Abstract:
A piezoelectric motor having a stator in which piezoelectric elements are contained in slots formed in the stator transverse to the desired wave motion. When an electric field is imposed on the elements, deformation of the elements imposes a force perpendicular to the sides of the slot, deforming the stator. Appropriate frequency and phase shifting of the electric field will produce a wave in the stator and motion in a rotor. In a preferred aspect, the piezoelectric elements are configured so that deformation of the elements in direction of an imposed electric field, generally referred to as the d 33  direction, is utilized to produce wave motion in the stator. In a further aspect, the elements are compressed into the slots so as to minimize tensile stresses on the elements in use.

Description:
The United States Government has rights in this invention pursuant to contract number DE-AC04-76-DP00613 with the United States Department of Energy. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to piezoelectric motors. More particularly, the present invention relates to a unique configuration for mounting piezoelectric elements in a piezoelectric wave motor. 
     2. Description of Related Art 
     Piezoelectric motors are utilized in a wide variety of applications in modern society, such as autofocusing camera lenses and automatic control units for window blinds. Piezoelectric motors are particularly well-suited for any application which requires a motor having a compact size (e.g. as small as the size of a fingertip), quiet operation, high torques at low speeds, quick response, and/or which is not effected by magnetic fields. 
     A typical design of an existing piezoelectric motor is shown in FIG. 1 designated by reference numeral  10 . Motor  10  is a rotary motor that includes a disk-shaped stator  12  having a comb-tooth top surface  14  and a flat bottom surface  16 . Motor  10  also includes a thin piezoelectric ring  18 , which is bonded to bottom surface  16  of stator  12  with an adhesive material, such as an epoxy resin. Dispersed around ring  18  are individual segments of piezoelectric ceramic which have been electrically poled in alternating opposite directions (indicated by “+” and “−”) along an axis of poling which is perpendicular to the plane of stator  12 . 
     Piezoelectric motor  10  further includes a disk-shaped rotor  20 , here shown as a geared rotor, which, together with stator  12  and piezoelectric ring  18  bonded to the stator, are mounted onto a shaft  22  which extends upwardly from the center of a rigid base  24 . A spring washer  26 , bearing  28 , and e-clip  30  function to hold rotor  20  in pressure contact with top surface  14  of stator  12 . A thin friction liner  32  is placed between stator  12  and rotor  20  to reduce sliding, energy losses during the operation of motor  10 . (It is known in the art to attach friction liners to rotors and further references to rotors herein will be understood to include a possible friction liner.) 
     A high frequency a.c. voltage drive source  34  is also provided to drive motor  10 . A first electrical lead  36  supplies a first a.c. voltage signal (typically, V o  sin ωt) to a first set of poled segments on ring  18 , and a second electrical lead  38  supplies a second a.c. voltage signal (V o  cos ωt) to a second set of poled segments on ring  18 , which are displaced along the stator from the first set as is known in the art. A third electrical lead  40  is connected to ground. 
     In operation, the a.c. voltage signals from drive source  34  cause the poled segments of piezoelectric material in ring  18  to expand and contract in such a manner that a traveling wave is generated in stator  12 . The comb-tooth top surface  14  of stator  12  amplifies this traveling wave, and the crests of the amplified traveling wave move in an elliptical motion such that a tangential force is created at the wave crests. As the wave crests contact rotor  20 , this tangential force causes movement of rotor  20  to thereby drive motor  10 . 
     Motor  10  has all of the desirable features which are generally associated with piezoelectric motors (e.g. compact size, quiet operation, high torques at low speeds, quick response, and not effected by magnetic fields); however, there are still several shortcomings associated with the design and operation of motor  10 . 
     First, the expansions and contractions of the individual segments (i.e., individual piezoelectric ceramics—typically referred to as elements) of ring  18  create alternating tensile and compressive stresses in the elements. Because piezoelectric elements are ceramics, and are typically weak in tension, these alternating tension stresses promote the growth of cracks within the elements. Over time, these cracks will decrease motor reliability and may eventually lead to the failure of motor  10 . 
