26-11-2012, 11:42 AM
Optimal frequency design of wind turbine blades
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Abstract
An optimization model for the design of a typical blade structure of horizontal-axis wind
turbines is presented. The main spar is represented by thin-walled tubular beam composed
of uniform segments each of which has different cross-sectional properties and length. qThe
optimization variables are chosen to be the cross-sectional area, radius of gyration and length
of each segment. The optimal design is pursued with respect to maximum frequency design
criterion. Global optimality is attainable by the proposed model and a novel mathematical
concept is given for placing the system frequencies. The problem is formulated as a non-linear
mathematical programming problem solved by multi-dimensional search techniques.
Structural analysis is restricted to the case of uncoupled flapping motion of the rotating
blade, where an exact method of solution is given for calculating the natural vibration
characteristics. Aeroelastic stability boundaries and steady-state response are calculated
using Floquet’s transition matrix theory. The results show that the approach used in this
study is efficient and produces improved designs as compared with a reference or baseline
design. r 2002 Elsevier Science Ltd. All rights reserved.
Introduction
The design of a wind turbine structure involves many considerations such as
strength, stability, cost and vibration. Reduction of vibration is a good measure for a
successful design of blade structure. It may foster other important design goals, such as low cost and high stability level. A good design philosophy for reducing vibration
is to separate the natural frequencies of the structure from the harmonics of rotor
speed. This would avoid resonance where large amplitudes of vibration could
severely damage the structure. Frequency placement is one of the techniques used for
separating frequencies. In Ref. [1], an objective function was formulated for
minimizing the discrepancies between the desired frequencies and the actual ones.
The chosen design variables were the values of a set of lumped masses located at
specified points along the blade span as well as the distribution of the wall thickness
of the main box-beam cross section. The resulting optimum solutions were strongly
dependent on the values of the desired (target) frequencies, which are rather
arbitrarily chosen. Pritchard and Adelman [2] formulated a mathematical programming
optimization model by considering minimization of the induced shearing forces
at rotor hub as a measure of vibration reduction. Design variables were taken to be
the sizes and locations of the tuning masses along blade span, which has the
disadvantages of increasing structural mass.
Blade analysis
This section describes briefly the method of analysis for the fundamental case of
flapping motion of an isolated, single rotating blade, which is usually given a major
consideration in wind turbine design.
Basic assumptions
1. The blade has a symmetric airfoil-shaped cross section. The main load-carrying
element is a thin-walled spar supporting the non-structural ribs and skin. An
equivalent long, slender cantilever beam built from uniform segments having
different cross-sectional properties and length represents the main spar structure.