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Abstract

The consideration of uncertainties in numerical simulation is generally reasonable and is often indicated in order to provide reliable results, and thus is gaining attraction in various fields of simulation technology. However, in multibody system analysis uncertainties have only been accounted for quite sporadically compared to other areas. The term uncertainties is frequently associated with those of random nature, i.e. aleatory uncertainties, which are successfully handled by the use of probability theory. Actually, a considerable proportion of uncertainties incorporated into dynamical systems, in general, or multibody systems, in particular, is attributed to so-called epistemic uncertainties, which include, amongst others, uncertainties due to a lack of knowledge, due to subjectivity in numerical implementation, and due to simplification or idealization. Hence, for the modeling of epistemic uncertainties in multibody systems an appropriate theory is required, which still remains a challenging topic. Against this background, a methodology will be presented which allows for the inclusion of epistemic uncertainties in modeling and analysis of multibody systems. This approach is based on fuzzy arithmetic, a special field of fuzzy set theory, where the uncertain values of the model parameters are represented by socalled fuzzy numbers, reflecting in a rather intuitive and plausible way the blurred range of possible parameter values. As a result of this advanced modeling technique, more comprehensive system models can be derived which outperform the conventional, crisp-parameterized models by providing simulation results that reflect both the system dynamics and the effect of the uncertainties. The methodology is illustrated by an exemplary application of multibody dynamics which reveals that advanced modeling and simulation techniques using some well-thought-out inclusion of the presumably limiting uncertainties can provide significant additional benefit.
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Abstract

In elastic multibody systems, one considers large nonlinear rigid body motion and small elastic deformations. In a rising number of applications, e.g. automotive engineering, turning and milling processes, the position of acting forces on the elastic body varies. The necessary model order reduction to enable efficient simulations requires the determination of ansatz functions, which depend on the moving force position. For a large number of possible interaction points, the size of the reduced system would increase drastically in the classical Component Mode Synthesis framework. If many nodes are potentially loaded, or the contact area is not known a-priori and only a small number of nodes is loaded simultaneously, the system is described in this contribution with the parameter-dependent force position. This enables the application of parametric model order reduction methods. Here, two techniques based on matrix interpolation are described which transform individually reduced systems and allow the interpolation of the reduced system matrices to determine reduced systems for any force position. The online-offline decomposition and description of the force distribution onto the reduced elastic body are presented in this contribution. The proposed framework enables the simulation of elastic multibody systems with moving loads efficiently because it solely depends on the size of the reduced system. Results in frequency and time domain for the simulation of a thin-walled cylinder with a moving load illustrate the applicability of the proposed method.
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Abstract

Redundant constraints in MBS models severely deteriorate the computational performance and accuracy of any numerical MBS dynamics simulation method. Classically this problem has been addressed by means of numerical decompositions of the constraint Jacobian within numerical integration steps. Such decompositions are computationally expensive. In this paper an elimination method is discussed that only requires a single numerical decomposition within the model preprocessing step rather than during the time integration. It is based on the determination of motion spaces making use of Lie group concepts. The method is able to reduce the set of loop constraints for a large class of technical systems. In any case it always retains a sufficient number of constraints. It is derived for single kinematic loops.
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Abstract

The purpose of the present research relates to the sensitivity analysis of road vehicle comfort and handling performances with respect to suspension technological parameters. The envisaged suspension being of semi-active nature, this implies first to consider an hybrid modeling approach consisting of a 3D multibody model of the full car - an Audi A6 in our case - coupled with the electro-hydraulic model of the suspension dampers. Concerning parameter sensitivitie, the goal is to capture them for themselves - and not necessarily for optimization purpose - because their knowledge is of a great interest for the damper manufacturer. An important issue of the research is to consider objective functions which are based on complete time integrations along a given trajectory, the goal being - for instance - to quantify the sensitivity of the carbody rms acceleration (comfort) or of the vehicle overturning character (handling) with respect to suspension parameters. On one hand, the accuracy of the various partial derivatives computation can be greatly enhanced thanks to the symbolic capabilities of our ROBOTRAN multibody program. On the other hand, the computational efficiency of the process also takes advantage of the recursive formulation of the multibody equations of motion which must be time integrated with respect to both the generalized coordinates and their partial derivatives in case of the so-called direct method underlying sensitivity analysis.
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Abstract

In high-performance optical systems, small disturbances can be sufficient to put the projected image out of focus. Little stochastic excitations, for example, are a huge problem in those extremely precise opto-mechanical systems. To avoid this problem or at least to reduce it, several possibilities are thinkable. One of these possibilities is the modification of the dynamical behavior. In this method the redistribution of masses and stiffnesses is utilized to decrease the aberrations caused by dynamical excitations. Here, a multidisciplinary optimization process is required for which the basics of coupling dynamical and optical simulation methods will be introduced. The optimization is based on a method for efficiently coupling the two types of simulations. In a concluding example, the rigid body dynamics of a lithography objective is optimized with respect to its dynamical-optical behavior.
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