding and heat exchange with the outside can be treated separately and then superimposed for the cooling channel region If the heat loss through the mold faces outweighs the heat to be removed from the molding, the mold has to be heated in accordance with the temperature differential This heating is only a protection for shielding the cooling area against the outside Cooling the molding remains in the foreground The above mentioned relationships, however, remain applicable for all kinds of molds for thermoplastics as well as for thermosets The latter case includes heat supply for curing Thus the term heat exchange can be applied under all conditions 8.1 Cooling Time Cooling begins with the mold filling, which occurs during the time tP The major amount of heat, however, is exchanged during the cooling time t c This is the time until the mold opens and the molding is ejected The design of the cooling system must depend on that section of the part that has to be cooled for the longest time period, until it has reached the permissible demolding temperature TE The heat exchange between plastic and coolant takes place through thermal conduction in the mold Thermal conduction is described by the Fourier differential equation Because moldings are primarily of a two-dimensional nature and heat is only removed in one direction, the direction of their thickness, a one-dimensional computation is sufficient (Solutions for one dimensional heat exchange in the form of approximations have been compiled by [8.3, 8.4] for a length-over-wall-thickness ratio L/s > 10.) Elastomers, however, may have very different shapes and Figure 8.14 presents, therefore, all conceivable geometries In the case of one-dimensional heat flow, the Fourier differential equation can be reduced to: (8.1) with a = = thermal diffusivity In these and the following equations: a Thermal diffusivity, aeff Effective thermal diffusivity, t Time, t c Cooling time, s Wall thickness, x Distance, p Density, k Thermal conductivity, Cp Specific heat capacity, TE Demolding temperature, TE Mean demolding temperature, TE Maximum demolding temperature, TM Melt temperature, T w Cavity-wall temperature, T w Average cavity-wall temperature, Cooling rate, Fo Fourier number Assuming that, immediately after injection, the melt temperature in the cavity has a uniform constant value of TM ^ f(x), the temperature of the cavity wall jumps abruptly to the constant value T w ^ f(tc) and remains constant, then according to [8.3] (8.2) is a solution of the differential Equation if only the first term of the rapidly converging series (8.3) is considered Hence (8.4) or resolved with respect to the cooling time: (8.5) If this equation is rearranged to (8.6) the dimensionless representation of the cooling process (Figure 8.2) for the average part temperature is obtained (8.7) It is called the excess temperature ratio and can be interpreted as cooling rate Figure 8.2 Cooling rate dependent on cooling time (left) and Fourier number (right) [8.1] Fo is the dimensionless Fourier number (8.8) According to Equation (8.6) the cooling rate is only a function of the Fourier number: (8.9a) If the term t c • 2i s = const., the cooling rate is always the same Instead, the average temperature the calculation can also be based on the maximum temperature in the center of the molding (Figure 8.3) Then the equation for the dimensionless cooling rate is: (8.9b) Figure 8.3 Temperature plot in molding [8.2] T M Temperature of material, T w Average temperature of cavity wall, T E Temperature at demolding, center of molding, T E Temperature at demolding, integral mean value, t c Cooling time The different patterns of cooling rates can be presented dimensionless by a single curve (Figure 8.2) Although injection molding does not exactly meet the required conditions, the cooling time can be calculated with adequate precision as experience confirms As far as injection molding of thermoplastics is concerned, investigations [8.5] have demonstrated that demolding usually takes place at the same dimensionless temperature, that is with the same cooling rate S=0.25 based on the maximum temperature in the center or 6=0.16 based on the average temperature of the molding Therefore, it was possible to come up with a mean value for the thermal diffusivity a, the effective thermal diffusivity aeff The thermal diffusivity proper for crystalline materials is presented by an unsteady function 8.2 T h e r m a l Diffusivity of Several Important Materials Figure 8.4 presents the effective