Low-speed shaft bending moments - LSSTipMys and LSSTipMzs

Wind & Water Computer-Aided Engineering Software Tools
1

Hello everybody,

I wish you all the best, success and especially healthiness. I am starting with the first question in this year :slight_smile:

I would like to know, how FAST is calculating the bending Moments LSSTipMys and LSSTipMzs on the lowspeed shaft?

My equations (see my attachment) are missing something, because i have a littlesome offset.

Best regards
Kemal

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2

Dear Kemal,

I see a few problems with your equations:

  • You haven’t stated which FAST/ElastoDyn outputs deltaM_y# refer to, but I’m assuming you mean RootMyc#.
  • If I am right about the first bullet, then I agree with the first terms on the right-hand side. But in ElastoDyn, blade 3 is ahead of blade 2, which is ahead of blade 1, so, the azimuth angle of blade 2 is psi+120 deg and the azimuth angle of blade 3 is psi+240 deg; you have the signs swapped.
  • In addition to RootMyc#, the blade-root pitching moments (RootMzc#) will contribute to the nontorque loading of the shaft whenever there is nonzero precone.
  • The hub mass and inertia will also contribute to the nontorque loading of the shaft.

I hope that helps.

Best regards,

3

Hi Jason,

you are right I mean RootMyc. I will check that with your azimuth angles. Do you have a formula for me which includes RootMzc, hub inertia and …? I am asking because I am comparing Bladed and OpenFAST and all bladeloads are identical except the Moment about z. The lowspeed shaft loads Fx, Mx, Fz are also identical. And I want to know how can it be, that My#shaft, Mz#shaft and Fy#shaft have offsets. I hope you can give me the equations for the loads which are different.

Best regards
Kemal

4

Dear Kemal,

It would not be trivial to write this equation down in closed form (it would take many lines). I don’t already have it written down in the form you seek. The equation would be simplified if PreCone = 0 and HubCM = 0.

From my prior list, I also forgot to include the contribution of the in-plane and out-of-plane blade-root shear forces to the nontorque loading of the shaft.

Best regards,

5

Hi,
well then, do you have maybe a paper or a book in mind, where it is described?

Best regards Kemal

6

Dear Kemal,

The equations implemented in FAST/ElastoDyn are documented in the “Unofficial FAST Theory Manual”, discussed in the following forum topic: FAST theory manual. But while the equations for LSSTipMys and LSSTipMzs are stated here, they are stated in terms of local variables, not spelled out explicitly in terms of the blade-root loads.

Best regards,

7

Thanks!

8

Dear Jason,
I’m currently deriving the equation for the relationship between low-speed shaft bending moment and blade load, and I’ve referenced the expressions mentioned above to get a more consistent result. However, there is still an error of about 5% to 10%, and I would like to get a more accurate relationship between low-speed shaft bending moment and blade load.
(1) According to your answer above, I have considered the effect of the blade shear you mentioned in the new expression, but the problem is that I don’t know what the force arm of the blade shear is, and I tried to use the value of “overhang” to calculate the moment, but I got a bigger error value. Should I use overhang to calculate the bending moment?
(2) Is my relation for the effect of shear force on shaft bending moment correct? If it is correct, what causes the larger error, and if not, how can I modify it?

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(3)I also have questions about the coned and shaft coordinate systems, is the coordinate system I have shown correct for a 5MW baseline wind turbine?

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Best regards,

9

Dear @Zhiyan.Dong,

While I agree with your coordinate system figure, your equations are not correct. Just a few comments/questions:

  • Are you neglecting precone by setting it to zero? I’ll assume precone = zero in my remaining comments.
  • Where along the LSS are you computing the bending moments? I’ll assume at the hub center in my remaining comments.
  • The moment arm from the blade-root to hub center should equal HubRad.
  • The axial force (RootFz) does not contribute to the bending moments in the shaft without precone, but both shear forces (RootFx and RootFy) will.
  • While the x-bending moment (RootMx) will contribute to the torque without precone, the y-bending and z-torsion moments (RootMy and RootMz) will both contribute to both bending moments in the shaft without precone.

Best regards,

10

Dear, jonkman:
Thank you very much for your previous reply, it helped me a lot, now I am doing development work related to multibody dynamics and I would like to ask you some questions. the assumed modal method used in Elastodyn considers modes in the direction of swing and pendulum oscillations, and torsional effects of the blade are considered by means of the Beamdyn module. Is it possible to consider torsional effects by adding torsional modes to Elastodyn?
Best regards,

11

Dear @Zhiyan.Dong,

A similar question has been asked and answered in the following forum topic: Coupled blade modes in FAST - #39 by Cao.Yuming.

Best regards,