# Damping of the rotor blades

Dear all,

I’d like to know your opinio about the damping of the rotor ? In my model i build the damping matrix (C) through the Rayleigh’s method for which the damping matrix C is function of the mass and stiffness matrices. Do you think that to evaluate C i have to consider also the geometric stiffness ?

I imagine that in FAST for the damping you consider the pulsations of the rotating blades, not just of the elastic still blades; is it correct?

Thanks for you advice, best regards

Lorenzo Montanari

Dear Lorenzo,

Damping in the rotor comes from aerodynamics, dynamics (gyroscopic / coriolis, etc.), and structural (natural damping in a material due to friction). The first two are intrinsicly included in FAST. The last term–the structural damping–is specified as an input in FAST.

The blade structural damping matrix in FAST is defined as follows: C_ij = zeta_jK_ij/(pif_j), where zeta_j is the damping ratio (in fraction of critical) of mode j and f_j is the natural frequency of mode j. The ratio of zeta_j to f_j comes from the stiffness-proportional term in Rayleigh damping—that is, a given stiffness-proportional damping coefficient produces a damping ratio that scales linearly with natural frequency.

In the absence of more specific information, I typically assume structural damping ratios (zeta) of 2-3% for composite blades and 0.5-1.5% for steel towers.

I hope that helps.

Best regards,

Dear Jason,

thanks for your help. Do the natural frequencies also come from the centrifugal force due the rotation of the blade (geometrical component of the blade stiffness) ?

Thanks a lot, best regards

Lorenzo

Dear Lorenzo,

In FAST, the natural frequency, f_j, that is used to calculate the structural damping, C_ij, is computed solely from a nonrotating, isolated, cantilevered blade. That is, f_j = SQRT( K_jj/M_jj )/(2*pi), where K_jj is the generalized stiffness from the given blade-stiffness (EI) distribution and M_jj is the generalized mass from the given blade-mass distribution.

I hope that helps.

Best regards,

Dear Jason,

when you say zeta is 2-3%, so logarithmic damping LogD =2pizeta = 12.5 to 18.8%, is that not very high?

The (expired) Danish wind turbine standard DS472 for example specified for glasfiber structures: LogD = 5%. In Flex5 and Phatas I normally use for the blade 1.5 - 3 %. All very much lower than 12.5 - 18.8 %

Tower:
For isolated steel tube towers the DS472 specifies LogD = 2%

Dear Gerrit,

These are simply the numbers I use in the absence of more specific information. They come from my own experience and conversations with others. Certainly a lower value is more conservative. It would be great if you could share a reference regarding more accepted values.

That said, I’ve not seen the logarithmic decrement given in terms of a percentage, as by definition it is the natural log of the ratio between two successive peaks. A damping ratio 2-3% of critical damping equates to a logarithmic decrement of 0.125-0.188.

Best regards,

Hi Jason,

The reference is DS472, ‘Danish code of practise for loads and safety of wind turbine constructions’, july 1992 (in danish).

I enclose the relevant page in the annex.

When I wrote logd in percentage, it was just multiplying the real logd with 100, so:

zeta =0.02 to 0.03 equates to logd 0.125-0.188
or in percentage:
zeta =2-3% equates to logd = 12.5% to 18.8%.

DS472 suggests (see annex) 5%. I normally use 2% for glasfiber blades, 3% foor wood.

For the tower I normally use 1% in phatas and flex5. In these programs the damping is specified for the mode including RNA. For FAST I would then use 2% (see [url]Natural frequency and damping ratio calculation - #9 by Ruiliang.Wang]). Which then nicely corresponds to the value of DS472: 2%.

So in summary:
Tower: 3.1-9.4% (nrel), 2% (DS472)

best regards,
Gerrit.