thermal diffusivity of unfilled materials with a cooling rate of S=0.25 Figure 8.5 depicts the change in thermal diffusivity dependent on the cooling rate with polystyrene as an example This information should permit a possible conversion into other cooling rates mm Figure 8.4 Effective mean thermal diffusivity of crystalline molding materials [8.6] C Temperature of cavity wall Tw Effective thermal diffusivity aeff 10-2rmn2 Polystyrene 168 N Temperature of cavity Tw Tw °C Figure 8.5 Effective mean thermal diffusivity versus mean temperature of cavity wall T w with as parameter [8.1] The thermal diffusivity of filled materials changes in accordance with the replaced volume [8.7] Figure 8.6 shows the effective thermal diffusivity of polyethylene with various quartz contents (percent by weight) as a function of the cooling rate Criteria such as shrinkage, distortion and residual stresses are unimportant in structural foam parts for all practical purposes The cooling time is solely determined by the outer skin, which has to have sufficient rigidity for demolding Otherwise, remaining pressure from the blowing agent causes swelling of the part after release from the retaining cavity Independent of the thickness of structural foam parts, the cooling rate can be taken = 0.18 to 0.22 (Figure 8.7) PE1800M Quartz powder Tw = 30 C Effective thermal diffusivity cy ]Q-2mm2 Percentage of filler Figure 8.6 Effective thermal diffusivity of polyethylene filled with quartz powder [8.1] Cooling gradient Effective thermal diffusivity aeff mm2 s g/cm3 Density gs 8.2.1 Figure 8.7 Effective thermal diffusivity dependent on density of structural foam [8.1] (Styrofoam parts 4-8 mm thick, cooling rate = 0.2) T h e r m a l Diffusivity of E l a s t o m e r s For elastomers, the heat of reaction can be neglected because of its small magnitude One can calculate and proceed like one does with thermoplastics Due to a high content of carbon black the thermal diffusivity is shifted to higher values similar to filled polyethylene (Figure 8.6): aeff ~ to mm2/s 8.2.2 T h e r m a l Diffusivity of T h e r m o s e t s Thermosets can develop a considerable higher heat of reaction The amount of released heat depends on the degree of cross-linking and the percentage of reacting volume of the Temperature polymer High contents of filling materials have a dampening effect Therefore, no data can be provided They can be obtained from the raw-material producer or by determining them with a differential calorimeter How much heat of reaction has to be expected can be measured with a reacting molding by plotting the increase in temperature versus the time, as is shown in Figure 8.8 The area of the "hump" is an assessment of the exothermic heat of reaction of this molding With a hump area of small size compared with the total area under the temperature curve, one can disregard its share Figure 8.8 Characteristic temperature development of a reactive material [8.8] 8.3 Timet C o m p u t a t i o n of Cooling T i m e of T h e r m o p l a s t i c s 8.3.1 Estimation Since cooling of all materials is physically similar, one can often estimate the cooling time with the simple correlation: t c = c c s2 (8.10) For unfilled thermoplastics c c = to [s/mm2], tc Cooling time, s Wall thickness 8.3.2 Computation of Cooling Time with N o m o g r a m s With the help of mean thermal diffusivities aeff, nomograms can be drawn, which allow for an especially simple and fast determination of the cooling time The cooling time t c is plotted against the cavity-wall temperature T w for a number of constant demolding temperatures t E and various wall thicknesses s The presented cooling-time dependence is valid for plane moldings (plates without edge effect) with symmetrical cooling (Figures 8.9 and 8.10) Besides the diagram presentation, nomograms (Figure 8.11) can be used which are derived from the following equation (valid for plates): Figure 8.9 Cooling time diagram (PS) [8.1] t«(s) aeff(f2) Cooling time tc Wall thickness of part s HDPE Wall thickness of part s Cooling time tc PS Figure 8.10 Cooling time diagram (HDPE) [8.1] s(mm) Exampel for Figure 8.11 Nomogram for computation of cooling time [8.1] (8.11) The following correlation is valid for cylindrical parts: (8.12) Reference data for melt, wall and demolding temperature as well as the average density between melt and demolding temperature can be found in Table 8.1 Table 8.1 Material data [8.12] Material Melt temperature (0C) Wall temperature (°C) Demolding temperature (0C) Average