# Relation between Stifness and Inertia?

**URL:** <https://forums.nlr.gov/t/relation-between-stifness-and-inertia/1646>\
**Category:** Rotor Aerodynamics\
**Created:** [June 19, 2017, 11:56am UTC](https://forums.nlr.gov/t/relation-between-stifness-and-inertia/1646 "2017-06-19T11:56:09Z")\
**Posts on this page:** 1\
**Showing post:** 2

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**Author:** ![Jason.Jonkman](https://dub1.discourse-cdn.com/nrel/user_avatar/forums.nlr.gov/jason.jonkman/32/3086_2.png) [@Jason.Jonkman](https://forums.nlr.gov/u/Jason.Jonkman)\
**Post date:** [June 22, 2017, 11:44am UTC](https://forums.nlr.gov/t/relation-between-stifness-and-inertia/1646/2 "2017-06-22T11:44:52Z")

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Dear Sami,

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: [Learizing Baseline 5MW Wind Turbine with FAST - #44 by Jason.Jonkman](http://forums.nlr.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 2_pi because 2_pi 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.

Best regards,

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