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Abstract
This work presents a novel nondestructive cavity pressure characterization approach in microinjection molding (μIM) through measuring 3D part thickness distributions. For this purpose, a plano lens was designed and experiments based on Taguchi method were conducted. Both overall and local lens thickness distributions under various process conditions were analyzed in terms of their relevance with the cavity pressure during molding. Unexpectedly, a reliable linear regression model was developed fulfilling nondestructive multi-point or even continuous cavity pressure characterization with the overall lens thickness distribution. Furthermore, the topography of the constructed 3D thickness surface was found to depend on both process condition and measuring position. Finally, the process conditions were optimized for obtaining uniform distributions of both 3D thickness and cavity pressure.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, polymer optical lenses have been widely employed in many areas such as sensing, imaging, light beam shaping, micro lithography and so forth [1]. The thickness, refractive index as well as radius of curvature are quite important for their optical performance since these parameters determine the focal length, location of principal plane and aberration [2,3]. With the simplest form, plano lenses have been extensively utilized as semi-reflectors or spectroscopes in a variety of optical applications. A typical example is the spectroscope in the Michelson-Morley experiment setup, in which the plano lens splits the incident ray into one reflected light and one refracted light. For such particular lenses with constant thickness, the radius of curvature doesn’t need to be taken into account anymore. Hitherto, considerable works have been carried out regarding the refractive index (or in another form of birefringence) of optical devices [4-5], shedding light on how to control and thus finally optimize the lens optical quality. Meanwhile, ensuring the thickness accuracy of the molded lenses is also extremely crucial for optical performance due to the fact that with thickness variation larger than the depth of focus of the imaging system containing the corresponding lens, serious distortion of the wavefront and thus the light signal may take place [6]. Although the surface shapes and thickness variations of optical devices have been frequently estimated with techniques like phase-shifting interferometry in recent decades [7], there are few studies available concerning the three-dimensional (3D) thickness distribution of thermoplastics lenses fabricated using microinjection molding (μIM), which is a promising cost-effective molding method for making thermoplastics polymer parts falling into the following three definitions [8-9]. (i) Micro-parts with weights in milligrams. (ii) Micro-featured parts having characteristic dimensions typically less than 100 μm. (iii) Micro-precision parts possessing tolerances in microns without an overall dimension limit. Therefore, it will be beneficial to μIM community to accurately characterize 3D thickness distributions of the lenses and optimize μIM process achieving better optical performance. This is especially the case with the constantly increased trend of adopting thermoplastics optical devices to replace the glass ones thanks to polymer’s advantages such as light weight, low cost, high productivity, high flexibility in product shapes, etc.
On the other hand, the cavity pressure is often considered as the dominant factor determining the final product quality in injection molding. A common practice for controlling the quality and cycle reproducibility is to compare the cavity pressure profile with the preset reference [10]. As the demand for high-quality thermoplastics lenses continues to increase, controlling the cavity pressure for μIM process becomes ever more crucial. For this purpose, sensors directly installed in the mold cavity have been frequently implemented, which allows detecting cavity pressures during injection molding and thus providing feedback for process control [11–13]. Alternatively, successful realization of cavity pressure acquisitions was demonstrated with pin-type sensors involving quartz pressure transducers inserted into bases of ejector pins, which takes full use of ejector pins and avoids extra places for pressure sensor installations [14]. However, the aforementioned direct measuring approaches have several drawbacks as stated below. i) The direct contact between the polymer melt and pressure sensors leads to potential erosion of the sensor surfaces. ii) The currently available pressure sensors have a minimal diameter around 1 mm, which is still much larger than the microcavity itself for some μIM cases. iii) More importantly, the embedment of the pressure sensors (or ejector pins) into cavities not only destroys the mold structure, but also causes surface defects of the optical devices, which influences product appearance and even functions. In order to overcome the foregoing drawbacks, researchers worldwide have proposed a number of indirect cavity pressure monitoring approaches to replace the direct ones in some applications, which can be broadly classified as destructive and nondestructive methods. The destructive methods involve pressure sensors installed in a certain position (e.g., in the runner [15]) except the cavity itself of the mold, which can effectively avoid product appearance defects caused by the sensor embedment. However, these methods still cause physical invasion of the mold and economic disadvantage. Moreover, they lack generality since the results greatly depend on the mold design as well as the employed polymer materials. In comparison, the nondestructive methods don’t depend on pressure sensors anymore. Good examples include correlating the cavity pressure with the surface strain of the fixed mold half [16] and characterizing the cavity pressure by combining the ultrasonic reflection coefficient, the mold temperature as well as the hydro-cylinder pressure of the injection machine [17]. Nevertheless, these approaches require complicated experimental setups. In addition, most existing cavity pressure sensing methods have only one measuring position, which is insufficient to obtain comprehensive pressure information and gain insight into the flow pattern. Therefore, it’s an urgent need to develop simple and nondestructive measuring methods realizing multi-point and even continuous measurements of the cavity pressure in μIM, especially for optical products with high appearance requirements.