density (g/cm3) ABS HDPE LDPE PA PA 6.6 PBTP PC PMMA POM PP PS PVC rigid PVC soft SAN 200-270 200-300 170-245 235-275 260-300 230-270 270-320 180-260 190-230 200-300 160-280 150-210 120-190 200-270 50-80 40-60 20-60 60-95 60-90 30-90 85-120 10-80 40-120 20-100 10-80 20-70 20-55 40-80 60-100 60-110 50-90 70-110 80-140 80-140 90-140 70-110 90-150 60-100 60-100 60-100 60-100 60-110 1.03 0.82 0.79 1.05 1.05 1.05 1.14 1.14 1.3 0.83 1.01 1.35 1.23 1.05 8.3.3 Cooling T i m e w i t h A s y m m e t r i c a l Wall T e m p e r a t u r e s If there are asymmetrical cooling conditions from different wall temperatures in the cavity, the cooling time can be estimated in the same manner by using a corrected part thickness [8.9] The asymmetrical temperature distribution is converted to a symmetrical one by the thickness complement s' (Figure 8.12) The following estimate results from a correlation, which is discussed in [8.9]: (8.13) q = Heat flux density For q2 = (one-sided cooling) s1 = 2s; the cooling time is four times that of two-sided cooling Figure 8.12 Illustration of corrected part thickness [8.1] The cavity-wall temperatures determine the different heat-flux densities, which in turn provide the corrected wall thickness The thickness finally allows the cooling time to be estimated 8.3.4 Cooling T i m e for O t h e r G e o m e t r i e s Besides flat moldings, almost any number of combinations from plates, cylinders, cubes, etc can be found in practice The correlation between cooling rate and Fourier number has already been demonstrated with a plane plate as an example This relationship can also be shown for other geometrical forms such as cylinder, sphere, and cube Figure 8.13 presents this correlation for the cooling rate in the center of a body according to [8.10 and 8.11] This also permits calculating or estimating other configurations The necessary formulae are summarized in Figure 8.14 For practical computation, additional simplification is possible The cooling rate can be expressed by the ratio of the average part temperature on demolding TE over the melt temperature TM = T0 and plotted versus the Fourier number for cylinder and plate (Figure 8.15) To determine the cooling characteristic of a part that can be represented by a combination of a cylinder and a plate (cylinder with finite length) or by three intersecting infinite plates (body with rectangular faces), the following simple law [8.10] can be applied: (8.14) c5 § CD CD E CD Plate s=2x Beam with square cross section, length = °o, a = 2x Cylinder, length = oo 1x = K „ Length = 2xJ Sphere Cube v > Fourier number Fo Figure 8.13 Temperature in center of molding if surface temperature is constant [8.10] 8.5.1 Analytical T h e r m a l Calculation The analytical thermal calculation can be subdivided into separate steps (Figure 8.27) The necessary time to cool down a molding from melt to demolding temperature with a given cavity-wall temperature is established in the cooling-time computation This can be done with equations for a variety of configurations (Section 8.3.4) for different sections of moldings, which have to be rigid enough to be demolded and ejected at the end of the cooling time The longest time found with this calculation is decisive for further proceedings Design steps Criteria Computation of cooling time Minimum cooling time down to demolding temperature Balance of heat flow Required heat flow through coolant Flow rate of coolant Uniform temperature along cooling line Diameter of cooling line Turbulent flow Position of cooling line Heat flow uniformity Computation of pressure drop Selection of heat exchanger Modification of diameter or flow rate Figure 8.27 Analytic computation of the cooling system [8.2] With the heat-flux balance, which has to be taken in by the coolant is computed This calls for consideration of additional heat input, heat exchange with the environment, and eventual insulation The heat exchange with the environment is found with the estimated outside dimensions of the mold and the temperature of the mold surface An approximation for the latter is the temperature of the coolant, which is assumed for the time being The heat-flux balance does not only provide information about the operating range of the heat-exchange system, but also indicates design problems along the way High heat flux, which has to be carried away by the coolant and which occurs particularly with thin, large moldings of crystalline material, requires a high flow rate of the coolant and results in a high pressure