Universität Stuttgart
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Item Open Access Analyzing and optimizing multibody systems(1992) Bestle, Dieter; Eberhard, PeterOptimization of holonomic as well as non-holonomic multibody systems is presented as a nonlinear programming problem that can be solved with general-purpose optimization codes. The adjoint variable approach is used for calculating design derivatives of a rather general integral type performance measure with respect to design parameters. The resulting equations are solved by numerical integration backward in time. A multi-step integration algorithm with order and step-size control is adapted for this application by including an interpolation scheme. Numerical experiments and a comparison to the common approach of approximating the gradient of the performance measure by finite differences show that high efficiency, accuracy, and reliability are achievable.Item Open Access Cooperative search by combining simulated and real robots in a swarm under the view of multibody system dynamics(2013) Tang, Qirong; Eberhard, PeterThis paper presents a new approach for cooperative search of a robot swarm. After modeling the robot, the mechanical Particle Swarm Optimization method is conducted based on physical robot properties. Benefiting from the effective localization and navigation by sensor data fusion, a mixed robot swarm which contains both simulated and real robots is then successfully used for searching a target cooperatively. With the promising results from experiments based on different scenarios, the feasibility, the interaction of real and simulated robots, the fault tolerance, and also the scalability of the proposed method are investigated.Item Open Access A note on the predictive control of non‐holonomic systems and underactuated vehicles in the presence of drift(2023) Ebel, Henrik; Rosenfelder, Mario; Eberhard, PeterMotion planning and control of non‐holonomic systems is challenging. Only very recently, it has become clear how model predictive controllers for such systems can be generally furnished in the driftless case, where the key is to design a cost function conforming to the geometry arising from the non‐holonomic constraints. However, in some applications, one cannot neglect drift since the time needed to accelerate is non‐negligible, for example, when operating vehicles with high inertia or at high velocities. Therefore, this contribution extends our previous work on the class of driftless non‐holonomic systems to systems with simple kinds of actuator dynamics that allow to represent the boundedness of acceleration in the model. Moreover, we show in a prototypical example of a simple boat‐like vehicle model that a similar procedure can also work for systems that are not non‐holonomic but still under‐actuated. While the contribution is rather technical in nature, to the knowledge of the authors, it is the first time that MPC controllers with theoretical guarantees are proposed for these kinds of models. Moreover, we expect that the resulting controllers are directly of practical value since even the simpler driftless models are employed successfully in various approaches to motion planning.Item Open Access 3D FEM simulation of titanium alloy (Ti6Al4V) machining with harmonic endmill tools(2023) Kalu-Uka, Abraham; Ozoegwu, Chigbogu; Eberhard, PeterUsually, end milling operations have been carried out using conventional uniform helix tools with fixed helix angles. Thus, many studies have been conducted to study the effects of these tools on the thermomechanical properties of a milling process. Recently, there have been works that point to the benefits of using harmonic endmills. Harmonic endmills consist of cutting edge profiles that have continuously harmonically varying helix angles. The variation is described using a harmonic function of axial position (elevation) of points on the cutting edge. In this work, a 3D finite element simulation using ABAQUS, is carried out for the complex milling process of Titanium alloy Ti6Al4V. The envelope of the harmonic tool is first generated using a set of MATLAB codes and stored in a Standard Triangle Language (.stl) format. The machine tool is introduced into an FEM program which has been designed to provide for dynamic effects, thermo‐mechanical coupling, material damage law and the criterion for contact associated with the milling process. A Johnson‐Cook material constitutive equation which combines the effects of strain hardening, strain softening, and temperature softening is used. To account for the chip separation criterion, the Johnson Cook damage evolution equation is used. The milling process simulation for Ti6Al4V is then carried out. In the end, the stress distribution and the cutting forces are obtained.Item Open Access Experimental research on the influence of modal nonlinearities of paintings under mechanical loads(2022) Gao, Yulong; Ziegler, Pascal; Heinemann, Carolin; Hartlieb, Eva; Eberhard, PeterIn the traditional transportation of paintings and the design of the packaging systems, paintings are usually assumed to behave like a linear system. In order to verify this hypothesis, in this contribution, by means of a hammer experiment and a sweep excitation experiment to simulate the shock and vibration during transportation, respectively, the modal nonlinearities of two real paintings and a dummy painting are experimentally studied. The experimental results show that paintings can be treated as a linear system only when being subjected to shock, but the modal nonlinearities of paintings cannot be ignored when being subjected to vibration. The general behaviour of the paintings modal nonlinearities is then summarised based on experimental results, and their consequences for painting transportation are discussed. First of all, the offset of the resonance frequency is the most important problem which will lead to failure of the original vibration isolation measures. Further, the decrease in the resonance peak amplitude will increase the probability of the eigenmode being excited. Besides, it is also necessary to attenuate the harmonic vibrations of paintings. Lastly, the different modal characteristics obtained by a sweep with increasing and decreasing frequency make the analysis