Figure 1 shows an LED reflector bowl for automotive headlights. Its dimensions are 113 mm * 94 mm * 47 mm, with a volume of 69.3 cm³ and an average wall thickness of 2.5 mm. To meet optical reflectivity requirements, vacuum aluminizing is required after injection molding. Simultaneously, according to optical requirements, deformation of optical area of plastic part should be controlled below 0.1 mm.

 

Figure 1: Reflector Bowl Shape
Since reflector bowl operates in a high-temperature environment, polyetherimide (PEI) is selected as material, with grade SABIC Ultem AUT 200. PEI is a high-performance engineering plastic with excellent mechanical properties and outstanding radiation resistance. Furthermore, PEI's resistance to high and low temperatures allows it to maintain good physicochemical properties even under extreme temperature conditions, its wear resistance ensures material's reliability during long-term use. Based on these excellent performance characteristics, PEI is one of indispensable materials in industrial field. Table 1 shows physical properties and molding process parameters of PEI material, Figure 2 shows viscosity curve and specific volume curve of PEI material.

Table 1 Physical properties and molding process parameters of PEI material

 

Figure 2 Viscosity curve and specific volume curve of PEI material

Due to high requirements for appearance and size of plastic parts, mold adopts a 2-cavity layout, with an overall size of 650 mm * 600 mm * 522 mm. In order to reduce material waste, shorten molding cycle, and reduce scrap rate of plastic parts, gating system adopts a 1-point needle valve hot runner + ordinary runner form. Diameter of hot runner is φ11 mm, and diameter of valve needle is φ5 mm. Ordinary runner is designed as a circle with a diameter of φ8 mm, which can effectively reduce pressure loss when molten plastic flows in runner. Gate adopts a submarine type with a diameter of φ2 mm, eliminating need for manual removal of solidified material from gate. To ensure uniform heating of plastic part, cooling system adopts a "conformal water channel + water well" design. Water channel follows the overall shape of plastic part, with water wells used for auxiliary cooling in areas where conformal water channels cannot be designed, thus ensuring uniform heating of plastic part as much as possible. Based on characteristics of PEI and structure of plastic part, cooling system is designed as an oil channel + water channel. One set of oil channels is designed for each of left and right cavities on moving mold side, connected in parallel to an oil collection block, and temperature is controlled by an oil temperature controller. One set of oil channels is designed for each of left and right non-optical areas, left and right optical areas on fixed mold side, connected in parallel to an oil collection block, and temperature is controlled by an oil temperature controller. A cooling water channel is designed at hot runner nozzle location for cooling hot runner valve pins, temperature is controlled by a mold temperature controller to prevent valve pins from overheating and causing defects such as silver streaks on the surface of plastic part during production.
Based on requirements for mold size and part quality, production equipment adopted is a ZE4500Ⅲ-1400-DES injection molding machine. Machine has a screw diameter of φ55 mm, a theoretical injection capacity of 617 cm³, a maximum clamping force of 4500 kN, a maximum injection pressure of 214 MPa, a maximum mold thickness of 910 mm, a minimum mold thickness of 350 mm, and a Greenwich Column spacing of 910 mm * 910 mm. Screw accounts for 25.7% of reflector bowl's mass (ratio of reflector bowl mass to screw injection volume). Required maximum injection pressure is 70 MPa, and maximum clamping force is 1100 kN. Therefore, equipment meets requirements for mold and part production.

Based on physical properties of plastic part material and actual production process parameters (melt temperature 380 ℃, moving mold temperature 170 ℃, fixed mold temperature 140 ℃, injection time 3.5 s, pressure switching position 98%, holding pressure 90 MPa, holding time 2 s, cooling time 35 s), an initial mold flow analysis was performed on plastic part. Simulation results of plastic part deformation are shown in Figure 3. As can be seen from Figure 3, in reflective area (optical area) of reflector bowl, maximum deformation is 0.544 mm (consistent on both sides), exceeding standard of 0.1 mm. This causes the overall light beam's optical shape to fail to meet design requirements, resulting in light distribution failure. Therefore, maximum warpage deformation in optical area of plastic part is used as optimization index.

 

Figure 3 Default Mold Flow Analysis Results

Based on initial mold flow parameter analysis results, maximum warpage deformation of plastic part is selected as optimization target. According to thermal shrinkage mechanism of plastic parts, when there are temperature differences in different parts of plastic part, their shrinkage rates are inconsistent. Lower-temperature areas cool down faster and shrink more quickly, while higher-temperature areas cool down slower and shrink more slowly. This difference causes plastic part to shrink and deform towards warmer side. Therefore, by controlling temperature difference in mold, deformation trend of plastic part can be effectively adjusted. Plastic melt shrinks as it cools in cavity, which may lead to shrinkage marks or deformation in plastic part. Holding pressure is a continuous pressure applied to cavity for a certain period after injection to replenish plastic melt, improve stability of plastic part, and avoid deformation caused by internal stress. Cooling time directly affects solidification state of plastic part in the cavity. The longer cooling time, the more fully plastic part solidifies, the lower internal stress, and the less deformation when plastic part is ejected. Melt temperature has a significant impact on flow properties of plastic part. Within a reasonable melt temperature range, the higher temperature, the better flow properties, which is conducive to full filling of cavity and avoids warping and deformation of molded plastic part due to uneven filling.
Five factors that have the greatest impact on warpage deformation of plastic parts were selected as experimental factors: moving mold temperature Tcore (A), fixed mold temperature Tcavity (B), holding pressure Ps (C), cooling time Ct (D), and melt temperature Tmelt (E). An orthogonal experimental design was then conducted. According to constraints of full factorial test, each factor has exactly two levels. Therefore, each factor in orthogonal experiment was designed with two levels, high and low. L16 (25) orthogonal experimental factor level design is shown in Table 2.

 

Table 2 Orthogonal Experiment Factor Level Design

According to orthogonal experimental factor level design table, one parameter factor was changed sequentially. Simultaneously, according to requirement of "repeated testing," one center point was added, enhancing ability to evaluate experimental errors and bending trends, and better assessing model's fit. A total of 17 experiments were conducted, and warpage deformation data were statistically analyzed. Full factorial DOE test results are shown in Table 3.

 

Table 3. Results of Full Factorial DOE Experiments

Main effect plot mainly statistically analyzes influence trend of a single experimental factor on maximum warpage deformation of plastic part. When analyzing main effect plot, it is necessary to eliminate influence of other multiple factors on experimental results. Main effect results of maximum warpage deformation of plastic part are shown in Figure 4. As can be seen from Figure 4, when moving mold temperature increases from 130 ℃ to 170 ℃, maximum warpage deformation of plastic part decreases from 0.5 mm to 0.05 mm, a reduction of 0.45 mm, showing a positive effect on maximum warpage deformation, and this effect is the greatest. When fixed mold temperature increases from 120 ℃ to 140 ℃, maximum warpage deformation of plastic part increases from 0.2 mm to 0.4 mm, an increase of 0.2 mm, showing a negative effect on maximum warpage deformation. Increasing holding pressure from 80 MPa to 100 MPa, cooling time from 40 s to 80 s, and melt temperature from 370 ℃ to 390 ℃ all reduced maximum warpage deformation of plastic part from 0.31 mm to 0.2 mm, a decrease of 0.11 mm. All three factors had a positive effect on maximum warpage deformation, but impact was relatively small.

 

Figure 4 Main effect diagram of warpage deformation.
Interaction effect diagram of warpage deformation reflects influence of interaction between factors on deformation of plastic part. If curves of factors show an intersecting trend, it indicates that two factors have a significant impact on maximum warpage deformation of plastic part; otherwise, it indicates that there is no significant influence between them. As shown in Figure 5, curves of various factors in experiment are basically parallel, with no obvious intersection or overlap trend, indicating that influence of each factor on maximum warpage deformation of plastic part is insignificant.

