Six-Degree-of-Freedom Rotor-Load Cross-Spectral Density from Rotor-Plane Turbulence Cross-Spectra
Abstract
A frequency-domain response analysis of a wind turbine rotor requires the complete hub-load spectrum, but the customary scalar thrust and torque spectra retain neither the four in-plane components nor the coupling between them. This paper derives the full six-degree-of-freedom (6-DOF) rotor-load cross-spectral-density (CSD) matrix from the IEC Kaimal turbulence model. By decoupling the spatial order of inflow coherence from the temporal Doppler shift, the formulation introduces a two-index rotational-sampling kernel. Rotor symmetry and azimuthal averaging constrain the observed Doppler carrier strictly to blade-passing harmonics pBfrot, while the azimuthal aerodynamic transfer shifts the spatial coherence order to pB+s. A convergence study of the retained azimuthal order s shows that lvert srvert≤4 suffices, the assembled CSD then deviating from the full-band result by less than 10−5 in relative norm. The formulation is compared with OpenFAST simulations of a rigid floating wind turbine over nine wind speeds: the six auto-spectral densities agree closely below 1~Hz, and the present theory over-predicts the spectra near the 6P and 9P rotational harmonics.
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BibTeX
@misc{yang2026sixdegreeoffreedom,
title = {{Six-Degree-of-Freedom Rotor-Load Cross-Spectral Density from Rotor-Plane Turbulence Cross-Spectra}},
author = {Haoran Yang and Zhaolong Han},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33513},
eprint = {2610.33513},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33513},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Six-Degree-of-Freedom Rotor-Load Cross-Spectral Density from Rotor-Plane Turbulence Cross-Spectra
AU - Haoran Yang
AU - Zhaolong Han
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33513
UR - https://arxiv.org/abs/2610.33513
AB - A frequency-domain response analysis of a wind turbine rotor requires the complete hub-load spectrum, but the customary scalar thrust and torque spectra retain neither the four in-plane components nor the coupling between them. This paper derives the full six-degree-of-freedom (6-DOF) rotor-load cross-spectral-density (CSD) matrix from the IEC Kaimal turbulence model. By decoupling the spatial order of inflow coherence from the temporal Doppler shift, the formulation introduces a two-index rotational-sampling kernel. Rotor symmetry and azimuthal averaging constrain the observed Doppler carrier strictly to blade-passing harmonics pBf_rot, while the azimuthal aerodynamic transfer shifts the spatial coherence order to pB+s. A convergence study of the retained azimuthal order s shows that lvert srvert≤4 suffices, the assembled CSD then deviating from the full-band result by less than 10^−5 in relative norm. The formulation is compared with OpenFAST simulations of a rigid floating wind turbine over nine wind speeds: the six auto-spectral densities agree closely below 1~Hz, and the present theory over-predicts the spectra near the 6P and 9P rotational harmonics.
ER -