Time-efficient dynamic analysis of structures exhibiting nonlinear peak bending - Sprock, Christian; Sextro, Walter (Instrumentation and Measurement Technology Conference (I2MTC) Proceedings, 2014 IEEE International)
A measurement method is presented that combines the advantages of the multisine measurement technique with a prediction method for peak bending behavior. This combination allows the analysis of the dynamic behavior of mechanical structures at distinctly reduced measurement durations and has the advantage of reducing high excitation impacts on the structure under test.
Keywords: bending; dynamic testing; measurement; structural engineering; vibrations; measurement durations; mechanical structures; multisine measurement technique; nonlinear peak bending behavior; prediction method; time-efficient dynamic analysis; Heuristic algorithms; Nonlinear systems; Oscillators; Time measurement; Time-frequency analysis; Vibrations

Time-efficient analysis of nonlinear dynamic behavior. - Sprock, Christian; Sextro, Walter (Proceedings in Applied Mathematics and Mechanics 14 (2014), Nr. 1,)
Many nonlinear mechanical oscillators show excitation-dependent behavior. In this paper, a new measurement approach is presented to analyze such structures. The main advantage of the presented method is the high efﬁciency, since measurement duration and loads to the structure are signiﬁcantly reduced.

Time-efficient analysis of nonlinear peak bending behavior. - Sprock, Christian; Sextro, Walter (Proceedings of ISMA - International Conference of Noise and Vibration. 2014)
A measurement method is presented that combines the advantages of the multisine measurement technique with a prediction method for peak bending behavior. This combination allows the analysis of the dynamic behavior of mechanical structures at distinctly reduced measurement durations and has the advantage of reducing high excitation impacts on the structure under test. After a brief presentation of the algorithm, the validity scope of the approach is investigated with emphasis on an exemplary error investigation.

Vibration Analysis of Mechanical Structures using Multisine Excitation Techniques - Sprock, Christian; Sextro, Walter (Proceedings of 31st Danubia-Adria Symposium. 2014)

Introduction to Self-optimization and Dependability - Trächtler, Ansgar; Hölscher, Christian; Rasche, Christoph; Priesterjahn, Claudia; Zimmer, Detmar; Henning Keßler, Jan; Stahl, Katharin; Flaßkamp, Kathrin; Vaßholz, Mareen; Krüger, Martin; Dellnitz, Michael; Iwanek, Peter; et al. (Dependability of Self-Optimizing Mechatronic Systems)

Case Study - Trächtler, Ansgar; Kleinjohann, Bernd; Heinzemann, Christian; Rasche, Christoph; Priesterjahn, Claudia; Steenken, Dominik; Wehrheim, Heike; Gausemeier, Jürgen; Flaßkamp, Kathrin; Kleinjohann, Lisa; Krüger, Martin; Iwanek, Peter; et al. (Dependability of Self-Optimizing Mechatronic Systems)

Experimental and Numerical Simulation Study of Pre-Deformed Heavy Copper Wire Wedge Bonds - Unger, Andreas; Sextro, Walter; Althoff, Simon; Eichwald, Paul; Meyer, Tobias; Eacock, Florian; Brökelmann, Michael (Proceedings of the 47th International Symposium on Microelectronics (IMAPS))
Power semiconductor modules are used to control and switch high electrical currents and voltages. Within the power module package wire bonding is used as an interconnection technology. In recent years, aluminum wire has been used preferably, but an ever-growing market of powerful and efficient power modules requires a material with better mechanical and electrical properties. For this reason, a technology change from aluminum to copper is indispensable. However, the copper wire bonding process reacts more sensitive to parameter changes. This makes manufacturing reliable copper bond connections a challenging task. The aim of the BMBF funded project Itsowl-InCuB is the development of self-optimizing techniques to enable the reliable production of copper bond connections under varying conditions. A model of the process is essential to achieve this aim. This model needs to include the dynamic elasto-plastic deformation, the ultrasonic softening effect and the proceeding adhesion between wire and substrate. This paper focusses on the pre-deformation process. In the touchdown phase, the wire is pressed into the V-groove of the tool and a small initial contact area between wire and substrate arise. The local characteristics of the material change abruptly because of the cold forming. Consequently, the pre-deformation has a strong effect on the joining process. In [1], a pre-cleaning effect during the touchdown process of aluminum wires by cracking of oxide layers was presented. These interactions of the process parameters are still largely unknown for copper. In a first step, this paper validates the importance of modeling the pre-deformation by showing its impact on the wire deformation characteristic experimentally. Creating cross-section views of pre-deformed copper wires has shown a low deformation degree compared to aluminum. By using a digital microscope and a scanning confocal microscope an analysis about the contact areas and penetration depths after touchdown has been made. Additionally, it has to be taken into account that the dynamical touchdown force depends on the touchdown speed and the touchdown force set in the bonding machine. In order to measure the overshoot in the force signals, a strain gauge sensor has been used. Subsequently, the affecting factors have been interpreted independently Furthermore, the material properties of copper wire have been investigated with tensile tests and hardness measurements. In a second step, the paper presents finite element models of the touchdown process for source and destination bonds. These models take the measured overshoot in the touchdown forces into account. A multi-linear, isotropic material model has been selected to map the material properties of the copper. A validation of the model with the experimental determined contact areas, normal pressures and penetration depths reveals the high model quality. Thus, the simulation is able to calculate and visualize the three dimensional pre-deformation with an integrated material parameter of the wire if the touchdown parameters of the bonding machine are known. Based on the calculated deformation degrees of wire and substrate, it is probably possible to investigate the effect of the pre-deformation on the pre-cleaning phase in the copper wire bonding.
Keywords: pre-deformation; copper wire bonding; finite element model

Data-driven Modeling of the Ultrasonic Softening Effect for Robust Copper Wire Bonding - Unger, Andreas; Sextro, Walter; Althoff, Simon; Meyer, Tobias; Brökelmann, Michael; Neumann, Klaus; Reimann, René Felix; Guth, Karsten; Bolowski, Daniel (Proceedings of 8th International Conference on Integrated Power Electronic Systems)
In power electronics, ultrasonic wire bonding is used to connect the electrical terminals of power modules. To implement a self-optimization technique for ultrasonic wire bonding machines, a model of the process is essential. This model needs to include the so called ultrasonic softening effect. It is a key effect within the wire bonding process primarily enabling the robust interconnection between the wire and a substrate. However, the physical modeling of the ultrasonic softening effect is notoriously difficult because of its highly non-linear character and the absence of a proper measurement method. In a first step, this paper validates the importance of modeling the ultrasonic softening by showing its impact on the wire deformation characteristic experimentally. In a second step, the paper presents a data-driven model of the ultrasonic softening effect which is constructed from data using machine learning techniques. A typical caveat of data-driven modeling is the need for training data that cover the considered domain of process parameters in order to achieve accurate generalization of the trained model to new process configurations. In practice, however, the space of process parameters can only be sampled sparsely. In this paper, a novel technique is applied which enables the integration of prior knowledge about the process into the datadriven modeling process. It turns out that this approach results in accurate generalization of the data-driven model to unseen process parameters from sparse data.

Increasing Intelligent Systems’ Reliability by using Reconfiguration - Meyer, Tobias; Kessler, Jan Henning; Sextro, Walter; Trächtler, Ansgar (The Annual Reliability and Maintainability Symposium (RAMS))
Self-optimizing mechatronic systems allow the adaptation of the system’s behavior to the current situation. This can be used to actively adapt the behavior to the current degradation state of the system or of some of its components. To this end, the Multi-Level Dependability Concept has been developed. In this contribution, we show how the Multi-Level Dependability Concept has been applied to the active suspension module of an innovative rail-bound vehicle. For this module, the usage of control reconfiguration, which is a novel approach to exploit complex redundancy systems, is required. We show that by combining self-optimization with the possibilities given by control reconfiguration, the dependability of a complex mechatronic system can be greatly improved.

Increasing the Dependability of Self-Optimizing Systems During Operation Using the Multi-Level Dependability Concept - Kessler, Jan Henning; Meyer, Tobias; Sextro, Walter; Sondermann-Wölke, Christoph; Trächtler, Ansgar (Dependability of Self-Optimizing Mechatronic Systems)

Increasing Intelligent Systems’ Reliability by using Reconfiguration - Meyer, Tobias; Kessler, Jan Henning; Sextro, Walter; Trächtler, Ansgar (The Annual Reliability and Maintainability Symposium (RAMS))

Applications of Self-Optimizing Systems - Hölscher, Christian; Kessler, Jan Henning; Meyer, Tobias; Rasche, Christoph; Reinold, Peter; Sextro, Walter; Sondermann-Wölke, Christoph; Zimmer, Detmar (Dependability of Self-Optimizing Mechatronic Systems)

Increasing the power of piezoelectric energy harvesters by magnetic stiffening - Al-Ashtari, Waleed; Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (Journal of Intelligent Material Systems and Structures)
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.

