Spiral bevel gears transmit motion between intersecting shafts through teeth whose traces curve across the face width. The tooth surface is not a simple extrusion: spiral angle, pressure angle, tooth depth and flank curvature all vary through the mesh. For forging, the die cavity must reproduce this three-dimensional geometry while allowing the billet to flow from a central region into narrow tooth spaces. This is why precision forging is more demanding for spiral bevel gears than for spur gears or straight bevel gears, and why die filling, dimensional accuracy and forming load must be considered together.
Near-net-shape forging can improve material utilization, shorten machining routes and produce a favorable grain structure, but these benefits depend on filling the tooth cavity without an excessive rise in load at the end of the stroke. The relevant process window is defined by billet temperature, deformation speed and interface friction. Each variable changes the flow stress of the workpiece and the pressure required to fill the die corners.
Closed pre-forging and divided-flow final forging
A practical route for spiral bevel gear precision forging is a closed-die pre-forging step followed by a divided-flow final forging step. In pre-forging, matching boss features above and below the cavity shape a preform progressively from the top downward. The preform distributes material before the tooth impressions are formed, avoiding an uncontrolled surge of material into the most confined regions of the die.
In final forging, the cavity is divided so that material can flow into the tooth impressions while part of the volume is free to move into a separate divided-flow cavity. The billet volume is set so that this cavity is not completely filled when tooth filling is complete. The unfilled volume acts as a pressure-control feature: it prevents a steep rise in cavity pressure at the tooth ends and reduces the risk of overload, die deflection and loss of tooth accuracy. The volume must still be tuned carefully. Too little relief produces a load spike; too much relief can leave teeth underfilled or promote folding.
Finite-element model and baseline conditions
A three-dimensional finite-element model of the spiral bevel gear forging sequence can be built in DEFORM-3D. The die components are treated as rigid bodies and the 20Cr billet as a plastic body. In the model discussed here, the billet is discretized into 52,936 elements. The gear and process parameters are summarized in Table 1.
| Item | Value |
|---|---|
| Number of teeth, Z | 18 |
| Normal module, m | 4 mm |
| Spiral angle, β | 31° |
| Pressure angle, α | 20° |
| Addendum coefficient, ha* | 1 |
| Normal clearance coefficient, c | 0.2 |
| Hand | Left-hand |
| Billet material | 20Cr |
| Die material | H13 |
| Billet temperature | 800 °C (baseline) |
| Die preheat temperature | 200 °C |
| Friction coefficient | 0.25 (baseline) |
| Deformation speed | 10 mm/s (baseline) |
| Billet mesh | 52,936 elements |
Within the plastic workpiece, flow stress is represented as a function of effective plastic strain, effective strain rate and temperature:
$$\bar{\sigma} = \bar{\sigma}(\bar{\varepsilon}, \dot{\bar{\varepsilon}}, T),$$
where \(\bar{\sigma}\) is flow stress, \(\bar{\varepsilon}\) is effective plastic strain, \(\dot{\bar{\varepsilon}}\) is effective strain rate and \(T\) is temperature. The die–workpiece interface is described by a constant shear friction law:
$$\tau_f = m k,$$
where \(\tau_f\) is friction stress, \(k\) is the shear yield stress of the workpiece and \(m\) is the friction coefficient. The model therefore captures the combined influence of material softening, strain-rate sensitivity and interface shear resistance on the load–stroke response.
Effect of billet temperature
Billet temperature has a direct effect on flow stress, die filling and final microstructure. Simulations at 600 °C, 700 °C and 800 °C show that, at a given stroke, the forming load decreases as temperature rises. The maximum forming load at 800 °C is 39.8% lower than at 600 °C.
This trend follows from thermal softening. As the 20Cr billet becomes hotter, its yield limit falls and its ductility increases, so less pressure is needed to make the material flow into the tooth impressions. The result is consistent with the practical requirement to forge 20Cr within a temperature range that provides adequate forgeability and a sound internal structure. The lower load at higher temperature should not, however, be read as a reason to raise temperature without limit. Excessive temperature can cause grain growth, scale formation and loss of dimensional control. Temperature selection must remain inside the metallurgical window for the material.
Effect of deformation speed
Deformation speed changes both the strain rate and the thermal history of the billet. With other conditions held constant, simulations at 1 mm/s, 10 mm/s and 20 mm/s show that increasing speed from 1 mm/s to 10 mm/s reduces the forming load. A further increase from 10 mm/s to 20 mm/s produces only a small change in the final load.
The two effects compete. A higher deformation speed raises the strain rate, which tends to increase flow stress and deformation resistance. At the same time, the contact time between the hot billet and the cooler die is shorter, so less heat is lost from the billet and the workpiece remains softer. In the range examined, the thermal effect offsets much of the strain-rate hardening, so the net load falls as speed increases, but the benefit diminishes beyond 10 mm/s. Deformation speed is therefore a secondary load-control variable compared with temperature and friction, although it still affects cavity filling and the thermal history of the part.
Effect of friction coefficient
Friction controls the resistance to material flow along the die surface. Using the constant shear friction model, simulations with friction coefficients of 0.15, 0.25 and 0.35 show that the maximum forming load increases as the friction coefficient rises. Higher friction raises the interface shear stress and requires greater cavity pressure to push material into the tooth corners.
The practical implication is that lubrication is not a secondary detail. A suitable lubricant reduces the friction coefficient, lowers the forming load and reduces die wear. It also helps maintain a more uniform flow pattern across the tooth space. Lubricant selection must still account for the die temperature, the surface condition and the need to avoid contamination or residue that could affect subsequent heat treatment.
| Parameter | Range examined | Effect on forming load |
|---|---|---|
| Billet temperature | 600, 700, 800 °C | Decreases with increasing temperature; 800 °C maximum load is 39.8% below 600 °C |
| Deformation speed | 1, 10, 20 mm/s | Decreases from 1 to 10 mm/s; change is small from 10 to 20 mm/s |
| Friction coefficient | 0.15, 0.25, 0.35 | Increases with increasing friction coefficient |
Process design implications
The load–stroke curves are strongly nonlinear. The load remains moderate while the preform is redistributed, then rises sharply as the tooth impressions approach complete filling. Press capacity should therefore be selected from the peak load near final filling, not from an average load over the stroke. The divided-flow cavity is an effective way to delay that peak, but its volume must be matched to the tooth-cavity volume and the intended amount of unfilled relief.
For spiral bevel gear precision forging, the parameters form a hierarchy. Billet temperature and interface friction have the strongest influence on forming load in the examined range. Deformation speed can be used for fine adjustment, but its effect flattens above 10 mm/s. A practical process window should therefore combine a controlled billet temperature, effective lubrication and a press capacity that accommodates the peak load during tooth filling.
Scope of the numerical trends
The trends above are based on a three-dimensional finite-element model with prescribed flow-stress data, rigid dies and a constant shear friction law. They are useful for comparing process parameters and for preliminary die and press design, but they do not replace forging trials. Actual loads and cavity filling depend on the accuracy of the 20Cr flow-stress data, heat-transfer conditions, die elasticity, surface roughness and lubricant behavior. Production validation should examine tooth accuracy, filling at the toe and heel, folding defects, grain structure and die life under repeated cycles.