Comparison Different Actuator Concepts Applications ...

International Journal ofRotating Machinery1994, Vol. 1, No. 1, pp. 61-71Reprints available directly from the publisherPhotocopying permitted by license only

(C) 1994 OPA (Overseas Publishers Association) Amsterdam B.V.Published under license by Gordon and Breach Science Publishers SA

Printed in the United States of America

Comparison of Different Actuator Concepts forApplications in Rotating Machinery

HEINZ ULBRICHDepartment of Mechanical Engineering, University of Essen, D-45117 Essen, Germany

Considerable improvements of machines can be expected in the near future through the use ofelectronics in combination withcontrol techniques. A key position will be held by the actuator systems that finally have to accomplish the controlled energytransfer according to the objectives. For rotating machine parts this is usually done via the bearings. Basically, there are twopossibilities to transmit the controlled forces; contact free via magnetic fields (magnetic bearings) or the traditional way viaconventional bearings. To realize the regulating actions multiple physical effects can be employed. In this paper some of thepromising types of actuators and their advantages and disadvantages will be discussed, as well as how effectively to use theseactive elements under different objectives. Questions concerning the practical realizations will be given high priority.

Key Words: Rotors; piezo-; hydraulic- and magnetic actuators; transfer characteristics, modeling; control techniques

he constant attempt to increase the productivity orefficiency of machines leads, in almost every field of

mechanical and automotive engineering, to problems thatcannot be solved by a mere adjustment of the constructionparameters. Improvements of already-existing machinesand vast innovations in new developments will be madepossible by the use of electronics in combination withcontrol techniques.The heart ofsuch new applications are the actuators. De-

pending on the objectives, they control the energy center ofthe system. In order to achieve this, some promising actu-ator concepts will be introduced and their strong and weakpoints will be discussed with regard to their industrial ap-plications. The procedure of integrating the actuators intothe whole system, the steering, and the design of an effi-cient control will be laid out. The objective of this paper isto give hints to help practically oriented engineers choosethe appropriate actuators for their specific application.

POSSIBLE ACTUATORS

In the future, the dynamics ofmachines will be specificallyand purposely adapted to the requirements of the particu-

lar technical task by the use of electronics in combinationwith control techniques. A key position will thereby beheld by the actuators, which will perform the energy trans-fer, depending on the objective. The actuators have thetask of transforming the information about the systemnsupplied by the sensors--into the desired physical actions.To realize these regulating actions, multiple and also verydifferent physical effects can be used. With regard to in-dustrial applications, the following demandsmas well asthe costsmshould be given high priority:

compactness, because usually the available space isquite limitedlarge forces, which has to be seen in relation to themasses to be moved and the necessary regulating dis-tances, as well as the regulating frequencies to be re-alizedregulating frequencies at least as high as the highestvibration to be controlledsimple actuator transfer characteristics to avoid addi-tional dynamic problems due to the actuator dynamiclight weight, which is a major criterion for applicationsin aeronautics and the space industry

In what follows some actuator concepts will be dis-cussed and commented upon regarding their advantagesand disadvantages.

62 H. ULBRICH

FIGURE Schematic of piezo actuator.

Piezo Actuators

Piezo actuators have been commonly used for some time.They are especially well suited when dealing with vi-brations with small amplitudes or to adjust mirror sys-tems or other components in high-precision constructionswithin the/zm-range (Haidenwanger and Klose [1992];Goto 1992]). They have also been investigated theoreti-cally and experimentally for their ability to influence ro-tors via conventional bearings (Palazzolo 1989], 1992];Santos and Ulbrich [1992]) and mechanisms in general(Liao and Sung [1990]). Piezo actuators’ special meritsare their high stiffness kp and their performance in high-frequency ranges. The realizable control forces can becalculated by

fp(t) IpCpkpu(t) kps(t) ()

where Ip is the piled height ofthe crystal wafers, Cp is theelectrostatic capacity (each crystal wafer is a capacitor),and kp is the stiffness of the actuator (see Figure 1). Theregulating distance is called s(t), the control voltage u(t).The crucial disadvantages that limit the application

range are the small, realizable, regulating distances(Ip/lO00) and the very low material damping of theactuators (impacts are transfered almost undamped). Due

to the dependency of the regulating distance on the to-tal height, the size of piezoelectric actuators can be quitelarge. Also the permissable compressive load is very smallso usually the control forces can only be applied throughadditional transfer elements (Palazzolo 1989]). A typicaltransfer function of a piezo actuator is shown in Figure 2.It can be seen that a strong reduction of amplitude beginsat 200 Hz and the phase lag progresses linearly with thefrequency. At 1000 Hz the phase lag is already -180.Hydraulic Actuators

Figure 3 shows a sectional view of a newly developed hy-draulic actuator. The operating part consists of two cylin-drical chambers which are closed in the working direction(in Figure 3 the vertical direction) by elastic membranes.The pressure difference Ap between the two chambersand 2, necessary to create the regulating operation, is

supplied by the servo valve.The special design of the actuator yields a high radial

stiffness and ensures a corresponding safety against tiltingeffects (depending on the distance between the two mem-branes as well as on their thickness). Through this arrange-ment the regulating movements can be applied completelywithout friction.The length IH of the hydraulic actuator is changed by

the length s(t) due to the regulating action. The controlforce can be expressed by an equation similar to that ofthe piezo system:

fH(t) A*Ap(t) kMs(t) (2)

where A* is the characteristic membrane area, kM 2CLthe effective membrane stiffness, CL the membrane stiff-ness, and s(t) the regulating distance in the direction ofthe force. The regulating force is generated by the pres-sure difference Ap and not (different from the piezo ac-tuator system) proportional to the control voltage. Unfor-tunately, the regulating pressure strongly depends on allfluidmechanical losses of the hydraulic and the dynamicof the servo valve. Thus the realizable regulating frequen-cies are mainly determined by the cut-off frequency ofthe used servo valve and some hydrodynamic influences(pipes, fluid). Due to these hydrodynamic influences theactuator has basically an integrating transfer character-istics, as can be seen in Figure 4 (Althaus and Ulbrich[1992]).Due to the choice of membranes (diameter, thickness)

a multitude of static characteristic curves can be real-ized. Also, the maximum control forces and regulatingdistances can be adapted in wide ranges with an adequatechoice of the membranes. The given design limit is al-

COMPARISON OF ACTUATOR CONCEPTS 63

Amplitude [m/v]

200 500 1000

[Hz]

Phase [degree]

440 1000

[Hz]

FIGURE 2 Measured transfer function of the investigated piezo actuator (ratio regulating distance s(t) over input voltage u(t)) (Santos [1993]).

ways the maximum material stress in the membranes. Thethicker the membranes at a given diameter, the larger thestiffness of the actuator and the smaller the maximumregulating distance. For practical purposes this is not aproblem because the generally high stiffnesses of the sys-tems under consideration allow only small deformationsand thus require only small regulations. In this context itshould also be noted that the physics comply with the reg-ulating actions since in the deflected state the controllergenerally has to apply resilient forces in opposite directionto the deflection s(t). This means the term kHs(t) fromeq. (2) will be superimposed by the control force A*Ap(t).A typical transfer function ofa hydraulic actuator is shownin Figure 5.When using these actuators to control rotor vibra-

tions, two actuators with radial working directions can

be positioned perpendicular to each other if necessary(Ulbrich 1992]).

Magnetic Actuators

Magnetic actuators can be classified into two types. Onetype are the magnetic bearings that permit a non-contactforce transfer. The other type are the electromagnetic ac-tuator systems where the regulating actions--as with theother presented actuator concepts--are applied indirectly,usually via conventional bearings. In both types the mag-netic forces can be controlled by either current or voltage.In the case of control by current (the power amplifiers areworking as a current source) the relationship between therealizable force f (t), the control current i(t) and the reg-

64

chamber 2

membrane 2

chamber 1

membrane 1

H. ULBRICH

/" /

IH

FIGURE 3 Hydraulic actuator.

ulating distance s(t) is strongly nonlinear. The resultingforce can be expressed by

:(’) s4s ) kskii 4- (ks kM)s 4- kwi2os-------

(kwiois2 4- sosi2)1 (3)

where so is the air gap in neutral position, i0 is the con-stant premagnetizing current, and ki, ks, kw and kM areconstants depending mainly on the geometry of the actu-ator design, the used magnetic material and the employedelectrical components. Under the assumptions of smallcontrol currents (t) << i0 and small regulating distancess(t) << so the following linear correlation between thecontrol current and the resulting force can be obtained:

f(t) kii(t) 4- (ks kM)s(t) (4)

The constants ki (force-current coefficient), ks (force-displacement coefficient) and kM 2CL (stiffness factorof the assembly in working direction, CL stiffness of themembranes) permit large varieties in layout and construc-tion of the actuators. Equation 4 shows the destabilizingeffect of such a magnetic actuator system due to a negativestiffness indicated by the 4-ks factor. The most severe caseof this destabilizing effect occurs in non-contact magneticbearings (kM 0!).

Figure 6 shows two types of magnetic actuator systemsthat are currently being developed. The difference betweenboth types is basically the realization of the premagnetiz-ing. In type I, the necessary premagnetizing is realizedelectrically (indirectly) and in type II, it is realized by spe-cial permanent magnets (directly). The magnetic potentialis realized in type I through the product iow (io is the pre-magnetizing current, to is the number of windings in thepremagnetizing coil) and in type II the circulation ioto with


3500

2100

1400

700

Nmembrane thickness: t=1.20 mm

membrane thickness: t=0.80 mm

,,0 0.1 0.2 0.3 0.4

regulating distance (mm)FIGURE 4 Force--distance relations for the hydraulic actuator.

0.5

c)

o

Amplitude [dB]

,I

,o "* ,o ’" Fequency [Hz]

o

Phase [degree]

10 t.o l0 2.0

Frequency [Hz]

FIGURE 5 Measured transfer characteristic of an investigated hydraulic actuator (ratio regulating distance s(t) over input voltage to servo valveu(t)) (Althaus and Ulbrich [1992]).

66 H. ULBRICH

electromagnetic actuator (type I)(pre-rnagnetizing with electromagnet)

electromagnetic actuator (type II)(pre-magnetizing with permanent magnet)

li i---i_.i I:-(R)--; ill-,,,, ’." ’.:

FIGURE 6 Comparison of different magnetic actuator concepts.

1000

400

a gap ir neutaiposition: xo=1.oopre-magnetizing with electromagnet O 540 A 1

FIGURE 7 Comparison of the regulating forces in magnetic actuators as a function of the control current (electrical premagnetizing--, permanentmagnet premagnetizing--).

2 3 4 5control current (A)


respect to the premagnetizing is realized by the integratedpermanent magnets (magnetic potential (R)pm A iow). Fig-ure 7 shows the control force as a function of the controlcurrent for both types. Tuning of both systems with theobjective of maximizing the control forces at a constantactuator size shows that using permanent magnets for thepremagnetizing results into a control force about 2.5 timesas high as in the case of indirect premagnetizing.

Figure 8 shows the measured control force frequencycurve for type I up to a frequency of 300. Hz. It turnsout that the phase lag at 300 Hz is already -60. Sub-stantial improvements can be expected here by the use ofnew soft-magnetic materials. These experimental investi-gations have not yet been finished.

SUMMARY

Figure 9 gives an overview of the discussed actuator sys-tems with regard to their realizable regulating distancesand frequencies. Table I shows a rating of some character-istics of the different actuator systems with regard to theirspecific requirements. This should just be understood as arough classification, but it already allows to make out thetypical applications of all the discussed actuator systems.New developments in the field ofmagnetic materials let usexpect an even stronger shifting of their attributes towardmagnetic actuators (Meeks [1992]; O’Connor [1992]).

INCLUDING THE ACTUATORS INTOTHE SYSTEM TO BE CONTROLLED

An efficient use of actuators requires a mathematical de-scription of the open-loop system that has been adaptedto the problem and where the actuators, which are alsorepresented by their mathematical models, have been in-tegrated. The resulting model is able to describe the physi-cal relations ofthe complete dynamic interactions betweenthe open-loop system and the actuators.

Mathematical Description of the System

General movements of systems consisting ofrigid, elastic,and fluid components can be mathematically described bya system of differential equations (Bremer [1989]):

M(q, t)ij + f(q, (1, t) jT (q)hcontroller(t) b(q, t)(5)

Vector q(t) represents the generalized coordinates thatdescribe the movements of the system. The mass matrixM(q, t) generally depends on q and explicitly the time t.Vector f(q, 1, t) considers all the forces involved in the en-ergy household (except the control forces). Vector b(q, t)contains the forces resulting from the steering and controlwhose components act in the direction of the generalizedcoordinates (this results immediately from the multiplica-tion of h(t) with the Jacobian matrix jT). Closed kine-matic loops can be treated with this method as well aselastic components (e.g., in actively controlled four-barlinkages; Ulbrich and Ahlemeyer [1994]). For the designof the control it is important whether the geometrical pa-rameters (e.g., the distance s(t) may be given as a forcedcondition) or the forces (an additional degree of freedomwill be introduced if not already included) are controlled.

In general, a reference movement, for example, the rigidbody motion of a function-generating mechanism or aflight maneuver of an airplane turbine--is given by thevector q(t). The nonlinear equation of motion for this ref-erence movement can be gained from eq. 5:

Mr(qr)ir q- g(qr, qr) br(t) Ur(t) (6)

With a given qr(t), tr(t) and lr(t) the steering vectorUr(t) to realize this reference movement can now directlybe calculated. Given the case that undesired small su-perimposed deviations appearmrepresented by the vectore(t)mthat are composed ofsmall rigid body movements oralso possibly elastic deformations of the structure, a con-trol can be added. The starting point for the design of sucha control is the linearized system (linearized around thereference movement, i.e. q(t) qr(t) + e(t), lel << Iqrl,eq. 4):

Me(t)(t) -+- Pe(t)(t) + Qe(t)e(t) be(t) Ue(t) (7)

Comments on the Control

The realization of an efficient control will be decisively in-fluenced by the choice of the actuator- and sensor systemsand their positioning within the whole system as well asthe choice of the control concepts including the optimiza-tion of the controller. The optimization of the controllerstrongly depends on the chosen objectives. In any case thecontroller will be optimized with respect to a criterion forthe quality of the employed control. Discussions of differ-ent quality criteria and some remarks on the further proce-dure can be found in Bremer [1990] and Ulbrich [1992].

For the optimization of controllers there are already amultitude of computer programs available that usually re-sult into a parameter optimization, that is, tuning of the

68 H. ULBRICH

10

O.8

Amplitude [dB]

air gap in neutral position: x=l.00 mm(magnetic material: St-37)

number of windings: Wo 108; W. 106/pre-magnetizing current: Io 5.0 Acontrol current: h 1.5 A

,.l ,llll ,I,,,I I,.2 4 6 8 10 20 40 60 80 100 200

frequency (Hz)

Phase [deg]

60

40

20

0o

.20o

-40

-6O

-8O

air gap in neutral position: xo=l.00 mm(magnetic material: St-37)

number of windings: Wo 108; W 106pre-magnetizing current: I. 5.0 A /control current: I 1.5 A

,I,,,I l,,i ,,.il,i,l

2 4 6 8 10 20 40 60 80 100 200frequency (Hz)

FIGURE 8 Transfer characteristic of the magnetic actuator system with electrical premagnetizing and ordinary magnetic material (Steel ST37).

70 H. ULBRICH

TABLERating of different actuator concepts

Actuator Type

Characteristic Electromagnetic Piezoelectric Hydraulic

Frequency range + + + + + +Regulating distance ++Stiffness + + + +Realizable forces/weight + +(active element without periphery)Realizable forces/size +Realizable forces/total weight +(including periphery, e.g., hydraulics)Possibility of stimulation of vibrations ++ +due to nonlinearities

+++++++++

+++

Applying the Actuators for the Control of High-Speed Rotors

Characteristic Electromagnetic Piezoelectric Hydraulic

Requirements against wearPower loss (e.g., due to bearing friction)Temperature rangeCleanlinessEmergency operation characteristicsLongevity or life

excellent; ++ good; + average; weak; poor

++++

controller amplifications to optimize the quality criterionto obtain an optimal system performance according tothe objectives.The realization of the control can be analog, digital,

or "hybrid". An analog control will, in most cases, not beflexible enough and is only employed in so-called constantcontrollers. When system changes during the operationare considered or nonlinear controllers are realized thenusually the advantages ofa digital control can be exploited.The only problem that can arise in digital controllers isthe limited cycle time, but that depends on the particulartask to be solved. Also, new developments in the field ofparallel computer design (transputer) will further reducethe cycle times and can as such constitute a solution. Ifcycle times are still not fast enough it can sometimes beuseful to employ a "hybrid control" in order to separate thetime-critical components, for example, the rotorfrequentvibrations of high-speed rotors (Ulbrich [1982]), and tocombine a fast analog control with a digital adaptation ofthe control parameters.

CONCLUSION

The advance of electronics in combination with automaticcontrol technology will continue. Through constantly in-

creasing the speed of computers as well as improvingthe precision of analog elements, more and more com-plicated calculations and simulations, embedded into theinformation circuits of controlled systems, will contributeto improve further the dynamics of these systems. It isjust a matter of time before active bearings will be regu-larly employed in machine tools, gas turbines, terrestrialturbines, engine suspensions, valve control, and variousother mechanisms. To account for these future require-ments a practically oriented development of actuators thatare specifically adapted to the particular problem with asimultaneous integration of the necessary sensors is ofhigh importance. To realize this, some concepts that arepartially still under development have been presented anddiscussed and the task of how to come to an efficient useof such active components to improve machines in theirdynamic characteristics, has been explained.

Nomenclature

b(q, t)br(t)e(t)

f(q, 1, t)fH(t)fM(t)fp(t)g(qr, r)

vector of generalized control forcescontrol vector for realizing the reference motionerror vector considering the deviation from referencemotionvector of generalized forcescontrol force of hydraulic actuator [N]control force of magnetic actuator [N]control force of piezo actuator [N]generalized control forces for reference motion


i(t)knkikgkp

lpAp(t)q(t)qr(t)

S(t)U(t)Be(t)A*CpJq(q)M(q, t)Me(t)Mr (qr)Pe(t)Qe(t)

control current of magnetic actuator [A]effective membrane stiffness of hydraulic actuator [N/m]force-current coefficient [N/A]membrane stiffness of magnetic actuator [N/m]stiffness of piezo actuator IN/m]force-displacement coefficient [N/m]length of piezo actuator [m]control pressure [Pa]vector of generalized coordinatesvector of generalized coordinates of the lineadzedcoordinatesregulating distance [m]input voltage of the piezo actuator [V]control vector to minimize the error e(t) [N]effective membrane area [m2]capacity of the piezo actuator [F]Jacobian matrixmass matrixmass matrix of error systemmass matrix of reference systemdamping matrix of error systemstiffness matrix of error system

References

Althaus, J., and Ulbrich, H., 1992. A Fast Hydraulic Actuator for ActiveVibration Control, Proceedings of the Institute ofMechanical Engi-neers, International Conference "Vibrations in Rotating Machinery,"Bath, England.

Bremer, 1989. Dynamik und Regelung Mechanischer Systeme, B.G.Teubner, Stuttgart.

Goto, H. et al., 1992. Miniature 2-Dimensional Optical Scanner Utilizinga Multilayered Piezoelectric Actuator with New Displacement Expan-

sion Mechanism, Proceedings ofthe 3rd International Conference onNew Actuators, Bremen, Germany June 24-26.

Haidenwanger, H.-G. and Klose, P. L. M., 1992.004 Isolation and Com-pensation of Vibration by Means of Active Piezo-Ceramic Mounts,International Symp. on Advanced Vehicle Control, AVEG 92, Japan.

Liao and Sung, 1990. An Elastodynamic Analysis and Control of Flexi-ble Linkages Using Piezoceramic Sensors and Actuators, ASME DesEng Div Pub, DE v 24, Flexible Mechanisms, Dynamics and RobotTrajectories, 21st Biennial Mechanism Conference, Chicago. ASME,New York pp. 503-510.

Meeks, R., 1992. Magnetic Bearings Boost Performance, Global GasTurbine News.

O’Connor, L., 1992. Active Magnetic Bearings Give Systems a Lift,Journal ofMechanical Engineering.

Palazzolo, A. B. et al., 1989. Piezoelectric Pushers for Active VibrationControl of Rotating Machinery, Transactions of the ASME, Journal

of Vibration, Acoustics, Stress, Reliability in Design, Vol. 111, pp.298-305.

Palazzolo, A. B. et al., 1992. Hybrid Active Vibration Control of RotorBearing Systems Using Piezoelectric Actuators, Transactions of theASME, Journal of Vibration and Acoustics.

Santos, I., and Ulbrich, H., 1992. Actively Controlled Tilting Pad JournalBearings Fourth International Symposium on Transport Phenomenaand Dynamical Machinery, Honolulu, HI.

Santos, I., 1993. Aktive Kippsegmentlagerung--Theorie and Exper-iment, Dissertation, VDI-Fortschdtberichte, Reihe 11, Nr. 189,Diisseldorf.

Ulbrich, H., 1992. Active Bearing Support for Rotating Machine Ele-ments, Journal ofMachine Vibration, Springer-Verlag, London.

Ulbrich, H., and Ahlemeyer, E., 1994. Prizise Bewegung nichtlinearer0bertragungsgetdebe dutch aktive Elemente, ZAMM, Nr. 74, 4,pp. TS1-T88.

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