# Simulation of a Mold-Cooling Process for Gas-Assisted Injection Molded Parts Designed With a Top Rib on the Gas Channel.

The same CAE model used for the filling and packing stage in the gas-assisted injection molding (GAIM) process simulation was also applied to simulate the cooling phase. This was made possible by using the line source method for modeling cooling channels. The cycle-averaged and cyclic transient mold cavity surface temperature distribution within a steady cycle was calculated using the three-dimensional modified boundary element technique similar to that used in conventional injection molding. The analysis results for GAIM plates of a semicircular gas channel design attached with a top rib are illustrated and discussed. It was found that the difference in cycle-averaged mold wall temperatures may be as high as 10[degrees]C, and within a steady cycle, part temperatures may also vary by about 15[degrees]C. The conversion of the gas channel into equivalent circular pipe and further simplification into two-node elements using the line source method not only affects the mold wall temperature calculation very sligh tly but also reduces the computer time by 93%. This indicates that it is feasible to achieve an integrated process simulation for GAIM under one CAE model, resulting in great computational efficiency for industrial application.INTRODUCTION

The gas-assisted injection molding (GAIM) process [1-4], being an innovative injection molding process, can substantially reduce production expenses through a reduction in material cost, a reduction in clamp tonnage, and a reduction in cycle time for thick parts. In addition, part qualities can also be greatly improved by a reduction in residual stress, warpage, sink marks, and shrinkage. The process also allows more design freedom in using structural ribs and bosses that would introduce sink mark and other associated issues on the surface appearance if conventional injection molding (CIM) were used. Although gas-assisted injection provides many advantages when compared with CIM, it also introduces new processing parameters and makes the application more critical. One of the key factors is the design of gas channels that guide the gas flow to the desired locations. If the layout of gas channels and their corresponding dimensions and shapes in cross sections are not properly designed, a catastrophe often occur s, leading to failure during part molding. In addition to the design parameters introduced by gas channels, other processing parameters, such as the numbers as well as the locations of gas injection points, the amount of polymer melt injection, the delay time, the injected gas pressure, and the holding time for gas injection, etc., are important in obtaining good molded parts. In other words, only when the design and processing parameters are well understood can the GAIM process obtain its advantages. Owing to the complexity of gas channel design and processing control, computer simulation is expected to become an important and necessary tool to assist in part design, mold design, and process evaluation.

At the present stage, process simulation for the melt filling and gas-assisted filling stages [3-8] has been developed, and it has been incorporated into several commercial packages, such as C-GASFLOW, Moldflow/Gas, and CADMOULD-MEGIT, etc. Two key factors that affect the simulation accuracy the most are the algorithm used for the calculation of skin melt thickness and the geometrical modeling approach used to represent gas channels.

The most popular modeling for gas channels is to use a circular pipe of an equivalent hydraulic diameter and a superimposition approach [3, 6-8] to represent the mixed one-dimensional and two-dimensional flow characteristics for melt and gas flow in the gas channel of a noncircular cross section. A schematic of such modeling is shown in Fig. 1 for the semicircular gas channel attached with a short rib on its top. Such an analysis model has recently been verified for melt flow in a thin cavity with channels of semicircular and quadrantal cross sections [7-9]. Although the approach of assigning variable thickness to gas channels was used by CADMOULD-MEGIT [4] and STRIMFLOW/Gas, it meets some difficulty describing gas channels with a long, thin rib attached on top. Basically, gas cannot easily penetrate this thin rib on the top of the gas channel. However, assigning a large thickness to a gas channel with a long tail rib may overpredict the gas penetration within this gas channel. Simulation results on the seco ndary gas penetration by both C-GASFLOW and Moldflow/gas show only very rough accuracy. A recent study [10, 11] suggests that to obtain good simulation results for the secondary gas penetration in the gas-assisted packing stage, a new algorithm and a flow model of the shrinkage-induced origin may have to be introduced instead of just following the pressure-induced flow model used for the post-filling simulation of CIM.

