This section provides descriptions of the various modelling options and definitions for simulating wind turbine blades. Bladed provides a versatile method of defining complex blade properties:
- The user can define a series of 2D blade sections along the neutral axes of the blade. At each section, a set of blade section coordinate systems are defined for structural and aerodynamic properties. This approach enables the possibility of defining aerofoil orientations and changing structural properties along the blade.
- Advanced flexibility options are available to accurately capture the non-linear nature of long and anisotropic blades. Options include a finite element model capable of modal reduction, a multi-part blade method for increased accuracy of large deflections and a geometric stiffness model to capture second-order effects.
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.
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 .
叶片根部方向受变桨轴承内侧和外侧属性的影响，如图2所示，并在下表总结如下。这些属性决定了叶片相对于变桨轴的安装角度。如果未施加安装锥角或安装展向角mounting sweep or cone angles，则叶片根部Z轴与变桨轴对齐。叶片安装锥角或叶片安装展向角存在非零角度时，会导致变桨轴和叶片根部Z轴之间的方向差异，如图2所示。所有后续的叶片属性均相对于叶片根部Z轴定义。
Table 1: Blade mounting properties and their effects on the blade root z-axis
<html><body><table><tr><td>Property</td><td>Location</td><td>Unit</td><td>Description</td></tr><tr><td>Cone angle</td><td>Inboard of pitch bearing</td><td></td><td>deg A positive angle cones the tip away from the nacelle. Defined in Rotor screen.</td></tr><tr><td>Blade mounting cone angle</td><td>Outboard of pitch bearing</td><td></td><td>deg A positive angle cones the tip away from the nacelle. Defined in Blades screen.</td></tr><tr><td>Blade mounting sweep angle</td><td>Outboard of pitch bearing</td><td>deg</td><td>Indicates how much the blade tip is swept back from the pitch axis, away from the rotation direction. Defined in Blades screen.</td></tr></table></body></html>
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.
The origin of the neutral axes system is defined using the following variables:
Neutral axis (x) Neutral axis (y)
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:
-`Distance along blade`or`Distance along blade root Z-axis`(See[Distance Along Blade](https://mysoftware.dnv.com/download/public/renewables/bladed/documentation/4_17/modelling/blades/RootAndNeutralAxes.html#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.
The blades in Bladed 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.
Each section has an aerofoil that is oriented according to the Aerodynamic twist , with an associated chord axes system origin located at the leading edge as shown in Figure 1. The aerofoil must be positioned relative to the neutral z-axis, which passes through the elastic centre of each blade section. This is done by defining the location of the elastic centre as a percentage of the Chord length, measured from the aerofoil leading edge along the chord axes that follow the Aerodynamic twist :
Not all coordinate systems are relevant in every model; their inclusion depends on the model's complexity. For example, the principal shear axes coordinate system is not needed if Shear stiffness is omitted.
<html><body><table><tr><td>Coordinate System</td><td>Description</td></tr><tr><td>Root axes</td><td>Fixed to the blade root, and it does not rotate with twist or blade deflection but rotates about the z-axis with pitch.</td></tr><tr><td>Chord axes</td><td>Located at the leading edge of the aerofoil and follows the Aerodynamic twist.</td></tr><tr><td>Principal elastic axes</td><td>Located at the Elastic centre and follows the Principal elastic axes orientation (xe, ye).</td></tr><tr><td>Principal shear axes</td><td>Located at the Shear centre and follows the Principal shear axes orientation (xs, ys) .</td></tr><tr><td>Principal inertia axes</td><td>Located at the Mass centre and follows the Principal inertia axes orientation (xm, ym) .</td></tr><tr><td>User axis</td><td>Located at the User axis , specified by the user for additional loads output. See Loads Outputs at User Axes for details.</td></tr></table></body></html>
The centres, including the Elastic centre, Shear centre, Mass centre and User axis,are all defined with respect to the chord axes, which are controlled by the Aerodynamic twist . The locations of these centres are specified as a percentage of the chord length measured from the aerofoil leading edge. An example of this is illustrated in Figure 3 for the Shear centre definition.
Figure 3: Top: Definition of shear centre (x'). Bottom: Definition of Shear centre (y').
Furthermore,the orientations of the Aerodynamic twist , Principal elastic axes orientation (xe, ye), Principal shear axes orientation (xs, ys),and Principal inertia axes orientation (xm, ym) are all defined with respect to the root axes and are positive in the clockwise direction as shown in Figure 4. In the GUl, the unit of the inputs is in degrees, whereas in the project file, it is in radians.
This section provides an overview of the structural properties defined in the various coordinate systems. For more details, see Blade Section Stiffness and Blade Section Mass.
The blade geometry is defined for each blade station. Select the option at the bottom of the screen to specify either the distance along blade or distance along blade root Z-axis .The alternate value will be automatically calculated using the neutral axis values. For example, selecting Distance along blade will automatically calculate the Distance along blade root Zaxis , and vice versa. For details refer to the section on Distance Along Blade. The following geometry data is required at each blade station:
<html><body><table><tr><td>Variable identifier</td><td> Unit </td><td> Description </td></tr><tr><td>Distance along blade</td><td>m</td><td>The distance from the blade root to the current station along the neutral axis, which may not be straight. It must be zero for the first station.</td></tr><tr><td>Distance along blade root Z-axis</td><td>m</td><td>The distance of the blade station along the blade root Z-axis.</td></tr><tr><td>Chord</td><td>m</td><td>The distance from the leading edge to the trailing edge along the chord line.</td></tr><tr><td></td><td></td><td>Aerodynamic twist deg The local angle of the chord line. More positive values of twist and set angle push the leading edge further upwind in the direction from which the flow is coming.</td></tr><tr><td>Thickness</td><td>%</td><td>The thickness of the blade as a percentage of the chord at that station.</td></tr><tr><td>Neutral axis (x)</td><td>m</td><td>The distance from the blade root Z-axis to the neutral axis in the x- direction. This would be non-zero if, for example, the blade was pre- bent.</td></tr><tr><td>Neutral axis (y)</td><td>m</td><td>The distance from the blade root Z-axis to the neutral axis in the y- direction.</td></tr><tr><td>Elastic centre (x')</td><td>%</td><td>The distance from the leading edge to the elastic centre along the chord x-axis, as a percentage of the chord.</td></tr><tr><td>Elastic centre (y')</td><td>%</td><td>The distance from the leading edge to the elastic centre along the chord y-axis, as a percentage of the chord.</td></tr><tr><td>Foil section</td><td></td><td>An index number defining the aerofoil section at that station.</td></tr><tr><td>Moving/Fixed</td><td></td><td>Differentiates between fixed and movable parts of the blade for pitch of that part of the blade, or by deploying an aileron, flap or other aerodynamic control surfaces.</td></tr></table></body></html>
Figure 1 and Figure 2 illustrate a blade station for Clockwise and Anticlockwise rotor configurations. It is assumed that the perspective is from the tip toward the root, aligned to the root axes plane.
The blade inputs for an Anticlockwise rotor use a left-handed coordinate system, in contrast to the right-handed system for clockwise rotors. As a result, no changes are needed to the input data when switching between Clockwise and Anticlockwise rotors. See Figure 2 for an illustration of the Anticlockwise blade definition.
To model flexible blades or analyse vibrational dynamics, it is necessary to define the stiffness distribution of the rotor blade. Begin by selecting the appropriate degrees of freedom to include in the model by enabling/disabling the following options in the Blades screen under the Mass and Stiffness tab:
The blade sectional stiffness inputs all relate to the cross-sectional $6\!\times\!6$ stiffness matrix used in the Bladed beam model as shown in Equation (1). This matrix is associated with the principal elastic axes coordinate system, which is defined by the Principal elastic axes orientation (xe, ye) and the Elastic centre as described in Blade Section Coordinate Systems. The constitutive relationship for the full beam model can be expressed as:
The shear-shear coupling stiffness $G A_{x y}$ and shear-twist coupling stiffness terms $G A_{x}y_{c s}$ and $G A_{y}{\pmb x}_{c s}$ are calculated automatically by Bladed based on the input values.
Bending-twist and bending-bending coupling terms can be specified through Project Info. More details on how the inputs are used in the simulation can be found in the theory article Bend-Twist Coupling Relationships in Beam Elements.
