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 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 Interpolation‐based parametric model order reduction of automotive brake systems for frequency‐domain analyses(2023) Matter, Fabian; Iroz, Igor; Eberhard, PeterBrake squeal describes noise with different frequencies that can be emitted during the braking process. Typically, the frequencies are in the range of 1 to 16 kHz. Although the noise has virtually no effect on braking performance, strong attempts are made to identify and eliminate the noise as it can be very unpleasant and annoying. In the field of numerical simulation, the brake is typically modeled using the Finite Element method, and this results in a high‐dimensional equation of motion. For the analysis of brake squeal, gyroscopic and circulatory effects, as well as damping and friction, must be considered correctly. For the subsequent analysis, the high‐dimensional damped nonlinear equation system is linearized. This results in terms that are non‐symmetric and dependent on the rotational frequency of the brake rotor. Many parameter points to be evaluated implies many evaluations to determine the relevant parameters of the unstable system. In order to increase the efficiency of the process, the system is typically reduced with a truncated modal transformation. However, with this method the damping and the velocity‐dependent terms, which have a significant influence on the system, are neglected for the calculation of the eigenmodes, and this can lead to inaccurate reduced models. In this paper, we present results of other methods of model order reduction applied on an industrial high‐dimensional brake model. Using moment matching methods combined with parametric model order reduction, both the damping and the various parameter‐dependent terms of the brake model can be taken into account in the reduction step. Thus, better results in the frequency domain can be obtained. On the one hand, as usual in brake analysis, the complex eigenvalues are evaluated, but on the other hand also the transfer behavior in terms of the frequency response. In each case, the classical and the new reduction method are compared with each other.Item Open Access Force-based organization and control scheme for the non-prehensile cooperative transportation of objects(2023) Rosenfelder, Mario; Ebel, Henrik; Eberhard, PeterItem Open Access Towards intelligent design assistants for planar multibody mechanisms(2023) Röder, Benedict; Ebel, Henrik; Eberhard, PeterGeneral‐purpose mechanisms can perform a broad range of tasks but are usually rather heavy and expensive. If only particular movements need to be executed, more efficient special‐purpose mechanisms can be employed. However, they typically require an expert to design the system based on manual inspection of simulations and experimental results. This procedure is not only time‐consuming, but the outcome also depends on the expert's experience. Hence, the design process stems from subjective criteria while only a limited number of structurally different mechanisms can be considered. In contrast, a design assistant can consider a broad range of mechanisms and leverage multi‐objective optimization to retrieve optimal designs for the given task. Due to the systems being synthesized based on mathematical functions rather than individual experience, the assistant allows a more transparent development of optimal problem‐specific mechanisms compared to the conventional process. Experts can then fine‐tune and analyze the proposed designs to compose the final system. In recent years, neural networks have been utilized to directly learn the inverse mapping from a trajectory to a mechanism design. This requires some parameterization of the trajectory to be fed into the network. In this work, we evaluate various preprocessing methods for the trajectory on a simple mechanism design model problem. We assess multiple configurations such as different neural network sizes, applying input‐output normalization, and varying the number of features. Consequently, we investigate and compare the trends and robustness of the implemented methods.