Enhanced energy harvesting using multiple piezoelectric elements: Theory and experiments - Al-Ashtari, Waleed; Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (Sensors and Actuators A: Physical)
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.
Keywords: Energy harvesting; Cantilever array; Bandwidth; Power increase

Characteristics of Piezoelectric Energy Harvesters in Autonomous Systems - Al-Ashtari, Waleed; Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (Proceedings of 10th International Workshop on Piezoelectric Materials and Applications and 8th Energy Harvesting Workshop, Hannover, Germany, 14.-17.7.2013)
A basic autonomous system powered by a piezoelectric harvester contains three components apart from the harvester: a fullwave rectifier, a reservoir capacitor and an electronic device performing the primary task of the system. In this contribution, a model describing the operation of such a system is derived. It is found that in steady-state operation, the piezoelectric harvester experiences two alternating load conditions due to the rectification process. These alternating load conditions can have a significant effect on the operation of the harvester and must be considered in the design of autonomous systems. The results also show that such an autonomous system works efficiently if it is connected to a high impedance load and excited by a frequency matching the anti-resonance frequency of the piezoelectric harvester.
Keywords: Energy harvesting; harvester modeling; load dependence; generated voltage

A friction based approach for modeling wire bonding - Althoff, Simon; Neuhaus, Jan; Hemsel, Tobias; Sextro, Walter (IMAPS 2013, 46th International Symposium on Microelectronics)
A model approach for wedge/wedge bonding copper wire is presented. The connection between wire and substrate is based on a variety of physical effects, but the dominant one is the friction based welding while applying ultrasound. Consequently, a friction model was used to investigate the welding process. This model is built up universal and can be used to describe the formation of micro welds in the time variant contact area between wire and substrate. Aim of the model is to identify the interactions between touchdown, bond normal force, ultrasonic power and bonding time. To do so, the contact area is discretized into partial areas where a Point Contact Model is applied. Based on this approach it is possible to simulate micro and macro slip inside the contact area between wire and substrate. The work done by friction force is a main criterion to define occurring micro joints which influence the subsequent welding.
Keywords: Wire bonding; friction modeling; wire bond quality; contact element modeling

Influences of Bonding Parameters on the Tool Wear for Copper Wire Bonding - Eichwald, Paul; Sextro, Walter; Althoff, Simon; Eacock, Florian; Schnietz, Mark; Guth, Karsten; Brökelmann, Michael (15th Electronics Packaging Technology Conference)
Ultrasonic wire bonding is a common technology for manufacturing electrical interconnects. In the field of power electronics, new thermal and electrical obligations arose due to increasing power density requirements. One approach to achieve these aims is replacing the wire material for heavy wire bonds from aluminum to copper. This material change leads to challenging tasks and problems, for instance the occurring wear of the bond tool. The wear is significantly higher using copper wire instead of aluminum and results in a dramatic loss in the amount of interconnects which can be produced reliable by a single tool. To reduce setting-up time in the production and minimizing costs, an enlarged bonding tool lifetime is desirable. Therefore, the paper discusses the influences of bonding parameters on the wear. The key question is which of the tasks cannot be fulfilled with increased wear of the tool, e.g. loss of process capability. The main functions are fixing the wire in the tool groove, predeformation, applying normal force and transmission of ultrasonic oscillation to the wire. To identify the most affecting factors, four bonding parameters are varied and their influences are investigated. These parameters are: (I) ultrasonic power, (II) tool geometry, (III) the way of tangential force transmission and (IV) loop trajectory.

Leistungs- und Bandbreitensteigerung von Energy-Harvesting-Generatoren für Energieautarke Systeme - Hunstig, Matthias; Al-Ashtari, Waleed; Hemsel, Tobias; Sextro, Walter (9. Paderborner Workshop Entwurf mechatronischer Systeme)

High-Velocity Slip-Slip Operation of Piezoelectric Inertia Motors - Experimental Validation - Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (Proceedings of 10th International Workshop on Piezoelectric Materials and Applications and 8th Energy Harvesting Workshop)
It has been shown previously that ``slip-slip'' operation of piezoelectric inertia motors allows higher velocities and smoother movements than classic ``stick-slip'' operation. One very promising driving option is to use a superposition of multiple sinusoidal signals. In this contribution, previous theoretical results are validated experimentally. The results confirm the theoretical result that for a given maximum frequency, usually defined by the actuator characteristics, a signal with high fundamental frequency and consisting of two superposed sine waves leads to the highest velocity and the smoothest motion. This result is of fundamental importance for the further development of high-velocity piezoelectric inertia motors.
Keywords: Piezoelectric inertia motor; stick-slip motor; driving signal; velocity; smoothness

Modelling the friction contact in an inertia motor - Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (Journal of Intelligent Material Systems and Structures)
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 $μ$ 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.
Keywords: Actuator; friction; motor; piezoelectric

Stick-slip and slip-slip operation of piezoelectric inertia drives - Part II: Frequency-limited excitation - Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (Sensors and Actuators A: Physical)
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' σ 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.
Keywords: Inertia motor

Stick-slip and slip-slip operation of piezoelectric inertia drives - Part I: Ideal Excitation. - Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (Sensors and Actuators A: Physical)
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.
Keywords: Inertia motor; Stick--slip drive; Mode of operation; Performance indicator; Velocity maximization; Actuator stroke

Machinery Prognostic Method Based on Multi-Class Support Vector Machines and Hybrid Differential Evolution -- Particle Swarm Optimization - Kimotho, James Kuria; Sondermann-Wölke, Christopher; Meyer, Tobias; Sextro, Walter (Chemical Engineering Transactions)
Recently, focus on maintenance strategies has been shifted towards prognostic health management (PHM) and a number of state of the art algorithms based on data-driven prognostics have been developed to predict the health states of degrading components based on sensory data. Amongst these algorithms, Multiclass Support Vector Machines (MC-SVM) has gained popularity due to its relatively high classification accuracy, ability to classify multiple patterns and capability to handle noisy /incomplete data. However, its application is limited by the difficulty in determining the required kernel function and penalty parameters. To address this problem, this paper proposes a hybrid differential evolution -- particle swarm optimization (DE-PSO) algorithm to optimize the MC-SVM kernel function and penalty parameters. The differential algorithm (DE) obtains the search limit for the SVM parameters, while the particle swarm optimization algorithm (PSO) determines the global optimum parameters for a given training data set. Since degrading machinery components display several degradation stages in their lifetime, the MC-SVM trained with optimum parameters are used to estimate the health states of a degrading machinery component, from which the remaining useful life (RUL) is predicted. This method improves the classification accuracy of MC-SVM in predicting the health states of a machinery component and consequently increases the accuracy of RUL predictions. The feasibility of the method is validated using bearing prognostic run-to-failure data obtained from NASA public data repository. A comparative study between MC-SVM with parameters obtained using simple grid search with n-fold cross validation and MCSVM with DE-PSO based on prognostic performance metrics reveals that the proposed method has better performance, with all the cases considered falling within a 10 % error margin. The method also outperforms other soft computing methods proposed in literature.

Application of Event Based Decision Tree and Ensemble of Data Driven Methods for Maintenance Action Recommendation - Kimotho, James Kuria; Sondermann-Wölke, Chritoph; Meyer, Tobias; Sextro, Walter (International Journal of Prognostics and Health Management)
This study presents the methods employed by a team from the department of Mechatronics and Dynamics at the University of Paderborn, Germany for the 2013 PHM data challenge. The focus of the challenge was on maintenance action recommendation for an industrial machinery based on remote monitoring and diagnosis. Since an ensemble of data driven methods has been considered as the state of the art approach in diagnosis and prognosis, the first approach was to evaluate the performance of an ensemble of data driven methods using the parametric data as input and problems (recommended maintenance action) as the output. Due to close correlation of parametric data of different problems, this approach produced high misclassification rate. Event-based decision trees were then constructed to identify problems associated with particular events. To distinguish between problems associated with events that appeared in multiple problems, support vector machine (SVM) with parameters optimally tuned using particle swarm optimization (PSO) was employed. Parametric data was used as the input to the SVM algorithm and majority voting was employed to determine the final decision for cases with multiple events. A total of 165 SVM models were constructed. This approach improved the overall score from 21 to 48. The method was further enhanced by employing an ensemble of three data driven methods, that is, SVM, random forests (RF) and bagged trees (BT), to build the event based models. With this approach, a score of 51 was obtained . The results demonstrate that the proposed event based method can be effective in maintenance action recommendation based on events codes and parametric data acquired remotely from an industrial equipment.
Keywords: maintenance decision; Bagged trees; Decision trees; PSO-SVM; Random forests