     Second, motor  10  is driven by the expansions and contractions of the poled segments of piezoelectric element ring  18 , which expansions and contractions are transverse to the element&#39;s axis of poling. (Expansions and contraction transverse to the piezoelectric element&#39;s axis of poling are commonly referred to as being in the “d 31  direction”). It is well known in the art that expansions and contractions parallel to the element&#39;s axis of poling (commonly referred to as the “d 33  direction”) are approximately twice the magnitude of those in the d 31  direction for a given electrical field. Thus, motor  10  does not fully utilize the piezoelectric properties of the elements. 
     Third, in order to transmit forces to the stator  12 , piezoelectric element ring  18  is directly bonded to stator  12  such that shear stress is placed on the bond as the segments of ring  18  expand and contract in such a manner that a traveling wave is generated in stator  12 . Over time, this shear stress on the bond between ring  18  and stator  12  may lead to the failure of motor  10 . 
     SUMMARY OF THE INVENTION 
     Accordingly, it is an object of this invention to provide a piezoelectric motor in which the mounting of the piezoelectric elements is configured to reduce operating stresses in the piezoelectric elements by reduction of tensile stresses in the elements, shear stresses in the element bond, or both. It is a further object of this invention to provide a piezoelectric motor in which deformation of piezoelectric elements in the d 33  direction may be utilized to produce motion. 
     In order to address these objects, the present invention utilizes a series of slots formed in the stator transverse to the desired wave motion. Piezoelectric elements are contained within these slots. Upon imposing an appropriate electric field, the elements deform, exerting forces perpendicular to the sides of the slots (i.e., in the direction of the desired wave motion). Because the elements so mounted impart forces resulting from their deformation in a direction perpendicular to the surface of the slots, shear forces imposed upon the elements are minimized or eliminated. 
     In a preferred aspect of the invention, piezoelectric elements contained in slots may be compressively fitted into the slots in the stator. Because the elements have an initial resting compression, the magnitude of tension experienced by these elements in operation is minimized or eliminated. Further, the elements may be compressed to such an amount that no tensile forces exist in the elements during operation. 
     In another preferred aspect, the piezoelectric elements contained in slots may be operated in the d 33  mode. Operation in this mode maximizes the deformation achieved from an element for a given electric field, thus maximizing relative motion of the stator. 
     In a further preferred aspect, the individual piezoelectric elements contained in slots are stacked together to form what will be referred to as piezoelectric stacks. As the term is used herein, a piezoelectric stack consists of a plurality of piezoelectric elements mechanically connected side-to-side, with the elements being poled and electrically connected so that when an electric field is imposed, the deformation of the stacked elements is additive. Stacking may readily be accomplished where the elements are operated in the d 33  mode so that contiguous portions of adjacent elements may be electrically connected (operated at the same potential). 
     In one aspect, the present invention may be a rotary piezoelectric motor having a design similar to the motor illustrated in FIG. 1, with the exception that the stator and piezoelectric element ring are replaced with a new stator and utilizing piezoelectric stack assemblies. The replacement stator and piezoelectric stack assemblies of the present invention generally comprise a stator, typically disk-shaped with a generally circular surface, the stator having a plurality of levers dispersed along and extending outwardly from the periphery of the stator surface. (As used herein, levers are projections either affixed or bonded to the stator or consist of part of the stator cut or formed into the stator material.) These levers define a plurality of slots between the levers, the slots extending along radials from the axis of the stator (i.e., transverse to the desired motion). Mounted within each of these slots is a piezoelectric element or stack. 
     In operation, the stacked piezoelectric elements expand and contract within the slots and act upon the levers in such a manner that a wave is generated in the stator. As with existing piezoelectric wave motors, the crests of the wave move in an elliptical motion such that a tangential force is created at the wave crests. As the wave crests contact the rotor, the tangential force causes movement of the rotor to thereby drive the piezoelectric motor. Wave motion in typical piezoelectric wave motors is a travelling wave, however the present invention also includes standing wave motors producing an elliptical motion at the crests of the waves. 
     The piezoelectric motor of the present invention is described below with regard to several specific embodiments of the stator and piezoelectric stack assembly, together referred to as a stator-piezoelectric stack assembly. It should be understood, however, that these embodiments are provided to show the variety of stator and/or piezoelectric stack configurations that can be utilized in a particular application, and are not intended to limit the scope of the present invention. 