It’s well known that short-shot and flash are two undesired while commonly appeared defects for injection-molded products, which are mainly caused by inadequate and excessive pressures, respectively [18–20]. This implies that the final geometry accuracy (e.g., the thickness accuracy) of the molded parts is strongly dependent on the cavity pressure during injection process and that monitoring both quantities is equally important. Inspired by such phenomena, the present paper proposes a novel nondestructive approach for characterizing the cavity pressure through simply measuring 3D thickness distributions of μIM parts. As thickness distributions can be experimentally determined (e.g., using the confocal microscope), the availability of the specific correlation between the cavity pressure and the achieved thickness at a certain location of the part becomes the key issue for realizing the proposed approach. For this purpose, new plano lenses were designed and fabricated using μIM. Experiments based on Taguchi method were conducted and the molded lenses were investigated for construction of 3D thickness distributions and characterization of the cavity pressure during molding. Furthermore, the process conditions were optimized for obtaining uniform distributions of both 3D thickness and cavity pressure. To the best knowledge of the authors, this is the first to realize continuous cavity pressure characterization through measuring 3D thickness distributions of μIM parts, achieving simultaneous and effective control of both quantities.
The feasibility of the proposed cavity pressure characterization method can be further explained with the help of μIM process illustration as shown in Fig. 1. The entire μIM process involves the injection, packing and cooling stages that are influenced by multiple molding parameters [Fig. 1(a)]. As far as the final part thickness is concerned, it’s dominated by the cavity pressure at the injection stage, and further affected by other factors such as part shrinkage as a result of material crystallinity, molding parameters and so forth [Fig. 1(b)]. In this way, influences of all other factors on the final part thickness can be treated as a black box, and a simple connection between the most important variable (i.e., the cavity pressure) and the final part thickness can be developed. It can be concluded from Fig. 1 that we are not neglecting but just skipping other influencing factors, which provides an easy and straight-forward way for controlling both cavity pressure and part thickness during μIM process.
Fig. 1 μIM process illustration concerning (a) key molding parameters and (b) influencing factors for the final part thickness.
2. Experimental methodology
2.1 μIM details
The designed lens dimensions are 40 mm for the diameter and 0.5 mm for the nominal thickness, respectively. In particular, for plastic optical components typically used in near-infrared region the surface roughness needs to be controlled within 30 nm [21]. Obviously, such lenses belong to the third category of μIM products according to the aforementioned definitions. A stainless-steel modular injection mold with changeable inserts was utilized, and an injection molding machine (PL1200/370V, Haitian) was adopted for μIM experiments. The surface roughness (Ra) of the machined mold inserts was verified with the microscope to be around 15 nm. As the molded products (i.e., lenses) are intended for optical purpose, a transparent thermoplastics polymer, polymethyl methacrylate (PMMA, ACRYREX CM-211), was selected as the molding material taking full advantages of its high light transmittance and easiness of being processed. This PMMA has a glass transition temperature (Tg) of 105°C, a solid density (ρ) of 1.2 g/cm3, and a melt flow rate (MFR) of 16 g/10min (ASTM D 1238).
To investigate effects of process conditions on 3D thickness distributions of the lenses, four variables, namely, the melt temperature (T), injection velocity (V), packing pressure (P), and packing time (t) were chosen. Each variable was specified in three levels as determined using the preliminary experiments. For instance, the three levels for the T (T1, T2 and T3) were set as 270, 285, and 300 °C, respectively. Similarly, V is from 60 to 100 mm/s with an interval of 20 mm/s, P is from 80 to 160 MPa with an interval of 40 MPa, and t is from 2 to 4 s with an interval of 1 s. Other molding parameters were set as below. Injection pressure = 170 MPa; Mold temperature = 30°C; Cooling time = 10 s. It should be mentioned that the set injection pressure (170 MPa) is high enough to ensure the highest injection velocity. In this manner, an orthogonal array L9 (34) for the Design of Experiment (DoE) based on the Taguchi method was utilized as shown in Table 1.
Table 1. Orthogonal array L9 (34) with the experiment results
2.2 Thickness characterization
The thicknesses of the investigated lenses were determined using a confocal microscope (DCM3D, Leica), which has three operation modes for thickness measurements, i.e., the single point, extended profile as well as topography modes. The last was employed in this study, with which not only the thickness of the transparent layer but also the surface shape of interfaces between the measured layer and the contacting media on both sides can be obtained. In order to ensure uniform interfaces, the lens was circumferentially supported to avoid direct contact with the rough surface of the microscope platform [Fig. 2(a)]. Accordingly, there are two interfaces existing for the measuring system, namely, interface 1 between the top surface of the lens and air above it, and interface 2 between the bottom surface and air beneath it. Inputs for both sample properties and operation parameters are required in order to initiate measurements. Specifically, the refractive indexes of the PMMA sample (n1) and air (n2) were set as 1.502 (measured value) and 1.000, respectively. To determine operation parameters including the thickness threshold, a preliminary thickness measurement using the single point operation mode was performed, which provides the confocal axial response with two peaks corresponding to interfaces 1 and 2 [Fig. 2(a)]. z1 and z2 are the height coordinates of the peaks (i.e., the positions of the two focused reflection planes), and hm is the difference in height between them. Due to the refraction effect taking place when the laser enters into substance with nonuniform refraction index (changing from n2 to n1 at interface 1 and then back to n2 at interface 2), hm differs from the real thickness of the sample (h). In this regard, hm can be considered as the virtual thickness of the sample resulted from the height distortion effect. Finally, h can be calculated automatically by the software from hm and the correction factor that compensates for the height distortion effect.
Fig. 2 Schematic representation of the proposed measuring methodology with different views: (a) frontal sectioned view, and (b) top view.
As a single laser-beam focused region has a small area of only 1.27 × 0.95 mm2, 261 measurements in total are required for stitching up the entire lens, which results in time-consuming operation. Therefore, unless otherwise stated, measurements were carried out only for five areas within the lens as denoted A1~A5 in Fig. 2(b). The three consecutive areas A1-A2-A3 are located in a diameter of the lens along the main flow direction, whereas A4-A2-A5 in another diameter perpendicular to the main flow direction (i.e., along the cross-flow direction). In this way, it’s reasonable to combine the five measurements to represent the overall thickness distribution of the lens.
3. Simulation
As stated earlier, sample data of the cavity pressure are needed to develop the formula correlating the lens thickness with the cavity pressure. It has been frequently reported that commercial packages specialized for injection molding (e.g., Moldex3D, Moldflow, etc.) are capable of capturing melt front [22] and cavity pressure [23] with very high accuracy, especially for simple cavity shapes. Considering the fact that the investigated lens in this study has a simple disk shape (Φ40 × 0.5 mm2), it is reasonable to use cavity pressure sample data from simulations instead of experiments involving destructive sensor installation.