Modelbased Investigations of Gyroscopic Effect on the (Elasto-)Kinematics of Suspension Systems - Kohl, Sergej; Zuber, Armin; Sextro, Walter (Proc. Appl. Math. Mech.)
During wheel bumping caused by stochastic road excitation, the wheel performs rotational and translational movements. The bump and rebound wheel velocity leads to significant angular velocities based on the (elasto-)kinematics of the suspension system. Based on the gyroscopic effect, moments arise about the rotating wheel induced by the angular change while bumping. Therefore it leads to undesirable wheel changes and degrades the tire contact and finally decreases the driving stability. A flexible MBS-model of the five-link rear axle system that includes these effects has been built up to allow a detailed investigation of the gyroscopic effect. Using the simulation results, conclusions can be drawn for refining design criteria for the kinematics, elastokinematics and topology of the suspension system to increase the active safety of the vehicle

Multiobjective Optimization including Safety of Operation Applied to a Linear Drive System - Meyer, Tobias; Hölscher, Christina; Menke, Michael; Sextro, Walter; Zimmer, Detmar (Proc. Appl. Math. Mech.)
In this contribution, we introduce a multiobjective optimization used to calculate safe optimal working points for a mechatronic system by including stochastic safety-critical signals in an objective function. Our application example consists of a linear drive for a rail-bound vehicle and an actuation unit. The linear drive's secondary part is fixed; the primary part is vehicle-mounted and can be adjusted vertically to account for deviations of the height of the secondary part. A small air gap between both parts improves efficiency, but increases the risk of a collision between the two parts. Using height data of the secondary part, a trajectory for the vertical adjustment of the primary part is calculated. However, unexpected deviations necessitate a readjustment of the air gap. The probability of such unexpected height deviations can be calculated from the readjustment data. The system is equipped with sensors to measure the air gap. Assuming that the sensor noise is normally distributed, noise characteristics are determined. Using this information and the probability distribution of unexpected height deviations, the probability of a collision is determined.T he sensor noise and the probability of a collision between both parts of the linear drive are included in the dynamical model of the system. Using multiobjective optimization, pareto-optimal working points for the controller of the air gap are obtained. By selecting an appropriate working point, safe operation can be ensured.

Increasing Intelligent Systems' Reliability by Using Reconfiguration - Meyer , Tobias; Henning Keßler, Jan; Sextro, Walter; Trächtler, Ansgar (Proceedings of the Annual Reliability and Maintainability Symposium (RAMS))
Self-optimizing mechatronic systems allow the adaptation of the system's behavior to the current situation. This can be used to actively adapt the behavior to the current degradation state of the system or of some of its components. To this end, the Multi-Level Dependability Concept has been developed. In this contribution, we show how the Multi-Level Dependability Concept has been applied to the active suspension module of an innovative rail-bound vehicle. For this module, the usage of control reconfiguration, which is a novel approach to exploit complex redundancy systems, is required. We show that by combining self-optimization with the possibilities given by control reconfiguration, the dependability of a complex mechatronic system can be greatly improved.

Controlling the Remaining Useful Lifetime using Self-Optimization - Meyer, Tobias; Sondermann-Wölke, Christoph; Kimotho, James Kuria; Sextro, Walter (Chemical Engineering Transactions)
Self-optimizing mechatronic systems offer possibilities well beyond those of traditional mechatronic systems. Among these is the adaptation of the system behavior to the current situation. To do so, they are able to choose from different working points, which are pre-calculated using multiobjective optimization and are thus Pareto-optimal with regard to the chosen objective functions. In this contribution, a method is presented that allows to continuously control the system degradation by adapting the behavior of a selfoptimizing system throughout its complete lifetime. The current remaining useful lifetime is estimated and then related to the spent lifetime and the desired useful lifetime. Using this information, a reliability-related objective is prioritized using a closed-loop control, which in turn is used to determine the working point of the self-optimizing system. This way, the desired useful lifetime can be achieved. To exemplify the setup of the controller structure and to demonstrate the adaptation of the system behavior, a dynamic model of a clutch system is used. It can be seen that the closed loop controller is able to correct for external perturbations, such as changed requirements, as well as changed system parameters. This way, the modeled system is able to achieve the desired lifetime reliably.

Bewertung der Zuverlässigkeit selbstoptimierender Systeme mit dem LARES-Framework - Meyer, Tobias; Sondermann-Wölke, Christoph; Sextro, Walter; Riedl, Martin; Gouberman, Alexander; Siegle, Markus (9. Paderborner Workshop Entwurf mechatronischer Systeme)
Selbstoptimierende mechatronische Systeme bieten die Möglichkeit, ihr Verhalten an geänderte Umgebungsbedingungen anzupassen. Dazu werden beispielsweise redundante Strukturen genutzt, Reglerparameter angepasst oder Regelstrategien umgeschaltet. Dies kann auch genutzt werden, um die Zuverlässigkeit des Systems zu steigern. Zugleich entstehen aber durch die gesteigerte Komplexität dieser Systeme zusätzliche Risiken. Um sicherzustellen, dass das System dennoch die gestellten Anforderungen bezüglich der Zuverlässigkeit erfüllt, ist eine Modellierung des Gesamtsystems und anschließende Zuverlässigkeitsbewertung notwendig. Dies ist aufgrund der situationsabhängigen Verhaltensanpassung und des nicht intuitiv vorhersehbaren Verhaltens jedoch nicht mit klassischen Verfahren möglich. Ein Modellierungsverfahren, das diese Eigenschaften abbilden kann, ist LARES (LAnguage for REconfigurable dependable Systems). Die Anwendung von LARES zur Bewertung der Zuverlässigkeit eines selbstoptimierenden Systems wird anhand des Feder-Neige-Moduls gezeigt. Es ist eine Baugruppe der Fahrzeuge eines innovativen Bahnsystems, der RailCabs. Das Feder-Neige-Modul dient dazu, unerwünschte Schwingungen des Fahrzeugaufbaus zu minimieren. Mit LARES können die Hardware-Komponenten des Systems, ihre in Abhängigkeit von der aktuellen Situation veränderten Belastungen sowie die nicht-deterministische Verhaltensadaption modelliert werden.

Frequency tuning of piezoelectric energy harvesters by magnetic force - Al-Ashtari, Waleed; Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (Smart Materials and Structures)
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%.

Analytical determination of characteristic frequencies and equivalent circuit parameters of a piezoelectric bimorph - Al-Ashtari, Waleed; Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (Journal of Intelligent Material Systems and Structures)
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.

Non-perturbing cavitation detection / monitoring in sonochemical reactors - Bornmann, Peter; Hemsel, Tobias; Sextro, Walter; Maeda, Takafumi; Morita, Takeshi (Ultrasonics Symposium (IUS), 2012 IEEE International)
To optimize the ultrasound irradiation for cavitation based ultrasound applications like sonochemistry or ultrasound cleaning, the correlation between cavitation intensity and the resulting effect on the process is of interest. Furthermore, changing conditions like temperature and pressure result in varying acoustic properties of the liquid. That might necessitate an adaption of the ultrasound irradiation. To detect such changes during operation, process monitoring is desired. Labor intensive processes, that might be carried out for several hours, also require process monitoring to increase their reliability by detection of changes or malfunctions during operation. In some applications cavitation detection and monitoring can be achieved by the application of sensors in the sound field. Though the application of sensors is possible, this necessitates modifications on the system and the sensor might disturb the sound field. In other applications harsh, process conditions prohibit the application of sensors in the sound field. Therefore alternative techniques for cavitation detection and monitoring are desired. The applicability of an external microphone and a self-sensing ultrasound transducer for cavitation detection were experimentally investigated. Both methods were found to be suitable and easily applicable.
Keywords: cavitation; chemical reactors; microphones; process monitoring; reliability; ultrasonic applications; ultrasonic waves; acoustic properties; cavitation based ultrasound applications; cavitation intensity; change detection reliability; external microphone; malfunction detection reliability; nonperturbing cavitation detection; nonperturbing cavitation monitoring; process monitoring; self-sensing ultrasound transducer; sonochemical reactors; sonochemistry; ultrasound cleaning; ultrasound irradiation; Acoustics; Liquids; Monitoring; Sensors; Sonar equipment; Transducers; Ultrasonic imaging

Benteler Vehicle Dynamics -- Fahrdynamikentwicklung basierend auf einer neuen Auslegungstheorie - Kohl, Sergej; Sextro, Walter; Zuber, Armin (8. Tag des Fahrwerks, Aachen, 2012)