    
    
     The present invention will be better understood from the following description of the invention, read in connection with the drawings described below. 
     DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is an exploded perspective view of an existing rotary piezoelectric motor. 
     FIGS. 2A and 2B are perspective views of a first embodiment of a stator-piezoelectric stack assembly of the present invention, shown from the rotor side, conveniently referred to as “upright” and inverted positions respectively, wherein the piezoelectric stacks are fixedly attached between inwardly tapering levers on the bottom surface of the stator. FIG. 2B also shows the wiring configuration for the stator and piezoelectric stacks. 
     FIG. 3 is a perspective view of an alternative embodiment of the stator-piezoelectric stack assembly of the present invention, shown in the inverted position, wherein the piezoelectric stacks are fixedly attached between untapered levers on the bottom surface of the stator. 
     FIG. 4 is a fragmentary side view of another alternative embodiment of the stator-piezoelectric stack assembly of the present invention, wherein the piezoelectric stacks are fixedly attached between downwardly tapering levers on the bottom surface of the stator. 
     FIG. 5 is a fragmentary side view of another alternative embodiment of the stator-piezoelectric stack assembly of the present invention, wherein the piezoelectric stacks are fixedly attached between upwardly tapering levers on the bottom surface of the stator. 
     FIG. 6 is a fragmentary side view of another alternative embodiment of the stator-piezoelectric stack assembly of the present invention, wherein flat end caps attached to the end surfaces of the piezoelectric stacks are utilized to fixedly attach the piezoelectric stacks between levers on the bottom surface of the stator. 
     FIG. 7 is a fragmentary side view of another alternative embodiment of the stator-piezoelectric stack assembly of the present invention, wherein rounded end caps attached to the end surfaces of the piezoelectric stacks are utilized to fixedly attach the piezoelectric stacks between levers on the bottom surface of the stator. 
     FIG. 8 is a fragmentary perspective view of another alternative embodiment of the stator-piezoelectric stack assembly of the present invention, wherein end caps attached to the end surfaces of the piezoelectric stacks are utilized to screw the piezoelectric stacks into levers on the bottom surface of the stator. 
     FIG. 9 is a fragmentary perspective view of another alternative embodiment of the stator-piezoelectric stack assembly of the present invention, wherein end caps attached to the end surfaces of the piezoelectric stacks are screwed into levers on the bottom surface of the stator with a pair of side screws. 
     FIG. 10 is a fragmentary perspective view of another alternative embodiment of the stator-piezoelectric stack assembly of the present invention, wherein end caps attached to the end surfaces of the piezoelectric stacks are utilized to fit the piezoelectric stacks into dimples formed in levers on the bottom surface of the stator. 
     FIG. 11 is a fragmentary side view of another alternative embodiment of the stator-piezoelectric stack assembly of the present invention, wherein the piezoelectric stacks are fixedly attached between the teeth on the top surface of the stator. 
     FIG. 12 is a fragmentary side view of another alternative embodiment of the stator-piezoelectric stack assembly of the present invention, wherein thin bar-shaped piezoelectric elements are stacked on top of each other and fixedly attached between levers on the bottom surface of the stator. 
     FIG. 13 is a partial top view of a typical wiring configuration for the stator-piezoelectric stack assembly of FIG.  11 . 
     FIGS. 14A and 14B,  15 A and  15 B, and  16 A and  16 B are finite-element-analysis plots showing the deflection when various amounts of piezoelectric material are bonded to the bottom surface of a segment of stator material. 
     FIGS. 17A and 17B are finite-element-analysis plots showing the deflection when piezoelectric material is bonded between levers extending outwardly from the bottom surface of stator material. 
    
    
     DETAILED DESCRIPTION 
     Referring to FIGS. 2A and 2B, an embodiment of the stator-piezoelectric stack assembly is designated generally as reference numeral  100 , wherein FIG. 2A illustrates assembly  100  in its original upright position and FIG. 2B illustrates assembly  100  in an inverted position. 
