Regarding the issue of pitch damping ratio

[hounan126100]

Dear Developer, hello!
"I was attempting to calculate the pitch damping ratio ζₓ = Cₓ / (2·√(Kₓ·Mₓ)) for the NREL 5MW OC4-DeepCwind semi-submersible floating offshore wind turbine. I learned that at f=0.037 Hz, B₅₅ = 0 and Bvis = 3.7 × 10¹⁰. Thus, Cₓ = (B₅₅ + Bvis) / (H²) = 4,567,901, Kₓ = (C₅₅ + CLine + CHydro) / (H²) = 127,397, and Mₓ = (I_Mass + A₅₅) / (H²) = 2,456,913. Based on the formula ζₓ = Cₓ / (2·√(Kₓ·Mₓ)), the damping ratio I calculated is approximately 4.08. I’m uncertain whether this value is reasonable.
I look forward to your reply soon.
Best regards,

[jjonkman]

Dear @hounan126100,

Presumably you are following the approach for calculating pitch damping from my AIAA 2008 paper: https://www.nrel.gov/docs/fy08osti/42589.pdf; is that correct?

Can you clarify where you found and/or how you obtaining the various terms in your calculation?

FYI: The linearization functionality of OpenFAST can be used to compute the linearized natural frequencies and damping of various full-system modes of floating offshore wind turbines, including the platform-pitch mode. Using this functionality may be easier than trying to estimate each term from your equation separately. This would also avoid the limitation of the equation you are using that assumes single degree-of-freedom motion because platform-pitch is often coupled with other modes of motion.

Best regards,

[hounan126100]

Dear Dr. Jonkman,
As you mentioned, I am currently using Formulas 5 and 6 from the literature you referred to to calculate the natural frequency and damping ratio of the pitch degree of freedom, respectively.
My question is similar to the one you discussed with yangyangyang98 (#2192 (reply in thread)). From your discussion with yangyangyang98, I obtained some parameters (as shown in the figure), and I also arrived at a result of 0.037 Hz. When I used Equation 6 to calculate the damping ratio, I found B_Vis = 3.7 × 10¹⁰ N·m·s²/rad² in ‘Definition of the Semisubmersible Floating System for Phase II of OC4.’ It seems that linearizing B_Vis requires the maximum pitch angle. From your discussion with Andre.White, I learned that the maximum pitch angle is 1.9 degrees (https://forums.nrel.gov/t/running-oc4-deepcwind-for-wind-only/2455/4). I would like to know if there is a specific literature reference supporting “maximum pitch angle = 1.9 degrees”.
I look forward to your reply soon.
Best regards,

[jjonkman]

Dear @hounan126100,

I'm not sure I follow you.

Though I've not used this approach myself yet, my understanding is that Borgman linearization involves the standard deviation of the velocity, not the maximum displacement.

Best regards,

[hounan126100]

Dear Dr. Jonkman,
Are you referring to the linearization method as this formula?

Can the data for calculating the standard deviation here be obtained from the PtfmRVyi records in the FAST system?
I look forward to your reply soon.
Best regards,

[jjonkman]

Dear @hounan126100,

You are referring to a formula, which I don't see in your post.

Regardless, "yes", you can derive the standard deviation of velocity from OpenFAST simulations.

Best regards,