Simulation of gas-assisted cooling is not currently available. Although the development for the simulation of the gas-assisted cooling process is not too difficult, it needs to incorporate the geometry of the gas channels and the hollowed gas core. The situation becomes even more complicated when the gas channel is attached to a short or long rib. It is not known exactly how the geometrical simplification of a gas channel will affect the accuracy of a cooling simulation. Generally speaking, a complete CAE package for the entire phase of the GAIM process is not available. On the other hand, a gas channel provides the capability of structural reinforcement and makes the reduction of part thickness possible. From the part designer's viewpoint, requirements in the evaluation of part structural performance and warpage become much more important in GAIM than they do in conventional injection. Structural analysis for GAIM parts using three-dimensional analysis packages such as ANSYS or ABAQUS, etc., is very time-co nsuming, especially when detailed geometry of the hollowed core caused by gas penetration is taken into consideration in the design/analysis stage. If warpage analysis also follows a three-dimensional analysis approach, it meets not only the time-consuming issue, but also the interface issue about how the results of process simulation conducted under 2 1/2-dimensional analysis characteristics can be transferred. Whether or not a unified finite element model can be used for process simulation (including melt filling, gas-assisted melt filling, and gas-assisted packing and cooling stages) as well as structural analysis and warpage calculation are great concerns for CAE package development.

In our previous studies [7-11], simulations regarding primary gas penetration in the filling stage and secondary gas penetration in the post-filling stage based on constant mold temperature have been reported. Structural analyses in the part design stage based on the same CAE finite model used for process simulation were also addressed and verified [12-14]. All previous process simulations developed by different groups [3, 5-10] assume constant mold wall temperatures. This is not true, as known from CIM. Particularly, the contribution of thermal stress to warpage formation will be even more significant than in CIM because GAIM requires much lower molding pressure, resulting in a lower flow-induced residual stress. In such a situation, accurate mold cavity surface temperature and part temperature distributions will be crucial to the thermally induced residual stress calculation. Gas penetration is very sensitive to melt temperature, mold temperature, cavity dimension accuracy, etc. Small variations in these f actors may result in uneven gas penetration for symmetrical gas channel design. As a result, only after a nonconstant mold temperature during the cooling phase of GAIM has been obtained does the accurate prediction of gas penetration, as well as warpage, become possible for parts with a complicated geometry. Basically, the cyclic cooling process (Fig. 2) in the GAIM process is a three-dimensional, time-dependent heat conduction problem with convective boundary conditions similar to those of CIM [15-20]. Complicated boundary geometry is introduced by the cooling channel and gas channel layout. Besides, there are many design parameters involved in the injection molding cooling process [21]. Although a complete simulations analysis of the transient temperature variations of the mold and polymer melt is possible in principle, the computational cost is too high to be implemented during the actual design process.

To reduce the computing cost, a popular approach used in conventional injection mold cooling analysis is to use the boundary element method (BEM), in which the heat flux is introduced on the plastic-mold interface on a cycle-averaged basis [16-19] from which the cycle-averaged cavity surface temperatures was obtained. Then, the transient variations of cavity surface temperature within a steady cycle are analyzed from the time-varying heat flux coming from each element representing local part thickness and melt temperature.

This paper investigates the mold-cooling stage simulation of GAIM, considering the influence from the mold cooling system so that the cyclic, transient variations of mold cavity surface temperatures as well as part temperature distribution can be calculated. Basically, the same approach used for cooling analysis in CIM was followed. Analyses were applied to the GAIM parts represented by a model with a top-rib attached to a semicircular gas channel associated with a hollowed core (Fig. 3) and by a CAE model that con-verts the semicircular gas channel into an equivalent circular pipe with an exterior surface, as well as a two-node element model that is simplified from the circular gas channel model using the line source method. The latter is a common CAE model approach used for structural performance evaluation [14] as well as for simulations of melt filling and gas-assisted melt filling/holding phases [3, 6-11]. Comparisons were also made to evaluate the differences in the predicted mold wall temperatures as well as their cyclic, transient variations due to the gas channel conversion and simplification.

THEORETICAL FORMULATION

In previous studies [15-19], the periodic transient mold temperature was separated into two components: 1) a steady cycle-averaged component, [T.sub.m,s], and 2) a time-varying component, [T.sub.m,t], within a typical cycle, i.e.,

[T.sub.m]([vec{r}], t) = [T.sub.m,s]([vec{r}]) + [T.sub.m,t](z, t) for [vec{r}] [epsilon] [[Omega].sub.m] (1)

The steady temperature component, [T.sub.m,s], is obtained by cycle-averaged boundary element analysis. The temperature field in the mold is governed by a steady-state heat conduction equation of the Laplacian type:

[[nabla].sup.2][T.sub.m,s] = 0 for [vec{r}] [epsilon] [[Omega].sub.m] (2)

