the following terminology and definitions apply as used in the present application . the phrase “ inhomogeneous resonator ” refers to a component , such as for example , but not limitation , a rod , bar , spring , with a non - uniform cross sectional region that generates torsional and longitudinal motion . in some embodiments , an inhomogeneous resonator is a spiral spring or a twisted bar . in other embodiments , a inhomogeneous resonator is a rod with one or more slots . the phrase “ piezoelectric stack ” means a two or more piezoelectric elements , such as for example , but not limited to , piezoelectric rings , electrically connected in parallel , which are stacked or held in compression by a bolt or other means . a piezoelectric stack can optionally have an endmass coupled to one or both of the outer piezoelectric elements . the present invention is directed to ultrasonic transducer subassemblies and systems designed to operate in torsional modes of vibration or l - t modes of vibrations and , more particularly , to those used for surgical , dental , and industrial welding applications . methods and devices employing ultrasonic torsional or l - t mode transducers subassemblies and systems in accordance with the present invention may incorporate one or more of the features , structures , methods , or combinations thereof described herein below . for example , but not limited to , ultrasonic l - t mode transducers can be designed to include one or more of the features and / or processes described below . it is intended that such a device or method need not include all of the features and functions described herein , but may be implemented to include one or more features and functions that , alone or in combination , provide for unique structures and / or functionality . one aspect of the invention provides piezoelectric transducer subassemblies and systems comprising an inhomogeneous resonator between two piezoelectric stacks , for simplicity the first embodiment is best illustrated by initially considering the mode of operation of a subassembly prior to the attachment of a horn as shown in fig6 . in fig6 piezoelectric stacks 601 and 602 are coupled to a resonator 603 that comprises an inhomogeneous cross section region including one or more slots 625 . this inhomogeneous resonator performs a helical spring function by converting longitudinal motion to torsional motion . any component that allows for this converting longitudinal motion to torsional motion can be used . some non - limiting examples of inhomogeneous resonators include a spiral spring or a twisted bar . in other embodiments , a inhomogeneous resonator is a rod with one or more slots . piezoelectric stack 601 contains piezoelectric elements , e . g ., rings 607 that are electrically connected in parallel and have their negative poles at ground potential . there can be any even number of piezoelectric elements 607 that are stacked together and held in compression by bolt 610 . piezoelectric stack 602 contains piezoelectric elements 608 that are electrically connected in parallel and have their positive poles at ground potential . in one preferred embodiment , piezoelectric stack 602 has the same number of piezoelectric elements as piezoelectric stack 601 . in other embodiments , piezoelectric stack 602 has a different number of piezoelectric elements than piezoelectric stack 601 . piezoelectric elements 608 are stacked together and held in compression by bolt 610 . the components within the subassembly shown are generally of annular cross section . the subassembly is electrically connected to a generator 611 . in some embodiments , the metal components within piezoelectric stacks 601 and 602 are at ground potential as shown . in other alternate embodiments , electrical insulators such as alumina oxide ceramic rings ( not shown ) could be disposed between the distal and proximal ends of the stacks of piezoelectric elements 607 and 608 and end masses 605 and 606 . the generator can then be configured to operate in a manner whereby the output is isolated from ground potential . it is also possible that when the generator is isolated from ground potential that piezoelectric stack 601 can be electrically connected with reverse polarity with respect the polarity of piezoelectric stack 602 , thereby enabling the poles of the piezoelectric rings within each stack to be the same ( i . e . ), one piezoelectric stack operates with in - phase synchronism and the second piezoelectric stack operates with phase - opposite synchronism ). to determine the optimal configuration , the high power measurement instrumentation shown in fig7 was used . the torsional mode of vibration was measured at points signified by an * in fig8 . an end mill was used to machine a reflective surface approximately 1 mm in diameter that is perpendicular to the focused laser beam . the transducer subassembly 800 was compliantly mounted by means of teflon cradles 810 , 820 located at the positions shown . the laser vibrometer was used to measure the velocity at points a 8 , b 8 , c 8 , and d 8 . for each measurement the power was adjusted to 1 watt and the frequency fine tuned for maximum velocity ( at the 29 khz torsional resonance ). the displacements were calculated from the velocity and frequency measurements and the results are tabulated in table 1 . the results indicate that point b 8 is located very close to a node , defined as a region of minimum displacement . anti - nodes defined as regions of maximum displacement occur at point a 8 and close to point c 8 . the results also confirm that the longitudinal component of vibration is very small ( 0 . 