Christian Zehetner

Mathematical Analysis of Piezoelectric Sandwich Torsion Transducers Based on the d36-Effect

In the present article, we analyze a d36-effect piezoelectric torsion transducer following the Saint-Venant torsion theory taking the electrical field into account. A representation of the stress function, the electric potential, and the warping function are derived and solved with finite differences. Then, the one-dimensional governing equations at the structural beam level, including the constitutive relations as well as the balance equations for the dynamics of the transducer, are presented. The axial moment and the total charge are computed as functions of the rate of twist and the applied potential difference. As an example, a cantilevered transducer is studied.

Mechatronics - The Innovation Request

Smart structures, which are equipped with piezoelectric actuators and sensors, and which involve automatic control, represent an important branch of Mechatronics. This paper gives a review over own research on smart structures, which has been performed during the last decade based on the principles of analogy and interdisciplinarity. The latter principles form a research strategy, which seems to be perfectly suited in order to answer the innovation request in Mechatronics, namely to decrease the time-lag between consecutive steps in the scientific development, and to keep fundamental and applied research in close co-operation. We start our report with a short excursion into the history of engineering sciences, in order to demonstrate this time-lag, where we use the history of elastic and piezoelastic plates as an example, and we discuss the notions of analogy and interdisciplinarity as means to systematically decrease the timelag. In our own work, we particularly have used an eigenstrain analogy as guideline. In the light of this analogy, various own works in the following fields are reviewed: Accurate electromechanically modeling; dynamic shape control by piezoelectric actuation and sensing; extension of dynamic shape control to closed loop control and active noise cancellation.

Compensation of Deformations in Elastic Solids and Structures in the Presence of Rigid-Body Motions

The present Lecture is concerned with vibrations of linear elastic solids and structures. Some part of the boundary of the structure is suffering a prescribed large rigid-body motion, while an imposed external traction is acting at the remaining part of the boundary, together with given body forces in the interior. Due to this combined loading, vibrations take place. The latter are assumed to remain small, such that the linear theory of elasticity can be applied. As an illustrative example for the type of problems in hand, we mention the flexible wing of an aircraft in flight. In this example, the rigid-body motion is defined through the motion of the comparatively stiff fuselage to which a part of the boundary of the wing is attached. The goal of the present paper is to derive a time-dependent distribution of actuating stresses produced by additional eigenstrains, such that the deformations produced by the imposed forces and the rigid-body motion are exactly compensated. This is called a shape control problem, or a deformation compensation problem. We show that the distribution of the actuating stresses for shape control must be equal to a quasi-static stress distribution that is in temporal equilibrium with the imposed forces and the inertia forces due to the rigid-body motion. Our solution thus explicitly reflects the non-uniqueness of the inverse problem under consideration. The present Lecture extends previous results by Irschik and Pichler (2001, 2004) for problems without rigid-body degrees of freedom. As a computational example, we present results for a rectangular domain in a state of plane strain under the action of a translatory support motion.

Nonlinear Finite Element Modelling of Moving Beam Vibrations Controlled by Distributed Actuators

In many applications, nonlinear beams undergoing bending, axial and shear deformation are important structural elements. In the present paper, a shear deformable beam finite element is presented for such applications. Since displacements and displacement gradients are chosen as the nodal degrees of freedom, an equivalent displacement and rotation interpolation is retrieved. The definition of strain energy is based on Reissner’s nonlinear rod theory with special strain measures for axial strain, shear strain and bending strain. Furthermore, a thickness deformation is introduced by adding an according term to the virtual work of internal forces. This underlying formulation is extended for piezo-electric actuation. The obtained beam finite elements are applied to a two-link robot with two flexible arms with tip masses. Distributed and concentrated masses cause flexural vibrations, which are compensated by means of piezo-electric actuators attached to the arms. A numerical example of a highly flexible robot with piezo-electric actuation and feedforward control is presented to show the applicability of the finite element.

LEAN PANEL BENDER – Einige mechanische Aspekte der Modellierung in Echtzeit für Produktion in Losgröße 1

ZusammenfassungNachfolgend werden einige wissenschaftliche Aspekte der Echtzeit-Materialerkennungsstrategie MAC diskutiert, die in der neuen Maschinenfamilie LEAN PANEL BENDER der Firma Salvagnini Maschinenbau realisiert ist und die eine hochpräzise und hocheffiziente Herstellung von komplex geformten Blechprodukten sowohl bei Losgröße 1 als auch in der Serie erlaubt.AbstractIn this paper, we discuss some scientific aspects of the real-time material detection strategy MAC, which is realized in the novel LEAN PANEL BENDER generation of the company Salvagnini Maschinenbau GmbH and which allows the production of complex metal devices in a highly efficient and accurate manner for both, single-slot production and production in series.

NUMERICAL MODELLING AND SIMULATION OF SHEET METAL CUTTING PROCESSES

Material processing is a very important industrial sector. In order to guarantee high precision and quality of the products, reliable numerical simulation models are required. This contribution concerns the simulation of material cutting. As a benchmark example, a sheet metal is fixed by two clamping tools and the cutting process is controlled by a moving blade. The tools are modelled as linear elastic materials, and the sheet metal as elasto-plastic material with hardening. Main scope is the comparison of two simulation methods with respect to industrial application: (i) Coupled Eulerian-Lagrangian Finite Element Method and (ii) Coupled Lagrangian Finite Element and Smoothed Particle Analysis. Numerical simulation models for the two variants of the above benchmark example are implemented in the commercial code Abaqus. The numerical results of the two models are compared with respect to accuracy and numerical effort, and the advantages and disadvantages of the two methods are investigated. The implemented models for the cutting process and the materials can be applied to several other kinds of industrial material processing like stamping or punching.

EFFICIENT NUMERICAL SIMULATION OF INDUSTRIAL SHEET METAL BENDING PROCESSES

Abstract. In industrial production processes focus is given to high precision, quality, resource efficiency and productivity. In order to achieve these goals, efficient numerical simulation models are required. In the following, we consider an industrial sheet metal bending process, in which the sheet is fixed on one side and formed by a moving tool. On the one hand, there is a very large number of process parameters. On the other hand, the production sites are complex and have to be modelled in detail. Parameter studies are very extensive and take a large numerical effort. Therefore high efficient simulation tools are necessary to handle this challenge. In this paper two strategies for increasing the efficiency of modelling are investigated. First, the main focus is set to an efficient Finite Element model for sheet bending. Two Finite Element formulations are compared based on 3D-continuum elements and continuum shell elements. Secondly, a proper normalized formulation (similarity solution) of the bending process is derived starting from a reduced-order model, which subsequently is successfully applied to the complex bending process. Utilizing the concept of similarity, the number of cases in parameter studies can be reduced significantly.

Vibration Control and Structural Damping of a Rotating Beam by Using Piezoelectric Actuators

In this paper, the application of piezoelectric vibration control in flexible multibody systems is studied and verified. Exemplarily, beam-type structures are considered that are subject to inertial and external forces. The equations of motion for three-dimensional flexible and torsional vibrations are presented considering the influence of piezoelectric actuation strains. In the framework of Bernoulli-Euler beam theory the shape control solution is derived, i.e. the distribution of actuation strains such that the flexible displacements are completely compensated. For the experimental verification, a laboratory model has been developed, in which the theoretical distribution of actuation strains is discretized by piezoelectric patches. A suitable control algorithm is implemented within a dSpace environment. Finally, the results are validated by numerical computations utilizing ABAQUS and HOTINT, and verified by experimental evaluation.