Corresponding boundary conditions defined over the boundary surface of the mold are described in the following:

- [K.sub.m] [frac{[partial][T.sub.m,s]}{[partial]n} = [h.sub.atr] ([T.sub.m,s] - [T.sub.air]) for [vec{r}] [epsilon] [S.sub.e] (3)

- [K.sub.m] [frac{[partial][T.sub.m,s]}{[partial]n}] = [h.sub.c] ([T.sub.m,s] - [T.sub.air]) for [vec{r}] [epsilon] [S.sub.c] (4)

- [K.sub.m] [frac{[partial][T.sub.m,s]}{[partial]n}] = [[bar{q}].sub.cp] for [vec{r}] [epsilon] [S.sub.cp] (5)

- [K.sub.m] [frac{[partial][T.sub.m,s]}{[partial]n}] = [[bar{J}].sub.av] for [vec{r}] [epsilon] [S.sub.p] (6)

where [S.sub.e], [S.sub.c], [S.sub.cp], [S.sub.p], and [[Omega].sub.m] represent the mold exterior surface, the cooling channel surface, the clamping surface, the melt-mold interface, and the domain of the mold, respectively. The corresponding heat transfer coefficients for air and coolant are designated as [h.sub.air], and [h.sub.c]; [[bar{q}].sub.cp], is the heat flux value defined at the mold clamping surface; [[bar{J}].sub.av], is the cycle-averaged heat flux transferred from the polymer melt into the cavity surface and is defined as follows. The ambient environment temperatures, with respect to the mold, [T.sub.air] and [T.sub.c], are defined for air and coolant correspondingly. [K.sub.m] is the thermal conductivity of the mold. The cycle-averaged heat flux [[bar{J}].sub.av] is evaluated through numerical iterations. The time-varying component, [T.sub.m,t], within a typical cycle is approximated by one-dimensional transient heat conduction expressed as

[[rho].sub.m][C.sub.m] [frac{[partial][T.sub.m,t](z,t)}{[partial]t}] = [frac{[partial]}{[partial]z}] [lgroup][K.sub.m][frac{[partial][T.sub.m,t](z,t)}{[partial]z}][rgroup ] for z [epsilon] [S.sub.p] (7)

where [[rho].sub.m], [C.sub.m], and [K.sub.m] are the density, specific heat, and thermal conductivity of the mold, respectively.

Within the mold cavity, the polymer melt also satisfies the transient conduction equation of

[[rho].sub.p][C.sub.p] [frac{[partial][T.sub.p]}{[partial]t}] = [frac{[partial]}{[partial]z}] [lgroup][K.sub.p] [frac{[partial][T.sub.p]}{[partial]z}] for [vec{r}] [epsilon] [[Omega].sub.p] (8)

where [[rho].sub.p], [C.sub.p], [K.sub.p] and [[Omega].sub.p] are the density, specific heat, thermal conductivity, and domain of the polymer melt, respectively. On the mold cavity surface, [S.sub.p], compatible conditions must be fulfilled. That is,

[K.sub.m] [frac{[partial][T.sub.m]}{[partial]n}] = - [K.sub.p] [frac{[partial][T.sub.p]}{[partial]n}] for [vec{r}] [epsilon] [S.sub.p] (9)

[T.sub.m] = [T.sub.p] for [vec{r}] [epsilon] [S.sub.p] (10)

In addition, on the hollowed-core surface, [S.sub.gc], located within a gas channel, the boundary condition must satisfy

- [K.sub.p] [frac{[partial][T.sub.p]}{[partial]n}] = [h.sub.[N.sub.2]]([T.sub.p] - [T.sub.[N.sub.2]]) for [vec{r}] [epsilon] [S.sub.gc] (11)

where [h.sub.[N.sub.2]] and [T.sub.[N.sub.2]] are the heat transfer coefficient and the temperature of nitrogen injected during the gas-assisted filling and packing phases, respectively. Along the mold cavity surface, it is subjected to a periodic boundary condition specified by the time-varying flux, [J.sub.t] = J(t) - [[bar{J}].sub.av], at the cavity surface. During the analysis instant, [t.sub.i], the instantaneous heat flux J([t.sub.i]) at the mold plastic interface is computed from the polymer melt temperature when the mold is closed. When the mold is open, a convective boundary condition similar to Eq 3 is defined for the cavity surface. The cycle-averaged heat flux [[bar{J}].sub.av] is then obtained by

[[bar{J}].sub.av] = [frac{[Sigma]J([t.sub.i])[Delta][t.sub.i]}{[t.sub.cycle]}] (12)

where [Delta][t.sub.i] is the interval between two computations and [t.sub.cycle] is the cycle time. Analysis, as well as iteration algorithms, have been reported previously [16-19].

