Introduction
Spiral bevel gears are critical components in mechanical transmission systems, widely used in automotive, aerospace, and marine industries due to their high load capacity, smooth operation, and compact structure. Traditional milling processes for spiral bevel gears face challenges such as low material utilization, discontinuous metal flow lines, and reduced fatigue strength. Near-net rolling forming technology has emerged as a promising alternative, offering enhanced mechanical properties and reduced manufacturing costs. This study focuses on the quality control strategies for spiral bevel gear pinion rolling forming, emphasizing defect suppression, material flow optimization, and process parameter tuning.
High-Temperature Deformation Behavior of 20CrMnTiH
The material 20CrMnTiH, a common gear steel, exhibits complex flow stress characteristics under high-temperature conditions. Uniaxial compression tests were conducted at temperatures ranging from 900°C to 1100°C and strain rates of 0.01–5 s⁻¹. The flow stress curves (Figure 1) reveal that:
- Temperature dependency: Flow stress decreases with increasing temperature due to dynamic recrystallization and thermal softening.
- Strain rate sensitivity: Higher strain rates delay dynamic recrystallization, leading to increased flow stress.
The constitutive relationship is modeled using the Arrhenius equation:ϵ˙=A⋅[sinh(ασ)]n⋅exp(−RTQ)
where ϵ˙ is the strain rate, σ is flow stress, Q is activation energy, R is the gas constant, and T is temperature.
Mathematical Modeling of Spiral Bevel Gear Tooth Surfaces
The tooth surface of the spiral bevel gear pinion is derived using local synthesis theory. The coordinate transformation between the tool and workpiece during machining is expressed as:r1(up,θp)=Mc2c1⋅Mpc2⋅rc1(up,θp)
where Mc2c1 and Mpc2 are transformation matrices, and rc1 defines the tool surface. The meshing equation ensures conjugate tooth surfaces:n⋅v(12)=0
where n is the normal vector and v(12) is the relative velocity.
Finite Element Analysis of Induction-Heated Rolling
A coupled electromagnetic-thermal-mechanical model was developed to simulate the rolling process. Key parameters include:
- Induction heating: A frequency of 15 kHz and current density of 50 A/mm² achieve a temperature gradient of 1000°C (surface) to 170°C (inner hole).
- Material flow: Localized heating reduces forming load by 30–40% while preserving inner hole rigidity.
Defect Formation Mechanisms and Control
- Spline Damage:
Radial forces during rolling cause plastic deformation of the spline. Local induction heating limits inner hole temperatures to <200°C, reducing spline damage by 90% (Table 1).Heating MethodSpline Deformation (%)Temperature Gradient (°C/mm)Global Heating25–355–10Local Heating3–850–80 - Tooth Surface Folding:
Folding defects arise from uneven material flow at the tooth root. Optimizing preform geometry and process parameters minimizes folding height (hf):hf=k⋅(Nvf⋅μ)0.5where vf is feed rate, μ is friction coefficient, and N is rotational speed.
Multi-Objective Process Optimization
A response surface methodology (RSM) was employed to optimize rolling parameters. The design matrix and results are summarized below:
| Factor | Range | Optimal Value |
|---|---|---|
| Feed Rate (mm/s) | 0.1–0.3 | 0.2 |
| Rotational Speed (rpm) | 30–70 | 50 |
| Friction Coefficient | 0.1–0.3 | 0.2 |
The optimized parameters reduced folding height by 62% and improved tooth filling uniformity (Figure 2).
Tooth Height Compensation and Die Design
Axial material flow causes underfilling at gear ends. A compensation coefficient k is introduced to adjust preform geometry:k=1+htheoryΔheff
where Δheff is the effective height deviation. Modifying the die root profile (Figure 3) increased end filling by 1 mm, providing sufficient machining allowance for flash removal.
Experimental Validation
A rolling test platform validated simulation results:
- Tooth profile accuracy: Achieved DIN 6–7 grade after post-machining.
- Mechanical properties: Rolling-formed gears exhibited 15–20% higher bending strength than milled gears due to continuous fiber orientation.
Conclusion
Local induction-heated rolling enables high-quality spiral bevel gear manufacturing with controlled defects and enhanced material utilization. Key findings include:
- Temperature gradients from induction heating improve inner hole rigidity and reduce spline damage.
- Folding defects are minimized through preform geometry optimization and RSM-based parameter tuning.
- Tooth height compensation and die root modification ensure uniform material flow.
Future work will focus on real-time temperature control and adaptive rolling strategies for complex gear geometries.