tuma icsv19

ICSV19, Vilnius, Lithuania, July 8-12, 2012 1

ACTIVE VIBRATION CONTROL OF JOURNAL BEARINGS WITH THE USE OF PIEZOACTUATORS Jiří Tůma and Jaromír Škuta Faculty of Mechanical Engineering, VSB – Technical University of Ostrava, 17. listopadu 15, CZ 708 33, Ostrava, Czech Republic, [email protected], [email protected]

Jiří Šimek TECHLAB Ltd., Prague, Sokolovská 207, CZ 190 00, Praha 9, Czech Republic, [email protected]

Rotor instability is one of the most serious problems of high-speed rotors supported by slid-ing or journal bearings. With constantly increasing parameters of new machines problems with rotor instability are encountered more and more often. Even though there are many solu-tion 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 ac-tive vibration control of journal bearings with the use of piezoactuators. The controllable journal bearing is a part of a test stand, 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 prox-imity probes. 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 con-trol extends considerably the range of the operational speed.

1. Introduction One of the most serious problems is instability of high-speed rotors due to the journal bearing

oil film. To study possibilities of affecting rotor behaviour by controlled movement of bearing bushings, a test stand was built. Even though there are many solution 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, etc., the approach to preventing the journal bearing instabil-ity, presented in the paper, is based on the use of the active vibration control.

Many authors pay attention to the active control of journal bearings with the use of magnetic actuators as for example1. Piezoactuators as a tool to control of rotating machines have been inten-sively investigated in the literature since the end of 1980's. One of the first original contributions2 dated from the beginning of the 1990's. These papers did not study the effect of the oil film on the onset of instability and its suppression using the active vibration control. Worth mentioning are pa-pers3,4 dealing with the problem of the rotor instability. As the VSB - Technical University, Faculty of Mechanical Engineering and TECHLAB Ltd., Prague, are focused on long-term research in the field of rotor dynamics, it was decided to start research of methods suppressing journal bearing in-

19th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8-12, 2012

2

stability by the active vibration control. The research work was granted by the Czech Science Foun-dation 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 electronic feedback to the rotor-bearing system actuating the position of a movable bushing. The current passive damper changes into an active component of the system with controllable properties. The laboratory test facilities, including the journal bearing equipped with the movable bushing was designed and put into opera-tion5,6.

2. Test rig The photos and sketch of a controllable journal bearing arrangement, which is implemented

for the active vibration control, are shown in Fig. 1. The test stand consists of a rigid shaft support-ed in two cylindrical hydrodynamic journal bearings. Bearing bushings are supported in rubber “O” rings, which ensure sealing of oil inlet and at the same time enable movement of bushings within the clearance in bearing casing. Bearing bushings can be excited by means of piezoactuators orient-ed in vertical and horizontal directions and fastened to the frames. The preloaded open-loop LVPZT piezoactuators are of the P-842.40 and P-844.60 type. Both the piezoactuator types require a low voltage amplifier with the 100 V peak value at the output. The pushing force produced by the P-842.40 type is of 800 N and the pulling force only 300 N. The piezoactuator travel range is up to 90 μm. The same travel range reaches the LVPZT piezoactuator of the P-844.60 type while the push-ing force is up to 3 000 N and the pulling force is up to 700 N in contrast to the P-842.40 type. The test shaft is driven by high-frequency motor through an elastic membrane coupling, constituting two joints, so that the shaft is decoupled from motor and free to move.

Figure 1. Arrangement of the controllable journal bearing.

Shaft movement is measured by two pairs of proximity probes. These sensors are working on eddy current and electrical capacitive principles. The eddy current sensors IN-085 are a product of the Brüel & Kjær company, but the sensors from Bently Nevada Rotor Kit were alternatively tested as well. After some problems with the measurement errors 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 stand was designed for speeds up to 23 000 rpm.

