Reference problem
=====================

The objective of this test case is to validate the 3D gyroscopic modeling of a rotor (options MECA_GYRO and RIGI_ROTA) in Code_Aster.

The results obtained by modeling Code_Aster are compared with those obtained in ANSYS.




Geometry
---------

Consider the rotor shown in the diagram below. It is a shaft of length 0.3454 m and of variable cross section, supported on two bearings located respectively at positions 0.1651 m (level 1) and 0.287 m (level 2). The rotor has a disk with an internal radius 0.0203 m and an external radius of 0.0495 m (thickness 0.028 m).


.. image:: images/10000200000002510000017B245BEDA12AF2C3F7.png
    :width: 2.8827in
    :height: 1.8217in


.. _RefImage_10000200000002510000017B245BEDA12AF2C3F7.png:

Image 1.1-1: Rotor geometry




Material properties
-----------------------

The cylinder has a density of :math:`\rho \mathrm{=}7800\mathit{kg}\mathrm{/}{m}^{3}`.

The Young's modulus is :math:`E\mathrm{=}207.{10}^{9}N{m}^{\mathrm{-}2}` and the Poisson's ratio is :math:`\nu \mathrm{=}\mathrm{0,3}`.




Boundary conditions and loads
-------------------------------------

The shaft is based on two bearings (Stage 1 and Stage 2) having the following stiffness characteristics:


* Setup A: Kxx = Kyy = 4.378x107N/m, Kxy = Kyx = 0


* Configuration B: Kxx = Kyy = 3.503x107N/m, Kxy = Kyx = -8.756 x106

It is stationary or rotating at a speed of 100,000 rpm.