Journal of Materials Processing Technology 113 (2001) 189±195
`
`A statistical experimental study of the injection molding of optical lenses
`
`Xuehong Lua,*, Lau Soo Khimb
`aNanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore
`bGintic Institute of Manufacturing Technology, 71 Nanyang Drive, Singapore, Singapore
`
`Abstract
`
`In the injection molding of plastic optical lenses, the processing conditions have critical effects on the quality of the molded lenses. Since
`there are many process parameters involved in an injection molding process, and more importantly, an optical lens needs precisely
`controlled surface contours, determination of the processing conditions for lens molding is very complicated. The objective of this work is
`to investigate experimentally some effects of the molding conditions on the surface contours of injection molded lenses. A spherical lens
`was molded using polycarbonate. The surface pro®les of the lenses molded under different processing conditions were measured using a
`laser interferometer. The birefringence of the lenses was measured using a specially designed polarimeter to characterize the residual stress
`in the lenses. Statistical methods were employed in the experimental studies in order to systematically analyze the effects of various process
`parameters on the lens contour errors. The process parameters studied include injection speed, holding pressure and mold temperature, etc.
`The contour errors were correlated to the mold shrinkage and the residual stress in the molded lenses. The study shows that in addition to
`the mold shrinkage the stress also plays a vital role in determining the lens surface contours. # 2001 Elsevier Science B.V. All rights
`reserved.
`
`Keywords: Injection molding; Optical lenses; Molded
`
`1. Introduction
`
`The injection molding technique is now used increasingly
`more widely in the manufacturing of precision plastic parts,
`such as optical lenses. This trend is driven primarily by the
`strong needs for the manufacturing of these parts at high
`production rates and low cost. An optical lens needs pre-
`cisely controlled surface contours to realize its optical
`design. In general, the injection molding process is not ideal
`for such products since excellent replication of the mold
`contour is very dif®cult to be achieved using this process due
`to free mold shrinkage and stress induced distortion, espe-
`cially when highly viscous molding materials are used.
`Injection±compression molding has been proven to be a
`better solution for the molding of high-end plastic optical
`lenses [1]. On the other hand, it has also been proven that
`through proper mold design and process optimization, an
`injection molded lens can achieve reasonably well con-
`trolled surface contours, although not exactly replication
`of that of the mold, which provides a low cost solution for
`the manufacturing of plastic optical lenses. In this case, the
`injection molding conditions have critical effects on the
`quality and productivity of the molded lenses [2,3]. Since
`
`* Corresponding author.
`E-mail address: asxhlu@ntu.edu.sg (X. Lu).
`
`there are many process parameters involved in an injection
`molding process, determination of the processing conditions
`for lens molding is very complicated, and no established
`design rules are available.
`Deviation of the contours of a molded lens from those of
`the mold caused by free mold shrinkage has been studied
`previously [4]. If the shrinkage is uniform, although it may
`cause the thickness and radii of curvatures of a lens to
`deviate from those of the mold, but the resultant contour
`errors are predictable and can be well corrected in the mold
`design stage. Practically, the mold shrinkage is, however,
`non-uniform, which may cause not only undesirable varia-
`tion in lens thickness and hence contour errors, but also
`frozen-in stresses and hence further distortion of the pro-
`ducts. For optical lenses, a very small distortion may result
`in relatively large deviation of the lens contours from those
`designed.
`There is another source of residual stresses in injection
`molded parts. During an injection molding process, polymer
`melt is forced to ¯ow in a narrow channel by high pressures.
`This may result in an anisotropic structure of the polymer
`melt, and it may be frozen in moldings to some extent. The
`in¯uences of the anisotropic polymer structure on properties
`of the molded plastic lenses are twofold. Firstly, the products
`may display ¯ow-induced birefringence. Secondly, asso-
`ciated with the anisotropic structure, stress is present in
`
`0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved.
`PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 0 6 0 6 - 9
`
`APL1106
`Apple v. Valencell
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`
`

`

`190
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`X. Lu, L.S. Khim / Journal of Materials Processing Technology 113 (2001) 189±195
`
`the molded lenses, which may also cause distortion of the
`products. In this case, since the stress is directly related to
`the birefringence, study of the effects of process parameters
`on the birefringence patterns can provide important clues for
`process optimization. It is worth noting that the birefrin-
`gence is also material dependent. The most commonly used
`optical plastic, polycarbonate, has a relatively large positive
`stress±optical coef®cient [5]. It is, therefore, an ideal can-
`didate for injection molding process studies.
`The objective of this work is to study some effects of
`injection molding conditions on surface contours of a
`molded polycarbonate lens. In order to systematically ana-
`lyze the effects of various process parameters on the lens
`contours, statistical methods were used in conducting the
`experiments. The contour errors were correlated to mold
`shrinkage and the level of the ¯ow-induced stress in the
`molded lenses to evaluate the importance of these two
`factors in determining the lens contours.
`
`2. Experimental work
`
`2.1. Molding materials
`
`The material used in this study was a commercially avail-
`able injection-molding grade of polycarbonate. The material
`was pre-conditioned at 1208C for 4 h using a dehumidifying
`drier before molding. The trade name, manufacturer and melt
`¯ow index of the material are shown in Table 1.
`
`2.2. Part geometry and mold design
`
`All of the molding experiments were conducted using a
`two-cavity test mold especially designed for this study. The
`product is a mono-axis spherical lens. The designed geo-
`metry and dimensions of the test part are shown in Fig. 1.
`The test mold includes two pairs of inserts to form the lens
`contours. Each of the concave and convex inserts was
`fabricated separately using tool
`steel Assab Stavax
`HRC40-52. The mold was designed with a cold round runner
`system of diameter 6 mm and a sprue of diameter 8 mm. An
`edge gate of dimensions 10 mm  5 mm  3 mm was used.
`
`2.3. Injection molding process
`
`The molding experiments were performed on a 100 t HP
`1000-220/Netstal injection molding machine. The experi-
`
`Table 1
`Molding material used in this study
`
`Material name
`Category
`Manufacturer
`Trade name
`Grade
`Melt flow index (g/10 min)
`
`Polycarbonate
`General purpose
`Mitsubishi
`Iupilon
`S-2000
`10
`
`Fig. 1. Designed geometry and dimensions of the test part.
`
`ments were conducted under various designs of experiments,
`as explained in the following sections. Under each set of
`process conditions, 10 shots were made to ensure that the
`process was stable before samples were collected. If no
`signi®cant variation was observed during these ®rst 10 runs,
`the molded parts from the next ®ve runs were collected as
`the samples for product characterization.
`
`2.4. Design of experiments (DOE)
`
`Full two-level three-factorial (23) molding experiments
`were designed to determine the effects of various process
`parameters on the sample weight, and the radii of curvature
`of the molded lenses and the level of the ¯ow-induced stress
`in the lenses. The process parameters under consideration
`were the injection speed, the holding pressure and the mold
`temperature. The high and low levels of these process
`parameters are tabulated in Table 2. Other process parameter
`settings were held constant throughout the experiments, as
`listed in Table 2.
`After the 23 experiments, molding experiments were
`further conducted to study the effects of two-stage holding
`pressure and pressure holding time on the quality of the
`molded lenses. Three types of holding pressure pro®les were
`used, as shown in Fig. 2. For the second type of two-stage
`holding, the holding times used were 5, 7.5, 10, 12.5, 15 and
`20 s, respectively. The other processing parameters used in
`these experiments were the same as those in the 23 molding
`experiments.
`
`2.5. Product characterization
`
`In this study, it has been observed that there are slight
`differences in product quality between the lenses molded in
`cavity I and cavity II, which is due to their difference in
`cooling ef®ciency. To focus on the major task of this study,
`in this paper only the characterization data for lenses molded
`in the cavity I are discussed. All the data presented in this
`paper corresponds to lenses obtained from cavity I.
`
`2.5.1. Part weight
`the runner systems were carefully
`Before weighing,
`trimmed from the lens samples. For each set of process
`conditions, all ®ve collected parts were weighed and the
`average part weight was calculated. Among the ®ve samples,
`
`

`

`X. Lu, L.S. Khim / Journal of Materials Processing Technology 113 (2001) 189±195
`
`191
`
`Table 2
`Process parameters used in full two-level three-factorial (23) molding experiments
`
`Factor
`
`Injection speed (mm/s)
`Holding pressure (bar)
`Mold temperature (8C)
`
`Other process parameters
`
`Screw rotation speed
`Back pressure
`Feed stroke
`Cushion setting
`Holding pressure time
`Cooling time
`Barrel temperature setting
`
`Low level
`
`20
`1000
`60
`
`High level
`
`100
`1560
`140
`
`100 mm/s
`100 bar
`50/52 (for suck back)
`12 mm (V/P switch over at 8 mm)
`5 s, one-stage
`30 s
`3008C (melt), 3008C (nozzle), 3008C (cylinder head), 3008C (metering zone),
`2708C (compression zone), 2708C (feed zone), 508C (feeder throat)
`
`the part with a weight closest to the average value was
`chosen for the further measurements described below.
`
`2.5.2. Radius of curvature
`A GPI XP laser interferometer was used to measure the
`radii of curvatures of the mold inserts and molded lenses.
`The maximum peak to valley (PV) measurable using the
`interferometer is 10 mm at 320 pixels and 20 mm at 640
`pixels. The surface pro®les of the mold inserts were mea-
`sured at normal resolution, i.e., 320 pixels. The surface
`pro®les of the mold lenses were measured at a higher
`resolution, i.e., 640 pixels.
`In this study contour error was used to quantify the quality
`of the molded lenses in terms of their radii of curvature,
`which is de®ned as
`Contour error ˆ Rlens Rinsert
`where Rlens and Rinsert represent the radii of curvature of a
`lens and that of the corresponding mold insert, respectively.
`
`2.5.3. Photoelastic stress analysis
`The photoelastic stress analysis system used in this study
`was custom-built. It consists of a conventional polarimeter, a
`CCD camera and an IBM PC with photoelasticity stress
`analysis software.
`
`Fig. 2. Holding pressure pro®les used in this study: (a) one-stage holding;
`(b) two-stage holding, type I; (c) two-stage holding, type II.
`
`In the quantitative stress analysis of the plastic lenses,
`®rstly an immersion ¯uid was made [6], which has exactly
`the same refractive index, n, as that of the part under test.
`Since polycarbonate has a refractive index of 1.586, the
`immersion ¯uid used in this study was made by mixing
`silicone oil …n ˆ 1:5568† and diiodomethane …n ˆ 1:7†. The
`lens was then immersed in the ¯uid in a stress-free glass
`container and put under the polarimeter to let polarized light
`pass through the sample. The optical images were recorded
`by the CCD camera when using a different combination of
`polarizers and analyzers, and then analyzed using the photo-
`elasticity software. The radii of curvature, diameter and
`center thickness of the lens were input into the computer
`to account for the thickness of the lens at a particular point.
`In multi-fringe analysis the fringe number was assigned by
`the operators [7,8].
`Qualitative stress analysis was conducted in a similar way,
`but after the optical images were recorded no further ana-
`lysis was done. The images were compared to each other
`visually and assigned as low, medium or high stress level,
`based on the number of fringes observed. All of the parts
`collected from the eight molding experiments were rated
`based on the observed birefringence patterns. The rating of
`0.0 was given to the parts with a low level of stress, and 0.5
`and 1.0 to the parts with a medium and a high level of stress,
`respectively. Two representative birefringence patterns for
`the low and high level of stresses are shown in Fig. 3 as
`examples.
`
`2.6. Data analysis
`
`In this study, the method adopted to analyze the full two-
`level three-factorial experiments (23) was to treat the data as
`a series of paired comparisons, one parameter at a time [9].
`The comparisons were carried out under various conditions
`for the other factors. The effect of the jth factor (Ej) was
`calculated using the equation
`Pn
`iˆ1…lij  Ri†
`Ej ˆ
`…j ˆ 1; 2; . . . ; n†
`Pn
`iˆ1Ri
`
`(1)
`
`

`

`192
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`X. Lu, L.S. Khim / Journal of Materials Processing Technology 113 (2001) 189±195
`
`Fig. 3. Representative birefringence patterns observed: (a) low level of
`stress; (b) high level of stress.
`
`where i is the combination number, n the total number of
`combinations (i.e. the total number of experiments; for the
`23 design, n equal to 8), Ri the responsible variable for the ith
`combination, lij equal to 1 for low level of the jth factor, ‡1
`Pn
`iˆ1lij ˆ 0.
`for high level of the jth factor and
`The interaction between the jth and kth factor (Ijk) was
`calculated using the equation
`Pn
`iˆ1‰…lij  lik†  RiŠ
`Ijk ˆ
`…j ˆ 1; 2; . . . ; n†
`Pn
`iˆ1Ri
`The product characterization results were analyzed using the
`conventional 23 matrix [9].
`
`(2)
`
`3. Results and discussion
`
`3.1. Sources of contour errors
`
`In the lens manufacturing industry, the contour errors of a
`lens refer to the deviation of the lens surface contours from
`the designed contours. The contour errors for a molded
`plastic lens may come from three sources. Firstly,
`the
`contours of a mold insert may deviate from the designed
`contours. The test mold inserts used in this study were
`fabricated using conventional machining and polishing tech-
`niques. The contours and surface ®nish of the inserts were
`measured using the laser interferometer. The maximum
`peak-to-valley measured for
`the inserts
`is
`less
`than
`10 mm, although the edge regions of the convex inserts were
`out of range during the measurements. The measurement
`plots for the two inserts used to form cavity I of the test mold
`are shown in Fig. 4.
`The radii of curvatures of the test mold inserts measured
`using the interferometer are tabulated in Table 3. These
`values deviate signi®cantly from the designed values. Never-
`theless, the focus of this paper is to study the effects of the
`
`Table 3
`the mold inserts measured using the laser
`Radii of curvature of
`interferometer at room temperature
`
`Radius of curvature
`
`Concave surface
`
`Convex surface
`
`Cavity I
`Cavity II
`
`176.12
`178.93
`
`80.42
`81.31
`
`Fig. 4. Surface roughness map of the test mold inserts measured using the
`laser interferometer: (a) concave insert for cavity I, having a maximum
`peak-to-valley of 2.670 mm; (b) convex insert for cavity I, having a
`maximum peak-to-valley of 2.487 mm.
`
`molding process parameters on the contour errors of the
`molded lenses. Therefore, these inserts can still serve the
`major purpose of this study. In this work, the contour errors
`of a lens refer to the deviation of the radii of curvature of a
`molded lens from those of the mold inserts, rather than the
`designed values.
`It is also worth noting that the radii of curvature shown in
`Table 3 were obtained at room temperature. At relatively
`high mold temperature, thermal expansion of the inserts may
`also cause deviation of the mold surface contours from the
`designed contours, but such deviation is usually fairly small.
`When the radii of curvature are relatively large compared to
`the diameter of the mold, the surface contours of the mold,
`especially that of the center area, would not be affected by
`this signi®cantly, which is the case in this study.
`For the molding of high-end optical lenses, ultra-precision
`machining is required for making high precision molds. In a
`parallel research to this work, the authors have used a single-
`point diamond turning machine to make aluminum test mold
`inserts. The surface pro®les of the inserts were also mea-
`sured using the laser interferometer. In contrast to those
`fabricated using conventional machining methods, in this
`case the entire insert surface, including the edge region, has
`a very good surface ®nish. The maximum peak-to-valley
`was less than 0.2 mm, which is about 15 times better than the
`inserts used in this study. Despite the high precision achiev-
`able by the diamond turning machine, the short tool life for
`an aluminum insert makes it a costly option. At present, how
`to achieve high precision for a lens mold at a reasonably low
`price is still a great challenge faced in the mold manufactur-
`ing industry, although the topic is beyond the scope of this
`paper.
