As a researcher in the field of metal forming, I have long been fascinated by the challenges and opportunities in precision forging of spur gears. Spur gears are critical components in various mechanical systems, including automotive transmissions and industrial machinery, due to their ability to transmit motion and power efficiently. Traditionally, spur gears are manufactured through machining processes such as cutting, which, while effective, suffer from significant drawbacks. These include low material utilization, high production costs, and reduced mechanical properties due to the disruption of material grain flow. In contrast, precision forging offers a net-shape or near-net-shape alternative that enhances material savings, improves productivity, and yields superior mechanical characteristics. Specifically, precision forged spur gears exhibit dense and homogeneous microstructures, continuous metal flow lines along the tooth profile, and a work-hardened surface layer, all of which contribute to enhanced wear resistance, corrosion resistance, bending strength, and fatigue performance. However, the practical application of precision forging for spur gears has been hindered by excessive forming loads, which lead to模具 elastic deformation, reduced tool life, ejection difficulties, and incomplete tooth filling. In this study, we propose a novel precision forging process for spur gears that addresses these issues through a pre-forging分流区 and分流终锻 approach, significantly reducing forming loads while ensuring full tooth filling and flat end surfaces.
The conventional closed-die forging process for spur gears, often referred to as闭式徽挤, involves deforming a billet within a confined die cavity to form the gear teeth. As illustrated in the process schematic, this method typically results in high forming pressures due to restricted metal flow at the billet ends. During deformation, the central teeth fill first, but as the process continues, the end regions experience constrained flow, causing a sharp increase in load. This load surge can exceed 1000 kN for steel spur gears, making it impractical for industrial-scale production. To mitigate this, various分流-based techniques have been explored, but many involve complex multi-step operations or insufficient load reduction. Our innovative process, termed “pre-forging分流区—分流终锻,” simplifies the procedure and achieves substantial load reduction. The key idea is to create pre-formed分流 zones at both ends of the billet during the pre-forging stage, which facilitate controlled metal flow during the final forging stage. This allows部分 material to flow inward toward the center while the ends fill, preventing pressure peaks and lowering overall forces.
To elucidate the mechanics, consider the forming load \( F \) in precision forging of spur gears, which can be approximated by the following equation based on slab analysis:
$$ F = A \cdot \sigma_f \cdot \left(1 + \frac{\mu \cdot d}{h}\right) $$
where \( A \) is the contact area, \( \sigma_f \) is the flow stress of the material, \( \mu \) is the friction coefficient, \( d \) is the gear diameter, and \( h \) is the billet height. In conventional closed-die forging, the term \( \frac{\mu \cdot d}{h} \) becomes dominant as \( h \) decreases, leading to exponential load increases. Our new process introduces a分流 factor \( k \) that modifies this relationship by allowing additional flow paths:
$$ F_{\text{new}} = A \cdot \sigma_f \cdot \left(1 + k \cdot \frac{\mu \cdot d}{h}\right) $$
with \( k < 1 \), typically ranging from 0.3 to 0.7 depending on the分流区 design. This reduction in the friction-dominated term directly translates to lower forming loads, as confirmed by our experimental results.
In this study, we conducted comprehensive experiments to validate the proposed process for spur gears. The试验 focused on comparing the new pre-forging分流区—分流终锻 method with the traditional闭式徽挤 approach, using both hollow tube billets and solid cylindrical billets. The spur gear parameters were standardized: number of teeth \( z = 20 \), module \( m = 2 \, \text{mm} \), pressure angle \( \alpha = 20^\circ \), height \( h = 20 \, \text{mm} \), and inner diameter \( d_i = 30 \, \text{mm} \) for hollow billets. The material selected was industrial pure lead, chosen for its low flow stress and similarity to steel in terms of forming behavior at room temperature. The试验 equipment consisted of a微机屏显液压万能试验机 with a maximum load capacity of 1000 kN, equipped with a computer-based data acquisition system to record forming loads and displacements in real-time. The试验流程 involved two main paths: one for hollow tube billets and another for solid cylindrical billets, each subjected to both the conventional and new processes.
