In modern manufacturing, the demand for efficient and precise production of gear shafts is increasingly critical, especially under the requirements of energy saving, emission reduction, and green economy. Traditional machining methods, such as cutting, are not only inefficient but also result in significant material waste. To address these challenges, cross-wedge rolling (CWR) has emerged as an advanced forming technology for shaft-like components, offering high production efficiency, cleanliness, minimal cutting, dense material structure, high strength, no impact, and high material utilization rates. Although CWR is well-established for forming shaft parts, its application to gear shafts remains underexplored. This study innovates an integrated forming method for gear shafts using cross-wedge rolling, combining gear and shaft forming into a single process to achieve short-flow, high-efficiency, and precise manufacturing. By analyzing the plastic forming principles of gear teeth, we synthesize key parameters for the processing mold, derive formulas that satisfy tooth separation conditions, and design a dedicated CWR mold for gear shafts. Through simulations using Deform software, we identify the optimal stage for the tooth mold to engage in the process, specifically during the first widening stage of the stepped shaft, resulting in the best forming quality. Further analysis of stress, strain, and temperature fields elucidates the forming mechanism of integrated gear-shaft CWR. Experimental validation shows errors below 8.2%, confirming the reliability of the simulation results. This research lays a theoretical foundation for the precise short-process forming of integrated gear shafts, with broad implications for advancing manufacturing technologies.
The integrated forming process for gear shafts using cross-wedge rolling combines the advantages of CWR for shaft forming with the generating method for gear processing. This approach eliminates the need for separate machining steps, reducing material waste and shortening the production cycle. The mold assembly consists of an upper mold, a lower mold, and a blank. The upper mold includes two main components: a wedge-shaped mold for forming the stepped shaft and a tooth-shaped mold for forming the gear teeth. The wedge mold follows a standard CWR structure but omits the knifing section due to its minimal impact on the final result. The tooth mold employs a free indexing and segmented feeding mechanism, where the first rotation of the blank ensures precise tooth division, and subsequent rotations involve progressive feeding to gradually form the complete tooth profile. During processing, the upper and lower molds move oppositely, while the blank, constrained by a baffle, rotates at the center driven by the molds. The process begins with the blank being compressed by a small ramp at the mold front to achieve the required dimensions, as the blank is initially oversized to ensure full tooth formation. Then, stepped shaft forming commences, starting with the wedge section where the mold gradually penetrates the blank, followed by the widening section where the penetrated area expands. Simultaneously, the tooth mold begins forming the gear teeth after a certain period in the widening stage. Subsequently, shaft processing enters the sizing stage and synchronizes with gear processing until the entire gear shaft is complete. This integrated method enhances material utilization and process efficiency, making it a promising solution for gear shaft manufacturing.
In the design of the integrated mold for gear shafts, the wedge mold is tailored based on the gear parameters, such as modulus and number of teeth. For instance, considering a gear shaft with a modulus of 2 and 18 teeth, the forming angle and spreading angle are selected according to standard CWR principles. The blank diameter and length are calculated to ensure volume consistency before and after forming. Key parameters include the forming angle, spreading angle, and various dimensional factors, which are summarized in the table below. These parameters guide the construction of the wedge mold, which is modeled in 3D software for simulation purposes. Due to the symmetry of the gear shaft, only half of the model is used in simulations to improve efficiency without compromising accuracy.