You need enough entries for the number of elements in the blade. Each node in the Bladed user interface defines the properties for both the end of one element and the beginning of the next, unless it is a split station so there must be $2N_{e l}-2$ entries, where $N_{e l}$ is the number of blade elements.
To accurately model the dynamic behavior of rotor blades, it is essential to define their mass and inertia distribution. This is primarily done in the Blades screen under the Mass and Stiffness tab by enabling the Mass checkbox. Additional options are available to model point masses and blade icing:
If the Radii of gyration ratio is not specified, it defaults to the relative profile thickness given by ratio of Thickness to Chord , but it can be defined explicitly by un-checking the Use default radii of gyration ratio checkbox. It can be calculated with the following equation:
$\boldsymbol{r}_{x}$ is the radius of gyration in the principal inertia x-axis direction, $r_{y}$ is the radius of gyration in the principal inertia y-axis direction, $\mu$ is the Mass/unit length ,
If additional point masses are required at specific locations along the blade, click the Additional Mass/Inertia tab and enter the point masses in the table. Additional pitching inertia should also be specified on this screen. Click the Add button to add each point mass, and then enter the data required by clicking on the appropriate entry. Note that masses are automatically sorted by radial position. To remove a mass, highlight it by clicking on its number, and click Delete . For each point mass, the following data is required:
Bladed represents blade ice accretion by adding mass to the blade at the aerofoil leading edge. It is defined in the Blades screen under the Blade Information tab. This additional mass will modify the blade mass totals and mass distribution properties such as Polar mass moment of inertia/unit length and the location of the Mass centre .
There are two available methods for the calculation of ice mass on the turbine blades.
For both ice models, the radial distance from the rotor axis is assumed to be a nominal radius i.e. ignoring the effect of rotor cone, blade prebend and blade root mounting angle. The GL 2010 rotorradius $\boldsymbol{R}$ is always half of the Nominal rotor diameter as shown in the Turbine and Rotor screen found in under the Rotor screen in the Bladed GUl. Each blade station radial position r can be calculated using the blade root length added to the blade station Distance along blade root Z-axis at each blade station.
The change in mass due to blade icing is not reflected in the Turbine Information screen accessed when clicking the Mass totals... . Instead, the mass distribution and blade mass with ice are provided in the verification file .\$vE output when simulations are run.
Ice accretion can also modify the aerodynamic properties of aerofoils. No modification is applied to the aerofoil data that has been input into Bladed. If design standards require these modifications to be made then it is recommended that the user applies these corrections manually to the aerofoil input data.
The methodology used for the GL 2010 approach is as follows. The mass distribution increases linearly from zero at the rotor axis to the value $\mu_{e}$ at half the radius and then remains constant up the blade tip. The value $\mu_{e}$ is calculated as follows:
$\boldsymbol{R}$ is the rotor radius in ${\bf m},$
$c_{\mathrm{max}}$ is the maximum chord in ${\bf m},$
$c_{\mathrm{min}}$ is tip chord in m,
$\rho$ is the ice density with default value $700\;\mathrm{kg/m^{3}}$
The chord length at the blade tip is an input in Bladed. The maximum chord value is computed using the values from the Blade Geometry information input by the user.
The methodology used for the IEC Ed 4 is to apply a mass distribution that increases linearly from zero at the rotor axis to the maximum value at the blade tip. The ice mass distribution is calculated Using:
$$
M(r)=\rho C_{85}r
$$
where
$M(r)$ is the mass distribution on the leading edge of the rotor blade in ${\bf k g}/{\bf m},$ $\rho$ is a constant parameter with default value of $0.125\;\mathrm{kg/m^{3}}$
$C_{85}$ is the chord length at $85\%$ rotor radius in m,
$_r$ is the radial position measured from the rotor axis in m.
The parameter $C_{85}$ is calculated by Bladed based on the geometry information input by the user. Last updated 13-12-2024
Consider a blade element with an inboard node A and further outboard node B, as shown in Figure 1. The difference in coordinates between points A and are expressed in the Root Axes coordinates as $r_{x},r_{y}$ and $\boldsymbol{r}_{z},$ which correspond to the difference in the variables Neutral axis $(\mathsf{x})$ Neutral axis (y) and Distance along blade root Z axis respectively.To fully define the blade local element coordinate system, two of the three vectors that form the coordinate basis are calculated by Bladed from the user inputs. The element coordinate system is defined as shown in red in the diagram below. The element $\times$ direction vector is known based on the difference in positions of nodes A and B. The local element z direction needs to be calculated to fully define the local element coordinate system for the structural model.