drop in the cooling system Then the use of several cooling circuits can offer an advantage A low heat flux to be taken up by the coolant may result in a small flow rate of the coolant in channels with common diameter and with this in a laminar flow For this reason, a higher flow rate should be accomplished than that resulting from the criterion of temperature difference between coolant entrance and exit After the flow rate of the coolant has been calculated, the requirement of a turbulent flow sets an upper limit for the diameter The position of the cooling channels to one another as well as their distance from the surface of the molding result from the calculated heat flux including compliance with the limits of homogeneity (Figure 8.28) The calculation can be done with a number of preconditions: - specification of cooling error and computation of distances, specification of distance from molding surface, specification of distances among cooling channels, specification of whole length of cooling line, specification of both channel distances and computation of required flow rate of coolant In this case another heat-flux balance becomes necessary Distance from surface I Tabulating the points of the functions presented with Figure 8.28 is an additional beneficial option Such a table makes it possible to fit the position of individual cooling channels into the mold design without relocating parting lines or ejector pins For the analytical calculation, the configuration of the molding is simplified by a plate with the same volume and surface as the molding This allows segmenting the internal mm Nonuniform Figure 8.28 Position of cooling line and temperature uniformity [8.2] mm Distance between channels b area of the mold with each segment having a width equal to the calculated distance between the cooling channels With the position of the cooling channels one can determine the whole length of the cooling system, the length of supply lines, the number of corners, elbows and connectors and enter them into the drawing This information permits the computation of the pressure loss and the necessary capacity of heat exchangers In the same way one can calculate the minimum diameter of the cooling channel or the maximum flow rate of the coolant for a given permissible pressure drop One has to consider that a large part of the pressure drop does not occur solely in the cooling line in the mold, but also in connecting lines, connectors and turns, which must also be taken into account 8.5.1.1 Calculating the Cooling Time With the aid of the equations presented in Section 8.3.4 (Figure 8.14), it is possible to calculate the necessary cooling time To ensure a dependable design, it is always better to use the critical (i.e., thickest) cross-section of the part for the calculation 8.5.1.2 Heat Flux Balance The efficiency of the heat-exchange system of a mold depends on the amount of heat that can b e extracted from the plastic material in the cavity at a certain cavity-wall temperature in the shortest time span possible Therefore it is the task of the heatexchange system to ensure the desired temperature of the cavity wall (see also Section 8.4) In contrast to [8.34, 8.35] one can apparently without a transfer coefficient between cavity wall and material if the wall temperature is defined as the contact temperature between plastic and cavity wall, which, as shown below, has to b e calculated This holds for as long as the molded part is still lying against the cavity wall The contact temperature is the m a x i m u m temperature during the cycle that establishes itself when the molding compound is in contact with the wall It is expressed as: (8.30) Tc T p max Tw b k p c Contact temperature, Material temperature before contact, Cavity-wall temperature before contact, Heat penetrability, Thermal conductivity, Density, Specific heat capacity Depending on time and cycle, the temperature of the cavity surface varies between contact and minimum temperature, which is determined by the temperature of the coolant T h e average of both provides sufficient accuracy for calculating cooling time and necessary heat-exchange capacity Therefore this average temperature represents the cavity-wall temperature T w (8.31) In a steady state the cavity surface with the temperature T w acts as a heat sink for the molding and a heat source for the mold The resulting heat flux can be determined as follows: Quantity of heat from the molding: (8.32) Heat flux from the molding into each mold half: (8.33) Ah p