Linearization in FAST with unbalanced Rotor

Dear All,

I performed linearization analysis using FAST (3-bladed NREL turbine with blade properties from ‘UPWIND’ project) for two scenarios:

Scenario 1): No imbalance in 3 blades
Scenario 2): 5%, 0 % and -5% Imbalance in Blades

Attached is a excel sheet Campbell.xlsx for these two scenarios. I see there is a ‘slight increase’ in frequencies of blade and tower modes as we move from scenario 1 to scenario 2. My parameters are as follows:

AnalMode = 2
YCMode = 0
TMax = 9900
PCMode = 0
GenTiStr = True
GenTiStp = True
TimGenOn = 0.0
TimGenOf = 9999.9
THSSBrDp = 9999.9
TiDynBrk = 9999.9
TTpBrDp(i) = 9999.9
TYawManS = 9999.9
TPitManS(i) = 9999.9
TBDepISp(i) = 9999.9

StallMod = STEADY
InfModel = EQUIL
Wind: 3.5m/s hub higher steady wind (vertical shear)

Enabled DOF:

RotSpeed = 7 rpm

CalcStdy = True
TrimCase = 2 (As indicated in FAST Manual for Variable Speed, Region 2 Linearization)
DispTol = 0.0001
VelTol = 0.00001
NAzimStep = 12
NInputs = 2
CntrlInpt = 3,4
NDisturbs = 2
Disturbnc = 1, 5

I have three questions:

i) Why is there a drop in frequency; I would expect unbalanced case to be more prone to resonance than a balanced case?

ii) Could you help me in deciphering the modes from this.
Mode----> Description
1,2----> Rigid modes of Generator
3---->1st Tower Fore-aft
4----> 1st Tower side to side
5----> Drive train torsion OR 1st Blade Asymmetric Flapwise Yaw??
6,7—>1st Blade Asymmetric Flapwise Pitch and 1st Blade Collective Flap
8,9,10—> 1st Blade Edgewise Pitch, Yaw, Collective??
11,12,13,14,15,16,17–> ???

CampbellDiagram_lin_1_5%_imbalance.xls (265 KB)
CampbellDiagram_lin_1_No_imbalance.xls (256 KB)

iii) As elasticity of yaw system and tower are taken into account the mass imbalance should induce a tower torsion instability, which should effect the blades? Is it true?

Thanks a lot,

Dear Neelabh,

Regarding your first question, I see very little difference in the natural frequencies between these two cases – most of the differences are in the third significant digit or higher. I’m not surprised by these results because I wouldn’t expect a rotor mass imbalance to impact the natural frequencies much.

Regarding your second question, here’s how I interepret your linearization output:

Mode → Description
1/2 → Generator rigid body
3 → 1st Tower Side-to-Side
4 → 1st Tower Fore-Aft
5 → 1st Blade Flap Asymmetric - Sine
6 → 1st Blade Flap Collective
7 → 1st Blade Flap Asymmetric - Cosine
8 → 1st Blade Edgewise Asymmetric - Sine
9 → 1st Blade Edgewise Asymmetric - Cosine
10 → Drivetrain torsion
11 → 2nd Tower Fore-Aft
12 → 2nd Tower Side-to-Side
13 → Other
14 → 2nd Blade Flap Asymmetric - Sine
15 → 2nd Blade Flap Collective
16 → 2nd Blade Flap Asymmetric - Cosine
17 → Nacelle yaw

When the rotor is spinning (as in your example), it is not proper to refer to an asymmetric mode as “pitch” or “yaw” as is common with a nonspinning rotor. So, above, I simply referred to the asymmetric modes with “sine” or “cosine” as used by MBC3.

Regarding your third question, a mass imbalance in the rotor may cause a problem with resonance, not instability. A “resonance” typically refers to excitation forces occuring at or near natural frequencies (as would be the case for a rotor imbalance). An “instability” typically refers to negative damping.

Best regards,

To account for manufacturing variability, all simulations also included a mass imbalance in the rotor, which instigates a once-per-rev excitation of the system when the rotor is spinning. The rotor mass imbalance was achieved by making one blade 0.5% heavier and one blade 0.5% lighter than the mass of the nominal (reference) blade. But I do not know how to realize it. That is , I cannot find where to change the mass of the blade. Thank You.

Dear Yiqing,

A mass imbalance can be achieved in FAST by definining different blade structural files for each blade (via input BldFile1, BldFile2, and BldFile3).

Best regards,

Thank You. I download the model of “NRELOffshrBsline5MW_ITIBarge4”. And there is only one kind of Bldfile.