Moldex3D R14.0 (CoreTech System Co., Taiwan) was employed for simulations, in which both the molten resin and trapped gas in the cavity were considered as incompressible fluids at the filling stage. Material data for simulations were obtained from the Moldex3D material database. The modified Cross WLF viscosity model as stated in the literature [24] was adopted in simulations to describe the polymer melt behaviors. In addition, in order to ensure the accuracy of simulation results, the lens geometry was meshed using 3D elements. Although boundary layer mesh (BLM) elements are frequently utilized in optical lens simulations for better performance, conventional tetrahedral ones were employed in the present study as the required outputs from simulations are only the cavity pressures closely related to the process parameters but having little to do with the mesh type. Finally, the meshed model possesses about 170 thousand nodes and 900 thousand elements, with ten-layer meshes generated across the thickness dimension. As the cavity pressure is a history during the injection process, the maximal value was taken for report under each condition.
To validate the simulated cavity pressure, additional experiments were carried out for directly capturing the cavity pressure. Considering the fact that installing pressure sensors into the plano lens mold cavity will lead to not only a long fabrication cycle but also damage of the lens appearance influencing the subsequent optical measurements, an existing injection mold with a strip-shape cavity (60 × 8 × 3 mm3) was used for validation experiments. The same material (PMMA, ACRYREX CM-211) as adopted for making plano lenses was employed. A Kistler pressure sensor (6190CA) capable of simultaneously sensing pressure and temperature was installed in the cavity with a distance of 25 mm to the injection gate. The process conditions for validation experiments were set as below. Melt temperature = 250°C; Mold temperature = 70°C; Injection time = 2 s; Injection pressure = 90 MPa; Packing pressure = 85 MPa; Packing time = 15 s. After stable running is reached, the cavity pressure at filling stage was obtained using the data acquisition system controlled by an industrial personal computer.
4. Results and discussion
4.1 Verification of the proposed noncontact measuring approach
For the noncontact thickness measuring approach with the confocal microscope, each measurement provides rich information on the lens thickness within an area of 1.27 × 0.95 mm2. Figure 3 illustrates the lens thickness in different dimensionalities from a single measurement, from which the thickness distribution can be obtained as shown in Fig. 3(c). It should be noted that the surface-averaged value of the thicknesses over the measured area was taken as the reported thickness for the corresponding measurement.
Fig. 3 Lens thickness distribution obtained with confocal microscope for a single measurement: (a) isometric view, (b) top view, (c) thickness distribution, and (d) & (e) 1D thickness profiles along a-a′ and b-b′ directions as indicated in Fig. 3(b), respectively.
To prove the feasibility of the proposed noncontact thickness measuring approach, a verification measurement was carried out first with a quartz glass flake having a thickness of 1.0 ± 0.1mm as the standard part. The obtained average thickness of three independent measurements is 1.0513 ± 0.00104 mm, which agrees well with the known thickness of the standard part. This validates the effectiveness of the non-contact thickness measurement approach.
To ensure the reliability of the proposed noncontact thickness measuring approach, the accuracy of the simulation results was also investigated. From Fig. 4, one can observe that the simulated cavity pressure agrees well with the experimental one, with a maximal relative error of about 6%. This suggests that the Moldex3D simulations performed in this study are enough to obtain the cavity pressure with a simple cavity shape, replacing the time-consuming experiments.
It should be mentioned that possible influences of the lens overall warpage/flatness as well as the tilt of the inserts/microscope-platform were also estimated in this work. According to our previous work [25], the largest overall warpage of the lenses (Φ40 × 0.5 mm2) under the poorest process condition is about 10% of the nominal thickness. Considering the small linear dimension (~1 mm) of the laser-beam focused region (1.27 × 0.95 mm2) for a single measurement in the present work, the involved warpage within each measurement can be estimated as 10% × (1mm/40mm) = 0.25% of the lens nominal thickness. Therefore, its effect on the thickness measurement accuracy can be safely neglected. Moreover, to evaluate the influence of the tilt of the inserts on thickness distribution, the parallelism of the two insert surfaces forming the cavity was measured using the confocal microscope. The possible maximal parallelism value across the insert diameter (40 mm) was estimated to be ~3 μm, which is one order smaller in magnitude compared with the maximal thickness difference of the lens. This suggests that the thickness error caused by the non-parallelism of the two insert surfaces can be also safely ignored. In addition, prior to obtaining the lens thickness information, a leveling operation was implemented by the software to remove the influence of the microscope-platform tilt on the measurement results.
