Mechanical Systems and Signal Processinghomel.vsb.cz/~tum52/publications/MSSP.pdf · Both the VSB—Technical University, Faculty of Mechanical Engineering, and TECHLAB Ltd., Prague,

Contents lists available at SciVerse ScienceDirect

Mechanical Systems and Signal Processing

Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]]

0888-32

http://d

n Corr

E-m

PleasMech

journal homepage: www.elsevier.com/locate/ymssp

Active vibrations control of journal bearings with the useof piezoactuators

Jirı Tuma a,n, Jirı Simek b, Jaromır Skuta a, Jaroslav Los a

a Faculty of Mechanical Engineering, VSB—Technical University of Ostrava, 17. listopadu 15, CZ 708 33, Ostrava, Czech Republicb TECHLAB Ltd., Prague, Sokolovska 207, CZ 190 00, Praha 9, Czech Republic

a r t i c l e i n f o

Article history:

Received 19 April 2011

Received in revised form

28 October 2012

Accepted 28 November 2012

Keywords:

Active vibration control

Journal bearings

Hydrodynamic bearings

Piezoactuators

Rotor instability

Fluid-induced vibration

70/$ - see front matter & 2012 Elsevier Ltd.

x.doi.org/10.1016/j.ymssp.2012.11.010

esponding author. Tel.: þ420 59 699 3482;

ail addresses: [email protected] (J. Tuma), j.si

e cite this article as: J. Tuma, et al. Syst. Signal Process. (2013), http

a b s t r a c t

Rotor instability is one of the most serious problems of high-speed rotors supported by

sliding bearings. With constantly increasing parameters, new machines problems with

rotor instability are encountered more and more often. Even though there are many

solutions based on passive improvement of the bearing geometry to enlarge the

operational speed range of the journal bearing, the paper deals with a working prototype

of a system for the active vibration control of journal bearings with the use of

piezoactuators. The controllable journal bearing is a part of a test rig, which consists of

a rotor driven by an inductive motor up to 23,000 rpm. The actively controlled journal

bearing consists of a movable bushing, which is actuated by two piezoactuators. The

journal vibration is measured by a pair of proximity probes. The control system enables

run-up, coast-down and steady-state rotation. A real-time simulator dSpace encloses the

control loop. Force produced by piezoactuators and acting at the bushing is controlled

according to error signals derived from the proximity probe output signals. As it was

proved by experiments the active vibration control extends considerably the range of the

operational speed.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Both the VSB—Technical University, Faculty of Mechanical Engineering, and TECHLAB Ltd., Prague, are focused on long-term research in the field of rotor dynamics. One of the most serious problems is instability of high-speed rotors due to thejournal bearing oil film. To study possibilities of affecting rotor behavior by controlled movement of bearing bushings, atest rig was designed, manufactured and assembled. Even though there are many solutions based on passive improve-ments of the bearing geometry to enlarge the operational speed range of the journal bearing, such as a lemon bore,pressure dam, tilting pad, parametric stiffness excitation [1], etc., the approach to preventing the journal bearinginstability, presented in the paper, is based on the use of the active vibration control (AVC). In the introduction it should beemphasized that research of active vibration control was aimed at rigid rotors and the standard design of sliding bearings,where the journal displacement is measured at the closest position to the bearing bushing. Some publications address thevibration of flexible rotors, where there is large displacement of the rotor. Such a large displacement is easily measurableby eddy-current sensors [2,3]. Problems with the measurement of displacements with the use of this sensor type arediscussed in this article.

All rights reserved.

fax: þ420 59 699 6129.

[email protected] (J. Simek), [email protected] (J. Skuta), [email protected] (J. Los).

., Active vibrations control of journal bearings with the use of piezoactuators,://dx.doi.org/10.1016/j.ymssp.2012.11.010i

www.elsevier.com/locate/ymssp

www.elsevier.com/locate/ymssp

http://dx.doi.org/10.1016/j.ymssp.2012.11.010



mailto:[email protected]










J. Tuma et al. / Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]]2

Many authors pay attention to the active control of sliding bearings with the use of active magnetic bearings (AMB) [4]and giant magnetostrictive material (GMM) [5]. Although the authors of the paper on using GMM state that experimentscan be carried out up to 1700 rpm, they publish only measurements at 350 rpm. The instability due to the oil film is aproblem of high-speed rotors. With utmost probability instability could not arise at such low rotational speed as 350 rpm.Therefore, the active vibration control was not aimed at eliminating instability of sliding bearings, but only at positioningthe shaft axis. Favorite means for rotor control are magnetorheological liquids, but the delayed response of the liquidviscosity to the magnetic field change does not allow using this method for closed loop control of high-speed rotors [6].Piezoactuators as a tool to control of rotating machines have been intensively investigated in the literature since the end of1980s. The advantage of journal bearings with piezoactuators is that the bearing bushing mounting stiffness remainsunchanged in the case of an accidental loss of electric power supply. One of the first original contributions dated from thebeginning of the 1990s [7]. These papers did not study the effect of the oil film on the onset of instability and itssuppression using the active vibration control. Worth mentioning are papers [8,9] dealing with the problem of the rotorinstability.