     Assembly  100  includes a disk-shaped stator  102  having a generally circular top surface  104  (see FIG. 2A) and a generally circular bottom surface  106  (see FIG.  2 B). Cut into top surface  104  of stator  102  are a plurality of comb-like teeth  108  which are uniformly dispersed around and extend upwardly from the periphery of top surface  104 . As is known in the art, teeth  108  function to amplify the traveling wave generated in stator  102  during the operation of the piezoelectric motor. Similarly, projecting from the bottom surface  106  of stator  102  are a plurality of levers  1   10  which are uniformly dispersed around and extend downwardly from the periphery of bottom surface  106 . In this embodiment, levers  110  taper inwardly from an outer surface  112  to an inner surface  113  such that the sidewalls  114  of levers  110  define a plurality of slots  116  between the levers  110  which have a constant width. Stator  102  can be formed of any material with low frictional damping losses, and is preferably a conductive metal such as titanium alloy, stainless steel or phosphor bronze. The stator may advantageously also be formed of a shape memory alloy so as to facilitate compressive preloading of the piezoelectric stack assemblies. 
     Assembly  100  also includes a plurality of piezoelectric stacks  118 , each of which consists of identical piezoelectric elements  120 , typically cube-shaped, which have been stacked together and tightly pressed into slots  116  between levers  110  of stator  102 . By pressing piezoelectric stacks  118  between levers  110 , an initial compressive stress is induced in piezoelectric elements  120  to prevent them from experiencing tensile stresses during operation of the piezoelectric motor. Although the friction fit between piezoelectric stacks  118  and levers  110  would likely secure stacks  118  in place, stacks  118  are preferably captured between levers  110  by epoxy bonding, soldering, diffusion bonding, or otherwise fixedly attaching the end surfaces  122  of piezoelectric stacks  118  to sidewalls  114  of levers  110 . Piezoelectric elements  120  can be formed of any piezoelectric material, and are preferably formed of PZT (i.e. any material that is created from Pb(Zr—Ti)O 3 ). 
     The number of piezoelectric stacks mounted between the levers of the stator is generally equal to four times the number of wavelengths chosen for the traveling wave generated in the stator (i.e. the number of contact points upon which the rotor rests). For example, in the embodiment illustrated in FIG. 2B, twelve piezoelectric stacks  118  will generate a three-wavelength traveling wave in stator  102  (i.e. three contact points upon which the rotor rests). For stability reasons, it is generally preferred to have at least a three-wavelength motor; however, there is no particular maximum number of wavelengths, which could be utilized in accordance with the present invention. Rather, the number of wavelengths chosen for a particular embodiment would be determined by a number of design factors which are familiar to one skilled in the art. 
     In addition, any number, preferably an even number, of individual piezoelectric elements can be stacked together to form a piezoelectric stack. In the embodiment illustrated in FIG. 2B, four individual piezoelectric elements  120  are stacked together and, preferably, tightly pressed between levers  110  of stator  102 . As is known in the art, the voltage required to drive a piezoelectric motor is directly proportional to the thickness of the individual piezoelectric elements. In this regard, it may be preferable to use a larger number of thin piezoelectric elements so that a lower driving voltage can be used. However, a larger number of piezoelectric elements results in a larger number of electrical leads needed to connect the elements to a drive source. Therefore, the optimum number of individual piezoelectric elements chosen for a particular embodiment must balance the voltage requirements against the complexity of the wiring configuration. 
     Looking again to FIG. 2B, piezoelectric stacks  118  have been electrically poled along an axis of poling which is perpendicular to sidewalls  114  of levers  110 . In the illustrated embodiment, two piezoelectric stacks  118  having the same polarity are followed by two piezoelectric stacks having the opposite polarity, wherein the “+” and “−” signs designate the direction of poling for each individual piezoelectric element  120 . It should be noted that the poling of piezoelectric elements  120  is preferably done before elements  120  are stacked together and pressed between levers  110  of stator  102 . 