Conceptual Design of Advanced Condition Monitoring for a Self-Optimizing System based on its Principle Solution - Sondermann-Wölke , Christoph; Meyer, Tobias; Dorociak, Rafal; Gausemeier, Jürgen; Sextro, Walter (Proceedings of the 11th International Probabilistic Safety Assessment and Management Conference (PSAM11) and The Annual European Safety and Reliability Conference (ESREL2012))
The rapid development of communication and information technology opens up fascinating perspectives, which go far beyond the state of the art in mechatronics: mechatronic systems with inherent partial intelligence. These so called self-optimizing systems adapt their objectives and behavior autonomously and flexibly to changing operating conditions. On the one hand, securing the dependability of such systems is challenging due to their complexity and non-deterministic behavior. On the other hand, self-optimization can be used to increase the dependability of the system during its operation. However, it has to be ensured, that the self-optimization works dependable itself. To cope with these challenges, the multi-level dependability concept was developed. It enables predictive condition monitoring, influences the objectives of the system and determines suitable means to improve the system's dependability during its operation. In this contribution we introduce a procedure for the conceptual design of an advanced condition monitoring based on the system's principle solution. The principle solution describes the principal operation mode of the system and its desired behavior. It is modeled using the specification technique for the domain-spanning description of the principle solution of a self-optimizing system and consists of a coherent system of eight partial models (e.g. requirements, active structure, system of objectives, behavior, etc.). The partial models are analyzed separately in order to derive the components of the multi-level dependability concept. In particular, the reliability analysis of the partial model active structure is performed to identify the system elements to be monitored and parameters to be measured. The principle solution is extended accordingly: e.g. with system elements required for the realization of the dependability concept. The advantages of the method are shown on the self-optimizing guidance module of a railroad vehicle.
Keywords: Mechatronic Systems; Principle Solution; Condition Monitoring; Conceptual Design

Analysis of different operation modes for inertia motors - Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (ACTUATOR 2012 Conference Proceedings)
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.
Keywords: Piezoelectric Inertia Motors; Drive Signals; Stick-slip; Slip-slip

Zuverlässigkeitsorientierte Mehrzieloptimierung zur Aktorrekonfiguration eines X-by-wire-Fahrzeugs - Sondermann-Wölke, Christoph; Sextro, Walter; Reinold, Peter; Trächtler, Ansgar (Technische Zuverlässigkeit TTZ)

Verlässlichkeitsanalyse des Degradationsverhaltens mechatronischer Systeme mit mehreren Betriebsstrategien - Lurye, Oleg; Sondermann-Wölke, Christoph; Kromov, Ivan; Sextro, Walter; Trächtler, Ansgar (VDI Bericht zur Tagung Technische Zuverlässigkeit)

Zuverlässigkeitsorientierte Mehrzieloptimierung zur Aktorrekonfiguration eines X-by-wire-Fahrzeugs - Sondermann-Wölke, Christoph; Sextro, Walter; Reinold, Peter; Trächtler, Ansgar (Technische Zuverlässigkeit TTZ)

Dependability Analysis of the Degradation Behavior of Mechatronics Systems with Different Operating Strategies - Lurie, Oleg; Kromov, Ivan; Trächtler, Ansgar; Sondermann-Wölke, Christoph; Sextro, Walter (25. Tagung Technische Zuverlässigkeit (TTZ 2011) - Entwicklung und Betrieb zuverlässiger Produkte)

Zuverlässigkeitsorientierte Mehrzieloptimierung zur Aktorrekonfiguration eines X-by-wire-Fahrzeugs - Sondermann-Wölke, Christoph; Sextro, Walter; Reinold, Peter; Trächtler, Ansgar (25. Tagung Technische Zuverlässigkeit (TTZ 2011) - Entwicklung und Betrieb zuverlässiger Produkte)
Dieser Beitrag stellt ein Konzept vor, welches die Methode der Mehrzieloptimierung mit einer Online-Bewertung des aktuellen Systemzustands kombiniert. Dieses erlaubt Maßnahmen zur Zuverlässigkeitssteigerung abzuleiten. Das Konzept wird auf ein X-by-wire-Fahrzeug mit Einzelradaktorik angewandt. Dabei steht zunächst die Beeinflussung der Ziele der Mehrzieloptimierung zugunsten der Zuverlässigkeit des Systems im Vordergrund. In Simulationen wird gezeigt, dass über die Wahl und Gewichtung der Zielfunktionen die Quer- und Längskräfte an den Rädern vorteilhaft verteilt werden können. In this contribution a concept is illustrated, which combines the multi-objective optimization technique with an online assessment of the current system state. This allows deriving measures to increase the reliability of the system. The concept is applied to an X-by-wire vehicle with single-wheel actuators. The emphasis is here mostly on the influence of the objectives of the multiobjective optimization for the benefit of the reliability of the system. It is demonstrated in simulations, that the lateral and longitudinal forces at the wheels can be distributed advantageously by the selection of the suitable objective functions and the appropriate weights.

Friction in wheel--rail contact: A model comprising interfacial fluids, surface roughness and temperature - Tomberger, Christoph; Dietmaier, Peter; Sextro, Walter; Six, Klaus (Wear)
A profound description of friction in wheel--rail contact plays an essential role for optimization of traction control strategies, as input quantity for railway simulations in general and for the estimation of wear and rolling contact fatigue. A multitude of wheel--rail contact models exists, however, traction--creepage curves obtained from measurements show quantitative and qualitative deviations. There are several phenomena which influence the traction--creepage characteristics: Mechanisms resulting from surface roughness, frictional heating or the presence of interfacial fluids can have a dominating influence on friction. In this paper, a new wheel--rail contact model, accounting for these influential parameters, will be presented. The presented model accounts for the interaction of an interfacial fluid model for combined boundary and mixed lubrication of rough surfaces with a wheel--rail contact model that additionally accounts for frictional heating. A quantitative comparison with measurements found in the literature is not conducted, since the exact conditions of the measurements are mostly unknown and parameters can easily be adjusted to fit the measurements. Emphasis is placed on the qualitative behavior of the model with respect to the measurements and good agreement is found. The dependence of the maximum traction coefficient on rolling velocity, surface roughness and normal load is studied under dry and water lubricated conditions.
Keywords: Wheel--rail contact; Rolling contact; Friction; Interfacial fluid; Lubrication; Surface roughness; Contact temperature

Patent DE10201003395: Anordnung und Verfahren zur mehrdimensionalen Messung von Schwingungen eines Objekts. - Sextro, Walter; Hunstig, Matthias; Bornmann, Peter; Hemsel, Tobias
Es wird eine Anordnung zur mehrdimensionalen Messung von Schwingungen eines Objektes vorgeschlagen, umfassend ein Vibrometer und eine erste Ablenkeinheit, mittels welcher der Messstrahl des Vibrometers in wenigstens zwei erste Raumrichtungen ablenkbar ist, sowie wenigstens eine zweite Ablenkeinheit, mittels welcher der aus einer der wenigstens zwei ersten Raumrichtungen auf eine zweite Ablenkeinheit eintreffende Messstrahl derart ablenkbar ist, dass ein Messpunkt des Objekts aus einer ersten Raumrichtung und wenigstens einer zweiten Raumrichtung oder wenigstens zwei zweiten Raumrichtungen damit erfassbar ist. Bei dem zum Betrieb der Anordnung vorgesehenen Verfahren wird der Messstrahl eines Vibrometers in wenigstens zwei erste Raumrichtungen abgelenkt, woraufhin wenigstens ein Messstrahl einer ersten Raumrichtung ein zweites Mal derart abgelenkt wird, dass ein Messpunkt des Objekts aus einer ersten Raumrichtung und wenigstens einer zweiten Raumrichtung oder wenigstens zwei zweiten Raumrichtungen erfasst wird, insbesondere so dass die zu untersuchenden Bewegungskomponenten in den Messsignalen, welche entlang der ersten und zweiten Raumrichtungen gewonnen werden, enthalten sind. The arrangement has a first deflecting unit (3) for deflecting a measuring beam of a vibrometer (2) in spatial directions (4-6, 4-6). Second and third deflecting units (7, 8) deflect the beam arriving from one of the spatial directions such that a measuring point (9) of an object (1) is detectable with the beam from the spatial direction or the spatial directions. The first deflecting unit is designed as a scanning unit, where the measuring point is detected by the scanning unit. A measuring instrument measures focus quality and is connected to actuators for adjustment of the focus quality. An independent claim is also included for a method for multidimensional measurement of oscillations of an object.

