1. Introduction
Polyvinyl Chloride (PVC) is one of the most widely used polymers due to its versatile nature; it is a durable and long-lasting material used for hundreds of healthcare and construction products around the world. This material accounts for about 20% of all plastic manufactured world-wide, second only to polyethylene [
1]. PVC’s flow characteristics lend themselves to extrusion for pipes and continuous parts. Early trials conducted using PVC in injection molding applications met with very unsuccessful results due to the higher viscosity of the melt polymer during the filling stage in plastic injection molding. PVC injection molding meets defects on molded parts which are similar to the other plastics [
2]. A different characteristic of PVC injection molding is that the melt PVC is sensitive to temperature, and the thermo-viscoelastic effect gives an additional temperature increase due to this higher shear rate in injection molding [
3]. Under a high temperature, melt PVC often decomposes and burns during the injection molding process [
4]. Until the low-viscosity PVC compounded for injection molding in the 1980s, injection-molding-grade PVC gradually contributed parts utilized in healthcare, industrial, and consumer goods [
5]. High-flow PVC for injection molding has made significant contributions to healthcare and consumer goods, for instance, the fittings of the blood pipelines for hemodialysis in healthcare, transportation pipelines for chemicals in industry, and water pipelines in the consumer market. The fittings of these pipelines directly connect as adaptors and/or veering connect as elbows to the extruded PVC pipes. These fittings are mainly manufactured via a PVC injection molding process. However, the ranges of the melt temperature and filling rate in PVC injection molding are limited due to PVC degradation [
6]. Under the real settings of the machine specifications, simulations by molding flow software have been successfully implemented to derive molding parameters for practical operations [
7,
8,
9,
10,
11]. To avoid PVC degradation during injection molding, simulations may also help to construct a successful set of parameters to enhance the molding efficiency by examining the temperature distribution of the cavity during the filling stage [
12]. The taper of the sprue for PVC injection molding may also induce degradation [
13].
The complexity of the chemistry of PVC in thermal degradation calls for several lumping procedures to handle it. Many studies have aimed to constrain the degradation of PVC in injection molding. One of the approaches is to add heat stabilizers into the PVC. Traditional added fillers, such as lead and/or calcium zinc, mixed with PVC may increase the temperature of PVC degradation and decrease the release rate of hydrogen chloride (HCl) from PVC. However, the PVC industry made a voluntary commitment to replace lead-based stabilizers by the end of 2015 [
14]. Organic-based stabilizer is thus an approach to successfully decrease the HCl release rate from PVC [
15]. Another approach is to absorb HCl, which is the start of the degradation chain reaction [
16,
17]. By using nanometer particles of silica to absorb HCl, it was verified that the degradation temperature was thereby elevated, with a minor effect on color change of the compounded sample [
18]. By simulation of the temperature distribution in the filling stage, molding parts can be produced under degradation-free conditions in injection molding. A filling simulation of PVC injection molding must be very particular due to its high viscosity and high temperature sensitivity. The viscosities of the melt PVC in the runners and gates of a mold with multiple cavities are of different levels, even when the runners and gates of the cavities are laid out in a geometric arrangement. These different viscosities in the gates and runners are induced by the non-symmetric distribution of the shear rate, which leads to imbalanced flow fronts into symmetric cavities in the geometry. Two principal factors affect filling imbalance in injection molding: the shear rate distribution of the melt polymer and the temperature distribution of the mold [
19]. Simulation is desired to handle this phenomenon of imbalanced filling effectively [
20]. Via the three procedures of response surface methodology, the Taguchi method, and artificial neural networks, the filling balance can be optimized on the basis of the injection rate, melt temperature, mold temperature, and geometry of the runner. The artificial neural network approach is the most efficient optimization procedure to solve the imbalance phenomenon [
21].
By the Taguchi method and an artificial neural network, a set of optimal process parameters can be derived. The most important factor of the injection parameters affecting filling imbalance is the shear rate of the melt polymer [
22]. A “melt flipper”, which is a melt rotation technology, was inserted at the intersection of the primary and secondary runners to reduce the shear rate variation across the melt [
23,
24]. The numerical results showed that this flipper reduced the imbalance in an “H”-patterned eight-cavity runner system [
25]. Geometrically balanced multi-cavities of a mold do not ensure uniform filling in injection molding. Under a greater filling pressure, the firstly filled cavity may induce leakage of the melt polymer. Polymer leakage occurs in the form of plastic burrs associated with the molded parts acquired under this filling imbalance in plastic injection molding. Filling imbalance can also lead the firstly filled cavity to an over-packing situation [
7]. The short-shot technique by an empirical approach [
10,
11] can reveal filling imbalance. Based on the revealed results, the sizes of the runners and/or gates of the mold can be changed using machine tools via a traditional trial-and-error approach. In the design phase, simulation is an essential approach to define the sizes of the runners and gates of a multi-cavity mold.