     As with existing rotary piezoelectric motors, a high frequency a.c. voltage source (which consists of two a.c. voltage signals having a 90° phase shift between the signals) is provided to drive the piezoelectric motor. As illustrated in FIG. 2B, a first a.c. voltage signal (typically V o  sin ωt) and a second a.c. voltage signal (V o  cos ωt) are applied to piezoelectric stacks  118  in an alternating manner such that every other stack is connected to V o  sin ωt and every other stack is connected to V o  cos ωt. These signals preferably are applied to a thin metallization layer placed between the first/second and third/fourth elements of each piezoelectric stack  118 . In addition, it should be noted that stator  102  is electrically grounded, and piezoelectric elements  120  are grounded to stator  102  by connecting the appropriate leads and end surfaces of each piezoelectric stack  118  to stator  102 . 
     It should be apparent that all of the piezoelectric stacks which have the same polarity and are driven by the same a.c. voltage signal will expand and contract together during operation of the piezoelectric motor. In other words, all of the stacks which have a positive polarity and are driven by V o  sin ωt will expand and contract together, all of the piezoelectric stacks which have a positive polarity and are driven by V o  cos ωt will expand and contract together, all of the piezoelectric stacks which have a negative polarity and are driven by V o  sin ωt will expand and contract together, and all of the piezoelectric stacks which have a negative polarity and are driven by V o  cos ωt will expand and contract together. 
     In operation, these alternating expansions and contractions cause piezoelectric stacks  118  to press against levers  110  in such a manner that a wave is generated in stator  102 . As with existing piezoelectric wave motors, the crests of the wave generated in stator  102  move in an elliptical motion such that a tangential force is created at the wave crests. As the wave crests contact the rotor, the tangential force causes movement of the rotor to thereby drive the piezoelectric motor. 
     Significantly, the embodiment of the stator-piezoelectric stack assembly described and illustrated above overcomes all of the above-cited shortcomings associated with existing rotary piezoelectric motors. 
     First, piezoelectric stacks  118  may be pressed between levers  110  such that an initial compressive stress is induced in piezoelectric elements  120 . Thus, when a piezoelectric stack  118  contracts during operation of the piezoelectric motor, the initial compressive stress in piezoelectric elements  120  will reduce the magnitude of tension experienced in the element. If sufficiently pre-compressed, elements  120  will never go into tension. As such, the reliability and life span of the piezoelectric motor will substantially increase. 
     Second, piezoelectric elements  120  may be electrically poled along an axis of poling which is perpendicular to sidewalls  114  of levers  110 . And, the expansions and contractions of piezoelectric elements  120  which are parallel to the axis of poling (i.e. in the d 33  direction) are utilized to act upon sidewalls  114  of levers  110  to generate a traveling wave in stator  102 . Therefore, the piezoelectric properties of piezoelectric elements  120  may be more fully utilized. 
     Third, piezoelectric stacks  118  act upon levers  110  either directly or through an axial compression of the bond between end surfaces  122  of stacks  118  and sidewalls  114  of levers  110 . This method of translating force from piezoelectric stacks  118  to stator  102  is much more efficient than the shear loading of the bond of existing motors and, as such, the reliability and life span of the piezoelectric motor will substantially increase. 
     Various alternative embodiments of the stator-piezoelectric stack assembly of the present invention are illustrated in FIGS. 3-12. Specifically, FIGS. 3-5 illustrate alternative embodiments in which the inwardly tapering levers of the embodiment shown in FIG. 2 have been replaced with other lever configurations, FIGS. 6-10 illustrate alternative embodiments in which end caps are attached to the end surfaces of the piezoelectric stacks, FIG. 11 illustrates an alternative embodiment in which the stator of the embodiment shown in FIG. 2 has been replaced with a stator having the same design as that of existing rotary piezoelectric motors, and FIG. 12 illustrates an alternative embodiment in which the cube-shaped piezoelectric elements of the embodiment shown in FIG. 2 have been replaced with thin bar-shaped piezoelectric elements which have been stacked on top of each other and pressed between the levers of the stator. Unless otherwise noted, all of these alternative embodiments overcome the above-cited shortcomings associated with existing rotary piezoelectric motors. 
