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.
The dynamics of the turning process of a thin-walled cylinder in manufacturing is modeled using flexible multibody system theory. The obtained model is time varying due to workpiece rotation and tool feed and retarded, due to repeated cutting of the same surface. Instabilities can occur due to these consecutive cuts that must be avoided in practical application because of the detrimental effects on workpiece, tool and possibly the machine. Neglecting the small feed, the stability of the resulting periodic system with time-delay can be analyzed using the semi-discretization method. The use of an adaptronic tool holder comprising actuators and sensors to improve the dynamic stability is then investigated. Different control concepts, two collocated and two model-based, are implemented in simulation and tuned to increase the domain of stable cutting. Cutting of a moderately thin workpiece exhibits instabilities mainly due to tool vibration. In this case, the stability boundary can be significantly improved. When the instability is due to workpiece vibration, the collocated concepts fail completely. Model based concepts can still obtain some improvements, but are sensitive to modeling errors in the coupling of workpiece and tool.
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.
The use of elastic bodies within a multibody simulation became more and more important within the last years. To include the elastic bodies, described as a finite element model in multibody simulations, the dimension of the system of ordinary differential equations must be reduced by projection. For this purpose, in this work, the modal reduction method, a component mode synthesis based method and a moment-matching method are used. Due to the always increasing size of the non-reduced systems, the calculation of the projection matrix leads to a large demand of computational resources and cannot be done on usual serial computers with available memory. In this paper, the model reduction software Morembs++ is presented using a parallelization concept based on the message passing interface to satisfy the need of memory and reduce the runtime of the model reduction process. Additionally, the behaviour of the Block-Krylov-Schur eigensolver, implemented in the Anasazi package of the Trilinos project, is analysed with regard to the choice of the size of the Krylov base, the blocksize and the number of blocks. Besides, an iterative solver is considered within the CMS-based method.
There exist cases where precise simulations of contact forces do not allow modeling the gears as rigid bodies but a fully elastic description is needed. In this paper, a modally reduced elastic multibody system including gear contact based on a floating frame of reference formulation is proposed that allows very precise simulations of fully elastic gears with appropriately meshed gears in reasonable time even for many rotations. One advantage of this approach is that there is no assumption about the geometry of the gears and, therefore, it allows precise investigations of contacts between gears with almost arbitrary non-standard tooth geometries including flank profile corrections. This study presents simulation results that show how this modal approach can be used to efficiently investigate the interaction between elastic deformations and flank profile corrections as well as their influence on the contact forces. It is shown that the elastic approach is able to describe important phenomena like early addendum contact for insufficiently corrected profiles in dependence of the transmitted load. Furthermore, it is shown how this approach can be used for precise and efficient simulations of beveloid gears.