# Natural Frequency of Tower and Control System

Hello,

When a Control System skips the Rotational Speed of a turbine in-order to avoid the Natural Frequency of a Tower, why does it has to consider multiples of 3P frequency say 6P, 9P etc.

I understand the blade passing frequency 3P must be skipped but don’t see why 6P should be skipped. Itsn’t 6P just 3P at the second rotation meaning 3P/ 3P / 3P is how the tower would see the frequencies along say 1st, 2nd and 3rd rotations.

So if I just skip 3P it should take care of all subsequent cycles?

Also tell me how do I determine the operating strategy of a gearless turbine?

Thanks.

Dear Anurag,

I’m not really sure I understand your question. Perhaps someone else can comment.

What I will say is that the tower for a three-bladed rotor gets excited at 0P due to mean effects, at 1P due to imbalances in the rotor, and at 3P, 6P, 9P etc. due to blades passing through turbulence, tower-influence effects, etc.

Best regards,

Thank you for your reply Jason. My doubt was why 6P, 9P excitation frequencies are seen?
Isn’t this a multiple of 3P in subsequent revolutions or is it separate entirely.

I was thinking since 3P doesn’t have enough time to damp out, as the very next revolution takes place this adds up to a new 3P generated to become 6P and so-on for 9P. Correct me if wrong.

Thanks

Dear Anurag,

No, that is not correct.

An excitation that is purely sinusoidal at 1P in the rotating frame (following a blade) will result in 3P excitation in the fixed frame for a 3-bladed rotor (without 6P, 9P etc.). However, a 1P excitation in the rotating frame that is not purely sinusoidal in the rotating frame (e.g. due to shear) will result in excitation in the fixed frame at 3P and its harmonics (6P, 9P etc.) for a 3-bladed rotor. Moreover, excitations in the rotating frame that are not 1P (e.g. due to turbulence) will be sampled at 3P and its harmonics for a 3-bladed rotor in the fixed frame by the rotating blades.

Best regards,

Thank you Jason for clearing that, in your reply you said:

Is this not-purely-sinusoidal excitation periodic?

And what determines the extent of the harmonics 6P, 9P etc. Is say 12P or 18P important. If not why?

Dear Anurag,

A wind shear will induce periodic excitation, but likely not sinusoidal in form due to the shear profile, rotor induction, nonlinearity of aerodynamic excitation, etc.

Each harmonic will have a diminishing effect on its importance to wind turbine structural loads (3P will be more important than 6P, etc.). Normally aeroelastic simulations attempt to resolve all loading and structural response up to 5-10 Hz (depending on the size of the wind turbine, with higher frequencies more important for smaller wind turbines).

Best regards,