nano- and micro-scale piezomotors
TRANSCRIPT
ISSN 1068�798X, Russian Engineering Research, 2012, Vol. 32, No. 7–8, pp. 519–522. © Allerton Press, Inc., 2012.Original Russian Text © S.M. Afonin, 2012, published in Vestnik Mashinostroeniya, 2012, No. 6, pp. 3–6.
519
Nano� and micro�scale piezodrives for precisionelectromechanical systems are intended for use innanotechnological and nanobiological equipment andalso in microelectronics, electron microscopy, astro�nomical equipment, and adaptive optics. It ensuresprecise positioning and combination of equipment,compensation of temperature and gravitational defor�mation, and compensation of atmospheric turbulenceby wavefront correction [1–6].
The inverse piezo effect is employed in nano� andmicro�scale piezomotors: the displacement is due todeformation of the piezocomponent when an externalelectric stress is applied.
Piezoelectric devices that convert electrical energyinto the mechanical energy of the object being movedmay be described as piezoelectric motors or, for short,piezomotors. The operation of piezomotors is basedon the ability of piezoelectrics to be deformed in pro�portion to the applied electric potential. Piezoelectricmaterials include quartz, tourmaline, potassiumsodium tartrate, ammonium dihydrophosphate, lith�ium sulfate, barium titanate, and ferroelectric ceram�ics. At present, ferroelectric ceramics are widely usedas piezoceramics.
The benefits of piezoceramics over other piezoelec�tric materials include a larger piezoelectric effect; highCurie point; stability of the properties over time andover a broad temperature range; great mechanicalstrength; and relatively simple manufacturing technol�ogy, with the possibility of obtaining piezocomponentsof the required configuration. The correspondingpiezodrives are characterized by high precision, smallsize, simple structure and control, a broad operationaltemperature range, reliability, and low cost [7–15].
The piezoelectric effect appears in ferroelectricceramics after polarization by a strong constant field.When the field is switched off, the residual polariza�tion remains, on account of domain reorientation.The piezoceramics most commonly used are based onlead zircotitanate PbZr1 – xTixO3, with considerableelectromechanical activity [16, 17]. The exceptionalpiezoelectric properties of lead zircotitanate are ofparticular interest. In PbZr1 – xTixO3 solid solutions, amorphotropic phase boundary exists at a composition
with 53 mol. % PbZrO3. This almost vertical boundarydivides the regions of tetragonal and rhombohedralferroelectric phases on the phase diagram. Close to themorphotropic phase boundary in solid solutions with�out additives, maximum values of the piezomodulusand the electromechanical coupling coefficient areobtained. These values may reach 0.6 and will be evenhigher on introducing small quantities of Bi3+, La3+,Nb5+, and W6+.
Piezomotors are made from ceramics such asTsTS�19, TsTS�21, TsTS�23, TsTS�26, TsTBS�3,PKR�7, PKR�7M, PZT�4, and PZT�5N.
The deformation of the basic piezoconverter in thepiezomotor corresponds to its stress state. If mechani�cal stress T is created in the piezoconverter, strain Swill appear. There are six components of the stress: T1,T2, T3, T4, T5, T6. Of these, T1–T3 correspond to ten�sile–compressive stress, and T4–T6 to shear stress(Fig. 1).
For a polarized piezoceramic, the matrix equationsof state relating the electric and elastic variables takethe form [16, 17]
The first equation describes the direct piezo effect; thesecond describes the inverse piezo effect. Here [D] is
D[ ] d[ ] T[ ] εT
[ ] E[ ];+=
S[ ] sE[ ] T[ ] d[ ]
t E[ ].+=
Nano� and Micro�Scale PiezomotorsS. M. Afonin
Moscow State Institute of Electronic Technology (Technological University)
Abstract—The use of nano� and micro�scale piezomotors in precision electromechanical systems is consid�ered. The deformation of the piezoconverter corresponding to its stress state is investigated.
DOI: 10.3103/S1068798X12060032
T3
T1
T2
T4
T5
T6
1
2
3
1
2
3
(a) (b)
Fig. 1. Components of the tensile–compressive (a) andshear (b) stress.
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AFONIN
the column matrix of the electric induction; [S] is thecolumn matrix of the strain; [T] is the column matrixof the mechanical stress; [E] is the column matrix ofthe electric field strength; [sE] is the electric�pliabilitymatrix when E = const; [d]t is the transposed piezo�electric�modulus matrix; [εT] is the dielectric�permit�tivity matrix when T = const.
The polarized piezoceramic is characterized bypiezoelectric texture with symmetry ∞, m. Therefore,the electric�pliability matrix for polarized piezocer�
amic contains five independent components
and
In that case, the matrix [d]t takes the form
s11E
, s12E
,
s13E
, s33E
, s55E
sijE
[ ]
s11E s12
E s13E 0 0 0
s12E s11
E s13E 0 0 0
s13E s13
E s33E 0 0 0
0 0 0 s55E
0 0
0 0 0 0 s55E 0
0 0 0 0 0 2 s11E s12
E–( )
.=
dij[ ]t
0 0 d31
0 0 d31
0 0 d33
0 d15 0
d15 0 0
0 0 0
.=
When T = const, we may write
We may divide the known nano� and micro�scalepiezomotors into four basic classes [6–22].
A. The first class consists of vibrational piezoelec�tric motors, of the following types [18–22].
(1) Vibrational piezomotors based on frictionalcontact anisotropy of the vibrating component and arotor (that is being turned) or a surface (that is beingtransported), with frequency from a few hundred Hzto a few MHz (Fig. 2). In this case, the motion cannotbe reversed without changing the angle α. Such motorsmay convert longitudinal vibration of the piezocom�ponent 2 to rotation of rotor 1 (Fig. 2a) or flexuralvibration of piezocomponent 2 to translation of body 1(Fig. 2b).
