**5. Conclusions**

where the dynamic matrix is:

64 Advances in Vibration Engineering and Structural Dynamics

ê

ê ê ê ê ê ê

gain matrix doesn't have to be defined.

**A**

and casing of the machine.

2 2 2 2 0 0 0 0 2 22 2 0 00 0

0 0 0 0

0 00 0

êLL L L


<sup>ê</sup> - - <sup>ê</sup> <sup>=</sup> <sup>ê</sup>

<sup>1</sup> 00 0 0 0 0 0 0 0

é ù - ê ú

<sup>1</sup> 00 0 0 0 0 0 0 0


*r*

ú ú ú ú ú ú ú ú ú ú ú ú ú ú ú ú ú

(23)

*m*

*r*

*m*

*R*

*R*

<sup>1</sup> 00 0 0 0 0 0

*s s s y y*

*m m m c k*

*s s s*

*m m m*

*x x*

*c k*

<sup>1</sup> 00 0 0 0 0 0

10 0 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 00 0 1 0 0 0 0 0 0

<sup>ê</sup> - W - W - -W <sup>ê</sup> <sup>ê</sup> L LL L <sup>ê</sup> - -W W W - êë û

*L LL L L*

From the stability point of view the inputs of the linear system are irrelevant and the input

**Figure 9.** Stabilization speed of the rotor on homopolar EDB with anisotropic connections between bearing stator

To study the possibility of taking advantage of anisotropy of the connections to reduce the stabilization threshold speed, the stabilization speed is calculated for different values of the

*L L L LL*

The present paper presents the development of a dynamic model of the radial suspension us‐ ing electrodynamic bearings that is adopted to study the mechanical properties of the supports that allow guaranteeing rotordynamic stability. A simple procedure is used to identify the characteristics of the bearing, in case of heteropolar bearings, and of the elastic support that al‐ low obtaining the best performance in terms of minimization of stabilization speed.

The effect of anisotropy of the supports in the stabilization threshold speed is also investi‐ gated. It is noticed that the anisotropy of the EDB's properties in case of heteropolar configu‐ rations can be advantageous independently of the amount of nonrotating damping that can be introduced. The anisotropy allows obtaining stabilization speeds that are lower than the isotropic case. In fact the isotropic bearing represents a critical case, with extremely high sta‐ bilization speeds with respect to an anisotropic configuration.

In case of homopolar EDB configurations it is not possible to devise an anisotropic bearing because of the intrinsically axisymmetric distribution of the magnetic field. Hence the aniso‐ tropy of the elastic elements connecting the EDB's stator to the casing of the machine has been analyzed under the same hypothesis assumed in the case of heteropolar configura‐ tions. It has been observed that anisotropic characteristics of the supports can be advanta‐ geous only at low damping levels. For higher values of damping of the connection element the advantages of anisotropy vanish, and the isotropic configuration becomes optimal. Fur‐ thermore, it has been observed that is more advantageous to increase damping instead of resorting to anisotropic configurations in the case of anisotropy of the elastic connections be‐ cause the stabilization threshold speed is more sensitive to the first than to the latter.