 

Figure 5. Interaction effect diagram of warpage deformation

Based on standardized effect normal diagram and Pareto chart of primary model (see Figure 6), second-order factors have virtually no effect on maximum warpage deformation of plastic part, while first-order factors A, B, C, and E have a significant effect on maximum warpage deformation of plastic part. Among them, A, C, and E have a positive effect on deformation of plastic part, while B has a negative effect. Therefore, second-order insignificant factors are deleted, and only first-order significant factors are used to construct quadratic model, so as to more accurately analyze influence of factors on maximum warpage deformation of plastic part.

 

Figure 6. Standardized effect normal diagram and Pareto chart

Regression analysis is mainly used to explore correlation between a single variable and multiple variables. Its core lies in revealing dependency law between variables that is obscured by random factors through experimental or observational data. In statistics, sum of squares of all deviations reflects dispersion of data, and calculation formula is shown in Equation (1).
 
Where SS is sum of squares of deviation, representing degree of deviation between measured value and mean; N is total sample size; Xi is specific value of key factor affecting deformation in i-th measurement, and  shows average value of key factor.
According to principle of sum of squares decomposition in regression analysis:
 
Where SSTotal is total sum of squares of deviation, reflecting dispersion of warping deformation; SSMode is within-group sum of squares of deviation, reflecting random error within all populations; SSError is between-group sum of squares of deviation, reflecting main effect within all populations.
Goodness of fit of linear regression model can be evaluated by R², which reveals proportion of independent variable's common explanation for degree of variation of dependent variable.
 
R-Sq is multivariate total correlation regression coefficient, which is ratio of regression sum of squares to total sum of squares of deviation.
 
When there is only one independent variable, R-Sq equals R², and the closer value is to 1, the better.
When a new independent variable is added to model, regardless of whether effect of newly added independent variable is significant, R-Sq will be inaccurate. To accurately evaluate model, R-Sq(adj) was introduced. R-Sq(adj) is correlation coefficient after deducting influence of number of terms in regression equation, thus accurately reflecting model, i.e.:
 
Where p is total number of terms in regression equation (including constant term); n is total number of observations.
Therefore, R-Sq = 96.24%, R-Sq(adj) = 93.98%. According to judgment criteria of regression equation in DOE algorithm, both R-Sq and R-Sq(adj) are close to 1, and difference between them is small, indicating that model fits well.
Results of experimental variance analysis are shown in Table 4. P-values of all main effects are less than significance level of 0.05, indicating that model effect is significant. F-value determines degree of influence; the larger F-value, the more significant effect on warpage deformation. This analysis result provides an important theoretical basis for subsequent optimization of process parameters, helps to identify key factors that play a major role in maximum warpage deformation of plastic parts and formulate corresponding improvement strategies.

 

Table 4. Results of Analysis of Variance

Purpose of residual analysis is to diagnose fit between model and data based on residuals. Distribution of warpage deformation residuals is shown in Figure 7. Data points exhibit a relatively uniform spatial distribution, ensuring high reliability of warpage deformation test results after excluding measurement errors and random interference factors.

 

Figure 7. Distribution of Warpage Deformation Residuals
Normal probability distribution of residuals is shown in Figure 7(a). Linear regression equation is presented as a straight line, distribution of scatter points reflects degree of fit between measured data and predicted curve. Vast majority of data points are distributed near reference line, confirming reliability of measured data and indicating that warpage deformation accurately reflects actual deformation characteristics.
Distribution of residuals and fitted values is shown in Figure 7(b), reflecting degree of deviation between observed data and theoretical expectation. Scatter point distribution characteristics show that measured data exhibits uniformity, indicating a high degree of agreement with predicted results.
Residual histogram (see Figure 7(c)) reveals probability distribution characteristics of measured values. Based on confidence level, measurement results have the best reliability when absolute value of residual is 0.05.
Observation sequence plot (see Figure 7(d)) is used to verify assumption that residuals are independent of other residuals. Residuals are randomly distributed around center line, indicating effectiveness of model.

