As a researcher in metal forming technologies, I have extensively studied the challenges faced by internal gear manufacturers in producing high-quality internal gears efficiently. Internal gears are pivotal components in transmission systems like automotive gearboxes and planetary reducers, where precision and durability are paramount. Traditional machining methods, such as cutting, often lead to high production costs, material waste, and limited mechanical properties due to disrupted fiber lines. In contrast, precision plastic forming offers a promising alternative by enabling near-net-shape production with enhanced material strength and reduced waste. However, conventional closed-die forging for internal gears suffers from issues like difficult corner filling and excessive forming forces, which can compromise tool life and increase energy consumption. This study explores an innovative expansion die cavity technique designed to address these limitations, providing a viable solution for internal gear manufacturers seeking to optimize their processes.
The expansion die cavity method modifies the die structure to facilitate metal flow during forming, significantly lowering loads and improving fill quality. Internal gears, with their complex tooth profiles, require precise control over deformation to avoid defects. By integrating principles from closed-die forging and constrained flow forming, this new approach divides the process into two stages: upsetting and ejection. During upsetting, the billet is compressed axially, with material flowing radially into the die cavity, while a deliberately designed expansion space at the bottom corner allows for a “bulge” formation that reduces resistance. In the ejection phase, this bulge is guided back into the main cavity under the constraint of the inclined walls, ensuring complete corner filling and easy demolding. This mechanism not only enhances formability but also reduces the overall forming force by over 70%, making it an attractive option for internal gear manufacturers aiming to improve efficiency and reduce costs.
To implement this technique, the design of the expansion cavity is critical, with key geometric parameters—expansion angle α, dimension in tooth width direction b, and dimension in tooth height direction h—directly influencing the outcome. For instance, α determines the inclination of the cavity walls, affecting metal flow and stress distribution. Similarly, b and h control the volume and shape of the expansion space, which must be optimized to prevent issues like folding or excessive waste. Internal gear manufacturers can leverage these insights to tailor dies for specific gear specifications, such as those with a modulus of 3 mm and 18 teeth, as studied here. Through systematic analysis, I have identified optimal ranges for these parameters to achieve full tooth filling with minimal defects, ensuring that internal gears meet the stringent requirements of modern applications.
In the numerical simulation phase, I employed DEFORM-3D finite element software to model the forming process for a spur internal gear with an external diameter of Φ80 mm. The workpiece material was set to AISI-1045, heated to 1100°C, while the dies were maintained at 350°C to simulate realistic conditions. A friction coefficient of 0.3 was applied using a shear model, and the billet—a ring with an outer diameter of Φ80 mm and inner diameter of Φ62 mm—was discretized into 50,000 elements, with refined meshing around the tooth regions to capture detailed deformation. The upper and lower punches moved at a speed of 10 mm/s, replicating industrial press operations. This setup allowed me to analyze load-stroke curves, stress-strain distributions, and the effects of geometric variations, providing a comprehensive understanding of how internal gears behave under this novel process.
The load-stroke curves revealed a dramatic reduction in forming force compared to traditional closed-die forging. In conventional methods, the force peaks at around 187 kN as the corners become difficult to fill, whereas the expansion cavity technique limits the upsetting force to approximately 50 kN, with ejection forces remaining below 5 kN. This reduction is attributed to the controlled metal flow and the presence of free surfaces in the expansion space, which alleviate pressure buildup. For internal gear manufacturers, this translates to lower energy consumption and extended die life, enabling more sustainable production. The following table summarizes the impact of the expansion angle α on forming forces and fill quality, based on simulations with b = 7 mm and h = 2 mm:
| Expansion Angle α (°) | Upsetting Force (kN) | Ejection Force (kN) | Corner Filling Quality |
|---|---|---|---|
| 6 | 58.5 | 4.8 | Good |
| 8 | 56.2 | 4.5 | Excellent |
| 10 | 54.0 | 4.2 | Excellent |
| 12 | 51.8 | 3.9 | Good |
| 14 | 49.5 | 3.6 | Good |
| 16 | 47.0 | 3.3 | Fair (Risk of Waste) |
| 20 | 42.5 | 2.8 | Poor (Folding Observed) |
As shown, larger α values generally decrease upsetting forces but increase the risk of defects if excessive. This trend highlights the importance of balancing parameters to achieve optimal results for internal gears. Similarly, variations in b and h were studied to establish practical guidelines. For b, representing the width-wise dimension of the expansion space, values between 7 mm and 11 mm (approximately 1/4 to 1/2 of the tooth width B) yielded the best outcomes, with full corner filling and no defects. The table below illustrates this for α = 10° and h = 2 mm:
| Dimension b (mm) | Upsetting Force (kN) | Ejection Force (kN) | Corner Filling Quality |
|---|---|---|---|
| 6 | 59.1 | 4.9 | Good |
| 7 | 57.2 | 4.2 | Excellent |
| 8 | 55.3 | 3.8 | Excellent |
| 9 | 53.4 | 3.5 | Good |
| 10 | 51.5 | 3.1 | Good |
| 11 | 49.6 | 2.7 | Fair |
| 12 | 47.7 | 2.3 | Poor (Waste Formation) |
For h, the height-wise dimension, values between 2 mm and 3.5 mm (1/4 to 1/2 of the tooth height H) proved effective, with larger h promoting better fill but risking overflow if too high. The equivalent stress and strain distributions further validated the process efficiency. The von Mises stress, calculated as $$\sigma_{eq} = \sqrt{\frac{1}{2}\left[(\sigma_1 – \sigma_2)^2 + (\sigma_2 – \sigma_3)^2 + (\sigma_3 – \sigma_1)^2\right]}$$, showed uniform patterns with maxima around 408 MPa during upsetting and 209 MPa during ejection, well within safe limits for tool materials. Strain analysis, using the formula $$\epsilon_{eq} = \sqrt{\frac{2}{3}\epsilon_{ij}\epsilon_{ij}}$$, indicated concentrated deformation in the tooth regions, ensuring thorough work hardening without defects. These findings reassure internal gear manufacturers that the method maintains structural integrity while minimizing loads.
Physical simulation experiments using lead billets and a custom-designed die confirmed the numerical results. The lead internal gears exhibited full tooth profiles, sharp contours, and no folding, aligning perfectly with the simulations. This practical validation underscores the reliability of the expansion cavity technique for mass production, offering internal gear manufacturers a scalable solution to enhance product quality. In conclusion, this study demonstrates that optimizing geometric parameters like α, b, and h can revolutionize internal gear forming, reducing forces by over 70% and ensuring precise corner filling. By adopting this approach, internal gear manufacturers can achieve higher efficiency, lower costs, and superior performance in transmission systems, paving the way for advanced applications in industries such as automotive and aerospace. Further research could explore adaptations for helical internal gears or other complex profiles, expanding the benefits across the manufacturing sector.