4 μm p - p ). with the laser focused at point a , the frequency was swept over the range 5 khz to 70 khz in order to search for torsional resonances . the search procedure was repeated for longitudinal resonances with the laser focused at point d 8 . for each resonance frequency the power was adjusted to 1 watt and the velocity was measured using the laser vibrometer . a map of the relative intensity of the resonant modes is shown in fig9 . the transducer system was then reconfigured such that the negative poles of the piezoelectric rings were at ground potential for both piezoelectric stack 801 and piezoelectric stack 802 . the resonance search procedure for both torsional and longitudinal modes was repeated and a map of the relative intensity of the resonant modes is shown in fig1 . an analysis of the experimental data indicates that configuring piezoelectric stack 801 and piezoelectric stack 802 so that both piezoelectric stacks operate with in - phase synchronism suppresses the level longitudinal vibration over the frequency range of 5 khz to 70 khz . a relatively strong torsional mode was detected at 39 . 6 khz . configuring piezoelectric stack 801 and piezoelectric stack 802 such that one piezoelectric stack operates with in - phase synchronism and the second piezoelectric stack operates with phase - opposite synchronism ( i . e ., with reverse polarity ) is the preferred embodiment because it has the most efficient torsional mode at the lowest frequency ( 29 khz ). it can also be operated in a combined l - t mode at 50 khz . the subassembly &# 39 ; s relatively low measured torsional and longitudinal displacements can be amplified by attaching a horn as illustrated in fig1 . the bias bolt for piezoelectric stack 1102 can be an integral part of horn 1104 and is coupled ( for example , but not limited to threadingly engaged ) to end mass 1105 . the bias bolt 1110 applies a compressive force to the piezoelectric stack 1107 . piezo stacks 1107 and 1108 include a metal terminating washer 1106 . stacks 1107 and 1108 are coupled to a resonator 1103 that incorporates an inhomogeneous cross section region including one or more slots 1125 . horn 1104 is proximally coupled to piezoelectric stack 1102 . the horn is typically designed such that a cross section of the horn distal to the piezoelectric stack is smaller than a cross section proximal to the piezoelectric stack . the components within the assembly shown are generally of annular cross section with the exception of the end effector 1109 . for purposes of an illustrative example , flats were formed in order to facilitate the measurement of torsional velocity as shown in fig1 . the flats also help demonstrate functionality by coupling torsional mode energy into a fluid medium such as water . a laser vibrometer was used to measure both the longitudinal and torsional vibrations of the distal horn region 1209 . the laser beam at point a 12 was aligned with the longitudinal motion of the distal tip of the horn 1204 . the laser beam at point b 12 was perpendicular to the machined flats at the distal tip 1209 of the horn , illustrated in cross - section 1225 . the beam was adjusted such that it is focused off the axis rotation in order to measure the maximum torsional vibration . the high power performance of the transducer system shown in fig1 was measured using the instrumentation shown in fig7 . the input power was held constant at 1 watt and the frequency fine tuned for the maximum velocity measured by the laser vibrometer . a velocity map of the torsional and longitudinal resonant modes is shown in fig1 . the same measurement method was used for a more detailed analysis of the torsional mode at 31 . 7 khz . in all cases , the frequency was in the range 31 . 7 khz ± 0 . 1 khz . the transducer system shown in fig1 was electrically connected to the power source in 3 different configurations . initially , just piezoelectric stack 1101 was driven with piezoelectric stack 1102 not connected and left in an open circuit condition . following this , piezoelectric stack 1102 was driven with piezoelectric stack 1101 not connected and left in an open circuit condition . finally , both piezoelectric stacks were connected as shown in fig1 ( with one piezoelectric stack operating with in - phase synchronism and the second piezoelectric stack operating with phase - opposite synchronism ; i . e ., with piezoelectric stack 1101 having a reverse polarity with respect to piezoelectric stack 1102 ). the measured data is tabulated below in table 2 . the system with only piezoelectric stack 1101 is representative of the geometry used in prior art transducers , such as those illustrated by wuchinich in fig5 . the distal piezoelectric elements 1108 become passive components that form part of a modified resonator section . one aspect of this invention is based on the measured performance improvement when a resonator is sandwiched between two separate piezoelectric stacks ( system 1101 + 1102 ) in table 2 . for this configuration , the drive voltage was reduced as a result of lower impedance and a more favorable phase angle between the voltage and current . reducing the drive voltage to an absolute minimum improves patient safety for medical applications and improves reliability by reducing the risk of voltage breakdown . in yet further embodiments of this aspect of the invention , the horn is attached at a nodal position on torsional mode transducer systems . in u . s . pat . no . 3 , 681 , 627 , murry et al describes a method whereby the shaft of an operative tool is attached at a nodal position and reverses direction such that it passes back through the center of the transducer . the murry patent is limited , however , only to longitudinal modes of vibration . the present invention provides for configurations that are applicable for use with torsional mode transducers . the measured data relating to fig1 indicates the presence of a shear mode displacement node in the region distal to the inhomogeneous resonator section 1103 and proximal to piezoelectric stack 1102 . referring now to fig1 ; by anchoring a reverse direction torsional mode horn at the nodal location ns , the overall length of the transducer assembly can be reduced as shown . in fig1 , the piezoelectric elements 1507 are stacked together and held in compression by bolt 1510 . the bolt 1510 differs in the design illustrated in fig1 in that it has an annular hollow cross section . also , for this embodiment the piezoelectric elements 1507 and 1508 have a relatively large internal diameter such that horn 1512 can pass through the center of piezoelectric stack 1502 . stacks 1507 and 1508 are coupled to a resonator that incorporates an inhomogeneous cross section region including one or more slots 1525 . horn 1512 is attached at a torsional ( shear wave ) nodal location defined in fig1 as ns . the horn can be attached to the body of the transducer system by means known to those skilled in the art . examples include , by are not limited to , a threading engagement of the horn 1512 or by dimensioning the diameter of the horn 1512 and the hole in the transducer system to achieve an interference press fit . the length of the horn is typically one quarter wavelength with the physical length being related to the shear mode velocity and the frequency of operation . any number of additional half wavelength sections can be added to the length of the horn . a second aspect of this invention provides for piezoelectric transducer subassemblies and systems comprising an inhomogeneous resonator coupled proximal to a single piezoelectric stack . this design is based on the measured performance improvement when the torsional mode resonator is coupled proximal to a single piezoelectric stack ( 1102 only in table 2 ). by means of an illustrative example of the second aspect of this invention , an improved phacoemulsification transducer system design is compared with a prior art design geometry which is illustrated in fig1 a . this prior art transducer system design geometry has a longitudinal resonant frequency corresponding with an accumulated component length of one and a half wavelengths ( 1 . 5λ ). a central annular aspiration lumen extends along the entire length of the assembly and extends proximally as a tube 1401 and distally through a hollow needle 1406 . the rear mass 1402 is attached to piezoelectric rings that are stacked together and pre - compressed by a bolt section ( not shown ) that is an integral part of the rear mass 1402 and is threadingly engaged in front mass 1407 . when connected to an electrical generator , the piezoelectric ceramic stack provides the motive force and couples mechanical vibrations to front mass 1407 . front mass 1407 is mechanically attached to an inhomogeneous resonator section 1403 . the resonator has one or more slots , which performs a helical spring function and converts longitudinal motion to torsional motion . the resonator section 1403 is mechanically coupled to a velocity amplifying horn 1405 . solid horns are sometimes referred to as concentrators , rods , tools , and amplitude or velocity transformers . the horn illustrated has a stepped geometry with transitional radius but other geometries such as conical and exponential could be used . the distal tip of hollow needle is the end effector 1406 and is threadingly engaged in horn 1405 . for torsional out of plane motion , the distal end of the needle is bent such that torsional motion within the needle shaft is translated into transverse motion at the operative tip . the second aspect of this invention is illustrated in fig1 b . the design geometry has been changed from the prior art design discussed above , in that the transducer system has a longitudinal resonant frequency corresponding with a half wavelength ( λ / 2 ). the location of the inhomogeneous resonator 1403 has been changed such that it is coupled proximal to the piezoelectric stack 1403 . the rear mass 1407 in the prior art transducer has been eliminated . in this illustrative example of the invention , all the metal components were fabricated from 6al - 4v titanium alloy and the piezoelectric elements 1404 were fabricated from a generic navy type iii material . alternative materials for component manufacture include aluminum alloy for horn 1405 . alternate materials for the inhomogeneous resonator 1403 and end mass 1402 include aluminum alloy , stainless steel and beryllium copper . the inhomogeneous resonator could also be fabricated from fiberglass composite . alternative piezoelectric materials include those that conform to us navy type i specifications and also lead free materials such as barium titanate . the four piezoelectric elements 1404 are electrically connected in parallel and have an outside diameter of 12 mm an inside diameter of 5 mm and a thickness of 2 mm . for medical handpiece applications the outside diameter of the piezoelectric elements can be in the range 6 mm to 35 mm , the inside diameter can be in the range 3 mm to 25 mm , and the thickness in the range 1 mm to 5 mm . the end effector 1406 ( e . g ., a bent hollow titanium needle ) is available from micro surgical technologies . referring to fig1 b , the lengths of the component parts are as follows : 1401 6 mm ; 1402 5 mm ; 1403 17 mm ; 1405 29 mm . the major diameter of horn 1405 is 12 mm and the minor diameter is 3 . 8 mm . the inhomogeneous resonator 1403 has an outside diameter of 12 mm , and a total length of 17 mm . 8 slots on the resonator have a width of 1 mm , a depth of 3 . 5 mm and a pitch of 34 mm . as will be apparent to one of skill in the art various pitches , and widths of slots can be used . mitskevich ( cited above ) concludes that the degree of transformation of longitudinal into torsional vibration depends on the depth of the helical grooves and their pitch and increases within defined limits as the depth of the grooves is increased and their pitch is decreased . the transducer design illustrated in fig1 b was tested using the instrumentation illustrated in fig7 . the laser was focused side on to the tip of the needle 1406 and the frequency adjusted for maximum displacement . a pure torsional mode could only be sustained up to a maximum value of 21 μm p - p at a frequency of 32 . 644 khz . the test results are summarized in table 3 the above test data relates to measurements made with the transducer operating in air . under operational conditions water would be continuously aspirated through the central lumen and this would increase the impedance and drive voltage . the aspiration water also cools the piezoelectric rings and allows operation at power levels up to a maximum of about 30 watts . as can be seen the design has been optimized for torsional mode rather than longitudinal mode of operation . in another aspect of this invention , a means of mechanically decoupling the torsional and longitudinal vibrations within the transducer assembly from the housing is disclosed . in u . s . pat . no . 6 , 984 , 220 b2 , wuchinich gives a detailed description of the problem but concludes that possible simple solutions would ineffective . for medical ultrasonic handpieces mechanical coupling of either longitudinal or torsional motion will cause localized heat and the generation of audible sub - harmonic frequencies . the fundamental design problem is associated with the difference in the longitudinal speed of sound c l in a cylindrical or rectangular bar shaped component compared with the shear mode speed of sound c s . for example , titanium alloy 6al - 4v has a longitudinal speed of sound c l ≈ 4916 m / s and a shear mode speed of sound c s ≈ 3100 m / s . for the piezoelectric material pzt4 the stiffened shear wave propagation is ≈ 2630 m / s and the longitudinal wave propagation is ≈ 2900 m / s . the wavelength ( λ ) □ frequency ( f ) and speed of sound ( c ) by the formula : for example , the longitudinal resonance of a 12 mm diameter titanium alloy bar occurs when the length of the bar equals one half wavelength ( λ / 2 ). for a bar that is 100 mm in length the longitudinal resonant frequency will be 24 . 58 khz and the torsional mode resonance frequency will be 15 . 5 khz . however , as can be seen in fig1 , practical transducers contain components that have complex shapes such as the inhomogeneous resonator 1403 , horn 1405 and end effector 1406 . the mode of vibration of the resonator 1403 can be determined using finite element analysis or by practical measurements using a laser vibrometer . fig1 a illustrates the position of the nodes ( n s ) and antinodes ( a s ) at the torsional mode resonance frequency of 32 . 644 khz . a node is defined as a point of minimum torsional displacement and is ideally positioned close to the step in the horn . fig1 b illustrates the position of the node ( n l ) and antinodes ( a l ) at the longitudinal mode resonance frequency of 38 . 127 khz . as can be seen the torsional mode node and longitudinal mode node are spatially separated . thus a design optimized for torsional mode would have the housing attached close to the node at the step of the horn . however , while operating at the longitudinal resonance frequency , there will be significant motion at the horn step and this will result in energy being coupled into the housing . within a transducer system , the coupling of torsional energy ( k eff ) from the relatively small longitudinal motion within the piezoelectric stack is typically within the range 0 . 02 to 0 . 08 . for unity gain longitudinal transducer systems without a horn attached , i . e ., subassemblies , the effective coupling coefficient ( k eff ) is typically within the range 0 . 2 to 0 . 4 . as low values of k eff result in higher impedance and drive voltage , it is therefore , more important to optimize the decoupling mechanism for torsional rather than longitudinal motion . a typical method used to decouple energy within an ultrasonic handpiece designed for phacoemulsification is illustrated in fig1 a . the transducer system 1700 is located within a cylindrical housing ( not shown ). the inside diameter of the housing is dimensioned such that the ‘ o ’ ring seals 1701 and 1703 are compressed but still provide an air gap between the internal components and the housing . typical ‘ o ’ ring materials include nitrile , neoprene , butyl , silicone , ethylene propylene ( epdm ), and polytetrafluoroethylene ( ptfe ). the housing is permanently attached to the heel mass 1704 by either bonding adhesive , brazing , or laser welding . typically a silicone rubber adhesive such as dow corning 577 is used . additional mechanical decoupling of both torsional and longitudinal motion is achieved by attaching the heel mass 1704 to the transducer assembly by means of a very thin walled small diameter tube 1702 . typically this tube would be fabricated from titanium alloy or stainless steel , have a length between 10 mm and 20 mm , an outside diameter between 2 . 5 mm and 3 . 5 mm and the thinnest possible wall thickness ( between 0 . 3 mm and 0 . 5 mm ). the combination of this very compliant tube 1702 and the relatively large heel mass 1704 provide decoupling for both torsional and longitudinal motion that is generated within the transducer assembly . the problem is associated with the distal mounting location at the step of the horn in that ‘ o ’ ring 1701 will tend to convert motional energy into heat and will not anchor or adequately center the transducer assembly within the housing . in this aspect of the invention , a means is provided that properly anchors the assembly within the housing while maintaining electrical continuity between components . one embodiment of the means used is a spring . in some embodiments , the spring is a metal coil spring . in more preferred embodiments , the spring is a canted coil spring ™ manufactured by bal seal engineering inc . this spring is illustrated in fig1 b as component 1705 . the spring is designed to perform a latching and holding function that centrally locates annular shaped components within the bore of a housing and to maintain electrical continuity between components . preferable grooves are placed in a surface region of the transducer system for mounting or holding the transducer system in the housing and the spring is frictionally engaged between the groove on the transducer system and the housing . the prototype transducer used to evaluate the performance of this aspect of this invention was initially tested with a prior art ‘ o ’ 1701 and then modified to substitute a bal seal 1705 with the following specification : spring id 2 . 9 mm ; coil width ( ref ) 2 . 3 mm ; coil height ( ref ) 2 . 0 mm ; wire diameter 0 . 4 mm ; deflection 1 . 4 mm ; material type 316 stainless steel . a cylindrical housing was slid over the transducer assembly thereby compressing the bal seal and clamping the transducer assembly within the housing . the tabulated data in table 4 is the longitudinal mode low power impedance analyzer measurements . the table 4 test data indicates that the bal seal has very low losses compared with the ‘ o ’ ring at the longitudinal mode resonance frequency . as can be seen in fig1 b , the longitudinal node n l is spatially separated from the bal seal or ‘ o ’ ring located at the step in the horn . under typical operational conditions , the stroke at the distal tip of the end effector would be approximately 50 μmp - p resulting in a computed longitudinal displacement at the step in the horn of 10 μmp - p . the table 5 torsional mode test data has a smaller variation in mechanical q and real impedance because the bal seal and ‘ o ’ ring are located very close to the node at the step of the horn as illustrated in fig1 a . in this aspect of the invention , any seal that is functionally similar can be used , including but not limited to springs encapsulated in a polymer or plastic material . for example , bal seal engineering inc . manufactures a range of seals that incorporate the canted metal coil springs and parker seals also manufacture a ptfe flexiseals ™ that incorporates a metal coil spring . in the certain embodiments , of this invention the bal seal can be located at a torsional shear wave node at the step of a horn . alternatively , it could also be located within any metal component within the transducer subassembly . a bal seal could also be used to replace ‘ o ’ ring 1703 that is located in heel mass 1704 . one skilled in the art would readily appreciate that the present invention is well adapted to carry out the objects and obtain the ends and advantages mentioned , as well as those inherent therein . the methods and compositions described herein , as presently representative of preferred embodiments , are exemplary and are not intended as limitations on the scope of the invention . changes therein and other uses will occur to those skilled in the art , which are encompassed within the spirit of the invention , are defined by the scope of the claims .
the present invention relates to the design of piezoelectric transducer subassemblies and systems primarily intended for medical and dental applications . the invention also provides transducer subassemblies and systems with improved performance and a capability to operate more efficiently in torsional or a combined longitudinal - torsional mode of vibration . the invention enables the size and weight of torsional mode transducers to be reduced . additionally , the electrical characteristics of these transducer systems are improved , thus enabling the transducer end effector to deliver more power to the operative site .