QM s AM tc tc Enthalpy difference (Figure 8.17), Density of melt, Heat flux from melt, Wall thickness, Surface area of molding, Cooling time = C c • s , Cycle time t c + tn (tn is the nonproductive time for opening, closing and ejecting) with (8.34) Heat-flux density from molding: (8.35) For the first estimate, the nonproductive time (the period of time during which no molding compound is in the cavity) is ignored initially When the nonproductive time is ignored, the equation can be simplified further: (8.36) If one now combines ^- = K into a single material constant, then K (8.37) Within the usual range of processing temperature the heat-flux density only depends on the material It is obvious that it has to increase with decreasing wall thickness to ensure the required cavity temperature Besides this, the heat-flux density, in future called specific heat flux, represents a specific material characterization if the generally small machine effect is neglected The machine effect becomes apparent by the extra time needed for the completion of movements (ejection, etc.) The heat flow from the molding to the mold is interrupted with the demolding process; the coolant, however, continues to cool the mold during this secondary time, which reduces the specific heat flux accordingly Figures 8.29 and 8.30 present the specific heat flux for PS and HDPE as a function of secondary machine time The maximum occurs with a wall thickness for which cooling and secondary time are equal The specific heat flux as a function of cavity temperature is shown in Figures 8.31 and 8.32 for a number of wall thicknesses The specific heat flux can facilitate the selection of the right mold concept already in the planning stage and also presents a basis for the design of the heat-exchange system of the mold JL cm2 JL cm2 Ide lm it e tn mm Wall thickness of part s Figure 8.29 Specific heat flux q PS as a function of wall thickness [8.1] HDPE Specific heat flux q Specific heat flux q PS Ide lm it e tn mm Wall thickness of part s Figure 8.30 Specific heat flux q HDPE as a function of wall thickness [8.1] 8.5.1.3 Coolant Throughput For the determination of the coolant throughput, the specific heat flux q (Figures 8.31 and 8.32) is the central design parameter Multiplying the specific heat flux by the corresponding surface area of the molding AM results in the amount of heat which has to be removed by the coolant during one cycle, which belongs to AM The necessary flow rate of the coolant Vc is determined by the permissible rise in coolant temperature ATC The difference in coolant temperature AT should not exceed to 0C in order to ensure adequate homogeneous cooling along the cooling circuit The maximum permissible temperature difference may be used to calculate the minimum necessary coolant throughput ATmax Wall thickness of part sin mm TM = 220 0C TE = 90 0C TN = 5s W Cm2 PS Specific heat flux q Specific heat flux q JL Cm2 Wall thickness of part sin mm TM = 220 0C lE = 100°C HDPE TN= 5s 0 C C Temperature of cavity wall Tw Temperature of cavity wall Tw Figure 8.32 Specific heat flux q HDPE as a function of temperature of cavity wall [8.1] Flow rate (water) V Figure 8.31 Specific heat flux q PS as a function of temperature of cavity wall [8.1] Figure 8.33 Computation of flow rate of cooling water (molding surface = 100 cm2) [8.1] W/cm2 Specific heat flux q (8.39) Density of coolant, Specific heat of coolant 8.5.1.4 Temperature of the Cooling Channel If a pressure drop Ap and common channel geometry are given, the necessary flow rate for the coolant (which is predetermined by the pressure generated by the heating unit with a deduction for pressure losses in the feed lines to the mold) can only be ensured by the channel diameter d c to be selected (8.39) fc Lc nc Kc Vc dc Ap Friction factor in pipes (= 0.05 in Figure 8.34), Channel length in cm (= 200 in Figure 8.34), Number of turns (= 10 in Figure 8.34), Resistance coefficient (= 1.9 in Figure 8.34), Flow rate of coolant, 1/min, Diameter of cooling channel, cm, Pressure drop, 102 kPa Flow rate (water) V I Diameter of cooling channel dc mm Figure 8.34 Determination of cooling channel diameter d c and coefficient of heat transfer [8.1] Since the final cooling-channel arrangement is not yet established, the number of turns and the length-over-diameter ratio L c /d c have to be estimated for the time being To avoid iteration, a rather small pressure drop should be chosen Because it represents a minimum requirement, variations of line pressure, length of