1. Introduction
Wind turbine gearboxes are critical components in renewable energy systems, where reliability directly impacts operational efficiency and maintenance costs. Among gearbox failures, bearing-related issues account for over 60% of incidents, often linked to axial cracking and spalling. Fatigue cracks in bearings typically originate in subsurface regions of raceways, driven by cyclic loading and stress concentrations. This study investigates the directional mechanisms of fatigue crack initiation and propagation in wind turbine gearbox bearings, combining theoretical models with experimental validations to guide bearing design and failure analysis.
2. Crack Initiation Direction
2.1 Theoretical Framework
Fatigue crack initiation in bearings is governed by the maximum shear stress amplitude at localized regions. For homogeneous materials, cracks initiate along planes experiencing the highest cyclic shear stress. The critical plane stress criterion, validated for contact fatigue problems, is expressed as:τamp+C1(σamp+σmean)=C2τamp+C1(σamp+σmean)=C2
where:
- τampτamp: Shear stress amplitude on the critical plane.
- σampσamp: Normal stress amplitude.
- σmeanσmean: Mean normal stress.
- C1,C2C1,C2: Material constants.
In heterogeneous materials (e.g., with inclusions or white etching areas), crack initiation shifts to phase boundaries where stress concentrations exceed dislocation slip thresholds.
2.2 Subsurface Stress Analysis
Using Hertz contact theory, subsurface stresses in roller bearings are calculated as:σxz=puzπb[(b2+2z2+2×2)Φ1−2π−3xbΦ2]σxz=πbpuz[(b2+2z2+2x2)Φ1−2π−3xbΦ2]σzz=puzπ(bΦ1−xΦ2)σzz=πpuz(bΦ1−xΦ2)
Principal stresses (σ1,σ3σ1,σ3) and principal shear stress (τaτa) are derived as:τa=12(σ1−σ3)τa=21(σ1−σ3)
Key Findings:
- Shallow Layers (<1.5<1.5 mm): Orthogonal shear stress (τorthoτortho) dominates, aligning parallel to the raceway.
- Deeper Layers (>1.5>1.5 mm): Principal shear stress (τprincipalτprincipal) prevails, oriented at 45° to the raceway.
Table 1: Shear Stress Amplitude Comparison
| Depth (mm) | τorthoτortho (MPa) | τprincipalτprincipal (MPa) | Dominant Mode |
|---|---|---|---|
| 0.3 | 342 | 278 | Orthogonal |
| 1.0 | 210 | 195 | Orthogonal |
| 2.0 | 85 | 112 | Principal |
3. Crack Propagation Direction
3.1 Fracture Mechanics Model
Crack propagation direction depends on the stress intensity factors (KI,KIIKI,KII) at the crack tip. For mixed-mode loading, the maximum circumferential stress (σθθσθθ) criterion predicts the crack angle (θθ):σθθ=KI2πrcos3θ2+KII2πr(−32sinθcosθ2)σθθ=2πrKIcos32θ+2πrKII(−23sinθcos2θ)
Pure shear (Mode II) loading results in a theoretical crack angle of −70.5∘−70.5∘. However, superimposed compressive stresses (e.g., Hertz contact pressure) suppress Mode I opening, favoring Mode II propagation.
3.2 Residual Stress Effects
Residual stresses from heat treatment significantly alter crack paths:
- Martensitic Steel: Tensile residual stresses (+40+40 to +100+100 MPa) promote Mode I (perpendicular to raceway).
- Bainitic Steel: Compressive residual stresses (−200−200 MPa) favor Mode II (parallel to raceway).
Table 2: Crack Propagation Modes
| Material | Residual Stress (MPa) | Crack Mode | Orientation |
|---|---|---|---|
| Martensitic Steel | +80+80 | I (Opening) | Perpendicular to Raceway |
| Bainitic Steel | −200−200 | II (Shear) | Parallel to Raceway |
3.3 Assembly Interference
Interference fits introduce circumferential tensile stresses (σassemblyσassembly), amplifying Mode I tendencies:σθθtotal=σθθcontact+σassemblyσθθtotal=σθθcontact+σassembly
4. Experimental Validation
4.1 Case Studies
- Case 1: Martensitic bearing failure showed vertical cracks (Mode I) due to residual tensile stresses.
- Case 2: Bainitic bearings exhibited shallow spalling (Mode II) under compressive residual stresses.
Table 3: Failure Analysis Summary
| Bearing Type | Crack Depth (mm) | Crack Angle | Failure Mode |
|---|---|---|---|
| Martensitic | 0.5–1.2 | 90° | Axial Crack |
| Bainitic | 0.2–0.8 | 10° | Spalling |
5. Conclusions
- Crack Initiation:
- Shallow cracks align with raceways (τorthoτortho dominance).
- Deep cracks (>1.5>1.5 mm) deviate by 45° (τprincipalτprincipal dominance).
- Crack Propagation:
- Martensitic gearbox bearings fail via Mode I under tensile residuals.
- Bainitic bearings resist cracking via Mode II under compressive residuals.
- Design Recommendations:
- Optimize heat treatment to induce compressive residual stresses.
- Avoid excessive interference fits to mitigate Mode I risks.
This study provides a foundation for enhancing wind turbine gearbox bearing durability, directly addressing the challenges of renewable energy systems.