Environmental Engineering Reference
In-Depth Information
When a tower is stiff and a teeter hinge is not used, the analysis of blade bending loads
in a two-bladed HAWT becomes extremely complex. Rotor blade models must be coupled
to the nacelle and tower models in a manner that involves large cyclic variations in the
spring and inertial coupling terms in the
equations of motion.
The necessary analysis can
certainly be achieved, but it is of declining interest because the large cyclic loads in such
a system prohibit economic success.
The difficulties of analyzing a two-bladed hingeless HAWT on any tower (stiff or soft)
and the knowledge that adding a third blade eliminates both the tower shake and the need
for a coupled rotor-tower analysis have led to the prevalence of three-bladed rotors. In
three-bladed HAWTs much more freedom of tower frequency placement has been evident.
Nothing done to adjust tower frequency has any influence on the blade bending and shaft
bending loads that occur. The tower sees these loads as large steady loads that it can be
designed to carry. Thus, if the fatigue loads on hingeless blades are acceptable and three
or more blades are used, the way is opened for use of relatively soft, lightweight towers
without the need for a sophisticated dynamic analysis of the coupled rotor and tower.
When the teeter hinge is adopted in the design of a two-bladed HAWT, the most
troublesome dynamic coupling of the blades to the nacelle and tower is eliminated. This
greatly simplifies the adequate simulation of the resulting system. It is then found that
dynamic motions of the rotor are very little influenced by tower stiffness. However, loads
are generally benefitted by reducing the stiffness of the tower, both in bending and torsion.
It is of course true that some tower modal frequencies may respond excessively to whatever
loads may remain at integer multiples of the rotor speed. It has been found that with soft
or soft-soft tower design, tower vibration modes that involve substantial upwind-downwind
motion will pick up good aerodynamic damping from the rotor blades. Those modes that
involve only lateral or vertical motion of the rotor hub will have to be avoided, or suitable
hardware provided that is designed to mechanically dampen a specific mode of vibration.
Modeling Dynamic Characteristics and Behavior
Natural Vibration Modes of HAWTs and VAWTs
It is of very great significance that the periodic loads in any subsystem of a wind
turbine will depend upon the response of the system as a whole in its
natural
or
free-
vibration modes.
These are the patterns of vibration that the system assumes after it has
been set in motion but without any external applied loads. Each pattern has a distinctive
shape and frequency, termed the
mode shape
and
modal
or
natural frequency
, respectively.
It is only when the natural modes of elements such as the blades, power train, and support
system have been fully coupled together to derive the system modes that structural dynamic
analysis can be successful. Thus, the simulation model of the wind turbine must start with
suitably detailed models of the subsystem elements and then combine them in a manner that
enables
aeroelastic analysis
(
i.e.
analysis that permits elastic deflections to change angles
of attack) of the system as a whole.
The complete wind turbine will, of course, have a very large number of natural modes,
each at its own natural frequency. They may differ greatly from the uncoupled mode
shapes and natural frequencies of the isolated subsystem elements. Also, the number and
type of structurally significant system modes will depend upon how stiffly the subsystem
elements are coupled together. As discussed earlier, there are design features that can
uncouple subsystem elements, reducing the number of system modes that will present
significant responses. There is little value or dependability in modal analysis except that
of the fully-coupled system. In a wind turbine designed according to the soft-system
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