A study of rib geometry for gas-assisted injection molding.
The development of the gas-assisted process for injection molding has received increased attention during recent years. When gas is injected to assist filling and packing, many of the problems such as sink marks in thick ribs and warpage in large thin plates with conventional injection molding can be overcome. However, with gas interacted with melt, many traditional design guidelines may not be applicable to gas-assisted molding design. To enable better application of GAIM, systematic investigation of design guidelines is needed. Rib design guidelines are among the most essential ones.
Many injection molded parts are large, thin, plate-shaped parts, which are typically strengthened with structural ribs. Rib design guidelines for conventional molds are well established. The width w of the rib should be less than half the part thickness t to prevent sink marks, according to guidelines suggested by Fallows (1). To verify whether this guideline is applicable to molds for gas-assisted molding, a part with rib of w/t 0.5 was molded by means of gas-assisted injection molding. Results indicate that after short-shot, the gas was not able to displace the melt, and thus the cavity was not completely filled (2). Obviously, the rib design guidelines for conventional molding cannot be applied directly to gas-assisted molding. Available literature on gas-assisted injection molding is mostly general introductory (3-6) or theoretical (7-11). Zheng et al. (12) and Findeisen (13) carried out analytical and experimental studies on gas-assisted injection molding, but did not focus on fundamental rib design. Baxi (14) suggested several proven rib geometries for GAIM molds. However, these have not been systematically investigated.
In this study, the effect of rib geometry, including aspect ratio and fillet geometry, on GAIM are investigated. The criteria examined are moldability, and the geometry and position of the void formed in the rib section. The range of allowable short-shot weight variations to produce good parts is selected as an index of moldability: the wider the allowable short shot variation, the better the moldability. The geometry and position of the voids formed in the rib and their relation to part rigidity are observed with sliced cross sections and tested with bending loads. To aid understanding of melt-gas interaction phenomena and geometry of the formed void at various sections for different rib shapes, the gas-assisted injection molding processes are observed using a flow visualization facility.
Machine, Gas Injection Unit, and Molds
Gas-assisted injection molding experiments were conducted with a 4.1 oz injection molding machine (Cheng-Shong SM-80, Taiwan). A lab-made gas injection unit was attached to the machine. The gas injection system was composed of a nitrogen tank, pressure regulators, valves, a solenoid, and a controller for gas-injection delay control as shown in Fig. 1. The gas pressure could be regulated with a pressure regulator (TKR-100, Japan). When the valve was opened by the solenoid, the gas with regulated pressure was injected through the injection needles in the cavity. The timing was controlled by the signal from the controller. A counter circuit was triggered by the melt-injection signal from the injection molding machine. After a preset delay, a DC voltage was applied to the solid-state relay. The solenoid then opened the valve to the gas injection needle.
The mold was composed of two plates (as shown in [ILLUSTRATION FOR FIGURE 2 OMITTED]) clamped vertically between platens of the machine. A thick tempered-glass window with rubber sealing was mounted on the upper plate to allow for flow visualization. The cavity bottom piece was seated on the lower plate. The bottom piece was exchanged for molding parts with different rib shapes. The part geometry for three types of ribs, i.e., ribs without fillet, ribs with straight and circular fillets are shown in Fig. 3. A-series ribs are of typical rectangular shape. B-series ribs are rectangular ribs filleted with 45 [degrees] edges at transitional comers. C-series ribs are rectangular ribs with circular fillets at transitional comers. A summary of the rib types with the width-to-thickness aspect ratios (w/t) used in this experiment is listed in Table 1.
Since these rib shapes are combined from basic geometry, a second set of molds was constructed to further analyze the contribution of these basic geometrical components to moldability and rigidity. This second set of molds had U-shaped cavity to lengthen the flow path as shown in Fig. 4. The rib cross sections are rectangular (R), semicircular (S), and trapezoidal (T) in shape.
