Mitarbeiter des Lehrstuhls für Dynamik und Mechatronik

Ultrasonic joining is a common industrial process. In the electronics industry it is used to form electrical connections, including those of dissimilar materials. Multiple influencing factors in ultrasonic joining are known and extensively investigated; process parameters like ultrasonic power, bond force, and bonding frequency of the ultrasonic vibration are known to have a high impact on a reliable joining process and need to be adapted for each new application with different geometry or materials. This contribution is focused on increasing ultrasonic power transmitted to the interface and keeping mechanical stresses during ultrasonic bonding low by using a multi-dimensional ultrasonic transducer concept. Bonding results for a new designed connector pin in IGBT-modules achieved by multi- and one-dimensional bonding are discussed.

The handling of fine powders is an important task in modern production processes. However, as fine powders strongly tend to adhesion and agglomeration, their processing with conventional methods is difficult or impossible. Especially when processing small amounts of highly sensitive fine powders, conventional methods reach their technical limits. In process steps such as dosing, transport, and especially mixing of fine powders new methods are required. Apart from the well-known method of manipulating powder properties by adding chemical additives, this contribution aims at improving the handling of dry fine powders by using vibrations at different frequencies. Modules are presented, which enable the continuous dosing, the homogeneous mixing and the transport of dry fine powders. Finally, these modules are combined for the production of a homogeneous mixture of two dry fine powders.

Abstract:Since fine powders tend strongly to adhesion and agglomeration, their processing withconventional methods is difficult or impossible. Typically, in order to enable the handling of finepowders, chemicals are added to increase the flowability and reduce adhesion. This contributionshows that instead of additives also vibrations can be used to increase the flowability, to reduceadhesion and cohesion, and thus to enable or improve processes such as precision dosing, mixing,and transport of very fine powders. The methods for manipulating powder properties are describedin detail and prototypes for experimental studies are presented. It is shown that the handling of finepowders can be improved by using low-frequency, high-frequency or a combination of low- andhigh-frequency vibration.

The transportation of dry fine powders is an emerging technologic task, as in biotechnology, pharmaceu-tical and coatings industry the particle sizes of processed powders get smaller and smaller. Fine powdersare primarily defined by the fact that adhesive and cohesive forces outweigh the weight forces, leadingto mostly unwanted agglomeration (clumping) and adhesion to surfaces. Thereby it gets more difficult touse conventional conveyor systems (e.g. pneumatic or vibratory conveyors) for transport. A rather newmethod for transporting these fine powders is based on ultrasonic vibrations, which are used to reducefriction between powder and substrate. Within this contribution an experimental set-up consisting of apipe, a solenoid actuator for axial vibration and an annular piezoelectric actuator for the high frequencyradial vibration of the pipe is described. Since amplitudes of the radial pipe vibration should be as large aspossible to get high effects of friction reduction, the pipe is excited to vibrate in resonance. To determinethe optimum excitation frequency and actuator position the vibration modes and resonance frequenciesof the pipe are calculated and measured. Results are in good accordance.

Eine Vielzahl von Prozessen in der Chemie und Verfahrenstechnik kann durch Ultraschall positiv beeinflusst werden. Oftmals ist ultraschallinduzierte Kavitation der Hauptwirkmechanismus für die positiven Effekte der Beschallung. Daher ist es notwendig die Kavitationsaktivität während des Prozesses zu quantifizieren um die Beschallung für den jeweiligen Prozess optimal gestalten und überwachen zu können. Eine Möglichkeit der prozessbegleitenden Kavitationsdetektion ist die Auswertung der akustischen Emissionen von oszillierenden und kollabierenden Kavitationsblasen mittels Drucksensoren in der Flüssigkeit. Raue Prozessrandbedingungen wie hohe Temperaturen oder aggressive Flüssigkeiten erschweren es jedoch geeignete Sensoren zu finden. Als Alternative wurde daher die Nutzbarkeit der Rückwirkung von Kavitationsereignissen auf das elektrische Eingansgssignal des Ultraschallwandlers zur Quantifizierung von Kavitation untersucht. Die experimentelle Analyse hat ergeben, dass das Einsetzen und in einigen Fällen auch die Art der Kavitation auf Basis der Rückwirkung auf das Stromsignal des Ultraschallwandlers bestimmt werden kann. Die Stärke der Kavitation war hingegen nicht aus den Stromsignalen abzuleiten.

Piezoelectric inertia motors use the inertia of a body to drive it by means of a friction contact in a series of small steps. It has been shown previously in theoretical investigations that higher velocities and smoother movements can be obtained if these steps do not contain phases of stiction (''stick-slip`` operation), but use sliding friction only (''slip-slip`` operation). One very promising driving option for such motors is the superposition of multiple sinusoidal signals or harmonics. In this contribution, the theoretical results are validated experimentally. In this context, a quick and reliable identification process for parameters describing the friction contact is proposed. Additionally, the force generation potential of inertia motors is investigated theoretically and experimentally. The experimental results confirm the theoretical result that for a given maximum frequency, a signal with a high fundamental frequency and consisting of two superposed sine waves leads to the highest velocity and the smoothest motion, while the maximum motor force is obtained with signals containing more harmonics. These results are of fundamental importance for the further development of high-velocity piezoelectric inertia motors.

(K,Na)NbO3 ceramics have attracted much attention as lead-free piezoelectric materials with high piezoelectric properties. High-quality (K,Na)NbO3 ceramics can be sintered using KNbO3 and NaNbO3 powders synthesized by a hydrothermal method. In this study, to enhance the quality factor of the ceramics, high-power ultrasonic irradiation was employed during the hydrothermal method, which led to a reduction in the particle size of the resultant powders.

We report the piezoelectric properties of CuO-doped hydrothermal (K,Na)NbO3 ceramics that can be applied as hard-type lead-free piezoelectric ceramics. To date, we have succeeded in synthesizing high-quality KNbO3 and NaNbO3 powders by the hydrothermal method, which is based on an ionic reaction at high temperature (around 210 $\,^{\circ}$C) and pressure. Increasing both the piezoelectric constant d and the mechanical quality factor (Qm) is important for resonance-type piezoelectric devices, such as ultrasonic motors and transformers. CuO doping into hydrothermal (K,Na)NbO3 ceramics was examined to realize hard-type lead-free piezoelectric ceramics. By doping with 1.2 mol \% CuO, Qm was increased and the dielectric loss (tan δ) was decreased to 0.5\%. The grain size was also influenced by the amount of CuO doping, which indicates that Qm is related to the density. To achieve a higher Qm value, the grain size is required to be less than 5 µm; however, excessive CuO doping leads to anomalous grain growth. Optimal piezoelectric properties were obtained for 1.2 mol \% CuO-doped (K,Na)NbO3; k31 = 0.32, d31 = -44 pC/N, Qm (radial) = 959, and tan δ= 0.5\%. These characteristics showed that CuO doping with hydrothermal powders is effective for obtaining hard-type ceramics, and the mechanical quality factor is more than ten times higher than that of nondoped hydrothermal (K,Na)NbO3 ceramics. Therefore, compared with the conventional solid-state method, we could succeed in obtaining hard-type ceramics by a simple and short process.

Piezoelectric inertia motors, also known as ``stick--slip drives'', use the inertia of a body to drive it in small steps by means of a friction contact. While these steps are classically assumed to involve stiction and sliding, the motors can also operate in ``slip--slip'' mode without any phase of static friction. This contribution provides a systematic investigation and performance comparison of different stick--slip and slip--slip modes of operation. Different criteria for comparing the motional performance of inertia motors are defined: Steady state velocity, smoothness of motion, and start-up time. Using the example of a translational inertia motor excited by an ideal displacement signal, it is found that the maximum velocity reachable in stick--slip operation is limited principally, while continuous slip--slip operation allows very high velocities. For the investigated driving signals, the motor velocity is proportional to the square root of the actuator stroke. The motor performance with these ideal signals defines an upper boundary for the performance of real motors.

A piezoelectric cantilever beam with a tip mass at its free end is a common energy harvester configuration. This article introduces a new principle of designing such a harvester that increases the generated power without changing the resonance frequency of the harvester: the attraction force between two permanent magnets is used to add stiffness to the system. This magnetic stiffening counters the effect of the tip mass on the efficient operation frequency. Five set-ups incorporating piezoelectric bimorph cantilevers of the same type in different mechanical configurations are compared theoretically and experimentally to investigate the feasibility of this principle: theoretical and experimental results show that magnetically stiffened harvesters have important advantages over conventional set-ups with and without tip mass. They generate more power while only slightly increasing the deflection in the piezoelectric harvester and they can be tuned across a wide range of excitation frequencies.

Power and bandwidth of piezoelectric harvesters can be increased by using multiple piezoelectric elements in one harvester. In this contribution, a novel energy harvesting cantilever array with magnetic tuning including three piezoelectric bimorphs is investigated theoretically and experimentally, with a good agreement between model and experiment. Other than harvester designs proposed before, this array is easy to manufacture and insensitive to manufacturing tolerances because its optimum operation frequency can be re-adjusted after fabrication. Using the superposition principle, the Butterworth-Van Dyke model and a mechanical lumped parameters model, the generated voltage and current are determined analytically. Formulas for calculating the power generated by array harvesters with an arbitrary number of piezoelectric elements connected in series or in parallel are derived. It is shown that optimum harvester design must take both the connected load and the operating frequency into account. Strategies for connecting multiple bimorphs to increase the maximum generated power and/or enhance the bandwidth compared to a single bimorph harvester are investigated. For bandwidth enhancement it is essential that individual rectifiers are used for the bimorphs. An example with three bimorphs shows that, depending on the chosen tuning strategy, the power is increased by about 340\% or the bandwidth is increased by about 500\%, compared to one single bimorph.

Piezoelectric inertia motors, also known as stickslip drives or (smooth) impact drives, use the inertia of a body to drive it by a friction contact in small steps, in the majority of motors composed of a stick phase and a slip phase between the friction partners. For optimizing inertia motors, it is important to understand the friction contact correctly and to measure its properties appropriately. This contribution presents experimental set-ups for measuring the contact force, friction force and relative displacement in an actual inertia motor with a dry friction contact and numerical simulations of the motor operation. The motor uses a pre-stressed multilayer actuator with a displacement in the range of 20 $\mu$ m. It is shown that a previously postulated condition for the applicability of simple kinetic friction models is well fulfilled for the investigated motor. The friction contact in the motor is simulated using different kinetic friction models. The input for the friction models is the measured motion of the rod. The models qualitatively reproduce the measured motion but show quantitative deviations varying with frequency. These can be explained by vibrations of the driving rod that are experimentally investigated.

This contribution provides a systematic investigation and performance comparison of different modes of operation for piezoelectric inertia drives. The movement of these motors is classically assumed to consist of steps involving stiction and sliding, resulting in the term ``stick-slip drives''. In the first part of this contribution it has been found that using ideal driving signals, ``slip-slip'' operation without phases of stiction allows very high velocities, while the maximum velocity is limited principally in stick-slip operation. In this part it is shown that slip-slip operation is also suitable for use with real actuators, driven with frequency-limited versions of the ideal signals presented in part I. The motional performance of the motor as well as its wear and the required electric power are investigated for operation with different signals. It is found that for high velocity inertia motors it is recommendable to use actuators with large stroke and to drive them with a signal consisting of two harmonics at a high fundamental frequency, a result that is supported by similar setups implemented experimentally by other authors. Using Lanczos' \sigma factors to calculate the frequency-limited excitation signals instead of standard Fourier series additionally increases the motor performance significantly. The results help motor designers to choose the appropriate mode of operation and to optimise the motor parameters for their individual applications.

The hydrothermal method utilizes a solution-based chemical reaction to synthesize piezoelectric thin films and powders. This method has a number of advantages, such as low-temperature synthesis, and high purity and high quality of the product. In order to promote hydrothermal reactions, we developed an ultrasonic assisted hydrothermal method and confirmed that it produces dense and thick lead--zirconate--titanate (PZT) films. In the hydrothermal method, a crystal growth process follows the nucleation process. In this study, we verified that ultrasonic irradiation is effective for the nucleation process, and there is an optimum irradiation period to obtain thicker PZT films. With this optimization, a 9.2-$\mu$ m-thick PZT polycrystalline film was obtained in a single deposition process. For this film, ultrasonic irradiation was carried out from the beginning of the reaction for 18 h, followed by a 6 h deposition without ultrasonic irradiation. These results indicate that the ultrasonic irradiation mainly promotes the nucleation process.

Piezoelectric inertia motors, also known as ``stick-slip-drives'', use the inertia of a body to drive it by means of a friction contact in small steps. While these steps normally involve stiction and sliding, the motors can also operate in ``slip-slip'' mode without any phase of static friction. In this contribution, a one degree of freedom model of an inertia motor driven by an ideal actuator is analysed. Start-up and constant velocity operation of the motor are investigated and appropriate quantities to compare ``stick-slip'' and ``slip-slip'' operation are determined. Different aspects such as velocity, uniformity of motion, load capacity, robustness, efficiency, and wear are considered. The analysis allows both modes to be applied advantageously in different applications and can widen the field of application of piezoelectric inertia motors. Motor designers are enabled to choose the appropriate mode of operation and the best drive parameters for their individual applications.

A piezoelectric energy harvester is an electromechanical device that converts ambient mechanical vibration into electric power. Most existing vibration energy harvesting devices operate effectively at a single frequency only, dictated by the design of the device. This frequency must match the frequency of the host structure vibration. However, real world structural vibrations rarely have a specific constant frequency. Therefore, piezoelectric harvesters that generate usable power across a range of exciting frequencies are required to make this technology commercially viable. Currently known harvester tuning techniques have many limitations, in particular they miss the ability to work during harvester operation and most often cannot perform a precise tuning. This paper describes the design and testing of a vibration energy harvester with tunable resonance frequency, wherein the tuning is accomplished by changing the attraction force between two permanent magnets by adjusting the distance between the magnets. This tuning technique allows the natural frequency to be manipulated before and during operation of the harvester. Furthermore the paper presents a physical description of the frequency tuning effect. The experimental results achieved with a piezoelectric bimorph fit the calculated results very well. The calculation and experimental results show that using this tuning technique the natural frequency of the harvester can be varied efficiently within a wide range: in the test setup, the natural frequency of the piezoelectric bimorph could be increased by more than 70\%.

Piezoelectric structures are nowadays used in many different applications. A better understanding of the influence of material properties and geometrical design on the performance of these structures helps to develop piezoelectric structures specifically designed for their application. Different equivalent circuits have been introduced in the literature to investigate the behaviour of piezoelectric transducers. The model parameters are usually determined from measurements covering the characteristic frequencies of the piezoelectric transducer. This article introduces an analytical technique for calculating the mechanical and electrical equivalent system parameters and characteristic frequencies based on material properties and geometry for a cantilever bimorph structure. The model is validated by measurements using a cantilever bimorph and fits the experimental results better than previous models. The model gives a full set of piezoelectric transducer parameters and is therefore well suited for further theoretical investigations of piezoelectric transducers for different applications. The results also show that even small manufacturing tolerances have a considerable effect on the system parameters and characteristic frequencies. This might lead to intolerable deviations, especially in dynamic applications and should be avoided by careful design and production.

[$Li_x(Na_0.52K_0.48)_1-x]NbO_3 (0 \leq x \leq 0.091)$ ceramics were synthesized using hydrothermal powders and the lithium doping content was controlled to optimize their piezoelectric properties. The raw KNbO$_3$ and NaNbO$_3$ powders were obtained separately by a hydrothermal method and LiNbO$_3$ powders were prepared by milling a commercial LiNbO$_3$ single crystal. These powders were mixed with ethanol at a molar ratio LiNbO$_3$: ($Na_0.52K_0.48$)NbO$_3 = x : 1-x$. The synthesized powders were sintered at 1060--1120 $\,^{\circ}$C for 2 h. We succeeded in obtaining highly dense [$Li_x(Na_0.52K_0.48)_1-x]NbO_3$ ceramics using hydrothermal powder. The X-ray diffraction patterns revealed that the crystal phase changed from orthorhombic to tetragonal at around x = 0.06. At this morphotropic phase boundary (MPB), the c/a ratio changed from 1.016 to 1.024 and the highest piezoelectric constant was obtained with the chemical component of [$Li_x(Na_0.52K_0.48)_1-x]NbO_3$. The obtained piezoelectric properties were as follows: $k_33 = 0.51, \epsilon 33^T/ \epsilon _0 = 836$ , $c_33^E = 46$ GPa, $d_33 = 203$ pC/N, and $T_c = 482 $\,^{\circ}$C$.

The paper presents the results of numerical and experimental investigation of cylindrical piezoelectric actuator used for achieving independent three degrees of freedom oscillations of the contact point. The design of actuator based on a hollow piezoelectric cylinder mounted on a metal rod. The piezoceramic cylinder has a radial polarization and special configuration of the electrodes that cover inner and outer surface of the cylinder. The main advantage of actuator's design is that solid metallic rod operates as a part of inner electrode of the cylinder and a stator of actuator. The geometry of piezoelectric actuator was adopted to reach resonance of oscillations for the first longitudinal mode and the third flexural mode at same frequency. The actuator is designed to move positioned object through contact point which is located on the top of the rod. The optimal topology of electrodes was found to achieve longitudinal and flexural oscillations of the actuator in two perpendicular planes. Three degrees of freedom of the positioning object can be achieved and control of the system can be implemented by applying different excitation schemes and regimes. The numerical simulation and experimental study of piezoelectric actuator was performed. Impedance of actuator was analyzed under different excitation regimes. The results of numerical modeling and experimental study were compared. Recommendations for the further development of this type of actuator are given.

In this study, we report some improvements in a hydrothermal method for lead-free piezoelectric powders and the performance of the sintered (K$_{0.48}$Na$_{0.52}$)NbO$_{3}$ ceramics. To increase the obtained powder weight per source solution volume, the hydrothermal reaction conditions were modified. This improvement is important for mass production; however, it resulted in a larger particle size dispersion. Therefore, we examined to introduced the ball milling process that is useful for dense (K$_{0.48}$Na$_{0.52}$)NbO$_{3}$ ceramics. When a large amount of powder was obtained, it took a long time to eliminate the residual alkaline ions in the hydrothermal powders by a washing process. Therefore, a neutralization was conducted in the powder washing process. Using this powder, a solid solution of (K,Na)NbO$_{3}$ceramics was synthesized. The relative density was successfully increased. Concerning the electrical properties, the relative permittivity was improved, and the piezoelectric constant d$_{33}$ was also increased from 114 to 130 pC/N.

The multi-objective optimal design of a piezoelectric sandwich ultrasonic transducer is studied. The maximum vibration amplitude and the minimum electrical input power are considered as optimization objectives. Design variables involve continuous variables (dimensions of the transducer) and discrete variables (material types). Based on analytical models, the optimal design is formulated as a constrained multi-objective optimization problem. The optimization problem is then solved by using the elitist non-dominated sorting genetic algorithm (NSGA-II) and Pareto-optimal designs are obtained. The optimized results are analyzed and the preferred design is proposed. The optimization procedure presented in this contribution can be applied in multi-objective optimization problems of other piezoelectric transducers.

Among various lead-free piezoelectric materials, (K,Na)NbO$_{3}$ is a very promising candidate. In this study, (K,Na)NbO$_{3}$ ceramics were sintered from mixed (K,Na)NbO$_{3}$ and NaNbO$_{3}$ powders prepared by hydrothermal reaction. These two powders were mixed with distilled water in a KNbO$_{3}$/NaNbO$_{3}$ molar ratio of 1. After sintering the mixed powder, the solid solution of (Na,K)NbO$_{3}$ ceramics was obtained. The electrical properties such as the electromechanical coupling factors k$_{p}$ and k$_{33}$, the mechanical quality factor, Q$_{m}$, and the piezoelectric constant d$_{33}$ of the sintered (K,Na)NbO$_{3}$ ceramics were 0.32, 0.48, 71 (radial mode), 118 ((33)mode), and 107 pC/N, respectively.

The hydrothermal method enables the production of high-quality piezoelectric materials. In this study, we propose to irradiate the reaction solutions with ultrasonic power during the hydrothermal method to obtain a shorter reaction time and a smooth film surface. A high-pressure reaction container for the ultrasonic transducer was newly developed, and the ultrasonically-assisted hydrothermal method was examined by using this container. The effect of ultrasonic assist on the synthesis of lead-zirconate-titanate (PZT) thin films and (K,Na)NbO$_{3}$ powders was verified. Thicker PZT film, thickness around 10 ${\mu}$m, could be obtained in one process, and (K,Na)NbO$_{3}$ powder was synthesized in half the previous reaction time.

Dieser Beitrag fasst die bekannten analytischen Berechnungsmethoden für piezoelektrische Ultraschallverbundschwinger zusammen und gibt anhand typischer Beispiele Anleitungen zur Lösung theoretischer und technischer Fragen bei deren Entwicklung. Zunächst werden die passiven, in der Regel metallischen Komponenten von Verbundschwingern als Stab- oder Plattensysteme mit homogen verteilten Feder-, Masse und Dämpfungseigenschaften beschrieben. Hier breitet sich die Schwingungsenergie in Form stehender und fortschreitender Wellen zum akustischen Verbraucher hin aus. Es folgt eine gleichwertige und schaltungstreue Darstellung durch elektrische oder mechanische Vierpole, die für den Entwicklungsingenieur leichter zu handhaben sind und in Netzwerken direkt mit Masons Ersatzschaltung des piezoelektrischen Wandlers gekoppelt werden können. Danach werden die wichtigsten, messtechnisch zugänglichen Parameter anhand eines in Resonanznähe zulässigen Ersatzmodells mit konzentrierten elektrischen bzw. mechanischen Komponenten definiert. Als Schwerpunkt wird anschließend deren analytische Berechnung und messtechnische Verifizierung an typischen Beispielen demonstriert. Es folgen wichtige technische Informationen über Frequenzkorrekturen, Schallgeschwindigkeitsdispersion, Leistungs- und Belastbarkeitsgrenzen der Komponenten und andere wertvolle praktische Hinweise.

Piezoelectric inertia motors have a simple construction and are controlled by a single driving signal. This allows for miniaturization and low cost production. One of the main questions to be answered during the design process of a piezoelectric inertia motor is which electrical excitation signal yields optimum motor characteristics. Three signals and their variants are widely used in literature: sawtooth, parabolic and cycloidic signals. It can be shown that neither of these can drive the motor at its maximum possible velocity in non-resonant operation. Within this paper we propose to use a rigid body model of a simple inertia motor to predict the motor characteristics depending on the movement pattern of the driving element. Advantages and disadvantages of three different drive signals that maximize the motor velocity are discussed.

Direct ultrasound irradiation is advantageous to increase the efficiency of the hydrothermal method which can be used for the production of piezoelectric thin films and lead free piezoelectric ceramics. To apply ultrasound directly to the process transducer prototypes were developed regarding the boundary conditions of the hydrothermal method. LiNbO$_{3}$ and PIC 181 were proven as feasible materials for high temperature resistant transducers ($\geq 200^\circ C$). Resistance of the transducers horn against the corrosive mineralizer was achieved by using Hastelloy C-22. The efficiency of the ultrasound assisted hydrothermal method depends on the generated sound field. Impedance and sound field measurements have shown that the sound field depends on the filling level and the position and design of the transducer.

Piezoelectric materials find wide application in technical systems. Most often, a combination of piezoelectric and other materials is advantageous. The position and the amount of the piezoelectric material within the overall system depends on various aspects like maximum mechanical output to the load, maximum electromechanical efficiency of the system, maximum utilization of the piezoelectric material, minimum self-heating of the piezoelectric material, and controllability of the system, which might be key aspects for the optimisation of the system design. For a composite longitudinal vibrator (bolted Langevin transducer), which is a base for many technical applications, this contribution shows in detail, how above mentioned aspects depend on the position and volume of the piezoelectric material related to the mode shape.

Piezoelectric inertia motors make use of the inertia of a slider to drive the slider by friction contact in a series of small steps which are generally composed of a stick phase and a slip phase. If the best electrical drive signal for the piezoelectric actuator in an inertia motor is to be determined, its dynamical behaviour must be known. A classic dynamic lumped parameter model for piezoelectric actuators is valid only in resonance and, therefore, is not suitable for modelling the actuator in an inertia motor. A reduced dynamic model is used instead. Its parameters are identified using a step response measurement. This model is used to predict the movement of the actuator in response to a velocity-optimized signal introduced in a separate contribution. Results show that the model cannot represent the dynamical characteristics of the actuator completely. For determining voltage signals that let piezoelectric actuators follow a calculated movement pattern exactly, the model can, therefore, only be used with limitations.

In the modeling of piezoelectric Langevin transducers using usual transfer matrix methods, some simplifications have been adopted. This leads to reduction of the model quality. A mixed transfer matrix method is employed in the modeling of Langevin transducers, where the pre-stressed bolt is modeled as a separate four-pole element, which is connected to other elements in parallel. Based on the mixed transfer matrix method, the four (six)-pole element description of the piezoelectric Langevin transducer is built up and the total transfer matrix relation is derived. The resonance frequencies of the transducer are calculated and then measured using the impedance analyzer (HP4192). Experimental result shows that the mixed transfer matrix method has better modeling quality than the usual transfer matrix method for the vibration analysis of piezoelectric Langevin transducers.

As a lead-free piezoelectric ceramics, (K,Na)NbO$_{3}$ is a promising material because of its good piezoelectric properties. In this study, (K$_{1-x}$Na$_{x}$)NbO$_{3}$ ceramics were synthesized from a KNbO$_{3}$ and NaNbO$_{3}$ mixture powder prepared by the hydrothermal reaction. The hydrothermal reaction enables the production of high quality powder for the ceramics fabrication process. To obtain (K$_{1-x}$Na$_{x}$)NbO$_{3}$ ceramics, these two powders KNbO$_{3}$ and NaNbO$_{3}$ were mixed and then sintered together. X-Ray diffraction analysis revealed that the solid solution ceramics (K$_{1-x}$Na$_{x}$)NbO$_{3}$ was produced by the sintering process. The K/Na ratio in (K$_{1-x}$Na$_{x}$)NbO$_{3}$ ceramics was optimized for the best piezoelectric properties. The optimized forms was (K$_{0.48}$Na$_{0.52}$)NbO$_{3}$, which showed the following piezoelectric properties; k$_{33}$=0.56, d$_{33}$=114pC/N. In addition, the ferroelectric properties, P$_{r}$=7.72mC/cm$^{2}$, E$_{c}$=857V/mm, and the Curie temperature T$_{c}$=420$_{o}$C were also measured.

Ultrasonic hyperthermia and thermo-ablation are two promising alternatives for local overheating of deep-seated human tumours. After a short characterisation of the two techniques and the identification of the main parameters, results of an analytical theory of local heat up, cooling, and heat diffusion are presented. The theory is based on a spherical model for hyperthermia with a critical thermal dose and on a cylinder-symmetrical model for thermo-ablation with a critical temperature threshold for thermal toxicity and cell death through coagulative necrosis. Two representative hard ware concepts are discussed. The hyperthermia applicator consists of a MHz transducer, which rotates concentrically in a water filled capsule with acoustically transparent window, and radiates collimated or focussed ultrasound under 45$\,^{\circ}$ into a concentric target area of nearly spherical symmetry. The applicator for thermo-ablation is a MHz transducer which radiates high intensity focussed ultrasound (HIFU) into "cigar shaped" target areas at the focal zone. Typical therapy diagrams for both techniques are presented. They show therapeutic target volumes as functions of the therapy time with the peak temperature or the radiated acoustic power as parameters. These diagrams are discussed under consideration of power requirement, maximal sound intensity, and power efficiency at close to optimized frequency conditions.

Several positioning tasks demand translatory drive instead of rotary motion. To achieve drives that are capable, e.g., to drive the sunroof of a car or to lift a car's window, multiple miniaturized motors can be combined. But in this case many other questions arise: The electromechanical behavior of the individual motors differs slightly, the motor characteristics are strongly dependent on the driving parameters and the driven load, many applications need some extra power for special cases like overcoming higher forces periodically. Thus, the bundle of motors has to act well-organized and at last controlled to get an optimized drive that is not oversized and costly.

For devices having non-linear contact, load plays a fundamental role. Variations in the characteristics of the load cause change in eigenfrequency and amplitude of the vibration. In most technical applications, this unwanted behaviour is cancelled by the use of control algorithms. However, multiple applications, like bond quality monitoring or chemical and pressure sensors, have found that the load may be characterised by interpreting the change in characteristics of a resonant vibrating device used as a sensor. Surgical resection of tumours is a very difficult task. After localising the tumour by the use of imaging techniques, the resection demands the surgeon to decide where and what to resect based on visual and tactile differentiation of tumour and healthy tissue. Exactness of this process could be enhanced if we can provide the surgeon with a device capable of evaluating mechanical characteristics of the tissue much more accurately than the surgeon himself can do. As the mechanical characteristics of tumour and healthy tissue differ but slightly, the task is to design a system with high sensitivity. Therefore, we have developed a resonant actuator-sensor that allows the differentiation among distinct media that have similar mechanical characteristics to tumour and healthy tissue using a piezoelectric bimorph. The design is based on the detection and evaluation of frequency shift and amplitude variation of the fundamental and higher harmonics using one layer for the resonant excitation of vibration and the other one as the sensing element.

Many ultrasonic processes are based on the mechanical contact of oscillating parts. Within ultrasonic machining (drilling, milling, grinding) micro impacts lead to abrasion at the processed workpiece and hopefully do not damage the tool. In ultrasonic motors ideally neither part gets worn. Thus the appropriate design of contact partners as well as their kinematics is a substantial task during the development of such devices. A first step to optimize contact mechanics is to understand their behavior and dependencies on parameter variations, such as vibration amplitude and pre-stress of the impacting parts. For a detailed understanding models validated with convincing experimental data from measurements are absolutely essential. This paper focuses on simple vibro-impact experiments which can be used as benchmark data for future models. The setup of the experiment and first experimental investigations are described in detail.

Surgical resection of brain tumours is a difficult task. To enhance surgery results, a tactile sensor is wanted that gives better resolution and sensitivity than the human tactile sense. The characteristics of resonant vibrating piezoelectric elements change with varying load. This allows for calculation of mechanical load parameters by measuring electrical quantities. Different setups of piezoelectric sensors have been used to investigate soft materials. Finally, a piezoelectric bimorph sensor gave good results for distinguishing tissue mimicking gel-phantoms with different gelatine concentrations.

The design of piezoelectric transducers is usually based on single-objective optimization only. In most practical applications of piezoelectric transducers, however, there exist multiple design objectives that often are contradictory to each other by their very nature. It is impossible to find a solution at which each objective function gets its optimal value simultaneously. Our design approach is to first find a set of Pareto-optimal solutions, which can be considered to be best compromises among multiple design objectives. Among these Pareto-optimal solutions, the designer can then select the one solution which he considers to be the best one. In this paper we investigate the optimal design of a Langevin transducer. The design problem is formulated mathematically as a constrained multiobjective optimization problem. The maximum vibration amplitude and the minimum electrical input power are considered as optimization objectives. Design variables involve continuous variables (dimensions of the transducer) and discrete variables (the number of piezoelectric rings and material types). In order to formulate the optimization problem, the behavior of piezoelectric transducers is modeled using the transfer matrix method based on analytical models. Multiobjective evolutionary algorithms are applied in the optimization process and a set of Pareto-optimal designs is calculated. The optimized results are analyzed and the preferred design is determined.

Classically, rotary motors with gears and spindle mechanisms are used to achieve translatory motion. In means of miniaturization and weight reduction piezoelectric linear motors are of interest. Several ultrasonic linear motors found in literature base on the use of two different vibration modes. Most often flexural and longitudinal modes are combined to achieve an elliptic micro-motion of surface points. This micro-motion is converted to direct linear (or translatory) motion of a driven slider. To gain high amplitudes of the micro-motion and thus having a powerful motor, the ultrasonic vibrator should be driven near the eigenfrequency of its modes. Additionally, low mechanical and electrical losses lead to increased efficiency and large amplitude magnification in resonance. This demands a geometrical design that fits the eigenfrequencies of the two different modes. A frequency-deviation of only a few percent leads to non-acceptable disturbance of the elliptical motion. Thus, the mechanical design of the vibrators has to be done very carefully. Within this contribution we discuss different motor designs based on the coupling of two the same longitudinal vibrations within one structure to generate an elliptic motion of surface points. Different concepts based on piezoelectric plates and Langevin transducers are compared. Benefits and drawbacks against the combination of longitudinal and bending modes will be discussed. Numerical results of the stator vibration as well as motor characteristics are validated by measurements on different prototypes.

Rotary ultrasonic motors have found broad industrial application in camera lens drives and other systems. Linear ultrasonic motors in contrast have only found limited applications. The main reason for the limited range of application of these very attractive devices seems to be their small force and power range. Attempts to build linear ultrasonic motors for high forces and high power applications have not been truly successful yet. To achieve larger force and higher power, multiple miniaturized motors can be combined. This approach, however, is not as simple as it appears at first glance. The electromechanical behaviour of the individual motors differs slightly due to manufacturing and assembly tolerances. The individual motor characteristics are strongly dependent on the driving parameters (frequency, voltage, temperature, pre-stress, etc.) and the driven load and the collective behaviour of the swarm of motors is not just the linear superposition of the individual drive's forces. Thus, the bundle of motors has to be synchronized and controlled appropriately in order to obtain an optimized drive that is not oversized and costly. We have investigated driving and control strategies of a set of linear ultrasonic motors. Our contribution will be divided into three main parts. In part I ultrasonic linear motors will be introduced. In part II driving strategies for a single motor as well as for a bundle of motors will be presented. These concepts will be verified by simulation results and experimental data. In part III a simplified model for the motor's electromechanical behaviour will be given.

Piezoelectric transformers are increasingly getting popular in the electrical devices owing to several advantages such as small size, high efficiency, no electromagnetic noise and non-flammable. In addition to the conventional applications such as ballast for back light inverter in notebook computers, camera flash, and fuel ignition several new applications have emerged such as AC/DC converter, battery charger and automobile lighting. These new applications demand high power density and wide range of voltage gain. Currently, the transformer power density is limited to $40 W/cm{^3}$ obtained at low voltage gain. The purpose of this study was to investigate a transformer design that has the potential of providing higher power density and wider range of voltage gain. The new transformer design utilizes radial mode both at the input and output port and has the unidirectional polarization in the ceramics. This design was found to provide 30 W power with an efficiency of 98\% and 30 $\,^{\circ}$C temperature rise from the room temperature. An electro-mechanical equivalent circuit model was developed to describe the characteristics of the piezoelectric transformer. The model was found to successfully predict the characteristics of the transformer. Excellent matching was found between the computed and experimental results. The results of this study will allow to deterministically design unipoled piezoelectric transformers with specified performance. It is expected that in near future the unipoled transformer will gain significant importance in various electrical components.

An improved concept for ultrasonic hyperthermia of tumors is presented. This concept is based on past experience of a German government supported project [1], which ended in 1984. It offers a low cost alternative to common RF- and microwave methods for hyperthermia of tumors with volumes between 1 and 40 ml at treatment times between 30 and 60 min. Our new version of the system considerably improves the temperature suppression in the healthy tissue around the target area and enables the adjustment of the beam width to the actual tumor size and the field geometry to the depth and shape of the tumor. The applicator can be used for moderate hyperthermia with tissue overheating up to 10 K or for ablation therapy with short high temperature pulses. Its central area is free for the integration of a commercial ultrasonic diagnostic sector scanner or a Doppler flow sensor in order to support the adjustment of the transducer and to monitor the whole area during the therapy.