3. Journal bearing model There are many ways how to model journal bearings, but this paper prefers a lumped parame-

ter model, which is based on the concept developed by Muszynska7 with the support of Bently Ro-tor Dynamics Research Corporation8. The reason for using this concept was that it offers an effec-tive way to understand the rotor instability problem and to create a model of a journal vibration ac-


3

tive control by manipulating the bushing position by actuators, which are a part of the closed loop system composed of proximity probes and a controller. Another approach can be based on the lubri-cant flow prediction using a FE method for Reynolds equation solution. This more sophisticated method does not allow analyzing behavior of the active vibration control to design the controller.

Let the rotor angular velocity be designated by Ω of the unit in radians per a second. It is as-sumed that the bushing is a movable part in two perpendicular directions while the rotor is rotating. This mathematical model proposes to use complex variables as position vectors to describe motion of the rotor and bushing in the plane, which is perpendicular to the rotor axis. The real part of the position vector r is a horizontal coordinate x(t) while the imaginary part is a vertical coordinate y(t) of the journal centre. The coordinate system is tied to stationary bearing housing with a cylindrical hole, inside of which is inserted movable bearing bushing. The origin (0, 0) of the coordinate sys-tem in the complex plane is situated in the centre of the mentioned cylindrical bore as it is shown in Fig. 2. The positions of the journal centre and bushing mean the intersection of both movable com-ponent axes with the complex plane. The position of the journal centre in the complex plane is des-ignated by the mentioned position vector r, while the position of the bushing centre is designated by the position vector u (see Fig. 2). The coordinates of the end-point of this vector are r = x(t) + j y(t) for the journal (rotor) centre and u = ux(t) + j uy(t) for the bushing centre, where j is an imaginary unit.

Figure 2. Coordinate system.

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 forces are considered as an input for the mathematical model. The fluid pressure wedge is the actual source of the fluid film stiffness in a journal bearing and maintains the rotor in equilibrium. The bearing forces can be modeled by a spring and damper system7,9, which is rotating at the angular velocity Ωλ , where λ is a dimensionless parameter, which is slightly less than 0.5.

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

( ) ( ) ( ) Fururr =−Ωλ−+−+ jDKDM . (1)

where scalar parameters, K and D , are specifying proportionality of stiffness and damping to the relative position of the journal centre displacement vector, M is the total rotor mass and F is pertur-bation force. The trajectory of the rotor centerline is called an orbit. The complex Eq. (1) can be replaced by two real equations. The complex variables are used to simplify not only writing mathe-matical formulas but for easy creation of the simulation model in Matlab-Simulink10.

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

λ=Ω MKCRIT . (2)


4

As can be experimentally verified, the frequency spectrum of the fluid-induced vibration con-tains the single dominating component, which would be a solution of the second order linear differ-ential equation without damping. The journal lateral vibration is limited by the inner bearing sur-face. The stiffness and damping coefficients are non-linear functions of the eccentricity ratio, espe-cially 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 orbital motion.

4. Model of the closed control loop Active vibration control of journal bearings uses the bushing position as the control variable u

and the shaft position as a controlled variable r. The control variable is an output of a controller. The controller transforms an error signal computed as a difference of a set point and actual position of the shaft. As is evident from the block diagram in Fig. 3, the controller is of the proportional type with the gain PK .

+

Kp GS (jω) -

Controller Plant r u

Negative feedback Figure 3. Closed control loop.

Provided that the perturbation force is zero 0=F the equation of motion is as follows

( ) ( )uurrr Ωλ−+=Ωλ−++ jDKDjDKDM . (3)

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

( ) 2)()(ω−Ωλ−+ω

Ωλ−+ω=ω

MjDKDjjDKDjKjG Po . (4)

For the stability margin the open-loop frequency transfer function ( )ω0G is equal to -1. The frequency of the steady-state vibration at the stability margin is given by Ωλ=ω and

12 −ω= KMKP . If the feedback gain PK is positive then the maximal rotational speed MAXΩ for the rotor stable behavior is greater than the critical rotational speed without any control which is given by Eq. (4). Increasing of the margin for the rotational speed is given by the formula

.1+Ω=Ω PCRITMAX K (5)

The control system does not stabilize the behavior of the journal bearing directly by changing the position of the bearing bushing, but indirectly by changing force that acts on this bushing. Ex-cept of the controller gain, the displacement of the bushing depends on stiffness of its connection with the bearing body through rubber seal rings as it is shown in Fig. 4. The dependence of force acting to the bushing on the bushing displacement is shown in Fig. 5. The gain PK in Fig. 3 results not only from the setting up of the controller, but from the property of the bushing clamping as well. Properties of the piezoactuator of the P-844.60 type (catalogue values) and measured stiffness of clamping (5.5x106 N/m) gives the bushing travel range which is equivalent to the control variable range (see right part of diagram in Fig. 4). The piezoactuators are powered by voltage ranging from 0 to 100V which corresponds to the amplifier input voltage ranging from 0 to 12V. The range of the rotor stable rotational speed is limited by the travel range of piezoactuators and measurement errors of the proximity probes.


5

ForcePiezoactuator Y

Piezoactuator X

Displacement

Voltage

90 μm

3000 NP-844.60

00

O-ring seal

5.5x106 N/m

77

- 0 +Control variable range

Figure 4. Force acting at the bushing vs. bushing displacement in horizontal direction (axis X).

-1500-1000

-5000

50010001500

-200-100 0 100 200

Forc

e [N

]

Displacement [µm]

Figure 5. Dependence of piezoac-tuator force on bushing displace-

ment.

5. Operational conditions of the test rig When putting the test stand into operation, we met these problems:

• 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.

5.1 Lubrication To reach the maximum motor speed higher than 6 000 rpm it was necessary to increase bear-

ing clearance to 90 μm 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 °C) used as a lubricant was then substituted by bearing oil of the OL-P03 type (VG 10 grade, kinematic viscosity 2.5 to 4 mm2/s at 40 °C). The hydraulic oil enabled to reach the maximum rotational speed of 16 000 rpm and the instability onset at the same speed. The bearing oil enabled to reach the motor maximum nominal speed 23 600 rpm, while the instability onset was at 4 300 rpm. All tests were undertaken at ambi-ent temperature about 20 °C. Lubricating oil was not preheated during tests.

5.2 Measurement of the shaft position The first measurements showed the shape of the rotor centerline trajectory (orbit) considera-

bly differing from a circle or an ellipse. To explain this phenomenon, the reasons were looked for in the uniformity of motor rotation, the misalignment of the motor and rotor axes, the oil pump and the interference of the proximity probe output signals. To achieve perfect decoupling of the test shaft from driving motor, another flexible coupling was installed between original coupling and the shaft. The rotation uniformity is not as smooth as in case of using a DC motor. The interference between signals causes an error below 1 μm in measurements. Inspection of the shaft non-circularity showed, that the deviation from the circle is less than 1 μm as well. Finally it was proved, that non-homogeneity of the rotor material magnetic and electric conductivity properties is the main source of the proximity probe periodical error. The error signal is repeated synchronously with rotor rota-tion. The same material is passing-by below the tip of the second proximity 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 μm.


6

0 30 60-460

-440

-420

-400

-380

-360

IN 085

Time [s]

Dis

p X

[mic

rom

eter

s]

0 30 60-760

-740

-720

-700

-680

-660

-640

Time [s]

Dis

p X

[mic

rom

eter

]

capaNCDT CS05

Figure 6. 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).

The measurement of the shaft displacement with the use of the eddy-current sensor in the hor-izontal direction (X) is shown in Fig. 6 on the right side. The rotor run-up is at the rate of 7 000 rpm per a minute. The sampling frequency was set to 2048 Hz. The measurement with the use of the capacitive sensor is shown in the same Fig. 6 on the left side.

The measurements of the shaft displacement during run up proceeded with extremely low vis-cous oil VG10 without preheating. It is technically impossible to increase the rotor rotational speed smoothly from 0 rpm. Rotor starts at the speed of 230 rpm and then the speed is continuously in-creased up to the onset of instability. The journal movement begins at the bottom of the bearing sleeve and with increasing speed it moves up in direction of rotation. At the level of the sleeve cen-tre the journal starts to move towards the bearing centre. With infinite speed or zero load the journal centre coincidences with bearing centre, which is generally unstable position in circular bearing. The instability onset is at about 4 300 rpm.

5.3 Mounting of piezoactuators Choice of the piezoactuator type was verified by measurement of the dependence of acting

force on the open-loop piezoactuator travel. As was shown in Fig. 5, 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 of misalignment and possible bending load.

The test stand instrumentation allows active vibration control only in the journal bearing at the opposite side to the driving motor. Before beginning of operational tests, the initial position of the piezoactuators has to be adjusted in the middle position of the operating travel range. This posi-tion corresponds to half the output voltage of the controller, the full range of which is equal to 12V. A screw at a piezoactuator holder is tightened in this position. The range of the shaft displacement for the full scale of the controller output voltage is shown in Fig. 4 for the horizontal (Axis X) direc-tion of the shaft displacement.

6. Experiments with active vibration control As was mentioned earlier, the signal from the proximity probes is connected to the dSpace

signal processor. The output of the signal processor is connected to the input of the amplifier that powers the piezoactuator. The electronic feedback (see Fig. 7) in the below presented experiments was of the proportional controller type. Although improved dynamic properties of the control loop require adding a derivative component, the noisy signal produced by the proximity probes is the reason, for which the derivative feedback was not used11. Even if the sensors based on the electrical capacity principle have a smaller error than the eddy current ones, the active vibration control has been tested with sensors based on eddy currents.

capaNCDT CS05 IN-085


7

Load +

Journal position

Set point

Piezoelectric actuators

Rotor system

+ - Controller dSpace

Proximity prob es +

Amplifier

Bushing 0 to 100 V 0 to 12 V

Figure 7. Active vibration control system.

0 50 100-800

-700

-600

Dis

p X

[mic

ron]

Active Control OFF

0 50 100-800

-700

-600D

isp

X [m

icro

n]

Active Control ON (50%)

0 50 100-800

-700

-600

Dis

p X

[mic

ron]

Active Control ON (100%)

0 50 100-800

-700

-600

Dis

p Y

[mic

ron]

0 50 100-800

-700

-600

Dis

p Y

[mic

ron]

0 50 100-800

-700

-600

Dis

p Y

[mic

ron]

0 50 100-505

1015

Act

uato

r X

0 50 100-505

1015

Act

uato

r X

0 50 100-505

1015

Act

uato

r X

0 50 100-505

1015

Time [s]

Act

uato

r Y

0 50 100-505

1015

Time [s]

Act

uato

r Y

0 50 100-505

1015

Time [s]

Act

uato

r Y

7340 RPM6200 RPM4300 RPM

Figure 8. Results of experiments with the active vibration control of journal bearings.

The rate of increasing rotational speed is the same for the tests under active control (ON) and without active control (OFF). For the oil of the VG 10 grade the onset of instability starts at 4 300 rpm. Because the piezoactuator travel range cannot cover the change of the shaft position from the very beginning up to the level of the bushing centre position, the active vibration control is switched ON when the shaft lifts up into the stabilized position, which corresponds approximately to 3 000 rpm. Due to the measurement error the controller out voltage starts to oscillate with a limited mag-nitude. As is clear from Fig. 8, if the active control is switched ON during the rotor run-up, the on-set of instability is changed to 7 300 rpm. This increasing of the limit speed corresponds to the con-troller gain 2≈PK . The result of measurements at half the open-loop gain (50%) is shown in the middle part of Fig. 8. The onset of instability occurs at about 6 200 rpm. The active vibration con-trol is naturally immediately switched OFF after starting the unstable vibration with subharmonic frequency of the shaft rotation. The output of the signal processor is saturated on the full voltage range from 0 to 12 V.