To help understanding the effect of rib geometry on molding process, a high speed video camera (NAC-1000, Japan) was mounted above the glass window to record the displacements of the melt front and gas tip during filling and post-filling of gas-assisted injection molding. A stopwatch display showing the time elapsed since the start of molding cycle, and two LED displays, indicating melt injection and gas injection, respectively, were also recorded. An injection grade polystyrene PG-79 (CHI-MEI, Taiwan) was used in this study. The molding condition employed were:
maximum time for filling: 8 sec; injection speed and pressure (stage 1): 40%, 30%; injection speed and pressure (stage 2): 40%, 30%; rear zone set point temperature: 205 [degrees] C; front zone set point temperature: 220 [degrees] C; delay time after short-shot filling: 0.5 s; gas pressure: 60 kg/[cm.sup.2].
Indices for Comparing Rib Performance
Moldability and rigidity are key design and manufacturing criteria for rib performance. The range of allowable processing conditions to produce good parts has been selected as an index of moldability. A completely filled part with a gas penetration extending over 70% of the plate length (or 80% of the plate length in the U-shaped plate) is required. According to Yang and Liou (15), the two most sensitive parameters affecting the success of gas-assisted molding are short-shot weight and melt temperature. For the U-shaped plate cavity in the second set of molds, the operation windows showing the allowable variation in melt temperature and short-shot weight are used to compare the moldability of cavities with ribs of basic geometry. For the plate cavity in the first set of molds, the melt temperature is set at 220 [degrees] C, and a diagram showing gas penetration length versus variation in short-shot weights is employed to evaluate the moldability of cavities with ribs of different aspect ratios and fillet shapes.
Table 1. Rib With Different Aspect Ratios and Fillet Shapes. Aspect Ribs Ratio w/t Fillet A1 0.5 none A2 1.0 none A3 1.5 none A4 2.0 none B1 0.5 straight B2 1.0 straight B3 1.5 straight B4 2.0 straight C1 0.5 circular C2 1.0 circular
The shape of the rib, along with the geometry and location of the gas void formed, has a crucial effect on the part rigidity. For the ribs of basic geometry (from the second set of molds), the cross-sectional area and the height of each rib are designed to be nearly the same. The rigidities can then be directly evaluated based on the maximum bending strength in a three-point bending test. Since the cross-sectional areas of the ribs of different aspect ratios and fillet shapes are not the same, the rigidity of parts molded from the first set of molds cannot be directly evaluated with bending resistance. Only the shape and the location of gas voids are observed and used to predict the degree of weakening.
RESULTS AND DISCUSSION
Gas penetration distances vs. short-shot weights with melt temperature at 220 [degrees] C for ribs with different w/t ratios and fillet shapes are shown in Fig. 5. The allowable ranges of short-shot weight increase as the aspect ratio w/t's increase from A2 to A4. The moldability of non-filleted rectangular ribs improves as the width-to-thickness ratio increases. The slope also indicates the sensitivity of gas penetration distance to short shot weight. The sensitivity decreases with rib width, indicating that greater rib width improves the stability of GAIM process.
Adding a 45 [degrees] fillet near the comer as transition from the rib to the base could be expected to improve moldability. The moldability of ribs with straight fillets (B2-B4) and without fillets (A2-A4) are also compared in Fig. 4. Moldability is enhanced with the addition of fillets. The molded parts with narrow filleted ribs (B2, w/t 1.0) have wider processing ranges than those with non-filleted wider ribs (A3, w/t 1.5). Figure 4 further shows a comparison of moldability for ribs with different fillet shapes. Addition of circular fillets (C2) enhances the moldability slightly more than addition of straight fillets (B2).
Poslinski et al. (8) studied the isothermal gas-assisted displacement of viscoplastic liquids in tubes. They concluded that larger tube radius reduces the flow resistance, resulting in larger gas bubble velocity. This increases the extents of gas penetration. The hydraulic radius of wide and filleted ribs are larger than narrow and non-filleted ones, resulting in larger extents of gas penetration and better part moldability.
Flow Leading Effects
Rib aspect ratio and fillet geometry determine the degree to which the melt advancement in the rib leads that in the neighboring regions. They thus determine the melt front profile during cavity filling. The melt front profiles before gas injection for cavities with different rib shapes are shown in Fig. 6. These melt front profiles indicate that the initial conditions are different in cavities with various rib shapes for the subsequent gas-assisted filling.
