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- ItemDiscretisation and error analysis for a mathematical model of milling processes(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Hömberg, Dietmar; Rott, Oliver; Sturm, KevinWe investigate a mathematical model for milling where the cutting tool dynamics is considered together with an elastic workpiece model. Both are coupled by the cutting forces consisting of two dynamic components representing vibrations of the tool and of the workpiece, respectively, at the present and previous tooth periods. We develop a numerical solution algorithm and derive error estimates both for the semi-discrete and the fully discrete numerical scheme. Numerical computations in the last section support the analytically derived error estimates.
- ItemOptimal control of a cooling line for production of hot rolled dual phase steel(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Bleck, Wolfgang; Hömberg, Dietmar; Prahl, Ulrich; Suwanpinij, Piyada; Togobytska, NataliyaIn this article, the optimal control of a cooling line for production of dual phase steel in a hot rolling process is discussed. In order to achieve a desired dual phase steel microstructure an optimal cooling strategy has to be found. The cooling strategy should be such that a desired final distribution of ferrite in the steel slab is reached most accurately. This problem has been solved by means of mathematical control theory. The results of the optimal control of the cooling line have been verified in hot rolling experiments at the pilot hot rolling mill at the Institute for Metal Forming (IMF), TU Bergakademie Freiberg.
- ItemTask assignment, sequencing and path-planning in robotic welding cells(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Landry, Chantal; Welz, Wolfgang; Henrion, René; Hömberg, Dietmar; Skutella, MartinA workcell composed of a workpiece and several welding robots is considered. We are interested in minimizing the makespan in the workcell. Hence, one needs i) to assign tasks between the robots, ii) to do the sequencing of the tasks for each robot and iii) to compute the fastest collisionfree paths between the tasks. Up to now, task assignment and path-planning were always handled separately, the former being a typical Vehicle Routing Problem whereas the later is modelled using an optimal control problem. In this paper, we present a complete algorithm which combines discrete optimization techniques with collision detection and optimal control problems efficiently
- ItemIdentification of the thermal growth characteristics of coagulated tumor tissue in laser-induced thermotherapy(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Hömberg, Dietmar; Liu, Jujun; Togobytska, NataliyaWe consider an inverse problem arising in laser-induced thermotherapy, a minimally invasive method for cancer treatment, in which cancer tissues is destroyed by coagulation. For the dosage planning numerical simulation play an important role. To this end a crucial problem is to identify the thermal growth kinetics of the coagulated zone. Mathematically, this problem is a nonlinear and nonlocal parabolic heat source inverse problem. The solution to this inverse problem is defined as the minimizer of a nonconvex cost functional. The existence of the minimizer is proven. We derive the Gateaux derivative of the cost functional, which is based on the adjoint system, and use it for a numerical approximation of the optimal coefficient.
- ItemDevelopment of a stability prediction tool for the identification of stable milling processes(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Hömberg, Dietmar; Uhlmann, Eckart; Rott, Oliver; Rasper, PatrickThis paper deals with a new mathematical model to characterise the interaction between machine and work piece in a milling process. The model consists of a multi-body system representing the milling machine and a linear thermo-elastic work piece model. An extensive experimental analysis supported the development of the governing model equations. A numerical solution strategy is outlined and complemented by simulations of stable and unstable milling processes including work piece effects. The last part covers the development of a new algorithm for the stability analysis of large milling systems.
- ItemShape optimization for a sharp interface model of distortion compensation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Sturm, Kevin; Hintermüller, Michael; Hömberg, DietmarWe study a mechanical equilibrium problem for a material consisting of two components with different densities, which allows to change the outer shape by changing the interface between the subdomains. We formulate the shape design problem of compensating unwanted workpiece changes by controlling the interface, employ regularity results for transmission problems for a rigorous derivation of optimality conditions based on the speed method, and conclude with some numerical results based on a spline approximation of the interface.
- ItemAdditive manufacturing graded-material design based on phase-field and topology optimization(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Carraturo, Massimo; Rocca, Elisabetta; Bonetti, Elena; Hömberg, Dietmar; Reali, Alessandro; Auricchio, FerdinandoIn the present work we introduce a novel graded-material design for additive manufacturing based on phase-field and topology optimization. The main novelty of this work comes from the introduction of an additional phase-field variable in the classical single-material phase-field topology optimization algorithm. This new variable is used to grade the material properties in a continuous fashion. Two different numerical examples are discussed, in both of them we perform sensitivity studies to asses the effects of different model parameters onto the resulting structure. From the presented results we can observe that the proposed algorithm adds additional freedom in the design, exploiting the higher flexibility coming from additive manufacturing technology.
- ItemParameter identification in non-isothermal nucleation and growth processes(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Hömberg, Dietmar; Lu, Shuai; Sakamoto, Kenichi; Yamamoto, MasahiroWe study non-isothermal nucleation and growth phase transformations, which are described by a generalized Avrami model for the phase transition coupled with an energy balance to account for recalescence effects. The main novelty of our work is the identification of temperature dependent nucleation rates. We prove that such rates can be uniquely identified from measurements in a subdomain and apply an optimal control approach to develop a numerical strategy for its computation.
- ItemNumerical cooling strategy design for hot rolled dual phase steel(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Suwanpinij, Piyada; Togobytska, Nataliya; Prahl, Ulrich; Weiss, Wolf; Hömberg, Dietmar; Bleck, WolfgangIn this article, the Mo-Mn dual phase steel and its process parameters in hot rolling are discussed. The process window was derived by combining the experimental work in a hot deformation dilatometer and numerical calculation of process parameters using rate law models for ferrite and martensite transformation. The ferrite formation model is based on the Leblond and Devaux approach while martensite formation is based on the Koistinen-Marburger (K-M) formula. The carbon enrichment during ferrite formation is taken into account for the following martensite formation. After the completion of the parameter identification for the rate law model, the evolution of phases in multiphase steel can be addressed. Particularly, the simulations allow for predicting the preferable degree of retained strain and holding temperature on the run out table (ROT) for the required ferrite fraction.
- ItemPath planning and collision avoidance for robots : dedicated to Prof. Dr. Helmut Maurer on the occasion of his 65th birthday(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Gerdts, Matthias; Henrion, René; Hömberg, Dietmar; Landry, Chantal; Maurer, HelmutAn optimal control problem to find the fastest collision-free trajectory of a robot surrounded by obstacles is presented. The collision avoidance is based on linear programming arguments and expressed as state constraints. The optimal control problem is solved with a sequential programming method. In order to decrease the number of unknowns and constraints a backface culling active set strategy is added to the resolution technique.