**1. Introduction**

The conversion of energy in rotating machines is accompanied by phenomena that cause the additional dissipation of energy, affect technological processes, lower the endurance of machine elements and sometimes cause damages. Among these phenomena there are synchronous vibrations and self-excited lateral vibrations of the rotor and momentary pitches of amplitude of the rotor-bearings-foundation system vibrations.

Among the machines used in power engineering, rotary machines (compressors, pumps, blowers and turbines) are the ones used most often. Recent studies have put emphasis on the dynamics of rotating machines. This allows us to minimise the vibrations of the machine both during the period of its construction and at the time of its operation. The growing demand for reliability of rotating systems (i.e. API code) makes it necessary to specify their vibration parameters (critical frequencies, separation margins, amplitude of synchronous vibrations, permissible unbalance, etc.).

The search for new solutions of bearing systems in modern rotary machines that have to satisfy special performance demands has resulted in interest in rotor active magnetic suspension systems. The application of magnetic bearings as a system of shaft suspensions gives supplementary, unparalleled in classical solutions, diagnostic capabilities [10-14]. There are, however, also high requirements concerning the control system of the shaft position. New solutions in bearing systems have been more and more frequently applied in modern rotating machines. These include magnetic bearings that enable the active control of rotor vibrations.

A machine with a rotor supported in magnetic bearings allows for:

© 2012 Kozanecka, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Kozanecka, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Theoretical and Experimental Investigations of

Dynamics of the Flexible Rotor with an Additional Active Magnetic Bearing 165

An active magnetic bearing comprises two distinct components:

A radial bearing comprises a rotor on which ferromagnetic laminations are fitted. The rotor is held in position by four electromagnets placed equally around the rotor, normally at 45 degrees to the vertical axis (Figure 2). The position of rotor (1) is monitored constantly by sensors (3) that detect any deviation from the nominal position. Any such deviation results in a signal which, by means of electronic control system (4, 5), is compared to the reference value. The resulting signal increases or decreases the current flowing to electromagnets (2) and thus returns the rotor to its nominal position. Each electromagnet produces an attractive

An increase in high-speed turbomachinery applications has led to a significant progress in the research of rotor dynamics in the last decade. The evaluation of the dynamic stability and response to unbalance has become a standard calculation procedure for all new

In order to apply magnetic bearings to suspend rotors of real machines, proper design methods that account for a special character of their operation and that are adapted to the requirements the bearings are to satisfy are needed. There is a desirable tendency in rotating machines to design rigid rotors because of a relatively low level of vibrations in their whole operating range which is observed. This aim can also be achieved by using flexible rotors with auxiliary magnetic bearings whose adjustable characteristics may be used to exceed safely the critical frequency of the rotor - bearing system with low

This work presents an idea of maintaining a low level of vibrations in the whole operating range of the rotating system of the flexible rotor (including critical speeds) by using an additional active magnetic bearing where the biggest anticipated dynamic deflection of the rotor occurs. What is achieved is the momentary operation of an additional magnetic bearing in the rotating system before a high level of the amplitude, which corresponds to the critical frequency of lateral vibrations. This causes a qualitative change in the dynamic properties of the system. It also allows one to reach the nominal revolutions of the machine without the dangerous effects connected with exceeding the critical frequencies of the

The realisation of the presented idea for the real rotating system requires a preparation of the theoretical and experimental methods of investigations and numerical simulations for

In this work the theoretical and experimental investigations of the digitally controlled active magnetic bearing and the theoretical and experimental investigations the flexible rotor dynamics carried out on the test stands with an auxiliary active magnetic bearing with a


force acting on the rotor.

turbomachinery designs.

amplitude of vibrations.

flexible rotor.

the model of active magnetic suspension.

digital control system are discussed [5,6,9].



An active magnetic bearing system is a qualitatively different technology in comparison with classical solutions and requires the co-operation of specialists from two branches of technology, as it is a combination of a mechanical system with an electronic automatic control system, which controls this mechanical system [1,10].

A scheme in Figure 1 presents an active magnetic bearing as an automatic control system for one of the control axes - *y*. The voltage signal from the displacement transducer *UDT* is conditioned. A change in the position of the journal with respect to the reference position *(URef -UDT)* activates the control current flowing through the bearing bush winding (electromagnet) in the electronic control system. This control results in a change in the electromagnet forces *Fm* that brings the journal to the assigned position.

**Figure 1.** Scheme of the active magnetic bearing as an automatic control system (one of the control axes - *y*).

A proper value of the current is generated by the power amplifier on the basis of the signal provided by the controller according to the assumed control algorithm as a function of the present position *y* of the journal, measured by means of displacement transducers (Figures 1, 2).