Figure 1: Definition of the blade local element x direction
The element local z-direction vector is calculated by applying 3 successive rotations to the local element z-axis. The 3 rotations are about the blade root axes $\mathsf{X},\mathsf{Y}$ and Z directions. The element local z-axis is assumed initially to be aligned with the $X_{r o o t}$ direction.
The first rotation is a rotation about an axis parallel to the $Z_{r o o t}$ axis. The angle of rotation is the Principal elastic axes orientation as specified in the blade inputs screen. This is illustrated in Figure 2.
Bladed utilises a finite element (FE) model to simulate the flexibility of the blades. Additionally, it can incorporate a modal reduction technique to enhance computational efficiency. To account for the non-linear behaviour of larger blades, Bladed offers several geometric stiffness models and supports the definition of multi-part blades.
Users have the option to model the blades in three different ways. These are located in the Flexibility Screen of the GUl and include the following options:
· Finite element (no modal reduction) : This approach involves structural modelling of the blade using finite element analysis without modal reduction.
· Modal reduction : In this method, the blade's structural modelling combines a finite element model with modal reduction.
·Rigid : Disable the Flexibility Enabled option to make the blade completely rigid.
Changing between these three options allows for a convenient way of changing between rigid, modal reduced, or complete finite element blades.
The structural formulation in Bladed is based on the finite element method (FEM), which is a computational technique used for solving structural dynamics problems. It discretises a structural system into smaller elements, each with specific physical properties (such as density, Young's modulus, shear modulus and so on). These elements are interconnected at discrete points called nodes, forming the overall structural model which is referred to as the flexible body. An illustration of how the blade is discretised into a flexible body can be seen in Figure 1 using a fixed boundary condition. For further details refer to the introduction to flexible components section.
With the basic finite element method the flexible body is described by six degrees of freedom at each node, which means that the complete flexible body will have $6(n-1)$ degrees of freedom taking into account that the displacement at the proximal node is assumed to vanish (fixed boundary condition). Figure 2 shows the degrees of freedom at each node of a flexible body consisting of a single beam in three dimensions.
The flexible body of the blade is based on the structural properties of the blade sections, such as stiffness and mass, which are defined in specific blade section coordinate systems. This will create 6(Sections - 1) degrees of freedom, which can significantly increase the computational effort due to the large number of freedoms involved for long and complex blades. Hence a method to effectively reduce the number of freedoms while still keeping the fidelity and accuracy is preferable and Bladed utilises the method of Modal Reduction.
The user can enable the complete finite element model by using the Finite element (no modal reduction) option found in the Flexibility screen. However, this is not recommended from a calculation speed perspective.
An efficient way of increasing the calculation speed is to reduce the number of degrees of freedom that describes the present deformation state of the system by eliminating high frequency modes that do not contribute significantly to the dynamics of the body. This is achieved by expressing the current deformation state in terms of a number of so-called mode shape functions that describe a pre-calculated pattern of the nodal coordinates. This functionality can be switched on by using the Modal reduction option in the Flexibility screen. The number of included mode shapes is determined by the input Number of modes on part , where the "part" refers to the multipart blade definition.
The flexible body of the blades can be represented as a finite element model with fixed boundary condition at one end, as depicted in Figure 1. By performing an eigenvalue analysis on this structure, we can compute a set of mode shapes corresponding to the number of degrees of freedom in the model. The eigenvectors of the analysis correspond to the mode shapes which
describe the different vibrational patterns. The resulting eigenvalues correspond to associated frequencies.
The types of mode shapes of a blade are (see Figure 4 for visualisation):
- Flapwise : Refers to the bending of the blade about the Y-axis. Imagine the blade flexing up and down like a flap. This will often be the most flexible degree of freedom with the lowest frequency.
- Edgewise : Involves bending of the blade about the X-axis. Picture the blade bending from side to side. Often stiffer than the flapwise direction.