The flow leading effect demonstrates the geometry-caused flow resistance difference. The resistance to flow of Newtonian fluid between two parallel plates at a distance t apart per unit width is
R = [Delta]P/q = 12[Mu]L/([t.sup.3]Fp) (1)
where P is the pressure at entrance driving the flow, q is the flow rate per unit width, [Mu] is the viscosity, L is the distance to the entrance, and Fp is the shape factor, which takes the edge effect into account (16). The shape factor Fp equals 1 for flow channels with infinite width and is less than 1 for those with finite width.
The ratio of flow resistance between the rib and the neighboring cavity is
[Mathematical Expression Omitted] (2)
Since the length ratio is close to 1 and the cube of the thickness ratio between cavity and rib [t.sub.cavity]/[t.sub.rib] is much less than 1, the flow resistance is always higher in the cavity; thus, the flow in the rib leads that in the neighboring cavity. The degree of leading effect depends on the shape factor F[p.sub.r], determined by the rib aspect ratio and fillet geometry.
The gas and melt flow interaction is even more sensitive to the flow resistance difference than simply melt flow; little variation in the flow resistance will result in large differences in the filling patterns during gas-assisted filling. Figure 7 shows the filling patterns in two cavities during gas-assisted filling. The geometry-caused flow resistance not only affects the initial melt front profile upon gas injection, but also influences the filling pattern during the subsequent gas-assisted filling.
Computer simulation of the GAIM process is expected to be an important aid to mold design and process optimization. Precisely accounting the geometry-caused flow resistance and accurately predicting the flow leading effects are the critical factors to the success of the simulation of the gas-assisted injection molding. However, most injection molding simulation models are based on Hele-Shaw-type flow. Shape factors are employed to estimate the geometry-caused flow resistance and thermal condition in rib sections. This approach would not be sufficiently precise for simulating the gas-assisted filling process, owing to the resistance sensitivity of the gas penetration as well as the complicated interaction between melt and gas flows. Chen et al. (17) have pointed out this challenge. They have attempted to simulate the melt front advancement during filling a cavity of plate with a rib of semicircular cross section. Rod and rectangular elements superimposed or interlinked to the shell elements are used to represent the semicircular rib. Further research to refine the approximation method is expected to ensure the accuracy of GAIM simulation.
Typical cross sections of molded parts with various rib aspect ratios and fillet shapes are shown in Fig. 8. Two distinct void sizes were observed: large and small. Most small voids formed during secondary penetration are circular in shape. The shapes of large voids depend on the aspect ratio and fillet geometry. With non-filleted ribs, triangular gas voids with large height-to-base ratios are formed near the rib roots. For ribs with 45 [degrees] straight fillets, voids of equilateral triangular shape are formed. For ribs with circular fillets, voids of semicircular shape are formed. The residual part thickness at the transitional corner is the most uniform in ribs with circular fillets. Because of this, the weakening effect of the void at the transitional corner in the circular fillet case is expected to be the least.
These two types of voids (large and small) are formed during primary and secondary penetrations, which occur in the gas-assisted filling [ILLUSTRATION FOR FIGURE 9c-d OMITTED] and gas-assisted packing/cooling [ILLUSTRATION FOR FIGURE 9e-f OMITTED] stages, respectively. The ratios of secondary gas penetration to total penetration for different rib widths are summarized in Table 2. From this Table, it is clear that the ratio of secondary to total penetration is higher in cavities with narrow ribs than those with wide ones, and this ratio of secondary penetration decreases with the addition of fillets, especially circular ones.
Gas Penetration Behavior (Primary and Secondary)
As soon as gas is injected, it seeks the path of least resistance for penetration. The flow resistance depends on L/[t.sup.3], where L is the distance from gas tip to melt front. Flow resistance for gas is minimum along the partially filled ribs. Gas penetrates along the rib, and the melt in the rib core is displaced. As shown in Fig. 9c-d, the gas pressure source moves forward as gas penetrates along the rib. At a certain point (depending on the shape of melt front), the flow resistance in other directions become comparable to that along the rib. The melt fronts in all directions are then pushed forward and soon fill the whole cavity (as shown in [ILLUSTRATION FOR FIGURE 7 OMITTED]).