There are two promising ways how to control the rotor movement, either by magnetic bearings or by piezoactuators,which are added to the system. However, AMB are still very expensive and cases, where it is possible to install AMB toalready designed rotor, are very rare. As already mentioned, the ABM requires retainer bearings in case of power failure,which complicates machine design. On the other hand, installation of piezoactuator into bearing housing is relatively easy.The non-rotating loose bushing can be inserted into any bearing housing. The only problem is to find piezoactuators forreasonable prize.

The topic of this paper is focused at research of methods suppressing sliding journal bearing instability by the activevibration control with the use of piezoactuators [10,11]. Stacked piezoactuators are modern actuators acting with greatforce and in a wide frequency range to several kHz. The only disadvantage of the piezoactuators is a small travel range.As it was mentioned before the active vibration control system of journal bearings with the use of the piezoactuatorswhich is described in this paper differs from the other attempts to test such a system by this that our bearing design ismuch closer to the industrial design than academic laboratory models [1,2,12]. The rotor is rigid and the position of thejournal inside the bearing bushing is measured in close distance to it. Closest to our solution is to use giantmagnetostrictive material [5]. Unfortunately, the authors have not noticed a positive effect on the operating rotationalspeed range.

The research work was granted by the Czech Science Foundation as a part of the research project No. 101/07/1345‘‘Active control of journal bearings aimed at suppressing the rotor instability’’. The control system adds an electronicfeedback to the rotor-bearing system actuating the position of a movable bushing. The current passive damper changesinto an active component of the system with controllable properties. The laboratory test facilities, including the journalbearing equipped with the movable bushing, were designed by TECHLAB Ltd., Prague. The research group of TechnicalUniversity of Ostrava developed the control system, which is based on piezoactuators, and put the system into operation[13,14].

2. Test rig

The sketch of a controllable journal bearing arrangement, which is implemented for the active vibration control, isshown in Fig. 1 while some details can be seen on photos in Fig. 2. The test rig consists of a rigid shaft of 30 mm diametersupported in two cylindrical hydro-dynamic journal bearings of the length of 30 mm. An input for the oil inlet is in thehorizontal plane of symmetry of the bushing. Shafts with various radial clearances are available for testing but results of

Fig. 1. Arrangement of the controllable journal bearing.

Please cite this article as: J. Tuma, et al., Active vibrations control of journal bearings with the use of piezoactuators,Mech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2012.11.010i




Fig. 2. Test rig for active vibration control research.

J. Tuma et al. / Mechanical Systems and Signal Processing ] (]]]]) ]]]–]]] 3

the experiments are presented only for radial clearance of 45 mm. The bearing span is 200 mm. Bearing bushings aresupported in rubber ‘‘O’’ rings, which ensure sealing of oil inlet and at the same time enable movement of bushings withinthe clearance in bearing casing. Bearing bushings can be excited by means of piezoactuators oriented in vertical andhorizontal directions and fastened to the rig frames. The preloaded open-loop LVPZT piezoactuators are of the P-844.60type, the product of the Physik Instrumente Company. The piezoactuator require a low voltage amplifier with the 100 Vpeak value at the output. The piezoactuator travel range is up to 90 mm, the pushing force is up to 3000 N and the pullingforce is up to 700 N. The resonant frequency of piezoactuators is of order thousands of hertz while the frequency range fortransferring a control signal with no distortion is required to be of order hundreds of hertz, which is half the frequency ofthe rotor rotation speed.

The test shaft is driven by high-frequency motor through an elastic membrane coupling, constituting two joints, so thatthe shaft is decoupled from motor and free to move. Concerning a lubricant, it was initially used the hydraulic oil of the VG32 grade and then bearing special oil for high-speed grinder spindle bearing of the OL-P03 grade.

Shaft movement is measured by two pairs of proximity probes. These sensors are working on eddy-current andelectrical capacitive principles. The eddy current sensors IN-085 are a product of the Bruel & Kjær Company, but thesensors from Bently Nevada Rotor Kit were alternatively tested as well. After some problems with the measurement errorsof the eddy-current sensors the capacitive sensors of the capaNCDT CS05 type supplied by the Micro Epsilon Company,were installed. It is possible to put one or two discs on the shaft, thus increasing bearing load and rotor mass. However,lowest stability limit should be achieved with the minimum bearing load, i.e. with hollow shaft without discs. The test rigwas designed for speeds up to 23,000 rpm. This paper describes tests in which the rotor instability with AVC ON and AVCOFF due to the oil film begins at much lower speeds, as reported in the section dealing with lubrication. The speed range ofthe rotor during tests depends on combination of the journal clearance and the oil viscosity.

3. Journal bearing model

There are many ways how to model journal bearings [15–17], but this paper prefers a lumped parameter model, whichis based on the concept developed by Muszynska [18] with the support of Bently Rotor Dynamics Research Corporation[19]. The reason for using this concept was that it offers an effective way to understand the rotor instability problem and tocreate a model of a journal vibration active control by manipulating the bushing position by actuators, which are a part ofthe closed loop system composed of proximity probes and a controller. Another approach can be based on the lubricantflow prediction using a FE method for Reynolds equation solution. This more sophisticated method does not allowanalyzing behavior of the vibration active control to design and tune the controller.

