07 Fakultät Konstruktions-, Produktions- und Fahrzeugtechnik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/8
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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 Investigation of chip jamming in deep-hole drilling(2023) Baumann, Andreas; Eberhard, PeterIn this paper, we show the recent progress and first insights in modeling chip jamming in the deep-hole drilling process. Chip jamming is a significant problem when chips wrap around the tool, leading to marks on the borehole wall and an increased drilling torque causing sudden tool failure. Recent investigations focused on chip evacuation and fluid distribution along the cutting edge. This work extends the existing models by adding an artificial barrier in the chip flute. This barrier approximates a chip jammed between the drill shaft and the borehole wall. In the first approach, this barrier blocks the complete chip flute but allows fluid to pass, only blocking the chips from their evacuation. In the second approach presented, a non-permeable artificial barrier partially blocks the chip flute. Furthermore, we show the validation of the model and evaluate the assumption of rigid chips for the chip evacuation as they are applied in earlier investigations. Finally, we show the deformation of the chip as it blocks the fluid from its evacuation and the impact on the fluid flow during the process.Item Open Access Methods of model order reduction for coupled systems applied to a brake disc‐wheel composite(2023) Matter, Fabian; Iroz, Igor; Eberhard, PeterIn this contribution, investigations on model order reduction for coupled systems composed from components of a passenger car are shown. In today's development processes, the simulation of mechanical components is indispensable and large Finite Element models are often used for this purpose. For the calculation of time‐domain or frequency‐domain analyses, for example, a lot of computing power is required. However, with the application of model order reduction methods, this effort can be reduced, but this results in a trade‐off between the reduction error and the computational time. Since the computation of reduction bases for complete systems can be computationally expensive, it is of interest to be able to reduce components individually and then assemble them into a reduced overall model. This can result in both, a saving of computational effort when creating the bases, as well as a saving of the required memory space. Furthermore, there are many possible combinations of components in the modular systems of today's automotive industry, which emphasizes the model order reduction by parts and not by assemblies. In this work, methods of model order reduction for coupled systems are presented and will be tested on components in the chassis of a sports car. Therefore, an assembly consisting of a brake disc and wheel rim together with the wheel hub are investigated. For this purpose, the eigenmodes and transfer functions of the overall model, the reduced overall model and the assembly built from individual reduced bodies are compared.Item Open Access Hybrid modeling of multibody systems : comparison of two discrepancy models for trajectory prediction(2024) Wohlleben, Meike; Röder, Benedict; Ebel, Henrik; Muth, Lars; Sextro, Walter; Eberhard, PeterThis study focuses on hybrid modeling approaches that combine physical and data‐driven methods to create more effective dynamical system models. In particular, it examines discrepancy models, a type of hybrid model that integrates a physical system model with data‐driven compensation for inaccuracies. The study applies two discrepancy modeling methods to a multibody system using discrepancies in the state vector and its time derivative, respectively. As an application example, a four‐bar linkage with nonlinear damping is investigated, using a simplified conservative system as a physical model. The comparative analysis of the two methods shows that the continuous approach generally outperforms the discrete method in terms of accuracy and computational efficiency, especially for velocity prediction and prediction horizon. However, scenarios, where input signals for training and testing differ, present nuanced findings. When the continuous method is trained on complex signals (sine) and tested on simpler ones (stair), it struggles to deliver satisfactory results, exhibiting notably higher root mean square error (RMSE) values, particularly in angular velocity prediction. Conversely, training on simple signals (stair) and testing on complex ones (sine) surprisingly yields low RMSE values, indicating the continuous method's adaptability. While the discrete method aligns more closely with expectations and performs better in certain scenarios, its results are consistently moderate, neither exceptional nor particularly poor. The study also introduces a selection framework for choosing the most suitable algorithm based on the specific characteristics of the modeling task. This framework provides guidance for researchers and practitioners in leveraging hybrid modeling effectively. Finally, the study concludes with an outlook on future research directions.Item Open Access Transient optical simulation by coupling elastic multibody systems, finite elements, and ray tracing(2023) Hahn, Luzia; Matter, Fabian; Eberhard, PeterItem Open Access Modeling of the Transrapid’s electromagnets and the application to large mechatronic vehicle models(2022) Schmid, Patrick; Schneider, Georg; Kargl, Arnim; Dignath, Florian; Liang, Xin; Eberhard, PeterThis work gives an overview of a general approach for modeling the electromagnets of a magnetic levitation (Maglev) vehicle based on electromagnetic suspension. The method intends to map the magnets’ static and dynamic behavior in a frequency range relevant for use in mechatronic simulation models and Maglev control or observer design. The methodology starts with setting up the equivalent magnetic circuit considering magnetic reluctances, fringing and leakage flux, magnetic saturation, and eddy currents. Then, the resulting equations are coupled with the magnet’s electric circuits using Ampère’s law and Faraday’s law of induction. Further, a numerical model reduction technique is sketched, which yields a simplified version of the previously derived magnet model with nearly the same input-output structure and input-output behavior, suitable for large simulation models and control design. The approach’s capabilities and strengths are shown by the agreement to measurements and by implementing the resulting models in large mechatronic vehicle models of the Transrapid.
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