Enquiring about the modal damping ratio

[PaulKSmith]

Campbell_Summary.txt
Hello everyone,

I am wondering how to change the modal damping ratio in blade ElastoDyn input file corresponding to the minor change in stiffness distribution. I am trying to derive by the following manner, however, I am not confident if this makes sense actually. Could anyone comment if this calculation makes sense?

zeta_1, zeta_2, zeta_3 are the modal damping ratios corresponding to mode 1,2 and 3 used in ED file, which comes with the stable verison of the OpenFAST setup (e.g. NREL 5MW/ DTU 10MW).

Since, only the stiffness proportional damping is considered [I read in another post about tower damping], the relationship between zeta_j and beta_j is following,

beta_j = zeta_j/(pi*f_j),      [eq.1]
where:
f_j = 1/(2*pi)*SQRT(K_jj/M_jj),

Step1: Derive the value of beta_j, corresponding to the original stiffness distribution and calculated value of f_j using BModes. 
Step2: Then calculate the natural frequency due to chnaged stiffness distribution using BModes.
Step3: Plugin the value of beta_j, calculated using [Step1], and the modified f_j  from [Step2] in [eq.1] to derive the modified zeta_j

In this calculation beta_j is not changing between two systems. 

[2nd query]
I am using MATLAB_toolbox to generate the Campbell diagram of natural frequency and damping of NREL 5MW. I noticed that the damping ratio is increasing with RPM. I am curious, if the damping is variable with RPM, how the input damping ratio coming into play? For example, 0.477465 is the damping value used for the first 2 flap modes and first 1 Edge mode in ED file in case of NREL 5MW original case setup. However, when I see the campbell summary details 0.477465 is not reflected for zero RPM.

Any suggestion would help me a lot. Thank you in advance.

Regards,

[jjonkman]

Dear @PaulKSmith,

Regarding (1), if your goal is to use the same stiffness-proportional damping coefficient (beta_j) between two models of different stiffness, I agree with your approach. (That said, you could compute f_j using software other than BModes.)

Regarding (2), the damping of the rotor modes (collective, progressive, regressive) will change with rotor speed. If your Campbell diagram is generated without aerodynamics (leaving only structural damping), I would expect you'd see the damping ratio close to 0.005 for the flapwise and edgewise rotor modes at zero rotor speed.

Best regards,

[PaulKSmith]

Hello @jjonkman

Thank you so much for confirming.
By turning off the CompAero and CompInFlow in *.fst file, and only keeping 'CompElast' on, I am getting following table. Shall I consider these values close to 0.005 ? Also, for the tower, input damping is 1% of critical, however, in the below table it is less. Maybe it is coupled effect?

Another advice would be helpful to me: How the damping values are set in the given NREL 5MW case? I might perform the same if needed due to change in the stiffness distribution.

---

--- OP 1 - WS 0.0 - RPM -0.00

01 ; 0.314 ; 0.0035 ; ED 1st EDGE cos - ED Nacelle yaw DOF - ED 1st tower SS -
02 ; 0.324 ; 0.0035 ; ED 1st tower FA - ED 1st FLAP coll. -
03 ; 0.621 ; 0.0093 ; ED 1st EDGE coll. - ED DT-ROT -
04 ; 0.667 ; 0.0047 ; ED 1st FLAP cos -
05 ; 0.699 ; 0.0055 ; ED 2nd FLAP cos - ED 1st tower FA - ED 2nd FLAP coll. - ED 1st FLAP sin - ED DT-ROT - ED 1st EDGE coll. - ED 1st FLAP cos - ED 1st FLAP coll. - NoMax -
06 ; 0.961 ; 0.0060 ; ED 1st FLAP sin -
07 ; 1.084 ; 0.0047 ; ED 1st EDGE sin -
08 ; 1.161 ; 0.0055 ; ED DT-ROT - ED 2nd FLAP cos - ED 1st FLAP cos - ED 2nd FLAP sin - ED Nacelle yaw DOF - ED 1st EDGE sin - ED 1st EDGE cos - ED 1st FLAP sin - NoMax -
09 ; 1.911 ; 0.0049 ; ED 2nd FLAP cos -
10 ; 2.007 ; 0.0050 ; ED 2nd FLAP coll. -
11 ; 2.538 ; 0.0075 ; ED 2nd FLAP sin -
12 ; 2.916 ; 0.0095 ; ED 2nd tower FA -
13 ; 2.955 ; 0.0101 ; ED 2nd tower SS -
14 ; 3.688 ; 0.0395 ; ED 1st EDGE sin - ED Nacelle yaw DOF - ED 2nd FLAP sin - ED 1st FLAP sin - ED 2nd FLAP coll. - ED 1st FLAP coll. - ED DT-ROT - ED 1st EDGE coll. - NoMax -

Regards,

[jjonkman]

Dear @PaulKSmith,

The first blade-flapwise modes (with frequencies around 0.65 Hz) and the first blade-edgewise modes (with frequencies around 1.1 Hz) in your table all have damping ratios near 0.005. These are not exactly equal to 0.00477465 because these are full-system modes that have coupling between blades and with the drivetrain and tower. (You should see much closer to 0.00477465 if you consider a rigid system with only blade-bending DOFs enabled, and no coupling to other system modes.)

For the tower, the situation is similar, except that full-system damping ratios of the first tower fore-aft and first tower side-side modes (with frequencies around 0.32 Hz) are much lower than 0.01 because the tower damping inputs are defined for an isolated tower with clamped base and without the tower-top mass/inertia.

Best regards,

[PaulKSmith]

Hello @jjonkman
Thank you for the explanation. Tower-top inertia missed my calculation.
I am trying to understand the blade modes named as collective, progressive and regressive. Is there any existing discussion regarding this on this forum? How the MATLAB code differentiate among these ? Any insight could be helpful.

Regards,

[jjonkman]

Dear @PaulKSmith,

I provide a brief summary of what the terms "collective", "sine", "cosine", "progressive", and "regressive" mean for rotor modes in my post dates March 5, 2024 in the following topic on our forum: https://forums.nrel.gov/t/eigenanalysis-fast/362.

Best regards,