`The second source of contour errors of a molded lens is
`the free mold shrinkage of the lens. As mentioned in Section
`1, both uniform and non-uniform mold shrinkage can cause
`
`

`

`X. Lu, L.S. Khim / Journal of Materials Processing Technology 113 (2001) 189±195
`
`193
`
`Table 4
`Process parameter matrix and product characterization results
`
`Process parameter
`
`Responsible variable
`
`severe contour errors for the molded lenses. Flow simulation
`and systematical process study may help to minimize such
`contour errors, although this is also beyond the scope of the
`present paper. In this work, sample weight was used to
`indirectly characterize mold shrinkage, therefore non-uni-
`formity of the shrinkage is not under consideration. Only the
`average effect of mold shrinkage on contour errors will be
`discussed.
`Thirdly, the ¯ow-induced stress may also cause distortion
`of a plastic lens in the mold and hence contour errors. The
`same as the free mold shrinkage, the stress is also very much
`dependent on the processing conditions. In this study, the
`authors will mainly discuss the effects of the processing
`conditions on the lens contour errors and their relations to
`the mold shrinkage and ¯ow-induced stress.
`
`3.2. General observation
`
`In general, the molded lenses have slightly poorer surface
`®nish compared to the corresponding inserts. The maximum
`peak-to-valley is between 10 and 20 mm. In addition, for
`most lens samples, only the center sections of the lens
`surfaces, typically with a diameter of 25 mm, fall within
`measurable peak-to-valley range for the instrument. There-
`fore, all the radii of curvature of the lenses reported in this
`paper refer to the values for the center sections of the lenses.
`For the lens design used in this study, if considering only
`uniform mold shrinkage, the contour errors would occur in
`the form of
`Rconcave  R0
`Rconvex  R0
`concave;
`convex
`where Rconcave and R0
`concave are the radii of curvature of the
`concave surface of the lens and the corresponding insert,
`respectively, and Rconvex and R0
`convex are the radii of curvature
`of the convex surface of the lens and the corresponding
`insert, respectively.
`However, in this study, for all of the molded lenses, it was
`found that
`Rconvex  R0
`Rconcave  R0
`concave;
`The situation is illustrated schematically in Fig. 5. Such a
`shrinking pattern indicates that stress plays a very important
`role in the determination of the lens contour errors. The
`stress causes the lens warp in the mold. The stress could be
`induced by non-uniform shrinkage or ¯ow-induced orienta-
`tion. In this paper, the two components are not separated.
`
`convex
`
`Fig. 5. A schematic diagram of the contour errors of a molded lens.
`
`Injection
`speed
`‡a
`‡
`‡
`‡
`
`
`
`
`
`Holding
`pressure
`‡
`‡
`
`
`‡
`‡
`
`
`
`Mold
`temperature
`‡
`a
`‡
`
`‡
`
`‡
`
`
`Contour
`error
`5.4
`2.4
`4.4
`2.4
`3.4
`1.4
`4.4
`2.4
`3.3
`Average value
`7.41
`0.5
`a ‡ and represent the high and low level of the process parameters,
`respectively.
`
`Sample
`weight
`
`7.44
`7.65
`7.25
`7.38
`7.43
`7.59
`7.14
`7.36
`
`Stress
`level
`
`1.0
`0.5
`0.5
`0.0
`1.0
`0.5
`0.5
`0.0
`
`3.3. Factorial analysis based on product characterization
`
`To study the effects of process parameters on contour
`errors and their relation to mold shrinkage and residual
`stress, a factorial experimental study was conducted. The
`detailed experimental design and production characteriza-
`tion methods have been illustrated in Section 2. The experi-
`mental results are shown in Table 4. In the table, the contour
`error was measured from the concave surface of the lenses.
`The effect of each process parameter was calculated using
`Eq. (1) described in Section 2. For example, the effect of a
`process parameter on the stress level was calculated such
`that a rating of 1.0 was given to high level of birefringence
`and 0.0 to birefringence patterns with less fringe number.
`The effect of the holding pressure on the stress level is
`‡50%, which means that an increase of holding pressure
`from the low to high level will cause an average stress rating
`increase of 50% of the average level. Note that the effect of
`each process parameter is an averaged value over eight
`experiments. An interaction between parameters exists
`when the difference in the response variables between the
`low and high levels of each parameter is not the same at all
`levels of the other parameters. The interactions were calcu-
`lated using Eq. (2) described in Section 2. When the inter-
`action is large, the effect of a single process parameter has
`little practical signi®cance.
`The results of the 23 factorial analysis are listed in Table 5,
`from which can be seen clearly the effect of an individual
`process parameter on the contour error.
`From Table 5, it can be seen that the contour error is
`in¯uenced dominantly by the mold temperature. As the mold
`temperature increases from the low to high level the contour
`error will increase by 34%, i.e. the radius of curvature of the
`concave surface of the lens will be 34% smaller than the
`average value for the eight run experiments, which is 3.3.
`The large effect of the mold temperature on the contour error
`can be attributed to both free mold shrinkage and stress. This
`can be seen clearly from the relatively large effect of the mold
`
`

`

`194
`
`X. Lu, L.S. Khim / Journal of Materials Processing Technology 113 (2001) 189±195
`
`Table 5
`Results of full two-level three-factorial analysis
`
`Effect of process parameter
`
`Injection
`speed
`(A) (%)
`‡11
`‡0.34
`0.0
`
`Holding
`pressure
`(B) (%)
`0.04
`‡1.7
`‡50
`
`Contour error
`Sample weight
`Stress level
`
`Effect of interaction between process parameters
`
`Contour error
`Sample weight
`Stress level
`
`AB (%)
`‡11
`0.10
`0.0
`
`AC (%)
`‡3.8
`0.07
`0.0
`
`Mold
`temperature
`(C) (%)
`‡34
`1.2
`‡50
`
`BC (%)
`‡3.8
`0.03
`0.0
`
`temperature on the sample weight and stress level. Please
`note that the sample weight variable has a negative sign. This
`means that the increase of mold temperature from the low to
`high level will cause an average sample weight decrease of
`1.2%, which implies a large increase in mold shrinkage. The
`stress variable has a positive sign, which means that an
`increase of mold temperature from the low to high level
`will cause an average stress increase of 50%. Both of these
`effects promote large contour errors.
`In contrast to the mold temperature, the experimental
`results show that holding pressure has only a very slight
`in¯uence on the contour error. As the holding pressure
`increases from the low to high level no signi®cant change
`in the contour error is observed. The reason for this is that in
`this case the effects of holding pressure on mold shrinkage
`and residual stress work against each other. Increasing the
`holding pressure would result in more material being packed
`into the cavities and thus a closer surface replication, but it
`also has the action of increasing the residual stress, since
`under higher packing pressure the polymer chains are more
`dif®cult to relax. The addition of these two effects makes the
`contour error not very sensitive to the holding pressure.
`The effect of the injection speed on the contour error is
`more complicated. Apparently, increase of the injection
`
`speed will result in a larger contour error. There is a strong
`interaction between the effects of mold temperature and
`holding pressure. The contour error is likely to be improved
`only when the combination of low injection speed and low
`holding pressure is used.
`
`3.4. Quantitative stress analysis
`
`Quantitative stress analysis was conducted to compare
`lenses that have similar levels of stress but different stress
`distribution. This is particularly important for study of the
`effect of injection speed on the lens contours. In qualitative
`stress analysis the effect of injection speed on the stress level
`is insigni®cant. To investigate the effect more clearly, two
`lens samples molded under injection speed of 20 and
`100 mm/s were analyzed quantitatively. Based on the quan-
`titative stress analysis, three-dimensional stress distributions
`for the lenses were generated as shown in Fig. 6.
`From the above two diagrams, it can be seen that in both
`lenses, the stress is high at the lens edge and center regions,
`while their stress distributions are different. In the lens
`molded using an injection speed of 20 mm/s, the stress goes
`up at the center more sharply than that in the lens molded at
`an injection speed of 100 mm/s. In principle, it should
`always be expected that at the center the stress level is
`higher since the thin section there is cooled more quickly
`and therefore the relaxation of polymer chains does not
`occur. From this study, an important ®nding is that this high-
`stress center region is small when a low injection speed was
`used but fairly large when a high injection speed was used.