As is demonstrated in Fig. 8, the active vibration control significantly extends the range of operating rotational speed. With active control ON, onset of instability is increased by about 3 000 rpm in comparison with the operating range without the active vibration control. The electronic feedback is clearly seen as a complementary way to the traditional journal bearing design modifica-tions and other tools, which prevent instability or shift the rotor instability onset to higher rotational speed.


8

7. Conclusion The lumped parameter model of the journal motion inside the hydrodynamic bearing is based

on the concept developed by Muszynska. This concept enables to predict the stability margin for rpm and verify it by experiments.

The test rig for experimental investigation of possibilities how to affect behavior of the rotor supported in journal bearings by external excitation was designed and manufactured. The tests car-ried out showed some features, which had to be cleared before experiments with bearing bushing control could be started. Standard behavior of the rotor was achieved with low viscosity oil, with which the oil film had insufficient load capacity to shift journal centre into unstable position at the bearing centre. The proposed goal of the project was achieved by substantially increasing the onset of instability through controlled movement of only one bearing bushing. It seems, that there is a large potential for further improvements, which could lead to active control of high-speed rotor be-havior in real operating conditions.

REFERENCES 1 Fürst, S. and Ulbrich, H. An Active Support System for Rotors with Oil-Film Bearings, Pro-

ceedings of IMechE, Serie C, 1988, pp. 61-68, paper 261/88. 2 Palazzolo, A.B., Lin, R. R., Alexande, R. M., Kascak, A. F. and Montague, G. Test and

Theory of Piezoactuators - Active Vibration Control of Rotating Machinery, ASME Trans. Journal of Vibration and Accoustics, 1991, 113(2) 167-175.

3 Carmignani, C., Forte, P. and Rustighi, E. Active Control of Rotor Vibrations by Means of Piezoelectric Actuators. Proc. DETC2001 18th Biennial Conference on Mech Vibration and Noise, Pitts-burgh, Pennsylvania, 2001

4 Rho, B-H. and Kim, K-W. The Effect of Active Control on Stability Characteristics of Hy-drodynamic Journal Bearings with an Axial Groove. Proceedings of the Institution of Mech Engineers, Part C: Journal of Mechanical Engineering Science, Volume 216, Number 9 / 2002, 2002, pp. 939-946.

5 Tůma, J., Škuta, J., Klečka, R., Los, J. and Šimek, J. A Laboratory Test Stand for Active Control of Journal bearings. Proc. Colloquium Dynamics of Machines 2010, Inst. of Ther-momechanics, Prague, February 2-3, 2010, pp. 95-100.

6 Šimek, J., Tůma, J., Škuta, J. and Klečka. R. Unorthodox Behavior of a Rigid Rotor Sup-ported in Sliding Bearings. Proc. Colloquium Dynamics of Machines 2010, Inst. of Ther-momechanics, Prague, February 2-3, 2010, pp. 85-90.

7 Muszynska, A. Whirl and Whip – Rotor / Bearing Stability Problems. Journal of Sound and Vibration (1986) 110(3), pp 443-462.

8 Bently, D.E. and Muszynska, A. Fluid-Generated Instabilities of Rotors, Orbit, Volume 10, No. I, April, 1989.

9 Tondl, A. Quenching of self-excited vibrations. Academia, Prague 1991. 10 Tůma, J., Šimek, J. and Víteček, A. Simulation Study of a Rotor System Response to Kine-

matic Perturbation. Acta Mechanica Slovaca, 3/2008 11 Víteček, A., Tůma, J. and Vítečková, M., Stability of Rigid Rotor in Journal Bearing. Trans-

actions of the VŠB – Technical University of Ostrava. Mechanical Series. No. 2, 2008, vol. LIV, paper 1638, pp. 159-164.

Acknowledgement This research has been supported by the Czech Grant Agency project No. P101/12/2520 “Ac-

tive vibration damping of rotor with the use of parametric excitation of journal bearings”.

tuma icsv19

Documents