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| Forming Reduction (%) | 48 | Blank Diameter (mm) | 36 |
| Forming Angle (°) | 30 | Blank Length (mm) | 60 |
| Spreading Angle (°) | 9 | Step Height 1 (mm) | 3 |
| Step Height 2 (mm) | 2 | Section Length 1 (mm) | 32.8 |
| Section Length 2 (mm) | 103.5 | Section Length 3 (mm) | 56.5 |
| Section Length 4 (mm) | 21.9 | Section Length 5 (mm) | 69 |
| Section Length 6 (mm) | 49 |
The tooth mold design focuses on two critical parameters: feed amount and tooth pitch. The feed amount determines the growth of tooth height and ensures a full tooth profile, while the tooth pitch guarantees stable engagement between the mold and blank, preventing defects like misalignment or slipping. The total feed amount for the mold is derived from the difference between the blank diameter and the gear root circle diameter, expressed as:
$$E = \frac{d_b}{2} – \frac{d_f}{2}$$
where \(E\) is the total feed amount, \(d_b\) is the blank diameter, and \(d_f\) is the root circle diameter of the gear. The blank diameter is calculated based on the principle of volume conservation, where the cross-sectional area of the blank equals that of the gear. For a gear with teeth, the cross-sectional area involves complex geometry due to the involute profile. The area calculation depends on whether the root circle is larger or smaller than the base circle. For a root circle larger than the base circle, the gear cross-sectional area \(S_g\) is given by:
$$S_g = \frac{\pi d_f^2}{4} + z \left[ \frac{1}{4} d_a^2 \left( \frac{\pi}{2z} + \text{inv} \alpha – \text{inv} \alpha_a \right) + \frac{r_b^2}{3} \left( \tan^3 \alpha_a – \tan^3 \alpha_f \right) – \frac{1}{4} d_f^2 \left( \frac{\pi}{2z} + \text{inv} \alpha – \text{inv} \alpha_f \right) \right]$$
where \(z\) is the number of teeth, \(d_a\) is the addendum circle diameter, \(\alpha\) is the pressure angle at the reference circle, \(\alpha_a\) is the pressure angle at the addendum circle, \(\alpha_f\) is the pressure angle at the root circle, and \(r_b\) is the base circle radius. The blank diameter is then:
$$d_b = \sqrt{ d_f^2 + \frac{z}{\pi} \left[ d_a^2 \left( \frac{\pi}{2z} + \text{inv} \alpha – \text{inv} \alpha_a \right) + \frac{4r_b^2}{3} \left( \tan^3 \alpha_a – \tan^3 \alpha_f \right) – d_f^2 \left( \frac{\pi}{2z} + \text{inv} \alpha – \text{inv} \alpha_f \right) \right] }$$
For cases where the root circle is smaller than the base circle, a modified formula accounts for the non-involute portion near the root. The tooth pitch \(p\) is crucial for proper indexing and is derived from the gear mesh principle. Under ideal conditions, the mold moves horizontally by a distance \(p\) while the blank rotates by an angle \(2\theta\), leading to:
$$p = d_b \sin \theta = d_b \sin \left( \frac{\pi}{z} \right)$$
However, practical factors like friction and material flow require adjustments, so the formula is optimized as:
$$p = d_b \sin \left( \frac{\pi}{z} \right) + \Delta$$
where \(\Delta\) is an empirical compensation value. Based on these calculations, the tooth mold parameters are determined, as shown in the table below, ensuring precise forming of the gear teeth during the CWR process.
| Parameter | Value (mm) | Parameter | Value (mm) |
|---|---|---|---|
| First Feed | 1.0 | Pitch Between First and Second Feed | 6.41 |
| Second Feed | 0.65 | Second Pitch | 6.28 |
| Third Feed | 0.6 | Pitch Between Second and Third Feed | 6.28 |
| Fourth Feed | 0.5 | Third Pitch | 6.28 |
| Blank Diameter | 37.5 | Pitch Between Third and Fourth Feed | 6.28 |
| Reference Circle Distance | 37.5 | Fourth Pitch | 6.28 |
| First Pitch | 6.54 |
The finite element model for simulating the integrated forming process is established using Deform-3D software. The geometric model, created in SolidWorks, is imported as an STL file, and simulation parameters are set to reflect real-world conditions. The blank material is AISI-1045 steel, with an initial temperature of 1100°C, while the mold temperature is set to 300°C and the environment at 20°C. The mold moves at a constant speed of 30 mm/s, with a shear friction coefficient of 0.99 between the mold and blank, and 0.12 between the baffle and blank. The mesh consists of 100,000 tetrahedral elements, with local refinement in the deformation zone using a scale factor of 0.01. The simulation step size is 0.25 mm over 2,000 steps. Due to symmetry, only half of the model is simulated to reduce computational time. This setup allows for detailed analysis of the forming mechanics, including stress, strain, and temperature distributions during the process.