Dear Jason,

I am reading the Fast Theory Manual and come across two questions about the damping and centrifugal stiffening.
Same as the first post, the classic damping (Rayleigh damping) is proportional to the mass and stiffness.
In the code, the damping is assumed to be only proportional to the stiffness.
So my first question is how the damping (due to mass and gyroscopic damping) treated intrinsically in the code. Would you care to explain it more?

Second, when computing the generalized stiffness of the blade, the centrifugal stiffening effects are not included.
Since this part is very important for computing the natural frequencies of the blade, I imagine that it is also treated intrinsically and implicitly in the code.
Could you explain it?

Thank you.

Best,
Xiao

Dear Xiao,

The use of mass- and stiffness-proportional terms in Rayleigh damping is important in finite-element analysis because the mass-proportional term will have a damping effect that decreases with frequency and the stiffness proportional term will have a damping effect that increases with frequency. However, in FAST v7 and the ElastoDyn module of FAST v8, the user supplies a damping ratio separately for each bending mode, so mass- and stiffness-proportionality is irrelevant.

The elastic stiffness and modal damping in FAST v7 and the ElastoDyn module of FAST v8 are treated separately from the structural kinematics/kinetics, which directly account for the centrifugal stiffening, gyroscopic damping, etc. in the implementation of the equations of motion.

Best regards,

Sir!
Concerning the damping part of the structural model, any tips on how to approach structural damping?
[1] In Modeling of the UAE Wind Turbine for Refinement of FAST_AD there’s the structural damping ratio for 1F, 2F and 1E (0.925, 1.345 and 0.705 respectively…) Could I use this? My wind turbine model is also NREL’s Phase VI.
[2] I’m wondering if there’s a damping ratio for torsional modes for NREL Phase VI…
[2a] Given that I included torsion dof in the equation of motion (e.g… x, y, theta), could I neglect the torsional damping?
[2b] Limit to the first three modes 1E, 1F, 2F… OR
[2c] Could I use a certain value of structural damping ratio for all modes (e.g. 2-3 % for composite blades, 1E, 1F, 2F, 1T…)

From the three options (2a-2c) concerning torsional damping, I’m wondering if 2C is fine.

Kind regards,
Wesley

Dear Wesley,

You’d have to check the references of the report you mentioned (Modeling of the UAE…) to find the original source of the damping values, and to check whether a damping of the first torsion mode has been published (I don’t recall myself). Otherwise, I suggest assuming a value suitable for your purposes similar to the level of damping of the two modes where damping has been published (on the order of 1%).

That said, the blades of the UAE wind turbine are very stiff, and it is often OK to neglect the consideration of any flexural modes (both bending and torsion) when modeling this wind turbine.

Best regards,

Hi Jason, Gerrit, all,

Q1. As stated by Jason- ‘in FATS - the user supplies a damping ratio separately for each bending mode, so mass- and stiffness-proportionality is irrelevant’ - Is this same in the case of Flex → or in Flex only the logarithmic decrement for structural damping is used as input?

Q2. For a polyester resin composite, blade Is it possible to have logD structural damping different for edgewise as well as flap-wise direction. If yes then is there any physical reason for that?
could it be due to different stiffness in edgewise and flap-wise direction?

Thank you.

Anjan

Dear Anjan,

Sorry, but I’m not familiar with how damping is specified within FLEX.

I’m sure it is possible to have different structural damping in the edgewise and flapwise directions. The damping is related to the natural damping in a material due to friction, and so, will depend on how the blade deforms.

Best regards,

Hi Jason,

I checked in Flex through a reference and it seems in Flex logD is used as input.
as a generalized damping is calculated from logarithmic decrement as
GD(J) -= Globvar.LOGD(J) * GM(J) * OMV (J)/pi
where GM is generalized mass
OMV is eigenmode shapes

Additionally, thanks for explaining why damping can be different in edgewise and flapwise direction- as you said it depends on how blade deforms.

Is there a method to understand if damping in edgewise direction will be higher or lower as compared to in flap-wise direction or vice versa if we already have details such as eignen frequencies available.