Before injection molding, molding flow simulations, in the early stage of the design phase, reveal not only the temperature distribution under degradation of PVC injection molding, but also the filling imbalance of multiple cavities of the mold. Using the simulation results, the design details on the mold dimensions can be changed to optimize the design, and the operation parameters for real trials can be enhanced for successful molding. Once filling imbalance is present within the injection mold, the mold must be dismantled to change the sizes of runners and/or gates using machine tools, which increases the cost of time and tooling. More efforts are required to address filling imbalance in PVC injection molding thanks to its temperature sensitivity affecting the viscosity of the melt polymer. Beyond changes to the sizes of runners and gates, this study aims at constructing a multi-stage injection rate method in the filling stage using Moldex3D [
26] to reduce the filling imbalance of a multi-cavity mold for PVC injection molding. Based on existing imbalanced PVC fittings, the numerical model under the PVC properties, injection parameters, and machine is compared. Using the Taguchi method to optimize the molding parameters, a new setting for a multi-stage injection rate is established and implemented to reduce filling imbalance in the multi-cavity mold. With this new injection rate setting, experimental injection-molded PVC fittings are then used to verify the numerical results.
2. Materials and Methods
The polymer in this study is a rigid PVC of Suspension S-60 [
27], from Formosa Plastic co. Suspension S-60 is a standard material used for the injection molding of PVC fittings [
28]. The following are some of the properties used for the simulation: density, 1400 kg/m
3; coefficient of thermal conductivity, 0.08 W/(m °C); and Vicat softening Temperature, 76 °C. The PVC was measured using a differential scanning calorimetry (DSC) instrument (TA Instruments Discovery DSC 25, New Castle, DE, USA) under a nitrogen atmosphere. Suspension S-60 PVC was heated to 240 °C under a ramp of 10 °C/min, held isothermally for 1 min, cooled to 25 °C at a rate of 10 °C/min, held isothermally for 1 min, and heated to 250 °C again at 10 °C/min for the melting temperature measurements. As shown in
Figure 1a, the Suspension S-60 PVC analyzed via DSC presented starting melt temperatures of about 109.9 °C; a peak melting temperature occurred at 111.1 °C. The heating enthalpies of the first and second peaks were 9.7526 J/g and 0.1043 J/g, respectively. The glass transition temperature was 74.9 °C.
Figure 1b depicts the PvT data (Pressure, Volume, Temperature) of Suspension S-60 PVC measured using a pvT-500, GÖTTFERT (Buchen, Germany). The specific volume of Suspension S-60 PVC varies with pressure and temperature. Under zero pressure, the specific volume can change significantly at the 77 °C encountered during processes such as the injection molding of PVC. The significant changes in specific volume in this figure gradually increase with respect to the endured pressure. In
Figure 1c, the specific heat curve of Suspension S-60 PVC was also measured using the previously mentioned DSC instrument. Below 75 °C, the specific heat of PVC is constant. The specific heat increases when the temperature is greater than 75 °C. The maximum value of the specific heat of PVC occurred at 207 °C. Thermo-gravimetric analysis was applied to derive the degradation temperature of PVC using a Netzsch STA 409PC. Suspension S-60 PVC showed weight loss at 210 °C in
Figure 1d. Careful control of the PVC temperature below this temperature may avoid thermal degradation of the PVC.
Figure 1e shows that the shear rate and temperature of the S-60 PVC are negatively proportional to their viscosity.
Below 110 °C, the thermal conductivity of PVC is 6.254 × 10
−4 (W/cm °C), while from 110 to 170 °C, the function of thermal conductivity of melt PVC is 5.698 + 0.005055T (W/cm °C). The thermal conductivity of melt PVC is 8.024 × 10
−4 (W/cm °C) once the temperature is greater than 190 °C. The viscosity of this Suspension S-60 PVC is given by the modified Cross model [
26] as
where
is the shear rate of molten PVC,
n = 0.257813,
, and
T is the temperature of the molten PVC in degrees Kelvin.
Figure 2 shows the molding parts of twelve PVC fittings. Each fitting has a 32 mm outer diameter and a 90° elbow for water supply. The thickness of this fitting is 3.5 mm. The diameter of primary runners is 10 mm, and the secondary runners are 8 mm in diameter for the outer four cavities and 7 mm in diameter for the others. The filling gates of the twelve cavities are 3.0–4.2 mm.
