Abstract: Taking commercial centrifugal pump heads as research object, injection molding process was simulated using Moldex3D mold flow analysis software. Three gating schemes were set according to structural characteristics of product. Optimal scheme was selected through simulation analysis of injection molding process to obtain mold design ideas and predict potential quality problems after product molding. Results show that balanced gating scheme has the best overall performance, with a warpage deformation of 1.588 mm and a volume shrinkage rate of 2.444%. After confirming optimal gating scheme, filling time (A), holding time (B), cooling time (C), and mold temperature (D) were used as experimental factors. A five-factor, four-level orthogonal experiment was constructed using Taguchi method to obtain optimal process parameters, range and variance analyses were used to test confidence level of results. Using the total warpage displacement as primary weighting factor, range analysis determined optimal combination of molding parameters to be A1B1C1D1, and variance analysis verified that confidence level of range analysis results was higher than 99%. Compared to initial scheme, warpage deformation of product decreased from 1.588 mm to 1.214 mm, a reduction of 23.6%; cooling time decreased to 10 s, a reduction of 40%. This demonstrates that use of mold flow analysis technology significantly optimized product quality and production efficiency, providing a feasible method for predicting plastic part performance, reducing production costs, and improving production efficiency.
Injection molding is the most commonly used method in plastics industry. It is applicable to production of most plastic products and has advantages such as short production cycle, high degree of automation, diverse product shapes and material selection. However, to produce high-quality, high-performance injection molded products, it is necessary to summarize experience and gain a deep understanding of polymer processing, especially rheology research. Therefore, many polymer product manufacturers adopt a trial-and-error approach in the early stages of new product design, accumulating experience through multiple adjustments to obtain relatively ideal results. This method yields highly accurate results, but consumes a large amount of human and time resources. With continuous development and maturation of modern injection molding technology, traditional trial-and-error method for exploring processes and making molds can no longer meet market demands. Driven by this technological development trend, some commercial computer-aided engineering software has gradually been used by mold manufacturers to achieve low-cost, high-efficiency mold design. Moldex3D is one of these professional finite element analysis software programs. Moldex3D software has a more precise three-dimensional mesh generation technology, which can improve accuracy of results while reducing analysis time and can accurately reflect various situations in injection molding process. Output results can be used to guide mold design and confirm process parameters, saving manpower and time costs in trial and error process to a certain extent, especially losses caused by mold trial and error. Centrifugal pump heads need to play role of bearing impeller and conveying liquid substances during normal use. They need to endure high-speed flushing and long-term corrosion of liquid and pressure brought by impeller rotation. Therefore, high mechanical strength, high wear resistance, weather resistance and high dimensional stability are crucial for centrifugal pump heads. Polyphenylene sulfide (PPS) and polymer of tetrafluoroethylene, hexafluoropropylene and vinylidene fluoride (THV) are two special engineering plastics. PPS has high mechanical strength and high weather resistance and strong dimensional stability. THV, as a fluoroplastic, has extremely strong wear resistance and weather resistance. Composite material formed by combination of two fully meets all requirements for preparing centrifugal pump head materials. We selected glass fiber (GF) modified PPS/THV composite material, whose tensile strength and flexural strength reached 110 MPa and 154 MPa respectively, and average friction coefficient was 0.24. It has extremely high mechanical properties, wear resistance and weather resistance, is an excellent material for producing centrifugal pump heads. Material information of self-made GF modified PPS/THV composite material was imported into Moldex3D. Material was used to perform mold flow simulation analysis on centrifugal pump head, molding parameters were optimized by Taguchi method orthogonal experiment to ensure that product with superior performance and high production efficiency was obtained.

Referring to design drawings in Figure 1, centrifugal pump head was modeled in three dimensions using UG modeling software. Obtained model was repaired by CADdoctor and then imported into Moldex3D for mold flow analysis. Dimensions of plastic part after import are 346 mm * 354 mm * 160.8 mm, and thickness distribution is 2.29~76.46 mm. Most of thickness is distributed between 2.29~25.35 mm, and average thickness is 16.7 mm. The overall thickness distribution is relatively uniform, and there are few sudden changes in thickness. This can ensure stable transmission of pressure during melt filling process and reduce uneven distribution of volume shrinkage.

 

Fig. 1 Design drawing of centrifugal pump head

Due to large volume of product, in order to ensure sufficient melt filling and smooth pressure transmission, a multi-gate gating scheme should be selected. In order to meet appearance requirements of plastic part, gate should not be set on a smooth surface. At the same time, generation of a large number of low-quality stitch lines should be avoided. Therefore, the only available positions are upper and lower end faces, inlet end face, and middle of plastic part. Wall thickness of inlet is relatively thin and there are some abrupt changes in thickness, which easily leads to flow stagnation and makes it difficult to set gate. Finally, three gate schemes were set on upper and lower end faces and middle of plastic part. Runner system of scheme (a) and scheme (b) is set as a circular cold runner with a diameter of 8 mm and gate is a circular cross section of 4π mm2; scheme (c) is a balanced injection scheme, which uses a hot runner with a diameter of 8 mm and gate is a rectangular interface of 24 mm2. Specific distribution is shown in Figure 2.

 

Fig. 2 Design of different gates
(a) Bottom injection (b) Top injection (c) Equilibrium injection
When melt cools and forms in mold, temperature change will directly affect performance of product[8]. A reasonable water channel design can effectively remove heat accumulated inside product, improve production efficiency of product, reduce problems such as warping deformation and stress cracking caused by uneven heat dissipation. Due to large volume of product and presence of some concave structures, water channel on the outside alone cannot smoothly remove heat accumulated. Therefore, based on structural characteristics of product, multiple water channels were added at inlet and bottom reinforcing ribs. Diameter of bottom annular water channel is 8 mm, and diameter of remaining cooling water channels is 12 mm. The overall layout is shown in Figure 3.

 

Figure 3: Design of cooling water system
(a) Front view (b) Bottom view

Plastic part was processed using Moldex3D Studio, with denser point-spreading in local circular areas to ensure circular features were maintained during mesh generation. Mesh type was Solid, with parameters set to BLM3 layers and an offset ratio of 0.5. Generated solid mesh had 4.72 million elements, achieving a mesh matching degree of 94%, which met analysis requirements while balancing computational efficiency and accuracy.

 

Fig. 4 Mesh distribution of centrifugal pump head

Material selected for analysis was GF-modified PPS/THV alloy, composed of PPS (90 parts), THV (10 parts), GF (30 parts), KH570 (2.0 parts), and ethylene-methyl acrylate-glycidyl methacrylate (8 parts) melt blend. This material has excellent mechanical properties, weather resistance, and wear resistance, can maintain long-term use even in harsh working environments. Material parameters were imported into software for subsequent simulation. Recommended processing temperature for injection molding was 300~320 ℃, recommended mold temperature was 100 ℃, Poisson's ratio was 0.385, specific heat was 3702.2 J/(kg·℃). To ensure comparability of results, same process parameters were set for three schemes, as shown in Table 1.

Table 1 Initial process parameters

Figure 5 shows distribution of melt in mold when 60% filled. As can be seen from data axis on the right, filling time for all three schemes is approximately 5.4 s, consistent with filling time set in process parameters. No flow lag occurred during filling process. In schemes (a) and (b), due to gate design, portion closer to gate will complete filling process first and enter holding pressure state. This significant flow imbalance will cause unevenness in melt holding pressure and cooling process, affecting warpage deformation of material.

 

Fig. 5 Flow wavefront time results of various schemes when filling 60%

Due to large volume of plastic part, only multi-gate injection can be used to ensure transmission of melt filling and holding pressure. Therefore, there are many stitching lines formed by meeting of multiple melts inside plastic part. Quality of these stitching lines mainly depends on temperature and angle of convergence when melts meet. The smaller convergence angle, the more obvious stitching line, the greater impact on appearance and strength of part. The larger convergence angle, the more fully two melts can be mixed, and the smaller impact on product. Distribution and average value of stitching lines of different runner designs are shown in Figure 6. From average value of convergence angle of stitching lines, scheme (c) > scheme (a) > scheme (b). Quality of stitching line of scheme (c) is significantly higher than that of the other two design schemes. From distribution of sutures, schemes (b) and (c) have fewer sutures, and their distribution is far from stress points of product assembly. Scheme (a) has a large number of sutures, and their extensive distribution on both sides of holes seriously affects strength of product. Considering suture convergence angle and distribution, scheme (c) is the most reasonable design.

 

Fig. 6 Distribution of stitches of each scheme
(a) Bottom injection (b) Top injection (c) Equilibrium injection

Distribution of volumetric shrinkage rate has a direct impact on the total warpage displacement. Distribution of volumetric shrinkage rate within product can be used to assess product's quality and stability. Figure 7 shows results of volumetric shrinkage rate. Product is cut open from center using XY plane to observe distribution more clearly. As can be seen from figure, scheme (c) has the lowest volumetric shrinkage rate, only 2.444%, and the most uniform distribution. This is mainly because gate located in the middle of product provides a higher flow balance to melt, and smaller flow length ratio compared to previous two schemes allows for smoother pressure transmission during holding.

 

Fig. 7 Distribution of volume shrinkage of each scheme
(a) Bottom injection (b) Top injection (c) Equilibrium injection

Warpage deformation analysis is the most direct data for inspecting product quality and is an important indicator for evaluating dimensional stability, appearance, and quality of product. Figure 8 shows results of the total warpage displacement analysis. From values at probe positions in figure, it can be seen that warpage deformation near gate is smaller than that far from gate. This is due to uneven shrinkage of plastic part caused by flow imbalance. Maximum warpage deformation in schemes (a) and (b) is around 2.45 mm, and deformation at the bottom hole is larger, affecting assembly quality. In scheme (c), maximum warpage deformation is 1.588 mm, which is 35.2% lower than previous two schemes. Deformation is within a reasonable range, indicating that flow channel design of scheme (c) is more reasonable and can ensure molding accuracy of product.

 

Fig. 8 Distribution of total warpage displacement of each scheme
(a) Bottom injection (b) Top injection (c) Equilibrium injection

When filling reaches 60%, injection side of product in schemes (a) and (b) is basically filled, entering holding pressure stage prematurely. This will increase difference in warpage deformation between top and bottom of product, easily leading to defects such as uneven ends. From stitching results, scheme (c) has 33.2% high-quality stitches with an angle greater than 122°, while the other two schemes only have about 20% of high-quality stitches. Meanwhile, scheme (c) exhibits the smallest volumetric shrinkage rate and the most evenly distributed warpage deformation, with volumetric shrinkage rate and total warpage displacement reduced by more than 40% and 35% respectively compared to the other two schemes. Based on above simulation results, scheme (c) was ultimately chosen as basis for subsequent process optimization design.

Orthogonal experiments are a method to quickly find optimal combination of process parameters with fewer experiments. They are characterized by high efficiency, high reliability, comprehensive and balanced combinations. Applying this method can effectively reduce R&D costs and time while ensuring product quality. Based on analysis results above, orthogonal experimental design was selected for scheme (c). The total warpage displacement and volume shrinkage rate of product were used as optimization indicators. Filling time (A), holding time (B), cooling time (C), and mold temperature (D) were used as experimental factors. A Taguchi-type standard orthogonal array of L16 (45) was selected to establish a five-factor, four-level orthogonal experiment (where factor E is a blank group, established as variance error group). Table 2 shows level values of each factor.

 

Table 2 Factors and levels of orthogonal test

For products that need to be assembled with other components, warpage and volume shrinkage rate are important factors determining performance. Large warpage and uneven volume shrinkage rate will lead to a decrease in fit of assembled parts. It should be noted that Ki in Tables 4 and 5 represents arithmetic mean of any column of tests at level i, and R is range. A larger R value indicates a more significant impact of parameter on optimization index.

 

Table 3 Results of orthogonal test

 

Table 4 Range analysis of total warpage displacement
According to results in Table 4, range of each experimental factor is ranked as R(C) > R(B) > R(A) > R(D). That is, for the total warpage displacement, factor C (cooling time) has the greatest impact, while factor D (mold temperature) has the least impact. Optimal combination is A1B1C1D1, meaning that when filling time is 4.6 s, holding time is 8 s, cooling time is 15 s, and mold temperature is 100 ℃, the total warpage displacement of product is minimized. Similarly, data in Table 5 shows that factor with the greatest impact on volume shrinkage rate is holding time. When combination is A1B1C1D3, volume shrinkage rate of product is minimized. Effect curves of each factor in figure provide a more intuitive view of influence trend of different factors on optimization index.

 

Table 5 Range analysis of volume shrinkage

 

Fig. 9 Effect curve of each factor
Compared to range analysis, analysis of variance can further analyze interaction between factors based on range analysis, eliminating data fluctuations caused by experimental errors. By comparing F-value and P-value with standard value, variables with significant influence on optimization index can be identified among multiple control variables, resulting in more accurate and confident conclusions. Based on degrees of freedom of factors and errors, F-test critical value table was consulted, and F-standard value with a confidence level of 99% was obtained as 26.45. Comparing data in Table 6, it can be seen that F-values of factors A, B, C are greater than F-standard value, indicating that confidence level of conclusion that these factors have a significant influence on optimization index is greater than 99%. The larger F-value, the greater influence of factor on optimization index. At the same time, F-value of factor D is much smaller than F-standard value, indicating that factor D has basically no influence on experimental results of total warpage displacement.

 

Table 6. Variance analysis of total warpage displacement
Based on F-test, experimental conclusions were further tested using p-value. P-values for factors A, B, and C were much less than 0.01, while p-value for factor D was much greater than 0.01, consistent with pattern observed by F-value test, indicating reliability of conclusions (see Table 6). Similarly, comparing data in Table 7, it can be seen that factors A and B have a significant impact on optimization indicators, with factor B having the greatest impact on volume shrinkage rate. Comparing results of variance analysis and range analysis, patterns obtained by two analyses are same, proving accuracy of analysis.

 

Table 7. Variance analysis of volume shrinkage

Combining orthogonal experimental design and range and variance analysis, two optimal process parameter combinations, A1B1C1D1 and A1B1C1D3, were confirmed. Setting A1B1C1D1 as parameter group (A) and A1B1C1D3 as parameter group (B), importing them into Moldex3D for analysis and verification, following results were obtained: As shown in Figure 10, volume shrinkage rate of product in parameter group (A) was 2.444%, and the total warpage displacement was 1.214 mm. Compared with parameter group (B), volume shrinkage rate increased by 5.5%, and the total warpage displacement decreased by 15.2%. The total warpage displacement is a major factor affecting performance of product, directly impacting its appearance and assembly, therefore has a higher weight than volume shrinkage rate in optimization process. Therefore, parameter group (A) was selected as optimal process parameter.

 

Figure 10: Result of volume shrinkage and total warpage displacement after optimization
Comparing results with initial scheme (c), it was found that volume shrinkage rate of parameter group (A) remained unchanged, while the total warpage displacement decreased by 23.6%. Based on this, cooling time of optimized scheme was reduced by 10 s compared to initial scheme, a reduction of 40%, significantly improving production efficiency. This demonstrates that using orthogonal experiments to improve product quality, optimize production efficiency is feasible.

(1) By performing mold flow analysis on centrifugal pump head, a type of injection molded part, potential defects such as seam lines and warpage in finished product were predicted. Comparing results of three gate design schemes, scheme (c) was determined to be optimal gate design. Product produced by this scheme had a volume shrinkage rate of 2.444% and a total warpage displacement of 1.588 mm. Compared to the other two schemes, warpage deformation was reduced by 35%, providing insights and guidance for mold design.
(2) Range analysis of orthogonal analysis results revealed that factor C had the greatest impact on the total warpage displacement, while factor B had the most significant impact on volume shrinkage rate. Analysis of variance verified that confidence level of this conclusion was greater than 99%. After comprehensive consideration, optimal combination of product process parameters was determined to be A1B1C1D1.
(3) Optimal process combination was then simulated and analyzed again in software. Under optimal process conditions, volume shrinkage rate of product was 2.444%, and the total warpage displacement was 1.214 mm. Compared with initial analysis results of scheme (c), volume shrinkage rate remained unchanged, while the total warpage displacement decreased by 23.6%. Cooling time was reduced by 10 s compared to initial scheme, a reduction of 40%. Use of mold flow analysis technology significantly improved production efficiency and product quality.