In Eq 13, the heat transfer coefficient, [h.sub.c], is calculated using the following Dittus-Boetler correlation [22] for internal forced convective heat transfer:

[h.sub.c] = 0.023 [frac{[K.sub.c]}{D}][Re.sup.0.8][Pr.sup.0.4] (13)

where Re is the Reynolds number = 4Q/[pi]Dv and Pr is the Prandtl number defined as v/[alpha]. Here, Q denotes the volumetric flow rate, D is the diameter of the cooling channel, and v is the kinematic viscosity of the coolant, with [alpha] and [K.sub.c] being its thermal diffusivity and conductivity, respectively. This correlation is valid for 10,000[less than]Re[less than]120,000 and 0.7[less than]Pr[less than]120.

NUMERICAL METHODOLOGY

Numerical methods for steady-state boundary element analysis on a cycle-averaged basis have been reported previously [16-19]. The finite difference method for polymer melt heat transfer is also introduced with the same criteria for the adjustment of analysis interval.

The heat conduction Eq 2 is then transformed into an integral equation using Green's second identity, the fundamental solution technique [23], and the fundamental solution of the Laplace equation:

[C.sub.i][T.sub.i] = [[integral of].sub.[Gamma]] [T.sup.*]qd[Gamma] - [[integral of].sub.[Gamma]] [q.sup.*]Td[Gamma] (14)

where [T.sup.*] is 1/4[pi]r, [q.sup.*] is ([partial][T.sup.*]/[partial]n), and r is the distance between the integral source point and field point. Equation 14 is a typical formulation used in the previous studies for parts and molds represented by triangular elements for all related surface boundaries, [Gamma].

To avoid discretization of the circular channel along the circumference, which would require a lot of small triangular shell elements, and thus save a substantial amount of computer memory, the so-called line source (sink) approach first developed by Barone and Caulk [24] and further extended by Rezayat and Burton [25] for cooling channel simplification in three-dimensional parts was implemented. In this approach, the line source (sink) analog is applied to temperature and heat flux on each segment of the circular cooling channel. A schematic is shown in Fig. 4. In such a situation, for the elements on the axis of the jth cylindrical segment of the cooling lines, Eq 14 can be further extended and expressed by [25]

[[integral of].sub.[l.sub.j]] [[integral of].sub.[Gamma]] ([T.sup.*]q - [q.sup.*]T)d[Gamma]dl(P) + [[integral of].sub.[l.sub.j]] [[[sum].sup.N].sub.j=1] [[integral of].sub.[e.sub.j]] ([T.sup.*]q - [q.sup.*]T) d[Gamma]dl(P) = 0 (15)

where P, [l.sub.j], and N are the source point on the axis of the jth cylindrical segment, the axis of the jth segment, and the total segment number of the cooling channels, respectively. Details have been reported [24-26]. In the evaluation of the integrals over the cooling channel segments described herein, one can derive analytical expressions for integrals in the [theta] direction for circular geometry and thus avoid the necessity of a mesh for cooling channels in the azimuthal direction.

Similarly, the method described herein can also be applied to a gas channel represented by two-node elements attributed with equivalent diameters. However, the gas channel behaves like a heat source, in contrast with the heat sink behavior of cooling channels. The residual wall thickness (resulting from gas penetration) of the gas channel must be included for heat flux calculation. This approach not only minimizes the use of tiny triangular elements on the cooling channel surfaces, as well as the exterior gas channel surfaces, but also avoids the aspect ratios issue [27] that will increase the large number of triangular elements required for the mold exterior surface during analysis, considering the numerical stability caused by the aspect ratio issue.

Because the constant planar triangular element is implemented in this formulation, C = 1/2 for boundary points. The detailed mathematical procedure for this direct-formulation technique are described elsewhere [16-19]. After discretization over the boundary Eq 3 can be discretized into a set of linear equations

[H]{T} = [G]{q} [16]

where {T} and {q} represent column matrices for temperature and heat flux, respectively. By introducing the boundary values, Eq 16 can be rearranged to be in the form of

[A]{T} = {B} [17]

Solving Eq 17, the cycle-averaged mold wall temperatures, including plastic-mold interface temperature, are obtained. The mold cavity surface temperatures are then used to compute the polymer melt temperature profile and distribution by Eq 8. Equation 8 is solved by the finite difference method. For the gas channel, the heat conduction equation for the hollowed cylinder must be used, discretized and solved.

