**6. Modification of the dynamics of the rotating system**

The last step of this work is to present the experimental results of maintaining a low level of vibrations in the whole operating range of the flexible rotor by the application of an auxiliary active magnetic bearing where the biggest anticipated dynamic deflection of the rotor occurs.

Theoretical and Experimental Investigations of

Dynamics of the Flexible Rotor with an Additional Active Magnetic Bearing 185

In order to modify the dynamic properties of this structure, an additional journal magnetic

When a machine is supported in the whole system of magnetic bearings, the bearings carry the main load that comes from the rotor (lateral, thrust). The role of the magnetic bearing in the system under consideration is to introduce an additional instantaneous point of support for the rotor and to carry a part of the dynamical (lateral) load. Thrust load is always carried by classical (ball) bearings. The proposed additional magnetic bearing does not introduce any additional thrust load. That is why in the proposed analysis, the effect of the active

magnetic bearing on thrust force acting on the rotor system isn't under consideration.

The operation of an auxiliary magnetic bearing in the rotating system just before a high level of the amplitude is achieved, causes a qualitative change in dynamic properties of the system. It corresponds to the critical frequency of lateral vibrations and allows for reaching the nominal revolutions of the machine without dangerous effects connected with exceeding

The test stand as presented in Figure 22 was modelled numerically. A professional program *DYROBES* that allows for modelling the dynamics of the shaft line of rotary machines was employed in the numerical calculations. Numerical calculation methods allow one to carry out a complete analysis of machine rotor vibrations. The geometry of the rotating system was modelled with discrete elements. The magnetic bearing journal is situated in the centre

In Figures 23a and b a shaft line model and calculated modes of critical frequencies of the rotating system for two configurations, i.e. when the magnetic bearing is turned off and

In the configuration under consideration, the dynamic properties of the magnetic bearing are a vital element that decides about a value of the critical frequency of the analysed shaft line. These properties are connected with the assumed parameters of the control system and

The analysis of the rotating system dynamics was performed and the first lateral critical frequency and its respective deflection line of the rotor supported in ball bearings were determined *(38.2Hz)*. The required value of the dynamic stiffness of the magnetic bearing that allows for avoiding the necessity of exceeding the critical value at the start-up of the

The second stage of calculations consisted in a determination of the theoretical start-up curve of the modelled shaft line of the test stand. After introducing the linearized


bearing should be introduced. The following two cases are considered:

the magnetic bearing turned on.

the critical frequencies of the flexible rotor.

of the shaft line (Figure 23).

model shaft line is equal to *KM*

**7. Numerical calculations and verifications** 

when it provides an additional support of the stand, are depicted.

were identified through the analysis of the bearing simulation model.

 *3E+5 N/m*.

The application of an auxiliary magnetic bearing to modify the dynamics of the rotating system demands the comparison of the classical (without a magnetic bearing) and modified design. In the proposed construction of the test stand, a flexible rotor is supported in ball bearings. An electric engine integrated with the shaft is used as a drive (Figure 22).

**Figure 22.** Scheme of the rotating system with an auxiliary active magnetic bearing

The length and the diameter of the shaft is 700 mm and 17 mm, respectively. Each bearing support is connected to the foundation by rigid elements. The mechanical parameters of the designed magnetic bearings are as follows:


In this design, the feasible assembly and disassembly of the auxiliary magnetic bearing is assumed. It is the position of the auxiliary magnetic bearing, mounted on the shaft of the test stand, which allows one to model the mode of lateral vibrations. A numerical experiment shows the usefulness of this concept in the case of the test stand rotor. However, the practical application of the presented idea demands serious experimental verification. The aim of this work is to present the results of the experimental investigations of the dynamic response of the system to the synchronous excitation corresponding to the unbalance occurring in the centre of the rotor.

In order to modify the dynamic properties of this structure, an additional journal magnetic bearing should be introduced. The following two cases are considered:


When a machine is supported in the whole system of magnetic bearings, the bearings carry the main load that comes from the rotor (lateral, thrust). The role of the magnetic bearing in the system under consideration is to introduce an additional instantaneous point of support for the rotor and to carry a part of the dynamical (lateral) load. Thrust load is always carried by classical (ball) bearings. The proposed additional magnetic bearing does not introduce any additional thrust load. That is why in the proposed analysis, the effect of the active magnetic bearing on thrust force acting on the rotor system isn't under consideration.

The operation of an auxiliary magnetic bearing in the rotating system just before a high level of the amplitude is achieved, causes a qualitative change in dynamic properties of the system. It corresponds to the critical frequency of lateral vibrations and allows for reaching the nominal revolutions of the machine without dangerous effects connected with exceeding the critical frequencies of the flexible rotor.
