Piezoceramic transducers are extensively used in nondestructive testing (NDT), structural health monitoring (SHM) and condition monitoring (CM) of various mechanical systems including wind turbines, aircraft structures, bridges and pipeline systems. Piezoelectric transducers are surface bonded on the host structure and are excited to produce structural responses. This article highlights the effect of the adhesive layer between the studied structure and the transducer on the contact characteristics and the structural wave fields. The research also focuses on the efficiency of the both methods used for calculation of the occuring wave fields: finite-element (FE) method and semi-analytical approach based on the Green's matrix representations and the Fourier transform.

A novel nano-to-elastohydrodynamic lubrication (EHL) multiscale approach, developed to integrate molecular-scale phenomena into macroscopic lubrication models based on the continuum hypothesis, is applied to a lubricated contact problem with a ceramic–steel interface and a nanometric film thickness. Molecular dynamics (MD) simulations are used to quantify wall slip occurring under severe confinement. Its dependence on the sliding velocity, film thickness, pressure, and different wall materials is described through representative analytical laws. These are then coupled to a modified Reynolds equation, where a no-slip condition applies to the ceramic surface and slip occurring on the steel wall is described through a Navier-type boundary condition. The results of this nano-to-EHL approach can contradict the well-established lubrication theory for thin films. In fact, slip can occur over the whole contact length, leading to a significant modification of the lubricant flow and consequently of the film thickness. If both walls move at the same velocity, the flow is reduced at the contact inlet and the film thickness decreases. If the nonslipping wall entrains the fluid, this one is accelerated resulting in a larger mass flow; nevertheless, the surface separation is reduced as the lubricant flows even faster in the contact center. The opposite effect occurs if the slipping surface entrains the fluid, causing a lower mass flow but higher film thickness. Finally, friction is generally smaller compared to the classical no-slip case and becomes independent of the sliding velocity as total slip is approached.

A model order reduction procedure is derived for the elastohydrodynamic (EHD) problem, Reynolds and elasticity part, to increase the calculation speed. The method is derived for stationary and transient isothermal Newtonian line and point contacts. The reduction of the EHD contact model with exit boundary condition is performed in three steps. The first is a reduction of the system by projection using proper orthogonal decomposition. Within the second step, the complexity of system functions is reduced. The last reduces the computational costs for the exit boundary problem by employing a local scheme. Furthermore, a contact size related nondimensionalization is introduced. The method allows for considerable reduction of the calculation time while achieving excellent correspondence to results obtained by other approaches.

The following article presents an approach for a novel positioning stage as basic component of a small machine tool. It is a parallelkinematic machine (BiGlide mechanism), which converts the linear motion of two linear axes into a planar motion. The novel features, which were identified to be crucial for the transition from conventional machine tools to small ones, are: compact and precise feed axes, backlash free motion transmission, and direct measurement of the tool-center-point position and the ability of additional fine positioning. The proposed implementations are: hydraulic feed units, dry slide bearings as rotational joints, highly precise radar sensors and active variable-length struts of the parallelkinematic machine. Some of the simulation results are presented along with measurements of a currently designed prototype.

Very often elastic joints are used in high precision applications. In the case of rotational joints flexure hinges do have some advantages compared to conventional ones. However, the most important disadvantages are the complicated and complex kinematics and kinetics. As consequence, the control of mechanisms comprised of flexure hinges gets more difficult. The strategy pursued here is to reduce flexure hinges to pseudo rigid-body systems that fit into the elaborated framework of multi-body dynamics, in particular pre-control in combination with a feedback controller. The inherent deviations of these reduced models are described as uncertainties. Methods from robust control are used to synthesize controllers for such systems with uncertainty. The procedure is illustrated by examining an example of a single flexure hinge (leaf spring type).

Analytical pressure solutions are a simple and robust way to model plain journal bearings in rotordynamics, but cannot be extended to porous journal bearings. Using the method of weighted residuals—viz. Galerkin's method with global shape functions—a novel and fast approach to solve the dynamical porous journal bearing problem is proposed. This approach allows for the influence of rough surfaces on the hydrodynamic pressure implemented through flow-factors, journal misalignment and calculation of stiffness and damping coefficients for finite bearings. The proposed method will be verified using analytical expressions and new results will be shown for porous journal bearings including the influence of rough surfaces.

An eigenfrequency can be tracked by resonant excitation with a phase-locked loop (PLL) in order to monitor a certain parameter, e.g. the mass distribution. In this contribution the frequency response function (FRF) of a beam is derived, which is prerequisite for the following resonant excitation. Special emphasis is put on higher oscillation modes. The modified PLL-design for resonant excitation is explained. The result of a proof-of-concept experiment completes this paper.