To test the numerical accuracy of the presently developed BEM software, a hollow cylinder was used, with both flat ends insulated and with the inner and outer lateral surfaces maintained at temperatures of 0[degrees]C and 100[degrees]C, respectively. The exact solution for the temperature in this case is simply a logarithmic variation with the radius. The numerical prediction was consistent with the exact solution [28, 29].

SIMULATED RESULTS AND DISCUSSION

All the material properties and the cooling operation conditions are of the simulations listed in Table 1. A plate part of semicircular gas channel cross-section design attached with a rib on its top was used as the analysis case. Three types of BEM models of plate parts and molds including [1] real gas channel geometry (case 1, Fig. 5a); [2] an equivalent gas channel approach represented by a circular gas channel (while keeping the top rib unchanged) meshed with triangular elements along the channel surface (case 2, Fig. 5b); and [3] a two-node element model of a gas channel similar to that of the cooling channel (case 3, Fig. 5c) were used. Due to the gas channel conversion, the distances from the gas channel surface to the cooling channels may be varied. Basically, triangular elements were implemented on the mold exterior surface, the parting surface, the part surface (cavity surface), and the surface of a semicircular gas channel (case 1) or the equivalent circular gas channel surface (case 2). The cooli ng channel mesh was also reduced and represented by a two-node element. Due to the small triangular elements required for the gas channel surface (case 1 and case 2) and the associated aspect ratio issue, the total number of triangular elements during analyses for both case 1 and case 2 is 4,824. Both cases require 4,056 triangular elements for the mold exterior and parting surface (half model due to the symmetry). For case 3, the required number of triangular elements is 180 for the part, plus 12 two-node elements for the gas channel. However, the required number for the mold exterior and the parting surface has been reduced to 1,064. As a result, the total BEM element numbers is 1,268 in case 3. For all cases, each cooling channel needs 16 two-node elements. Because of asymmetry of the gas channel shape referred to the parting surface, both the core side and the cavity side must be included in the BEM model for case 1, case 2 and case 3.

Simulated cycle-averaged mold cavity surface temperature distribution of the cavity side for a GAIM plate with real gas channel geometry modeling (case 1) is depicted in Fig. 6. Maximum temperatures are around middle locations of the gas channel. Also, around the plate center, the distance is farthest from the mold's exterior surface. Therefore, the mold temperatures show the highest values. For the GAIM plate with equivalent circular gas channel geometry modeling (case 2), the calculated cycle-averaged cavity surface temperature distribution for the cavity side is displayed in Fig. 7. In case 3, with the gas channel modeled by two-node elements while remaining top-rib unconverted, the predicted cycle-averaged cavity surface temperature distribution is illustrated in Fig. 8. The maximum and minimum values of the predicted mold surface temperatures of the cavity and core sides for all three cases are listed in Table 2. Due to the influence of the cooling system and mold configuration, the cycle-averaged mold wall temperatures may differ by 10[degrees]C even though the cooling channel design is symmetrical on the core side and the cavity side. The influence of the cooling system on the mold wall temperatures should not be neglected. Because of the existence of the gas channel, the maximum cycle-averaged temperature on the cavity side is higher than that of the core side by about 5[degrees]C. It can also be noted that on the cavity side, the differences in these predicted temperatures using three different models are only about l.5[degrees]C (minimum values) to 3[degrees]C (maximum values). On the core sides, the predicted values of case 1 differ from others by about 1[degrees]C to 3[degrees]C. Although the computer times for case 1 and case 2 are roughly the same, in case 3 they have been reduced by 93%. This does not include the additional time required to rebuild the gas channel surface and mesh model for analyses.

