Optimized gearbox design - Wind Power Generation and Wind Turbine Design - page 510

which require complementary changes in the rotor speed, blade pitch and nacelle
orientation. However, because of inertia effects such changes cannot be made
within a compatible time scale during which, the rotor hub is transiently required
to sustain whatever loads this might entail.
Since power is proportional to wind speed cubed, a transient speed increase of
only 50% will more than double the torque and treble the power. Even if the wind
speed remains constant, a change of its direction with respect to the axis of rota-
tion means that the rotor will run yawed such that the angle of attack on the indi-
vidual blades will vary continuously as they rotate. Since it is virtually impossible
to keep moving the nacelle in step with every transient it is only practicable to
respond to a sustained change of direction. Thus, the turbine could spend a
signifi cant amount of its time running yawed.
In any case, most wind turbines face upwind with their rotor axes tilted some 5°
up at the front to reduce overhang from the nacelle and the danger of blades col-
liding with the tower. The rotor therefore, will always be yawed even if in other
respects it is perfectly aligned to the wind. Over the large swept area of a turbine
there are signifi cant variations in wind speeds, angles of attack and blade defl ec-
tions which inevitably promote angular fl uctuations at the rotor hub and conse-
quentially, large cyclic torque and electrical power variations in the generator.
While the electrical fl uctuations may be dealt with electronically, the associated
mechanical torque fl uctuations due to the referred inertia of the generator rotor can
only be absorbed by strain energy defl ections in the drive train and/or an active
form of torque control.
Assuming similar density materials, a direct drive generator will have 100 times
the torque and weight of with a step up ratio of 100/1 the geared version and if their
respective generator rotor lengths are approximately the same, it would have the same
polar moment of inertia as that of the high speed generator whose inertia is multiplied
by gear ratio squared when referred to the turbine rotor. The power to weight ratio of
the direct drive generator, like the turbine will be subject to the same disproportionate
decrease in its power to weight ratio, whereas that of a geared generator is constant.
Due to the universal application of constant frequency grid systems and cheap
standardised high speed generators produced in large numbers, the cost of direct
drive generators produced in relatively small numbers is inevitably much greater.
As power increases, the input shaft of a gearbox is subject not only to the same
disproportionate increase in turbine torque but also a bigger step up ratio. How-
ever, this incurs a much smaller increase in overall weight and cost of the nacelle/
tower assembly compared with the direct drive alternative. Thus, despite their reli-
ability problems, geared generators have generally been the preferred option for
the vast majority of wind turbines.
2 Basic gear tooth design
Toothed gearing is historically the most effective and effi cient mechanism for cou-
pling machines having different optimum speeds. Its development has therefore
been driven by purely economic considerations.