But
===

The purpose of this document is to describe the macro commands needed to draw the Campbell diagram in*Code_Aster*. The approach is based on the one already developed in the software ROTORINSA [:ref:`bib1 <bib1>`].

The Campbell diagram is a graphical representation of the natural frequencies of a rotating system as a function of its rotation speed. The natural frequencies and modes of a rotating system are obtained by solving the dynamic equilibrium equation of a rotating shaft system, without a second member and including the effects due to damping.


.. _Ref383400607:

 :math:`M\ddot{\delta }+C(\Omega )\dot{\delta }+K\delta =0` **eq** **1-** 1-1

Where :math:`M` is the mass matrix of the system, :math:`C(\Omega )` is a non-symmetric matrix, a function of the speed of rotation, including the gyroscopic effect (antisymmetric) and the damping characteristics of the bearings, and :math:`K` is the stiffness matrix of the system.

The data required to draw the Campbell Diagram are therefore the natural frequencies, as well as the corresponding modes, as a function of the rotation speed in table form. The step allowing the calculation of these modes is already developed in *Code_Aster* (cf. [:ref:`R5.01.01 <R5.01.01>`]).

Two macro controls are developed. The first macro command CALC_MODE_ROTATION calculates the frequencies and modes on the complete system according to the rotation speeds. The second macro command IMPR_DIAG_CAMPBELL classifies the flexure, torsional, and traction/compression modes, standardizes these modes, determines the direction of precession of the flexure modes, sorts the frequencies according to different mode tracking methods, and then draws the Campbell diagram.