Fatigue Design of Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 694

produces the design trend graph in Figure 12-15. These load ratios apply to all probabilities
of exceedance. Blade cyclic loads are changed the most by scale changes, while the generator
cyclic power density (which is already a normalized quantity) changes the least. The effects
on loads of changing other parameters (hub d 3 angle, steady wind speed, surface roughness,
and tip chord) are given in [Spera 1994] for this same baseline case.

Figure 12-15. Typical design trend chart showing the relative changes in fatigue loads as
the size of a HAWT is changed. [Spera 1994]

The load trends in Figure 12-15 can be used to estimate stress trends when the size of a
turbine is changed but its geometry remains similar. In wind turbine components like blades
and towers, bending stress is usually the design driver and section modulus is the strength
parameter of interest. Because the section moduli of geometrically similar cross-sections are
proportional to the cube of their relative dimensions, it follows that

D o
D 3

Bending stress
Baseline bending stress

Bending moment
Baseline bending moment

(12-8a)

=

where D 0 is the baseline diameter. Bending moments on the tower are directly proportional
to the thrust density times the cube of the diameter (from rotor area x tower height), so the
cubic ratios cancel out and

Tower bending stress
Baseline tower bending stress

Sha f t thrust density
Baseline sha f t thrust density

(12-8b)

=

Torque on the turbine shaft is proportional to the power density times the cube of the diam-
eter (from rotor area/shaft speed) and so is torsional section modulus. Again, cubic ratios
cancel out and

Sha f t shear stress
Baseline sha f t shear stress

Generator power density
Baseline generator power density

(12-8c)

=