Structural Dynamic Behavior of Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 609

Coordinate System Definitions
Figure 11-1 shows the orientation of the HAWT blade under analysis with all the
intermediate coordinates required to represent the blade motion. The X-Y-Z coordinates are
the fixed reference system. The mean wind velocity at the hub elevation, V hub , and its
fluctuating components -- dV X , d V Y , d V Z -- are given in this system. The rotor axis may
be tilted at a fixed angle c. It may also have a prescribed, time-dependent yawing motion
given by the yaw angle f( t ) . The yaw axis is coincident with the Z -coordinate axis. The
center of the rotor hub, H , is located a distance a from the yaw axis. The blade may be
rigid from the axis outward to a distance h , which may also be interpreted as the outer
radius of the hub. The blade airfoil shape may begin at h or at a station further out along
the blade z axis. The blade may be coned at a prescribed angle b 0 , as shown in the figure.
The x,y,z coordinates are located in the surface of revolution that a rigid blade would
trace in space, with the y -axis normal to this surface. The x p -y p -z p system are the blade's
principal bending coordinates, where the z p -axis is coincident with the elastic axis of the
undeformed blade. Bending takes place about the x p -axis. It is further assumed that the
blade principal axes of area inertia remain parallel along the z p -axis. Any influence of
blade twist on bending displacements is neglected. As a reference for computations, the
angle q p is set equal to the orientation of the principal bending plane relative to the cone
of rotation ( i.e. , the x-y-z system) at a selected station of primary interest along the blade
span. The third coordinate system illustrated in Figure 11-1 is the h-z-x system, which
is on the principal axes of the deformed blade along each point along the elastic axis.
Figure 11-1. Fixed, rotating, and deformed-blade coordinate systems. Positive
displacements and rotations are shown. [Wright et al . 1988]