The calculated cyclic, transient variations of cavity wall temperatures at different locations of the plate and gas channel for case 3 are also shown in Fig. 9. The mold surface temperature measured at location P2 once the mold was open is also shown. It is also clear that within a steady cycle, the cavity surface temperatures may vary by as much as 15[degrees]C. A comparison of predicted cyclic, transient cavity wall temperatures at two gas channel locations designated as G1, G2 and one rib location identified as T2, using three different models, is given in Fig. 10. All three BEM models result in predicted values of less than a 3% difference. This indicates that the current CAE model used for the simulations of filling and packing phases can also be used for cooling simulation. However, skin thickness within the gas channel must be attributed to the CAE model for heat flux analyses. This does not require additional modeling. The cooling channel mesh (two-node elements), as well as the mold exterior mesh mu st be added in order to account for the influence of the mold cooling system. The mold exterior mesh can be further reduced and/or removed if the assumption of an adiabatic condition or a constant temperature on the mold exterior surface can be imposed.

CONCLUSIONS

This study investigated whether or not it is feasible to perform an integrated simulation for structural analysis, process simulation, and warpage calculation based on a unified CAE model for GAIM. Particularly, the modeling issue related to cooling phase simulation was investigated. Numerical algorithms, which were based on the same finite element mesh used for process simulation regarding melt filling, gas-assisted melt filling, and gas-assisted packing stages, were developed to simulate the cooling phase of GAIM using a three-dimensional modified boundary element technique. The cycle-averaged mold cavity surface temperature distribution within a steady cycle was first calculated based on a steady-state approach to account for the overall mold heat balance. The part temperature distribution and profiles, as well as the associated transient heat flux on the plastic-mold interface, were then computed by the finite difference method in a decoupled manner. Finally, the difference between the cycle-averaged hea t flux and transient heat flux was analyzed to obtain the cyclic, transient mold cavity surface temperatures. Three BEM models were analyzed, including a real gas channel surface and an equivalent circular gas channel surface meshed with triangular elements as well as an equivalent circular gas channel represented by two-node elements using a line source approach. The following observations were made:

1. Cycle-averaged mold wall temperatures may differ by 10[degrees]C because of the influence of the cooling system, even under the symmetrical cooling channel design on the core and cavity sides. Cavity surface temperatures may also vary by [sim] 15[degrees]C Within a steady cycle. Nonconstant mold wall temperatures should be considered for an accurate simulation.

2. The CAE model of real gas channel geometry requires about the same degree of freedom and CPU time compared with the CAE model defined by an equivalent circular gas channel using triangular elements along the channel surface. However, when the gas channel is further converted into the two-node element model based on the line source approach, the degree of freedom is reduced to [sim] 25%, and CPU time becomes 7% of the original real gas channel model.

3. The differences in maximum and minimum cycle-averaged temperatures on the cavity side in all three analysis models are only [sim] 30[degrees]C and [sim] 1.5[degrees]C One the core side, the differences are similar. All three BEM models result in predicted values in cyclic, transient gas channel temperatures within 3%.

4. This investigation indicates that it is feasible to achieve an integrated process simulation for the GAIM process under one CAE model resulting in great computational efficiency for industrial application.

ACKNOWLEDGMENTS

This work was supported by the National Science Council under NSC grant 87-2216-E033-007 and by Chung Yuan University under distinguished research funding.

SHIA-CHUNG CHEN, SHENG-YAN HU, and SHER-MENG CHAO

Mechanical Engineering Department

Chung Yuan University

Chung-Li, Taiwan 32023, Republic of China

REAN-DER CHIEN

Mechanical Engineering Department

Nan Ya Junior College

Chung-Li, Taiwan 32024, Republic of China

REFERENCES

(1.) K. C. Rush. Plast. Eng., July 1989 p. 35.

(2.) S. Shah. SPE Tech. Papers, 37, 1494 (1991).

(3.) L. S. Turng, SPE Tech. Papers, 38, 452 (1992).

(4.) S. Shah and D. Hlavaty, SPE Tech. Papers, 37, 1479 (1991).

(5.) A. Lanvers and W. Michaeli, SPE Tech. Papers, 38, 1796 (1992).

(6.) G. Sherbelis, SPE Tech. Papers, 40, 411 (1994).

(7.) S. C. Chen, N. T. Cheng and K. S. Hsu. Int. J. Mech. Sci., 39, 335 (1996).

(8.) S. C. Chen, K. F. Hsu and K. S. Hsu, Int. J. Heat Mass Transfer, 39, 2957 (1996).

(9.) S. C. Chen and K. F. Hsu, Numerical Heat transfer, Part A, 28, 121 (1995).

(10.) S. C. Chen, N. T. Cheng and K. S. Hsu, Int. Commun. Heat Mass, 22, 319 (1995).

(11.) S. C. Chen, N. T. Cheng and S. Y. Hu, J. Appl. Polym. Sci., 67, 1553 (1998).

(12.) S. Y. Hu, R. D. Chien, S. C. Chen and Y. Kang, Plast. Rub. Compos. Pro., 26, 172 (1997).

(13.) S. C. Chen, S. Y. Hu, J. S. Huang and R. D. Chien, Polym. Eng. Sci., 38, 1085 (1998).

(14.) S. C. Chen, S. Y. Hu, R. D. Chien and J. S. Huang, J. Appl. Polym. Sci., 68, 417 (1998).

(15.) C. Austin, SPE Tech. Papers, 31, 764 (1985).

(16.) T. H. Kwon, S. F. Shen and K. K. Wang, SPE Tech. Papers, 32, 110 (1986).

(17.) L. S. Turng and K. K. Wang, ASME J. Eng. Ind., 112, 161 (1990).

(18.) S.C. Chen and Y. C. Chung, Int. Comm. Heat Mass, 19, 559 (1992).

(19.) K. Himasekhar, L. Lottey and K. K. Wang, ASME J. Eng. Ind., 114, 213 (1992).

(20.) S. C. Chen and Y. C. Chung, ASME, J. Heat Transfer, 117, 550 (1995).

(21.) S. Y. Hu, N. T. Cheng and S. C. Chen, Plast. Rub. Compos. Pro., 23, 221 (1995).

(22.) J. P. Holman, Heat Transfer, 274, McGraw-Hill, New York (1989).

(23.) C. A. Brebbia, J. C. F. Telles and L. C. Wrobe, Boundary Element Technique, 60, Springer-Verlag, New York (1984).

(24.) M. R. Barone and D. A. Caulk, J. Applied Mech., 35, 311 (1985).

(25.) M. Rezayat and T. Burton, Symposium of Advanced Boundary Element Methods: Application in Solid and Fluid Mechanics, T. A. Cruse, ed., Springer-Verlag, Berlin, New York (1987).

(26.) S. C. Chen and Y. C. Chung, Int. Commun. Heat and Mass, 21, 323 (1994).

(27.) S. C. Chen and S. Y. Hu, Int. Commun. Heat Mass, 18, 823 (1991).

(28.) S. C. Chen, S. Y. Hu and W. R Jong, to appear in J. Appl. Polym. Sci., 70 (1998).

(29.) S. Y. Hu, A Study on the Integrated Simulations of Structural Performance, Molding Process and Warpage for Gas-Assisted Injection Molded Parts, PhD thesis, Material Properties and Processing Parameters.

Material Properties and Processing Parameters.

1. Thermal properties of polymer melt and mold:

[K.sub.[rho]] = 0.15 W/m[cdotp]K, [C.sub.[rho]] = 2.1 kJ/kg[cdotp]K, and [rho] = 1040 kg/[m.sup.3]

[K.sub.m] = 36.5 W/m[cdotp]K, [C.sub.m] = 0.46 kJ/kg[cdotp]K, and [[rho].sub.m] = 7820 kg/[m.sup.3]

2. Flow rate of coolant: 10 1/min, Diameter of cooling channel: 10mm

3. Ambient air temperature: 25[degrees]C, Heat transfer coeeficient of nitrogen: 10 W/[m.sup.2][cdotp]K

4. Nitrogen temperature: 25[degrees]C, Heat transfer coefficient of nitrogen: 10 W/[m.sup.2][cdotp]K

5. Thickness of plate for the GAIM part: 2.5 mm

6. Initial polymer melt temperature: 230[degrees]C, Coolant temperature: 40[degrees]C

7. Mold cooling time: 35 seconds, Mold open time: 5 seconds

Maximum and Minimum Cycle-Average Mold Cavity Temperatures. Maximum/Minimum Maximum/Minimum (Cavity Side) (Core Side) Case 1 55.93[degrees]C / 46.36[degrees]C 50.73[degrees]C / 46.48[degrees]C Case 2 55.63[degrees]C / 46.26[degrees]C 52.85[degrees]C / 45.46[degrees]C Case 3 58.60[degrees]C / 47.86[degrees]C 53.89[degrees]C / 46.76[degrees]C

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Author: | CHEN, SHIA-CHUNG; HU, SHENG-YAN; CHAO, SHER-MENG; CHIEN, REAN-DER |
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Publication: | Polymer Engineering and Science |

Date: | Mar 1, 2000 |

Words: | 5302 |

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