3.1. Analysis of Finished Product Quality Under Varying Melt Temperatures
Following the parameter settings described above, for the melt temperature variation study, the mold temperature was held constant at 120 °C for PET and 90 °C for PA6, while the melt temperature was incrementally increased at intervals of 10 °C. Simulations were conducted using the filling–packing–warping analysis sequence.
As shown in
Figure 2, with the melt temperature increasing at intervals of 10 °C, the maximum residual stress in both PET and PA6 injection-molded parts exhibits an initial rise followed by a decline, with peak values occurring near 270 °C for both materials. The variation range of residual stress is 12.8 MPa, corresponding to a 12.4% relative change for PET, and 12.1 MPa, corresponding to an 11.1% relative change for PA6. The deformation of both materials shows a steady upward trend with increasing melt temperature, with PA6 displaying slightly less deformation than PET. The analysis of finished product quality under varying melt temperatures concludes that the influence of melt temperature on key parameters follows the order: residual stress > deformation > volumetric shrinkage. The volumetric shrinkage of injection-molded parts is minimally affected by changes in melt temperature. Similarly, simulations were conducted by holding the melt temperature constant while incrementally increasing the mold temperature at intervals of 10 °C.
As shown in
Figure 3, as the mold temperature increases from 80 °C to 130 °C, the maximum residual stress of PET exhibits a pattern of initial fluctuation followed by a continuous decline: in the range of 80–100 °C, the stress remains between 103.5 and −105.0 MPa; above 100 °C, the stress continuously decreases from 104.5 MPa at 100 °C to 91.0 MPa at 130 °C. The maximum residual stress of PA6 exhibits an initial increase followed by a decrease: in the range of 70–100 °C, the stress continuously rises, reaching a peak of 111 MPa at 100 °C; above 100 °C, the stress continuously decreases to 102 MPa at 130 °C. The deformation of both materials continuously increases with higher mold temperature, with PA6 deformation being more sensitive to temperature variations; The volumetric shrinkage of both PET and PA6 increases nearly linearly with rising mold temperature, indicating that mold temperature is a key process parameter controlling the volumetric shrinkage of injection-molded parts. Within the same temperature variation range (from 80 °C to 130 °C for PET and from 70 °C to 120 °C for PA6), PA6 shows a greater change in volumetric shrinkage than PET. Quantitatively, the average shrinkage–temperature slope for PA6 is approximately 0.030%/°C, compared to 0.023%/°C for PET. This represents a 30% higher sensitivity for PA6. In terms of total change, the volumetric shrinkage of PA6 increases by 1.48% across its investigated mold temperature range, while PET increases by 1.15% across its range, making the absolute change in PA6 approximately 29% larger than that of PET.
This quantitative difference indicates that the thermal shrinkage behavior of PA6 is more sensitive to mold temperature variations than that of PET. The analysis of finished product quality under varying mold temperatures concludes that as the mold temperature increases, the volumetric shrinkage of injection-molded parts exhibits an approximately linear increase. The extent of influence of mold temperature on the three parameters can be ranked roughly as follows: volumetric shrinkage > residual stress > deformation. This ranking reflects the different sensitivities of these parameters to mold temperature variations, as discussed below. Volumetric shrinkage shows the largest absolute and relative changes (PET: 1.15%, 150.9%; PA6: 1.48%, 103.4%), indicating that it is most directly influenced by mold temperature. Residual stress exhibits moderate changes (PET: 14.0 MPa, 13.1%; PA6: 10.2 MPa, 9.3%), while deformation shows the smallest changes, suggesting that it is least sensitive to mold temperature variations among the three parameters.
Through comparison, it can be observed that residual stress is influenced almost equally by melt temperature and mold temperature, and the effect is significant. Deformation is also affected by both melt and mold temperatures, but to a lesser extent compared to residual stress. In contrast, volumetric shrinkage is almost exclusively directly influenced by mold temperature. By comparing the performance of PET and PA6 across different simulation parameter settings in terms of the three key parameters, it is observed that both materials exhibit roughly similar levels of residual stress. However, PET can achieve a slightly lower minimum stress than PA6 through optimization. In terms of deformation, PET and PA6 also demonstrate comparable performance. Regarding volumetric shrinkage, PA6 is more sensitive to changes in mold temperature compared to PET, exhibiting a larger variation range in volumetric shrinkage.
Based on the above analysis, an optimization function was developed to comprehensively evaluate the combined effect of the three key quality indicators. For a given set of parameters, the deviation from the minimum achievable value of each indicator (across all simulated parameter combinations for that material) is denoted as Δp (MPa) for residual stress, Δx (mm) for deformation, and Δs (%) for volumetric shrinkage.