3.1. Lumped parameter model of the journal bearing

Methods for controller design are based on the lumped parameter model which enables to derive a transfer functionbetween the controlled variables and the control variable of the closed loop control systems. Partial differential equationslike Reynolds equations or the Navier–Stokes equations do not produce a transfer function. The transfer function is a toolfor tuning the controller aimed to the stability of the closed loop and a suitable response to disturbance.

Let the rotor angular velocity be designated by O of the unit in radians per a second. It is assumed that the bushing is amovable part in two perpendicular directions while the rotor is rotating. This mathematical model proposes to usecomplex variables as position vectors to describe motion of the rotor and bushing in the plane, which is perpendicular tothe rotor axis. The real part of the position vector r is a horizontal coordinate x(t) while the imaginary part is a verticalcoordinate y(t) of the journal centre. The coordinate system is tied to stationary bearing housing with a cylindrical bore,inside of which is inserted movable bearing bushing. The origin (0, 0) of the coordinate system in the complex plane issituated in the centre of the mentioned cylindrical bore as it is shown in Fig. 3. The positions of the journal centre andbushing mean the intersection of both movable component axes with the complex plane. The position of the journal centrein the complex plane is designated by the mentioned position vector r, while the position of the bushing centre is





Fig. 3. Coordinate system in the complex plane.


designated by the position vector u (see Fig. 3). The coordinates of the end-point of this vector are

0,0ð Þ cylindricalborecentre

r¼ xðtÞþ jyðtÞ journal ðrotorÞ centre

u¼ uxðtÞþ juyðtÞ bushingcentre

where j is an imaginary unit.The internal spring, damping and tangential forces are acting on the rotor. The external forces refer to forces that are

applied to the rotor, such as unbalance, impacts and preloads in the form of constant radial forces. All these external forcesare considered as an input for the mathematical model. The fluid pressure wedge is the actual source of the fluid filmstiffness in a journal bearing and maintains the rotor in equilibrium. As it is stated in [18,20] these bearing forces can bemodeled by a spring and damper system, which is rotating at the angular velocity lO, where lis a dimensionlessparameter, which is slightly less than 0.5. This model is an approximation, but as will be shown later the modelsatisfactorily explains the onset of instability.

The parameter l is denominated as the fluid averaged circumferential velocity ratio. It is assumed that the rotatingjournal drags the fluid in a space between two cylinders into motion and acts as a pump. It is easy to understand that thefluid circular velocity is varying across the gap as a consequence of fluid viscosity. The validity of the assumption can beverified experimentally. It is known that an oscillation (an onset of instability) of the rotor starts when the rotor rotationalspeed exceeds a certain value and stops when the speed decreases under the other one. It can be shown by experiments,that when the rotor system is excited by a non-synchronous perturbation force with respect to the rotor rotational speedthe resonance appears at the frequency, which is approximately equal to l O.

Fluid forces acting on the rotor in coordinates rotating at the same angular frequency as the spring and damper systemare determined by the position of the journal centre relating to the bushing centre and therefore they are given by theformula

Frot ¼ K rrot�urotð ÞþD _rrot� _urotð Þ ð1Þ

where scalar parameters, K and D, are specifying proportionality of stiffness and damping to the relative position of thejournal centre displacement vector rrot�urot and velocity vector _rrot� _urot , respectively. Eq. (1) represents relationshipbetween complex variables and replaces two real equations in fact.

To create the model of the rotor system, the fluid forces have to be expressed in the stationary coordinate system, inwhich the rotor centerline displacement and velocity vectors are designated by r and _r, respectively. Conversion of thecomplex rotating vector rrot to the stationary coordinate system can be done by multiplication of this vector by a factorexp j lO tð Þ, which is the same as multiplying the vector in the stationary coordinates by the factor exp j l O tð Þ. Therelationship between the mentioned vectors in rotating and stationary coordinates are given by the formulas:

F¼ K r�uð ÞþD _r� _uð Þ�jDlO r�uð Þ ð2Þ

where the complex term j Dl O r has the meaning of the force acting tangentially to the direction of the vector r. As therotor angular velocity increases, this force can become very large and can cause rotor instability.

As was mentioned, the rotor is under the influence of the external forces, for instance produced by unbalance or simplyby gravity. To obtain general solution this external perturbation force, resulting from unbalance, is assumed to be rotatingat the angular velocity o, which is considered to be completely independent of the rotor angular velocity O. The unbalanceforce, which is produced by unbalance mass m located at a radius ru, acts in the radial direction and has a phase d at timet¼ 0

FP ¼mruo2ej otþdð Þ ð3Þ






The equation of motion for a rigid rotor operating in a small, localized region in the journal bearing, is as follows:

M €rþD _r� _uð Þþ K�jDlOð Þ r�uð Þ ¼ FP ð4Þ

where M is the total rotor mass. The trajectory of the rotor centerline is called an orbit. As in the case of Eq. (1) the complexEq. (4) can be replaced by two real equations. The complex variables are used to simplify not only writing mathematicalformulas but for easy creation of the simulation model in Matlab-Simulink [21] for testing a control system.

