B modeling
==============




Characteristics of modeling and meshing
--------------------------------------------------

The rotor is meshed in 3 uniformly distributed POU_D_T type finite shaft elements and includes 1 discrete DIS_TRpour type element: the bearing modeling.

 Number of knots: 4

 Number and type of elements: 3 SEG2

     1 POI1




Loading
----------

The unbalance is installed on the disk node. It is characterized by a mass of :math:`{10}^{-4}\mathit{kg}`, a distance

to the neutral fiber of the :math:`0.15m` tree and an initial phase shift of zero. Its value is :math:`{15.10}^{\mathrm{-}6}\mathit{m.kg}`.

The exponential law of increase in speed imposed is as follows:

:math:`\dot{\phi }\mathrm{=}5100(1\mathrm{-}{\mathrm{exp}}^{\mathrm{-}\mathrm{0.3273t}})`




Results
---------

We test the moment for which the vibratory eccentricity reaches its maximum as well as the corresponding maximum amplitude.


.. csv-table::

    "Result", ":math:`{A}_{\mathit{max}}^{2}` (:math:`m`)", ":math:`{t}_{\mathit{max}}` (:math:`s`)"
    "Reference CADYRO ", "2.0160E-009", "3.19"
    "Reference LALANNE ", "1.8063E-009", "3.5"
    "Code_Aster", "2.02538E-009", "3.1956"
    "Relative error Aster/ CADYRO "," 0.5% "," 0.17%"
    "Relative error Aster/ LALANNE "," 12.1% "," 8.70%"


**Table** 4.3-1 **: Quantities tested for an exponential law of increase in speed**


.. image:: images/10000200000001DD0000013C77563C9D2CE0A57C.png
    :width: 5.3252in
    :height: 3.2925in


.. _RefImage_10000200000001DD0000013C77563C9D2CE0A57C.png:


.. image:: images/10000200000002E8000001C49C86BA4887DD2FA3.png
    :width: 5.4547in
    :height: 3.1583in


.. _RefImage_10000200000002E8000001C49C86BA4887DD2FA3.png: