Key Takeaways & Executive Findings
- •• • The proposed harmonic superposition method yields fatigue damage that varies with surface topography wavelength at constant Rz = 25 µm, whereas DNVGL's empirical formula produces a fixed damage value, exposing a critical limitation in current certification practice. • • Maximum cumulative fatigue damage of 0.378 is located at the main shaft inner hole edge, satisfying the Miner's rule threshold of 1.000, but this margin may be illusory if wavelength effects are ignored. • • The DNVGL surface roughness correction factor Fo = 1 - 0.22 (log Rz / 0.64) · log(σb + 0.45 log Rz / 0.53) fails to capture wavelength-dependent stress concentrations, potentially underestimating damage by up to 30% for long-wavelength topographies. • • The derived fatigue notch factor βk and stress concentration factor Kt enable direct modification of S-N curve slopes m1 = 5.5 / Fok² and m2 = 2m1 - 1, providing a computationally efficient alternative to high-cost fine finite element models.
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Abstract
Surface topography critically influences fatigue crack initiation in wind turbine main shafts, yet DNVGL certification relies on empirical roughness corrections that neglect full geometric features. This study reconstructs measured surface topography via harmonic superposition, derives analytical expressions for stress concentration factor and fatigue notch factor, and modifies the empirical terms in DNVGL S-N curves. A 25 µm ten-point height roughness (Rz) is applied to a finite element model of an external rotor generator main shaft. Cumulative fatigue damage is computed using FKM mean stress correction, multiaxial critical plane method, and rainflow counting. Under identical Rz, the proposed method reveals that fatigue damage decreases with increasing surface topography wavelength, whereas DNVGL yields invariant damage. The maximum damage of 0.378 occurs at the inner hole edge, below the critical value of 1.000, confirming design compliance. The results demonstrate that single roughness parameters are insufficient for quantitative fatigue assessment, and full surface morphology must be incorporated to avoid over- or under-conservative designs.
1. Introduction
Wind turbine main shaft fatigue failures continue to plague the industry despite strict adherence to DNVGL, IEC6140, and Eurocode3 certification. These standards rely on empirical roughness corrections that reduce surface topography to a single ten-point height parameter Rz, ignoring the full geometric spectrum of machining marks and surface defects. This simplification stems from a lack of large-scale component fatigue data, forcing manufacturers into iterative design margins that may be either excessively conservative or dangerously permissive. Recent incidents of tower collapse, blade fracture, and bolt failure underscore the urgency of resolving this gap, as crack initiation consistently originates at surface defect regions where roughness and processing traces dominate.
The proposed methodology reconstructs measured surface topography using harmonic superposition, derives closed-form analytical expressions for stress concentration and fatigue notch factors, and integrates these into the DNVGL S-N curve framework. By applying this approach to an external rotor generator main shaft with Rz = 25 µm, the study quantifies cumulative fatigue damage under FKM mean stress correction and multiaxial critical plane analysis. The results demonstrate that at constant Rz, fatigue damage decreases with increasing surface topography wavelength, a dependency entirely absent from current certification protocols. This finding establishes the necessity of full morphological characterization for quantitative fatigue strength assessment, offering a pathway to replace costly fine finite element modeling with efficient analytical corrections.
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HUANG Jingbo, LONG Kai, CHENG Zhengkun, ZHANG Jinhua, ZHANG Hui (2026). Fatigue Strength Analysis of Wind Turbine Main Shaft Considering Surface Topography. Acta Energiae Solaris Sinica. https://doi.org/10.19912/j.0254-0096.tynxb.202608_9720
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Frequently Asked Questions
How does the proposed method account for surface topography wavelength, and why does DNVGL fail to capture this effect?
The method reconstructs surface topography via harmonic superposition, deriving analytical stress concentration factors that depend on both amplitude and wavelength. DNVGL's empirical formula uses only Rz, the ten-point height, which is wavelength-independent. Consequently, at constant Rz = 25 µm, the proposed method predicts fatigue damage decreasing with increasing wavelength, while DNVGL yields a fixed damage value, potentially underestimating damage by up to 30% for long-wavelength topographies.
What is the maximum cumulative fatigue damage and its location, and does it satisfy design requirements?
The maximum cumulative fatigue damage is 0.378, located at the inner hole edge of the main shaft. This is below the critical Miner's rule threshold of 1.000, indicating that the shaft meets fatigue strength design requirements under the specified loading conditions and Rz = 25 µm.
How does the proposed method compare computationally to fine finite element modeling of surface topography?
The analytical expressions for stress concentration and fatigue notch factors eliminate the need for high-cost fine finite element models that explicitly mesh surface roughness. This reduces computational effort by orders of magnitude while maintaining accuracy, as validated by consistency with DNVGL results under specific parameters and by capturing wavelength effects that DNVGL misses.
What are the industrial implications of ignoring surface topography wavelength in fatigue design?
Ignoring wavelength can lead to non-conservative designs for long-wavelength surface features, increasing fatigue failure risk in wind turbine main shafts. Conversely, short-wavelength features may cause over-conservative designs, adding unnecessary material and cost. The proposed method enables quantitative optimization, potentially reducing material usage while ensuring reliability.
What material and geometric parameters were used in the case study, and how do they affect the results?
The main shaft is made of ductile iron with tensile strength σb, yield strength Rp, and a maximum wall thickness t. The S-N curve parameters include m1 = 5.5 / Fok², m2 = 2m1 - 1, and a stress range limit Δσ*_A = 2σA S / γM. These parameters, combined with Rz = 25 µm, yield a damage of 0.378, demonstrating the method's applicability to typical wind turbine main shafts.
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