Model parameters for simulation are related to the above-described test rig. The mass M of the rotor is 1.6 kg and theexperiments result in the value of l¼0.475. The stiffness K and damping D of the oil film depend on the distance betweenthe journal axis and the bushing axis. If the position of the journal axis is close to the bushing axis then both parametersare almost constant. When the journal is approaching the bushing wall then both parameters grow to infinity. In thesimulation calculations the oil film stiffness is set in such a way to match the onset of instability during the experiment.The damping parameter is adjusted to the value which ensures that the journal orbits of the simulation and experimentare similar. Typical values for the dimensions of the test rig is K¼4000 N/m and D¼1000 Ns/m. The value of the product m

ru¼0.00001 kg m corresponds to the ISO balancing class between G 1 and G 2.5 at 2500 rpm.

3.2. Equation of motion as a servomechanism

For the stability analysis of the journal bearing it is assumed that the bushing is not moving u¼0. According to themodel (2), the rotor and fluid wedge bearing systems can be demonstrated as a servomechanism working in the closedloop, which is shown in Fig. 4. According to the direction of the acting force at the shaft the direct and quadrature dynamicstiffness is introduced. To obtain the Laplace transform of the motion equation, the imaginary variable jo is replaced by acomplex variable s

KDirectðsÞ ¼ KþDsþMs2, KQuadratureðsÞ ¼�jlOD ð5Þ

and the equation of motion (4) takes the form

r¼ ðFPerturbation�KQuadratureðsÞ rÞ=KDirectðsÞ ð6Þ

The transfer function 1=KDirectðsÞ (dynamic compliance) is stable due to the positive value of coefficients. The feedbackpath in the closed-loop system acts as a positive feedback and introduces instability for the closed-loop system. The gain ofthe positive feedback depends on the rotor angular velocity O. The closed-loop system is stable for the low rotor rotationalspeed. But there is a margin for the stable behavior. If the gain of the positive feedback crosses over some limit value thenthe system becomes unstable.

The stability of the closed-loop dynamic system depends on the open-loop frequency transfer function

G0 joð Þ ¼KQuadratureðjoÞ

KDirectðjoÞ¼

�l O D

o D�j K�Mo2� � ð7Þ

As is known, the closed-loop dynamic system is stable according to the Nyquist stability criterion if, and only if, thelocus of the function G0ðjoÞ in the complex plane does not enclose the point (�1,0) as o is varied from zero to infinity [22],see Fig. 5. Enclosing the point (�1,0) is interpreted as passing to the left of the mentioned point. The locus of the functionG0ðjoÞ for three different values of the rotor angular velocity O is shown in Nyquist diagram in Fig. 5, which is plotted as anillustrating example for K/D¼100 rad/s. All the contour plots are of the same shape, but they are differing only in a scaleand correspond to the stable, steady-state and unstable vibration. When the steady-state vibration occurs, the stabilitymargin is achieved. In this case the locus of the G0ðjoÞ function meets the point (�1,0), therefore

G0 joCRITð Þ ¼�1 ð8Þ

The complex equation (8) represents two real equations. Solution of the imaginary part of the Eq. (8) results in formulafor an angular frequency, at which a system can oscillate without damping. This frequency is designated by oCRIT . Solution

Fig. 4. Shaft and fluid wedge bearing systems as a servomechanism.





Fig. 5. Nyquist diagram showing stable, margin and unstable locus.

Fig. 6. Closed control loop.


of the real part of the Eq. (8) results in the formula for mechanical resonance

o2CRIT ¼ K=M and oCRIT ¼ lO ð9Þ

It can be concluded that the frequency of the rotor subharmonic oscillation is the same, as the fluid averagecircumferential angular velocity. The measurement shows that the value of the parameter l is equal to approximately0.475. The stability margin corresponds to the mechanical resonances of the rigid rotor mass supported by the oil wedge asa spring. It can be noted that the frequency oCRIT is not equal to the rotor critical speed as a result of the rotor bendingwhen the vibration is excited by the rotor unbalance.

If the system was linear, then the unstable rotor vibration would spiral out to infinity when the rotor angular frequencycrosses some threshold. The rotor angular frequency threshold is inversely proportional to the ratio l.

OCRIT ¼ffiffiffiffiffiffiffiffiffiffiffiK=M

p=l ð10Þ

As can be experimentally verified, the frequency spectrum of the fluid-induced vibration contains the single dominatingcomponent, which would be a solution of the second order linear differential equation without damping. The journallateral vibration is limited by the inner bearing surface. The stiffness and damping coefficients are non-linear functions ofthe eccentricity ratio, especially when the rotor is approaching the journal wall. If the magnitude of vibration is increasing,the oil-film stiffness and damping increases as well. A new balance forms a steady-state limit cycle of the rotor orbitalmotion.