of different excitation schemes more complicated. Therefore, the identification of the paintings modal nonlinearities is necessary and important.Item Open Access Reversible inter-particle bonding in SPH for improved simulation of friction stir welding(2022) Shishova, Elizaveta; Panzer, Florian; Werz, Martin; Eberhard, PeterFriction stir welding (FSW) is a complex joining process which is governed by multiple intertwined physical phenomena. Besides friction, inelastic heat generation, and heat conduction, it involves high plastic deformations, resulting in a need for a numerical method being able to handle all these. Such a scheme is smoothed particle hydrodynamics (SPH), which is a mesh-free computational technique. Absence of a fixed mesh results in the ability of the method to deal with another challenge of friction stir welding, a coalescence of initially separate workpieces into one due to bonding mechanisms. The background of this phenomenon is a transition from contact between two pieces to one continuum due to enormous changes in several material condition, such as temperature, pressure, strain, and strain rate. This work deals with a new development related to bonding, which will provide deeper understanding about the physical weld formation during FSW. The SPH framework must be extended to consider this bonding mechanism. This involves the bonding criterion definition, the interaction type change, and the SPH-SPH contact formulation. Then, the implementation is tested for two different examples, a compression test and FSW.Item Open Access On shift selection for Krylov subspace based model order reduction : an iterative greedy approach combined with singular value decomposition(2023) Frie, Lennart; Eberhard, PeterMechanical systems are often modeled with the multibody system method or the finite element method and numerically described with systems of differential equations. Increasing demands on detail and the resulting high complexity of these systems make the use of model order reduction inevitable. Frequently, moment matching based on Krylov subspaces is used for the reduction. There, the transfer functions of the full system and of the reduced system are matched at distinct frequency shifts. The selection of these shifts, however, is not trivial. In this contribution we suggest an algorithm that evaluates an increasing number of shifts iteratively until a reduced model that approximates the full model in a subspace with very low approximation error is found. Thereafter, the projection matrix that spans this subspace is decomposed with singular value decomposition and only most important directions are retained. In this way, small reduced models with good approximation properties that do not exceed a predefined error bound can be found or low-error models for a given reduced order can be generated. The evaluation of more shifts than necessary and further reduction by means of singular value decomposition is the novelty of this contribution. In this paper, this novel approach is extensively studied and, furthermore, applied to the numerical example of an industrial helicopter model.Item Open Access A physically based material model for the simulation of friction stir welding(2020) Panzer, Florian; Shishova, Elizaveta; Werz, Martin; Weihe, Stefan; Eberhard, Peter; Schmauder, SiegfriedA physically based material model, taking into account the interdependence of material microstructure and yield strength, is presented for an Al 5182 series aluminum alloy for the simulation of friction stir welding using continuum mechanics approaches. A microstructure evolution equation considering dislocation density and grain size is used in conjunction with a description of yield stress. In order to fit experimental stress-strain curves, obtained from compression tests at various strain rates and temperatures, phenomenological relationships are developed for some of the model parameters. The material model is implemented in smoothed particle hydrodynamic research code as well as in the commercial finite element code Abaqus. Simulations for various strain rates and temperatures were performed and compared with experimental results as well as between the two discretization methods in order to verify the material model and the implementation. Simulations provide not only an accurate approximation of stress based on temperature, strain rate, and strain but also an improved insight into the microstructural evolution of the material.Item Open Access Model-based vibration control for optical lenses(2020) Störkle, Johannes; Eberhard, PeterThis work presents a contribution to the active image stabilization of optical systems, involving model development, control design, and the hardware setup. A laboratory experiment is built, which demonstrates the vibration sensitivity of a mechanical-optical system. In order to stabilize the undesired image motion actively, a model-based compensation of the image vibration is developed, realized and tested. Beside a linear actuator motion system, a force sensor system and a position sensor system are introduced and analyzed. In particular, various low-cost hardware components of the Arduino platform are used, which support the deployment of the controller software based on Matlab-Simulink. The remaining image motion is measured with a high-speed vision sensor system and the performance of the overall system is assessed.Item Open Access Comparison of local and global approaches for parametric model order reduction for systems with distributed moving loads(2017) Fröhlich, Benjamin; Eberhard, PeterIn order to ensure a numerically efficient simulation of elastic multibody systems, model order reduction has to be employed for reducing the complexity of the underlying Finite-Element-Models. Elastic multibody systems with moving loads can be modeled as parameter dependent systems for which methods from parametric model order reduction have to be applied. In this contribution, two local and a global approach from parametric model order reduction are investigated. A comparison is made with respect to their approximation quality in frequency domain and time domain and their numerical cost in transient simulations. As a numerical example, a linear drive with a distributed moving load is considered.