The optimization objective function is defined as: Y = Δp/20 + Δx/0.5 + Δs/1.8. The denominators (20, 0.5, and 1.8) represent the typical variation ranges of each parameter based on the simulation results. The absolute and relative changes in each parameter with melt temperature are summarized in
Table 4, while those with mold temperature are summarized in
Table 5. As shown in these tables, residual stress (Δp) varies by approximately 15–20 MPa across the parameter space (PET: 12.8–14.0 MPa, PA6: 10.2–12.1 MPa), deformation (Δx) varies by approximately 0.5 mm (PET: 0.093–0.116 mm, PA6: 0.031–0.102 mm), and volumetric shrinkage (Δs) varies by approximately 1.8% (PET: 0.043–1.15%, PA6: 0.022–1.48%). By normalizing each deviation by its typical variation range, the three independent quality indicators are scaled to comparable magnitudes, allowing them to be combined into a single objective function. This prevents any single parameter from dominating the optimization due to differences in units or absolute magnitudes.
The additive linear form was chosen for its simplicity and interpretability, as it allows for the direct assessment of each parameter’s contribution to the overall quality index. This approach is commonly used in multi-objective engineering optimization, where multiple quality indicators must be balanced. This form assumes that the three quality indicators are independent and that their effects on overall part quality are approximately additive, which is reasonable given that they represent distinct physical phenomena (mechanical stress, geometric accuracy, and dimensional stability). Multiplicative forms were considered but deemed unsuitable because: (1) different units cannot be meaningfully multiplied, (2) a zero value for any single indicator would force the entire function to zero, which is overly restrictive, and (3) multiplicative forms do not align with the engineering intuition that quality losses from independent factors should be additive.
To verify the robustness of the weight selection, a sensitivity analysis was performed by varying each weight by ±20% and re-evaluating the optimal parameter combinations. The results showed that varying the weights by ±20% changed the optimal parameter selection by less than one temperature increment (10 °C), indicating that the optimization is robust to reasonable variations in weight selection.
Based on the above objective function, the optimal process parameters for the two materials are determined as follows:
PET: Melt temperature of 290 °C, mold temperature of 120 °C.
PA6: Melt temperature of 250 °C, mold temperature of 70 °C.
These optimal parameters correspond to the minimum values of the objective function Y across all simulated parameter combinations. Both optimal parameter sets fall within the extended parameter ranges studied: PET 290 °C melt (260–310 °C) and 120 °C mold (80–130 °C); PA6 250 °C melt (250–300 °C) and 70 °C mold (70–120 °C). Compared to the recommended processing ranges in the material datasheets, PET’s mold temperature (120 °C) is slightly above the recommended 100–110 °C, while PA6’s melt temperature (250 °C) and mold temperature (70 °C) are slightly below the recommended ranges (270–290 °C melt, 80–90 °C mold). These small deviations are within the extended parameter space investigated and are considered acceptable for the purposes of this study.
3.2. Coupled Simulation Analysis of Hydraulic Pressure Testing
Under a hydraulic pressure of 2.4 MPa without considering residual stress from the injection molding process, the stress results at the insert contact surface and within the bulk of both PET and PA6 are significantly below the compliance standard, with both materials exhibiting comparable stress levels.
As shown in
Table 6, the stress levels of both materials are comparable. For hydraulic pressure testing at 2.4 MPa [
12], the typical compliance requirements specify that the insert contact surface stress should not exceed 20 MPa and the bulk surface stress should not exceed 70–90 MPa. The simulation results for both PET (contact: 8.81 MPa, bulk: 19.04 MPa) and PA6 (contact: 9.12 MPa, bulk: 19.57 MPa) are significantly below these thresholds. This indicates that, in the absence of residual stress, both materials would meet the requirements of the hydraulic pressure test.
Taking the von Mises equivalent stress as the key indicator, the simulation shows that the pressure distribution characteristics of the injection-molded parts under different process parameters are generally consistent for both materials. The stress concentration occurs primarily at the inclined boundary region of the insulator, while the overall surface stress distribution remains relatively uniform, as illustrated in
Figure 4.
As shown in
Table 7, referring to the compliance criteria for hydraulic pressure testing (insert contact surface stress ≤ 20 MPa, bulk surface stress ≤ 70–90 MPa), the surface stress of the injection-molded part’s bulk ranges between 70 MPa and 90 MPa. When adopting a higher tolerance limit of 90 MPa, it meets the compliance requirements of the hydraulic pressure test. For PET material, under all parameter conditions, the insert contact surface stress ranges from 24.25 MPa to 27.55 MPa, with all values exceeding the 20 MPa compliance threshold. This indicates that PET injection-molded parts fail to pass the 2.4 MPa hydraulic pressure test under all parameter combinations investigated. In contrast, PA6 material exhibits insert contact surface stresses ranging from 18.29 MPa to 23.36 MPa. The minimum contact stress (18.29 MPa) falls below the 20 MPa compliance threshold, while the maximum contact stress (23.36 MPa) exceeds it. This indicates that under certain parameter combinations, PA6 can meet the hydraulic pressure test requirements.
Specifically, based on the detailed simulation results shown in
Figure 5, PA6 meets the compliance requirements when the melt temperature is below 270 °C and mold temperature is below 120 °C. Under these conditions, the insert contact surface stress remains below the 20 MPa threshold. For example, at the optimal processing parameters identified in
Section 3.1 (melt temperature 250 °C, mold temperature 70 °C), the contact stress is approximately 18.5 MPa, well within the compliance limit. In contrast, parameter combinations with higher temperatures, such as melt temperature > 270 °C or mold temperature > 120 °C, result in contact stresses exceeding 20 MPa, with the maximum value of 23.36 MPa observed at the highest temperature combinations.