The maximal angular velocity of journal stable behavior is given by the theoretical formula (10). This formula allowscalculating the stiffness of an oil film for the known mass of the rotor, the lambda factor and known angular velocity of theonset of instability. Experiments have shown that the limit angular velocity for the journal stable rotation depends on theradial clearance of the journal inside a bushing and the viscosity of the lubricant.

4. Closed control loop

Active vibration control of journal bearings uses the bushing position as the control variable u and the shaft position asa controlled variable r. The control variable is an output of a controller. The controller transforms an error signal computedas a difference of a set point and actual position of the shaft. As is evident from the block diagram in Fig. 6, the controller isof the proportional type with the gain KP .

Provided that the perturbation force is zero FP ¼ 0 the equation of motion is as follows:

M €rþD _rþ K�jDlOð Þ r ¼D _uþ K�jDlOð Þ u ð11Þ

The Laplace transfer function relating the displacement of the bushing to the displacement of the shaft is given by

Go sð Þ ¼ KPDsþ K�jDl Oð Þ

M s2þDsþ K�jDl Oð Þ

Go joð Þ ¼ KPjo Dþ K�jDl Oð Þ

jo Dþ K�jDl Oð Þ�Mo2ð12Þ





Fig. 7. Force acting at the bushing vs. bushing displacement in horizontal direction (axis X).

Fig. 8. Dependence of piezoactuator force on bushing displacement.


For the stability margin the open-loop frequency transfer function G0ðoÞ is equal to �1. The frequency of the steady-state vibration at the stability margin is given by o¼ l O and KP ¼o2M=K�1. If the feedback gain KP is positive then themaximal rotational speed OMAX for the rotor stable behavior is greater than the critical rotational speed without anycontrol which is given by Eq. (10). Increasing of the margin for the rotational speed is given by the formula

OMAX ¼OCRIT

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiKPþ1

p: ð13Þ

The control system does not stabilize the behavior of the journal bearing directly by changing the position of thebearing bushing, but indirectly by changing force that acts on this bushing. Except of the controller gain, the displacementof the bushing depends on stiffness of its connection with the bearing body through rubber seal rings as it is shown inFig. 7. The dependence of force acting to the bushing on the bushing displacement is shown in Fig. 8. The working point ofthe electromechanical system results from the voltage which is supplied to the piezoactuator. The gain KP in Fig. 6 resultsnot only from the setting up of the controller, but from the property of the bushing clamping as well. Properties of thepiezoactuator of the P-844.60 type (catalogue values) and measured stiffness of clamping (5.5�106 N/m) gives thebushing travel range which is equivalent to the control variable range (see right part of diagram in Fig. 7). Thepiezoactuators are energized by voltage ranging from 0 to 100 V which corresponds to the amplifier input voltage rangingfrom 0 to 12 V. The range of the rotor stable rotational speed is limited by the travel range of piezoactuators andmeasurement errors of the proximity probes.

5. Operation without active vibration control

When putting the test rig into operation, we met these problems:

�

PM

choice of lubricating oil determining bearing friction looses,
� measurement accuracy of shaft position, � mounting of piezoactuators to avoid torsional loading and enable adjusting position at the accuracy of micrometers.
lease cite this article as: J. Tuma, et al., Active vibrations control of journal bearings with the use of piezoactuators,ech. Syst. Signal Process. (2013), http://dx.doi.org/10.1016/j.ymssp.2012.11.010i





5.1. Lubrication

To reach the maximum motor speed higher than 6000 rpm it was necessary to increase bearing clearance to 90 mm(radial clearance 45 mm) with simultaneous decrease of the calculated rotor stability limit. Hydraulic oil of the VG 32 grade(kinematic viscosity of up to 32 mm2/s at 40 1C) used as a lubricant was then substituted by bearing special oil of theOL-P03 type (VG 10 grade, kinematic viscosity 2.5–4 mm2/s at 40 1C). The hydraulic oil enables to reach the maximumrotational speed of 16,000 rpm and the instability onset at the same value of speed. The bearing special oil enables to reachthe motor maximum nominal rotational speed 23,600 rpm, while the instability onset starts at 4300 rpm. All tests wereundertaken at ambient temperature about 20 1C. Lubricating oil was not preheated during tests.

5.2. Measurement of shaft position

The choice of sensor type for small displacements is crucial to the success of experiments. The first experiment with theuse of proximity probes, which are based on the eddy-current principle, showed the shape of the rotor centerlinetrajectory (orbit) considerably differing from a circle or an ellipse. To explain this phenomenon, the reasons were lookedfor in the uniformity of motor rotation, the misalignment of the motor and rotor axes, the oil pump and the interference ofthe proximity probe output signals. To achieve perfect decoupling of the test shaft from driving motor, another flexiblecoupling was installed between original coupling and the shaft. The rotation uniformity is not as smooth as in case of usinga DC motor. According to the catalogue data for eddy-current sensors the interference between signals causes an errorbelow 1 mm in measurements. Inspection of the shaft non-circularity showed, that the deviation from the circle is less than1 mm as well. Finally it was proved for the eddy-current sensors that the main source of the proximity probe periodicalerror is non-homogeneity of the rotor material magnetic and electric conductivity properties of the shaft surface. The errorsignal is repeated synchronously with rotor rotation. The same material is passing-by below the tip of the secondproximity probe after one quarter of the rotor revolution; therefore a phase shift of the period quarter may be discovered.The peak-to-peak value of the regular periodic error reaches 11 mm. The spectrum of the measurement periodic error iscomposed from low harmonics of the rotor rotational frequency.