---------------------- FAST INDIVIDUAL BLADE FILE ------------------------------
NREL 5.0 MW offshore baseline blade input properties.
---------------------- BLADE PARAMETERS ----------------------------------------
49 NBlInpSt - Number of blade input stations (-)
False CalcBMode - Calculate blade mode shapes internally {T: ignore mode shapes from below, F: use mode shapes from below} [CURRENTLY IGNORED] (flag)
0.477465 BldFlDmp(1) - Blade flap mode #1 structural damping in percent of critical (%)
0.477465 BldFlDmp(2) - Blade flap mode #2 structural damping in percent of critical (%)
0.477465 BldEdDmp(1) - Blade edge mode #1 structural damping in percent of critical (%)
---------------------- BLADE ADJUSTMENT FACTORS --------------------------------
1.0 FlStTunr(1) - Blade flapwise modal stiffness tuner, 1st mode (-)
1.0 FlStTunr(2) - Blade flapwise modal stiffness tuner, 2nd mode (-)
1.04536 AdjBlMs - Factor to adjust blade mass density (-)
1.0 AdjFlSt - Factor to adjust blade flap stiffness (-)
1.0 AdjEdSt - Factor to adjust blade edge stiffness (-)
---------------------- DISTRIBUTED BLADE PROPERTIES ----------------------------
BlFract AeroCent StrcTwst BMassDen FlpStff EdgStff GJStff EAStff Alpha FlpIner EdgIner PrecrvRef PreswpRef FlpcgOf EdgcgOf FlpEAOf EdgEAOf
(-) (-) (deg) (kg/m) (Nm^2) (Nm^2) (Nm^2) (N) (-) (kg m) (kg m) (m) (m) (m) (m) (m) (m)
0.00000 0.25000 13.308 678.935 18110.00E6 18113.60E6 5564.40E6 9729.48E6 0.0 972.86 973.04 0.0 0.0 0.0 0.00017 0.0 0.0
0.00325 0.25000 13.308 678.935 18110.00E6 18113.60E6 5564.40E6 9729.48E6 0.0 972.86 973.04 0.0

What I can do to change it is to get a different Bldfile so that a mass imbalance can be simulated in the rotor. Thanks.

Dear Yiqing,

Simply create multiple blade structural input files, each with a different setting for AdjBlMs. (Or you could more specifically tailor the mass distribution of each blade.)

Best regards,

Hi Jason,
I am simulating mass imbalance on 5MW baseline.
To change a mass density of a particular section of a blade, do I need to make changes in the files mentioned in elastodyn(NRELOffshrBsline5MW_Blade.dat) or the files mentioned in the main file(NRELOffshrBsline5MW_BeamDyn.dat)?
Warm regards

Dear @Ahmed.Hassan,

Are you modeling the structural dynamics of the blades within ElastoDyn (CompElast = 1) or BeamDyn (CompElast = 2)? If the former, then you should introduce a mass imbalance by creating distinct ElastoDyn blade files (NRELOffshrBsline5MW_Blade.dat for the NREL 5-MW baseline wind turbine); the distinct filenames are specified in the ElastoDyn primary input file (e.g., NRELOffshrBsline5MW_Onshore_ElastoDyn.dat for the land-based NREL 5-MW turbine).

Best regards,

Dear Jason,
Thank you for your kind response.
Indeed I am using CompElast=1 and I am using distinct files for the section of a blade that needs a change in mass density(by changing parameter “BMassDen”).
Also, I want to simulate pitch errors(3%,5%). Right now I am doing it by changing the initial condition “BlPitch” in the ElastoDyn file. Is this approach correct? Do I need to change TrimCase(right now 3) for simulation?
Warm regards

Dear @Ahmed.Hassan,

An aerodynamic imbalance can be set in OpenFAST by setting different blade-twist distributions in distinct AeroDyn v15 blade input files (similar to how you’ve set different mass distributions in distinct ElastoDyn blade input files). The blade pitch angles you’ve set are the initial conditions used by the controller, but these could be adapted by the control actions over time, which may eliminate the imbalance.

I’m not sure I understand your question about TrimCase; TrimCase = 3 is used to trim the blade-pitch angles to reach a desired rotor speed when finding a steady-state solution for linearization purposes.

Best regards,

1 Like

Hi Jason, I am applying mass(by plugging the blade file in ElastoDyn) and pitch imbalance(by plugging the blade file in ElastoDyn AeroDyn) in the 5MW test. I have the following questions:

  1. I want to see the impact of Imbalances on various output channels. Can I get the equations to see the impact e.g how can I solve for TipALxb1 if blade 1 is subjected to mass imbalance? I have gone through the user manual for ElastoDyn (FASTloads, FASTmotions, etc). But that seems to be very brief.
  2. Do we have a similar(theoretical) guide to AeroDyn so I can see the impact of pitch imbalance?

warm regards

Dear @Ahmed.Hassan,

I’m not sure I exactly understand your question, but the equations of motion of ElastoDyn do support mass imbalances and the theoretical basis of AeroDyn does support pitch imbalances. But I can’t point to a specific simplified equation that summarizes their effect. Naturally, imbalances in the rotor would result in once-per rev (1P) oscillations (and sometimes higher harmonics, 2P, etc.) in the fixed frame of reference.

I’m also not sure if you question is directly targeted at linearization (as the title indicates) or nonlinear time-domain simulation.

Best regards,

1 Like

Dear @Jason.Jonkman,
Thank you for your kind response. Definitely, the question doesn’t relate to linearization but to the imbalance of the rotor. I will post this and the response under the relevant topic.