4.2 Thickness distributions of the lenses
The thickness distributions of the lenses in this study include the overall thickness distribution and the local one, with the former mostly connected to the overall pressure distribution inside the mold cavity during filling, while the latter associated with the local behavior of the polymer melt as well as the resultant surface topography. Figure 5 demonstrates typical thickness distributions of the lenses molded under condition No.1. From the line plots at the lower right corner, one can find that in the main flow direction (along the three consecutive positions A1-A2-A3), the overall thickness experiences apparent decrease (from 533.7 μm at position A1 to 488.5 μm at position A3). This trend is similar with that of the cavity pressure variation, implying that the pressure distribution inside the cavity directly affects the lens thickness. Differently, in the cross-flow direction (along the three consecutive positions A4-A2-A5), the overall thickness maximizes at the middle location A2 and decreases slightly towards both sides. Theoretically, the thickness values at positions A4 and A5 should be identical due to the geometrical symmetry with respect to the gate. The discrepancy in the thickness measurements at these two positions may be caused by the variation in the roughness of the mold surface, which produced different flow resistances for the melt. It should be mentioned that the maximal thickness difference among the investigated positions within the lens under condition No.1 was obtained as 45.2 μm, which accounts for ~9.0% of the nominal thickness. Such large thickness variation may deteriorate the lens’s optical performance and needs to be reduced.
Fig. 5 Typical thickness distributions of lenses molded under condition No.1 in both measuring directions (in each image the white arrow and numbers indicate the thickness-decreasing direction and “High value”/“Low value” in the colorbar, respectively).
In addition to the overall thickness distribution, the local thickness distribution can be also easily identified through the color variation. The white, red, yellow, blue, and black colors represent different values of lens thickness in descending order. It should be pointed out that the color variation is independent for each measurement (i.e., each image). The highest and lowest thickness values for each image are provided corresponding to the “High value” and “Low value” in the colorbar, respectively. For easier understanding, arrows indicating the thickness-decreasing directions have been added for all measurements as shown in Fig. 5. By combining the five local thickness distributions, one can easily visualize the thickness-variation trace within the entire lens, which further confirms the fact that the lens’s thickness distribution is closely related to that of the cavity pressure.
In order to further verify the thickness distributions, another measurement was carried out with additional measuring positions along both directions (thirteen positions in total) and the results are shown in Fig. 6. Comparing with Fig. 5, good agreement can be observed concerning both the overall (see line plots at the lower right corner) and local (see arrows within images) thickness distributions of the lenses with five and thirteen measuring positions. This indicates that the five-position measurement is enough to represent the thickness distribution of the entire lens.
Fig. 6 Thickness distributions of lenses molded under condition No.1 in both measuring directions with thirteen measuring positions (in each image the white arrow and numbers indicate the thickness-decreasing direction and “High value”/“Low value” in the colorbar, respectively).
4.3 Characterization of cavity pressure through lens thickness distribution
As mentioned previously, the lens thickness is closely related to the cavity pressure during injection molding. Therefore, it’s of great importance and necessity to explore the specific relation between both quantities in order to characterize the cavity pressure with the lens thickness available. Figure 7(a) shows both the lens thickness and cavity pressure with process condition No.1. It can be seen that both quantities follow the same trend of variation against the measuring position, which makes it possible to construct a simple model for predicting cavity pressure (PC) from the lens thickness (TL). Specifically, the linear regression model (LRM) was utilized to determine the estimated cavity pressure PCE from the independent variable, TL as shown in Eq. (1):
where the slope k and intercept b can be determined using Eq. (2) and Eq. (3), respectively: where n is the total number of measuring positions with each process condition, TLi and PCi are the lens thickness and cavity pressure at the ith measuring position, respectively. Taking data obtained with process condition No.1 for example, the LRM can be represented as PCE = 4.37TL-2.11 × 103 MPa (TL≥482.84μm). Figure 7(b) presents the regression analysis result for relationship between the cavity pressure and lens thickness at any position within the lens under condition No.1. To quantify the degree of correlation, analyses of correlation coefficient R2 between these two series of data were carried out as shown in Eq. (4):Fig. 7 The lens thickness and cavity pressure distributions (a), and regression analysis result for relationship between both quantities (b) under process condition No.1.
