Numerical mold-flow simulations and experimental measurements for injection-molded lenses have been investigated in form accuracy on a two-cavity mold with various process conditions. First, form profiles of the molded lenses have been measured together with the corresponding simulated mold-temperature distribution and displacement distribution of the lens in the z direction. A flow-through type layout of cooling channels has been devised for balance of mold-temperature distribution in mold cavities with various parametric distances for assessments in uniformity of temperature distribution. Finally, a compression-molding process is proposed for the post-process of birefringence relaxation as well as adequate form accuracy of lenses. In conclusion, optimization of process parameters to achieve good form accuracy in a multicavity mold with symmetric geometry but nonuniform cooling conditions is difficult. A good design of cooling channels plus optimized process conditions could provide uniform mold-temperature distribution so that molded lenses of good quality would be possible. Then, the profile deviation of lenses could be further compensated by profile geometry corrections. In conclusion, the post-compression-molding process could make birefringence-free plastic lenses with good form accuracy.
© 2014 Optical Society of America
Optical theory has progressed for more than five centuries since Kepler published his papers on geometric optics. During the Middle Ages, scientists invented optical instruments to satisfy research interests in observation of micro-organisms and the mysterious universe. With the advent of optical engineering in the last decade, many consumer products based on optical image technology have appeared in our daily life. Inside the consumer products, lenses are among the essential components for capture or display of images. Because of the mass production in consumer products, cost reduction is always a challenge to the optics industry. Since the materials of lenses are either glass or plastics, glass lenses are made by grinding and polishing, whereas plastic lenses are made by injection molding or compression molding. Although glass lenses exhibit optical performances better than plastic lenses, it is typically laborious to manufacture glass lenses due to time-consuming grinding and polishing processes. On the contrary, the injection-molding process is known for the most effective mass-production method to date. However, the complex thermal-mechanical process in a short time has given the molded lenses various quality problems. From the literature [1–3], we know the image qualities of injection-molded lenses are mainly affected by two physical optics phenomena, namely residual birefringence and geometric surface deviations.
Based upon photoelasticity theory, the residual birefringence of isotropic optical polymers is described as linear dependence between residual stresses and refractive indices of materials as follows :5–7]. During the injection-molding process, polymer resins are heated to molten state, injected into the cavity under pressure in the filling phase, packed to compensate shrinkage due to cooling in the packing phase, and then cooled down in the cooling phase. Finally, the moldings are ejected into the ambient environment. In the filling and packing phases, shear stresses occur and molecules are frozen, resulting in flow-induced residual birefringence. Later, the thermal-induced residual birefringence is attributed to the frozen stresses from nonuniform cooling in the packing and cooling phases.
Geometric surface deviations are a major quality issue in all optical lenses, especially in injection-molded lenses. In the past two decades, many researchers have focused on the analysis of warpage behaviors between thin-shell parts and injection-molding process parameters [8–13]. The major process parameters are packing pressure, melt temperature, and mold temperature. High packing pressure, low melt temperature, and low mold temperature tend to largely reduce parts warpage. However, the results would be cumbersome to be exercised on the shop floor because process-window limits would not allow such processing conditions. It should be noted that the effects of cooling design on the warpage have not comprehensively studied in the literature. Since the design of the cooling channel affects the temperature gradient and uniformity of mold cavities, it is very interesting to note that residual birefringence could be relaxed down to 10% through the temperature annealing process . Furthermore, lenses with residual stresses would degrade the optical quality even after six months. Hence, stress relaxation is a necessary procedure for injection-molded lenses to circumvent quality variations versus time .
The compression-molding process has been developed for more than three decades with the product characteristics in low residual stresses compared to the injection-molding process . Therefore, compression molding has great potential for post-process of injection-molded lenses to relax most residual stresses. In recent years, compression molding has been widely used for manufacture of small aspheric glass lenses with satisfactory qualities [15–17]. It is reported that residual stresses are low at high mold temperature in compression-molded lenses, whereas high form accuracy can be achieved at low mold temperature and low cooling rate .