The模具 design was critical to enable flexible testing. We developed a modular试验模具 that could accommodate various凸台 configurations for pre-forging and final forging. As shown in the assembly diagram, the模具 comprised replaceable upper and lower凸台 sets, a die cavity for the spur gear teeth, and a core for hollow billets. For hollow tube billets, the凸台 were designed to form分流 zones at both ends during pre-forging, as depicted in the schematic. For solid cylindrical billets, the凸台 created a single central分流区. This modularity allowed us to perform multiple试验 combinations without重新 tooling, ensuring consistency and efficiency. The模具 materials were tool steel, hardened and ground to withstand repeated forming cycles, though the试验 used lead billets to minimize wear.
The试验现象 revealed distinct deformation patterns. For hollow tube billets under the new process, the pre-forging stage produced a slight双鼓形 shape at both ends, with incomplete tooth filling in the鼓形 regions. This is attributed to the high aspect ratio of the billet and the rapid outward flow of material near the分流 zones. Upon final forging, the spur gears exhibited full tooth filling, flat end surfaces, and only minor longitudinal flashes at the tooth tips. The load-displacement curves, plotted from the data acquisition system, showed a gradual increase in load during both pre-forging and final forging, with no sharp peaks. In contrast, the conventional闭式徽挤 process for hollow billets resulted in a steep load rise near the end of forming, indicating high pressure buildup. For solid cylindrical billets, the new process led to a single鼓形 in the central region during pre-forging, due to the greater resistance to deformation at the ends. Final forging produced fully filled spur gears with flat outer edges, though the central分流区 remained partially unfilled, which can be machined off in post-processing. Similarly, the load curves for solid billets demonstrated a significant reduction in maximum load compared to conventional forging.
To quantify the results, we analyzed the forming loads for both billet types and processes. The data are summarized in Table 1, which compares the maximum loads during pre-forging, final forging, and conventional闭式徽挤. The loads are expressed in kilonewtons (kN), and the percentage reduction is calculated relative to the conventional process.
| Billet Type | Process Stage | Maximum Load (kN) | Load Reduction vs. Conventional |
|---|---|---|---|
| Hollow Tube | Pre-forging (New Process) | 120 | ~60% |
| Final Forging (New Process) | 180 | ||
| Conventional闭式徽挤 | 450 | ||
| Solid Cylindrical | Pre-forging (New Process) | 150 | ~50% |
| Final Forging (New Process) | 220 | ||
| Conventional闭式徽挤 | 440 |
As seen in Table 1, the new process reduces forming loads by approximately 60% for hollow tube billets and 50% for solid cylindrical billets. This reduction is statistically significant and directly correlates with the分流 mechanism. Moreover, the load curves for the new process exhibit a smoother profile, which is beneficial for模具 life and part quality. We can further model the load reduction using a分流 efficiency parameter \( \eta \), defined as:
$$ \eta = \frac{F_{\text{conventional}} – F_{\text{new}}}{F_{\text{conventional}}} \times 100\% $$
For hollow billets, \( \eta \approx 60\% \), and for solid billets, \( \eta \approx 50\% \). This efficiency stems from the altered stress state during forming, which can be described by the yield criterion for plastic deformation. For spur gears, the effective stress \( \sigma_{\text{eff}} \) in the分流 zones is lower due to triaxial compression, reducing the required forming pressure \( p \):
$$ p = \sigma_{\text{eff}} \cdot \left(1 + \frac{\mu \cdot L}{t}\right) $$
where \( L \) is the contact length and \( t \) is the billet thickness. In the分流 zones, \( L \) is reduced, leading to a decrease in \( p \).
The material flow during forming was also analyzed using finite element simulation concepts, though the试验 relied on physical trials. For spur gears, the tooth filling sequence is crucial. In conventional forging, the central teeth fill first, creating a “blocking” effect that hinders end filling. In the new process, the分流 zones allow simultaneous filling from both ends and the center, as illustrated by the metal flow lines. This can be represented by a filling index \( \phi \), defined as the ratio of filled tooth volume to total tooth volume:
$$ \phi = \frac{V_{\text{filled}}}{V_{\text{total}}} $$
In our experiments, \( \phi \) reached 0.99 for both billet types under the new process, compared to 0.95 for conventional forging, indicating superior filling. Additionally, the flatness of the end surfaces was quantified using a flatness deviation \( \delta \), measured in millimeters. For the new process, \( \delta < 0.1 \, \text{mm} \), whereas conventional forging resulted in \( \delta \approx 0.5 \, \text{mm} \) due to uneven flow.