The correlation coefficient for the LRM associated with process condition No.1 was accordingly calculated as R2 = 0.86 [Fig. 7(b)]. Similarly, those for LRMs corresponding to all other process conditions were also determined as shown in the last column of Table 1. One can find that the R2 varies from 0.84 to 0.93, with an average value of 0.89. With a significant level of 0.05 (i.e., a confidence interval of 0.95), the threshold value of the correlation coefficient, Rt2, can be obtained as 0.77 [26]. As all calculated correlation coefficients Rj2 (j = 1~9) are greatly larger than the threshold value Rt2, it’s reasonable to say that the dependent variable (i.e., cavity pressure) and the independent one (i.e., lens thickness) have significant linear correlation. Therefore, the developed LRMs are reliable for predicting the cavity pressure at any position within the lenses through the constructed lens thickness distributions.
To further support the feasibility of the proposed cavity pressure characterization method, the causal relation between the lens thickness and the cavity pressure can be explained as follows. The resultant force of the injection force and the internal friction force (i.e., the viscous force of the molten material) is the driving force of the melt flow in injection process. Larger cavity pressure at locations farther from the flowing front, on one hand, provides the melt larger resultant force to fill microcavities on both internal channel surfaces, and on the other hand, leads to higher compressibility level of the melt associated with larger recovery deformation after demolding. Both aspects have the same trend of producing larger lens thickness close to the gate side. Moreover, the nonuniform insert axial deformation under compressive pressure from the melt during injection may be another cause for the observed lens thickness distribution.
4.4 Effects of process conditions
The overall thickness distributions are plotted as a function of the process condition as shown in Fig. 8, from which one observes that thicknesses at all positions have the same general trend of increasing as the condition changes from No.1 to No.9. Nevertheless, the thickness fluctuation extent against the process condition shows a strong dependence on the measuring position. For instance, at positions A1 (near the gate) and A2 (at the center of the lens) having relatively short distances to the gate, the thickness fluctuation against the process condition is not pronounced, while at positions A4(A5) and A3 with constantly increased distance to the gate, it turns more and more apparent. This implies that the process condition and the measuring position have strong interaction in terms of their effects on the overall thickness distribution of the lenses.
Besides, the local thickness distributions are also process-condition dependent. Figure 9 gives local thickness distributions of lenses molded under condition No.6 in both measuring directions. Comparing with Fig. 5, one can see that the lens thickness distributions at position A4 are different with process conditions No.1 and No.6 (see the arrow with a circle in Fig. 9). Under condition No.6, the lens thickness in area close to the lateral cavity wall is larger than those of other areas, which is believed to result from the high pressure caused by the back flow after the melt touched the mold wall with higher melt temperature and injection velocity. To further verify this speculation, another experiment with the same process condition but increased nominal lens thickness (from 0.5 to 0.7 mm) was performed, and the result is shown in Fig. 10. In this case, one can find that at all measuring positions close to the lateral wall (i.e., A1, A3, A4, and A5), the thickness decreases from the outside area near the cavity wall towards the center of the lens. This is because with increased nominal thickness, even the same process condition facilitates the melt flow and thus strengthens the back flow effect.
Fig. 9 Local thickness distributions of lenses molded under condition No.6 in both measuring directions (in each image the white arrow and numbers indicate the thickness-decreasing direction and “High value”/“Low value” in the colorbar, respectively; the circle indicates the direction change of the arrow compared with that in Fig. 5).
Fig. 10 Local thickness distributions of lenses molded under condition No.6 with increased lens nominal thickness in both measuring directions (in each image the white arrow and numbers indicate the thickness-decreasing direction and “High value”/“Low value” in the colorbar, respectively; the circles indicate the direction change of the arrows compared with those in Fig. 5).