supply lines and degree of contamination (from deposits and corrosion) have to be generously considered (corrosion during storage of the mold can be minimized by drying with compressed air at the end of operations and proper storage) Measurements on molds have demonstrated [8.9] that the friction factor in pipes without deposits can be described according to Blasius' law: (8.40) With few deposits (after about 100 working hours = usual operating range) one can estimate fc ~ 0.04 [8.9] Resistance coefficients for sharp and rounded bends were reported as follows: 90° sharp bend K = 1.9 [8.9], 90° round bend K = 0.4 [8.9] (Literature [8.36, 8.37] contains values for the 90° sharp bend of between 1.13 and 1.9 and for the 90° round bend of between 0.4 and 0.9) The coefficient of heat transfer can be calculated in combination with Nusselt, Reynolds and Prandtl numbers [8.38]: (8.41) dh Hydraulic diameter (4 x cross section/circumference), k c Thermal conductivity of coolant, Kf Correction factor The dimensionless parameters compute to: (8.42) (8.43) The equation for the heat transfer coefficient a applies to the range of turbulent flow with a considerably better heat transfer than with laminar flow (Re < 2300) Another disadvantage of the range of laminar flow is the transition into turbulent flow behind corners and changes in cross-sectional areas, which causes a better heat transfer for a certain length The demand for a turbulent flow results in an upper limit for the diameter: (8.44) Common diameters for cooling channels in most applications are far below this limit Arrival of laminar flow in water of 20 C can only be assumed with a flow rate of less than 1/min With the channel diameter determined, the coefficient of heat transfer can be computed with the flow rate of the coolant for 2300 < Re < 106, 0.7 < Pr < 500, and Simple channel Channel inserted cylinder Bubbler Channel with Channel baffle with twisted buffle Singlethreaded spiral bubbler Doublethreaded spiral bubbler Figure 8.35 Cooling elements [8.2] (8.45) Kinematic viscosity of coolant [cm2/s], Cooling channel diameter [cm], Prandtl number = v/a, Thermal conductivity of coolant [W/cm K] The dependency of the coefficient of heat transfer on flow rates (expressed in Figure 8.34 by Ap), temperature and channel diameter is demonstrated for several coolants in Figures 8.36, 8.37 and 8.38 It is evident that water is the most effective coolant 8.5.1.5 Position of the Cooling Channels The distance between two cooling channels in a mold is based on the relationship given in Figure 8.39 For the dimensions Figure 8.40 can be used The example is based on an average temperature of coolant of T c = 20 C and an average mold temperature of T w = 62 C The ratio AC/AM is presented with Figure 8.41 as a function of the distance of the channels between each other and their diameters x 10* Line pressure p Line pressure p Coefficient of heat transfer a Coefficient of heat transfer a fegrd^ Lo W } Da i meter of cooling channel dc Diameter of cooling channel dc Figure 8.37 Coefficient of heat transfer a, coolant: brine (20%) [8.1] Figure 8.36 Coefficient of heat transfer a, coolant: water [8.1] [ J 2o Ll m Ci Line pressure p Coefficient of heat transfer a xlO3 Figure 8.38 Coefficient of heat transfer a, coolant: oil (Marlotherm S) [8.1] Diameter of cooling channel dc Figure 8.39 Picture of thermal reactions (steady conduction) [8.1] (The ratio A c /A p is presented in Figure 8.41) Ap Surface of molding, A c Surface of cooling channel Figure 8.40 Computation of heat-transfer data [8.1] (8.46a) (8.46b) Average temperature of cavity wall, Temperature of cooling channel wall AM Figure 8.41 Cooling-channel layout [8.1] mm dc The same specific heat flux is transferred into the coolant This results, depending on the coefficient of heat transfer, in the temperature differential AT2 (convective heat transfer) (8.47) (8.48) T c Temperature of coolant The ratio between the areas of the cooling-channel wall A c w and the corresponding molding surface AM affects the specific heat flux qlike a the coefficient of heat transfer Hence: (8.49) The heat fluxes q transferred by thermal conduction and convection must naturally be equal, and the temperature differences AT1 and AT2 have the temperature of the coolingchannel wall T c w as common parameter In an alignment chart with four quadrants, appropriate common abscissa can, therefore, be selected (Figure 8.39) With the exception of q and T w , which are interdependent (Figures 8.31 and 8.32), all