Figure 2a shows an isometric view of the molded parts including the runners and the core of the sprue.
Figure 2b shows the top side of the molded 90° elbows. The whole sizes of the molded parts are 302 mm in length, 200 mm in width, and 60 mm in height. The pitch of the cavity is 22 mm. The bottom side of the molded 90° elbows is shown in
Figure 2c.
Figure 2d presents an isometric view of cooling channels within the core plate and molded parts, as well as the runner. Straight cooling pipes compose the cooling channels around the molded parts. The cooling channel within the cavity plate is shown in
Figure 2e.
The filling gates 4.2–5.0 mm in diameter allow the high-viscosity molten PVC material to flow into the mold cavity. The diameter of the primary runner is 9.8 mm, and those of the secondary runner are 8.0 mm for the outer four cavities and 6.0 mm for the inner eight cavities. Each fitting elbow of a cavity is 32.7 cm
3 in volume. The gates and runner have a volume of 46.2 cm
3. The solid mesh of the molded parts has 268,440 elements. The mesh of the cold runner has 36,814 elements. As shown in
Table 1, the initial injection parameters were a mold temperature of 40 °C, a PVC melt temperature of 175 °C, a filling time of 12.197 s, a cooling time of 40 s, a mold opening time of 5 s, and a cycle time of injection molding of 57.8 s.
Within the experiment and simulation, a 260-ton CI-260E injection machine (Creator, Kaohsiung, Taiwan) was used. This molding machine has screw diameters of 66 mm in the feed section, 85 mm in the transition section, and 77 mm in the melting section; a maximum screw stroke of 225 mm; a maximum injection pressure of 173.4 MPa; and a maximum injection weight of 626 g. The revolution speed of the screw is 25 rpm. The simulation analysis was performed using Moldex3D software. Following the pvT model in
Figure 1b, the melt PVC is a compressible and generalized non-Newtonian fluid under the modified Cross model in Equation (1). In the filling phase, the velocity and temperature are specified at the mold inlet. On the mold wall, the non-slip boundary condition is applied, and a fixed mold wall temperature is assumed. The finite volume method was used to discretize the Navier–Stokes equation based on the pressure-based decoupled procedure and solve the transient flow field in a complex three-dimensional geometry in Moldex3D. Modeling the flow field in Moldex3D is an iterative decoupled procedure for coupling velocity and pressure, in which the linearized momentum equations are solved for an initial estimated pressure field, followed by the solution of the pressure correction equation. Then, the mass fluxes and pressure are corrected in iterative calculations until the prescribed convergence condition [
9].
According to the injection parameters and machine, the molded parts under 75% and 98% filling by short-shot testing are presented in
Figure 3. A 75% short-shot sample was produced by the injection machine, shown in
Figure 3a. This 75% short-shot of the experimental injection PVC fitting was compared to the flow front on the top side of the PVC molded parts via a numerical approach, as shown in
Figure 3b. The profile of the experimental PVC molded parts agrees qualitatively with the simulated flow front of the parts. In
Figure 3c, the profile of the top surface of the PVC molded fittings produced by about 98% short-shot testing indicates a close fit with the numerical flow front, as shown in
Figure 3d. The outer four cavities of the mold are totally filled with melt PVC. However, the inner eight cavities are short-filled with melt PVC. This filling imbalance in the multi-cavity mold provides significant evidence of the prediction accuracy of the experimental and numerical results.
For improvement of the filling imbalance, a traditional approach is to enlarge the sizes of the gates and secondary runners of the mold to better balance the filling. In this study, the injection rates of four stages during filling were set at several levels according to the Taguchi experimental plan to reducing filling imbalance beyond the enlargements of gates and runners. The optimized four stages of filling rates at three different levels are selected and tabulated in
Table 2. The interactions between the parameters were not considered in this study. The levels of the parameters were selected based on the empirical operations and discussions through the injection molding process. From the number of parameters and number of levels in
Table 3, the use of the experimental layout L9 model was carried out to derive the responses by smaller-is-better signal to noise (S/N ratio) estimation. The effects induced by the noise factor, the uncontrolled factor in system, should be minimized since the noise is the result from all errors encountered in experiment. A higher value of S/N ratio indicates a minimum effect of the noise factor [
29,
30]. By S/N ratio, Taguchi method identifies the control factors and then moves the mean to target a smaller effect of the S/N ratio for optimization of the levels of control factors. In this study, the smaller differential imbalance fillings indicate better values, the corresponding S/N ratio (dB) is
where
n is the number of replications and
y is the experimental value [
31].