Dear @Kazuya.Nishiyama,
Yes, I agree.
Best regards,
Dear Jason.
Thank you for your answer.
I have calculated the matrix by varying the NacYIner and HubIner in the fst file and calculated in BModes, but the natural frequencies do not change. Is this normal? (I have not changed the weight.)
I would like to increase the natural frequencies of the tower, is there any other way than the following?
1,Increase the weight of the hub and nacelle
2,Increase the stiffness of the tower
Dear @Kazuya.Nishiyama,
I would expect a change to the tower-top mass and inertia properties to influence the natural frequencies calculated by BModes.
To increase the tower frequency, you could either decrease the mass/inertia of the tower and/or tower-top, increase the stiffness of tower, or shorten the length of the tower.
Best regards,
Dear Jason.
Thank you for your response.
・Is it possible to analyze with the effect of gravity in BModes?
・The area of the hollow circle is needed to determine the mass per unit length of the tower.
In the EXCEL sheet for WP1.5MW, this is calculated as π x diameter x thickness.
What is the difference between this and finding the hollow circle area = 1/4 x (diameter^2-(diameter - thickness x 2)^2)? (The values are slightly different.)
Dear @Kazuya.Nishiyama,
Here are my responses:
Regarding BModes, gravity is not accounted for, which is why you must include gravitational restoring directly in the stiffness matrix if you are using BModes to derive mode shapes and natural frequencies of a tower atop a floating platform.
Regarding the mass per unit length, your second formula appears to be missing a factor of pi. Once this is corrected, these formula are equivalent for thin-walled structures (as the thickness approaches zero), but the latter formula works for cross sections of any thickness.
Best regards,
Dear Jason
I previously asked you to review the following formula, but could you also tell me the formulas for calculating Ixy and Iyz?
Ixx(TowerTop)=Ixx(Ptfm)-m(z_g^2)
Iyy(TowerTop)=Iyy(Ptfm)-m(cm_loc^2+z_g^2)
Izz(Tower Top)=Izz(Ptfm)-m(cm_loc^2)
Izx(Tower Top)=Izx(Ptfm)+m(cm_loc)(z_g)
Ixy
Iyz
Dear @Kazuya.Nishiyama,
Your previous equations included mass offsets in the x (cm_loc) and z (z_g) directions, with the mass offset in the y direction equal to zero. In that case:
Ixy(TowerTop) = Ixy(Ptfm)
Iyz(Towertop) = Iyz(Ptfm)
Best regards,
Dear Jason
Thank you for your reply.
I would like to review the flow in more detail.I am testing the analysis method using FASTv7 when changing the parameters of the WindPact tower (length, stiffness, etc.), and the weight and position of the nacelle and hub.(I am performing the analysis based on Test.14.)
[Question 1] Is the following flow correct?
[Question 2] In the BModes analysis, can we assume that the RNA and ground are rigid?
① Calculate the tower’s stiffness, etc., and change the values in Tower.dat.
*However, only two points are entered to make the tower length almost zero.
② Input the weight and moment of inertia of the nacelle and hub into the fst file.
*NacYIner and HubIner are multiplied by the percentage increase or decrease in weight.
③ Perform linearization analysis.
*Change the positional relationship parameters of the nacelle and hub described in TURBINE CONFIGURATION in the fst file.
-
Set all 11 DOFs listed in the FEATURE FLAGS of the fst file to “FALSE”.
-
Set the 6 DOFs in the Ptfm file to “True”.
-
Enter the desired value for TowerHt, and set TwrRBHt to approximately TowerHt-(TowerHt-0.01) to make the tower height almost zero.
-
Set CalcStdy=False and MdlOrder=2 in the Linear.dat file.
④Calculate the moment of inertia based on Ptfm from the obtained 6x6 mass matrix, and then calculate the moment of inertia based on RNA.
・tip_mass=M(1,1)
x_g=cm_loc=M(2,6)/M(1,1)
y_g=M(3,5)/M(1,1)
z_g=M(1,4)/M(1,1)
cm_axial=z_g-TowerHT
Ixx(TowerTop)=Ixx(Ptfm)-m(z_g^2)=M(4,4)-m(z_g^2)
Iyy(TowerTop)=Iyy(Ptfm)-m(cm_loc^2+z_g^2)=M(5,5)-m(cm_loc^2+z_g^2)
Izz(Tower Top)=Izz(Ptfm)-m(cm_loc^2)=M(6,6)-m(cm_loc^2)
Izx(Tower Top) = Izx(Ptfm) + m(cm_loc)(z_g) Izx(Tower Top) = M(4,5) + m(cm_loc)(z_g)
Ixy(TowerTop) = Ixy(Ptfm) = M(5,6)
Iyz(Towertop) = Iyz(Ptfm) = M(6,4)
⑤ Perform analysis using Bmodes
⑥Input the obtained tower frequencies and mode shapes into ModeShapePolyFitting.xls to calculate the input values for TOWER FORE-AFT MODE SHAPES and TOWER SIDE-TO-SIDE MODE SHAPES for input into Tower.dat.
• x = span_loc
• y = s-s disp or f-a disp
• Slope = 0 (for s-s), = 0 (for F-A)
• Scaling factor of y = 0.29813 (Normalized Improved Direct Method)
⑦Run the analysis using Fast.