As shown in
Figure 5, according to the simulation results, when PA6 material is processed with a melt temperature < 270 °C and a mold temperature < 120 °C, the resulting injection-molded part can pass the 2.4 MPa hydraulic pressure test. Therefore, although PA6 did not exhibit significant differences compared to PET in the simulation of the injection molding process, it demonstrates clear advantages over PET in terms of process performance during hydraulic pressure testing. Compared with the simulation results without applying initial stress, the coupled simulation results with initial stress show significantly higher stress levels. This indicates that the residual stress from the injection molding process plays a crucial role in determining the performance of the workpiece during hydraulic pressure testing.
3.3. Electric Field Analysis and Morphology Design of Insulators
For surfaces directly exposed to SF
6 gas, which are susceptible to damage under extreme voltage impulses, it is essential to study their electric field distribution under lightning impulse voltage. Regarding the interior of the insulating component and the embedded parts, greater attention should be paid to the internal electric field distribution under operating conditions [
11].
In the morphological design of insulators, a two-dimensional axisymmetric model is established for typical insulator application scenarios in GIS/GIL. The simulation domain includes the insulator, SF
6 gas region, central high-voltage conductor (aluminum), and grounded enclosure (aluminum). The central conductor is assigned the operating voltage of 110 kV for rated conditions, while the enclosure is set to ground (0 V). For lightning impulse conditions, a voltage of 550 kV is applied to the central conductor [
14].
The relative permittivity values used in the simulation are based on material properties and operating conditions: for PA6 insulator material, εr = 3.8 (from material datasheet); for SF
6 gas at 0.4 MPa pressure, εr = 1.002; the aluminum electrodes were modeled as perfect electric conductors (PEC) [
14]. The gas pressure of 0.4 MPa represents typical operating conditions in GIS/GIL systems.
The mesh consists of approximately 50,000 triangular elements with refinement in regions of high electric field gradient, particularly near the triple junctions and curved surfaces. Electrostatic field simulations are performed using COMSOL Multiphysics.
Three different insulator–insert contact configurations are designed for electric field simulation, as shown in
Figure 6. The three configurations represent typical interface geometries used in basin-type insulators, namely concave, planar, and convex contact surfaces. Both the concave surface (
Figure 6a) and the planar surface (
Figure 6b) feature a consistent curvature radius of 16.5 mm.
Simulation results indicate that changes in the insert contact surface design primarily affect the electric field strength inside the insulator, while having a relatively minor impact on the electric field within the gas. Among the three designs (concave, planar, and convex contact surfaces), the maximum electric field strengths inside the insulator are 1.4 kV/mm, 1.3 kV/mm, and 1.2 kV/mm, respectively (as shown in
Figure 6). The convex contact surface achieves the lowest maximum internal electric field, indicating the most favorable field distribution, while the planar design exhibits the most uniform field distribution along the interface. All three designs meet the insulation design standards for internal fields under rated operating voltage (3 kV/mm).
Based on the insulation design standard of 3 kV/mm for internal insulator fields under rated operating voltage [
14], the maximum withstand rated operating voltage for each design can be calculated using linear scaling, since the electric field is proportional to the applied voltage under electrostatic conditions. The calculation is as follows:
Among the three designs, the convex contact surface exhibits the lowest maximum electric field inside the insulator, indicating a more favorable electric field distribution., while the convex design enables the highest rated operating voltage. Considering assembly and fixation from a component integration perspective, designing a flat contact surface for the insert may pose challenges in assembly and securing. Therefore, adopting a convex design is beneficial as it facilitates fixation while controlling the electric field strength inside the insulator, thereby enabling a higher rated operating voltage. The simulation was performed with adjustments to the thickness of the insulator near its outer edge, as shown in
Figure 7.
In this study, the edge thickness was reduced from 18 mm to 12.5 mm near the outer rim of the insulator, corresponding to a reduction of 5.5 mm (approximately 30.6%). This modification was chosen to evaluate the influence of edge thickness variations on electric field distribution.
As the edge thickness decreases, both the internal electric field of the insulator and the surface electric field exhibit an increasing trend, rising from approximately 2.1 kV/mm to 2.5 kV/mm (a 19% increase), while the maximum electric field on the housing surface shows a decreasing trend, falling from approximately 2.25 kV/mm to 1.95 kV/mm (a 13% decrease). These numerical values provide quantitative evidence for the observed trends.
The insulator’s ability to withstand lightning impulse is primarily constrained by the electric field intensity on the housing surface. Therefore, when necessary, appropriately reducing the edge thickness of the insulator can help reduce the electric field intensity on the housing surface by up to 13%, thereby enhancing the system’s ability to withstand lightning impulse conditions. However, this modification is also constrained by the 19% increase in internal electric field intensity, requiring a trade-off between this ability under the rated operating voltage and the lightning impulse voltage. For the original insulator design in this study, under the design requirements of a rated operating voltage of 110 kV and a lightning impulse voltage of 550 kV, the corresponding insulation standards can be met.