## Damping of the rotor blades

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Lorenzo.Montanari
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### 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

Jason.Jonkman
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### Re: Damping of the rotor blades

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_j*K_ij/(pi*f_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,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
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Lorenzo.Montanari
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### Re: Damping of the rotor blades

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

Jason.Jonkman
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### Re: Damping of the rotor blades

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,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Gerrit.Molenaar
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### Re: Damping of the rotor blades

Dear Jason,

when you say zeta is 2-3%, so logarithmic damping LogD =2*pi*zeta = 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%
Gerrit Molenaar

Jason.Jonkman
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### Re: Damping of the rotor blades

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,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Gerrit.Molenaar
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### Re: Damping of the rotor blades

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 https://wind.nrel.gov/forum/wind/viewtopic.php?f=3&t=789&p=4666&hilit=damping#p5064). Which then nicely corresponds to the value of DS472: 2%.

So in summary:
Blade: 12.5-18.8% (nrel), 5% (DS472)
Tower: 3.1-9.4% (nrel), 2% (DS472)

best regards,
Gerrit.
Attachments
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Gerrit Molenaar

Xiao.Sun
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### Re: Damping of the rotor blades

Dear Jason,

Jason.Jonkman wrote: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_j*K_ij/(pi*f_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,

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

Jason.Jonkman
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### Re: Damping of the rotor blades

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,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Wesley.Miguel
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### Re: Damping of the rotor blades

Jason.Jonkman wrote: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_j*K_ij/(pi*f_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,

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

Jason.Jonkman
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### Re: Damping of the rotor blades

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,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Anjan.Kumar
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### Re: Damping of the rotor blades

Hi Jason, Gerrit, all,

Interesting thread to read. I have a couple of basic questions.

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

Jason.Jonkman
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### Re: Damping of the rotor blades

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,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

Anjan.Kumar
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Organization: Suzlon
Location: Germany

### Re: Damping of the rotor blades

Hi Jason,

Thanks for the reply,

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

Jason.Jonkman
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### Re: Damping of the rotor blades

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,
Jason Jonkman, Ph.D.
Senior Engineer | National Wind Technology Center (NWTC)

National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway | Golden, CO 80401
+1 (303) 384 – 7026 | Fax: +1 (303) 384 – 6901
nwtc.nrel.gov