In this study, a two-cavity experimental mold, with various topographic layouts in cooling channels, is adopted for analysis of the form accuracy in injection-molded lenses based on settings of mold and melt temperature verified by experimental data. Three-dimensional (3D) mold-flow simulations are employed for observation of the mold-temperature distribution and part-displacement distribution in the z axis. To achieve uniform temperature distribution in each cavity, a flow-through layout type of cooling channels is selected with parameterization among the distance to the runner, the diameter of the cavity, and the diameter of the cooling channel. Based upon systematic methods to assess process parameters on optical qualities , injection-molded lenses with optimized process parameters in regular form accuracy are molded into preforms. A comprehensive study of compression-molded lenses is conducted with design of experiment (DOE) methods based on the Taguchi scheme for molding of birefringence-free lenses.
2. Experimental Apparatus
A. Materials of Lenses
This study uses cycle olefin polymer (COP) in optics grade for moldings of lenses; the trade name is ZEONEX 480R, produced by Zeon Corp., Japan. The main advantages of ZEONEX are high transparency, high heat resistance, low water absorption, low birefringence, and chemical resistance.
B. Design of Mold
A two-cavity injection mold with various layouts in the cooling channel is designed to study the effects of the cooling channel with basic schematics shown in Fig. 1. The runners and cavities are symmetric at the sprue, but the cooling channels are arranged around each cavity differently. The mold cavities are plano–convex shape with diameter of 25 mm, curvature radius of 70 mm, and maximum thickness of 1.125 mm. As the conventional lens design, a 3.5 mm rib with 0.8 mm thickness is adopted for the lens holding fixture outside the lens periphery. Cavity lens1 is close to the inlet and outlet of the cooling channel; hence the temperature gradient would be large due to the differential temperature between inlet and outlet ports. Cavity lens2 is at the opposite side close to the cooling channels. The temperature gradient is small and in better uniformity.
C. Compression-Molding Machine
An in-house built compression-molding machine is equipped with instruments for experiments of lens molding. Figure 2 shows the structural schematics and photo picture of the compression-molding machine not showing the instrument cabinet. The basic mechanical specifications are maximum compression forces at 2.5 kN, maximum die temperature below 250°C, and die-position resolution at 10 μm. Figure 3 shows a schematic plot of the die temperature during a complete cycle with stage A being a preform loaded in the die and then compressed before heating, stage B being a compressed preform at constant die temperature and load until cooling, and stage C being a slowly cooled die until the releasing temperature is reached. All the captioned parameters in the figure are assumed to be pertinent process parameters initially before the design of experiment data is analyzed. In the experimental investigation, all measured data are recorded for process parameter screening as shown in Fig. 4, where the die temperature, load forces, and die position are plotted in different color lines in a complete compression-molding cycle from a test run.
3. Form Accuracy Analysis
In the injection-molding process, the warpage of parts is mainly affected by packing pressure, melt temperature, and mold temperature [8–13]. To analyze the effects of the layouts of cooling channels, melt temperature and mold temperature are specifically chosen for key factors because of the cooling effects in the mold-temperature distribution. Due to the asymmetric layouts of the cooling channels, each cavity in the mold would experience different thermal-mechanical history and make the lenses show different form profiles. To further verify the above-mentioned behaviors, an instrument, called Ultra Accuracy 3-D Profilometer (UA3P), and made by Panasonic Corp. Japan, has been employed for the form accuracy measurements of molded lenses along the gate-wise and transverse directions.
As a further step to assess lens quality under uniform cooling in cavities, a commercial mold-flow analysis program, SigmaSoft, copyrighted by SIGMA Engineering GmbH in Aachen, Germany, has been chosen for 3D simulation of complete injection-molding processes with predictions of the temperature distribution inside the mold and the displacement distribution in the z axis when lenses are ejected to the ambient environment. Finally, rearrangement of cooling channels is conducted for uniform temperature distribution inside each cavity of the mold.