The dependence of the proximity probe regular error on the rotation angle can be approximated by a sum oftrigonometric functions differing in the number of waves. The reduction of the proximity probe error by subtraction of theerror signal requires a tacho pulses measurement and prediction of the rotational angle.

As mentioned earlier, it is preferable to use a proximity sensor based on the measurement of the electrical capacitancethan to compensate predictable measurement errors. The output signal of such a capacitive sensor does not contain anylow harmonics of the shaft rotational frequency. But the output signal of the electric capacity sensor contains an error partwith frequency that is greater than 1 kHz. The amplitude of this error signal at the mentioned frequency is greater thanone micrometer. The error signal is filtered out by an analog RC filter with a cut-off frequency of 200 Hz. The effect of thislow-pass filter is shown in Fig. 9.

Comparison of the signals measured by the sensor of the capacitive type and the sensor based on the eddy-currentprinciple is shown in Fig. 10. The sensors are oriented in the horizontal direction (X) and the shaft rotational speed isincreased up to 7000 RPM until the onset of instability starts up. The sampling frequency was set to 2048 Hz. On the leftpanel of this figure is a record of the output signal of the capacitive type sensor. The record on the right panel correspondsto the output of the sensor based on the eddy-current principle. The shaft does not vibrate before the onset of instability,therefore the output signal of the capacitance type sensor is without periodic oscillation of the shaft position while thispart of the record for the eddy-current sensor is corrupted by regular oscillation.

The frequency spectra of the displacement signal in the horizontal direction during the shaft run-up for both theproximity probe type are shown in Fig. 11. The shaft rotational speed begins at 0 rpm and reaches the speed, at whichstarts the instability. To compare the background noise level, the vertical scale ranges from �80 to �20 dB (reference1 mm). As was mentioned, the output signal of the sensor based on the eddy-current contains low harmonics of therotational frequency. In contrast to the eddy-current sensors the noise level of the sensors based on the capacitiveprinciple is considerably less.

The measurements of the shaft displacement during run up proceeded with extremely low viscous oil VG10 withoutpreheating. It is technically impossible to increase the rotor rotational speed smoothly from 0 rpm. Rotor starts at the

Fig. 9. Frequency spectrum of the filtered and unfiltered output signal of the sensor based on electrical capacity (capaNCDT CS05).





Fig. 10. Measurement of the shaft horizontal displacement using the sensor based on electrical capacity (capaNCDT CS05) and the sensor based on the

eddy current (IN-085).

Fig. 11. Multispectra of the shaft horizontal displacement using the sensor capaNCDT CS05 and the sensor IN-085 (dB reference 1 mm).


speed of 230 rpm and then the speed is continuously increased up to the onset of instability. The journal movement beginsat the bottom of the bearing sleeve and with increasing speed it moves up in direction of rotation. At the level of the sleevecentre the journal starts to move towards the bearing centre. With infinite speed or zero load the journal centrecoincidences with bearing centre, which is generally unstable position in circular bearing. The instability onset is at about4300 rpm.

5.3. Mounting of piezoactuators

Choice of the piezoactuator type was verified by measurement of the dependence of acting force on the open-looppiezoactuator travel. As is shown in Fig. 8, force of 500 N is sufficient to overcome flexibility of the sealing ‘‘O’’ rings.Flexible tip was used to attach the piezoactuator to the bushing rod and the frame structure for compensation ofmisalignment and possible bending load.

The test rig instrumentation allows active vibration control only in the journal bearing at the opposite side to thedriving motor. Before beginning of operational tests, the initial position of the piezoactuators has to be adjusted in themiddle position of the operating travel range. This position corresponds to half the output voltage of the controller, the fullrange of which is equal to 12 V. A screw at a piezoactuator holder is tightened in this position. The range of the shaftdisplacement for the full scale of the controller output voltage is shown in Fig. 7 for the horizontal (Axis X) direction of theshaft displacement.

6. Active vibration control

The test rig was designed for speeds up to 23,000 rpm. This paper is focused to prove safely and without doubt thestabilization effect of the active vibration control system. The speed range of the rotor during tests results from the journalclearance and the oil viscosity at 20 1C which were at disposal.






As was mentioned earlier, the signal from the proximity probes is connected to the dSpace signal processor. The outputof the signal processor is connected to the input of the amplifier that powers the piezoactuator. The electronic feedback(see Fig. 12) in the below presented experiments was of the proportional controller type. Although improved dynamicproperties of the control loop require adding a derivative component, the noisy signal produced by the proximity probes isthe reason, for which the derivative feedback was not used [23]. Even if the sensors based on the electrical capacityprinciple have a smaller error than the eddy current ones, the active vibration control has been tested with sensors basedon eddy currents.