- Torsional : Occurs when the blade twists around its longitudinal axis (Z-axis). Think of the blade twisting like a corkscrew, changing the angle of attack.
- Axial : It refers to changes along the blade's axial direction (Z-axis). Axial deformation is less commonly discussed in the context of wind turbine blades as it is often a very stiff degree of freedom, having a high frequency and low impact to the overall dynamics.
In the single-part blade model, only normal modes are used. When the multi-part blade model is selected, the inner parts use both normal and attachment modes, while the outermost part uses only normal modes. For further details, please see the normal and attachment modes and blade mode shapes theory sections.
An illustration of the 1st and 2nd edgewise mode shapes can be seen in Figure 3 and different mode shape types can be seen in Figure 4.
The simplest approach used in Bladed to model the blade flexibility is to model the blade as a single linear finite element body. Several linear mode shapes that include deflections of the whole blade are calculated to account for blade deflection. This is illustrated in Figure 1.
Using whole-blade linear modes results in fast simulations as the number of degrees of freedom to model the blade deflections is small, and the freedom frequencies are relatively low. This approach often gives an accurate representation of blade dynamics. However, for this approach to be valid, the deflections of the blade must be small. Many modern blade designs are very flexible, meaning that the small deflection assumption in the linear model become invalid. This can lead to inaccuracies in predicting the blade dynamic response, in particular the blade torsion.
One method to maintain the small angle assumption for the blade modes is to split the blade into several linear parts. Figure 2 shows a schematic of modelling a blade using two linear parts.
Figure 2: Non-linear wind turbine blade model using two linear parts
The outer blade part can undergo a rigid body rotation based on the deflection and rotation of the inner part, as well as including linear mode deflections. The deflections within each linear part are therefore smaller than if using a single linear blade part. Splitting the blade into several parts allows for non-linear load transfer between each linear part, and a more accurate model of the blade deflection.
The user needs to specify the boundaries of the parts in the blade. This is done in the Flexibility SCreen within the BladePartModalModeller,where the First station and Last station are required inputs. An illustration of a blade with 3 parts can be seen in Figure 3.
The number of included modes per part is specified using Number of modes on part property which is available for each added part. The user needs to carefully validate the included wholeblade modes and consider whether it includes the wanted dynamic responses such as torsional or flapwise modes etc.
For maximum accuracy, enough blade parts should be specified to ensure that deflections remain small within each blade part. When performing convergence tests for multi-part blade models, it is recommended to run some time domain tests with the maximum number of blade parts in order to establish a baseline converged dynamic response.
For blades with more than one part, it is recommended to use the implicit Newmark- $\cdot\upbeta$ integrator to improve simulation speed while retaining accurate solutions.
The user must specify whole-blade modes even when using multi-part blades, as Bladed will calculate the appropriate damping ratios for the individual blade parts based on the specified whole-blade damping. This is also valid for Finite element (no modal reduction) models, as Bladed will convert the whole-blade shapes into finite element degrees of freedom. Explained in further details below.
When a blade is split into several linear parts, mode shapes (or finite element degrees of freedom) are calculated for each linear part. In the Bladed modal structural dynamics formulation, modal damping must be specified for each mode on each blade part. However, in general the damping value for these individual modes would not be known by the blade designer, as these modes for the individual blade parts cannot be observed individually in reality to measure their damping.
To overcome this difficulty, Bladed calculates whole-blade modes for the multi-part blade by solving the Eigenvalue solution for all of the blade parts together. The whole-blade modes are made up of contributions from the individual blade part modes. The whole-blade modes should have very similar shapes and frequencies to the usual whole-blade mode shapes found for a linear blade model, if enough modes have been specified on each part. Damping ratios can then be specified for the whole-blade blade modes, and Bladed will calculate the appropriate damping ratios for the individual blade parts.
The number of whole-blade modes for the blade is equal to the total number of modes on all of the blade parts. For example, for a blade split into 4 parts with 8 modes on each part, there are 32 whole-blademodes.
Geometric stiffening models account for changes in structural response due to structural deflection from the reference (undeflected) state. Bladed provides models that include contributions from element axial and shear internal forces. They can be selected in the Flexibility SCreen under the Simulation flexibility settings $->$ Blade geometric stiffness model.