A. Injection-Molding Experiments
In order to analyze the effects of melt and mold temperature on lens profile deviations, two single-factor experiments set with three levels are chosen with the settings of parameters shown in Tables 1 and 2. Five random samples carefully cut at the gate edge several days after ejection from the mold are taken for each setting, and measured by UA3P. Tables 3 and 4 show the average result of form accuracy given in peak-to-valley (P-V) and RMS values. For lenses at Lens1, form accuracy becomes worse along with the increase of melt temperature and decrease of mold temperature. And form accuracy along the gate-wise direction is more sensitive to melt temperature than that along the transverse direction. The best form accuracy of lenses at Lens1 is low melt temperature when the mold temperature is set at 132°C. For lenses at Lens2, an increase in melt temperature deteriorates the form accuracy along the gate-wise direction but does not affect that along the transverse direction. Form accuracy with mold temperature set at 120°C is better than that from 108 and 132°C, respectively. Low melt temperature and mold temperature at 120°C would improve the form accuracy of lenses at Lens2.
Therefore, the form accuracy of lenses at Lens1 is best at melt temperature 275°C and mold temperature 132°C, whereas the form accuracy of lenses at Lens2 is best at melt temperature 247.5°C and mold temperature 120°C. It should be noted that Lens1 gives superior form accuracy to other conditions at mold temperature 132°C in Table 4. The rationale is the optimal process parameters happen to be the best molding conditions for the Lens1 cavity even though symmetry is considered in the mold design. This suggests that the form accuracy of the present two-cavity mold design is hard to improve by adjusting parameters due to the nonuniform cavity temperature resulting from the poor layout of cooling channels.
B. Verifications by Mold-Flow Simulations
A commercial mold-flow simulation program SigmaSoft has been chosen for simulating thermal-mechanical history in continuous cycles of the injection-molding process including preheat and external cooling effects. In the injection-molding process, heat is transferred from the polymeric melt to the cooling channels by convection, and the heat of the mold is dissipated into the ambient environment through conduction and convection. To calculate the rate of heat transfer by convection, the heat transfer coefficient is defined as follows :5 shows the simulated temperature distributions of the core side when the melt temperature is at 275°C together with the mold temperature at 120°C. The temperature difference between the two cavities is about 1.0°C with significant difference in temperature contour pattern. It is noted that the contour is longitudinal symmetric due to the temperature of the cooling channel only being able to be set at a constant value in simulation. On the contrary, the temperature difference between the inlet and outlet ports is 1 to 2°C from shop floor experiences. Based upon the layout of cooling channels, we note that the temperature distribution at Lens1 would be less uniform than that at Lens2 because the Lens1 cavity is close to the inlet and outlet ports, which exhibit large temperature difference. Figures 6 and 7 show the predicted distribution of displacement in the z axis of lenses after being cooled to ambient temperature. The color-shaded contours indicate that the displacement along the gate-wise direction is asymmetric, whereas the displacement along the transverse direction is symmetric. The displacement along the gate-wise direction is large because the temperature is relatively higher as shown in Fig. 5. It is evident that temperature distribution plays an important role in the form accuracy of lenses both at Lens1 and Lens2. In order to achieve uniform temperature distribution in each cavity, a new layout of cooling channels is proposed with the structural schematics shown in Fig. 8. To make the design parameter sensible for analysis, we define the layout of cooling channels as follows:
Figure 9 shows the temperature distribution at the end of the cycle with notable results for the temperature distribution of the cavity being uniform at . However, based upon the predicted displacement distribution shown in Fig. 10, the displacement distribution at is more symmetric than those from the other two cases. The rationale is that the shrinkage in the longitudinal direction is higher than that in the transverse direction in amorphous polymers so that shrinkage would increase along a gate-wise path because of the effects due to insufficient packing pressure . Therefore, the predicted displacement with uniform temperature distribution in cavities would still be asymmetric, and a nonuniform temperature distribution may contribute to more displacement in the z direction.
