**8. Conclusions**

188 Performance Evaluation of Bearings

frequency of the machine.

dynamic properties is activated or disactivated.

dynamics.

The transmittance of the system with the bearing turned on exhibits strong vibration damping. The applied pulse excitation is not able to generate self-vibrations of the rotor. The recorded frequency response (Figure 25b) is located on the level of noises and equals *6*

The first frequency of self-vibrations of the rotor in this configuration (estimated in the calculations to be equal to approx. *n = 60Hz* - cf. Figure 26b) does not occur in practice in the results of the experimental investigations. The investigations carried out when the rotor did not move have proven a significant influence of the auxiliary magnetic bearing on rotor

They have shown possibilities of obtaining an abrupt change in the dynamic properties of the rotating system, which complies with the idea of the safe exceeding of the critical

In the second stage of the experimental investigations, the dynamics of the model rotating system with a synchronous excitation with unbalance forces was analysed. The investigations were carried during the start-up and shut-down of the system rotor. Numerical simulations of the test stand rotor response to unbalance were performed. An example of the calculation results shown in Figure 26 indicates that for the nominal rotational frequency *50Hz*, the test stand rotor can be an overcritical or undercritical system, depending on the fact whether the auxiliary magnetic bearing characterised by specified

**Figure 26.** *A* – Experimental Bode plot *B* – Theoretical Bode plot *a* – start-up, the rotating system supported in ball bearings, *b* – shut-down, with the auxiliary magnetic bearing activated

was connected with an abrupt change in the vibration amplitude and phase.

An application of the auxiliary magnetic bearing allowed for a complete elimination of a dangerous increase (for the whole local system operation) in the vibration amplitude when the critical frequency had been exceeded. The optimal moment for activation and disactivation of the additional bearing system has been indicated by a solid line. At this moment, the vibration amplitudes of both the qualitatively different dynamic systems reach similar values. In the presented example, the switching took place above the optimal values of revolutions, which

*m*.

> The progress in the field of active magnetic bearings is based on new operating and diagnostic capabilities of these digitally controlled bearings in comparison to classical solutions. The overall goal of an *AMB* controller is to stabilise the plant and to reach the optimal technical performance. To achieve these goals, *AMB* systems have to be optimised in an overall mechatronics design approach. This leads to a new concept for control systems and actuators [11-14].

> In this work, an idea of the simulation model of magnetic levitation systems and its diagnostic capabilities is presented. Some results of the numerical simulations and experimental investigations are discussed.

The conducted investigations allowed one to verify experimentally stiffness and damping of the real rotor-magnetic bearing system by means of a numerically calculated model of the rotor.

Theoretical and Experimental Investigations of

Dynamics of the Flexible Rotor with an Additional Active Magnetic Bearing 191

[1] Schweitzer G., Traxler A., Bleuler H., (1993), *Magnetlager,* Springer-Verlag, Berlin (*in* 

[2] Kozanecka, D., et al., (1997), Application of an Auxiliary Active Magnetic Bearing for Modification of Dynamic Properties of Rotors, *Proc. of the XIV World Congress IMEKO*,

[3] Delprete, C., Genta, G., Repaci, A., (1998), Numerical Simulations of the Dynamic Behaviour of Rotors on Active Magnetic Bearing, *Proceedings of the 7 Int. Symp. on Transport Phenomena and Dynamics of Rotating Machinery,* Honolulu, Hawaii, February,

[4] Kozanecka D., (1999), Dynamic Properties of the Rotor Magnetic Suspension System*, Symkom'99* Łodz, Technical University of Łodz, Journal CMP – Turbomachinery, No

[5] Kozanecka D., 2001, *Dynamic of the Flexible Rotor with an Additional Active Magnetic Bearing,* Machine Dynamics Problems, 2001, Warsaw, Vol. 25, No. 2, pp. 21-38. [6] Kozanecka D., Kozanecki Z., 2001, *Modelling the Dynamics of Active Magnetic Bearing Actuators,* Proceedings of the World Multiconference on Systemics, Cybernetics and