There are two geometric stiffness settings available for the blades:
- Axial loads only : The effect of internal forces along the element axis on dynamic response is included. This primarily accounts for "centrifugal stiffening" in the blade dynamic response. Geometric stiffness axial and shear forces are included when calculating the internal member loads. See Geometric stiffness due to element axial forces for more details.
- Full model with orientation correction : The effect of internal axial and shear forces on dynamic response is included. This model can enhance the prediction of torsion deflection in the blade. This model should be used with caution as it is only accurate when deflections within each blade part remain small (less than $\mathord{\sim}5\mathord{-}7$ degrees). If several blade parts are used then this model can be activated to improve the accuracy of the solution, and will allow use of fewer blade parts than when using the AxialLoadsonly model. See Geometric stiffness due to element shear forces for more details.
When evaluating the geometric stiffness effect of shear forces, it is crucial to consider to account for the change in orientation of the torsion axis of the blade elements due to deflection.
Bladed is able to introduce modal damping by applying a damping ratio for each whole-blade mode. The user can choose how many whole-blade modes to specify damping ratios for using the Modes with damping defined variable in the Whole-blade modes found in the Flexibility screen. Any higher frequency modes will be assigned frequency proportional damping, based on the damping of the highest mode with damping defined. This approach applies high damping to high frequency modes and effectively excludes the higher whole-blade modes from the blade dynamic response, so that they do not cause erroneous instability. See the theory section description of blade damping for more details. Note that Bladed will then automatically calculate the damping values to assign to each individual blade part (see multi-part blade definition).
<html><body><table><tr><tdcolspan="8">Modal analysis results and damping inputs</td></tr><tr><td>Whole-blade modes</td><tdcolspan="5">Tower modes</td><td></td></tr><tr><td></td><tdcolspan="4"></td><td>View blade mode</td><td></td></tr><tr><tdcolspan="6">Modes with damping defined 10</td><tdrowspan="8"></td></tr><tr><td>ID</td><td>Damping Ratio (%)</td><td>Name</td><td>Modal Frequency (Hz)</td><td></td></tr><tr><td></td><td>0.491</td><td>1st flapwise normal mode</td><td>0.3851219</td><td></td></tr><tr><td>2</td><td>0.507</td><td>1st edgewise normal mode</td><td>0.5186781</td><td></td></tr><tr><td>3</td><td>1.336</td><td>2nd flapwise normal mode</td><td>1.059886</td><td></td></tr><tr><td>4</td><td>1.364</td><td>2nd edgewise normal mode</td><td>1.487568</td><td></td></tr><tr><td>5</td><td>2.749</td><td>3rd flapwise normal mode</td><td>2.21401</td><td></td></tr><tr><td>6</td><td>2.857</td><td>3rd edgewise normal mode</td><td>3.203897</td><td></td></tr><tr><td>7</td><td>3.555</td><td>4th flapwise normal mode</td><td>3.676734</td><td></td></tr><tr><td>8</td><td>1.896</td><td>5th flapwise normal mode</td><td>3.980007</td><td></td></tr><tr><td>9</td><td>5.689</td><td>6th flapwise normal mode</td><td>5.300175</td><td></td></tr><tr><td>10</td><td>5.109</td><td>7th flapwise normal mode</td><td>5.769784</td><td></td></tr><tr><td>11</td><td>Frequency proportionall</td><td>1st torsional normal mode</td><td>6.413283</td><td></td></tr><tr><td>12</td><td>Frequency proportional</td><td>8th flapwise normal mode</td><td>7.315367</td><td></td></tr><tr><td>13</td><td>Frequency proportional</td><td>4th edgewise normal mode</td><td>8.718863</td><td></td></tr><tr><td>14</td><td>Frequency proportional</td><td>9th flapwise normal mode</td><td>9.455891</td><td></td></tr><tr><td>15</td><td>Frequency proportional</td><td>10th flapwise normal mode</td><td>9.527341</td><td></td></tr><tr><td>16</td><td>Frequency proportional</td><td>11th flapwise normal mode</td><td>11.50475</td><td></td></tr><tr><td>17</td><td>Frequency proportional</td><td>5th edgewise normal mode</td><td>12.21184</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr></table></body></html>
Figure 1: Example of whole-blade modes screen for specifying damping ratios for each mode Last updated 13-12-2024
# Output of Blade Loads
View available Blade outputs ,as seen in Figure 1, by clicking the Calculation Outputs... button on the Calculations screen. The outputs must be for either the First blade, All blades , or not at all( None ). The output settings defined here do not affect the Aerodynamic Information , Performance Coefficients and Steady Power Curve calculations, as they produce a pre-defined set of outputs. A customised blade load output file can also be created and is described in the section on Load Configuration File.