During gas-assisted packing and cooling [ILLUSTRATION FOR FIGURE 9e-f OMITTED], the specific volume of the melt decreases as temperature drops. If the P-V-T behavior of the melt is described by a Spencer-Gilmore equation of state, the specific volume of the melt as function of temperature is
v = RT/(P + [Alpha]) + [Beta] (3)
where R, [Alpha] and [Beta] are constants. Since the rib portion is thickest and is slowest to cool, the gas penetrates along the rib. For the cavity with narrow rib such as w/t ratio of 1.0, the capacity or gas to displace the melt during gas-assisted filling (primary penetration) is extremely limited. But the gas easily penetrates as melt shrinks during gas-assisted packing and cooling. As a result, most penetration distance is accomplished by secondary penetration, as shown in Table 2. The small void formed by secondary penetration provides a channel for gas to exerting pressure for packing, effectively preventing sink marks without greatly degrading the rigidity. Secondary penetration phenomena are best used in critical sections, where no sink marks are demanded but rigidity cannot be sacrificed.
Table 2. Comparison of Secondary Penetrations in Ribs With Different Shapes. Secondary Penetration/Total Ribs Penetration (%) A2 100 B2 14.5 A3 33.0 B3 26.3 A4 30.0 B4 25.3
Moldability and Rigidity of Ribs of Basic Geometry
Figure 10 shows the operation windows for ribs of basic geometrical components, i.e. rectangular, semicircular, and trapezoidal (with the same area). The allowable ranges of operation for cavities with semicircular and trapezoidal shapes are similar, and are at least 10% wider than those with rectangular ribs. The moldability of cavities with semicircular and trapezoidal ribs is better than those with rectangular ribs. For moldability, rib geometry should contain a semicircular or trapezoidal component.
On the other hand, among the three basic geometrical components, a rectangular rib has the highest bending resistance. Table 3 shows the bending resistances of the molded parts with these three basic geometries. The bending resistance is best for parts with rectangular ribs, and is lowest for parts with semicircular ribs. For integrated functions of mold-ability for processing and rigidity for service, a gas-channel rib can be designed with a typical rectangular shape, and with semicircular fillets at transitional corners.
SUMMARY AND CONCLUSIONS
The effects of rib geometry were investigated in this work. The effects of width-to-part-thickness, and shape of transitional fillets on moldability and rigidity were examined. The gas-assisted molding processes for plates with various rib geometries were observed via the aid of flow visualization facilities.
The following conclusions can be drawn from this study:
1. Moldability improves with rib width. The limitation on rib width to avoid sink marks in conventional molding is removed with the gas-assisted molding technique. However, wide ribs increase the flow-leading effects. Flow leading affects the shape of the melt front before gas injection, which substantially influences the filling patterns during the stage of gas-assisted filling.
2. The addition of transitional fillets substantially enhances the moldability. Adding transitional fillets also smoothens out the shape of the melt front at end of short-shot filling. A circular fillet performs better than a straight one in improving moldability.
3. Voids formed during secondary penetration are small and circular in shape. Voids formed during primary penetration are large, and the shape depends on the rib geometry. Triangular voids with high height-to-base ratio, are formed with non-filleted rectangular ribs. Equilateral triangular voids are found with filled ribs.
Table 3. Bending Strength of Parts With Ribs of Basic Geometry. Melt Gas Bending temperature Pressure Strength Geometry ([degrees] C) (kg/[cm.sup.2]) (N/[mm.sup.2]) semicircular 210 50 3.72 semicircular 210 80 3.67 trapezoidal 210 50 4.18 trapezoidal 210 80 4.14 rectangular 210 50 4.74 rectangular 210 80 4.61
4. Comparison of parts with rectangular, semicircular, and trapezoidal ribs indicates that moldability is best with semicircular ribs, while rigidity is best with rectangular ones. For combination of rigidity and moldability, rectangular-shaped ribs filleted with semicircle at transitional comers are suggested.
The authors are grateful to the National Science Council of Taiwan, ROC, for funding this research under grant NSC 82-0401-E-002-199. The help from Grace Laboratory for polymer processing and Yuitsun plastic company is much appreciated.
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