Blade Root and Neutral Axes Systems

In Bladed, the blade sections are defined as a finite series of 2D sections along the blade's span, using the neutral axes system relative to the blade root axes system.

Origin of Blade Root Axes System

The root axes coordinate system is a body-fixed coordinate system, which coincides with the blade root centre.

Figure 1: Blade root coordinate system, illustrated for zero cone and pitch.

The orientation of the blade root is influenced by properties inboard and outboard of the pitch bearing, as illustrated in Figure 2 and summarised in the table below. These properties determine the blade's mounting angles relative to the pitch axis. If no mounting sweep or cone angles are applied, the Blade root Z-axis aligns with the pitch axis. Non-zero angles for either Blade mounting cone angle or Blade mounting sweep angle create an orientation difference between the pitch and blade root Z-axis, as seen in Figure 2. All subsequent blade properties are defined relative to the Blade root Z-axis.

Table 1: Blade mounting properties and their effects on the blade root z-axis

Property	Location	Unit	Description
Cone angle	Inboard of pitch bearing	\(\bunit{deg}\)	A positive angle cones the tip away from the nacelle. Defined in Rotor screen.
Blade mounting cone angle	Outboard of pitch bearing	\(\bunit{deg}\)	A positive angle cones the tip away from the nacelle. Defined in Blades screen.
Blade mounting sweep angle	Outboard of pitch bearing	\(\bunit{deg}\)	Indicates how much the blade tip is swept back from the pitch axis, away from the rotation direction. Defined in Blades screen.

Figure 2: Left: Positive cone angle (inboard and outboard). Right: Positive sweep angle (outboard only, inboard not supported).

Blade Neutral Axes System

The neutral axis passes through the elastic centre of each blade section. Required inputs can be found in the Blades screen under the Blade Geometry and Mass and Stiffness tabs.

Note

The neutral axis is also commonly known as the principal elastic axis, bending axis, or simply the elastic axis.

The origin of the neutral axes system is defined using the following variables:

• Neutral axis (x)
• Neutral axis (y)
• Distance along blade or Distance along blade root Z-axis (See Distance Along Blade)

All structural properties for the section, such as stiffness and mass, are then defined in specific blade section coordinate systems. The blade root and neutral axes system for a blade is showed in the figures below:

Figure 3: Blade root axes system and section planes

Figure 4: Blade neutral axes system and section planes

Distance Along Blade

Only one of the variables, Distance along blade or Distance along blade root Z-axis, is needed to define the position of the neutral z-axis; the other is calculated automatically.

• Distance along blade root Z-axis refers to the position of the blade station along the blade root Z-axis.
• Distance along blade is the cumulative distance from the blade root to the current blade station, along the blade neutral axis, which does not have to be a straight line. It must be zero for the first station.

\[ \begin{equation} \text { DistanceAlongBlade}_{\mathrm{n}}=\sum_{i=1}^{n-1} \mathrm{\Delta} d_{i+1, i}=\Delta d_{2,1}+\cdots+\mathrm{\Delta} d_{n, n-1} \label{eq:distance_along_blade} \end{equation} \]

Where \(\mathrm{\Delta} d_{i, j}\) is the distance between two section origins:

\[ \begin{equation} \mathrm{\Delta} d_{i, j} = \left| \begin{matrix} X_{0_i}-X_{0_j} \\ Y_{0_i}-Y_{0_j} \\ Z_{0_i}-Z_{0_j} \\ \end{matrix} \right| \label{eq:delta_d} \end{equation} \]

Figure 5: Illustration of the Distance along blade definition

Last updated 13-12-2024