As an internal gear manufacturer, we constantly face challenges in producing high-precision internal gears for automotive applications, where lightweight and noise reduction are critical. The double-headed spiral internal gear, with its complex geometry, requires meticulous cooling process design to minimize warpage and ensure dimensional accuracy. In this study, we explore the optimization of cooling strategies for such gears, focusing on how different cooling channel layouts impact key performance metrics like flow front temperature, cooling medium temperature, and warpage deformation. Our goal is to enhance the efficiency and precision of injection molding for internal gears, which are increasingly replacing metal components in vehicles to achieve carbon neutrality targets. By leveraging advanced modeling and simulation tools, we aim to provide insights that benefit internal gear manufacturers in achieving superior product quality.
The double-headed spiral internal gear features a cylindrical thin-walled structure with an inner cavity, external smooth surfaces, and internal helical teeth. Key dimensions include an outer diameter of 26 mm, inner diameter of 11 mm, and height of 39 mm, with wall thicknesses varying from 0.8 mm to 0.86 mm. The internal helical teeth must maintain a spacing tolerance within 0.05 mm to ensure proper meshing and low noise in transmission systems. For internal gears like these, uniform cooling is essential to prevent defects such as shrinkage, warping, or uneven filling, which can compromise the gear’s performance. As an internal gear manufacturer, we selected polyoxymethylene (POM) as the material due to its excellent mechanical properties, including high strength, wear resistance, and low friction, making it ideal for automotive internal gears. POM’s processing parameters include a melt temperature range of 205–225°C and a mold temperature range of 80–100°C, with maximum allowable shear stress of 0.45 MPa and shear rate of 40,000 s-1.
To begin the analysis, we used UG (Unigraphics NX) software to create a detailed 3D model of the double-headed spiral internal gear. This model was then imported into Moldflow for meshing and simulation. We employed a 3D mesh type to accurately capture the gear’s geometry, ensuring that the mesh quality met simulation requirements. The mesh had a maximum aspect ratio of 26.82, a minimum of 1.05, and an average of 3.07, with a matching rate exceeding 88%, which is sufficient for reliable mold flow analysis. This step is crucial for internal gears, as poor mesh quality can lead to inaccurate predictions of filling and cooling behavior. For internal gear manufacturers, such preparatory work helps in identifying potential issues early, reducing trial-and-error during production.
The gating system was designed to facilitate uniform filling and minimize defects. Given the small size of the internal gears, we implemented a cold runner system with a main runner diameter tapering from 4 mm to 7 mm, a U-shaped main channel of width 7.5 mm, and branch runners reducing from 7 mm to 3 mm. Each cavity was fed by three cold gates of diameter 1.5 mm. This design ensured a balanced fill, with a fill time of 1.378 seconds and a V/P switch at 98.5% cavity volume, corresponding to a switch pressure of 80.52 MPa. The maximum injection pressure was 80.53 MPa, and the holding pressure was set to 90 MPa. Such optimization is vital for internal gear manufacturers to achieve consistent part quality and reduce material waste.
Optimizing the injection molding parameters was essential to minimize warpage, a common issue in internal gears. We employed response surface methodology (RSM) with a Box-Behnken design to analyze the effects of melt temperature (180–240°C), mold temperature (40–110°C), holding pressure (50–100 MPa), and holding time (2–18 s) on warpage deformation. The quadratic model for warpage (Y) can be expressed as:
$$Y = \beta_0 + \sum_{i=1}^{4} \beta_i X_i + \sum_{i=1}^{4} \beta_{ii} X_i^2 + \sum_{i<j} +=""
where \(X_i\) represent the process parameters, \(\beta\) coefficients are determined through regression, and \(\epsilon\) is the error term. After analysis, the optimal parameters were set as follows: mold temperature of 90°C, melt temperature of 215°C, holding pressure of 90 MPa, and holding time of 10 s. These parameters were used in subsequent cooling process evaluations to ensure that the internal gears meet precision standards. For internal gear manufacturers, such statistical optimization helps in fine-tuning processes without extensive experimental runs.
| Parameter | Value |
|---|---|
| Mold Surface Temperature | 90°C |
| Melt Temperature | 215°C |
| Cooling Water Initial Temperature | 25°C |
| Holding Pressure | 90 MPa |
| Holding Time | 10 s |
| Fill Time | 1.3 s |
We proposed three cooling channel layouts to investigate their impact on the cooling efficiency for internal gears: traditional cooling (Scheme 1), axial cooling (Scheme 2), and spiral cooling (Scheme 3). All schemes used circular cross-section channels to maximize heat transfer. The cooling channel parameters, including diameter, distance between adjacent channels, and distance from the mold surface, were optimized using an orthogonal experimental design. The factors and levels are summarized in Table 2, and the orthogonal array L9 was applied to determine the optimal configuration. The response variable was warpage deformation, and the results indicated that the distance from the mold surface had the greatest influence, followed by channel diameter and inter-channel distance. The best combination was a channel diameter of 6 mm, inter-channel distance of 12 mm, and mold surface distance of 9 mm, which minimized warpage for internal gears.
