**2. Digitally controlled magnetic bearing**

Active magnetic suspension systems of machine rotors being built at present are equipped with digital control systems. Apart from a possibility of implementation of complex control algorithms, they provide also wide diagnostic possibilities resulting from an application of measurement techniques at different stages of the system design. Control systems of bearing responses decide about dynamic properties of the rotating system. Digital controllers allow for, e.g. a change in bearing dynamic properties during motion in different modes of the machine operation.

Theoretical and Experimental Investigations of

Dynamics of the Flexible Rotor with an Additional Active Magnetic Bearing 167

of individual electromagnets is an explicit function of this modulation. For the journal magnetic bearing, the differential control is used and it requires a generation of the bias current *I0 .* To obtain the bias current *I 0* for the designed bearing, the pulse-width

The basic assumption while developing the numerical model of the bearing system was to offer a tool that allows for tuning the parameters of its controller and for carrying out the investigations of the designed system dynamics in a wide range [4,14]. The condition to be met during the realisation of the idea of the numerical simulation of the bearing was to reproduce the algorithm of operation of the real bearing actuating system structure, and the measurement and control elements applied in this real system in the model. The fulfilment of this requirement has guaranteed the correctness of the operation of the model and

A general scheme of the system that has been employed in order to develop the numerical model is presented in Figure 3a. In this model, a motion of the mass *m* concentrated in the

A controller used in the system controls both the axes *x* and *y*. For each axis, differential control with a programmed value of the *pulse-width modulation* of the so-called *WB* base has been applied. Figure 3b shows system of the position of the journal with respect to the bearing bush: *EM1, EM2* – bush electromagnets interacting with the axis *y, EM4, EM3* – bush electromagnets interacting with the axis *x, FZ* – rotating vector of residual unbalancing, *Fm x* – electromagnet force acting along the axis *x, Fm y* – electromagnet force acting along the axis *y,* 

 *a. b.* 

*current I1*

*Electrom. Coil EM 1*

*Electromag. Coil EM 2*

*Force Fmy (one of control axes)*

*Amplifier*

*Amplifier*

*Kfb A/C*

*Kfb A/C*

**Figure 3.** a. - Diagram of the model conception, b. - Distribution of forces (one of the control axes - *y*)

*current I2*

An idea of this model assumes a possibility of numerical simulations of dynamic properties of the system, owing to three defined levels of data connected with the bearing system

modulation *WB*, which determines its operating point on the characteristics, is used.

**3. Numerical model of the magnetic bearing system** 

feasibility of its design.

structure, namely:

*A/C Controller*

*U*

*Displacement axis y*

geometrical center of the journal is analyzed.

*Fg + Fstat –* forces of gravity and static load.

*Wfb1*

+

*Wfb2*

*W1*

*W2 Wy WB*

**Figure 2.** System of the digitally controlled magnetic bearing (one of the control axes - *y*).

The research on active magnetic bearing technology, including works on digital controllers and algorithms, actuators and magnetic bearing-rotor system dynamics, has been carried out for several years in the Institute of Turbomachinery of the Technical University of Łodz [4-9]. The mechanical structure of the built active magnetic bearing, consists of a journal and a bush with four pairs of electromagnets placed equally around the rotor. The position of ferromagnetic journal (1) with respect to bush (2) is controlled by means of eddy-current displacement transducers (3) made by *Bently Nevada Corporation*, with the diameter *d=8 mm*  and the static sensitivity *7.870 V/mm*. They are mounted on two control axes *x, y* that are perpendicular with respect to each other and displaced by the angle 450 with respect to the journal axis. The control axes interact with respective pairs of electromagnets (Figure 2).

Each pair of the bush electromagnets of the journal bearing interacts with a digitally controlled power amplifier with a variable pulse width *PWM* (5)*.* The control pulse-width modulation *Wy* and *Wx* is counted by controller (4) on the basis of measurements of the position *y* and *x* of the journal, respectively. The control current that supplies the windings of individual electromagnets is an explicit function of this modulation. For the journal magnetic bearing, the differential control is used and it requires a generation of the bias current *I0 .* To obtain the bias current *I 0* for the designed bearing, the pulse-width modulation *WB*, which determines its operating point on the characteristics, is used.