     Referring to FIG. 3, a first alternative embodiment of the stator-piezoelectric stack assembly, illustrated in an inverted position, is designated generally as reference numeral  200 . Assembly  200  has the same design as assembly  100  of the embodiment shown in FIG. 2, with the exception that inwardly tapering levers  110  have been replaced with levers  210  which are not tapered (i.e. have a constant width) and piezoelectric stacks  118  have been replaced with inwardly tapering piezoelectric stacks  218 . In the embodiment illustrated in FIG. 3, each piezoelectric stack  218  consists of two identical inner cube-shaped piezoelectric elements  220   a  and two inwardly tapering outer piezoelectric elements  220   b  which are stacked together and tightly pressed between levers  210 . 
     Referring to FIG. 4, a fragmentary view of a second alternative embodiment of the stator-piezoelectric stack assembly is designated generally as reference numeral  300 . Assembly  300  has the same design as assembly  100  of the embodiment shown in FIG. 2, with the exception that inwardly tapering levers  110  have been replaced with downwardly tapering levers  310  and piezoelectric stacks  118  have been replaced with upwardly tapering piezoelectric stacks  318 . In the illustrated embodiment, each piezoelectric stack  318  consists of eight identical inner cube-shaped piezoelectric elements  320   a  and two upwardly tapering outer piezoelectric elements  320   b  which are stacked together and tightly pressed between levers  310 . 
     Referring to FIG. 5, a fragmentary view of a third alternative embodiment of the stator-piezoelectric stack assembly is designated generally as reference numeral  400 . The design of assembly  400  is simply an inversion of the design of assembly  300  illustrated in FIG. 4, wherein downwardly tapering piezoelectric stacks  418  are tightly pressed between upwardly tapering levers  410 . In the illustrated embodiment, each piezoelectric stack  418  consists of eight identical inner cube-shaped piezoelectric elements  420   a  and two downwardly tapering outer piezoelectric elements  420   b  which are stacked together and tightly pressed between levers  410 . 
     Referring to FIG. 6, a fragmentary view of a fourth alternative embodiment of the stator-piezoelectric stack assembly is designated generally as reference numeral  500 . Assembly  500  has the same design as assembly  100  of the embodiment shown in FIG. 2, with the exception that piezoelectric stacks  118  have been replaced with piezoelectric stacks  518  which have flat metal end caps  522  fixedly attached to the end surfaces of the stacks  518 . In the illustrated embodiment, each piezoelectric stack  518  consists of six identical inner piezoelectric elements  520  and two flat end caps  522  which are stacked together and tightly pressed between levers  510 . End caps  522  can be formed of any rigid material known in the art, and are preferably formed of a low damping metal commonly used in piezoelectric motor stator and rotor applications, such as phosphor-bronze and titanium alloys. In addition, end caps  522  could be formed of a shape memory alloy which would allow piezoelectric stacks  518  to be tightly fitted between levers  510 . 
     Referring to FIG. 7, a fragmentary view of a fifth alternative embodiment of the stator-piezoelectric stack assembly is designated generally as reference numeral  600 . Assembly  600  has the same design as assembly  500  illustrated in FIG. 6, with the exception that each of the piezoelectric elements  620  has a generally disk shape (see FIG. 8-10) and both of the end caps  622  are rounded. Of course, other end cap configurations (e.g. tapered or chamfered) could also be used in accordance with the present invention. 
     Referring to FIG. 8, a fragmentary view of a sixth alternative embodiment of the stator-piezoelectric stack assembly is designated generally as reference numeral  700 . Assembly  700  has the same design as assembly  600  illustrated in FIG. 7, with the exception that threaded extensions  724  projecting outwardly from the end caps  722  are utilized to screw piezoelectric stacks  718  into corresponding holes formed in the levers  710 . It should be noted that assembly  700  is expected to be particularly well-suited for larger-size piezoelectric motors. 
     Referring to FIG. 9, a fragmentary view of a seventh alternative embodiment of the stator-piezoelectric stack assembly is designated generally as reference numeral  800 . Assembly  800  has the same design as assembly  700  illustrated in FIG. 8, with the exception that the extensions  824  projecting outwardly from end caps  822  are configured to be inserted into slots  826  formed in the levers  810 . To secure piezoelectric stacks  818  to levers  810 , a pair of threaded side screws  828  are provided which can be screwed through holes  830  formed in extensions  824  and into corresponding holes  832  formed in levers  810 . Again, assembly  800  is expected to be particularly well-suited for larger-size piezoelectric motors. 