A systematic analysis was conducted on optimization problem of maximum warpage deformation of plastic part. Minimum and maximum values of maximum warpage deformation were both set to 0. Response optimizer module of Minitab software was used for parameter optimization. This module, by establishing a mathematical model and applying an optimization algorithm, can effectively identify optimal combination of key parameters. After optimization, desired performance reached 0.9997. Optimized parameter combination is shown in Figure 8: moving mold temperature 170 ℃, fixed mold temperature 150 ℃, holding pressure 100 MPa, cooling time 40 s, and melt temperature 388 ℃.

 

Figure 8: Output of optimal parameters for each factor

Parameters output from Minitab were imported into mold flow analysis software, and maximum warpage deformation of plastic part was analyzed again. As shown in Figure 9, under optimal process combination in full factorial experiment, maximum warpage deformation of reflector's optical region was 0.110 mm (consistent on both sides), a reduction of 0.434 mm compared to deformation under default process parameter combination. Through DOE experiment optimization, maximum warpage deformation of reflector's optical region plastic part was significantly improved compared to default parameters.

 

Figure 9. Optimal Parameter Mold Flow Analysis Results

Optimized parameter combination from DOE was applied to actual production process. A COMET L3D 2 5M blue light scanner was used to perform high-precision 3D scanning inspection of plastic parts. This device has a resolution of 2448*2050 and a measurement accuracy of 0.0015 mm. Inspection results are shown in Figure 10. Maximum warpage deformation in optical area of left plastic part is 0.04 mm, and maximum warpage deformation in optical area of right plastic part is 0.07 mm. Compared with plastic parts with default parameters (see Figure 11), optimized parameter combination significantly improved maximum warpage deformation in optical area, and deformation was controlled within a reasonable range.

 

Figure 10 Physical scan result of optimized parameters

 

Figure 11 Physical scan result of default parameters (unit: mm)

GB 4599-2007 "Automotive Headlights" standard stipulates that low beam lamps must have a clear cutoff line. Design function of this reflector bowl is precisely to produce this cutoff line when headlight is illuminating. Figure 12 shows light distribution result with default parameters. Cutoff line is unclear, and light source edge is blurred. Figure 13 shows light distribution result after optimizing parameters. Light pattern is complete, and cutoff line is clearly visible, meeting requirements.

 

Figure 12 Light distribution result with default parameters

 

Figure 13 Light distribution result with optimized parameters

To avoid interference from other factors on test results, only 5 factors were adjusted in Moldflow analysis, while other data settings remained unchanged. During melt injection, same injection molding machine was used, and only 5 experimental factors were adjusted, while other production conditions remained consistent. Five reflector bowls were produced using both data before and after optimization. In laboratory, same test conditions and equipment were used to perform blue light scanning and optical tests on plastic parts.
Based on comparison of data before and after experiment, experimental data are shown in Table 5. Before optimization, maximum warpage deformation in optical region of plastic part, as analyzed by mold flow analysis, was 0.544 mm. Blue light scanning results showed that maximum warpage deformation in optical region of left plastic part was 0.379 mm, and maximum warpage deformation in optical region of right plastic part was 0.597 mm. Optical experiment revealed that light source edge was blurry and cutoff line was unclear, resulting in a failed light distribution test. After optimization, maximum warpage deformation in optical region of plastic part, as analyzed by mold flow analysis, was 0.110 mm. Blue light scanning results showed that maximum warpage deformation in optical region of left plastic part was 0.04 mm, and maximum warpage deformation in optical region of right plastic part was 0.07 mm. Optical experiment showed that light source was intact, cutoff line was clearly visible, and light distribution test passed.

Table 5: Data Before and After Experiment