Dear @Kazuya.Nishiyama,
I generally agree with the approach you outlined, where steps 1-4 are used to obtain the RNA mass and inertias. I do see a few issues with the indices in the mass matrix you using, which I’ve corrected below:
・tip_mass=M(1,1)
x_g=cm_loc=M(2,6)/M(1,1)
y_g=M(3,4)/M(1,1)
z_g=M(1,5)/M(1,1)
cm_axial=z_g-TowerHT
Ixx(TowerTop)=Ixx(Ptfm)-m(z_g^2)=M(4,4)-m(z_g^2)
Iyy(TowerTop)=Iyy(Ptfm)-m(cm_loc^2+z_g^2)=M(5,5)-m(cm_loc^2+z_g^2)
Izz(Tower Top)=Izz(Ptfm)-m(cm_loc^2)=M(6,6)-m(cm_loc^2)
Izx(Tower Top) = Izx(Ptfm) + m(cm_loc)(z_g) Izx(Tower Top) = M(6,4) + m(cm_loc)(z_g)
Ixy(TowerTop) = Ixy(Ptfm) = M(4,5)
Iyz(Towertop) = Iyz(Ptfm) = M(5,6)
BModes does assume the RNA is rigid when computing tower mode shapes. Whether the “ground” should be rigid depends on if you are computing tower mode shapes for a turbine with a rigid foundation (where I would say “yes” it is OK to assume the ground is rigid with a slope of zero), or whether the tower is placed on a fixed or floating substructure or flexible foundation.
Best regards,
Dear Jason,
Thank you very much for your polite and detailed response. It has helped me greatly improve my understanding.
I also have some questions regarding the TURBINE CONFIGURATION. Please assume the WP 1.5 MW model for all of the following questions.
-
Is my understanding correct that Overhang takes a negative value when the hub center of gravity is located on the upwind side of the tower centerline?
-
Is my understanding correct that NacCMxn takes a negative value when the nacelle center of gravity is located on the upwind side of the tower centerline?
-
Is my understanding correct that ShftTilt takes a negative value when the shaft is tilted toward the downwind side?
-
Is my understanding correct that PreCone takes a negative value when the blades are coned inward toward the upwind side?
I look forward to your response.
Best regards,
Dear @Kazuya.Nishiyama,
I agree with the sign convention you explain for OverHang and NacCMxn.
I’m not fully sure what you are describing for ShftTilt and PreCone, but I would say these would generally be negative for an upwind rotor (to increase the blade clearance with the tower), and would be positive for downwind rotors.
There are figures explaining these sign conventions in the old FAST v6 User’s Guide: https://openfast.readthedocs.io/en/main/_downloads/d8bd014121d6505cb25cf49bee5eaa80/Old_FAST6_UsersGuide.pdf.
Best regards,
Dear Jason
Thank you for your reply.
I have three questions.
① Regarding NacMass and HubMass, why is there a difference between the values calculated in the Excel design and the input values in FAST and OpenFAST?
NacMass and HubMass were calculated as follows in the Excel design file:
NacMass = Mainframe (39325kg) + GenShaft (2105kg) + RotorShaft (11409kg) = 52839kg
hubMass = Hub (15105kg) + Pitch bearing (4082kg) = 19187kg
However, the input files for the WP1.5MW model in FAST and OpenFAST are set to NacMass = 51170kg and HubMass = 15139kg.
② I have a question about the calculation method for HubIner. Could you please explain the calculation method?
HubIner was calculated using the following formula in the Excel design file:
HubIner = 0.4 × m × (Ro⁵ − Ri⁵) / (Ro³ − Ri³)
m is the hub mass, Ro is the outer radius, and Ri is the inner radius (Ro − wall thickness).
Using this formula, a value of approximately 29,975 kg·m² was obtained.
However, applying the standard formula for a hollow cylinder, I = 0.5 × m × (Ro² + Ri²),
the result is significantly higher, approximately 44,960 kg·m².
③ Why is YawBrMass (Yaw bearing mass (kg)) = 0 kg in the WP1.5MW files provided by FAST and OpenFAST?
Best regards,
Dear @Kazuya.Nishiyama,
Here are my responses:
- It has been many years since the original FAST model of the WindPACT 1.5-MW wind turbine was created and don’t recall these details.
- The formula used in the Excel file represents the moment of inertia of a thick-walled hollow sphere (not a hollow cylinder).
- If I recall correctly,
YawBrMasswas not added to FAST until after the WindPACT 1.5-MW model was first released, and so, this mass was originally lumped into either the tower or the nacelle.
Best regards,
Dear Jason
Thank you for your reply.
I understand it very well now.
I will continue with the analysis using FAST.
Best regards,
Dear Jason
I would like to ask whether my understanding of the geometric definitions of FAST parameters is correct when modeling a wind turbine with a tilted shaft, as shown in the attached figure.
In particular, I would like to confirm whether Twr2Shft should be defined as the distance from the tower-top yaw center to the shaft centerline measured along the shaft axis direction.
Could you please review the figure and let me know if the dimensional interpretation of each parameter is appropriate?
Best regards,
Dear @Kazuya.Nishiyama,
I agree with your image with the following corrections:
OverHangin ElastoDyn is defined parallel to the shaft (not horizontally) and is positive downwind, negative upwind.NacCMxnin ElastoDyn is defined positive downwind, negative upwind.
See Figures 14-20 in the old FAST v6 User’s Guide for images from the official documentation: https://openfast.readthedocs.io/en/main/_downloads/d8bd014121d6505cb25cf49bee5eaa80/Old_FAST6_UsersGuide.pdf.
Best regards,