Another key aspect is the influence of billet geometry on process performance. Hollow tube billets offer inherent advantages for spur gears, as they reduce material usage and lower forming loads further. The load reduction for hollow billets is approximately 10% greater than for solid billets, as shown in Table 1. This can be attributed to the reduced cross-sectional area and the presence of an inner cavity that facilitates metal flow. The forming load for hollow billets can be estimated by modifying the area term in the load equation:
$$ A_{\text{hollow}} = \pi \cdot (d_o^2 – d_i^2) / 4 $$
where \( d_o \) is the outer diameter and \( d_i \) is the inner diameter. For our spur gears, \( d_o = 40 \, \text{mm} \) and \( d_i = 30 \, \text{mm} \), giving \( A_{\text{hollow}} = 550 \, \text{mm}^2 \), compared to \( A_{\text{solid}} = 1257 \, \text{mm}^2 \) for solid billets. This smaller area directly reduces the load, as \( F \propto A \). Moreover, the分流 zones in hollow billets are more effective due to the thinner wall thickness, which enhances metal mobility.
We also investigated the effect of process parameters on the quality of spur gears. Table 2 summarizes the optimal parameters for the new precision forging process, derived from our试验 data. These parameters include billet dimensions, pre-forging depth, and分流区 geometry, and they are essential for scaling up to industrial production.
| Parameter | Hollow Tube Billet | Solid Cylindrical Billet | Recommended Value |
|---|---|---|---|
| Billet Height (mm) | 25 | 25 | 1.25 × Gear Height |
| Billet Diameter (mm) | 40 (outer), 30 (inner) | 40 | Based on Gear Outer Diameter |
| Pre-forging Depth (mm) | 5 | 5 | 0.25 × Billet Height |
| 分流区 Width (mm) | 3 | 4 | 0.1-0.2 × Tooth Width |
| Friction Coefficient (μ) | 0.1 (lubricated) | 0.1 (lubricated) | ≤ 0.15 for Steel |
The pre-forging depth is critical for creating adequate分流 zones without causing defects. For spur gears, we found that a depth of 5 mm (25% of the billet height) optimal for both billet types. The分流区 width, defined as the radial extent of the pre-formed cavity, should be 10-20% of the tooth width to ensure sufficient metal flow without compromising tooth strength. In terms of friction, we used lubricant (graphite-based) to achieve a coefficient of 0.1, which is typical for cold forging of steel. Lower friction further reduces loads, as indicated by the equations above.
From a mechanical perspective, the新工艺 enhances the performance of spur gears by improving their microstructural integrity. The precision forging process induces compressive residual stresses on the tooth surfaces, which increase fatigue life. The residual stress \( \sigma_r \) can be estimated using the following empirical formula for forged spur gears:
$$ \sigma_r = C \cdot \ln\left(\frac{h_0}{h_f}\right) $$
where \( C \) is a material constant (approximately 500 MPa for lead, extrapolating to steel), \( h_0 \) is the initial billet height, and \( h_f \) is the final gear height. In our process, \( h_0/h_f = 1.25 \), yielding \( \sigma_r \approx 112 \, \text{MPa} \) in compression, compared to negligible stresses in machined spur gears. This compressive layer inhibits crack initiation and propagation, crucial for high-cycle fatigue applications.
Furthermore, the economic benefits of the new process are substantial for spur gears production. By reducing forming loads by 50-60%, the模具 costs decrease due to lower wear and longer life. The模具 life \( N \) can be approximated by the following relation based on load cycles:
$$ N = \left(\frac{F_{\text{max,容许}}}{F_{\text{实际}}}\right)^m $$
where \( F_{\text{max,容许}} \) is the allowable load for the模具 material (e.g., 800 MPa for tool steel), \( F_{\text{实际}} \) is the actual forming load, and \( m \) is an exponent typically around 3 for fatigue. For conventional forging of spur gears, \( F_{\text{实际}} = 450 \, \text{kN} \), giving \( N \approx 10^5 \) cycles. For the new process, \( F_{\text{实际}} = 180 \, \text{kN} \), so \( N \approx 10^6 \) cycles, a tenfold increase. This translates to lower tooling expenses and higher productivity.
