Page 200 - Fluid Power Engineering

172 Chapter Nine

FIGURE 9-2 Forces y
and moments x
acting on a blade. z

M x
F x

M r
F r
M t

F t
Forces and Moments
Since the blade is the exposed element, it takes the most complex set
of forces and moments, along each of the six axes. For convenience, all
the forces and moment are indicated along axial, radial, and tangential
directions, as shown in Fig. 9-2.
Axial force, F x . The lift and drag forces have components in

the tangential and axial directions. The change in the net axial
force is a function of the wind speed. This force is the primary
contributor to the thrust force on the rotor.
Radial force, F r . There are two primary sources of radial force:

Gravity and inertia. The weight of the blade is a constant force
acting vertically downward. From the point of view of the
blade, the force is cyclical—changing from radial to tangen-
tial with a frequency equal to the frequency of rotation. The
inertial force has two components, centrifugal force because of
rotationand forcesduringbrakingand acceleration.The blade
experiences radial acceleration (because of change in direction
of velocity) and, therefore, radial force. For a constant-speed
rotor, this force is constant when the turbine is rotating and
zero when the rotor is stationary.
Tangential force, F t . There are four primary sources of tangen-

tial force: Lift, drag, and gravity, and inertial forces. The iner-
tial forces are during startup and braking of the rotor. This is
the force that produces torque on the rotor.
Bending moment along the axis of rotation, also called edgewise

bending moment, M x . This bending moment arises because of
lift forces that increase radially when moving from hub to tip
of blade. This force reaches a peak close to the tip. Another
contributor to the bending moment is gravity. Measured at
the root of the blade, this bending moment oscillates between
positive and negative value with a frequency equal to the
frequency of rotation.