FlpStff and EdgStff

Hallo

I do not really understand what the flapwise and edgewise stiffness is. Are these stiffnesses around the principal axis?
Is the 1st principal axis oriented along the chord line and the 2nd perpendicular to it?

I always thought that flap and edgewise are terms concerning the whole blade and not a cross-section.

Please can you explain it for me or give me some hints.
I would also appreciate a tip for good literature or papers concerning this topic.

Thank you very much

Andreas Ferber

1 Like

Dear Andreas,

The flapwise stiffness and edgewise stiffness are defined about the principal elastic axes of a cross section. The principal elastic axes need not be parallel and perpendicular with the chordline, although they are often quite close to this in practice. The flapwise stiffness and edgewise stiffness are the integrals of the modulus of elasticity times the square of the flapwise and edgewise distances, respectively, from the blade section elastic center to the differential area element over the cross-sectional area of a section. That is, the flapwise stiffness = ∫∫ E(x,y)x^2dxdy and the edgewise stiffness = ∫∫ E(x,y)y^2dxdy, where E(x,y) is the modulus of elasticity and x and y are the flapwise and edgewise distances from the blade section elastic center to the differential area element, respectively. The stiffness and orientation of the principal elastic axes can vary for different cross sections along the length of a blade, depending on the blade geometry (external/airfoil shape and twist) and material constituency (composite laminate lay up, spar, etc.).

I hope that helps.

Best regards,

Thank you for your rapid reply. It helped me a lot.
In some weeks I have to validate the structural module of a wind turbine code, I wrote. Therefore I wanted to use NREL software and probably the wing described in this document:

“Definition of a 5-MW Reference Wind Turbine for Offshore System Development”

As long as there is no angle given for the difference to the chord line, I assume that the principal axes are along the chord line and perpendicular to it. When I reference to the blade coordinate system used in the FAST user’s guide, then the Flpstff is the stiffness for bending around the y-axis(the 1st principal axis) and the Edgstff the stiffness for bending around the x-axis (the 2nd principal axis) ?

Another question:
Do you know how I can get access to the NREL Unsteady Aerodynamics Experiment wind tunnel database
Dr. Schreck didn’t answer my requests and I do not want to bother him anymore

Thanks a lot again

Andreas

p.s.: I think there is a mistake on page 74/5 in the FAST user’s guide in the definition for the Edgstff

Dear Andreas,

In the NREL 5-MW baseline wind turbine report you refer to (nrel.gov/docs/fy09osti/38060.pdf), the structural twist is specified in Table 2-1 and the aerodynamic twist is specified in Table 3-1. The structural twist gives the orientation of one of the local principal elastic axes (the local x-axis; the local y-axis is perpenendicular to it). The aerodynamic twist gives the orientation of the chordline. While, in general, these twist distributions can differ, you are correct that in this turbine the distributions are the same. In FAST, you are correct that FlpStff is the bending stiffness about the principal elastic y-axis and the EdgStff is the bending stiffness about the principal elastic x-axis.

Scott Shreck is the correct contact at NREL for obtaining the UAE data. We simply are very busy and cannot always respond quickly.

Best regards,

Dear @Jason.Jonkman

What is the relationship between the Principal axis orientation and the flapwise stiffness and the edgewise stiffness?

Best regards,

Dear @Yuan.Hu,

I’m not sure I fully understand your question, but does the following paper help, especially Eqs. (5)-(7): https://openfast.readthedocs.io/en/main/_downloads/fd7a8bc10f2371a50828391f75170032/beamdyn_inputs_sectional_props.pdf?

Best regards,

Dear Jason Sir,
From the above discussions, I gather that the flapwise and edgewise stiffness are different for each cross-section of the blades. However I am interested in the overall edge-wise stiffness and flap-wise stiffness of the blade, if it exists. I came across the literature that the stiffness and natural frequency are related by the equation
K_edg=J* omega _e ^2;
K_flp=J*omega _f^2;
If there exists such a relation, where can I find the values of these parameters for the NREL 5MW turbine?
Another question I have is about the centrifugally stiffened edgewise and flapwise natural frequency of the blades. How can I obtain the values of these parameters for the 5MW turbine blades?

Dear @Nitin.Sivakumar,

Your equations are basic formulas for the natural frequency of a generalized mass-spring system, omega = SQRT(K/M), where K is the generalized stiffness and M (or J in your nomenclature) is the generalized mass. This equation applies to a lumped mass and spring, or for a flexible body like a blade, to the generalized mass and stiffness of a given mode. The ElastoDyn module will compute K and M from the distributed (cross-sectional) mass and stiffness of the blade by integrating along the blade with the user-specified mode shape.

The ElastoDyn module also computes the centrifugal stiffness (which gets added to the elastic stiffness K). You can obtain these generalized mass and stiffness values through the linearization functionality of OpenFAST (see other forum posts).

Best regards,

Dear Jason sir,
I don’t fully understand your reply. I linearized the 5MW_TLP_DLL_WTurb_WavesIrr_WavesMulti turbine, with the First flapwise blade mode DOF and First edgewise blade mode DOF modes on. But I don’t understand where I should search for the computed K and M from the distributed (cross-sectional) mass and stiffness of the blade and also the centrifugal stiffness values.
I read from the posts in the forum and gather that the OpenFast doesn’t directly calculate the Mass(M), Damping (C) and Stiffness (K) matrices directly but need to be calculated from the A (-M^-1K and -M^-1C ) and D ( for M ) matrices. Is that what you mean. Or is there any method wherein I can get the values directly after linearization?
I am attaching the drive link of 1 of the 36 .lin files, and the other summary files obtained after linearisation.

https://drive.google.com/drive/folders/1D1-9ayAOOszn66Qd3v6m_RCDXNxTIWrD?usp=sharing
Best Regards

Dear @Nitin.Sivakumar,

I agree that the OpenFAST linearization will calculate the first-order state matrix, e.g., A = -M^-1 * K, so, if you knew K or M, you could calculate the other. But the A matrix is the only thing needed if your goal is to calculate natural frequencies and mode shapes. In this A matrix, K includes both the elastic and centrifugal stiffness. You can obtain only the elastic part by linearizing when the rotor speed is zero.

There are forum posts that you can find that show you how to extract the mass (M) matrix from the input-transmission (D) matrix of ElastoDyn, but this approach is only valid for a rigid body.

Best regards,