Root moment of blades verification from mode shape function

Hello All,

We are currently developing a post processor for blade strain along the span-wise direction based on the given mode shapes (edge/flapwise). While doing so, we checked calculated outputs’ validity by comparing root moments (FAST outputs RootMEdg3, RootMFlp3 and our calculations) with various FAST input settings. Here are a few questions I want to ask you about.

First question: We found the patterns of two moments with respect to time were similar, but the values were different by factor of 2~10 on average. The formula for the root moment calculation we used was

M(0) = 2a2EI/L^2*TipDyb3 (for Edgewise bending moment)
,where a2 is the mode shape coeff. of x^2, EI is the stiffness given by FAST, TipDyb3 is Edgewise tip deflection.

Second question: Our study tells that the ratio of root moment over tip deflection (RootMFlp3/TipDxb3 or RootMEdg3/TipDyb3) should be constant; however, it is time-varying, even if rotor is set to be stopped, and other flexible modes are set to FALSE except edge- or flap-wise flex mode.

I appreciate your time and considerations, and look forward to any valuable comments!

Dong-Won Lim
Graduate Research Assistant
University of Minnesota

Dear Dong-Won Lim,

If I understand what you are trying to do is to compare the blade-root edgewise bending moment output by FAST to the moment calculated based on the product of the edgewise bendingstiffness (EI) and curvature at the root. While I agree in general that the formulation of bending stiffness times curvature equals the moment, this is not the equation FAST uses to calculate the blade-root bending moment. Instead, FAST uses the load summation method. That is, the blade-root bending moment is calculated in FAST by integrating along the blade the applied aerodynamic pitching moments + ( radial vector ) x ( applied aerodynamic forces + gravitation forces - inertia forces ). All of these forces, moments, and distances are vectors and are oriented with the blade as the blade deflects.

I see a couple problems with your approach:
*As you indicate, the only coefficient in the mode shape polynomial that influences the root curvature is the coefficienty of x^2. This mode shape coefficient would have to be perfectly accurate (including all boundary conditions) for the calculation to work. The load summation approach is more accurate if the mode shapes are only approximate. The biggest weakness of the modal-based method is the fact that mode shapes in real life change with operational conditions, such as rotor speed, pitch angle, and frequency of excitation. And because mode shapes are prescribed inputs in FAST, these changes are not captured in the model predictions. However, my experience has been that while the prescribed mode shapes should be reasonable, they do not need to be exact for accurate response predictions (unless you try to apply your approach).
*Your equation uses the edgewise tip displacement to characterize the contribution of the edgewise bending DOF. As described in the forum topic found here: http://forums.nrel.gov/t/coupled-blade-modes-in-fast/314/1, the structural pretwist couples flap and edge bending. So the edgewise tip displacement includes contributions from flap and edge bending. What you would want to use instead is the edgewise-bending DOF, which is an output newly added to FAST–in v7.01.00a-bjj. Please refer to the forum topic linked above for more information.

I hope that helps.

Best regards,