As an essential component in mechanical transmission systems, internal gears play a critical role in various high-precision industries, including aerospace and defense. The demand for high-quality internal gears from internal gear manufacturers has driven the development of advanced forming techniques to enhance mechanical properties and production efficiency. Traditional machining methods, such as cutting, often compromise the structural integrity and strength of gears due to material removal. In contrast, precision forging techniques, like closed-die forging and extrusion, preserve the grain flow and mechanical performance, resulting in superior fatigue resistance and operational stability. This study investigates a novel bidirectional upsetting-extrusion process for spur internal gears, utilizing Solidworks for numerical simulation and validation. The focus is on comparing traditional and innovative methods to optimize forming loads, mold longevity, and filling efficiency, which are crucial for internal gear manufacturers seeking to improve product quality and reduce costs.
Internal gears are widely used in planetary gear systems and compact transmissions due to their ability to provide high torque density and smooth operation. However, achieving full tooth profile filling without defects remains a challenge in precision forming. Existing methods for internal gear production include closed-die forging, extrusion, spinning, and splitting-extrusion processes. Each technique has limitations, such as high forming loads, incomplete corner filling, and模具 wear, which can increase costs for internal gear manufacturers. The bidirectional upsetting-extrusion process proposed here addresses these issues by applying opposing forces during deformation, reducing friction and facilitating complete cavity filling. This approach not only enhances the mechanical properties of internal gears but also aligns with the goals of internal gear manufacturers to adopt sustainable and efficient production methods.
The theoretical foundation of this process involves analyzing the friction distribution during deformation. In traditional closed-die forging, the workpiece experiences upward frictional forces (Fτ) along the side surfaces of the die and core, leading to increased forming loads and difficulties in corner filling. The resultant stress state can be described by the following equation for frictional force: $$ F_{\tau} = \mu \cdot P \cdot A $$ where μ is the friction coefficient, P is the contact pressure, and A is the contact area. In bidirectional upsetting-extrusion, the frictional forces act in opposite directions, effectively canceling each other out and reducing the net resistance. This reduction in friction minimizes the forming load, as expressed by the modified load equation: $$ F_{\text{total}} = F_{\text{deformation}} – \Delta F_{\tau} $$ where ΔFτ represents the friction reduction due to bidirectional action. This principle is pivotal for internal gear manufacturers aiming to optimize模具 design and extend service life.
| Parameter | Traditional Closed-Die Forging | Bidirectional Upsetting-Extrusion |
|---|---|---|
| Friction Coefficient (μ) | 0.3 | 0.3 |
| Forming Load (Max, kN) | Approximately 1200 | Approximately 520 |
| Corner Filling Efficiency | Moderate, with potential defects | High, with full saturation |
| 模具 Complexity | High, due to tooth profile on punch | Low, with toothless punch design |
To evaluate the proposed process, a numerical simulation was conducted using Solidworks, focusing on a spur internal gear with module m=2.5, tooth count z=20, tooth width b=20 mm, pressure angle α=20°, and pitch diameter d=50 mm. The workpiece material was AISI-1045 steel, heated to 1100°C to enhance plasticity, while the mold temperature was maintained at 350°C to prevent thermal cracking. The simulation involved 300,000 tetrahedral mesh elements to ensure accuracy, with a friction coefficient of 0.3 representing typical industrial conditions. The upper and lower punches moved at a velocity of 4.8 mm/s, and the step length was set to 0.05 mm/step to adhere to the principle of not exceeding one-third of the smallest element edge length. Volume compensation was applied to account for material flow, ensuring realistic deformation behavior. This setup is critical for internal gear manufacturers to predict forming outcomes and minimize trial-and-error costs.
The filling process was analyzed for both traditional (with-tooth punch) and innovative (toothless punch) bidirectional upsetting-extrusion methods. In the traditional approach, the punch with tooth profiles continuously engages the workpiece, leading to sustained contact and higher friction areas. In contrast, the toothless punch only contacts the workpiece at the final forming stage, significantly reducing the friction surface area. The metal flow during deformation can be modeled using the plasticity theory, where the effective strain (ε̄) is calculated as: $$ \bar{\epsilon} = \sqrt{\frac{2}{3} \epsilon_{ij} \epsilon_{ij}} $$ and the stress state follows the von Mises criterion: $$ \sigma_{\text{vm}} = \sqrt{\frac{3}{2} s_{ij} s_{ij}} $$ where sij is the deviatoric stress tensor. The simulation results showed that both methods achieved complete tooth cavity filling, but the toothless punch exhibited a more uniform strain distribution, reducing the risk of defects such as folding or incomplete filling. This advantage is vital for internal gear manufacturers producing high-precision components for critical applications.