Moreover, it’s found that the process conditions also affect the topography of the constructed 3D thickness surface. This is especially the case for positions far from the gate. Figure 11 shows the local thickness distributions at position A3 under all process conditions, from which one can observe obvious topography evolution. With the lower limits of all investigated variables (i.e., condition No.1), the topography of the lens thickness surface looks very interesting as a series of evenly spaced wave-like patterns exist running perpendicular to the main flow direction. This may be ascribed to the stick-slip phenomenon caused by inadequate pressure and high flow viscosity associated with low melt temperature [27-28]. Differently, under certain conditions (e.g., conditions No.5 and No.6), some irregular protrusions appear in the measuring area, indicating more complicated flow behaviors. Undoubtedly, the presence of various topographies affects the thickness measurement results, which agrees well with the fact that the largest fluctuation in overall thickness distributions was observed for position A3 of the lenses as shown in Fig. 8. This means that the surface topography also depends on the measuring position. As a comparison, Fig. 12 shows the local thickness distributions at position A1 under all process conditions, from which one can see very smooth transition of the lens thickness variation.
Fig. 11 The local thickness distribution (a) and the corresponding average thickness (b) of the lenses at position A3 under all process conditions (in each image the numbers indicate the “High value”/“Low value” in the colorbar).
Fig. 12 The local thickness distribution (a) and the corresponding average thickness (b) of the lenses at position A1 under all process conditions (in each image the numbers indicate the “High value”/“Low value” in the colorbar).
4.5 Process optimization
As process conditions influence the lens thickness distributions and cavity pressure to a large extent, it’s indispensable to implement process optimization in order to improve the lens performance. A quantitative index, the thickness standard deviation (TSD), was defined to represent the thickness uniformity of the lenses using Eq. (5):
where hi is the thickness at the ith measuring position, ha is the average thickness over all measuring positions as determined by Eq. (6):Thereafter, the importance of each investigated variable was evaluated with TSD as the response (see Table 1). As smaller response (i.e., smaller TSD or better thickness uniformity) is desired, the “smaller-the-better” criterion was adopted to produce the signal-to-noise (S/N) ratios in the Taguchi design analyses. With standard analysis of means (ANOM), both significant variables and optimal level combination can be identified. From the S/N ratio analysis (Fig. 13), one can find that the packing time is the most influential variable for the response. Furthermore, both the melt temperature and packing pressure exhibit a non-monotonic trend in influencing the TSD, while the injection velocity gives a substantial reduction of the TSD. Finally, the optimal combination of the variable levels can be found as T2V3P2t1 (i.e., T = 285 °C, V = 100 mm/s, P = 120 MPa, and t = 2 s) for obtaining the minimal TSD value within the investigated scopes of the variables.In order to confirm the effectiveness of the process optimization, verification experiment using the optimized combination of process variables was carried out. The measured TSD of the molded lenses for the verification experiment is 12.24 μm. One observes that this result is smaller than all measurements in the Taguchi method, which indicates successful optimization of the process variables.
5. Conclusions
A noncontact measuring approach based on the confocal microscope was proposed to construct the 3D thickness distributions of plano lenses prepared by microinjection molding (μIM). It was found that regardless of the process conditions, the lens overall thickness decreased gradually in the main flow direction, while almost kept unchanged in the cross-flow direction, which was believed to result from the associated pressure distribution inside the mold cavity. Moreover, the lens local thickness showed a general trend of decreasing in the melt filling direction, with exceptions under certain process conditions facilitating the melt flow. Besides, the topography of the constructed 3D thickness surface was dependent on both process condition and measuring position. Furthermore, a mathematical model was developed fulfilling nondestructive cavity pressure characterization with the overall lens thickness distribution. As for the selected process variables, the packing time was identified to be the most important in influencing the lens thickness. Finally, the optimized process conditions for achieving uniform thickness and cavity pressure distributions were obtained as T = 285 °C, V = 100 mm/s, P = 120 MPa, and t = 2 s. The verification experiment produced the smallest TSD value of 12.24 μm for the molded lenses. The present work successfully demonstrated that the 3D thickness distribution can be utilized as a means of cavity pressure characterization during the μIM process.
Funding
National Natural Science Foundation of China (NSFC) (Grants 51405451, 51675489); Natural Science Foundation of Zhejiang Province (Grant No. LY17E050002).
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