Due to leakage resistances measuring slowly changing loads using piezoelectric sensors is rather difficult while measuring static loads is impossible. Using the functional principle of a scale with a vibrating string a work-around to this problem is found. By evaluating the relation between the load onto the string and the eigenfrequencies of bending vibration of the string the external load onto the string can be determined. Instead of a string of circular cross-sectional area a thin beam can be used which leads to a preferential vibration direction in direction of least bending resistance. To achieve large signal amplitudes the beam should be excited and vibrating close to its eigenfrequency. To remain in a state of resonance at all times the frequency of excitation must follow frequency alterations due to external influences. Such a frequency locking can be achieved by applying phase-locked loops (PILL) which are widely used within communication technology. In this contribution an experimental set-up for resonant excitation of a composite beam is presented. A small mass is mounted onto the beam. Its position is adjustable to modify the eigenfrequency of the beam. Using piezoelectric macro-fiber composites for sensing and actuating as well as an integrated PLL circuit the resonant excitation of the beam can easily be achieved even for changing eigenfrequencies.

In this contribution, a micro-mechanically motivated constitutive model for rate-dependent domain switching effects is studied. The main focus consists in the development of a three-dimensional finite element framework capturing phase-transformations, whereby for the sake of simplicity each finite element will represent one individual grain. For the investigation of phase-transitions, the onset of so-called domain switching processes is initiated by means of an energy-based criterion. During such switching processes, nucleation and propagation of domain wall motion is incorporated via a straightforward volume fraction concept combined with a simple linear kinetics theory. Moreover, grain boundary effects are accounted for, whereby a macro-mechanically motivated probabilistic approach has been chosen. Based on the proposed formulation, representative simulations are elaborated which provide further insight into the highly nonlinear behaviour of ferroelectric and ferroelastic materials.

AbstractA system of piezoelectric flexible patch actuators bonded to an elastic layered substrate is considered. An integral equation based model for the smart structure under consideration has been developing. The rigorous solution to the patch–substrate dynamic contact problem extends the range of the model's utility far beyond the bounds of conventional simplified models that rely on plate, beam or shell equations for the waveguide part. The developed approach provides the possibility to reveal the effects of resonance energy radiation associated with higher modes that would be inaccessible using models accounting for the fundamental modes only. Algorithms that correctly account for the mutual wave interaction among the actuators via the host medium, for selective mode excitation in a layer as well as for body waves directed to required zones in a half–space, have also been elaborated and implemented in computer code. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Allgemein zeigen Werkzeugmaschinen Verlagerungen im statisch/quasistatischen und im dynamischen Lastbereich auf. Ziel des Projekts ist die adaptronische Kompensation dieser Verlagerungen mit paralleler Bewältigung von Sensorund Aktorfunktion. In den ersten zwei Projektphasen wurde dazu bis heute auf den statisch/quasistatischen Bereich fokussiert, um in einer weiteren dritten Phase die Ausweitung des Konzepts auf den dynamischen Bereich anzugehen. Unter Ausnutzung des Prinzips einer Schwingsaitenwaage werden statische Verformungszustände zur Messung in ein dynamisches Eingangssignal für piezoelektrische Wandler gewandelt. Bild 1 verdeutlicht hierzu den prinzipiellen Aufbau des Systems. Dr.-Ing. Christian Munzinger, Dipl.-Ing. Stefan Herder, Dipl.-Ing. Martin Weis Institut für Produktionstechnik (wbk) Universität Karlsruhe (TH) Kaiserstr. 12, D-76128 Karlsruhe Tel. +49 (0)721 / 608-2449, Fax +49 721 / 699 503 E-Mail: weis@wbk.uka.de Internet: www.wbk-ka.de

This article presents an analytical investigation on stability and bifurcation behaviour due to an exponential and a generalized friction characteristics in the sliding domain of a simple friction oscillator, which is commonly referred to as 'mass-on-a-belt' oscillator. The friction is described by a friction coefficient which depends on the relative velocity between the two tribological partners.The standard way of examining the steady-state only gives very rough insight in the behaviour and is not able to provide further informations about the steady-state's basin of attraction or about limit-cycles. It is found that the system may undergo bifurcations of Hopf type. Hereby, the character of the bifurcations strongly depends on the parameters of the friction characteristic.