Reibungsdämpfung in ausgedehnten, verschraubten Fügestellen - Hölzl, Johannes Sebastian; Sextro, Walter (PAMM)
Bei der Konstruktion von Maschinen ist es oftmals erforderlich, Schwingungen minimal zu halten. Um z.B. die Lebensdauer zu erhöhen, Material einzusparen oder den Geräuschpegel gering zu halten muss oft ein großer Aufwand zur Dämpfung von auftretenden Schwingungen betrieben werden. In vielen technischen Anwendungen werden Einzelteile miteinander verschraubt. Diese Fügestellen können gezielt und mit wenig Aufwand zur Schwingungsdämpfung herangezogen werden. Die Berechnung des dynamischen Verhaltens verschraubter Strukturen stellt immer noch eine Herausforderung dar. Es wurde eine Methode entwickelt, um den eingeschwungenen Zustand elastischer, miteinander verschraubter Körper mit rauen Fügestellen bei periodischer Anregung zu berechnen. Als Basis dienen Finite Elemente Modelle der einzelnen Teile, deren Freiheitsgrade durch modale Kondensation reduziert werden. Unter Anwendung des Verfahrens von Ritz und Galerkin wird eine Näherungslösung für den eingeschwungenen Zustand des nichtlinearen, gekoppelten Systems ermittelt. Abhängig von den Schraubenvorspannkräften sowie den bestimmenden Parametern der Kontaktflächen, Rautiefe und Reibungskoeffizient, kann die Systemantwort berechnet und optimiert werden. Um die Berechnungsmethode zu verifizieren wurden Experimente durchgeführt. Der Vergleich zwischen Messung und Rechnung zeigt eine gute Übereinstimmung. ({©} 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Simulation of the Dynamical Behavior of Elastic Multi-Body Systems with Bolted, Rough Contact Interfaces - Hölzl, Johannes Sebastian; Sextro, Walter (SAE International Journal of Passenger Cars- Mechanical Systems)
For many technical applications it is necessary to avoid or to reduce vibrations. Factors benefiting from vibration reduction are for example the durability of the application, which is increased, as well as cost expenses and the level of noise, which are both decreased. Rough, bolted interfaces are common in most machines and can be used as damping devices with some effort. Perhaps in future such contact surfaces could be used as damping devices at the interfaces of an automotive engine or exhaust system. Nevertheless it is difficult to predict the effect of a change in contact interface parameters on the dynamic behavior of the entire mechanical system. Therefore a method for calculating the steady state behavior of elastic multi-body systems was developed. The basis of this method is a finite element model of each contacting unit. On each model a modal reduction is applied in order to reduce the degrees of freedom. The method of Ritz and Galerkin is used to calculate the frequency response functions of the reduced system including contact. This method allows the calculation of the steady-state behavior of elastic multi-body systems with rough, bolted contact interfaces, by taking the pre-stress of the bolts, the roughness and the friction coefficient of the contacting surfaces as parameters. In order to verify calculated results, a test stand was built. The comparison of calculated and experimental results showed a satisfying correlation.
Keywords: Automotive

Anregungskonzepte und Modellierung piezoelektrischer Trägheitsmotoren - Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (7. Paderborner Workshop Entwurf mechatronischer Systeme)
Piezoelektrische Trägheitsmotoren nutzen die Trägheit einer bewegten Masse, um diese in kleinen Schritten durch abwechselnde Haft- und Gleitphasen voranzutreiben. Eine Kernfrage bei der Entwicklung eines piezoelektrischen Trägheitsmotors ist, welches elektrische Ansteuersignal für das gewünschte Motorverhalten optimal ist. Das elektrische Signal führt zu einer Bewegung des piezoelektrischen Aktors und damit der Antriebsstange, die den reibschlüssigen Vortrieb bewirkt. Entsprechend wird diese Fragestellung in zwei Teilen untersucht: Anhand eines Starrkörpermodells werden zunächst Bewegungsverläufe für die Antriebsstange ermittelt, mit denen die maximale Geschwindigkeit erreicht wird. Dabei werden drei Antriebsmodi identifiziert. Mit allen kann eine höhere Geschwindigkeit als mit der heute häufig verwendeten Sägezahnanregung erreicht werden. Anschließend wird ein einfaches dynamisches Modell eines piezoelektrischen Aktors genutzt, um die notwendigen elektrischen Ansteuersignale für die verschiedenen Antriebsmodi zu bestimmen. Es zeigt sich, dass das gewählte einfache Modell hierzu nur bedingt geeignet ist.
Keywords: Piezoelektrischer Trägheitsmotoren

Improving the Performance of Piezoelectric Inertia Motors - Hunstig, Matthias; Hemsel, Tobias; Sextro, Walter (ACTUATOR 2010 Conference Proceedings)
A model based design approach for improved piezoelectric inertia motors is presented. Three velocityoptimized movement patterns for the driving body have been derived. The influence of the motor parameters and the process of designing an application specific motor with maximum velocity are shown. A simple dynamic model of the piezoelectric actuator is used to calculate the voltage signal for achieving the desired movement pattern. Observed distortions of the optimum pattern, their influence on the motion of the driven body and different methods to reduce them are discussed.

Guideline for the dependability-oriented design of self-optimizing systems - Sondermann-Wölke, Christoph; Hemsel, Tobias; Sextro, Walter; Gausemeier, Jürgen; Pook, Sebastian (Industrial Informatics (INDIN), 2010 8th IEEE International Conference on)
Self-optimizing systems are able to adapt their behavior autonomously according to their current self-determined objectives. Unforeseen influences could lead to dependability-critical behavior of the system. Methods are required which secure self-optimizing systems during operation. These methods to increase the dependability of the system should already be taken into consideration in the design process. This paper presents a guideline for the dependability-oriented design of self-optimizing systems, which integrates established classical methods like failure mode and effects analysis as well as methods based on self-optimization. On the one hand self-optimization is used to increase the dependability of the system by integrating objectives like safety, availability, and reliability to the objectives of the system. On the other hand methods are required to ensure the self-optimization itself. As basis for this guideline serves the principle solution of the system. The six phases of the guideline extend the design process and lead to an enhanced principle solution. Additionally, the guideline illustrates phases to implement and validate the self-optimizing system. The proposed guideline is applied to an innovative rail-bound vehicle, called RailCab, which is equipped with self-optimizing function modules.
Keywords: RailCab; dependability-critical behavior; dependability-oriented design; failure mode; rail-bound vehicle; secure self-optimizing systems; self-optimizing function modules; optimisation; railways; self-adjusting systems

Integration of Condition Monitoring in Self-optimizing Function Modules Applied to the Active Railway Guidance Module - Sondermann-Wölke, Christoph; Sextro, Walter (International Journal On Advances in Intelligent Systems)
New mechatronic systems, called self-optimizing systems, are able to adapt their behavior according to environmental, user and system specific influences. Self-optimizing systems are complex and due to their non-deterministic behavior comprise hidden risks, which cannot be foreseen in the design phase of the system. Therefore, modifications of the ISO 17359 condition monitoring policy for being able to cope with this new kind of systems are presented. Besides avoiding critical situations evoked by self-optimization, the proposed concept uses self-optimization to increase the dependability of the system. This concept is applied to the active guidance module of an innovative rail-bound vehicle. First test drives provide information for the enhancement of the implementation of realtime switching to appropriate control strategies. The different control strategies are investigated in detail. It is illustrated that influences on the system like different track sections or the desired velocity of the RailCab effect the system and can lead to a higher amount of flange contacts, which indicate higher wear and thus a reduction of the availability of the system. Therefore, these influences should be minded within the condition monitoring policy. Consequently, this article presents the condition monitoring policy for self-optimizing function modules and its application to the active railway guidance module.
Keywords: dependability; condition monitoring; selfoptimization; active railway guidance module

Experimentelle Untersuchung der Selbstoptimierung innerhalb des RailCab-Spurführungsmoduls - Sondermann-Wölke, Christoph; Sextro, Walter; Geisler, Jens; Trächtler, Ansgar (Entwurf mechatronischer Systeme)
Die erweiterten Möglichkeiten der Informationsverarbeitung mechatronischer Systeme erlauben es, mechatronische Systeme selbstoptimierend zu gestalten. Dabei bezieht sich die Selbstoptimierung auf die Fähigkeit des Systems, sich an die aktuelle Umfeldsituation anzupassen; wobei das System im Allgemeinen mehrere relevante Ziele verfolgt. Wurde eine Umfeldveränderung bemerkt, so müssen diese Ziele an die neue Situation angepasst und das resultierende Verhalten ausgewählt werden. In diesem Beitrag wird das selbstoptimierende Spurführungsmodul näher untersucht. Das Spurführungsmodul ist Bestandteil eines innovativen schienengebundenen Verkehrssystems, genannt RailCab, und dient zur Lenkung des einzelnen Fahrzeugs. Ziele des Spurführungsmoduls bestehen darin, die Verlässlichkeit des Spurführungsmoduls zu erhöhen sowie möglichst wenig Energie zu verbrauchen. Um kritische Systemzustände zu erkennen bzw. frühzeitig zu verhindern wird eine Vorgehensweise zur Einrichtung einer Zustandsüberwachung für selbstoptimierende Systeme beschrieben. Diese wird auf dem realen Versuchsträger im Maßstab 1:2,5 implementiert. Die Auswertung von Versuchsfahrten zeigt, dass gerade beim Auftreten eines Fehlers das Umschalten vom Ziel ''Energieverbrauch minimieren`` auf das Ziel ''Verlässlichkeit maximieren`` sinnvoll ist.
Keywords: Selbstoptimierung; Spurführungsmodul