[8] Kozanecka D., et al., (2007), *Application of Active Magnetic Bearings for Identification of the Force Generated in the Labyrinth Seal*, Journal of Theoretical and Applied Mechanics,

[10] Schweitzer G., Maslen E.H., (2009), *Magnetic Bearings. Theory, Design and Application to* 

[11] Gizelska M., Kozanecka D., Kozanecki Z., (2009), *Integrated Diagnostics of the Rotating System with an Active Magnetic Bearing*, Solid State Phenomena, Trans Tech Publications Ltd, Switzerland, ISSN 1012-0394, Vol. 147-149 pp 137-142. (Online available since

[12] Łagodziński J., (2009), *Modeling of Magnetic Fields with the Finite Element Method in Machine Diagnostic Systems,* Solid State Phenomena, Trans Tech Publications Ltd, Switzerland, ISSN 1012-0394, Vol. 147–149, pp. 155–160. (Online available since

[13] Kozanecka D., Kozanecki Z., Łagodziński J., (2011), *Active Magnetic Damper in a Power Transmission System*, Communications in Nonlinear Science and Numerical Simulation,

Journal Elsevier, No 16, pp. 2273-2278 www.elsevier.com/locate/ cnsns\_1567.

Informatics, SCI 2001, July 22-25, USA, Vol. IX, Industrial Parts I, pp. 232-235. [7] Kozanecka D., et al., 2003, *New Concept of the Spin Test System with Active Magnetic Bearing,* Procds. 2nd International Symposium on Stability Control of Rotating

Polish Society of Theoretical and Applied Mechanics, No.1, Vol. 45, pp. 53-60. [9] Kozanecka D., et al., (2008)*, Experimental Identification of Dynamic Parameters for Active Magnetic Bearings,* Journal of Theoretical and Applied Mechanics*,* Polish Society of

Machinery, ISCORMA, Gdansk 4-8 August 2003, Poland, pp. 199-219.

Theoretical and Applied Mechanics, No.124, Vol. 46, pp. 41-50.

*Rotating Machinery,* Springer-Verlag, Berlin, Heidelberg.

2009/Jan/06, at http://www.scientific.net)

2009/Jan/06, at http://www.scientific.net)

**9. References** 

*German*).

Vol. A, pp. 48-57.

115, pp. 217-224.

June, Finland, Vol. IX, pp. 93-98.

The proposed methodology of measurement of response and dynamic coefficients of the magnetic bearing is a very important tool in designing dynamics and vibration control of machine rotors in which active magnetic bearings are applied. It allows one to find analogies to classical bearing systems and to employ professional calculation codes for evaluation of the effects of modification in the dynamic properties of shaft lines introduced through changes in the configuration of the program controlling its active magnetic supports.

A comparison of the theoretical time histories with those obtained experimentally confirms the correctness of the proposed method for the determination of dynamic coefficients of the magnetic bearing. Achieving the nominal speed of the flexible rotor and maintaining a low level of vibrations in the whole operating range of the rotating system (including critical speeds) by using an auxiliary active magnetic bearing is a very interesting idea for the rotating machinery.

The operation lets "omit" the zone of a dangerous increase in the amplitude of rotor vibrations, which is connected with the critical speed of lateral vibrations. The experiment shows the usefulness of this concept in the case of the real rotating system.

The symmetry of characteristics of individual actuator paths of bearings, which has been programmable corrected and experimentally verified, has made it possible to implement an idea of the application of a single controller to control the real journal bearing operation along both axes. A selection of values of controller parameters is based on the investigation of the simulation model of an active magnetic bearing system.

The procedures of numerical representations of the actuator characteristics have allowed for a development of the model whose operation is convergent with the real bearing system. It enables simulation investigations of the dynamics of the mass suspended in the bearing bush under widely variable values of controller parameters and under various disturbances and forces. A reliable theoretical model that allows for analysis of the bearing dynamics under hypothetical, extreme loads reduces the designing time and enables one to minimize errors that can occur at the system prototype start-up.

The experimental characteristic curves of the start-up and shut-down have confirmed possibilities of the programmable modelling of dynamics of the shaft line, and - in prospect of the designed machine that includes an additional active magnetic bearing.