The shaft rotational speed during the tests under active control (ON) and without active control (OFF) was increasing atthe ramp rate of 7000 rpm per a minute for all measurements. The onset of instability starts at 4300 rpm for the oil of theVG 10 grade. Because the piezoactuator travel range cannot cover the change of the shaft position from the very beginningup to the level of the bushing centre position, the active vibration control is switched ON when the shaft lifts up into thestabilized position, which corresponds approximately to 3000 rpm. Due to the measurement error the controller outputvoltage starts to oscillate with a limited magnitude. As is clear from Fig. 13, if the active control is switched ON during therotor run-up, the onset of instability is changed to 7300 rpm. This increasing of the limit speed corresponds to thecontroller gain KP � 2. The result of measurements at half the open-loop gain (50%) is shown in the middle part of Fig. 13.The onset of instability occurs at about 6200 rpm. The active vibration control is immediately switched OFF after startingthe unstable vibration with frequency, which is 0.475 multiple (factor l) of the shaft rotation frequency. This phenomenonis called ‘‘whirl’’ due to the oil film and is different from the first natural frequency of the shaft, which is equal to a constantvalue. The output of the signal processor is saturated on the full voltage range from 0 to 12 V.

Fig. 12. Active vibration control system.

Fig. 13. Time history of the rotor rotation speed when the active vibration control is ON and OFF.






As is demonstrated in Fig. 13, the active vibration control significantly extends the range of operating rotational speed.With active control ON, onset of instability is increased by about 3000 rpm in comparison with the operating rangewithout the active vibration control. The electronic feedback is clearly seen as a complementary way to the traditionaljournal bearing design modifications and other tools, which prevent instability or shift the rotor instability onset to higherrotational speed.

Experiments show that a movement of the bushing is transferred to the movement of the bearing journal. The oilwedge, which is created by pumping the oil below the journal, is stiff enough to be able to convey a motion of the bushingto the motion of the bearing journal. The operation of the control loop is the best proof that the movement of the bushingis transferred to the movement of the bearing journal. Closed loop control shows that the journal vibration in a wide speedrange is of low amplitude without knocking the journal at the bushing wall. The other important result of experiments isthat the journal bearing behavior may be described by a linear model of the journal bearing for small fluctuations aroundthe steady-state position.

It seems that parametric dampers whose stiffness alternates periodically in time are the future for vibration damping ofrotors. Research in this area is being conducted at the TU Darmstadt, Germany [24,25], and Vienna University ofTechnology, Austria [1]. The laboratory test rig which was built by the authors of this article may help in research of thistype of vibration damping for instability of the rotors due to the oil film.

7. Conclusion

The lumped parameter model of the journal motion inside the hydrodynamic bearing is based on the conceptdeveloped by Muszynska. According to the mentioned approach the bearing forces are modeled by a spring and dampersystem. This system is rotating at the angular velocity, which is a constant fraction of the rotor rotational speed. Theequation of motion contains the complex vector and parameters. Mathematical model allows predicting the behavior ofthe rotor, which confirms its suitability for the analysis of the control system.

The test rig for experimental investigation of affecting behavior of the rotor supported in sliding bearings by externalexcitation was put into operation. The rotational speed of the rotor is up to 23,000 rpm. The test rig consists of a rigid shaftof 30 mm diameter supported in two cylindrical hydrodynamic journal bearings with the span of 200 mm. Standardbehavior of the rotor was achieved with low viscosity oil, with which the oil film had insufficient load capacity to shiftjournal centre into unstable position at the bearing centre. The proposed goal of the project was achieved throughcontrolled movement of only one of two bearing bushings. The bearing bushing was being moved by means of twopiezoactuators oriented in vertical and horizontal directions. The shaft rotational velocity, at which occurs the onset ofinstability, was substantially increased. It seems, that there is a large potential for further improvements, which could leadto active control of high-speed rotor behavior in real operating conditions.

Acknowledgment

This research has been supported by the Czech Grant Agency project No. P101/12/2520 ‘‘Active vibration damping ofrotor with the use of parametric excitation of journal bearings’’.

References

[1] H. Ecker, A. Tondl, Increasing the stability threshold of a rotor by open loop control of the bearing mount stiffness, in: Proceedings of the ISCORMA-3,Cleveland, Ohio, 2005.

[2] F. Lebo, S. Rinderknecht, Modellbasierte Regelung eines Skalierten Elastischen Flugtriebwerkrotors mit Piezostapelaktoren, in: Proceedings of theSIRM 2011–9. Internationale Tagung Schwingungen in rotierenden Maschinen, Darmstadt, Deutschland, 21–23, Februar 2011 Paper ID-27.

[3] F. Dohnal, R. Markert, T. Hilsdorf, Enhancement of external damping of a flexible rotor in active magnetic bearings by time-periodic stiffnessvariation, in: Proceedings of the SIRM 2011–9. Internationale Tagung Schwingungen in rotierenden Maschinen, Darmstadt, Deutschland, 21–23.Februar 2011 Paper ID-08.