For each of the output categories in the Blade outputs ,the information may be generated at any or all of the blade stations. Click Select Output Stations to determine which information is required at which stations. Click Add to define additional points where interpolated loads will be Output.
<html><body><table><tr><tdcolspan="7">Blade Outputs</td></tr><tr><td>Distance along blade, m</td><td>Blade station number</td><td>Aero data?</td><td>Blade loads?</td><td>Blade motion?</td><td></td><td></td></tr><tr><td>0</td><td></td><td>Yes</td><td>Yes</td><td>Yes</td><tdrowspan="12"></td></tr><tr><td>2.756</td><td>2</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>4.1343</td><td>3</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>5.51253</td><td>4</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>6.89437</td><td>5</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>9.65766</td><td>6</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>12.4153</td><td>7</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>15.1714</td><td>8</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>17.9279</td><td>9</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>20.6845</td><td>10</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>23.441</td><td>11</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>26.1973</td><td>12</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>28.9534</td><td>13</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td></td><td></td><td></td><td></td><td></td></tr><tr><td>PP</td><tdcolspan="6"></td></tr><tr><tdcolspan="6"></td><td>OK</td><td>Cancel</td></tr></table></body></html>
It is important to note that the principal elastic axes and root axes stations coincide with the underlying finite beam element model nodes. The root axes coordinates have the same origin rotated to align with the blade root. The aerodynamic and user axes potentially have origins that do not coincide with the underlying finite element beam model nodes. These load outputs are found by transforming the finite element loads (in the principal elastic axes coordinates) to the aerodynamic or user axis coordinate centre. The transformation accounts for additional $M_{x}$ and $M_{y}$ bending moments that are generated at the aerodynamic or user axis centre by the element axial force $F_{z}$ in the principal elastic axes system, due to the offset in the aerofoil plane between these two coordinate centres. This effectively estimates the load that would have occurred if the load was carried through an axis at the aerodynamic axis or user axis centre. There is some approximation in this method as the aerodynamic and user axis loads are not the true load path. Any changes to the blade dynamics (e.g. deflections or loads) that might result from such a change in load path are not accounted for.
An additional set of blade root loads, using a coordinate system fixed to the blade root in the hub (i.e., inboard of the pitch bearing), is output as part of the Hub loads (Rotating frame) output group found in Other outputs , as seen in Figure 1. For more details on this coordinate system, refer to the article on Rotating Hub Loads.
A blade manufacturer may specify a customised blade load output format, for a particular blade, in an XML format load configuration file. Customised blade load output files can then be generated, from a dynamic simulation, by selecting the Load configuration checkbox and specifying the load configuration file in the XML Load specification field on the Blade Outputs tab of the Calculation Output Specification window, as shown below (this window can be opened using the Calculation Outputs.. button on the Calculations window, or the Outputs.. Option of the Specify menu.).
叶片制造商可能会针对特定叶片，在 XML 格式的载荷配置文件的载荷输出格式中指定自定义内容。 然后，可以通过在计算输出规范窗口的“叶片输出”选项卡中选中“载荷配置”复选框并在 XML 载荷规范字段中指定载荷配置文件的位置来，从动态模拟中生成自定义叶片载荷输出文件（该窗口可以通过“计算输出..” 按钮在“计算”窗口中打开，或通过“指定”菜单的“输出..” 选项打开）。
If the Extreme checkbox is also selected, customised extreme blade loads will be written to an output file with .blc filename extension. Extreme load output files can be generated for each blade using the Additional Items option of the Specify menu and selecting Output individual blade extreme loads .
Last updated 13-12-2024
# Blade Loads Outputs at Principal Elastic Axes System
· The positive z-axis follows the local deflected neutral axis at each blade station towards the blade tip. · The positive y-axis is defined by the principal elastic axes orientation.