In the integrated forming of gear shafts, the interaction between the tooth mold and wedge mold significantly influences the final quality. The tooth mold engages at different stages of the wedge mold process: during the wedging or widening sections of the first or second steps of the stepped shaft. Simulations reveal that the timing of tooth mold engagement affects synchronization between gear and shaft forming. If the tooth mold enters too early, it can cause misalignment or slipping; if too late, it may lead to incomplete tooth profiles or elongation. Comparative analysis of four scenarios shows that engaging the tooth mold during the widening section of the first step yields the best results, with proper indexing, full tooth profiles, and minimal defects. This stage ensures that the gear forming process complements the shaft forming, leveraging the larger diameter of the gear section to enhance overall efficiency. The stress, strain, and temperature fields during this optimal stage provide insights into the forming mechanism, highlighting areas of high deformation and thermal effects that impact material flow and structural integrity.
Stress field analysis during the forming process indicates that the blank experiences significant stress at contact points with the mold, especially during the initial compression and wedging stages. In the first step wedging section, the maximum stress increases from 196 MPa to 379 MPa, and further to 542 MPa in the second step, due to the combined effects of blank compression and the driving force from gear forming. The gear section shows high stress at the tooth roots and centers, resulting from torsional forces generated by the gear forming process. This stress distribution aligns with the localized deformation and axial stretching characteristics of CWR, confirming the mechanical integrity of the integrated approach.
Strain field analysis reveals that deformation concentrates in areas where the mold contacts the blank, with maximum strain occurring at the gear teeth during tooth forming. The strain distribution follows the mold movement, expanding during the widening sections and stabilizing during sizing. Notably, the gear端部 exhibits a ring-like strain pattern, indicating torsional effects from the gear driving the shaft rotation. This pattern persists throughout the process, emphasizing the interconnected nature of gear and shaft forming in the integrated system.
Temperature field analysis shows a rapid decrease in blank temperature upon mold contact, from 1100°C to lower values, due to heat exchange with the cooler mold and environment. The temperature drop is most pronounced in high-contact areas, gradually stabilizing as the process continues. The gear section displays a radial temperature gradient, with higher temperatures at the center and lower at the periphery, affecting material flow and formability. Understanding these thermal dynamics is crucial for optimizing process parameters to prevent defects like cracking or incomplete filling.
Experimental validation is conducted using a TN5.602.1 type plate CWR machine. The blank is heated to 1200°C and processed, with the final product cooled in water. Measurements of the stepped shaft dimensions, such as lengths and diameters, show errors within 2% compared to theoretical values, confirming simulation accuracy. For the gear section, parameters like base tangent length, tooth height, addendum diameter, and gear length are measured, with maximum errors of 8.2%. These results demonstrate the feasibility of the integrated forming process for gear shafts, providing a reliable foundation for industrial application.
In conclusion, this study establishes an integrated cross-wedge rolling method for gear shafts, achieving precise forming through optimized mold design and process parameters. The tooth mold design, based on feed amount and tooth pitch calculations, ensures full tooth profiles and stable engagement. Simulations identify the optimal engagement stage as the first step widening section, resulting in high-quality gear shafts with minimal defects. Analysis of stress, strain, and temperature fields elucidates the forming mechanism, highlighting the synergistic effects of gear and shaft forming. Experimental results validate the simulations, with errors below 8.2%, paving the way for short-process, efficient manufacturing of gear shafts. Future work could explore additional gear types and process optimizations to further enhance performance and applicability.