# Doubts about teeter motion reaction forces in ElastoDyn

Dear all,

I am investigating the inertial loads due to teetering motion of a two-bladed rotor. To that extent, I set up a simulation with ElastoDyn only. In a way, this is a rotor operating in vacuum. A theoretical formulation for the reaction forces on the teeter pin when dealing with small teeter angles can be found in “How a teeterd rotor with delta-3 really works (2000)” by D.J. Malcolm. There, the following analytical expression is found:

Note that Mz is in the hub coordinate system and points in the blade’s spanwise direction. In short, `B` is the teeter angle, `Omega` the rotational velocity of the shaft, `I_z` the mass moment of inertia of the rotor around its z-axis, `eta` is some non-zero constant and `psi` is the azimuthal position of the rotor.

The simulation that I set up prescribes an initial teeter angle of `1-degree` with `d3=0`. Since the rotor is operating in a vacuum, a sinusoidal motion of the teeter angle is expected:

However, ElastoDyn does not take a value for `I_z`. This does not necessarily pose a problem, as it might be handled internally. But, the results for `LSSTipMza` do look strange:

From the analytical expression, one expects a sinusoidal as the second term in the brackets equals `0`. Clearly, the result deviates from a sinus. Next to that, the rotor I have modeled has a rotor inertia of `176 kg*m^2`, which was confirmed by ElastoDyn’s summary file, but also `I_zz=3kg*m^2`. Additionally, `Omega=24rad/s` and `B=1deg=0.017rad`. This gives `M_z=0.060kNm`, which is a factor `100` times larger than ElastoDyn yields.

Thus,

• (How) Is `I_zz` implemented in ElastoDyn?
• Is LSSTipMza the correct variable to consider?

Best,
Luc

P.S. snippet of ElastoDyn DOFs:

Snippet of rotor mass properties:

Dear @Luc.vanBeek,

I have not reviewed David Malcolm’s paper that you reference in many years, but just a few comments:

• Does your blade have nonzero `PreCone` or `UndSling`? If not, I would expect `RotIner` from the ElastoDyn summary file to equal I_z.
• The ElastoDyn moment about the teeter pin is `LSSTipMya` (not `LSSTipMza`).
• Is the teeter angle sinusuidal from ElastoDyn as you expect? (You can output the teeter angle from ElastoDyn via `TeetDefl`.)
• Presumably you’ve disabled the teeter damping and stops not accounted for in Malcolm’s paper?

Best regards,

Dear @Jason.Jonkman

Does your blade have nonzero `PreCone` or `UndSling`? If not, I would expect `RotIner` from the ElastoDyn summary file to equal I_z.

No, the modelled blade has no PreCone nor UndSling. However, I do not understand why `RotIner` should be equal to I_z. When adhering to de blade coordinate system in the FAST manual, the z axis is aligned with the spanwise direction of the blade i.e. in the direction of the pitch axis. As far as I understand now, ElastoDyn uses the blade’s mass distribution in spanwise direction to calculate RotIner. But, it is impossible to derive I_z from this information while it is a relevant parameter for the hinge loads.

The ElastoDyn moment about the teeter pin is `LSSTipMya` (not `LSSTipMza`).

The moment governing the teeter motion is `LSSTipMya`, however the reaction i.e. restraint moment on the teeter hinge is `LSSTipMza` according to the FAST manual. Nevertheless, I have plotted `LSSTipMya` below.

Is the teeter angle sinusuidal from ElastoDyn as you expect? (You can output the teeter angle from ElastoDyn via `TeetDefl`.)

Yes, see the first post of this topic. The teeter angle varies sinusoidally between -1 and 1 degree. This makes sense as I prescribe 1 degree as initial condition and there is no aerodynamic damping. Thus, the system will just oscillate.

Presumably you’ve disabled the teeter damping and stops not accounted for in Malcolm’s paper?

Correct, I am just looking at the (rigid) body dynamics of the rotor.

Dear @Luc.vanBeek,

Given that all of the rotor mass is distributed along a line (the pitch azis), the inertia about any transverse axis–whether the teeter pin or the low-speed shaft of the drivetrain (`RotIner`)–will have the same inertia when the teeter angle is zero. Presumably this is what you are calling I_z.

I think we are saying the same thing regarding the moments. `LSSTipMya` is the moment about the teeter pin, which OpenFAST is calculating as zero as expected given that teeter damping and stops are not enabled. `LSSTipMza` is the transverse moment about the teeter pin not related to torque.

I’m not sure why the moment is not matching Malcom’s paper, but again, I have not reviewed this paper in many years.

Do you suspect `LSSTipMza` to not be correct? I’m not aware of any issues in ElastoDyn associated with this output.

Best regards,