other parameters can be arbitrarily varied With this, the required closed solution is made possible There has to be a functional correlation between the cooling-line distances and b, if the specific heat flux is constant The distance can be taken with adequate accuracy from the thermal conductance kM/l with the thermal conductivity of the mold material kM (Figure 8.42), if one remains in the range of validity b of to d c The goal of thermal design, aside from attaining the necessary heat flux for maintaining the predetermined mold wall temperature, is uniform cooling of the K/I mK W mK Sintered mm Distance I Figure 8.42 Distance between cavity wall and cooling line [8.1] molding There are different combinations of (distance from molding to cooling line) and b (distance between cooling lines) that produce the same temperature difference: - small values for b (many cooling lines) require large distances 1, - large values for b (few cooling lines) require small distances These two demands are equivalent in terms of thermal efficiency The uniformity of the cooling is, however, different and smaller in the second case To maximize homogeneity (uniform surface temperature) at the part surface, a small cooling error j is desirable The cooling error, j , which is defined by local differences in heat flux, can be used as a measure of uniformity (Figures 8.43 and 8.44) (8.50) (8.51) with = Cooling error, = Biot number = lnb/1 Range of validity for distances of cooling channels: = to d c , b = to d c j = Cooling error Distance from cavity wall L mm Line for mm Distance between channels b Figure 8.43 Feasible cooling line layout [8.1] Figure 8.44 Distribution of heat flow in segment [8.1] For crystalline plastics, the cooling error should be a maximum 2.5-5% and for amorphous plastics 5-10% in order to avoid inhomogeneous molded part properties (e.g., waviness, differences in gloss) [8.1] Distance b arises from the predetermined ratio of cooling channel to molded part area (e.g., AC/AM = 0.5 and 1), which establishes the line of equal cooling efficiency The line of equal cooling efficiency offers the designer a large number of alternative channel arrangements for avoiding bolts, ejector pins, etc 8.5.1.6 Design of Cooling Circuit 8.5.1.6.1 Flow Rate of Coolant The temperature of the coolant changes between entrance and exit in accordance with the heat flux (8.52) Next Page (8.53) The average temperature difference should not exceed a maximum of to 0C to ensure a uniform heat exchange over the whole length of the cooling line A required minimum flow rate V can be calculated from the permissible maximum temperature difference However, the rate also depends on the arrangement of the cooling elements With an arrangement in series the permissible temperature difference applies to the sum of heat fluxes from all segments; with parallel arrangement it applies to each segment Parallel arrangement results in a lower flow rate and smaller pressure drop However, parallel arrangement calls for an adjustment of flow rates with throttles [8.1] and a constant monitoring 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 an additional criterion for a controlled design of heat-exchange systems and a boundary condition for the heat exchanger If the pressure drop is higher than the capacity of the heat exchanger, then the necessary flow rate and, with this, the permissible temperature difference between coolant entrance and exit, cannot be met The consequences are nonuniform cooling of the molding and heterogeneous properties and distortion of the molding For calculating the pressure drop, different causes have to be considered: - pressure pressure pressure pressure pressure pressure drop from the length of the cooling element, drop from turnabouts, corners and elbows, drop from spiral flow, drop from changes in cross-sectional area, drop in connectors, drop from connecting lines The total pressure drop is the sum of all items The equations used to compute the pressure drop [8.1, 8.15, 8.40, 8.41, 8.42] are too extensive to be listed here because of all 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 the capacity of the heat exchanger: (8.54) Where = Pumping efficiency of the heating unit, = Pressure loss, = Volumetric flow, = Heating efficiency of the coolant 8.6 Numerical Computation for Thermal of M o l d e d Design Parts Through the use of simulation programs and thanks to the processing power of modern computers, it is possible to calculate the temperature range in the injection mold