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Dynamic analysis of geared transmission system for wind turbines with mixed aleatory and epistemic uncertainties

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Abstract

This paper deals with the co-existence of mixed aleatory and epistemic uncertainties in a wind turbine geared system for more reliable and robust vibration analyses. To this end, the regression-based polynomial chaos expansion (PCE) is used to track aleatory uncertainties, and the polynomial surrogate approach (PSA) is developed to treat the epistemic uncertainties. This non-intrusive dual-layer framework shares the same collocation pool, which is extracted from the Legendre series. Moreover, the regression technique has been implemented in both layers to enhance calculation efficiency. Numerical validation is carried out to show the effectiveness of the proposed method. New vibration behaviors of the geared transmission system are observed, and the mechanism behind is discussed in detail. The findings of this paper will contribute to the insightful understanding of such wind turbine geared systems under hybrid uncertainties and are beneficial for the condition monitoring.

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Abbreviations

P k(x):

Legendre polynomials

X k :

Legendre quadrature pool

ξ :

standard aleatory vector

ψ k(ξ):

Askey chaos basis

\({\boldsymbol{\tilde \gamma}}\) :

polynomial chaos (PC) coefficient vector

H :

transform matrix in polynomial chaos expansion (PCE)

μ k y :

statistic moments

φ j(ζ):

simplex polynomial basis

\({\boldsymbol{\tilde \eta}}\) :

surrogate coefficient vector

S :

transform matrix in polynomial surrogate approach (PSA)

K m :

mesh stiffness of gear pair

e :

dynamic transmission error

θ 1, θ 2, θ 3, θ 4 :

angular displacements of system

I 1,h, I 2, I 3, I 4 :

moments of inertia of system

K s1 , K s2 :

shaft stiffnesses

T b, T g :

torques on blade and generator

C s1 , C s2 C m :

dam** coefficients of shafts and meshing

ρ :

density of materials

w :

effective tooth width

R p, R g :

radii of pinion and gear

L l, L 2 :

lengths of shafts

ω :

revolution speed

F :

dynamic mesh force.

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Author information

Authors and Affiliations

  1. Institute of Vibration Engineering, Northwestern Polytechnical University, **’an, 710072, China

    Chao Fu, Kuan Lu & Yongfeng Yang

  2. Centre for Efficiency and Performance Engineering, University of Huddersfield, Huddersfield, HD1 3DH, U.K.

    Chao Fu & F. S. Gu

  3. Dynamics Group, Imperial College London, London, SW7 2AZ, U.K.

    Y. D. Xu

  4. School of Astronautics, Harbin Institute of Technology, Harbin, 150001, China

    Yushu Chen

Authors
  1. Chao Fu
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  2. Kuan Lu
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  5. F. S. Gu
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Corresponding author

Correspondence to Kuan Lu.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 12072263 and 11972295) and the Fundamental Research Funds for the Central Universities (No. G2021KY0601)

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Fu, C., Lu, K., Xu, Y.D. et al. Dynamic analysis of geared transmission system for wind turbines with mixed aleatory and epistemic uncertainties. Appl. Math. Mech.-Engl. Ed. 43, 275–294 (2022). https://doi.org/10.1007/s10483-022-2816-8

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  • DOI: https://doi.org/10.1007/s10483-022-2816-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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