# How are torsional spring and torsional damper calculated?

To whom it may concern
Hi,
I’d like to know how torsional spring (DTTorSpr) and torsional damper (DTTorDmp) are calculated. For test01, they are 50e6 and 1e6.
In FAST User’s Guide written “These values must not be negative”.

I would be grateful if you could please send me the respond.
regards

Dear Hamid Reza,

DTTorSpr in FAST is the equivalent torsional spring stiffness of the drivetrain, expressed relative to the low-speed shaft. This can be derived from knowledge of the drivetrain materials (steel), shaft diameters, shaft lengths, etc. The relationship between DTTorSpr and the natural frequency of the drivetrain torsion mode is explained in the following forum post: http://forums.nrel.gov/t/drive-train-natural-frequency/605/1.

DTTorDmp in FAST is the equivalent torsional damping of the drivetrain, expressed relative to the low-speed shaft. It determines the structural damping of the drivetrain torsion mode.

Best regards,

Dear Dr. Jonkman

I did a search and found the following formula for a geared system:
K=G J/L
where
K:DTTorSpr
G: Modulus of rigidity for the shaft material (for stainless steel: 79.3e9 N/m2);
J=pid1^4/32 and L=l1+(GBratio)^2l2*(d1/d2)^4
d1 and d2 are diameters of LSS and HSS, respectively;
l1 and l2 are lengths of LSS and HSS, respectively.

For test01, I obtained DTTorSpr=5.107e6. (parameters are d1=0.2 m,d2=0.1 m,l1=2.432 m, l2=0.5 m).

DTTorDmp can be calculated as follows:
DTTorDmp =Ccζ
where,
Cc is critical damping coefficient =2
sqrt*(K*rotor inertia);
ζ is fraction of critical damping or the percentage of damping.

I was wondering if I can ask the foregoing equations are used in FAST. If your response is yes, what is considered for the amount of ζ.

TNX.

Dear Hamid Reza,

None of these equations are included within FAST, but they seem like reasonable equations that can be used to derive inputs DTTorSpr and DTTorDmp for FAST.

Best regards,

Dear Dr. Jonkman

``````                         Can you please provide the equations to calculate DTTorSpr & DTTorDmp. I used above equations to calculate k or DTTorSpr for test01 with same d1,d2,l1 and l2, i got answer DTTorSpr = 3.0738e+03. Above equation seems wrong.
``````

best regards

Dear Muddassir,

I’m not sure I understand your question. What do you want equations for DTTorSpr and DTTorDmp based on…on materials/geometry (this will depend on the configuration of the drivetrain), on natural frequencies, or on something else? DTTorSpr and DTTorDmp are inputs to FAST, but FAST doesn’t require specific equations to derive them.

You may find the following related forum topics useful: http://forums.nrel.gov/t/drivetrain-2-2hz-frequency-and-natural-frequency-0-625hz-def/987/1.

Best regards,