· The positive x-axis is orthogonal to the y and z and follows the right-hand rule.
Figure 1: Blade principal elastic axes coordinate system
Note that there is a subtle difference between the principal elastic axes coordinate system and the underlying blade local element axes coordinate system, whereas the latter is used to calculate the orientation of the principal elastic axes. The Principal elastic axes orientation is calculated by taking the average orientation of the two blade elements at the node where the elements join. This is illustrated in Figure 2. The two adjoining local element frames are shown in green and red. The principal elastic axes output frame is shown in blue.
Figure 2: Principal elastic axes and local element axes orientations
Last updated 13-12-2024
# Blade Loads Outputs at Root Axes System
The body-fixed coordinate system of the blade is the root axes coordinate system. The blade root coordinate system serves as the reference frame for defining the blade's geometry. The orientation of the axes is fixed to the blade root and does not rotate with either twist or blade deflection. The axis set does rotate about the z axis with pitch. For output loads, the origin of the axes is on the neutral axis at each local deflected blade station.
· The x-axis is perpendicular to the local aerodynamic chord line.
· The positive y-axis is aligned along the local aerodynamic chord line from the leading edge to the trailing edge.
· The z-axis is parallel to the local deflected neutral axis at each blade station and increases towards the blade tip.
For output loads, the origin of the axes is on the chord line at $25\%$ chord from the leading edge at each local deflected blade station. In Figure 1 the $y_{r}$ -component points towards the trailing edge of the airfoil. However, for anti-clockwise configurations the $y_{r}$ -component points towards the leading edge as the airfoil is rotated. Thus the orientation of the aerodynamic axes does not change between clockwise and anti-clockwise rotors.
Figure 1: Blade aerodynamic axes coordinate system
# 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 zaxis 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 nth 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 $x^{\prime},y^{\prime}$ are defined by the user using the chord coordinate system. These are rotated and translated into the local element coordinate system creating the $\boldsymbol{r}_{u_{m}}$ vector as shown in Figure 3. The $\boldsymbol{r}_{u_{m}}$ vector lies in the $y_{e_{n,m}}\mathrm{~,~}z_{e_{n,m}}$ plane.
Figure 2 demonstrates that for intermediate nodes the same $\boldsymbol{r}_{u_{m}}$ vector is applied to the adjoining node for both the inbound and the outbound element as illustrated by the $\boldsymbol{r}_{u_{2}}$ vector. For each element, $\boldsymbol{r}_{u_{m}}$ 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 smal/neglible. Finally, igure 2 also shows that the $\boldsymbol{x}_{u_{n,m}}$ axis lies in the $x_{r},z_{r}$ plane.
Figure 3: Local aerofoil cross section at station 2 showing $x^{\prime},y^{\prime}$ 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 $\boldsymbol{x}_{u_{n,m}}$ -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.
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:
As the relative translation $\boldsymbol{r}_{u_{m}}$ 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 $\boldsymbol{u}_{1,1}$ coordinate system and for the remainder of the stations, the inboard user axis $_{u_{x,2}}$ coordinate system is used.
The location of the user axis points in the root coordinate system at the undeflected reference position can be evaluated in the verification file ( $\nleq\lor\in$ 一
The combination of both the z-axis follows user axis and y-axis follows principal elastic axes is not supported.
Blade deflections can be output at any station along the blade by activating Motion found in the Blade outputs ,as seen in Figure 1, by clicking the Calculation Outputs... button on the Calculations screen. The outputs must be for either the First blade , All blades , or not at all (None ).
The external controller is already provided with a set of loading data, but it is possible to add additional strain gauges at any station on the tower or blade. Although called "strain gauges", these actually report forces and moments. Once specified, these will be updated before each call to the discrete external controller. Strain gauges on the blades are defined with a distance with the following code in Project Info:
Figure 3: Blade strain gauge position specification
The resulting load can be retrieved in the external controller using the function GetMeasuredBladeStrainGaugeFx , changing the last two letters for the relevant load component.
There are already a number of locations where the accelerations are measured on each discrete controller time-step. Additional locations can be added to the blades in a similar manner as for strain gauges. Accelerometers on the blades are defined in a similar manner to strain gauges with the following code in Project Info:
