Hub Geometry

The hub system connects the drive shaft to a series of mounting points. This section describes the geometric parameters that can alter the position and orientation of the mounting points relative to the hub. The definition given below relate to upwind rotors with a clockwise rotational direction.

Hub Body-Fixed Coordinate System

The origin of the hub is referred to as the hub centre. The hub body-fixed frame is denoted \((x_{b}, y_{b}, z_{b})\). The body-fixed frame is shown in Figure 1 when looking at the side of the hub. When mounted on a drivetrain the hub will rotate about the \(x_b\) axis during turbine operation. The flat rotor plane (without coning) is defined by the \(y_b\) and \(z_b\) axes.

Mounting Points

The pitch system and blade will connect to the hub at the mounting points.

The user can specify a ConingAngle denoted \(\theta\) that defines a rotation between the pitch axis and the flat rotor plane as illustrated in Figure 1. The pitch axis is a line starting from the hub centre and travelling through the centre of the pitch bearing or mounting point. For both upwind and downwind turbines, a positive ConingAngle will rotate the pitch axis towards the nose of the hub and away from the nacelle.

A series of extension pieces link the hub centre to the mounting points. The mounting point is along the pitch axis at a radius given by the RadiusOfBladeConnection denoted \(R\). The radius is measured positively from the hub centre in the flat rotor plane. It is possible to define a zero radius.

Figure 1: Geometry of hub from the side. This is for an upwind clockwise rotor with three blades. Blade 1 is at 0 deg azimuth angle.

The azimuth angle \(\psi\) of the $i$th blade depends on the user-specified total number of blades \(N_b\) such that \(\psi = 2 \pi (i-1) /N_b\). The azimuth angle is positive about \(x_b\) and rotation is measured from the \(z_b\) axis as shown in Figure 2.

Figure 2: Geometry of hub from the turbine front. This is a clockwise upwind rotor with three blades and no coning angle. Blade 1 is at 0 deg azimuth angle.

Note

The blade index \(i\) refers to the order in which the blade passes through zero azimuth angle. The index ordering of the blades will therefore change with the rotational direction of the rotor. This is used for applying rotational offsets such as azimuth angle and set angle imbalances as these are assigned in order of blade index.

The SetAngle denoted \(\phi\) is a rigid rotational offset that alters the angle at which the blade is mounted onto the hub mounting point. The set angle enables whole blade rotation thereby changing the angle of attack without the need to re-define the twist distribution. More positive values of pitch angle or set angle push the leading edge further upstream by rotating about \(z_{d,i}\) as demonstrated in Figure 3.

Figure 3: Geometry of hub from above. This is a clockwise upwind rotor with three blades and no coning angle. Blade 1 is at 0 deg azimuth angle. The set angle is denoted by \(\phi\).

An example set of inputs that describe the hub mounting points for a clockwise upwind rotor with three blades is given below.

"IndependentPitchHub": {
      "ComponentType": "IndependentPitchHub",
      "NumberOfBlades": 3,
      },
      "RotationDirection": "CLOCKWISE_VIEWED_FROM_FRONT",
      "UpwindOrDownwind": "UPWIND",
      "MountingPoints": {
        "RadiusOfBladeConnection": 1.25,
        "ConingAngle": 0.06981317,
        "SetAngle": 0.0
      }

Extension Pieces

The user must specify the ExtensionPieceDiameter \(d\) and the CoefficientOfDrag such that the drag loads on the extension piece can be computed. It is assumed to be cylindrical. The drag load is computed on the exposed part of the extension piece as described below.

The drag loads will be applied to any part of the blade root section which is outside the spinner. Zero lift coefficient is assumed. The user should therefore input the Diameter of the spinner denoted \(D\). This is the diameter of any spinner or nose-cone, within which no aerodynamic forces are applied. If the spinner entirely covers the root section, the diameter and drag coefficient values of the extension piece are not required.

An example set of inputs for the spinner diameter and extension pieces is given below.

"Spinner": {
    "Diameter": 2.5,
    },
"ExtensionPieces": {
    "ExtensionPieceDiameter": 1.9,
    "CoefficientOfDrag": 0.8
    }

Hub Distal Frames

A distal frame of reference is located at the mounting points as shown in Figure 1 and Figure 2.

The transformation between body-fixed frame to the distal frame \((x_{d,i},y_{d,i},z_{d,i})\) is described using a series of translation and rotation operations. Initially the distal frame is assumed to match the hub-fixed frame for each mounting point. Then, for each mounting point:

1. Translate in the body-fixed frame by \((-R \tan(\theta),0, R)\) to move the origin of the distal frame.
2. A rotation about \(x_b\) equal to the azimuth angle \(\psi\) places the origin of the distal frame at the mounting point for each pitch bearing/blade.
3. A rotation about the \(y_{d,i}\) axis equal to \(\theta\).
4. A rotation about the \(z_{d,i}\) axis equal to \(\phi\).

Note

For a simulation without a rotary pitch actuator, the pitch degree of freedom is simulated as part of the hub component such that the distal frame rotates. If a rotary actuator is included then the pitch degree of freedom is simulated directly as part of the pitch system instead and the distal frame does not rotate about the \(z_{d,i}\) axis.