I am trying to figure out the first natural frequency, for that i want to know if there is any relationship between stiffness and inertia in order to calculate the Natural frequency, and I am also unable to derive its units.
From one article i found that
freq = sqrt(Ks/Js)
where Ks = Stifness or spring constant 867637000 N.m/rad
and Js am unable to find but should be in Kg.m^2
And I also want to know the unit of the frequency from this equation as i find the units to be (sec*sqrt(rad))^-1
Please help me over it.
Are you trying to figure out the first natural frequency of the drivetrain-torsion mode? Ks = 867637000 Nm/rad is the torsional spring stiffness of the drivetrain for the NREL 5-MW turbine. The corresponding inertia should be the rotor inertia, or Js = 38,759,228 kgm^2, as mentioned in my post dated Mar 14, 2016 from the following forum topic: http://forums.nrel.gov/t/learizing-baseline-5mw-wind-turbine-with-fast/494/44.
Your equation will yield the natural frequency of the fixed-free drivetrain-torsion mode for a rigid rotor with the units of rad/s (radians are effectively no units, so, the sqrt(rad) is eliminated). If you want the natural frequency in Hz = rev/s, you must divide this solution by 2pi because 2pi rad = 1 rev.
That said, this equation will yield the natural frequency of the fixed-free drivetrain-torsion mode for a rigid rotor i.e. with the generator parked. In practice, the rigid-body rotation of the generator and flexibility of the rotor will influence the drivetrain-torsion mode.
I hope that helps.