Dear Lorenzo,
I’m not exactly sure what you are asking. For example: What do you mean by the “resistant angular momentum”? Do you mean the rotational inertia?
The average rotor rotational speed as a function of mean wind speed for the NREL 5-MW turbine, as computed by FAST simulations, can be found in Figure 9-1 of the specifications document: nrel.gov/docs/fy09osti/38060.pdf. No such specifications documents have been published for the other models supplied in the FAST CertTest. You may be able to find reports that contain some information on these models (altough I can’t think of specific reports at the moment). To get exactly what you need, however, you will probably need to run the simulations yourself.
The rotor rotational speed is dictated by the overall system-dynamics equations of motions, including the effects of:
*Steady, periodic, and stochastic aerodynamic torque
*Rotor dynamics, including blade vibrations and hub inertia
*Generator inertia and generator reaction torque
*Gearbox friction
*Stiffness and damping of the drivetrain torsional spring
While the overall system-dynamics equations of motions would include rotor-rotation equations that couple with many other system DOFs, to clarify how the drivetrain model in FAST works, here are some points to note:
- HSShsftTq and GenTq are different. GenTq is the torque applied to the high-speed shaft from the generator, which is equally and oppositely applied as a reaction to the nacelle. HSShftTq is the torque transmitted through the HSS, which includes the inertia torque from generator acceleration or deceleration. (HSShftTq is the torque one would measure from a strain gage mounted on the HSS.) From a free-body diagram of a rigid drivetrain with no gearbox inefficiencies and the mass lumped in the rotor and generator, the equations are:
LSShftTq = T_Aero – J_RotorAlpha = HSShftTqGBRatio = T_GenGBRatio + J_GenAlpha*GBRatio^2
where:
LSShftTq = torque transmitted through the low-speed shaft (LSS) = RotTorq - positive in the direction of positive Alpha
HSShftTq = torque transmitted through the high-speed shaft (HSS) - positive in the direction of positive Alpha
T_Aero = aerodynamic torque applied to the LSS - positive in the direction of positive Alpha
T_Gen = generator torque applied to the HSS - negative in the direction of positive Alpha
GBRatio = HSS to LSS gearbox ratio
J_Rotor = rotor inertia relative to the LSS
J_Gen = generator inertia relative to the HSS
Alpha = LSS rotational acceleration
So: LSShftTq = T_Aero = HSShftTqGBRatio = T_GenGBRatio only when the drivetrain is not accelerating or decelerating (Alpha = 0). The problem gets more complicated if you have a gearbox efficiency less than 100%, and even more complicated if you enable other system DOFs, such as flexibility in the drivetrain or blades. The system must then be represented by a series of differential equations (the equations of motion).
-
A gearbox efficiency (GBoxEff) less than 100% causes the power of the output shaft to be less than the power of the input shaft by the efficiency. So, HSShftTq = LSShftTqGBoxEff/GBRatio (for positive torque) or HSShftTq = LSShftTq/(GBoxEffGBRatio) (for negative torque).
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A generator efficiency (GenEff) less than 100% causes the electrical power to be less than the mechanical power while generating or the mechanical power to be less than the electrical power while motoring. So, GenPwr = T_GenGenSpeedGenEff (for positive torque) or GenPwr = T_Gen*GenSpeed/GenEff (for negative torque).
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The drivetrain torsion DOF is modeled as part of the low-speed shaft. With appropriate units applied, in equation form: LSShftTq = DTTorSpr*(Azimuth-LSSGagPxs) + DTTorDmp*( RotSpeed- LSSGagVxs). This equation only applies when the drivetrain DOF is enabled. When the drivetrain is rigid, (Azimuth-LSSGagPxs) is zero, DTTorSpr is infinite, and their product is equal to the finite value of LSShftTq, as calculated in the first equation above.
I hope that helps.
Best regards,