Increasing the reliability of a self-optimizing railway guidance system - Sondermann-Wölke, Christoph; Geisler, Jens; Sextro, Walter (Reliability and Maintainability Symposium (RAMS), 2010 Proceedings - Annual)
Recent advances in information processing enable new kinds of technical systems, called self-optimizing systems. These systems are able to adapt their objectives and their behavior according to the current situation and influences autonomously. This behavior adaptation is non-deterministic and hence self-optimization is a risk to the system, e.g. if the result of the self-optimization process does not match the suddenly changed situation. In contrary, self-optimization could be used to increase the dependability by pursuing objectives like reliability and availability. In our preceding publications we introduced the so called multi-level dependability concept to cope with this new kind of systems (cf. [6]). This concept comprises the monitoring of the system behavior, the classification of the current situation, and the selection of the appropriate measure, if reliability limits are exceeded. In this paper we present for the first time experimental results. The dependability concept is implemented in the self-optimizing active guidance system of a railway vehicle. The test drives illustrate clearly that the proposed concept is able to cope with, e.g., sensor failures, and is able to increase the reliability and availability of the active guidance module.
Keywords: availability; dependability concept; multilevel dependability concept; railway vehicle; reliability; self optimizing active guidance system; self optimizing railway guidance system; situation classification; system behavior monitoring; optimal control; railways; reliability theory; self-adjusting systems

Einfluss von Oberflächenrauheit, fluiden Zwischenschichten und Kontakttemperaturen auf den Kraftschluss zwischen Rad und Schiene - Tomberger, Christoph; Dietmaier, Peter; Martin, Rosenberger; Sextro, Walter; Six, Klaus (ZEVrail)

Towards the Integration of Condition Monitoring in Self-Optimizing Function Modules - Sondermann-Wölke, Christoph; Sextro, Walter (Future Computing, Service Computation, Cognitive, Adaptive, Content, Patterns, 2009. COMPUTATIONWORLD '09. Computation World:)
New mechatronic systems, called self-optimizing systems, are able to adapt their behavior according to environmental, user and system specific influences. Self-optimizing systems are complex and due to their non-deterministic behavior comprise hidden risks, which cannot be foreseen in the design phase of the system. Therefore, this paper presents modifications of the current condition monitoring policy, to be able to cope with this new kind of systems. Beside avoiding critical situations evoked by self-optimization, the proposed concept uses self-optimization to increase the dependability of the system. In this case, the concept is applied to the active guidance module of an innovative rail-bound vehicle.
Keywords: condition monitoring; mechatronic systems; rail bound vehicle; rail guidance module; self-optimization; self-optimizing function modules; condition monitoring; mechatronics; railway rolling stock; self-adjusting systems

Modellierung der Hysterese- und Adhäsionseffekte zwischen Bremsbelag und Bremsscheibe - Tonchev, Anton; Hirschberg, Wolfgang; Sextro, Walter; Major, Zoltan; Neges, Josef (27. Internationales Mju-Symposium/Bremsen-Fachtagung)

Modelling of Hysteresis and Adhesion Effects between Brake Pad and Disc - Tonchev, Anton; Hirschberg, Wolfgang; Sextro, Walter; Major, Zoltan; Neges, Josef (27. Internationales Mju-Symposium/Bremsen-Fachtagung)

Schwingungsverhalten elastischer Körper mit nichtlinearen Kopplungen in ausgedehnten Reibkontakten - Genzo, Alexander; Sextro, Walter; Panning, Lars (VDI-Berichte)

On Nonlinear Forced Vibration of Shrouded Turbine Blades - Szwedowicz, J; Visser, R; Sextro, Walter; Masserey, P. A (Journal of Turbomachinery)
Numerical predictions of the forced vibration of a disk assembly including frictional effects between the shrouds are presented concerning engineering needs for the blade design process. Assuming a tuned disk assembly, numerical static, free, and then forced vibration analyses of a shrouded turbine blade measured in the spin pit are performed systematically. For the excitation forces of an air jet evaluated from the fairly linear behavior of the experimental blade resonance peaks, the reliability of the proposed approach is validated through the very close agreement of the computed and measured resonant peaks. These resonant peaks demonstrate either a fairly linear behavior or a nonlinear one like the jump effect of blade resonance amplitudes, or elastic impacts between the shrouds. Also, the damping performance for different contact configurations between the shrouds is numerically analyzed. These numerical results indicate that the shrouds generate higher frictional damping for small angles (0â30deg) between the circumferential direction and the normal vector to the contact surface.

Dynamic Behaviour of Elastic Bodies Coupled by Extended Friction Contacts - Genzo, Alexander; Sextro, Walter (Proceedings of ISMA - International conference on noise and vibration engineering)
Keywords: Noise; Vibration engineering

Unsteady rolling contact of rubber wheels - Gutzeit, F; Sextro, Walter; Kröger, Matthias (Analysis and Simulation of Contact Problems)
This paper presents a model for unsteady longitudinal slippage of a loaded rubber wheel. The aim of modelling was to calculate the dynamical contact behavior in a numerical efficient way. Further on, simulation results are compared to experimental data.

Error-Workspace Analysis of Plane Mechanisms - Hofmeisterro, Adolf; Sextro, Walter; Röschel, Otto (Proceedings of EUCOMES, the first European Conference on Mechanism Science)

Contact behaviour of a sliding rubber element - Sextro, Walter; Moldenhauer, Patrick; Wangenheim, M; Lindner, Markus; Kröger, Matthias (Analysis and Simulation of Contact Problems)
Friction occurs in the contact between tyre and road. The friction of rubber material on dry surfaces is dominated by hysteresis and adhesion effects. Hysterisis friction is characterised by the energy dissipation within the visco-elastic material, which is caused by its deformation while passing the surface roughness. Hysteresis effects are modelled by an extended linear visco-elastic material with several Maxwell elements. The development of a model in the time domain allows to consider nonlinear effects. Additionally temperature effects are taken into account based on the WLF-transformation. Adhesion forces originate from molecular bindings between the contact partners. This effect is simulated by applying a modified model of Achenbach on real surfaces. The temperature distribution within the friction contact region is investigated experimentally as well. Furthermore global stick-slip vibrations of a rubber block element are investigated using a global contact model. Numerical results are compared with experiments performed on a tribometer test rig.

