Theory of regressive, progressive and collective frequencies of rotor

Wind & Water Structural Analysis
1

Hello fellow researchers,

I am new here and exploring the structural dynamics of wind turbines for my master’s thesis. (I do not have structural background though).

Right now I have developed a Matlab code to find out the natural frequencies of the whole rotor from scratch and I aim to develop the same routine for openFOAM based simulation(High fidelity, inclding gyroscopic damping, gravitational and rotational stiffness.

So I am stuck at finding the regressive, collective and progressive frequencies (for flapwise, edgewise). I have developed a mass and stiffness matrix but I only get one frequency for all modes (e.g. 1 for 1st flap, 1 for 1st edge, 1 for 1st span, 1 for 2nd flap, and so on…) when I simply find eigenfrequencies using those matrices.

How to find the regressive, progressive and collective frequencies of rotor? I am not even sure if the frequencies I have are of what type of all three above. Would be helpful if I get the theory behind that.

Thanks!

2

Dear @Kishan.Gajjar,

Have you expressed the blade degrees of freedom in the fixed frame of reference (not rotating with the spinning rotor), e.g., by applying multi-blade coordinate (MBC) transformation? Performing the eigenanalysis in the fixed frame of reference should result in collective, progressive, and regressive modes of the rotor for each blade degree of freedom. See, e.g., the following paper by Gunjit Bir of NREL for more information: https://www.nrel.gov/docs/fy08osti/42553.pdf.

Best regards,