| Factor | Level 1 | Level 2 | Level 3 |
|---|---|---|---|
| Cooling Channel Diameter (mm) | 6 | 7 | 8 |
| Distance Between Channels (mm) | 12 | 15 | 18 |
| Distance from Mold Surface (mm) | 9 | 10 | 11 |
| Experiment No. | Channel Diameter (mm) | Inter-Channel Distance (mm) | Mold Surface Distance (mm) | Warpage Deformation (mm) |
|---|---|---|---|---|
| 1 | 6 | 12 | 9 | 0.2979 |
| 2 | 6 | 15 | 10 | 0.2986 |
| 3 | 6 | 18 | 11 | 0.3022 |
| 4 | 7 | 12 | 10 | 0.3011 |
| 5 | 7 | 15 | 11 | 0.3020 |
| 6 | 7 | 18 | 9 | 0.2998 |
| 7 | 8 | 12 | 11 | 0.3007 |
| 8 | 8 | 15 | 9 | 0.2995 |
| 9 | 8 | 18 | 10 | 0.2992 |
The range analysis from Table 3 showed that the distance from the mold surface had the largest range (R = 0.0025), indicating its dominant effect on warpage for internal gears. This is critical for internal gear manufacturers to consider when designing cooling systems, as improper channel placement can lead to uneven cooling and dimensional inaccuracies. The optimal parameters were applied to all three cooling schemes for further comparison using Moldflow simulations.
We evaluated the three cooling schemes based on flow front temperature, cooling medium temperature, and overall warpage deformation. Flow front temperature represents the temperature at the melt flow front during injection, and a smaller temperature difference indicates more uniform cooling. For internal gears, this is vital to prevent residual stresses and warping. The axial cooling scheme (Scheme 2) exhibited the smallest temperature difference of 23.7°C, compared to 26.1°C for spiral cooling (Scheme 3) and an intermediate value for traditional cooling (Scheme 1). This uniformity in Scheme 2 can be attributed to the axial alignment of channels, which provides consistent heat dissipation across the gear’s geometry. The cooling medium temperature, measured as the difference between inlet and outlet, should not exceed 3°C to ensure stable cooling. Scheme 2 again performed best, with the smallest temperature difference, while Scheme 3 had the largest, highlighting the superiority of axial cooling for internal gears.
Warpage deformation is a key indicator of molding precision for internal gears. The overall warpage was analyzed numerically, with Scheme 2 showing the lowest value of 0.2748 mm, followed by Scheme 3 at 0.2777 mm and Scheme 1 at 0.2979 mm. This can be expressed mathematically by considering the thermal-induced strain during cooling. The warpage deformation \(\delta\) can be related to the temperature gradient \(\nabla T\) and material properties through the equation:
$$\delta = \alpha \cdot L \cdot \Delta T \cdot f(\nabla T)$$
where \(\alpha\) is the coefficient of thermal expansion, \(L\) is a characteristic length, \(\Delta T\) is the temperature difference, and \(f(\nabla T)\) is a function of the temperature gradient. For internal gears, minimizing \(\nabla T\) through optimized cooling reduces \(\delta\), as achieved in Scheme 2. The results demonstrate that axial cooling not only enhances temperature uniformity but also significantly reduces deformation, making it the preferred choice for internal gear manufacturers aiming for high precision.
| Cooling Scheme | Flow Front Temperature Difference (°C) | Cooling Medium Temperature Difference (°C) | Overall Warpage Deformation (mm) |
|---|---|---|---|
| Traditional Cooling (Scheme 1) | 24.5 | 2.8 | 0.2979 |
| Axial Cooling (Scheme 2) | 23.7 | 2.2 | 0.2748 |
| Spiral Cooling (Scheme 3) | 26.1 | 3.1 | 0.2777 |
Based on the optimal axial cooling scheme, we designed an injection mold for the double-headed spiral internal gear. The mold assembly included components such as cavity inserts, core pins, sliders, and ejector systems, all tailored to accommodate the gear’s complex internal teeth. The cooling channels were integrated axially around the gear cavity to ensure efficient heat removal. This design not only shortens the cooling time but also improves part quality by maintaining uniform temperatures. For internal gear manufacturers, such mold designs can be adapted to various gear sizes and types, enhancing production flexibility.
To validate the simulation results, we conducted trial molding using the optimized mold and process parameters. The produced internal gears were inspected for dimensional accuracy and surface quality. The gears exhibited smooth surfaces without defects like flashes or sink marks, and the internal helical teeth met the required tolerance of ±0.05 mm. Measurement using a gear testing instrument confirmed that the gears achieved industrial grade 9 precision, satisfying the demands for automotive applications. This practical verification underscores the reliability of our cooling process optimization for internal gears, providing a reference for other internal gear manufacturers to improve their processes.
In conclusion, the cooling process plays a pivotal role in the precision injection molding of double-headed spiral internal gears. Through systematic optimization using response surface methodology and orthogonal experiments, we identified that axial cooling with specific channel parameters minimizes warpage and ensures uniform cooling. The axial cooling scheme reduced warpage deformation to 0.2748 mm, outperforming traditional and spiral layouts. This study highlights the importance of cooling channel design in enhancing the quality of internal gears, which are essential for automotive lightweighting and noise reduction. For internal gear manufacturers, adopting such optimized cooling strategies can lead to significant improvements in production efficiency and product performance, ultimately contributing to the advancement of plastic gear technology in the industry.