Analysis of the Forced Vibration of Two Bolted Half-Pipes with Extended Friction Contacts - Genzo, Alexander; Sextro, Walter; Popp, Karl (PAMM)
The present paper deals with the forced vibration analysis of a test structure. The test structure consists of two parts, an upper and a lower half pipe, joint in two bolted flanges which represent the extended friction contacts. Depending on the clamping loads different normal pressure distributions can be established in the contact interfaces. Since the test structure is loaded with a harmonic external force relative displacements occur in the contact interface. This leads to microslip effects affecting the dynamic behaviour. The experimental validation of the calculation method accounting for these effects is shown by comparing measured and calculated frequency response functions (FRF). (Â{©} 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Analysis of the Forced Vibration of Two Bolted Half-Pipes with Extended Friction Contacts - Genzo, Alexander; Sextro, Walter; Popp, Karl (PAMM)
The present paper deals with the forced vibration analysis of a test structure. The test structure consists of two parts, an upper and a lower half pipe, joint in two bolted flanges which represent the extended friction contacts. Depending on the clamping loads different normal pressure distributions can be established in the contact interfaces. Since the test structure is loaded with a harmonic external force relative displacements occur in the contact interface. This leads to microslip effects affecting the dynamic behaviour. The experimental validation of the calculation method accounting for these effects is shown by comparing measured and calculated frequency response functions (FRF). (Â{©} 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Unkontrollierbare Bewegungen ebener Mechanismen mit Gelenkspiel - Hofmeister, Adolf; Sextro, Walter; Röschel, Otto (PAMM)
In dieser Arbeit wird ein analytisches Berechnungsverfahren vorgestellt, mit dem der gesamte Positions- und Orientierungsraum (ErrorWorkspace) ebener Mechanismen mit spielbehafteten Gelenken kinematisch beschrieben bzw. dargestellt werden kann. Für die Berechnung wird der gesamte Positions- und Orientierungsraum im Kinematischen Bildraum dargestellt, wobei auf besondere Merkmale eingegangen wird. Der ErrorWorkspace, der mit Hilfe des Berechnungsverfahren bestimmt wird, wird an einem Koppelgetriebe, an einem Filmgreifergetriebe und an einem Double-rocker four-bar mechanism mit Kurbelantrieb dargestellt und analysiert. ({©} 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Systematic mistuning of bladed disk assemblies with friction contacts - Götting, Florian; Sextro, Walter; Panning, Lars; Popp, Karl (Proceedings of ASME TURBO Expo, Power for Land, Sea, and Air)
In turbomachinery, friction contacts are widely used to reduce dynamic stresses in turbine blades in order to avoid expensive damages. As a result of energy dissipation in the friction contacts the blade vibration amplitudes are reduced. In case of so-called friction dampers, which are pressed on the platforms of the blades by centrifugal forces, the damping effect can be optimized by varying the damper mass. This optimization can be done by means of a simulation model applying the so-called component mode synthesis and the Harmonic Balance Method to reduce computation time. It is based on the modal description of each substructure. In a real turbine or compressor blading great differences in the magnitude of the individual blade amplitudes occur caused by unavoidable mistuning of all system parameters like contact parameters and natural frequencies of the blades. It may happen that most of the blades experience only small stresses whereas a few blades experience critical stresses. Therefore, it is necessary to consider mistuning for all system parameters to simulate the forced response of bladed disk assemblies with friction contacts. For a mistuned bladed disk the complete system has to be modeled to calculate the dynamic response. In practice, usually the standard deviations instead of the distributions of the system parameters are known. Therefore, Monte-Carlo simulations are necessary to calculate the forced response of the blades for given mean values and standard deviations of the system parameters. To reduce the computational time, an approximate method has been developed and extended for small and moderate standard deviations of the system parameters to calculate the distribution and the envelopes of the frequency response functions for statistically varying system parameters, in the following called statistical mistuning. The approximate method is based on a sensitivity analysis and the assumption of a Weibull distribution of the vibration amplitudes of the blades. Both, the approximate method and the assumption of a Weibull distribution of the vibration amplitudes are validated by Monte-Carlo simulations. By these investigations the influence of different arrangements of the system parameters for given mean values and standard deviations of the vibration amplitudes of the blades can be determined, too. For the present investigations only a small influence of the arrangement of blades with respect to their natural frequencies has been observed. On the other hand, an intentional mistuning of the damper masses and the natural frequencies of the blades in a systematic way, in the following called systematic mistuning, can be investigated to reduce the amplitudes of the system. The simulation results of a systematic mistuning has been validated by a test rig with a rotating bladed disk assembly with friction dampers. The investigations show a good agreement between the simulations and the measurements but only a slight decrease of the maximum amplitudes in case of a systematic mistuning. Copyright {©} 2004 by ASME
Keywords: Friction; Disks

Hysteretic Friction of a Sliding Rubber Element - Lindner, Markus; Sextro, Walter; Popp, Karl (PAMM)
Friction, especially friction of elastomers, can cause acoustic problems like noise, squeal and comfort drawbacks like vibrations and wear. Therefore, rubber friction affects the function of many products in technical applications, e.g. seals, belts and tires. It can be classified according to different physical phenomena like adhesion, hysteresis, cohesion and viscous friction, see [3]. The topic of this paper is hysteresis friction of rubber that is caused by the energy dissipation due to internal material damping during the process of deformation. The deformation itself occurs during the sliding of a rubber element across the micro-scaled asperities of a rough surface. In this paper, the sliding process of a rubber element over real surfaces is simulated in time domain and compared to experiments. (Â{©} 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Asymmetrical Underplatform Dampers in Gas Turbine Bladings: Theory and Application - Panning, Lars; Popp, Karl; Sextro, Walter; Götting, Florian (Proceedings of ASME TURBO Expo, Power for Land, Sea, and Air)
During operation, the rotating blades of a gas turbine are subjected to centrifugal forces as well as fluctuating gas forces, resulting in blade vibrations. In addition to material damping, aerodynamical and blade root damping, underplatform dampers are widely used to increase the amount of damping and to decrease blade vibration amplitudes. The friction forces generated by the relative displacements between the underplatform damper and the blade platforms provide a significant amount of energy dissipation. In practice, a number of different underplatform damper designs are applied. Basically, these are wedge dampers with flat contact areas, cylindrical dampers with curved surfaces or asymmetrical dampers with both flat contact surfaces on one side and curved contact surfaces on the other. The latter damper type combines the advantages of both the wedge and the cylindrical damper by preventing the damper from pure rolling on the one hand as it has been observed for cylindrical dampers and on the other hand, avoiding a diverged plane area contact in case of a wedge damper, causing a damper lift-off. This paper will focus on the investigation of cylindrical and asymmetrical underplatform dampers. A comparison between measurements of rotating assemblies in Siemens PG gas turbines (V84.2, V64.3A and V94.3A(2)) under test and real operating conditions with cylindrical and asymmetrical underplatform dampers and the predictions of the developed theoretical model are presented. Special attention is paid to the frequency shift due to the application of an underplatform damper, since in particular for stationary gas turbines, in addition to the amplitude reduction, the accurate prediction of the resonance frequency is of major interest. Copyright {©} 2004 by ASME
Keywords: Dampers; Gas turbines

Schwingungsverhalten von verstimmten Beschaufelungen mit Reibelementen - Götting, Florian; Sextro, Walter; Panning, Lars; Popp, Karl (Schwingungen in rotierenden Maschinen VI SIRM, Referate der Tagung in Darmstadt)

Erzwungene Schwingungen von elastischen Mehrkörpersystemen mit Reibkontakten - Genzo, Alexander; Sextro, Walter; Popp, Karl (PAMM)
Im Folgenden wird eine Berechnungsmethode vorgestellt, die es erlaubt, das räumliche Schwingungsverhalten eines elastischen Mehrkörpersystems (EMKS) mit Reibkontakten in rechenzeit- und speicherplatzsparender Form zu analysieren. Der von trockener Reibung und Mikroschlupf geprägte, nichtlineare Dämpfungsmechanismus in den Reibkontakten eines EMKS wird dabei realitätsnahe abgebildet. Die Plausibilität der mit der Methode gewonnenen Berechnungsergebnisse wird beispielhaft an einem einfachen EMKS, einem in Längsrichtung geteilten, einseitig eingespannten Balken gezeigt. Für den geteilten Balken werden die Frequenzgänge des Torsionswinkels um die Längsachse und der Auslenkung um die biegeweiche Achse berechnet.

Design of Friction Dampers for Mistuned Bladed Disks - Panning, Lars; Sextro, Walter; Popp, Karl (PAMM)
Friction damping devices such as underplatform dampers are widely used in turbomachinery applications to reduce blade vibration amplitudes. In this paper, a model is presented briefly to calculate the forced response of mistuned bladed systems with friction dampers. Some results will give an insight in the vibrational behavior of frictionally damped bladed disks and how the damping gain is affected by the damper properties.

Spatial dynamics of tuned and mistuned bladed disks with cylindrical and wedge-shaped friction dampers - Panning, Lars; Sextro, Walter; Popp, Karl (International Journal of Rotating Machinery)

Vibration Damping by Friction Forces -Theory and Applications - Popp, Karl; Panning, Lars; Sextro, Walter (Journal of Vibration and Control)

Optimierung des Schwingungsverhaltens elastischer Strukturen mit Reibfugen am Beispiel von Turbomaschinenschaufeln - Sextro, Walter; Popp, Karl (Forschungsvereinigung Verbrennungskraftmaschinen (FW))

On forced vibration of shrouded turbine blades - Szwedowicz, J; Sextro, Walter; Visser, R; Masserey, P.A (ASME Turbo Expo 2003, collocated with the 2003 International Joint Power Generation Conference)
Numerical predictions of the forced vibration of a disc assembly including frictional effects between the shrouds are presented concerning engineering needs for the blade design process. Assuming a tuned disc assembly, numerical static, free and then forced vibration analyses of a shrouded turbine blade measured in the spin pit are performed systematically. For the excitation forces of an air jet evaluated from the fairly linear behavior of the experimental blade resonance peaks, the reliability of the proposed approach is validated through the very close agreement of the computed and measured resonant peaks. These resonant peaks demonstrate either a fairly linear behavior or a non-linear one like the jump effect of blade resonance amplitudes, or elastic impacts between the shrouds. Also, the damping performance for different contact configurations between the shrouds is numerically analyzed. These numerical results indicate that the shrouds generate higher frictional damping for small angles (0--30 deg) between the circumferential direction and the normal vector to the contact surface. Copyright {©} 2003 by ASME
Keywords: Turbine blades; Vibration

