Blade Loads Outputs at User Axes System

The user axes system is a custom coordinate system that can be defined by the user for outputting blade loads. It is defined in the Blades screen in the Blade Geometry tab. At the bottom of the screen it is possible to define the user defined axis directions for the z-axis and y-axis. The y-axis can follow either the untwisted root y-axis, principal elastic y-axis or the aerodynamic twist. The z-axis options and their implications are explained below.

User axes: Z-axis follows neutral axis or root z-axis

The origin of the axes is specified as percentages of chord, parallel and perpendicular to the chord at each blade station as shown in Figure 1. The user can specify whether the z-axis is parallel to the root axis or the local neutral axis. Similarly, the user can independently specify whether the y-axis is aligned to the principal elastic axes orientation, the aerodynamic twist, or the root axis.

Figure 1: Position of the user defined output axis

User axes: Z-axis follows user axis

This option enables the user to create a new custom output coordinate system. This system is defined relative to the local element coordinate system that is illustrated in Figure 2. A planar view of a simple blade comprising indexed blade stations with adjoining elements is provided. In this example, only prebend of the neutral and user axes is considered. Presweep, principal elastic axes orientation and aerodynamic twist are zero. The inboard station number near the blade root is 1 and the most outboard near the blade tip is 3. At each station, the position of the neutral axis node is provided by the user. The consecutive neutral axis nodes are connected via piecewise linear "elements" in order of ascending numerical station index.

The blade element coordinate system is denoted by the subscript \(e\). For the $n$th piecewise linear element at node \(m\), the \(x_{e_{n,m}}\)-axis runs parallel to the line adjoining consecutive neutral axis nodes. Positive direction is from the blade root to tip. The \(y_{e_{n,m}}\)-axis and \(z_{e_{n,m}}\)-axis are determined by the principal elastic axes orientation around the \(x_{e_{n,m}}\)-axis. The principal elastic axes orientation is specified by the user and per node. Hence, the direction of the \(y_{e_{n,m}}\)-axis depends on both the element and the node index. When the principal elastic axes orientation is zero \(z_{e_{n,m}}\) lies in the \(x_r\),\(z_r\) root axes plane.

Figure 2: Definition of the user axis location and orientation when z-axis follows user axis

Figure 3 illustrates a blade station and presents key geometric information necessary to understand the user axes coordinate system. The diagram is now drawn assuming a straight neutral axis (no blade prebend or presweep) in the spanwise direction. Also, the aerodynamic twist and principal elastic axis orientation are considered non-zero. In this simple case the various properties such as principal elastic axis orientation and aerodynamic twist along with user axis position are defined in the root axes plane denoted \(x_r\),\(y_r\).

The user axis coordinate systems are derived from the element frame. More generally, the user axis inputs \(x'\),\(y'\) are defined by the user using the chord coordinate system. These are rotated and translated into the local element coordinate system creating the \(r_{u_m}\) vector as shown in Figure 3. The \(r_{u_m}\) vector lies in the \(y_{e_{n,m}}\) , \(z_{e_{n,m}}\) plane.

Figure 2 demonstrates that for intermediate nodes the same \(r_{u_m}\) vector is applied to the adjoining node for both the inbound and the outbound element as illustrated by the \(r_{u_2}\) vector. For each element, \(r_{u_m}\) vectors are added to the pair of neutral axis nodes to create two points that lie on the user axis. The \(z_{u_{n,m}}\)-axis is parallel to the line connecting these points as illustrated in Figure 2. Figure 2 also demonstrates that the user axis is discontinuous between adjoining blade stations. It is assumed that the variation of the neutral axis orientation between blade stations is small resulting in the discontinuities being small/negligible. Finally, Figure 2 also shows that the \(x_{u_{n,m}}\)-axis lies in the \(x_r\),\(z_r\) plane.

Figure 3: Local aerofoil cross section at station 2 showing x',y' coordinate system.

Figure 4 provides an overview of the user axis in the more general case where the user specifies a blade with prebend and presweep, where the aerodynamic twist & principal elastic axis orientation are non-zero and the user axis values are also non-zero. The direction of the \(y_{u_{n,m}}\)-axis is determined by a rotation around the \(z_{u_{n,m}}\)-axis of either the aerodynamic twist (if y-axis follows aerodynamic twist is selected) or zero twist (if y-axis follows untwisted root axis is selected) as shown in Figure 4. Note that the aerodynamic twist and principal elastic axes orientation inputs are defined as positive clockwise rotations. The direction of the \(x_{u_{n,m}}\)-axis is the cross product of the \(y_{u_{n,m}}\)-axis and \(z_{u_{n,m}}\)-axis. This defines a right-handed coordinate system.

Figure 4: User axis illustrated in three dimensions show the twist

To compute the user axis load output the moments from the element coordinate system must be translated and rotated into the user axis frame. Note that the user axis potentially does not coincide with the blade element axis. An additional moment is added/subtracted at each station to account for this:

\[ M_u=R_{e u}\left(M_e - r_{u_1} \times F_e\right) \]

As the relative translation \(r_{u_m}\) and rotation \(R_{e u}\) between the user axis and the associated element coordinate system are independent of blade deflection, the same values at each blade station are used for the entire time domain simulation. Table 2 lists the coordinate system and location used at each station. The first station reports the loads in the outboard user axis \(u_{1,1}\) coordinate system and for the remainder of the stations, the inboard user axis \(u_{x,2}\) coordinate system is used.

Table 2: Load output for each station in Figure 2 and Figure 4.

Station	User Axis Coordinate System	Offset
1	\(u_{1,1}\)	\(r_{u_1}\)
2	\(u_{1,2}\)	\(r_{u_2}\)
3	\(u_{2,2}\)	\(r_{u_3}\)

The location of the user axis points in the root coordinate system at the undeflected reference position can be evaluated in the verification file ($VE).

The combination of both the z-axis follows user axis and y-axis follows principal elastic axes is not supported.

Last updated 13-12-2024