4. Compression Molding
In the study of injection-molded lenses, form accuracy and residual birefringence have been reported in detail elsewhere . Based upon the analysis of residual birefringence, flow-induced birefringence contributes more than 90% in total residual birefringence. Birefringence-free lenses are not available in the injection-molding process by simply adjusting process parameters or post-process annealing. Therefore, a compression-molding process is proposed to be a post-process of injection-molded preforms for birefringence-free with acceptable form accuracy. First, the preforms are molded by optimized parameters shown in Table 5 at the Lens2 cavity due to asymmetric cooling effects in the Lens1 cavity. Figure 11 shows the pertinent dimensions of injection-molded preforms. A circular polariscope is adopted for measurement of residual birefringence based on the principle of photelasticity as shown in Fig. 12 . The fringed pattern of a sample preform is shown in Fig. 13. In our previous study , residual birefringence decreases with increase in die temperature, but form accuracy is improved by decrease in die temperature with slow cooling rate. Therefore, a two-stage cooling process—slow cooling above the reference temperature and then fast cooling to ambient—is employed for short cycle time and better form accuracy. To relax residual birefringence and maintain good form accuracy, die temperature and reference temperature play an important role in the process. Furthermore, setting of load forces in the cooling phase is critical in the compression-molding machine because high load forces at high die temperature result in high melt flow to generate molecule orientation. Based on Taguchi method, seven main factors including load forces, compression time, cooling load forces, control mode, first switch point of temperature, second switch point of temperature, and die temperature are selected for two-level settings and the corresponding orthogonal array and settings of control factors are shown in Tables 6 and 7. In the above process parameters, the first switch point of temperature sets the temperature for reduced cooling load to change to second load, and the second switch point of temperature sets the temperature to change to third load and also sets the cooling rate to fast cooling, the same as the reference temperature. The control mode is the machine setting in the cooling phase. Force control is used to control the load as the setting of constant cooling load or reduced cooling load, and position and force control are used to make the die fixed first and then set to force control when the load is lowered to the third cooling load. The form accuracy of all molded lenses is measured by UA3P and averaged by three samples as shown in Table 6, and Fig. 14 shows the measured residual birefringence. Based on the “smaller-the-better” characteristics defined as follows [21,22]:15 and 16, birefringence is only affected by the die temperature. and form accuracy is affected mainly by the second switch point of temperature. The temperature setting for switching to fast cooling plays an important role in form accuracy of compression-molded lenses because the molded lenses are cooled rapidly only in solidus state as the temperature sets below the glass transition temperature. In order to relax residual birefringence, it is necessary to set high die temperature and the corresponding optimized process parameters as shown in Table 8. The residual birefringence in the lenses is fully relaxed as the fringed patterns shown in Fig. 17 with the homologous P-V value being 0.693 and 0.871 μm, and the RMS value being 0.127 and 0.160 μm.
In this paper, the effects of layout in cooling channels, melt temperature, and mold temperature on the form accuracy of injection-molded lenses have been investigated both in experiments and in numerical simulations. High melt temperature degrades the form accuracy with dominant effects in the gate-wise direction but not in the transverse direction. The influence of the original layout in the cooling channels on the mold-temperature distribution in each cavity is significant. Based on the analysis results, the form accuracy of lenses at Lens1 is superior to that at Lens2 with mold temperature at 132°C. It is evident that optimization of process parameters for a multicavity mold with inappropriate layout of cooling channels is barely possible. To improve the layout of cooling channels, various design options in cavity distance, the diameter of the lens, and the diameter of the cooling channels are planned and assessed. As a result, the case of gives uniform temperature distribution in cavities but asymmetric displacement distribution in the gate-wise direction due to insufficient packing effects. It is noted that the form accuracy could be improved by profile compensation in practice. Finally, uniform temperature distribution in each cavity has been devised in this study to achieve better control of form accuracy.
As a further step to comprehend the residual stress relaxation in molded lenses, the effects of process parameters on quality for compression-molded lenses have been studied by the DOE method. Based upon the analysis in the L8 design, die temperature plays the dominant role for total residual birefringence. However, increase in die temperature tends to degrade the form accuracy. Also from the analysis results, the second switch point of temperature is a dominant factor for form accuracy with the condition that it must be set below the glass transition temperature because the molded lenses are cooled rapidly only in solidus state as the temperature sets below the glass transition temperature. From the experimental results, it is noted that birefringence-free lenses with acceptable form accuracy could be compression molded if the process parameters are optimized.
The authors thank the Instrument Technology Research Center, National Applied Research Laboratories, for the support of measurement instruments, and the National Science Council in Taiwan, Republic of China, for research funds under Contract No. NSC100-2221-E007-039.
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