Thanks and regards,

Anjan

Dear Anjan,

Structural damping is hard to estimate. I would expect a physical modal test of the blade would be required to determine it.

Best regards,

Hi Jason,

I want to know if the formula C_ij = zeta_jK_ij/(pif_j) is only used for structural damping rather than viscous damping. I noticed that this formula is quite similar to Rayleigh damping (C =alphaM+betaK) which belongs to viscous damping. But Rayleigh damping is not related to specific modes and beta is only a scalar constant, right?

For example, in a beam element, where constitutive properties are 6D (3 components of linear strain and 3 components of angular strain), in case of linear viscoelasticity, with both K and C 6x6 matrices, and C = beta*K , with beta still just a single scalar.

I am confused between these two kinds of damping and their computing methods. For example, the structural damping ratio of NREL 5MW blades is zeta=0.4777465%. How should I calculate the stiffness-proportional constant beta? Can I still use the formula c = zeta/(pi*f)? But f is different for different modes. Should I use the first natural frequency?

Best regards,
Jun

Dear Jun,

I’m not sure I fully understand your question, but the structural damping specified for the blades and tower in ElastoDyn has similarities to, but is not identical to, Rayleigh damping. Instead, blade and tower damping in ElastoDyn is only based on the stiffness-proportional term and is specified independently for each mode. This is unlike Rayleigh damping, which as you point is, has both mass- and stiffness-proportional terms and is not mode-specific.

A similar topic was discussed in the following forum topic: http://forums.nrel.gov/t/natural-frequency-and-damping-ratio-calculation/646/10.

Best regards,

Dear Jason,

Thank you for your quick reply. I have read the topic you mentioned but I am still confused.

Did you mean the structural damping used in ElastoDyn represents the sliding friction force between different molecular layers rather than the viscous damping which is proportional to velocity? As far as I know, there are 3 types of damping: coulomb, viscous damping (proportional to velocity) and structural damping (sliding friction between layers, proportional to displacement). Which one does blade damping in ElastoDyn belong to?

Can I convert the blade structural damping ratio 0.477465% to the stiffness-proportional damping coefficient which is not mode-specific? How? I am using GEBT to simulate a 5MW blade but I don’t know how to calculate the single stiffness-proportional damping coefficient (not mode-specific) rather than different damping constants for different modes.

I am so confused. Can you tell me the difference among the structural damping, viscous damping in Mxdotdot + Cxdot + Kx = f, Rayleigh damping and viscous damping in fluid? Please forgive me if it is a stupid question.

Best regards,

Jun

Dear Jun,

The structural damping represents damping within the material (sliding friction, etc.). All damping is dependent on velocity. Aerodynamic (fluid) damping is computed elsewhere in the aero-elastic solution of OpenFAST.

Rayleigh damping is normally written as C = alphaM + betaK. If alpha = 0, beta is related to the damping ratio (zeta) and natural frequency (f, in Hz) by:

beta = zeta/(pi*f)

This matches what is done in ElastoDyn, except that all terms (zeta, beta, f) are mode-shape dependent. For an uncoupled N-DOF system (where M and K are diagonal matrices), this would be like having beta be a diagonal matrix instead of a scalar, with each diagonal element of beta corresponding to the proportional damping of each mode.

Best regards,

Dear jun,
The blade structural damping ratio: \eta = 0.477465% can be converted to Rayleigh damping coefficients : \alpha and \beta for limited specified frequencies.
Select two target (circular) frequencies: w1, w2 and corresponding damping ratio: \eta_1, \eta_2. A 2*2 linear equation then can be obtained :
\eta1 = 0.5( alpha / w1 + beta * w1 )
\eta2 = 0.5( alpha / w2 + beta * w2 )
solving the upper equation, you can get the \alpha and \beta of Rayleigh Damping for conventional Finite Element analysis., which indicates that you have specified the target two damping ratios for two target frequencies.