The load-stroke curves derived from the simulation provide insights into the forming stages: free deformation, cavity filling, and corner filling. In the free deformation stage, the load increases gradually due to the material’s plasticity, described by the power-law equation: $$ \sigma = K \epsilon^n $$ where K is the strength coefficient and n is the strain-hardening exponent. During cavity filling, the load rises steadily as the material contacts the die walls, and in the corner filling stage, the load peaks sharply to ensure complete saturation. For the traditional with-tooth punch method, the maximum load reached approximately 1200 kN, whereas the toothless punch method reduced it to about 520 kN—a decrease of 57%. This significant reduction alleviates模具 stress, enhancing durability and reducing maintenance costs for internal gear manufacturers. The load-stroke relationship can be expressed as: $$ F(s) = F_0 + k \cdot s^m $$ where F0 is the initial load, k is a constant, s is the stroke, and m is an exponent dependent on material behavior.
| Forming Stage | With-Tooth Punch Load (kN) | Toothless Punch Load (kN) | Reduction Percentage |
|---|---|---|---|
| Free Deformation | 200-400 | 180-350 | ~12% |
| Cavity Filling | 400-800 | 350-450 | ~44% |
| Corner Filling | 800-1200 | 450-520 | ~57% |
Physical simulation experiments were conducted to validate the numerical findings. A mold assembly for bidirectional upsetting-extrusion was fabricated, and cast iron billets were melted in a resistance furnace and poured into the model. After cooling, the castings were machined to produce spur internal gear specimens. The results demonstrated full tooth profile filling, clear contours, and smooth surfaces without folds or defects, corroborating the simulation predictions. This experimental validation is essential for internal gear manufacturers to implement the process in industrial settings, ensuring reliability and consistency. The success of the toothless punch approach underscores its practicality, as it simplifies模具 manufacturing and reduces lead times compared to complex tooth-profile punches.
Further analysis of the material behavior during forming involves the constitutive model for AISI-1045 steel, which accounts for temperature and strain rate effects. The flow stress can be represented as: $$ \sigma_f = A \cdot (\epsilon + \epsilon_0)^n \cdot \dot{\epsilon}^m \cdot e^{\beta T} $$ where A is a material constant, ε is the strain, ε0 is the initial strain, ṁ is the strain rate, m is the strain rate sensitivity, β is the temperature coefficient, and T is the temperature. In the bidirectional process, the strain rate is more uniform, reducing localized stress concentrations that could lead to cracking. This uniformity is beneficial for internal gears, which require high dimensional accuracy and structural integrity. Additionally, the reduction in forming load directly translates to energy savings, making the process environmentally friendly and cost-effective for internal gear manufacturers.
The implications of this research extend beyond spur internal gears to other gear types and complex geometries. For instance, the bidirectional upsetting-extrusion principle can be adapted for helical internal gears or splined components, with modifications to the punch and die designs. Future work could explore the integration of real-time monitoring systems to control forming parameters dynamically, further optimizing the process for mass production. Internal gear manufacturers can leverage these advancements to enhance competitiveness in global markets, offering products with superior performance and longer service life. Moreover, the use of simulation tools like Solidworks enables virtual prototyping, reducing development cycles and resource consumption.
In conclusion, the bidirectional upsetting-extrusion process with a toothless punch represents a significant improvement in the precision forming of spur internal gears. The numerical and experimental results confirm a 57% reduction in forming load, complete cavity filling, and simplified模具 design. These benefits directly address the challenges faced by internal gear manufacturers, such as high production costs and模具 wear. By adopting this innovative approach, manufacturers can achieve higher efficiency, better product quality, and sustainable operations. Continued research in material science and process optimization will further solidify the role of precision forming in advancing gear technology, meeting the evolving demands of industries reliant on internal gears for critical applications.