In addition to load reduction, the new process simplifies the production sequence for spur gears. Traditional multi-step forging methods for spur gears often involve three or more operations, such as pre-forming, blocking, and finishing. Our pre-forging分流区—分流终锻 method consolidates this into two steps: pre-forging and final forging. This reduces handling time, energy consumption, and cumulative误差. The total process time \( T \) can be expressed as:
$$ T = t_{\text{pre}} + t_{\text{final}} + t_{\text{handle}} $$
where \( t_{\text{pre}} \) and \( t_{\text{final}} \) are the forging times, and \( t_{\text{handle}} \) is the handling time. For our试验, \( t_{\text{pre}} = 2 \, \text{s} \), \( t_{\text{final}} = 3 \, \text{s} \), and \( t_{\text{handle}} = 5 \, \text{s} \), totaling 10 s per spur gear. In contrast, a three-step process might take 15 s or more, representing a 33% time saving.
The scalability of the new process for spur gears was also considered. We performed preliminary trials with scaled-up parameters for steel spur gears using simulation software, though the physical试验 used lead. The results indicate that the load reduction trends hold for steel, albeit at higher absolute loads due to its higher flow stress. The forming load for steel spur gears can be scaled using the flow stress ratio:
$$ F_{\text{steel}} = F_{\text{lead}} \cdot \frac{\sigma_{f,\text{steel}}}{\sigma_{f,\text{lead}}} $$
where \( \sigma_{f,\text{steel}} \approx 600 \, \text{MPa} \) for cold forging and \( \sigma_{f,\text{lead}} \approx 20 \, \text{MPa} \). Thus, for hollow tube billets, \( F_{\text{steel}} \approx 180 \, \text{kN} \times 30 = 5400 \, \text{kN} \) for conventional forging, but with the new process, it reduces to about 2160 kN, which is within the capacity of modern forging presses (e.g., 2500 kN). This makes the process feasible for industrial implementation.
To further optimize the process for spur gears, we developed a mathematical model for metal flow during分流终锻. The velocity field \( v(r,z) \) in the billet can be described by the continuity equation for incompressible plastic flow:
$$ \nabla \cdot \mathbf{v} = 0 $$
Assuming axisymmetric flow for spur gears (a reasonable approximation for歯形 filling), in cylindrical coordinates, this becomes:
$$ \frac{1}{r} \frac{\partial (r v_r)}{\partial r} + \frac{\partial v_z}{\partial z} = 0 $$
where \( v_r \) is the radial velocity and \( v_z \) is the axial velocity. In the分流 zones, \( v_r \) is positive (outward) near the ends and negative (inward) near the center, balancing the flow. This can be solved with boundary conditions from the die geometry, but for simplicity, we used a stream function approach. The resulting flow patterns confirm uniform tooth filling.
In terms of quality control, the新工艺 produces spur gears with consistent dimensions. We measured the tooth profile accuracy using coordinate measuring machines (CMM) on sampled gears. The results showed that the tooth thickness error \( \Delta t \) was within ±0.05 mm for the new process, compared to ±0.1 mm for conventional forging. This is due to the lower弹性 recovery after forming, as the residual stresses are more balanced. The弹性 recovery \( \Delta L \) can be estimated by:
$$ \Delta L = \frac{F}{E \cdot A} \cdot L $$
where \( E \) is Young’s modulus (70 GPa for lead, 210 GPa for steel). With lower \( F \), \( \Delta L \) is smaller, enhancing dimensional precision for spur gears.
Environmental impacts were also assessed. The precision forging process for spur gears reduces material waste by 20-30% compared to machining, as it eliminates chips and cuttings. The material utilization ratio \( U \) is defined as:
$$ U = \frac{\text{Weight of Finished Gear}}{\text{Weight of Billet}} $$
For our hollow tube billets, \( U = 0.85 \), while for machined spur gears from solid stock, \( U \approx 0.60 \). This not only saves raw materials but also reduces energy consumption in melting and processing. The carbon footprint per spur gear is thus lower, aligning with sustainable manufacturing goals.
In conclusion, the pre-forging分流区—分流终锻 process represents a significant advancement in precision forging of spur gears. Our experimental study demonstrates that this innovative method reduces forming loads by 50-60% compared to traditional闭式徽挤, ensures full tooth filling and flat end surfaces, and simplifies production to two steps. The use of hollow tube billets further enhances load reduction and material efficiency. The process is scalable to steel spur gears and offers economic benefits through extended模具 life and shorter cycle times. Future work will focus on industrial trials with high-strength alloys and integration with automated systems for mass production of spur gears. By addressing the key challenges of high loads and complex operations, this new precision forging process paves the way for widespread adoption in the manufacturing of spur gears, contributing to the advancement of net-shape technologies in the gear industry.