This article presents an analytical investigation on stability and local bifurcation behavior due to exponentially decaying friction characteristics in the sliding domain of a simple friction oscillator, which is commonly referred to as "mass-on-abelt"-oscillator. Friction is described by a friction coefficient which in the sense of Stribeck depends on the relative velocity between the two tribological partners.For such a characteristic the stability and bifurcation behavior are discussed. It is shown, that the system can undergo a subcritical Hopf-bifurcation from an unstable steady-state fixed-point to an unstable limit cycle, which separates the basins of the stable steady-state fixed-point and the self-sustained stick-slip limit cycle.Therefore, only a local examination of the eigenvalues at the steady-state, as is the classical approach when investigating conditions for the onset of friction-induced vibrations, may not give the whole picture, since the stable region around the steady-state fixed-point may be rather small.Furthermore, the results of above considerations are applied to a brake-noise problem. It is found that, in contrast to squeal, a decaying friction characteristic may be a satisfying explanation for the onset low-frequency groan. The analytical results are compared with experimental measurements. (C) 2006 Elsevier B. V. All rights reserved.

In this contribution a micromechanically motivated model for rate-dependent switching effects in piezoelectric materials is developed. The proposed framework is embedded into a three-dimensional finite element setting whereby each element is assumed to represent an individual grain. Related dipole (polarization) directions are thereby initially randomly oriented at the element level to realistically capture the originally un-poled state of grains in the bulk ceramics. The onset of domain switching processes is based on a representative energy criterion and combined with a linear kinetics theory accounting for time-dependent propagation of domain walls during switching processes. In addition, grain boundary effects are incorporated by making use of a macromechanically motivated probabilistic approach. Standard volume-averaging techniques with respect to the response on individual grains in the bulk ceramics are later on applied to obtain representative hysteresis and butterfly curves under macroscopically uniaxial loading conditions at different loading frequencies. It turns out that the simulations based on the developed finite element formulation nicely match experimental data reported in the literature.

The problem of a single required mode (or several modes) excitation in a plate-like structure by a system of thin flexible piezoelectric patches is considered. The algorithm for obtaining proper driving fields is developed in the context of a 2D mathematical model (strip patches on a layer), which takes strictly into account the patch-structure contact interaction, the mutual influence of the actuators and the multimode character of traveling waves propagation in the substructure. Numerical results illustrate the high level of selectivity provided by the method proposed.

A mathematical model of an electromechanical system excited by piezoceramic patch actuators is developed. The model is based on the solution to the dynamic contact problem for a set of flexible strips interacting with a free elastic layer. Unlike the conventional models, which describe the mechanical part by the dynamic equations for beams, plates, or shels, the proposed model, in addition to the first fundamental modes, also takes into account the higher normal modes of an elastic waveguide. Results obtained with the proposed model and with the simplified models prove to be in good agreement in the low-frequency range. Numerical examples illustrate resonance energy radiation associated with higher modes of the laminate strip-layer structure, as well as the possibility to control its directivity.

In this paper, a three-dimensional micromechanical model is presented for simulation of the rate dependent properties of certain perovskite type tetragonal piezoelectric materials. The model is based on linear constitutive, nonlinear domain switching, and linear kinetics theories. The simulation starts with a virgin bulk material of randomly oriented grains. Then the material is electrically loaded with an alternating voltage of various frequencies, which are in the order of 0.01Hz to 1Hz. An energy equation in combination with a probability function is used to determine the onset of the domain switching inside the grains. Such a probability function leads to a better phenomenological model for the domain switching even for electrical loadings, which are in a range far below the coercive fields. The propagation of the domain wall during the domain switching process in grains is modeled by means of linear kinetics relations after domain nucleation. The response of the bulk ceramic is predicted by averaging the response of individual grains using Euler angles for the transformation from local coordinates of the grains to global coordinate. Electric displacement hysteresis loops for different frequencies and amplitudes of the alternating electric fields are simulated. A simple micromechanical model without the probabilistic approach is compared with the one that takes it into account. Both models give important insights into the rate dependency of piezoelectric materials, which was observed in some experiments reported in the literature.

In this paper, a new longitudinal and torsional type ultrasonic motor with two stators is presented and investigated. Normally, such a motor consists of one rotor and one stator, and two types of transducers that are longitudinal PZT and torsional PZT are used to generate the desired elliptical locus on the stator surface. The operating frequency is at the resonance frequency of torsional transducer. In order to enhance the efficiency of the motor, however, the resonance frequencies of both transducers should be closed to each other. For the purpose of matching the resonance frequencies, a symmetrical structure is adopted in design of the motor. Furthermore, two rings are added to the stators in order to adjust the resonance frequencies of these two transducers. A finite element model is developed and ANSYS software is used to analyze the resonance frequencies of longitudinal vibration and torsional vibration as well as optimize the motor geometry. According to the FE results, an experimental prototype is fabricated and the experimental results agree well with the theoretical predictions.