[4] S. Furst, H. Ulbrich, An active support system for rotors with oil-film bearings, Proc. IMechE Ser. C (1988) 61–68. paper 261/88.[5] H.Y. Lau, K.P. Liu, W. Wang, P.L. Wong, Feasibility of using giant magnetostrictive material (GMM) based actuators in active control of journal

bearing system, in: Proceedings of the World Congress on Engineering 2009 vol II, WCE 2009, July 1–3, 2009, London, UK.[6] J. Zapomel, P. Ferfecki, Application of controllable magnetorheological dampers for reducing lateral vibration of rotors excited by a base plate

oscillation—a computational investigation, in: Proceedings of the SIRM 2011–9, Internationale Tagung Schwingungen in rotierenden Maschinen,Darmstadt, Deutschland, 21– 23, Februar 2011 Paper ID-51.

[7] A.B. Palazzolo, R.R. Lin, R.M. Alexande, A.F. Kascak, G. Montague, Test and theory of piezoactuators—active vibration control of rotating machinery,ASME Trans. J. Vib. Accoust. 113 (2) (1991) 167–175.

[8] C. Carmignani, P. Forte, E. Rustighi, Active control of rotor vibrations by means of piezoelectric actuators, in: Proceedings of the DETC2001 18thBiennial Conference on Mech Vibration and Noise, Pittsburgh, Pennsylvania, 2001.

[9] B.-H. Rho, K.-W. Kim, The effect of active control on stability characteristics of hydrodynamic journal bearings with an axial groove, Proc. Inst. Mech.Eng. Part C: J. Mech. Eng. Sci., vol. 216 (2002).

[10] S.J. Kim, J.D. Jones, Influence of piezo-actuator thickness on the active vibration control of a cantilever beam, J. Intell. Mater. Syst. Struct. 6 (1995) 61.[11] T. Ushijima, S. Kumakawa, Active engine mount with piezo-actuator for vibration control, SAE International Congress & Exposition, 1993.[12] A. Alizadeh, C. Ehmann, U. Schonhoff, R. Nordmann, Active bearing of rotors utilizing robust controlled piezo actuators, in: 19th Biennial Conference

on Mechanical Vibration and Noise, Parts A, B, and C. 5, 2003.






[13] J. Tuma, J. Skuta, R. Klecka, J. Los, J. Simek, A Laboratory test stand for active control of journal bearings, in: Proceedings of the Colloquium Dynamicsof Machines 2010, Inst. of Thermomechanics, Prague, February 2–3, 2010, pp. 95–100.

[14] J. Simek, J. Tuma, J. Skuta, R. Klecka, Unorthodox behavior of a rigid rotor supported in sliding bearings, in: Proceedings of theColloquium Dynamicsof Machines 2010, Inst. of Thermomechanics, Prague, February 2–3, 2010, pp. 85–90.

[15] J.W. Lund, Review of the concept of dynamic coefficients for fluid film journal bearings, Trans. ASME J. Tribol. 109 (1987) 37–41. January.[16] J.W. Lund, Spring and damping coefficients for the tilting pad journal bearings, Trans. ASLE 7 (1964) 342–352.[17] L. Malcher, Die Federungs- und Damfungseigenschaften von Gleitlagern fur Turbomaschinen, Dissertation, Fakultat fur Maschinenbau, Technischen

Hochschule Karlsruhe, 1975.[18] A. Muszynska, Whirl and whip—rotor/bearing stability problems, J. Sound Vib. 110 (3) (1986) 443–462.[19] D.E. Bently, A. Muszynska, Fluid-generated instabilities of rotors, Orbit 10 (I) (1989). April.[20] A. Tondl, Quenching of Self-Excited Vibrations, Academia, Prague, 1991.[21] J. Tuma, J. Simek, A. Vıtecek, Simulation study of a rotor system response to kinematic perturbation, Acta Mechanica Slovaca, 3/2008.[22] R. Burns, Advanced Control Engineering, Butterworth Heinemann, Oxford, 2001.[23] A. Vıtecek, J. Tuma, M. Vıteckova, Stability of rigid rotor in journal bearing. Transactions of the VSB—Technical University of Ostrava. Mechanical

Series No. 2. 2008, LIV, paper 1638, pp. 159–164.[24] A.A.G. Siqueira, R. Nicoletti, N. Nicklas, et al., Linear parameter varying control design for rotating systems supported by journal bearings. J. Sound

Vib. 331 (10) (2012) 2220–2232.[25] F. Dohnal, Experimental studies on damping by parametric excitation using electromagnets. Proc. Inst. Mech. Eng. Part C—J. Mech. Eng. Sci. 226 (C8)

(2012) 2015–2027.





Documents

Mechanical Systems and Signal Processinghomel.vsb.cz/~tum52/publications/MSSP.pdf · Both the VSB—Technical University, Faculty of Mechanical Engineering, and TECHLAB Ltd., Prague,