     Referring to FIG. 10, a fragmentary view of an eighth alternative embodiment of the stator-piezoelectric stack assembly is designated generally as reference numeral  900 . Assembly  900  has the same design as assembly  700  illustrated in FIG. 8, with the exception that the extensions  824  projecting outwardly from end caps  922  are configured to be fitted within dimples formed in the sidewalls  914  of levers  910 . As such, piezoelectric stacks  918  are securely held in place between levers  910 . Again, assembly  900  is expected to be particularly well-suited for larger-size piezoelectric motors. 
     Referring to FIG. 11, a fragmentary view of a ninth alternative embodiment of the stator-piezoelectric stack assembly is designated generally as reference numeral  1000 . Assembly  1000  includes a stator  1002  which has the same design as the stators of existing rotary piezoelectric motors, namely, a comb-tooth top surface  1004  and a flat bottom surface  1006 . A plurality of piezoelectric stacks  1018  are mounted between the teeth  1008  on top surface  1004  of stator  1002 , wherein teeth  1008  function in the same manner as the levers on the bottom surface of the stators described above. In the illustrated embodiment, each piezoelectric stack  1018  consists of two identical piezoelectric elements  1020  which are stacked together and tightly pressed between teeth  1008 . 
     FIG. 13 illustrates a typical wiring configuration for a one-third section of assembly  1000 . Piezoelectric stacks  1018  are divided into four-stack sections such that two sections having a positive polarity (as indicated by the “+” sign) are followed by two sections having a negative polarity (as indicated by the “−” sign). A first a.c. voltage signal (typically V o  sin ωt) and a second a.c. voltage signal (V o  cos ωt) are applied to the four-stack sections in an alternating pattern such that every other section is connected to V o  sin ωt and every other section is connected to V o cos ωt. As in the embodiment shown in FIG. 2, stator  1002  is electrically grounded, and piezoelectric elements  1020  are grounded to stator  1002  by connecting the end surfaces of each piezoelectric stack  1018  to stator  1002 . It should be noted that a number of schemes are known in the art to produce the voltage signals to drive these piezoelectric wave motors. The specific schemes need not be discussed here. 
     Referring to FIG. 12, a fragmentary view of a tenth alternative embodiment of the stator-piezoelectric stack assembly is designated generally as reference numeral  100 . Assembly  1100  has the same design as assembly  100  of the embodiment shown in FIG. 2, with the exception that the individual cube-shaped piezoelectric elements  120  have been replaced with thin bar-shaped piezoelectric elements  1120  which are stacked on top of each other and tightly pressed between the levers  1110  of the stator  1102 . Piezoelectric elements  1120  are preferably captured between levers  1110  by epoxy bonding, soldering, diffusion bonding, or otherwise fixedly attaching the end surfaces of piezoelectric elements  1120  to the sidewalls of levers  1110 . In this embodiment, however, the expansions and contractions of piezoelectric elements  1120  which are transverse to the element&#39;s axis of poling (i.e. in the d 31  direction) are utilized to generate a traveling wave in stator  1102 . 
     It is also noted that a schemes for driving piezoelectric motors, similar to the travelling wave embodiments shown here, have been developed using standing waves, but with stator tooth configuration and element placement configured to produce elliptical motion in the teeth to drive the rotor. As would be apparent to one skilled in the art, the present invention is adapted to be utilized in such standing wave motors. 
     Further, although rotary piezoelectric motors are the most common form of piezoelectric wave motors and the above embodiments show rotary piezoelectric wave motors, it is known that linear and other non-circular shapes piezoelectric motors may use wave motion to drive a rotor. Such motors include continuous loop motors as well as linear motors without a return loop. The present invention, including the unique stator and piezoelectric stack assemblies disclosed, are applicable to the various non-rotary piezoelectric wave motor designs utilizing non-circular stators and rotors. 