(2) Vibrational piezomotors based on the creationof different normal reactions within a single cycle, bythe superposition of additional periodic action of thevibrating components and the body being moved orturned. Such piezomotors take the form of elastic sys�tems performing longitudinal–transverse vibrations;vibrational systems associated with longitudinal–tor�sional waves; or plane elastic systems performingmotion along two axes at different frequency.
(3) Vibrational piezomotors based on asymmetricvibration cycles, with simultaneous use of the nonlin�ear properties of fluid and the speed dependence of thefrictional force. Continuous rotor motion is ensuredby a nonlinear speed dependence of the damping influid and the transfer of asymmetric torsional oscilla�tions to the vibrating component.
(4) Vibrational piezomotors based on a periodicallyvarying relation between the vibrating component andthe rotor or the displaced body. That relation may beprovided by materials with a controllable frictionalcoefficient, magnetoviscous or electroviscous fluids,or materials whose viscosity changes in an ultrasoundfield.
(5) Vibrational piezomotors based on the frictionalinteraction of wave motion of the converter and thebody being moved (vibrational wave motors).
B. The second class consists of force�based piezomo�tors, which may be divided into three groups [6–15].
(1) Simple piezomotors in which motion is theresult of longitudinal deformation of the piezocompo�nent on applying an external electric potential.
(2) Composite (multilayer) piezomotors in whichmotion is due to the longitudinal deformation of com�posite piezoconverters (assembled from piezocompo�nents coupled in mechanical series) on applying anexternal electric potential (Fig. 3).
εT
[ ]
ε11T 0 0
0 ε22T 0
0 0 ε33T
.=
(a) (b)α
α
1
2
3
1
2
3
Fig. 2. Operation of vibrational piezoelectric motors basedon frictional anisotropy of the vibrating component andthe surface being moved: (1) body being moved(or turned); (2) vibrational piezocomponent performinglongitudinal (a) or flexural (b) vibration; (3) contact madeof special material.
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NANO� AND MICRO�SCALE PIEZOMOTORS 521
(3) Piezomotors with hydraulic or mechanicaltransmission to amplify the small reciprocating dis�placements of the piezoconverters so as to obtain con�siderable displacement of the working component.
C. The third class consists of piezoelectric stepmotors, which may be divided into three groups.
(1) Step piezomotors based on an active centralpiezoelectric component, with attached restraints(which may be piezoelectric, electromagnetic, or elec�trodynamic).
(2) Step piezomotors based on an active centralpiezoelectric component, with external restraints(Fig. 4).
(3) Step piezomotors based on a passive movableworking body, with mobile restraints.
D. The fourth class consists of bimorphic and mul�timorphic piezomotors, which may be divided intofour groups.
(1) Linear bimorphic piezomotors based on theflexural motion of bimorphic piezoelectric plates anddisks that are attached at their contour.
(2) Linear bimorphic piezomotors with hydraulicamplifying or mechanical transmissions for consider�able displacement of the working component.
(3) Bimorphic piezomotors for angular motion ofmirrors by means of the flexural motion of bimorphs(Fig. 5).
(4) Torsional vibratory bimorphic piezomotorsbased on piezocomponents that are sensitive to surfaceshear.
The selection of a particular class of motorsdepends on the required range of motion, precision,load capacity, and speed of the executive motor for theprecision electromechanical system. All the classes areused in nanotechnology, microelectronics, and adap�tive optics.
Vibrational piezomotors are structurally simple,technologically convenient, and characterized by awide range of motion and by high precision. For linearvibrational piezomotors, the range of motion is tens ofmm, with an error no greater than 100 nm. A signifi�cant deficiency is the wear of the frictional surfaces inthe motor, which impairs its operational reliability.
Vibrational piezomotors can develop a torque of25 N cm and shaft power of around 10 W. Their powermay be further increased by improvements in piezoce�ramic and wear�resistant materials.
Bimorphic piezomotors are structurally simple andeasy to manufacture. Their range is a few hundredmicrons. Their rigidity is low and their load capacity isless than 10 N.
For step motors, the range is tens of mm, with anerror of a few nm. The load capacity is more than100 N. Deficiencies include relatively small transmis�sion band (≤5 Hz), problems in ensuring stable andprecise supporting surfaces of the restraints, changes
in the step due to wear and cold working of the fric�tional surfaces, and complexity of the design and con�trol system. The benefits are that lubrication is unnec�essary and operation in vacuum is a possibility.
The range of force�based piezomotors is tens ofmicrons; their sensitivity is ≤10 nm V–1, their loadcapacity is 1000 N, the power at the output shaft isaround 100 W, and the transmission band is around100 Hz.
Force�based piezomotors are the best option forprecision servo systems used to adjust the surface ofthe primary mirrors in large telescopes and for adjust�ments in optomechanical equipment that combinesnanotechnology and microelectronics (where the lin�ear range is no more than tens of microns and theangular range is tens of angular seconds, with errors nogreater than tenths of a nm and tenths of an angularsecond, respectively, while the transmission band istens of Hz and the load capacity is 1000 N). Suchmotors comply fully with the requirements on the dis�
21
Fig. 3. Composite force�based piezomotor: (1) compositepiezoconverter; (2) body being moved.
3
4 5
61
2
Fig. 4. Step piezomotor: (1) piezoconverter; (2–5) exter�nal restraints; (6) output shaft.
1
2
3
Fig. 5. Bimorphic piezomotor for angular motion:(1) bimorphic piezoplate; (2) mirror; (3) base.
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placement, precision, speed, load capacity, and struc�ture for such applications.
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