Apart from disturbances connected with forces coming from e.g. unbalancing *FZ* and static loading forces *Fstat*, the bearing system is affected by accidental interference *No* (noise) introduced by displacement transducers and interference following from heterogeneity of the measuring path of the runout type *Ru.* A level of these disturbances has a very significant influence from the viewpoint of stable operation of the system. A structure and algorithm of the applied controller have to ensure the system resistance to their effects.

An active magnetic bearing comprises two distinct components:


164 Performance Evaluation of Bearings

*URef*


*UDT*

**+ \_**



An active magnetic bearing system is a qualitatively different technology in comparison with classical solutions and requires the co-operation of specialists from two branches of technology, as it is a combination of a mechanical system with an electronic automatic

A scheme in Figure 1 presents an active magnetic bearing as an automatic control system for one of the control axes - *y*. The voltage signal from the displacement transducer *UDT* is conditioned. A change in the position of the journal with respect to the reference position *(URef -UDT)* activates the control current flowing through the bearing bush winding (electromagnet) in the electronic control system. This control results in a change in the

> *Electromagnet*

 *4 5 2 Fz 1 Ru* 

*Machine Rotor* 

**<sup>+</sup> <sup>+</sup> <sup>+</sup> <sup>+</sup>**

 *Fm <sup>Y</sup>*

case of an application of a high-speed electric engine integrated with the shaft, - operation under high rotational frequencies, in a wide range of temperatures (from –

1600 to 2500C) in chemically aggressive environments or in vacuum.

elimination of an oil system and seals connected with it,

control system, which controls this mechanical system [1,10].

electromagnet forces *Fm* that brings the journal to the assigned position.

*Power*

*No 3* 

*Ampl. Controller*

**<sup>+</sup> <sup>+</sup>**

*Displacement Transducer* 

**Figure 1.** Scheme of the active magnetic bearing as an automatic control system (one of the control axes

A proper value of the current is generated by the power amplifier on the basis of the signal provided by the controller according to the assumed control algorithm as a function of the present position *y* of the journal, measured by means of displacement transducers (Figures 1, 2).

Apart from disturbances connected with forces coming from e.g. unbalancing *FZ* and static loading forces *Fstat*, the bearing system is affected by accidental interference *No* (noise) introduced by displacement transducers and interference following from heterogeneity of the measuring path of the runout type *Ru.* A level of these disturbances has a very significant influence from the viewpoint of stable operation of the system. A structure and algorithm of the applied controller have to ensure the system resistance to their effects.


A radial bearing comprises a rotor on which ferromagnetic laminations are fitted. The rotor is held in position by four electromagnets placed equally around the rotor, normally at 45 degrees to the vertical axis (Figure 2). The position of rotor (1) is monitored constantly by sensors (3) that detect any deviation from the nominal position. Any such deviation results in a signal which, by means of electronic control system (4, 5), is compared to the reference value. The resulting signal increases or decreases the current flowing to electromagnets (2) and thus returns the rotor to its nominal position. Each electromagnet produces an attractive force acting on the rotor.

An increase in high-speed turbomachinery applications has led to a significant progress in the research of rotor dynamics in the last decade. The evaluation of the dynamic stability and response to unbalance has become a standard calculation procedure for all new turbomachinery designs.

In order to apply magnetic bearings to suspend rotors of real machines, proper design methods that account for a special character of their operation and that are adapted to the requirements the bearings are to satisfy are needed. There is a desirable tendency in rotating machines to design rigid rotors because of a relatively low level of vibrations in their whole operating range which is observed. This aim can also be achieved by using flexible rotors with auxiliary magnetic bearings whose adjustable characteristics may be used to exceed safely the critical frequency of the rotor - bearing system with low amplitude of vibrations.

This work presents an idea of maintaining a low level of vibrations in the whole operating range of the rotating system of the flexible rotor (including critical speeds) by using an additional active magnetic bearing where the biggest anticipated dynamic deflection of the rotor occurs. What is achieved is the momentary operation of an additional magnetic bearing in the rotating system before a high level of the amplitude, which corresponds to the critical frequency of lateral vibrations. This causes a qualitative change in the dynamic properties of the system. It also allows one to reach the nominal revolutions of the machine without the dangerous effects connected with exceeding the critical frequencies of the flexible rotor.

The realisation of the presented idea for the real rotating system requires a preparation of the theoretical and experimental methods of investigations and numerical simulations for the model of active magnetic suspension.

In this work the theoretical and experimental investigations of the digitally controlled active magnetic bearing and the theoretical and experimental investigations the flexible rotor dynamics carried out on the test stands with an auxiliary active magnetic bearing with a digital control system are discussed [5,6,9].