     Finite Element Analysis 
     In order to verify that the expansions and contractions of the piezoelectric stacks will generate a traveling wave in the stator of the rotary piezoelectric motor of the present invention, a computer simulation in the form of a finite element analysis (FEA) was performed to simulate the amount of deflection in various beams, which will be described below. FIGS. 14,  15  and  16  illustrate beams which were designed in accordance with existing rotary piezoelectric motors, and FIG. 17 illustrates a beam which was designed in accordance with the rotary piezoelectric motor of the present invention. 
     FIGS. 14A and 14B simulate an existing rotary piezoelectric motor, wherein a thin piezoelectric element ring is bonded to the bottom surface of a stator. Specifically, FIG. 14A is an FEA plot of a beam  50  consisting of 1 row by 2 columns of piezoelectric ceramic material  52  (i.e. 60 “cubes”) bonded to the bottom of 3 rows by 2 columns of stator material  54  (i.e. 180 “cubes”). When a voltage V was applied across beam  50 , it deflected as shown in FIG.  14 B. The magnitude of this deflection was 0.380e−1. 
     FIGS. 15A and 15B simulate an existing rotary piezoelectric motor, wherein a slightly thicker piezoelectric element ring is bonded to the bottom surface of a stator. Specifically, FIG. 15A is an FEA plot of a beam  60  consisting of 2 rows by 2 columns of piezoelectric element material  62  (i.e. 120 “cubes”) bonded to the bottom of 3 rows by 2 columns of stator material  64  (i.e. 180 “cubes”). When a voltage V was applied across beam  60 , it deflected as shown in FIG.  15 B. The magnitude of this deflection was 0.433e−1. Thus, even though beam  60  utilized twice as much piezoelectric element material as beam  50 , there was only a marginal increase in deflection. 
     FIGS. 16A and 16B simulate an existing rotary piezoelectric motor, wherein an even thicker piezoelectric element ring is bonded to the bottom surface of a stator. Specifically, FIG. 16A is an FEA plot of a beam  70  consisting of 3 rows by 2 columns of piezoelectric element material  72  (i.e. 180 “cubes”) bonded to the bottom of 3 rows by 2 columns of stator material  74  (i.e. 180 “cubes”). When a voltage V was applied across beam  70 , it deflected as shown in FIG.  16 B. The magnitude of this deflection was 0.398e−1. Thus, even though beam  70  utilized three times as much piezoelectric element material as beam  50 , there was only a marginal increase in deflection. And, even though beam  70  utilized one and one-half times as much piezoelectric element material as beam  60 , there was actually a decrease in deflection. Therefore, it can be seen that an increase in the amount of piezoelectric element material does not always result in an increase in deflection. In fact, for the existing rotary piezoelectric motor simulations, the optimum amount of piezoelectric element material was that of beam  60 . 
     FIGS. 17A and 17B simulate the rotary piezoelectric motor of the present invention, wherein piezoelectric stacks are pressed between levers extending downwardly from the bottom surface of a stator. Specifically, FIG. 17A is an FEA plot of a beam  80  consisting of 3 rows by 2 columns of piezoelectric element material  82  (i.e. 156 “cubes”) bonded to the bottom of 3 rows by 2 columns of stator material  84  (i.e. 180 “cubes”) and between two “levers” of 3 rows by 2 columns of stator material  86  (i.e. 12 “cubes” per lever). When a voltage V was applied across beam  80 , it deflected as shown in FIG.  17 B. The magnitude of this deflection was 0.857e−1. Thus, even though beam  80  utilized less piezoelectric element material than beam  70 , the deflection of beam  80  more than doubled. As a result, it is anticipated that the rotary piezoelectric motor of the present invention will be capable of generating substantially more torque than existing piezoelectric motors, due in large part to the utilization of the expansions and contractions of the individual piezoelectric elements in the d 33  direction. Of course, as with the design of existing rotary piezoelectric motors, there will be an optimum amount of piezoelectric element material which will generate the greatest deflection in beam  80 . 
     Although the rotary piezoelectric motor of the present invention has been described and illustrated with regard to specific embodiments, it should be understood that various modifications of the stator and/or piezoelectric stack design are possible without departing from the scope of the present invention. Therefore, the present invention is not to be limited to these embodiments, except insofar as such limitations are included in the following claims.