Optimization of the Contact Geometry between Turbine Blades and Underplatform Dampers with respect to Friction Damping - Panning, Lars; Sextro, Walter; Popp, Karl (Proceedings of ASME TURBO Expo, Power for Land, Sea, and Air)

Spatial dynamics of tuned and mistuned bladed disks with cylindrical and wedge-shaped friction dampers - Panning, Lars; Sextro, Walter; Popp, Karl (Proceedings of the 9th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC)

Fast Calculation of the Statistics of the Forced Response of Mistuned Bladed Disk Assemblies with Friction Contacts - Sextro, Walter; Panning, Lars; Götting, Florian (Proceedings of ASME TURBO Expo, Power for Land, Sea, and Air)

Optimierung des Schwingungsverhaltens elastischer Strukturen mit Reibfugen - Sextro, Walter; Popp, Karl (Forschungsvereinigung Verbrennungskraftmaschinen (FW) - lnformationstagung Turbinen)

Schwingungsanalyse verstimmter Schaufelkränze mit Reibelementen - Panning, Lars; Sextro, Walter; Popp, Karl (Schwingungen in rotierenden Maschinen VI SIRM, Referate der Tagung in Wien)

Heat and Wear Generation for Rolling Contacts - Sextro, Walter (Zeitschrift für angewandte Mathematik und Mechanik (ZAMM))

Development and Experimental Validation of a Point Contact Model for Dynamical Problems with Friction - Sextro, Walter (ASME Design Engineering Technical Conferences)

Localization in Nonlinear Mistuned Systems with Cyclic Symmetry - Sextro, Walter; Popp, Karl; Krzyzynski, Tomasz (Nonlinear Dynamics)
In forced systems with cyclic symmetry localization can occur due toparameter uncertainties. Often, Monte-Carlo simulations are used to findregions, where the system response is sensitive to parameteruncertainties. These simulations require a large computation time.Therefore, an approximate method to calculate the envelopes of thefrequency response functions is developed in this paper. An example of anonlinear system with cyclic symmetry is a bladed disk assembly withfriction dampers. Friction dampers can be installed underneath the bladeplatforms of turbine blades. Due to dry friction and the relative motionbetween blades and dampers, energy is dissipated, which results in areduction of blade vibration amplitudes. By optimizing the mass of thefriction dampers, the best damping effects are obtained, which lead toan increase in the reliability of the turbine. In this paper, thecalculated response of a mistuned bladed disk assembly with frictiondampers is discussed. An approximate method is developed to calculatethe envelopes of the corresponding frequency response function forstatistically varying eigenfrequencies of the blades. Regions wherelocalization can occur with a high probability, are calculated by thismethod.
Keywords: bladed disk assembly; mistuning; sensitivity; localization

On some regularities in dynamic response of cyclic periodic structures - Krzyzynski, Tomasz; Popp, Karl; Sextro, Walter (Chaos, Solitons & Fractals)
The paper deals with cyclic periodic structures modelling bladed disk assemblies of blades with friction elements for vibration damping. These elements placed between adjacent blades reduce the vibration amplitudes by means of dry friction resulting from centrifugal forces acting on the elements and relative displacements of the blades. However, the application of these friction elements results in an additional dynamical coupling which together with mistuning of some system parameters (e.g., blade eigenfrequency or contact parameters) may cause localization of vibration. In the present paper a linear approximation of such a system is investigated. The structure composed of cyclic periodic cells modelled each as a clamped-free beam interacting with each other by means of viscoelastic elements of complex stiffness is applied for dynamic system analysis. In case of free vibrations as well as in case of steady-state dynamic response to a harmonic pressure field, a perfect periodic structure and the structures with periodically mistuned parameters (blade eigenfrequencies and contact parameters) are studied. Some regularities in the dynamic response of the systems with mistuning have been noticed. Despite the fact that only a linear approximation has been used, the results and conclusions can be applied for models which describe the blade interaction in a nonlinear way.

Optimization of Interblade Friction Damper - Panning, Lars; Sextro, Walter; Popp, Karl (International Gas Turbine & Aeroengine Congress & Exhibition, ASME)
the vibration amplitudes of bladed disk assemblies can be reduced significantly by means of friction damping devices such as shrouds, damping wires and interblade Friction dampers. in practice, interblade Friction dampers are applied in rotating arrangements with various geometries showing curved or flat surfaces like so-called wedge-shaped dampers. this paper is focusing on a computation method to predict the dynamical behaviour of turbine blades with Friction dampers including both, curved and wedge-shaped dampers with hertzian and non-herutian contact conditions, respectively. the presented computation method uses a 3d contact model to calculate the contact forces, including normal and tangential stiffnesses, roughness and microslip effects. the relative displacements in the contact area can be expressed by means of 6 dof of the blade platforms and 6 rigid body dof of the damper including translational and rotational displacements. the relative displacement of the Friction damper with respect to the adjacent blades can be derived from the contact kinematics of the blade-damper-blade system and the equations of motion of the Friction damper. thus, the model can be applied to investigate spatial motions of the bladed disk assembly including bending and torsional vibrations. a comparison of different Friction damper designs with respect to an optimal damper geometry and damper mass is presented. the advantages and disadvantages of each design will be discussed. experimental results are shown to validate the developed computation method.

The Calculation of the Forced Response of Shrouded Blades with Friction Contacts and Its Experimental Verification - Sextro, Walter (International Gas Turbine & Aeroengine Congress & Exhibition, ASME)

Schwingungsanalyse von vorgespannten Schaufeln mit Deckplatten im Schaufelkranz - Popp, Karl; Sextro, Walter (Forschungsvereinigung Verbrennungskraftmaschinen (FW) -lnformationstagung Turbinen)

Experimental verification of a non-Hertzian contact model - Sextro, Walter (International conference on computational methods in contact mechanics)

Forced Vibration of Elastic Structures with Friction Contacts - Sextro, Walter (ASME Design Engineering Technical Conferences)

Ein ebenes Reibkontaktmodell zur Berechnung von Schaufelschwingungen mit Reibelementen - Sextro, Walter; Popp, Karl (Zeitschrift für angewandte Mathematik und Mechanik (ZAMM))

Schwingungsanalyse von vorgespannten Schaufeln mit Deckplatten im Schaufelkranz - Sextro, Walter; Popp, Karl (Forschungsvereinigung Verbrennungskraftmaschinen (FW))

Vibrational Behaviour of Tuned and Detuned Bladed Disks with Friction Dampers - Sextro, Walter; Popp, Karl; Wolter, I (International Congress on Combustion Engines, Proceedings of the 22nd CIMAC)

Three-Dimensional Vibration of Bladed Disk Assemblies with Friction Dampers - Sextro, Walter; Popp, Karl; Wolter, I (The 7th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Proceedings of ISROMAC-7)

Schwingungsverhalten von verstimmten Beschaufelungen mit Reibelementen - Popp, Karl; Sextro, Walter (Forschungsvereinigung Verbrennungskraftmaschinen (FW) -lnformationstagung Turbinen)

Schwingungsverhalten von Schaufelkränzen mit Reibelementen bei Frequenzverstimmung - Sextro, Walter (VDI-Reihe)

Improved reliability of bladed disks due to friction dampers - Sextro, Walter; Popp, Karl; Wolter, Ivo (The 1997 International Gas Turbine & Aeroengine Congress & Exposition)

Schwingungsverhalten eines Schaufelkranzes mit Reibelementen bei Frequenzverstimmung - Popp, Karl; Sextro, Walter (Forschungsvereinigung Verbrennungskraftmaschinen (FW) - lnformationstagung Turbinen)

Dynamical Behaviour of a Bladed Disk with Friction Dampers - Popp, Karl; Sextro, Walter (The 2nd European Nonlinear Oscillation Conference - Proceedings of EUROMECH)

Static Behaviour of Drill Strings in Curved Boreholes - Sextro, Walter; Schmalhorst, B (Zeitschrift für angewandte Mathematik und Mechanik (ZAMM))

Bifurcations in Dynamic Systems with Dry Friction - Stelter, Peter; Sextro, Walter (Bifurcation and Chaos: Analysis, Algorithms, Applications)
Dry friction is a main factor of self-sustained oscillations in dynamic systems. The mathematical modelling of dry friction forces result in strong nonlinear equations of motion. The bifurcation behaviour of a deterministic system has been investigated by the bifurcation theory. The stability of stationary solutions has been analyzed by the eigenvalues of the Jacobian. Period doublings and Hopf-bifurcations as well as turning points could be determined with the program package BIFPACK. Phase plane plots of periodic and chaotic motions have been shown for a better understanding of the bifurcation diagrams. Both, unstable branches and stable coexisting solutions have been calculated. Several jumping effects, which are typical for nonlinear systems, have been found.