`This gives a clue as to why increase of the injection speed
`results in larger contour errors.
`
`3.5. Effect of holding pressure pro®les and holding time
`
`The present study shows that the use of a gradually
`decaying holding pressure pro®le, i.e., one-stage holding,
`does not serve to give signi®cant reduction in stress level in
`the molded lenses. Compared to the use of one-stage hold-
`ing, with low injection speed, the stress level increases
`slightly when two-stage holding pressure was used. With
`
`Fig. 6. Stress distributions of the lenses molded at different injection speeds: (a) injection speed of 20 mm/s; (b) injection speed of 100 mm/s.
`
`

`

`X. Lu, L.S. Khim / Journal of Materials Processing Technology 113 (2001) 189±195
`
`195
`
`high injection speed, there is a strong interaction between
`the mold temperature and the holding pressure pro®les, i.e.
`at low mold temperature, the stress level increases slightly
`when two-stage holding is used, but at high mold tempera-
`ture stress level decreases slightly when two-stage holding is
`used. In contrast to its insigni®cant effect on the residual
`stress, the use of two-stage holding allowed more material to
`be packed into the cavities and provided a better surface
`replication. Therefore,
`the use of two-stage holding is
`favorable in lens molding.
`The effect of holding pressure time on the contour errors
`was also studied for the type II two-stage holding. In general,
`increasing the holding time does not cause a signi®cant
`increase in the sample weight. When the holding time
`increases from 5 to 7.5 s the sample weight
`increases
`slightly, while as the holding time increases further it
`appears to be stabilized. Similarly, at the holding time of
`7.5 s and mold temperature of 608C. the molded lenses
`appear to have acquired maximum surface replication, i.e.
`the radius of curvature of the concave surface approaches
`that of the mold insert. Further prolonging the holding time
`will not affect the contour errors.
`
`4. Conclusions
`
`1. The result from the factorial analysis indicates that mold
`temperature is the most important process parameter
`affecting the contour errors of injection molded lenses.
`Holding pressure has less in¯uence on the contour
`errors, while in both cases, mold shrinkage and residual
`stress play their roles.
`
`2. The effect of the injection speed on the residual stress is
`mainly to change the stress distribution.
`3. The use of two-stage holding pressure can provide better
`surface replication for the lenses.
`
`Acknowledgements
`
`The authors wish to express their gratitude to Gintic
`Institute of Manufacturing Technology for the funding of
`the research. They also would like to thank Dr. Zhao
`Jianhong, Mr. Ravi Varahamurthy, Mr. Chen Ge and Ms.
`Liu Yuchan of Gintic for their contribution to and technical
`support of the work.
`
`References
`
`[1] T.J. Wang, CAE and Intelligent Processing of Polymeric Materials,
`Vol. 79, American Society of Mechanical Engineers, Materials
`Division, Fair®eld, NJ, 1997, p. 83.
`[2] W. Michaeli, N. Kudlik, R.V. Aachen, Kunststoffe Plastic Eur. 86
`(1996) 478.
`[3] R.Y. Chang, Y.C. Hsieh, C.H. Hsu, J. Reinforced Plastics Composites
`18 (3) (1999) 261.
`[4] S.Y. Kim, M.H. Rim, W.S. Lim, W.Y. Kim, J. Injection Molding
`Technol. 4 (1) (2000) 29.
`[5] R. Wimbergerfriedl, Prog. Polym. Sci. 20 (3) (1995) 369.
`[6] H. Aben, Photoelasticity of Glass, Springer, Berlin, 1993.
`[7] A. Kuske, Photoelastic Stress Analysis, Wiley, New York, 1974.
`[8] J.W. Dally, Experimental Stress Analysis, McGraw-Hill, New York,
`1991.
`[9] R.D. Moen, T.W. Nolan, P.L. Provost, Improving Quality Through
`Planed Experimentation, McGraw-Hill, New York, 1991.
`
`